Finite Group Databasebeta

← C22×#37664 #72335656

Subgroups — C22×#37664 #72335656

Order 1024.

109713 conjugacy classes of subgroups.

The subgroup lattice has 1839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#542C211yesmaximal, characteristic, complemented
2C24×#121C211yesmaximal, characteristic
3C2×#37664C2196yesmaximal, direct product factor
4C22×#2701C212yesmaximal, complemented
5C22×#2672C212yesmaximal, complemented
6C22×#2686C212yesmaximal, complemented
7C22×#2691C212yesmaximal, complemented
8C22×#2848C211yesmaximal, characteristic, complemented
9C22×#2491C211yesmaximal, characteristic, complemented
10C22×#2426C211yesmaximal, characteristic, complemented
11C22×#2427C211yesmaximal, characteristic, complemented
12C22×#2435C211yesmaximal, characteristic, complemented
13C22×#2435C212yesmaximal, complemented
14C22×#2422C211yesmaximal, characteristic, complemented
15C22×#2440C211yesmaximal, characteristic, complemented
16C22×#2480C212yesmaximal, complemented
17C22×#2405C212yesmaximal, complemented
18C22×#2437C212yesmaximal, complemented
19C22×#2620C211yesmaximal, characteristic, complemented
20C22×#2624C211yesmaximal, characteristic, complemented
21C22×#2360C211yesmaximal, characteristic, complemented
22C22×D4×C22⋊C4C211yesmaximal, characteristic, complemented
23C22×#2324C211yesmaximal, characteristic, complemented
24C22×#2280C211yesmaximal, characteristic, complemented
25C25×D4C2211yescharacteristic
26C25×D4C2212yes—
27C26×C4C2211yescharacteristic
28C22×#542—232no—
29C22×#542C22148yescomplemented
30C23×C4⋊Q8C2211yescharacteristic, complemented
31C23×#126C2212yescomplemented
32C23×#124C2212yescomplemented
33C23×#124C2211yescharacteristic, complemented
34C23×#124C2212yescomplemented
35C23×#124C2211yescharacteristic, complemented
36C23×#123C2212yescomplemented
37C23×#123C2212yescomplemented
38C23×C22⋊Q8C2211yescharacteristic
39C23×C22⋊Q8C2212yes—
40C23×C22⋊Q8C2212yescomplemented
41C23×C22⋊Q8C2211yescharacteristic, complemented
42C23×C22⋊Q8C2211yescharacteristic, complemented
43C23×#121—232no—
44C23×#121C2212yes—
45C23×#121C2212yes—
46C23×#121C22148yes—
47C23×#121C2211yescharacteristic
48C23×#121C2211yescharacteristic
49C23×#121C2211yescharacteristic
50C23×#121C2211yescharacteristic
51C23×C4×Q8C2211yescharacteristic, complemented
52C23×C4×D4C2211yescharacteristic, complemented
53C23×C4×D4C2211yescharacteristic, complemented
54C23×#117C2211yescharacteristic, complemented
55C23×#117C2211yescharacteristic, complemented
56C24×C4⋊C4C2211yescharacteristic
57C24×C22⋊C4C2212yes—
58C24×C22⋊C4C2212yes—
59C2×#2701C22196yescomplemented
60C2×#2691C22196yescomplemented
61C2×#2686C22196yescomplemented
62C2×#2672C22196yescomplemented
63#37664C2211024yesdirect product factor
64C2×#2848C22148yescomplemented
65C2×#2491C22148yescomplemented
66C2×#2426C22148yescomplemented
67C2×#2427C22148yescomplemented
68C2×#2435C22148yescomplemented
69C2×#2435C22196yescomplemented
70C2×#2422C22148yescomplemented
71C2×#2440C22148yescomplemented
72C2×#2480C22196yescomplemented
73C2×#2405C22196yescomplemented
74C2×#2437C22196yescomplemented
75C2×#2620C22148yescomplemented
76C2×#2624C22148yescomplemented
77C22×#399C2212yescomplemented
78C22×#398C2212yescomplemented
79C22×#397C2212yescomplemented
80C22×#397C2212yescomplemented
81C22×#397C2212yescomplemented
82C22×#396C2212yescomplemented
83C22×#396C2212yescomplemented
84C22×#396C2212yescomplemented
85C22×#395C2212yescomplemented
86C22×#394C2212yescomplemented
87C22×#394C2212yescomplemented
88C22×#394C2212yescomplemented
89C22×#394C2212yescomplemented
90C22×#394C2212yescomplemented
91C22×#394C2212yescomplemented
92C22×#394C2212yescomplemented
93C22×#394C2212yescomplemented
94C22×#394C2212yescomplemented
95C22×#394C2212yescomplemented
96C22×#393C2212yescomplemented
97C2×#2360C22148yescomplemented
98C2×D4×C22⋊C4C22148yescomplemented
99C2×#2324C22148yescomplemented
100C22×#391C2211yescharacteristic, complemented
101C22×#390C2212yescomplemented
102C22×#390C2212yescomplemented
103C22×#390C2211yescharacteristic, complemented
104C22×#390C2211yescharacteristic, complemented
105C22×#390C2211yescharacteristic, complemented
106C22×#390C2211yescharacteristic, complemented
107C22×#389C2212yescomplemented
108C22×#389C2211yescharacteristic, complemented
109C22×#389C2211yescharacteristic, complemented
110C22×#389C2211yescharacteristic, complemented
111C22×#388C2212yescomplemented
112C22×#388C2212yescomplemented
113C22×#388C2212yescomplemented
114C22×#387C2212yescomplemented
115C22×#386C2212yescomplemented
116C22×#386C2212yescomplemented
117C22×#386C2212yescomplemented
118C22×#386C2212yescomplemented
119C22×#385C2212yes—
120C22×#385C2212yes—
121C22×#385C2212yes—
122C22×#385C2212yescomplemented
123C22×#385C2212yescomplemented
124C22×#385C2212yescomplemented
125C22×#385C2212yescomplemented
126C22×#384C2211yescharacteristic, complemented
127C2×#2280C22148yescomplemented
128C22×#381C2211yescharacteristic, complemented
129C22×#381C2211yescharacteristic, complemented
130C22×#380C2211yescharacteristic
131C22×#380C2211yescharacteristic
132C22×#380C2211yescharacteristic
133C22×#380C2211yescharacteristic, complemented
134C22×#380C2211yescharacteristic, complemented
135C22×#380C2212yescomplemented
136C22×#380C2211yescharacteristic, complemented
137C22×#380C2211yescharacteristic, complemented
138C22×#379C2211yescharacteristic
139C22×#379C2211yescharacteristic
140C22×#379C2212yes—
141C22×#379C2212yes—
142C22×#379C2212yes—
143C22×#379C2212yes—
144C22×C4×C4⋊C4C2211yescharacteristic, complemented
145C22×C4×C22⋊C4C2211yescharacteristic
146C22×C4×C22⋊C4C2211yescharacteristic
147C22×C4×C22⋊C4C2212yes—
148C22×C4×C22⋊C4C2211yescharacteristic, complemented
149C22×C4×C22⋊C4C2211yescharacteristic, complemented
150C27C2311yescharacteristic
151C27C2312yes—
152C24×Q8C2311yescharacteristic
153C24×Q8C2312yes—
154C24×D4—216no—
155C24×D4—232no—
156C24×D4—216no—
157C24×D4—48no—
158C24×D4—416no—
159C24×D4—416no—
160C24×D4C2311yescharacteristic
161C24×D4C23124yes—
162C24×D4C2312yes—
163C24×D4C2312yes—
164C24×D4C2312yes—
165C24×D4C2311yescharacteristic
166C24×D4C23148yes—
167C24×D4C2312yes—
168C24×D4C2312yes—
169C25×C4—216no—
170C25×C4—216no—
171C25×C4—48no—
172C25×C4C2311yescharacteristic
173C25×C4C23124yes—
174C25×C4C2311yescharacteristic
175C25×C4C2311yescharacteristic
176C25×C4C2311yescharacteristic
177C25×C4C2312yes—
178C25×C4C2311yescharacteristic
179C25×C4C2311yescharacteristic
180C25×C4C2312yes—
181C25×C4C2312yes—
182C2×#542—2768no—
183C2×#542C231256yescomplemented
184C22×C4⋊Q8—216no—
185C22×C4⋊Q8C23124yescomplemented
186C22×#126—232no—
187C22×#126C23148yescomplemented
188C22×#124—232no—
189C22×#124—216no—
190C22×#124—416no—
191C22×#124—48no—
192C22×#124C23124yescomplemented
193C22×#124C23148yescomplemented
194C22×#124C23124yescomplemented
195C22×#124C23148yescomplemented
196C22×#123—232no—
197C22×#123—416no—
198C22×#123C23148yescomplemented
199C22×#123C23148yescomplemented
200C22×C22⋊Q8—216no—
201C22×C22⋊Q8—216no—
202C22×C22⋊Q8—232no—
203C22×C22⋊Q8—416no—
204C22×C22⋊Q8—48no—
205C22×C22⋊Q8C23124yes—
206C22×C22⋊Q8C23148yes—
207C22×C22⋊Q8C23124yescomplemented
208C22×C22⋊Q8C23148yescomplemented
209C22×C22⋊Q8C23124yescomplemented
210C22×#121—216no—
211C22×#121—232no—
212C22×#121—216no—
213C22×#121—2768no—
214C22×#121—216no—
215C22×#121—232no—
216C22×#121D4132yes—
217C22×#121C231256yes—
218C22×#121C23124yes—
219C22×#121C23124yes—
220C22×#121C23148yes—
221C22×#121C23148yes—
222C22×#121C23124yes—
223C22×#121C23124yes—
224C22×C4×Q8—216no—
225C22×C4×Q8C23124yescomplemented
226C22×C4×D4—216no—
227C22×C4×D4—48no—
228C22×C4×D4C23124yescomplemented
229C22×C4×D4C23124yescomplemented
230C22×#117—216no—
231C22×#117—48no—
232C22×#117C23124yescomplemented
233C22×#117C23124yescomplemented
234C23×C4⋊C4—216no—
235C23×C4⋊C4C23124yes—
236C23×C4⋊C4C2311yescharacteristic
237C23×C4⋊C4C2312yes—
238C23×C4⋊C4C2311yescharacteristic
239C23×C4⋊C4C2311yescharacteristic
240C23×C4⋊C4C2311yescharacteristic
241C23×C4⋊C4C2311yescharacteristic
242C23×C4⋊C4C2312yes—
243C23×C4⋊C4C2311yescharacteristic
244C23×C4⋊C4C2312yes—
245C23×C4⋊C4C2312yes—
246C23×C4⋊C4C2312yes—
247C23×C4⋊C4C2311yescharacteristic
248C23×C4⋊C4C2311yescharacteristic
249C23×C4⋊C4C2312yes—
250C23×C4⋊C4C2312yes—
251C23×C4⋊C4C2312yes—
252C23×C4⋊C4C2312yes—
253C23×C4⋊C4C2312yes—
254C23×C4⋊C4C2312yes—
255C23×C4⋊C4C2311yescharacteristic
256C23×C22⋊C4—232no—
257C23×C22⋊C4—416no—
258C23×C22⋊C4C23148yes—
259C23×C22⋊C4C2311yescharacteristic
260C23×C22⋊C4C2312yes—
261C23×C22⋊C4C2312yes—
262C23×C22⋊C4C2312yes—
263C23×C22⋊C4C2312yes—
264C23×C22⋊C4C2311yescharacteristic
265C23×C22⋊C4C2311yescharacteristic
266C23×C22⋊C4C2312yes—
267C23×C22⋊C4C2311yescharacteristic
268C23×C22⋊C4C2312yes—
269C23×C22⋊C4C2312yes—
270C23×C22⋊C4C2312yes—
271C23×C22⋊C4C2311yescharacteristic
272C23×C22⋊C4C2312yes—
273C23×C22⋊C4C2312yes—
274C23×C22⋊C4C2311yescharacteristic
275C23×C22⋊C4C2311yescharacteristic
276C23×C22⋊C4C2311yescharacteristic
277C23×C22⋊C4C23148yes—
278C23×C22⋊C4C2312yes—
279C23×C22⋊C4C2312yes—
280C23×C22⋊C4C2311yescharacteristic
281C23×C22⋊C4C2311yescharacteristic
282C23×C22⋊C4C2312yes—
283C23×C22⋊C4C2312yes—
284C23×C22⋊C4C2312yes—
285C23×C22⋊C4C2311yescharacteristic
286C23×C22⋊C4C2311yescharacteristic
287C23×C22⋊C4C2312yes—
288C23×C22⋊C4C2312yes—
289C23×C22⋊C4C2312yes—
290C23×C22⋊C4C2312yes—
291C23×C22⋊C4C2312yes—
292C23×C22⋊C4C2312yes—
293C23×C22⋊C4C2312yes—
294C23×C22⋊C4C2312yes—
295C23×C22⋊C4C2312yes—
296C23×C42C2311yescharacteristic
297C23×C42C2311yescharacteristic
298C23×C42C2311yescharacteristic
299C23×C42C2311yescharacteristic
300C23×C42C2312yes—
301C23×C42C2312yes—
302#2848C231256yescomplemented
303#2701C231512yescomplemented
304#2691C231512yescomplemented
305#2686C231512yescomplemented
306#2672C231512yescomplemented
307#2624C231256yescomplemented
308#2620C231256yescomplemented
309#2491C231256yescomplemented
310#2480C231512yescomplemented
311#2440C231256yescomplemented
312#2437C231512yescomplemented
313#2435C231256yescomplemented
314#2435C231512yescomplemented
315#2427C231256yescomplemented
316#2426C231256yescomplemented
317#2422C231256yescomplemented
318#2405C231512yescomplemented
319C2×#399C23148yescomplemented
320C2×#398C23148yescomplemented
321C2×#397C23148yescomplemented
322C2×#397C23148yescomplemented
323C2×#397C23148yescomplemented
324C2×#396C23148yescomplemented
325C2×#396C23148yescomplemented
326C2×#396C23148yescomplemented
327C2×#395C23148yescomplemented
328C2×#394C23148yescomplemented
329C2×#394C23148yescomplemented
330C2×#394C23148yescomplemented
331C2×#394C23148yescomplemented
332C2×#394C23148yescomplemented
333C2×#394C23148yescomplemented
334C2×#394C23148yescomplemented
335C2×#394C23148yescomplemented
336C2×#394C23148yescomplemented
337C2×#394C23148yescomplemented
338C2×#393C23148yescomplemented
339#2360C231256yescomplemented
340D4×C22⋊C4C231256yescomplemented
341#2324C231256yescomplemented
342C2×#391C23124yescomplemented
343C2×#390C23124yescomplemented
344C2×#390C23148yescomplemented
345C2×#390C23124yescomplemented
346C2×#390C23124yescomplemented
347C2×#390C23124yescomplemented
348C2×#390C23148yescomplemented
349C2×#389C23124yescomplemented
350C2×#389C23124yescomplemented
351C2×#389C23124yescomplemented
352C2×#389C23148yescomplemented
353C2×#388C23148yescomplemented
354C2×#388C23148yescomplemented
355C2×#388C23148yescomplemented
356C2×#387C23148yescomplemented
357C2×#386C23148yescomplemented
358C2×#386C23148yescomplemented
359C2×#386C23148yescomplemented
360C2×#386C23148yescomplemented
361C2×#385C23148yes—
362C2×#385C23148yes—
363C2×#385C23148yes—
364C2×#385C23148yescomplemented
365C2×#385C23148yescomplemented
366C2×#385C23148yescomplemented
367C2×#385C23148yescomplemented
368C2×#384C23124yescomplemented
369#2280C231256yescomplemented
370C2×#381C23124yescomplemented
371C2×#381C23124yescomplemented
372C2×#380C23124yes—
373C2×#380C23124yes—
374C2×#380C23124yes—
375C2×#380C23124yescomplemented
376C2×#380C23124yescomplemented
377C2×#380C23148yescomplemented
378C2×#380C23124yescomplemented
379C2×#380C23124yescomplemented
380C2×#379C23148yes—
381C2×#379C23148yes—
382C2×#379C23148yes—
383C2×#379C23124yes—
384C2×#379C23148yes—
385C2×#379C23124yes—
386C2×C4×C4⋊C4C23124yescomplemented
387C2×C4×C22⋊C4C23124yes—
388C2×C4×C22⋊C4C23148yes—
389C2×C4×C22⋊C4C23124yes—
390C2×C4×C22⋊C4C23124yescomplemented
391C2×C4×C22⋊C4C23124yescomplemented
392C22×#95C2311yescharacteristic
393C22×#95C2311yescharacteristic
394C22×#95C2311yescharacteristic
395C22×#95C2311yescharacteristic
396C22×#95C2312yes—
397C22×#95C2312yes—
398C22×#95C2311yescharacteristic
399C22×#95C2311yescharacteristic
400C22×#95C2311yescharacteristic
401C22×#95C2311yescharacteristic
402C22×#95C2312yes—
403C22×#95C2312yes—
404C22×#95C2312yes—
405C22×#95C2312yes—
406C22×#95C2312yes—
407C22×#95C2312yes—
408C22×#95C2312yes—
409C26—28no—
410C26—28no—
411C26—28no—
412C26—216no—
413C26—28no—
414C26—28no—
415C26—216no—
416C26—216no—
417C26—216no—
418C26—44no—
419C26—44no—
420C26—48no—
421C26—48no—
422C26—48no—
423C26C2412yes—
424C26C2411yescharacteristic
425C26C2412yes—
426C26C2411yescharacteristic
427C26C24112yes—
428C26C24124yes—
429C26C2411yescharacteristic
430C23×Q8—28no—
431C23×Q8—216no—
432C23×Q8—28no—
433C23×Q8—28no—
434C23×Q8—48no—
435C23×Q8—48no—
436C23×Q8C24112yes—
437C23×Q8C24124yes—
438C23×D4—216no—
439C23×D4—216no—
440C23×D4—216no—
441C23×D4—216no—
442C23×D4—216no—
443C23×D4—2192no—
444C23×D4—2384no—
445C23×D4—216no—
446C23×D4—28no—
447C23×D4—28no—
448C23×D4—216no—
449C23×D4—2192no—
450C23×D4—28no—
451C23×D4—28no—
452C23×D4—28no—
453C23×D4—496no—
454C23×D4—4256no—
455C23×D4—48no—
456C23×D4—48no—
457C23×D4—48no—
458C23×D4—48no—
459C23×D4—48no—
460C23×D4—48no—
461C23×D4—48no—
462C23×D4—4192no—
463C23×D4—4192no—
464C23×D4—4512no—
465C23×D4C2×D4116yes—
466C23×D4C2×D4132yes—
467C23×D4C24112yes—
468C23×D4C24164yes—
469C23×D4C24124yes—
470C23×D4C24124yes—
471C23×D4C24124yes—
472C23×D4C24112yes—
473C23×D4C24124yes—
474C23×D4C241128yes—
475C23×D4C24124yes—
476C24×C4—28no—
477C24×C4—28no—
478C24×C4—28no—
479C24×C4—28no—
480C24×C4—28no—
481C24×C4—28no—
482C24×C4—216no—
483C24×C4—216no—
484C24×C4—28no—
485C24×C4—28no—
486C24×C4—2192no—
487C24×C4—28no—
488C24×C4—216no—
489C24×C4—28no—
490C24×C4—2192no—
491C24×C4—28no—
492C24×C4—28no—
493C24×C4—28no—
494C24×C4—496no—
495C24×C4—44no—
496C24×C4—44no—
497C24×C4—44no—
498C24×C4—48no—
499C24×C4—4256no—
500C24×C4—48no—
501C24×C4—48no—
502C24×C4—48no—
503C24×C4—48no—
504C24×C4—48no—
505C24×C4C2×D4116yes—
506C24×C4#41116yes—
507C24×C4C24112yes—
508C24×C4C2411yescharacteristic
509C24×C4C2411yescharacteristic
510C24×C4C2411yescharacteristic
511C24×C4C2412yes—
512C24×C4C2412yes—
513C24×C4C2412yes—
514C24×C4C2411yescharacteristic
515C24×C4C2412yes—
516C24×C4C2411yescharacteristic
517C24×C4C2411yescharacteristic
518C24×C4C2411yescharacteristic
519C24×C4C2411yescharacteristic
520C24×C4C2412yes—
521C24×C4C2411yescharacteristic
522C24×C4C24164yes—
523C24×C4C24112yes—
524C24×C4C24112yes—
525C24×C4C24112yes—
526C24×C4C24124yes—
527C24×C4C24112yes—
528C24×C4C2411yescharacteristic
529C24×C4C2412yes—
530C24×C4C24112yes—
531C24×C4C2411yescharacteristic
532C24×C4C24124yes—
533C24×C4C24124yes—
534C24×C4C2411yescharacteristic
535#542—22048no—
536C2×C4⋊Q8—2192no—
537C2×C4⋊Q8C24164yescomplemented
538C2×#126—2384no—
539C2×#126C241128yescomplemented
540C2×#124—2192no—
541C2×#124—2384no—
542C2×#124—496no—
543C2×#124—4192no—
544C2×#124C24164yescomplemented
545C2×#124C241128yescomplemented
546C2×#124C24164yescomplemented
547C2×#124C241128yescomplemented
548C2×#123—2384no—
549C2×#123—4192no—
550C2×#123C241128yescomplemented
551C2×#123C241128yescomplemented
552C2×C22⋊Q8—2192no—
553C2×C22⋊Q8—2192no—
554C2×C22⋊Q8—2384no—
555C2×C22⋊Q8—4192no—
556C2×C22⋊Q8—496no—
557C2×C22⋊Q8C24164yes—
558C2×C22⋊Q8C241128yes—
559C2×C22⋊Q8C24164yescomplemented
560C2×C22⋊Q8C241128yescomplemented
561C2×C22⋊Q8C24164yescomplemented
562C2×#121—2192no—
563C2×#121—2384no—
564C2×#121—2192no—
565C2×#121—22048no—
566C2×#121—2192no—
567C2×#121—2384no—
568C2×#121C2×D41384yes—
569C2×#121C24164yes—
570C2×#121C241128yes—
571C2×#121C24164yes—
572C2×#121C24164yes—
573C2×#121C241128yes—
574C2×#121C24164yes—
575C2×C4×Q8—2192no—
576C2×C4×Q8C24164yescomplemented
577C2×C4×D4—2192no—
578C2×C4×D4—496no—
579C2×C4×D4C24164yescomplemented
580C2×C4×D4C24164yescomplemented
581C2×#117—2192no—
582C2×#117—496no—
583C2×#117C24164yescomplemented
584C2×#117C24164yescomplemented
585C22×C4⋊C4—216no—
586C22×C4⋊C4—28no—
587C22×C4⋊C4—28no—
588C22×C4⋊C4—28no—
589C22×C4⋊C4—28no—
590C22×C4⋊C4—216no—
591C22×C4⋊C4—216no—
592C22×C4⋊C4—216no—
593C22×C4⋊C4—28no—
594C22×C4⋊C4—216no—
595C22×C4⋊C4—28no—
596C22×C4⋊C4—2192no—
597C22×C4⋊C4—44no—
598C22×C4⋊C4—44no—
599C22×C4⋊C4—48no—
600C22×C4⋊C4—48no—
601C22×C4⋊C4—48no—
602C22×C4⋊C4—48no—
603C22×C4⋊C4—48no—
604C22×C4⋊C4—48no—
605C22×C4⋊C4C2×D4116yes—
606C22×C4⋊C4C24164yes—
607C22×C4⋊C4C24124yes—
608C22×C4⋊C4C24124yes—
609C22×C4⋊C4C24124yes—
610C22×C4⋊C4C24124yes—
611C22×C4⋊C4C24124yes—
612C22×C4⋊C4C24112yes—
613C22×C4⋊C4C24112yes—
614C22×C4⋊C4C24112yes—
615C22×C4⋊C4C24112yes—
616C22×C4⋊C4C24112yes—
617C22×C4⋊C4C24112yes—
618C22×C4⋊C4C24124yes—
619C22×C4⋊C4C24124yes—
620C22×C4⋊C4C24124yes—
621C22×C4⋊C4C24124yes—
622C22×C4⋊C4C24112yes—
623C22×C4⋊C4C24112yes—
624C22×C4⋊C4C24124yes—
625C22×C4⋊C4C24124yes—
626C22×C4⋊C4C24112yes—
627C22×C22⋊C4—216no—
628C22×C22⋊C4—28no—
629C22×C22⋊C4—28no—
630C22×C22⋊C4—216no—
631C22×C22⋊C4—216no—
632C22×C22⋊C4—216no—
633C22×C22⋊C4—216no—
634C22×C22⋊C4—216no—
635C22×C22⋊C4—28no—
636C22×C22⋊C4—216no—
637C22×C22⋊C4—28no—
638C22×C22⋊C4—28no—
639C22×C22⋊C4—216no—
640C22×C22⋊C4—28no—
641C22×C22⋊C4—28no—
642C22×C22⋊C4—28no—
643C22×C22⋊C4—216no—
644C22×C22⋊C4—216no—
645C22×C22⋊C4—2384no—
646C22×C22⋊C4—4192no—
647C22×C22⋊C4—48no—
648C22×C22⋊C4—48no—
649C22×C22⋊C4—44no—
650C22×C22⋊C4—48no—
651C22×C22⋊C4—48no—
652C22×C22⋊C4—48no—
653C22×C22⋊C4—48no—
654C22×C22⋊C4—44no—
655C22×C22⋊C4—44no—
656C22×C22⋊C4—44no—
657C22×C22⋊C4—48no—
658C22×C22⋊C4—48no—
659C22×C22⋊C4—48no—
660C22×C22⋊C4—48no—
661C22×C22⋊C4—48no—
662C22×C22⋊C4—48no—
663C22×C22⋊C4—48no—
664C22×C22⋊C4C2×D4132yes—
665C22×C22⋊C4C24124yes—
666C22×C22⋊C4C24112yes—
667C22×C22⋊C4C24112yes—
668C22×C22⋊C4C24124yes—
669C22×C22⋊C4C24124yes—
670C22×C22⋊C4C24112yes—
671C22×C22⋊C4C24124yes—
672C22×C22⋊C4C24112yes—
673C22×C22⋊C4C24124yes—
674C22×C22⋊C4C24124yes—
675C22×C22⋊C4C24124yes—
676C22×C22⋊C4C24124yes—
677C22×C22⋊C4C24112yes—
678C22×C22⋊C4C241128yes—
679C22×C22⋊C4C24124yes—
680C22×C22⋊C4C24112yes—
681C22×C22⋊C4C24124yes—
682C22×C22⋊C4C24112yes—
683C22×C22⋊C4C24112yes—
684C22×C22⋊C4C241128yes—
685C22×C22⋊C4C24124yes—
686C22×C22⋊C4C24124yes—
687C22×C22⋊C4C24124yes—
688C22×C22⋊C4C24124yes—
689C22×C22⋊C4C24124yes—
690C22×C22⋊C4C24124yes—
691C22×C22⋊C4C24112yes—
692C22×C22⋊C4C24112yes—
693C22×C22⋊C4C24124yes—
694C22×C22⋊C4C24112yes—
695C22×C22⋊C4C24112yes—
696C22×C22⋊C4C24124yes—
697C22×C22⋊C4C24124yes—
698C22×C22⋊C4C24124yes—
699C22×C22⋊C4C24124yes—
700C22×C22⋊C4C24124yes—
701C22×C22⋊C4C24124yes—
702C22×C22⋊C4C24124yes—
703C22×C42—28no—
704C22×C42—28no—
705C22×C42—216no—
706C22×C42—28no—
707C22×C42—28no—
708C22×C42—48no—
709C22×C42C24112yes—
710C22×C42C24112yes—
711C22×C42C24112yes—
712C22×C42C24112yes—
713C22×C42C24124yes—
714C22×C42C24124yes—
715#399C241128yescomplemented
716#398C241128yescomplemented
717#397C241128yescomplemented
718#397C241128yescomplemented
719#397C241128yescomplemented
720#396C241128yescomplemented
721#396C241128yescomplemented
722#396C241128yescomplemented
723#395C241128yescomplemented
724#394C241128yescomplemented
725#394C241128yescomplemented
726#394C241128yescomplemented
727#394C241128yescomplemented
728#394C241128yescomplemented
729#394C241128yescomplemented
730#394C241128yescomplemented
731#394C241128yescomplemented
732#394C241128yescomplemented
733#394C241128yescomplemented
734#393C241128yescomplemented
735#391C24164yescomplemented
736#390C24164yescomplemented
737#390C241128yescomplemented
738#390C24164yescomplemented
739#390C24164yescomplemented
740#390C24164yescomplemented
741#390C241128yescomplemented
742#389C24164yescomplemented
743#389C24164yescomplemented
744#389C241128yescomplemented
745#389C24164yescomplemented
746#388C241128yescomplemented
747#388C241128yescomplemented
748#388C241128yescomplemented
749#387C241128yescomplemented
750#386C241128yescomplemented
751#386C241128yescomplemented
752#386C241128yescomplemented
753#386C241128yescomplemented
754#385C241128yes—
755#385C241128yes—
756#385C241128yes—
757#385C241128yescomplemented
758#385C241128yescomplemented
759#385C241128yescomplemented
760#385C241128yescomplemented
761#384C24164yescomplemented
762#381C24164yescomplemented
763#381C24164yescomplemented
764#380C24164yes—
765#380C24164yes—
766#380C24164yes—
767#380C24164yescomplemented
768#380C24164yescomplemented
769#380C24164yescomplemented
770#380C241128yescomplemented
771#380C24164yescomplemented
772#379C241128yes—
773#379C241128yes—
774#379C24164yes—
775#379C241128yes—
776#379C241128yes—
777#379C24164yes—
778C4×C4⋊C4C24164yescomplemented
779C4×C22⋊C4C24164yes—
780C4×C22⋊C4C241128yes—
781C4×C22⋊C4C24164yes—
782C4×C22⋊C4C24164yescomplemented
783C4×C22⋊C4C24164yescomplemented
784C2×#95C24112yes—
785C2×#95C24124yes—
786C2×#95C24124yes—
787C2×#95C24112yes—
788C2×#95C24124yes—
789C2×#95C24124yes—
790C2×#95C24112yes—
791C2×#95C24124yes—
792C2×#95C24124yes—
793C2×#95C24124yes—
794C2×#95C24124yes—
795C2×#95C24112yes—
796C2×#95C24112yes—
797C2×#95C24112yes—
798C2×#95C24124yes—
799C2×#95C24112yes—
800C2×#95C24112yes—
801C25—24no—
802C25—24no—
803C25—24no—
804C25—24no—
805C25—2128no—
806C25—248no—
807C25—24no—
808C25—24no—
809C25—24no—
810C25—28no—
811C25—24no—
812C25—24no—
813C25—28no—
814C25—28no—
815C25—28no—
816C25—248no—
817C25—248no—
818C25—24no—
819C25—24no—
820C25—24no—
821C25—24no—
822C25—28no—
823C25—24no—
824C25—24no—
825C25—24no—
826C25—28no—
827C25—296no—
828C25—28no—
829C25—248no—
830C25—28no—
831C25—28no—
832C25—28no—
833C25—28no—
834C25—248no—
835C25—28no—
836C25—28no—
837C25—296no—
838C25—296no—
839C25—296no—
840C25—424no—
841C25—424no—
842C25—448no—
843C25—448no—
844C25—448no—
845C25—464no—
846C25—464no—
847C25—464no—
848C25—464no—
849C25—4128no—
850C25—4128no—
851C25—4128no—
852C25—464no—
853C25—464no—
854C25—4128no—
855C25—864no—
856C25—864no—
857C25—864no—
858C25C22×D4116yes—
859C25C22×D418yes—
860C25C2×#4118yes—
861C25H(5,𝔽2)18yes—
862C25H(5,𝔽2)18yes—
863C252−1+418yes—
864C25C25112yes—
865C25C2516yes—
866C25C25112yes—
867C25C2516yes—
868C25C25116yes—
869C25C25132yes—
870C25C2516yes—
871C25C2511yescharacteristic
872C22×Q8—248no—
873C22×Q8—296no—
874C22×Q8—248no—
875C22×Q8—248no—
876C22×Q8—448no—
877C22×Q8—448no—
878C22×Q8—464no—
879C22×Q8—864no—
880C22×Q8C25116yes—
881C22×Q8C25132yes—
882C22×D4—296no—
883C22×D4—296no—
884C22×D4—296no—
885C22×D4—296no—
886C22×D4—296no—
887C22×D4—2256no—
888C22×D4—2512no—
889C22×D4—2128no—
890C22×D4—296no—
891C22×D4—248no—
892C22×D4—248no—
893C22×D4—296no—
894C22×D4—2256no—
895C22×D4—248no—
896C22×D4—248no—
897C22×D4—248no—
898C22×D4—4128no—
899C22×D4—41536no—
900C22×D4—4128no—
901C22×D4—448no—
902C22×D4—448no—
903C22×D4—448no—
904C22×D4—448no—
905C22×D4—448no—
906C22×D4—448no—
907C22×D4—448no—
908C22×D4—4256no—
909C22×D4—4128no—
910C22×D4—4128no—
911C22×D4—4256no—
912C22×D4—4128no—
913C22×D4—43072no—
914C22×D4—4128no—
915C22×D4—464no—
916C22×D4C22×D4196yes—
917C22×D4C22×D41192yes—
918C22×D4C25116yes—
919C22×D4C25132yes—
920C22×D4C25132yes—
921C22×D4C25132yes—
922C22×D4C25116yes—
923C22×D4C25132yes—
924C22×D4C25132yes—
925C23×C4—24no—
926C23×C4—24no—
927C23×C4—24no—
928C23×C4—28no—
929C23×C4—24no—
930C23×C4—28no—
931C23×C4—2128no—
932C23×C4—2128no—
933C23×C4—248no—
934C23×C4—248no—
935C23×C4—248no—
936C23×C4—248no—
937C23×C4—24no—
938C23×C4—24no—
939C23×C4—28no—
940C23×C4—24no—
941C23×C4—24no—
942C23×C4—28no—
943C23×C4—28no—
944C23×C4—24no—
945C23×C4—248no—
946C23×C4—28no—
947C23×C4—28no—
948C23×C4—248no—
949C23×C4—24no—
950C23×C4—24no—
951C23×C4—28no—
952C23×C4—24no—
953C23×C4—24no—
954C23×C4—24no—
955C23×C4—24no—
956C23×C4—28no—
957C23×C4—28no—
958C23×C4—28no—
959C23×C4—24no—
960C23×C4—24no—
961C23×C4—24no—
962C23×C4—28no—
963C23×C4—24no—
964C23×C4—24no—
965C23×C4—24no—
966C23×C4—28no—
967C23×C4—24no—
968C23×C4—24no—
969C23×C4—28no—
970C23×C4—28no—
971C23×C4—296no—
972C23×C4—24no—
973C23×C4—24no—
974C23×C4—24no—
975C23×C4—24no—
976C23×C4—24no—
977C23×C4—24no—
978C23×C4—28no—
979C23×C4—24no—
980C23×C4—28no—
981C23×C4—24no—
982C23×C4—296no—
983C23×C4—248no—
984C23×C4—296no—
985C23×C4—248no—
986C23×C4—2256no—
987C23×C4—248no—
988C23×C4—248no—
989C23×C4—2256no—
990C23×C4—248no—
991C23×C4—248no—
992C23×C4—248no—
993C23×C4—4128no—
994C23×C4—424no—
995C23×C4—424no—
996C23×C4—424no—
997C23×C4—448no—
998C23×C4—464no—
999C23×C4—41536no—
1000C23×C4—448no—
1001C23×C4—448no—
1002C23×C4—448no—
1003C23×C4—448no—
1004C23×C4—448no—
1005C23×C4—464no—
1006C23×C4—464no—
1007C23×C4—4128no—
1008C23×C4—464no—
1009C23×C4—864no—
1010C23×C4—864no—
1011C23×C4C22×D418yes—
1012C23×C4C22×D4116yes—
1013C23×C4C22×D4196yes—
1014C23×C4C22×D418yes—
1015C23×C4C2×#4118yes—
1016C23×C4C2×#41196yes—
1017C23×C4C2×#4118yes—
1018C23×C4H(5,𝔽2)18yes—
1019C23×C4C2516yes—
1020C23×C4C25112yes—
1021C23×C4C2516yes—
1022C23×C4C2516yes—
1023C23×C4C25112yes—
1024C23×C4C2516yes—
1025C23×C4C2516yes—
1026C23×C4C2516yes—
1027C23×C4C25112yes—
1028C23×C4C25112yes—
1029C23×C4C2516yes—
1030C23×C4C2516yes—
1031C23×C4C2516yes—
1032C23×C4C25112yes—
1033C23×C4C25116yes—
1034C23×C4C25116yes—
1035C23×C4C25132yes—
1036C23×C4C25116yes—
1037C23×C4C25116yes—
1038C23×C4C2516yes—
1039C23×C4C25112yes—
1040C23×C4C25116yes—
1041C23×C4C2516yes—
1042C23×C4C25116yes—
1043C23×C4C25132yes—
1044C23×C4C25132yes—
1045C23×C4C2516yes—
1046C4⋊Q8—2256no—
1047#126—2512no—
1048#124—2256no—
1049#124—2512no—
1050#124—4128no—
1051#124—4256no—
1052#123—2512no—
1053#123—4256no—
1054C22⋊Q8—2256no—
1055C22⋊Q8—2256no—
1056C22⋊Q8—2512no—
1057C22⋊Q8—4256no—
1058C22⋊Q8—4128no—
1059#121—2256no—
1060#121—2512no—
1061#121—2256no—
1062#121—2256no—
1063#121—2512no—
1064#121C22×D41512yes—
1065C4×Q8—2256no—
1066C4×D4—2256no—
1067C4×D4—4128no—
1068#117—2256no—
1069#117—4128no—
1070C2×C4⋊C4—296no—
1071C2×C4⋊C4—248no—
1072C2×C4⋊C4—248no—
1073C2×C4⋊C4—248no—
1074C2×C4⋊C4—248no—
1075C2×C4⋊C4—296no—
1076C2×C4⋊C4—296no—
1077C2×C4⋊C4—296no—
1078C2×C4⋊C4—248no—
1079C2×C4⋊C4—296no—
1080C2×C4⋊C4—248no—
1081C2×C4⋊C4—2256no—
1082C2×C4⋊C4—424no—
1083C2×C4⋊C4—424no—
1084C2×C4⋊C4—448no—
1085C2×C4⋊C4—448no—
1086C2×C4⋊C4—448no—
1087C2×C4⋊C4—448no—
1088C2×C4⋊C4—448no—
1089C2×C4⋊C4—448no—
1090C2×C4⋊C4C22×D4196yes—
1091C2×C4⋊C4C25116yes—
1092C2×C4⋊C4C25132yes—
1093C2×C4⋊C4C25116yes—
1094C2×C4⋊C4C25116yes—
1095C2×C4⋊C4C25116yes—
1096C2×C4⋊C4C25116yes—
1097C2×C4⋊C4C25132yes—
1098C2×C4⋊C4C25116yes—
1099C2×C4⋊C4C25132yes—
1100C2×C4⋊C4C25132yes—
1101C2×C4⋊C4C25132yes—
1102C2×C4⋊C4C25116yes—
1103C2×C4⋊C4C25116yes—
1104C2×C4⋊C4C25132yes—
1105C2×C4⋊C4C25132yes—
1106C2×C4⋊C4C25132yes—
1107C2×C4⋊C4C25132yes—
1108C2×C4⋊C4C25132yes—
1109C2×C4⋊C4C25132yes—
1110C2×C4⋊C4C25116yes—
1111C2×C22⋊C4—296no—
1112C2×C22⋊C4—248no—
1113C2×C22⋊C4—248no—
1114C2×C22⋊C4—296no—
1115C2×C22⋊C4—296no—
1116C2×C22⋊C4—296no—
1117C2×C22⋊C4—296no—
1118C2×C22⋊C4—296no—
1119C2×C22⋊C4—248no—
1120C2×C22⋊C4—296no—
1121C2×C22⋊C4—248no—
1122C2×C22⋊C4—248no—
1123C2×C22⋊C4—296no—
1124C2×C22⋊C4—248no—
1125C2×C22⋊C4—248no—
1126C2×C22⋊C4—248no—
1127C2×C22⋊C4—296no—
1128C2×C22⋊C4—296no—
1129C2×C22⋊C4—2512no—
1130C2×C22⋊C4—4256no—
1131C2×C22⋊C4—448no—
1132C2×C22⋊C4—448no—
1133C2×C22⋊C4—424no—
1134C2×C22⋊C4—448no—
1135C2×C22⋊C4—448no—
1136C2×C22⋊C4—448no—
1137C2×C22⋊C4—448no—
1138C2×C22⋊C4—424no—
1139C2×C22⋊C4—424no—
1140C2×C22⋊C4—424no—
1141C2×C22⋊C4—448no—
1142C2×C22⋊C4—448no—
1143C2×C22⋊C4—448no—
1144C2×C22⋊C4—448no—
1145C2×C22⋊C4—448no—
1146C2×C22⋊C4—448no—
1147C2×C22⋊C4—448no—
1148C2×C22⋊C4C22×D41192yes—
1149C2×C22⋊C4C25116yes—
1150C2×C22⋊C4C25132yes—
1151C2×C22⋊C4C25132yes—
1152C2×C22⋊C4C25132yes—
1153C2×C22⋊C4C25132yes—
1154C2×C22⋊C4C25116yes—
1155C2×C22⋊C4C25116yes—
1156C2×C22⋊C4C25132yes—
1157C2×C22⋊C4C25116yes—
1158C2×C22⋊C4C25132yes—
1159C2×C22⋊C4C25132yes—
1160C2×C22⋊C4C25132yes—
1161C2×C22⋊C4C25116yes—
1162C2×C22⋊C4C25132yes—
1163C2×C22⋊C4C25132yes—
1164C2×C22⋊C4C25116yes—
1165C2×C22⋊C4C25116yes—
1166C2×C22⋊C4C25116yes—
1167C2×C22⋊C4C25132yes—
1168C2×C22⋊C4C25132yes—
1169C2×C22⋊C4C25116yes—
1170C2×C22⋊C4C25116yes—
1171C2×C22⋊C4C25132yes—
1172C2×C22⋊C4C25132yes—
1173C2×C22⋊C4C25132yes—
1174C2×C22⋊C4C25132yes—
1175C2×C22⋊C4C25132yes—
1176C2×C22⋊C4C25132yes—
1177C2×C22⋊C4C25132yes—
1178C2×C22⋊C4C25116yes—
1179C2×C22⋊C4C25116yes—
1180C2×C22⋊C4C25132yes—
1181C2×C22⋊C4C25132yes—
1182C2×C22⋊C4C25132yes—
1183C2×C22⋊C4C25132yes—
1184C2×C22⋊C4C25132yes—
1185C2×C42—248no—
1186C2×C42—248no—
1187C2×C42—296no—
1188C2×C42—248no—
1189C2×C42—248no—
1190C2×C42—448no—
1191C2×C42C25116yes—
1192C2×C42C25116yes—
1193C2×C42C25116yes—
1194C2×C42C25116yes—
1195C2×C42C25132yes—
1196C2×C42C25132yes—
1197#95C25116yes—
1198#95C25116yes—
1199#95C25116yes—
1200#95C25116yes—
1201#95C25132yes—
1202#95C25132yes—
1203#95C25116yes—
1204#95C25116yes—
1205#95C25116yes—
1206#95C25116yes—
1207#95C25132yes—
1208#95C25132yes—
1209#95C25132yes—
1210#95C25132yes—
1211#95C25132yes—
1212#95C25132yes—
1213#95C25132yes—
1214C24—212no—
1215C24—212no—
1216C24—212no—
1217C24—212no—
1218C24—232no—
1219C24—232no—
1220C24—232no—
1221C24—232no—
1222C24—232no—
1223C24—232no—
1224C24—2384no—
1225C24—232no—
1226C24—212no—
1227C24—212no—
1228C24—212no—
1229C24—224no—
1230C24—212no—
1231C24—212no—
1232C24—224no—
1233C24—224no—
1234C24—224no—
1235C24—232no—
1236C24—232no—
1237C24—212no—
1238C24—212no—
1239C24—212no—
1240C24—212no—
1241C24—212no—
1242C24—224no—
1243C24—212no—
1244C24—212no—
1245C24—224no—
1246C24—232no—
1247C24—264no—
1248C24—264no—
1249C24—232no—
1250C24—232no—
1251C24—232no—
1252C24—264no—
1253C24—232no—
1254C24—232no—
1255C24—264no—
1256C24—224no—
1257C24—232no—
1258C24—224no—
1259C24—224no—
1260C24—224no—
1261C24—224no—
1262C24—232no—
1263C24—224no—
1264C24—224no—
1265C24—264no—
1266C24—264no—
1267C24—264no—
1268C24—416no—
1269C24—416no—
1270C24—432no—
1271C24—432no—
1272C24—432no—
1273C24—4192no—
1274C24—4192no—
1275C24—4192no—
1276C24—4192no—
1277C24—4384no—
1278C24—4384no—
1279C24—4384no—
1280C24—41024no—
1281C24—4192no—
1282C24—416no—
1283C24—416no—
1284C24—432no—
1285C24—4192no—
1286C24—416no—
1287C24—416no—
1288C24—416no—
1289C24—432no—
1290C24—416no—
1291C24—432no—
1292C24—432no—
1293C24—416no—
1294C24—416no—
1295C24—432no—
1296C24—4384no—
1297C24—432no—
1298C24—432no—
1299C24—432no—
1300C24—432no—
1301C24—432no—
1302C24—432no—
1303C24—8192no—
1304C24—8192no—
1305C24—8192no—
1306C24—81024no—
1307C24#542164yescomplemented
1308C24C23×D4148yes—
1309C24C23×D4124yes—
1310C24C23×D414yes—
1311C24C22×#41124yes—
1312C24C22×#4114yes—
1313C24C2×H(5,𝔽2)124yes—
1314C24C2×H(5,𝔽2)124yes—
1315C24C2×H(5,𝔽2)14yes—
1316C24C2×H(5,𝔽2)14yes—
1317C24C2×H(5,𝔽2)14yes—
1318C24C2×2−1+4124yes—
1319C24C2×2−1+414yes—
1320C24#58514yes—
1321C24C2618yes—
1322C24C2614yes—
1323C24C2618yes—
1324C24C2614yes—
1325C24C2614yes—
1326C24C2613yes—
1327C2×Q8—232no—
1328C2×Q8—264no—
1329C2×Q8—232no—
1330C2×Q8—232no—
1331C2×Q8—432no—
1332C2×Q8—432no—
1333C2×Q8—4192no—
1334C2×Q8—8192no—
1335C2×D4—264no—
1336C2×D4—264no—
1337C2×D4—264no—
1338C2×D4—264no—
1339C2×D4—264no—
1340C2×D4—264no—
1341C2×D4—232no—
1342C2×D4—232no—
1343C2×D4—264no—
1344C2×D4—232no—
1345C2×D4—232no—
1346C2×D4—232no—
1347C2×D4—2384no—
1348C2×D4—41024no—
1349C2×D4—4384no—
1350C2×D4—432no—
1351C2×D4—432no—
1352C2×D4—432no—
1353C2×D4—432no—
1354C2×D4—432no—
1355C2×D4—432no—
1356C2×D4—432no—
1357C2×D4—4384no—
1358C2×D4—4384no—
1359C2×D4—4384no—
1360C2×D4—42048no—
1361C2×D4—4384no—
1362C2×D4—4192no—
1363C2×D4C23×D4164yes—
1364C2×D4C23×D41128yes—
1365C22×C4—212no—
1366C22×C4—212no—
1367C22×C4—224no—
1368C22×C4—212no—
1369C22×C4—224no—
1370C22×C4—212no—
1371C22×C4—232no—
1372C22×C4—232no—
1373C22×C4—264no—
1374C22×C4—232no—
1375C22×C4—232no—
1376C22×C4—232no—
1377C22×C4—232no—
1378C22×C4—2384no—
1379C22×C4—2384no—
1380C22×C4—212no—
1381C22×C4—212no—
1382C22×C4—224no—
1383C22×C4—212no—
1384C22×C4—212no—
1385C22×C4—212no—
1386C22×C4—224no—
1387C22×C4—224no—
1388C22×C4—232no—
1389C22×C4—224no—
1390C22×C4—224no—
1391C22×C4—232no—
1392C22×C4—212no—
1393C22×C4—212no—
1394C22×C4—212no—
1395C22×C4—212no—
1396C22×C4—212no—
1397C22×C4—212no—
1398C22×C4—224no—
1399C22×C4—212no—
1400C22×C4—212no—
1401C22×C4—212no—
1402C22×C4—212no—
1403C22×C4—224no—
1404C22×C4—224no—
1405C22×C4—224no—
1406C22×C4—212no—
1407C22×C4—212no—
1408C22×C4—212no—
1409C22×C4—224no—
1410C22×C4—224no—
1411C22×C4—212no—
1412C22×C4—224no—
1413C22×C4—224no—
1414C22×C4—264no—
1415C22×C4—212no—
1416C22×C4—212no—
1417C22×C4—212no—
1418C22×C4—212no—
1419C22×C4—224no—
1420C22×C4—212no—
1421C22×C4—212no—
1422C22×C4—212no—
1423C22×C4—224no—
1424C22×C4—212no—
1425C22×C4—264no—
1426C22×C4—232no—
1427C22×C4—264no—
1428C22×C4—232no—
1429C22×C4—232no—
1430C22×C4—232no—
1431C22×C4—232no—
1432C22×C4—232no—
1433C22×C4—232no—
1434C22×C4—416no—
1435C22×C4—416no—
1436C22×C4—416no—
1437C22×C4—432no—
1438C22×C4—4192no—
1439C22×C4—41024no—
1440C22×C4—432no—
1441C22×C4—432no—
1442C22×C4—432no—
1443C22×C4—432no—
1444C22×C4—432no—
1445C22×C4—4192no—
1446C22×C4—4192no—
1447C22×C4—4384no—
1448C22×C4—416no—
1449C22×C4—432no—
1450C22×C4—432no—
1451C22×C4—416no—
1452C22×C4—432no—
1453C22×C4—416no—
1454C22×C4—416no—
1455C22×C4—416no—
1456C22×C4—432no—
1457C22×C4—416no—
1458C22×C4—416no—
1459C22×C4—416no—
1460C22×C4—432no—
1461C22×C4—416no—
1462C22×C4—4192no—
1463C22×C4—8192no—
1464C22×C4—8192no—
1465C22×C4#546164yes—
1466C22×C4C23×D4148yes—
1467C22×C4C23×D4124yes—
1468C22×C4C23×D4164yes—
1469C22×C4C23×D4124yes—
1470C22×C4C22×#41124yes—
1471C22×C4C22×#41164yes—
1472C22×C4C22×#41124yes—
1473C22×C4C2×H(5,𝔽2)124yes—
1474C22×C4C2614yes—
1475C22×C4C2614yes—
1476C22×C4C2614yes—
1477C22×C4C2614yes—
1478C22×C4C2614yes—
1479C22×C4C2618yes—
1480C22×C4C2614yes—
1481C22×C4C2618yes—
1482C22×C4C2618yes—
1483C22×C4C2614yes—
1484C22×C4C2618yes—
1485C22×C4C2614yes—
1486C22×C4C2614yes—
1487C22×C4C2618yes—
1488C22×C4C2618yes—
1489C22×C4C2614yes—
1490C22×C4C2614yes—
1491C22×C4C2614yes—
1492C4⋊C4—264no—
1493C4⋊C4—232no—
1494C4⋊C4—232no—
1495C4⋊C4—232no—
1496C4⋊C4—232no—
1497C4⋊C4—264no—
1498C4⋊C4—264no—
1499C4⋊C4—264no—
1500C4⋊C4—232no—
1501C4⋊C4—264no—
1502C4⋊C4—232no—
1503C4⋊C4—416no—
1504C4⋊C4—416no—
1505C4⋊C4—432no—
1506C4⋊C4—432no—
1507C4⋊C4—432no—
1508C4⋊C4—432no—
1509C4⋊C4—432no—
1510C4⋊C4—432no—
1511C4⋊C4C23×D4164yes—
1512C22⋊C4—264no—
1513C22⋊C4—232no—
1514C22⋊C4—232no—
1515C22⋊C4—264no—
1516C22⋊C4—264no—
1517C22⋊C4—264no—
1518C22⋊C4—264no—
1519C22⋊C4—264no—
1520C22⋊C4—232no—
1521C22⋊C4—264no—
1522C22⋊C4—232no—
1523C22⋊C4—232no—
1524C22⋊C4—264no—
1525C22⋊C4—232no—
1526C22⋊C4—232no—
1527C22⋊C4—232no—
1528C22⋊C4—264no—
1529C22⋊C4—264no—
1530C22⋊C4—432no—
1531C22⋊C4—432no—
1532C22⋊C4—416no—
1533C22⋊C4—432no—
1534C22⋊C4—432no—
1535C22⋊C4—432no—
1536C22⋊C4—432no—
1537C22⋊C4—416no—
1538C22⋊C4—416no—
1539C22⋊C4—416no—
1540C22⋊C4—432no—
1541C22⋊C4—432no—
1542C22⋊C4—432no—
1543C22⋊C4—432no—
1544C22⋊C4—432no—
1545C22⋊C4—432no—
1546C22⋊C4—432no—
1547C22⋊C4C23×D41128yes—
1548C42—232no—
1549C42—232no—
1550C42—264no—
1551C42—232no—
1552C42—232no—
1553C42—432no—
1554C23—248no—
1555C23—2256no—
1556C23—248no—
1557C23—248no—
1558C23—248no—
1559C23—24no—
1560C23—24no—
1561C23—24no—
1562C23—24no—
1563C23—248no—
1564C23—248no—
1565C23—2128no—
1566C23—248no—
1567C23—296no—
1568C23—248no—
1569C23—248no—
1570C23—248no—
1571C23—248no—
1572C23—296no—
1573C23—24no—
1574C23—24no—
1575C23—24no—
1576C23—28no—
1577C23—24no—
1578C23—24no—
1579C23—28no—
1580C23—28no—
1581C23—28no—
1582C23—24no—
1583C23—24no—
1584C23—24no—
1585C23—24no—
1586C23—24no—
1587C23—28no—
1588C23—24no—
1589C23—24no—
1590C23—28no—
1591C23—248no—
1592C23—296no—
1593C23—28no—
1594C23—28no—
1595C23—28no—
1596C23—28no—
1597C23—28no—
1598C23—28no—
1599C23—28no—
1600C23—464no—
1601C23—464no—
1602C23—464no—
1603C23—464no—
1604C23—4128no—
1605C23—4128no—
1606C23—4128no—
1607C23—464no—
1608C23—41536no—
1609C23—424no—
1610C23—448no—
1611C23—4128no—
1612C23—4128no—
1613C23—4256no—
1614C23—424no—
1615C23—448no—
1616C23—424no—
1617C23—424no—
1618C23—424no—
1619C23—448no—
1620C23—464no—
1621C23—424no—
1622C23—448no—
1623C23—424no—
1624C23—424no—
1625C23—448no—
1626C23—448no—
1627C23—448no—
1628C23—448no—
1629C23—448no—
1630C23—4128no—
1631C23—448no—
1632C23—448no—
1633C23—864no—
1634C23—864no—
1635C23—864no—
1636C23—81536no—
1637C23—8128no—
1638C23C2×#542116yes—
1639C23C2×#542196yescomplemented
1640C23C2×#546116yes—
1641C23#3484116yes—
1642C23#3489116yes—
1643C23#3494116yes—
1644C23#3536116yes—
1645C23#3542116yes—
1646C23C24×D4116yes—
1647C23C24×D418yes—
1648C23C24×D416yes—
1649C23C23×#4118yes—
1650C23C23×#4116yes—
1651C23C22×H(5,𝔽2)18yes—
1652C23C22×H(5,𝔽2)18yes—
1653C23C22×H(5,𝔽2)16yes—
1654C23C22×H(5,𝔽2)16yes—
1655C23C22×H(5,𝔽2)16yes—
1656C23C22×2−1+418yes—
1657C23C22×2−1+416yes—
1658C23C2×#58516yes—
1659C23C2711yescharacteristic
1660Q8—464no—
1661Q8—864no—
1662D4—2128no—
1663D4—4128no—
1664D4—4128no—
1665D4—4128no—
1666D4—4128no—
1667D4—4128no—
1668D4—464no—
1669C2×C4—296no—
1670C2×C4—24no—
1671C2×C4—24no—
1672C2×C4—28no—
1673C2×C4—24no—
1674C2×C4—28no—
1675C2×C4—24no—
1676C2×C4—248no—
1677C2×C4—248no—
1678C2×C4—2128no—
1679C2×C4—2128no—
1680C2×C4—24no—
1681C2×C4—24no—
1682C2×C4—28no—
1683C2×C4—24no—
1684C2×C4—24no—
1685C2×C4—24no—
1686C2×C4—28no—
1687C2×C4—28no—
1688C2×C4—28no—
1689C2×C4—28no—
1690C2×C4—24no—
1691C2×C4—24no—
1692C2×C4—24no—
1693C2×C4—24no—
1694C2×C4—24no—
1695C2×C4—24no—
1696C2×C4—28no—
1697C2×C4—24no—
1698C2×C4—24no—
1699C2×C4—24no—
1700C2×C4—24no—
1701C2×C4—28no—
1702C2×C4—28no—
1703C2×C4—28no—
1704C2×C4—24no—
1705C2×C4—24no—
1706C2×C4—24no—
1707C2×C4—28no—
1708C2×C4—28no—
1709C2×C4—24no—
1710C2×C4—28no—
1711C2×C4—28no—
1712C2×C4—24no—
1713C2×C4—24no—
1714C2×C4—24no—
1715C2×C4—24no—
1716C2×C4—24no—
1717C2×C4—28no—
1718C2×C4—24no—
1719C2×C4—24no—
1720C2×C4—28no—
1721C2×C4—24no—
1722C2×C4—464no—
1723C2×C4—464no—
1724C2×C4—464no—
1725C2×C4—4128no—
1726C2×C4—424no—
1727C2×C4—424no—
1728C2×C4—448no—
1729C2×C4—424no—
1730C2×C4—448no—
1731C2×C4—424no—
1732C2×C4—448no—
1733C2×C4—424no—
1734C2×C4—424no—
1735C2×C4—424no—
1736C2×C4—448no—
1737C2×C4—424no—
1738C2×C4—448no—
1739C2×C4—424no—
1740C2×C4—464no—
1741C2×C4—864no—
1742C2×C4—864no—
1743C2×C4C2×#546196yes—
1744C2×C4C24×D4116yes—
1745C2×C4C24×D418yes—
1746C2×C4C24×D418yes—
1747C2×C4C23×#4118yes—
1748C2×C4C23×#4118yes—
1749C2×C4C22×H(5,𝔽2)18yes—
1750C22—28no—
1751C22—28no—
1752C22—2192no—
1753C22—28no—
1754C22—28no—
1755C22—28no—
1756C22—28no—
1757C22—28no—
1758C22—28no—
1759C22—216no—
1760C22—216no—
1761C22—28no—
1762C22—28no—
1763C22—28no—
1764C22—28no—
1765C22—216no—
1766C22—4256no—
1767C22—48no—
1768C22—44no—
1769C22—44no—
1770C22—44no—
1771C22—48no—
1772C22—44no—
1773C22—44no—
1774C22—48no—
1775C22—496no—
1776C22—496no—
1777C22—4192no—
1778C22—44no—
1779C22—44no—
1780C22—48no—
1781C22—44no—
1782C22—48no—
1783C22—48no—
1784C22—48no—
1785C22—48no—
1786C22—48no—
1787C22—48no—
1788C22—48no—
1789C22—8256no—
1790C22—896no—
1791C22#37664164yesdirect product factor
1792C22C22×#542112yes—
1793C22C22×#542116yescomplemented
1794C22C22×#546112yes—
1795C22C2×#3542112yes—
1796C22C2×#3536112yes—
1797C22C2×#3484112yes—
1798C22C2×#3494112yes—
1799C22C2×#3489112yes—
1800C22C25×D411yescharacteristic
1801C22C24×#4111yescharacteristic
1802C22C23×H(5,𝔽2)11yescharacteristic
1803C22C23×H(5,𝔽2)11yescharacteristic
1804C22C23×H(5,𝔽2)11yescharacteristic
1805C22C23×2−1+411yescharacteristic
1806C22C22×#58511yescharacteristic
1807C4—28no—
1808C4—28no—
1809C4—216no—
1810C4—44no—
1811C4—48no—
1812C4—44no—
1813C4—44no—
1814C4—44no—
1815C4—44no—
1816C4—48no—
1817C4—48no—
1818C4—44no—
1819C4—48no—
1820C4—44no—
1821C4—48no—
1822C4—44no—
1823C4—44no—
1824C4C22×#546116yes—
1825C2—216no—
1826C2—48no—
1827C2—48no—
1828C2—416no—
1829C2—88no—
1830C2C2×#37664124yesdirect product factor
1831C2C23×#54211yescharacteristic
1832C2C23×#54611yescharacteristic
1833C2C22×#348411yescharacteristic
1834C2C22×#349411yescharacteristic
1835C2C22×#348911yescharacteristic
1836C2C22×#354211yescharacteristic
1837C2C22×#353611yescharacteristic
subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC23C27
prime radicalC24×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×#542C2semidirect
3. C2×#37664C2direct (N × H)
4. C22×#2701C2semidirect
5. C22×#2672C2semidirect
6. C22×#2686C2semidirect
7. C22×#2691C2semidirect
8. C22×#2848C2semidirect
9. C22×#2491C2semidirect
10. C22×#2426C2semidirect
11. C22×#2427C2semidirect
12. C22×#2435C2semidirect
13. C22×#2435C2semidirect
14. C22×#2422C2semidirect
15. C22×#2440C2semidirect
16. C22×#2480C2semidirect
17. C22×#2405C2semidirect
18. C22×#2437C2semidirect
19. C22×#2620C2semidirect
20. C22×#2624C2semidirect
21. C22×#2360C2semidirect
22. C22×D4×C22⋊C4C2semidirect
23. C22×#2324C2semidirect
24. C22×#2280C2semidirect
29. C22×#542C22semidirect
30. C23×C4⋊Q8C22semidirect
31. C23×#126C22semidirect
32. C23×#124C22semidirect
33. C23×#124C22semidirect
34. C23×#124C22semidirect
35. C23×#124C22semidirect
36. C23×#123C22semidirect
37. C23×#123C22semidirect
40. C23×C22⋊Q8C22semidirect
41. C23×C22⋊Q8C22semidirect
42. C23×C22⋊Q8C22semidirect
51. C23×C4×Q8C22semidirect
52. C23×C4×D4C22semidirect
53. C23×C4×D4C22semidirect
54. C23×#117C22semidirect
55. C23×#117C22semidirect
59. C2×#2701C22semidirect
60. C2×#2691C22semidirect
61. C2×#2686C22semidirect
62. C2×#2672C22semidirect
63. #37664C22direct (N × H)
64. C2×#2848C22semidirect
65. C2×#2491C22semidirect
66. C2×#2426C22semidirect
67. C2×#2427C22semidirect
68. C2×#2435C22semidirect
69. C2×#2435C22semidirect
70. C2×#2422C22semidirect
71. C2×#2440C22semidirect
72. C2×#2480C22semidirect
73. C2×#2405C22semidirect
74. C2×#2437C22semidirect
75. C2×#2620C22semidirect
76. C2×#2624C22semidirect
77. C22×#399C22semidirect
78. C22×#398C22semidirect
79. C22×#397C22semidirect
80. C22×#397C22semidirect
81. C22×#397C22semidirect
82. C22×#396C22semidirect
83. C22×#396C22semidirect
84. C22×#396C22semidirect
85. C22×#395C22semidirect
86. C22×#394C22semidirect
87. C22×#394C22semidirect
88. C22×#394C22semidirect
89. C22×#394C22semidirect
90. C22×#394C22semidirect
91. C22×#394C22semidirect
92. C22×#394C22semidirect
93. C22×#394C22semidirect
94. C22×#394C22semidirect
95. C22×#394C22semidirect
96. C22×#393C22semidirect
97. C2×#2360C22semidirect
98. C2×D4×C22⋊C4C22semidirect
99. C2×#2324C22semidirect
100. C22×#391C22semidirect
101. C22×#390C22semidirect
102. C22×#390C22semidirect
103. C22×#390C22semidirect
104. C22×#390C22semidirect
105. C22×#390C22semidirect
106. C22×#390C22semidirect
107. C22×#389C22semidirect
108. C22×#389C22semidirect
109. C22×#389C22semidirect
110. C22×#389C22semidirect
111. C22×#388C22semidirect
112. C22×#388C22semidirect
113. C22×#388C22semidirect
114. C22×#387C22semidirect
115. C22×#386C22semidirect
116. C22×#386C22semidirect
117. C22×#386C22semidirect
118. C22×#386C22semidirect
122. C22×#385C22semidirect
123. C22×#385C22semidirect
124. C22×#385C22semidirect
125. C22×#385C22semidirect
126. C22×#384C22semidirect
127. C2×#2280C22semidirect
128. C22×#381C22semidirect
129. C22×#381C22semidirect
133. C22×#380C22semidirect
134. C22×#380C22semidirect
135. C22×#380C22semidirect
136. C22×#380C22semidirect
137. C22×#380C22semidirect
144. C22×C4×C4⋊C4C22semidirect
148. C22×C4×C22⋊C4C22semidirect
149. C22×C4×C22⋊C4C22semidirect
183. C2×#542C23semidirect
185. C22×C4⋊Q8C23semidirect
187. C22×#126C23semidirect
192. C22×#124C23semidirect
193. C22×#124C23semidirect
194. C22×#124C23semidirect
195. C22×#124C23semidirect
198. C22×#123C23semidirect
199. C22×#123C23semidirect
207. C22×C22⋊Q8C23semidirect
208. C22×C22⋊Q8C23semidirect
209. C22×C22⋊Q8C23semidirect
225. C22×C4×Q8C23semidirect
228. C22×C4×D4C23semidirect
229. C22×C4×D4C23semidirect
232. C22×#117C23semidirect
233. C22×#117C23semidirect
302. #2848C23semidirect
303. #2701C23semidirect
304. #2691C23semidirect
305. #2686C23semidirect
306. #2672C23semidirect
307. #2624C23semidirect
308. #2620C23semidirect
309. #2491C23semidirect
310. #2480C23semidirect
311. #2440C23semidirect
312. #2437C23semidirect
313. #2435C23semidirect
314. #2435C23semidirect
315. #2427C23semidirect
316. #2426C23semidirect
317. #2422C23semidirect
318. #2405C23semidirect
319. C2×#399C23semidirect
320. C2×#398C23semidirect
321. C2×#397C23semidirect
322. C2×#397C23semidirect
323. C2×#397C23semidirect
324. C2×#396C23semidirect
325. C2×#396C23semidirect
326. C2×#396C23semidirect
327. C2×#395C23semidirect
328. C2×#394C23semidirect
329. C2×#394C23semidirect
330. C2×#394C23semidirect
331. C2×#394C23semidirect
332. C2×#394C23semidirect
333. C2×#394C23semidirect
334. C2×#394C23semidirect
335. C2×#394C23semidirect
336. C2×#394C23semidirect
337. C2×#394C23semidirect
338. C2×#393C23semidirect
339. #2360C23semidirect
340. D4×C22⋊C4C23semidirect
341. #2324C23semidirect
342. C2×#391C23semidirect
343. C2×#390C23semidirect
344. C2×#390C23semidirect
345. C2×#390C23semidirect
346. C2×#390C23semidirect
347. C2×#390C23semidirect
348. C2×#390C23semidirect
349. C2×#389C23semidirect
350. C2×#389C23semidirect
351. C2×#389C23semidirect
352. C2×#389C23semidirect
353. C2×#388C23semidirect
354. C2×#388C23semidirect
355. C2×#388C23semidirect
356. C2×#387C23semidirect
357. C2×#386C23semidirect
358. C2×#386C23semidirect
359. C2×#386C23semidirect
360. C2×#386C23semidirect
364. C2×#385C23semidirect
365. C2×#385C23semidirect
366. C2×#385C23semidirect
367. C2×#385C23semidirect
368. C2×#384C23semidirect
369. #2280C23semidirect
370. C2×#381C23semidirect
371. C2×#381C23semidirect
375. C2×#380C23semidirect
376. C2×#380C23semidirect
377. C2×#380C23semidirect
378. C2×#380C23semidirect
379. C2×#380C23semidirect
386. C2×C4×C4⋊C4C23semidirect
390. C2×C4×C22⋊C4C23semidirect
391. C2×C4×C22⋊C4C23semidirect
537. C2×C4⋊Q8C24semidirect
539. C2×#126C24semidirect
544. C2×#124C24semidirect
545. C2×#124C24semidirect
546. C2×#124C24semidirect
547. C2×#124C24semidirect
550. C2×#123C24semidirect
551. C2×#123C24semidirect
559. C2×C22⋊Q8C24semidirect
560. C2×C22⋊Q8C24semidirect
561. C2×C22⋊Q8C24semidirect
576. C2×C4×Q8C24semidirect
579. C2×C4×D4C24semidirect
580. C2×C4×D4C24semidirect
583. C2×#117C24semidirect
584. C2×#117C24semidirect
715. #399C24semidirect
716. #398C24semidirect
717. #397C24semidirect
718. #397C24semidirect
719. #397C24semidirect
720. #396C24semidirect
721. #396C24semidirect
722. #396C24semidirect
723. #395C24semidirect
724. #394C24semidirect
725. #394C24semidirect
726. #394C24semidirect
727. #394C24semidirect
728. #394C24semidirect
729. #394C24semidirect
730. #394C24semidirect
731. #394C24semidirect
732. #394C24semidirect
733. #394C24semidirect
734. #393C24semidirect
735. #391C24semidirect
736. #390C24semidirect
737. #390C24semidirect
738. #390C24semidirect
739. #390C24semidirect
740. #390C24semidirect
741. #390C24semidirect
742. #389C24semidirect
743. #389C24semidirect
744. #389C24semidirect
745. #389C24semidirect
746. #388C24semidirect
747. #388C24semidirect
748. #388C24semidirect
749. #387C24semidirect
750. #386C24semidirect
751. #386C24semidirect
752. #386C24semidirect
753. #386C24semidirect
757. #385C24semidirect
758. #385C24semidirect
759. #385C24semidirect
760. #385C24semidirect
761. #384C24semidirect
762. #381C24semidirect
763. #381C24semidirect
767. #380C24semidirect
768. #380C24semidirect
769. #380C24semidirect
770. #380C24semidirect
771. #380C24semidirect
778. C4×C4⋊C4C24semidirect
782. C4×C22⋊C4C24semidirect
783. C4×C22⋊C4C24semidirect
1307. C24#542semidirect
1639. C23C2×#542semidirect
1791. C22#37664direct (N × H)
1793. C22C22×#542semidirect
1830. C2C2×#37664direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#5422
C24×#1212
C2×#376642
C22×#27012
C22×#26722
C22×#26862
C22×#26912
C22×#28482
C22×#24912
C22×#24262
C22×#24272
C22×#24352
C22×#24222
C22×#24402
C22×#24802
C22×#24052
C22×#24372
C22×#26202
C22×#26242
C22×#23602
C22×D4×C22⋊C42
C22×#23242
C22×#22802