Finite Group Databasebeta

← C22×#38038 #72324646

Subgroups — C22×#38038 #72324646

Order 1024.

101513 conjugacy classes of subgroups.

The subgroup lattice has 1725 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#546C211yesmaximal, characteristic
2C24×#123C211yesmaximal, characteristic, complemented
3C2×#38038C2196yesmaximal, direct product factor
4C22×#2724C212yesmaximal, complemented
5C22×#2717C212yesmaximal, complemented
6C22×#2708C212yesmaximal, complemented
7C22×#2701C212yesmaximal, complemented
8C22×#2849C211yesmaximal, characteristic, complemented
9C22×#2583C211yesmaximal, characteristic, complemented
10C22×#2579C211yesmaximal, characteristic, complemented
11C22×#2486C212yesmaximal, complemented
12C22×#2483C211yesmaximal, characteristic, complemented
13C22×#2483C211yesmaximal, characteristic, complemented
14C22×#2406C212yesmaximal, complemented
15C22×#2425C212yesmaximal, complemented
16C22×#2419C212yesmaximal, complemented
17C22×#2412C211yesmaximal, characteristic, complemented
18C22×#2412C211yesmaximal, characteristic, complemented
19C22×#2627C211yesmaximal, characteristic, complemented
20C22×#2622C211yesmaximal, characteristic, complemented
21C22×D4×C22⋊C4C211yesmaximal, characteristic, complemented
22C22×#2322C211yesmaximal, characteristic, complemented
23C22×#2315C211yesmaximal, characteristic, complemented
24C23×#385C211yesmaximal, characteristic, complemented
25C24×#41C2211yescharacteristic
26C25×D4C2211yescharacteristic
27C26×C4C2211yescharacteristic
28C22×#546—232no—
29C22×#546C22148yes—
30C23×#124C2211yescharacteristic
31C23×#123—232no—
32C23×#123C2212yes—
33C23×#123C2212yes—
34C23×#123C2212yes—
35C23×#123C2212yes—
36C23×#123C2211yescharacteristic
37C23×#123C2211yescharacteristic
38C23×#123C2211yescharacteristic
39C23×#123C22148yescomplemented
40C23×#123C2212yescomplemented
41C23×C22⋊Q8C2211yescharacteristic
42C23×#121C2211yescharacteristic
43C23×#121C2211yescharacteristic
44C23×#121C2211yescharacteristic
45C23×#120C2211yescharacteristic
46C23×#120C2211yescharacteristic
47C23×C4×D4C2211yescharacteristic
48C23×C4×D4C2211yescharacteristic
49C23×C4×D4C2212yes—
50C24×C4⋊C4C2211yescharacteristic
51C24×C4⋊C4C2211yescharacteristic
52C24×C4⋊C4C2212yescomplemented
53C24×C22⋊C4C2211yescharacteristic
54C24×C22⋊C4C2211yescharacteristic
55C24×C22⋊C4C2211yescharacteristic
56C24×C22⋊C4C2211yescharacteristic
57C24×C22⋊C4C2211yescharacteristic
58C24×C22⋊C4C2211yescharacteristic
59C24×C22⋊C4C2211yescharacteristic
60C2×#2724C22196yescomplemented
61C2×#2717C22196yescomplemented
62C2×#2708C22196yescomplemented
63C2×#2701C22196yescomplemented
64#38038C2211024yesdirect product factor
65C2×#2849C22148yescomplemented
66C2×#2583C22148yescomplemented
67C2×#2579C22148yescomplemented
68C2×#2486C22196yescomplemented
69C2×#2483C22148yescomplemented
70C2×#2483C22148yescomplemented
71C2×#2406C22196yescomplemented
72C2×#2425C22196yescomplemented
73C2×#2419C22196yescomplemented
74C2×#2412C22148yescomplemented
75C2×#2412C22148yescomplemented
76C2×#2627C22148yescomplemented
77C2×#2622C22148yescomplemented
78C22×#400C2212yescomplemented
79C22×#398C2212yescomplemented
80C22×#398C2212yescomplemented
81C22×#398C2212yescomplemented
82C22×#398C2212yescomplemented
83C22×#397C2212yescomplemented
84C22×#397C2212yescomplemented
85C22×#397C2212yescomplemented
86C22×#397C2212yescomplemented
87C22×#397C2212yescomplemented
88C22×#397C2212yescomplemented
89C22×#397C2212yescomplemented
90C22×#397C2212yescomplemented
91C22×#396C2212yescomplemented
92C22×#395C2212yescomplemented
93C22×#395C2212yescomplemented
94C22×#394C2212yescomplemented
95C22×#394C2212yescomplemented
96C22×#394C2212yescomplemented
97C22×#394C2212yescomplemented
98C2×D4×C22⋊C4C22148yescomplemented
99C2×#2322C22148yescomplemented
100C2×#2315C22148yescomplemented
101C22×#390C2212yes—
102C22×#389C2212yescomplemented
103C22×#389C2212yescomplemented
104C22×#389C2212yescomplemented
105C22×#388C2212yescomplemented
106C22×#387C2212yescomplemented
107C22×#387C2212yescomplemented
108C22×#386C2211yescharacteristic
109C22×#386C2211yescharacteristic
110C22×#386C2212yes—
111C22×#386C2212yes—
112C22×#386C2211yescharacteristic
113C22×#386C2212yescomplemented
114C22×#386C2212yescomplemented
115C22×#386C2212yescomplemented
116C22×#385C2211yescharacteristic
117C22×#385C2211yescharacteristic
118C22×#385C2211yescharacteristic
119C22×#385C2211yescharacteristic
120C22×#385C2211yescharacteristic
121C22×#385C2211yescharacteristic
122C22×#385C2211yescharacteristic
123C22×#385C2211yescharacteristic
124C22×#385C2211yescharacteristic
125C22×#385C2212yescomplemented
126C22×#385C2212yescomplemented
127C22×#385C2212yescomplemented
128C22×#385C2212yescomplemented
129C22×#385C2212yescomplemented
130C22×#385C2212yescomplemented
131C22×#385C2212yescomplemented
132C22×#385C2212yescomplemented
133C22×#385C2212yescomplemented
134C22×#385C22148yescomplemented
135C22×#381C2211yescharacteristic
136C22×#381C2211yescharacteristic
137C22×#381C2211yescharacteristic
138C22×#381C2212yescomplemented
139C22×#381C2212yescomplemented
140C22×#381C2212yescomplemented
141C22×#380C2211yescharacteristic
142C22×#380C2212yescomplemented
143C22×#380C2212yescomplemented
144C22×#380C2212yescomplemented
145C22×#380C2212yescomplemented
146C22×#379C2211yescharacteristic
147C22×#379C2211yescharacteristic
148C22×C4×C22⋊C4C2211yescharacteristic
149C23×#95C2212yescomplemented
150C27C2311yescharacteristic
151C27C2311yescharacteristic
152C23×#41—216no—
153C23×#41—416no—
154C23×#41C23124yes—
155C24×Q8C2311yescharacteristic
156C24×D4—416no—
157C24×D4D4132yes—
158C24×D4C2311yescharacteristic
159C24×D4C2311yescharacteristic
160C24×D4C2311yescharacteristic
161C24×D4C2311yescharacteristic
162C24×D4C2311yescharacteristic
163C24×D4C2311yescharacteristic
164C24×D4C2311yescharacteristic
165C24×D4C23124yes—
166C24×D4C2311yescharacteristic
167C24×D4C2311yescharacteristic
168C25×C4—216no—
169C25×C4—416no—
170C25×C4C2312yes—
171C25×C4C2311yescharacteristic
172C25×C4C2311yescharacteristic
173C25×C4C2312yes—
174C25×C4C23124yes—
175C25×C4C2311yescharacteristic
176C25×C4C2311yescharacteristic
177C25×C4C2312yes—
178C25×C4C2311yescharacteristic
179C25×C4C2311yescharacteristic
180C25×C4C2311yescharacteristic
181C25×C4C2311yescharacteristic
182C25×C4C2311yescharacteristic
183C25×C4C2312yes—
184C25×C4C2311yescharacteristic
185C2×#546—2768no—
186C2×#546C231256yes—
187C22×#124—216no—
188C22×#124C23124yes—
189C22×#123—232no—
190C22×#123—232no—
191C22×#123—232no—
192C22×#123—232no—
193C22×#123—2768no—
194C22×#123—216no—
195C22×#123—216no—
196C22×#123—216no—
197C22×#123—416no—
198C22×#123C23124yes—
199C22×#123C23148yes—
200C22×#123C23148yes—
201C22×#123C23148yes—
202C22×#123C23148yes—
203C22×#123C23124yes—
204C22×#123C23124yes—
205C22×#123C231256yescomplemented
206C22×#123C23148yescomplemented
207C22×C22⋊Q8—216no—
208C22×C22⋊Q8C23124yes—
209C22×#121—216no—
210C22×#121—216no—
211C22×#121—216no—
212C22×#121C23124yes—
213C22×#121C23124yes—
214C22×#121C23124yes—
215C22×#120—216no—
216C22×#120—216no—
217C22×#120C23124yes—
218C22×#120C23124yes—
219C22×C4×D4—216no—
220C22×C4×D4—216no—
221C22×C4×D4—416no—
222C22×C4×D4C23124yes—
223C22×C4×D4C23124yes—
224C22×C4×D4C23148yes—
225C23×C4⋊C4—216no—
226C23×C4⋊C4—216no—
227C23×C4⋊C4—416no—
228C23×C4⋊C4C23124yes—
229C23×C4⋊C4C23124yes—
230C23×C4⋊C4C2312yes—
231C23×C4⋊C4C2312yes—
232C23×C4⋊C4C2312yes—
233C23×C4⋊C4C2312yes—
234C23×C4⋊C4C2311yescharacteristic
235C23×C4⋊C4C2311yescharacteristic
236C23×C4⋊C4C2311yescharacteristic
237C23×C4⋊C4C2311yescharacteristic
238C23×C4⋊C4C2312yes—
239C23×C4⋊C4C2312yes—
240C23×C4⋊C4C2312yes—
241C23×C4⋊C4C2312yes—
242C23×C4⋊C4C2312yes—
243C23×C4⋊C4C2312yes—
244C23×C4⋊C4C2312yes—
245C23×C4⋊C4C2312yes—
246C23×C4⋊C4C2312yes—
247C23×C4⋊C4C2312yes—
248C23×C4⋊C4C2312yes—
249C23×C4⋊C4C23148yescomplemented
250C23×C22⋊C4—216no—
251C23×C22⋊C4—216no—
252C23×C22⋊C4—216no—
253C23×C22⋊C4—216no—
254C23×C22⋊C4—216no—
255C23×C22⋊C4—216no—
256C23×C22⋊C4—216no—
257C23×C22⋊C4C23124yes—
258C23×C22⋊C4C23124yes—
259C23×C22⋊C4C23124yes—
260C23×C22⋊C4C23124yes—
261C23×C22⋊C4C23124yes—
262C23×C22⋊C4C23124yes—
263C23×C22⋊C4C2311yescharacteristic
264C23×C22⋊C4C23124yes—
265C23×C22⋊C4C2311yescharacteristic
266C23×C22⋊C4C2311yescharacteristic
267C23×C22⋊C4C2311yescharacteristic
268C23×C22⋊C4C2311yescharacteristic
269C23×C22⋊C4C2311yescharacteristic
270C23×C22⋊C4C2311yescharacteristic
271C23×C22⋊C4C2312yes—
272C23×C22⋊C4C2312yes—
273C23×C22⋊C4C2312yes—
274C23×C22⋊C4C2312yes—
275C23×C22⋊C4C2312yes—
276C23×C22⋊C4C2312yes—
277C23×C22⋊C4C2311yescharacteristic
278C23×C22⋊C4C2311yescharacteristic
279C23×C22⋊C4C2312yes—
280C23×C22⋊C4C2312yes—
281C23×C22⋊C4C2311yescharacteristic
282C23×C22⋊C4C2311yescharacteristic
283C23×C22⋊C4C2311yescharacteristic
284C23×C22⋊C4C2312yes—
285C23×C22⋊C4C2311yescharacteristic
286C23×C22⋊C4C2311yescharacteristic
287C23×C22⋊C4C2312yes—
288C23×C22⋊C4C2311yescharacteristic
289C23×C22⋊C4C2312yes—
290C23×C22⋊C4C2312yes—
291C23×C22⋊C4C2312yes—
292C23×C22⋊C4C2312yes—
293C23×C22⋊C4C2312yes—
294C23×C22⋊C4C2312yes—
295C23×C22⋊C4C2311yescharacteristic
296C23×C42C2311yescharacteristic
297C23×C42C2312yes—
298#2849C231256yescomplemented
299#2724C231512yescomplemented
300#2717C231512yescomplemented
301#2708C231512yescomplemented
302#2701C231512yescomplemented
303#2627C231256yescomplemented
304#2622C231256yescomplemented
305#2583C231256yescomplemented
306#2579C231256yescomplemented
307#2486C231512yescomplemented
308#2483C231256yescomplemented
309#2483C231256yescomplemented
310#2425C231512yescomplemented
311#2419C231512yescomplemented
312#2412C231256yescomplemented
313#2412C231256yescomplemented
314#2406C231512yescomplemented
315C2×#400C23148yescomplemented
316C2×#398C23148yescomplemented
317C2×#398C23148yescomplemented
318C2×#398C23148yescomplemented
319C2×#398C23148yescomplemented
320C2×#397C23148yescomplemented
321C2×#397C23148yescomplemented
322C2×#397C23148yescomplemented
323C2×#397C23148yescomplemented
324C2×#397C23148yescomplemented
325C2×#397C23148yescomplemented
326C2×#397C23148yescomplemented
327C2×#397C23148yescomplemented
328C2×#396C23148yescomplemented
329C2×#395C23148yescomplemented
330C2×#395C23148yescomplemented
331C2×#394C23148yescomplemented
332C2×#394C23148yescomplemented
333C2×#394C23148yescomplemented
334C2×#394C23148yescomplemented
335D4×C22⋊C4C231256yescomplemented
336#2322C231256yescomplemented
337#2315C231256yescomplemented
338C2×#390C23148yes—
339C2×#389C23148yescomplemented
340C2×#389C23148yescomplemented
341C2×#389C23148yescomplemented
342C2×#388C23148yescomplemented
343C2×#387C23148yescomplemented
344C2×#387C23148yescomplemented
345C2×#386C23124yes—
346C2×#386C23124yes—
347C2×#386C23124yes—
348C2×#386C23148yes—
349C2×#386C23148yes—
350C2×#386C23148yescomplemented
351C2×#386C23148yescomplemented
352C2×#386C23148yescomplemented
353C2×#385C23124yes—
354C2×#385C23124yes—
355C2×#385C23124yes—
356C2×#385C23124yes—
357C2×#385C23124yes—
358C2×#385C23124yes—
359C2×#385C23124yes—
360C2×#385C23124yes—
361C2×#385C23124yes—
362C2×#385C23148yescomplemented
363C2×#385C23148yescomplemented
364C2×#385C23148yescomplemented
365C2×#385C23148yescomplemented
366C2×#385C23148yescomplemented
367C2×#385C23148yescomplemented
368C2×#385C23148yescomplemented
369C2×#385C23148yescomplemented
370C2×#385C23148yescomplemented
371C2×#385C231256yescomplemented
372C2×#381C23124yes—
373C2×#381C23124yes—
374C2×#381C23124yes—
375C2×#381C23148yescomplemented
376C2×#381C23148yescomplemented
377C2×#381C23148yescomplemented
378C2×#380C23124yes—
379C2×#380C23148yescomplemented
380C2×#380C23148yescomplemented
381C2×#380C23148yescomplemented
382C2×#380C23148yescomplemented
383C2×#379C23124yes—
384C2×#379C23124yes—
385C2×C4×C22⋊C4C23124yes—
386C22×#95C2312yes—
387C22×#95C2312yes—
388C22×#95C2312yes—
389C22×#95C2312yes—
390C22×#95C2312yes—
391C22×#95C2312yes—
392C22×#95C2312yes—
393C22×#95C2312yes—
394C22×#95C2312yes—
395C22×#95C2312yes—
396C22×#95C2312yes—
397C22×#95C2312yes—
398C22×#95C2312yes—
399C22×#95C2312yes—
400C22×#95C2312yes—
401C22×#95C2312yes—
402C22×#95C2312yes—
403C22×#95C2312yes—
404C22×#95C2312yes—
405C22×#95C2312yes—
406C22×#95C23148yescomplemented
407C26—28no—
408C26—216no—
409C26—28no—
410C26—28no—
411C26—28no—
412C26—48no—
413C26—48no—
414C26—48no—
415C26C2×D4116yes—
416C26C2×D4116yes—
417C26C2411yescharacteristic
418C26C2411yescharacteristic
419C26C2411yescharacteristic
420C26C2411yescharacteristic
421C26C24112yes—
422C26C2411yescharacteristic
423C26C2411yescharacteristic
424C26C24112yes—
425C22×#41—2192no—
426C22×#41—4192no—
427C22×#41—4256no—
428C22×#41C24164yes—
429C23×Q8—28no—
430C23×Q8—48no—
431C23×Q8C24112yes—
432C23×D4—216no—
433C23×D4—216no—
434C23×D4—28no—
435C23×D4—28no—
436C23×D4—28no—
437C23×D4—28no—
438C23×D4—216no—
439C23×D4—28no—
440C23×D4—28no—
441C23×D4—28no—
442C23×D4—48no—
443C23×D4—48no—
444C23×D4—48no—
445C23×D4—48no—
446C23×D4—48no—
447C23×D4—4256no—
448C23×D4—4192no—
449C23×D4C2×D4116yes—
450C23×D4C2×D4116yes—
451C23×D4C2×D4116yes—
452C23×D4C2×D4116yes—
453C23×D4C2×D41384yes—
454C23×D4C24112yes—
455C23×D4C24112yes—
456C23×D4C24112yes—
457C23×D4C24112yes—
458C23×D4C24112yes—
459C23×D4C24112yes—
460C23×D4C24112yes—
461C23×D4C24164yes—
462C23×D4C24112yes—
463C23×D4C24112yes—
464C24×C4—28no—
465C24×C4—28no—
466C24×C4—216no—
467C24×C4—2192no—
468C24×C4—216no—
469C24×C4—28no—
470C24×C4—28no—
471C24×C4—28no—
472C24×C4—28no—
473C24×C4—28no—
474C24×C4—216no—
475C24×C4—216no—
476C24×C4—216no—
477C24×C4—216no—
478C24×C4—28no—
479C24×C4—28no—
480C24×C4—28no—
481C24×C4—28no—
482C24×C4—216no—
483C24×C4—216no—
484C24×C4—48no—
485C24×C4—48no—
486C24×C4—48no—
487C24×C4—48no—
488C24×C4—4192no—
489C24×C4—48no—
490C24×C4—48no—
491C24×C4—48no—
492C24×C4—48no—
493C24×C4—48no—
494C24×C4—48no—
495C24×C4—48no—
496C24×C4—48no—
497C24×C4—48no—
498C24×C4—4256no—
499C24×C4C2×D4116yes—
500C24×C4C24124yes—
501C24×C4C24112yes—
502C24×C4C24112yes—
503C24×C4C2411yescharacteristic
504C24×C4C2412yes—
505C24×C4C2412yes—
506C24×C4C2411yescharacteristic
507C24×C4C2411yescharacteristic
508C24×C4C2411yescharacteristic
509C24×C4C2411yescharacteristic
510C24×C4C2411yescharacteristic
511C24×C4C2412yes—
512C24×C4C2412yes—
513C24×C4C2412yes—
514C24×C4C2412yes—
515C24×C4C2411yescharacteristic
516C24×C4C2412yes—
517C24×C4C24124yes—
518C24×C4C2411yescharacteristic
519C24×C4C2411yescharacteristic
520C24×C4C2412yes—
521C24×C4C24164yes—
522C24×C4C24112yes—
523C24×C4C24112yes—
524C24×C4C24124yes—
525C24×C4C24112yes—
526C24×C4C24112yes—
527C24×C4C24112yes—
528C24×C4C24112yes—
529C24×C4C24112yes—
530C24×C4C24124yes—
531C24×C4C24112yes—
532#546—22048no—
533C2×#124—2192no—
534C2×#124C24164yes—
535C2×#123—2384no—
536C2×#123—2384no—
537C2×#123—2384no—
538C2×#123—2384no—
539C2×#123—22048no—
540C2×#123—2192no—
541C2×#123—2192no—
542C2×#123—2192no—
543C2×#123—4192no—
544C2×#123C24164yes—
545C2×#123C241128yes—
546C2×#123C241128yes—
547C2×#123C241128yes—
548C2×#123C241128yes—
549C2×#123C24164yes—
550C2×#123C24164yes—
551C2×#123C241128yescomplemented
552C2×C22⋊Q8—2192no—
553C2×C22⋊Q8C24164yes—
554C2×#121—2192no—
555C2×#121—2192no—
556C2×#121—2192no—
557C2×#121C24164yes—
558C2×#121C24164yes—
559C2×#121C24164yes—
560C2×#120—2192no—
561C2×#120—2192no—
562C2×#120C24164yes—
563C2×#120C24164yes—
564C2×C4×D4—2192no—
565C2×C4×D4—2192no—
566C2×C4×D4—4192no—
567C2×C4×D4C24164yes—
568C2×C4×D4C24164yes—
569C2×C4×D4C241128yes—
570C22×C4⋊C4—216no—
571C22×C4⋊C4—216no—
572C22×C4⋊C4—216no—
573C22×C4⋊C4—216no—
574C22×C4⋊C4—2192no—
575C22×C4⋊C4—2192no—
576C22×C4⋊C4—28no—
577C22×C4⋊C4—28no—
578C22×C4⋊C4—28no—
579C22×C4⋊C4—28no—
580C22×C4⋊C4—216no—
581C22×C4⋊C4—48no—
582C22×C4⋊C4—48no—
583C22×C4⋊C4—48no—
584C22×C4⋊C4—48no—
585C22×C4⋊C4—4192no—
586C22×C4⋊C4—48no—
587C22×C4⋊C4—48no—
588C22×C4⋊C4—48no—
589C22×C4⋊C4—48no—
590C22×C4⋊C4—48no—
591C22×C4⋊C4—48no—
592C22×C4⋊C4C24164yes—
593C22×C4⋊C4C24164yes—
594C22×C4⋊C4C24124yes—
595C22×C4⋊C4C24124yes—
596C22×C4⋊C4C24124yes—
597C22×C4⋊C4C24124yes—
598C22×C4⋊C4C24112yes—
599C22×C4⋊C4C24124yes—
600C22×C4⋊C4C24112yes—
601C22×C4⋊C4C24112yes—
602C22×C4⋊C4C24112yes—
603C22×C4⋊C4C24124yes—
604C22×C4⋊C4C24124yes—
605C22×C4⋊C4C24124yes—
606C22×C4⋊C4C24124yes—
607C22×C4⋊C4C24124yes—
608C22×C4⋊C4C24124yes—
609C22×C4⋊C4C24124yes—
610C22×C4⋊C4C24124yes—
611C22×C4⋊C4C24124yes—
612C22×C4⋊C4C24124yes—
613C22×C4⋊C4C241128yescomplemented
614C22×C22⋊C4—28no—
615C22×C22⋊C4—28no—
616C22×C22⋊C4—28no—
617C22×C22⋊C4—28no—
618C22×C22⋊C4—28no—
619C22×C22⋊C4—28no—
620C22×C22⋊C4—28no—
621C22×C22⋊C4—216no—
622C22×C22⋊C4—2192no—
623C22×C22⋊C4—216no—
624C22×C22⋊C4—216no—
625C22×C22⋊C4—216no—
626C22×C22⋊C4—216no—
627C22×C22⋊C4—216no—
628C22×C22⋊C4—2192no—
629C22×C22⋊C4—2192no—
630C22×C22⋊C4—2192no—
631C22×C22⋊C4—2192no—
632C22×C22⋊C4—28no—
633C22×C22⋊C4—28no—
634C22×C22⋊C4—28no—
635C22×C22⋊C4—28no—
636C22×C22⋊C4—28no—
637C22×C22⋊C4—28no—
638C22×C22⋊C4—216no—
639C22×C22⋊C4—28no—
640C22×C22⋊C4—28no—
641C22×C22⋊C4—216no—
642C22×C22⋊C4—216no—
643C22×C22⋊C4—216no—
644C22×C22⋊C4—2192no—
645C22×C22⋊C4—2192no—
646C22×C22⋊C4—48no—
647C22×C22⋊C4—48no—
648C22×C22⋊C4—48no—
649C22×C22⋊C4—48no—
650C22×C22⋊C4—48no—
651C22×C22⋊C4—48no—
652C22×C22⋊C4#41116yescomplemented
653C22×C22⋊C4C24164yes—
654C22×C22⋊C4C24164yes—
655C22×C22⋊C4C24164yes—
656C22×C22⋊C4C24164yes—
657C22×C22⋊C4C24124yes—
658C22×C22⋊C4C24124yes—
659C22×C22⋊C4C24124yes—
660C22×C22⋊C4C24124yes—
661C22×C22⋊C4C24124yes—
662C22×C22⋊C4C24124yes—
663C22×C22⋊C4C24124yes—
664C22×C22⋊C4C24112yes—
665C22×C22⋊C4C24112yes—
666C22×C22⋊C4C24112yes—
667C22×C22⋊C4C24112yes—
668C22×C22⋊C4C24112yes—
669C22×C22⋊C4C24112yes—
670C22×C22⋊C4C24124yes—
671C22×C22⋊C4C24112yes—
672C22×C22⋊C4C24112yes—
673C22×C22⋊C4C24112yes—
674C22×C22⋊C4C24112yes—
675C22×C22⋊C4C24112yes—
676C22×C22⋊C4C24124yes—
677C22×C22⋊C4C24164yes—
678C22×C22⋊C4C24164yes—
679C22×C22⋊C4C24164yes—
680C22×C22⋊C4C24112yes—
681C22×C22⋊C4C24112yes—
682C22×C22⋊C4C24112yes—
683C22×C22⋊C4C24124yes—
684C22×C22⋊C4C24112yes—
685C22×C22⋊C4C24124yes—
686C22×C22⋊C4C24124yes—
687C22×C22⋊C4C24124yes—
688C22×C22⋊C4C24124yes—
689C22×C22⋊C4C24124yes—
690C22×C22⋊C4C24124yes—
691C22×C22⋊C4C24112yes—
692C22×C42—28no—
693C22×C42—48no—
694C22×C42C24112yes—
695C22×C42C24124yes—
696#400C241128yescomplemented
697#398C241128yescomplemented
698#398C241128yescomplemented
699#398C241128yescomplemented
700#398C241128yescomplemented
701#397C241128yescomplemented
702#397C241128yescomplemented
703#397C241128yescomplemented
704#397C241128yescomplemented
705#397C241128yescomplemented
706#397C241128yescomplemented
707#397C241128yescomplemented
708#397C241128yescomplemented
709#396C241128yescomplemented
710#395C241128yescomplemented
711#395C241128yescomplemented
712#394C241128yescomplemented
713#394C241128yescomplemented
714#394C241128yescomplemented
715#394C241128yescomplemented
716#390C241128yes—
717#389C241128yescomplemented
718#389C241128yescomplemented
719#389C241128yescomplemented
720#388C241128yescomplemented
721#387C241128yescomplemented
722#387C241128yescomplemented
723#386C24164yes—
724#386C24164yes—
725#386C24164yes—
726#386C241128yes—
727#386C241128yes—
728#386C241128yescomplemented
729#386C241128yescomplemented
730#386C241128yescomplemented
731#385C24164yes—
732#385C24164yes—
733#385C24164yes—
734#385C24164yes—
735#385C24164yes—
736#385C24164yes—
737#385C24164yes—
738#385C24164yes—
739#385C24164yes—
740#385C241128yescomplemented
741#385C241128yescomplemented
742#385C241128yescomplemented
743#385C241128yescomplemented
744#385C241128yescomplemented
745#385C241128yescomplemented
746#385C241128yescomplemented
747#385C241128yescomplemented
748#385C241128yescomplemented
749#381C24164yes—
750#381C24164yes—
751#381C24164yes—
752#381C241128yescomplemented
753#381C241128yescomplemented
754#381C241128yescomplemented
755#380C24164yes—
756#380C241128yescomplemented
757#380C241128yescomplemented
758#380C241128yescomplemented
759#380C241128yescomplemented
760#379C24164yes—
761#379C24164yes—
762C4×C22⋊C4C24164yes—
763C2×#95C24124yes—
764C2×#95C24124yes—
765C2×#95C24124yes—
766C2×#95C24124yes—
767C2×#95C24124yes—
768C2×#95C24124yes—
769C2×#95C24124yes—
770C2×#95C24124yes—
771C2×#95C24124yes—
772C2×#95C24124yes—
773C2×#95C24124yes—
774C2×#95C24124yes—
775C2×#95C24124yes—
776C2×#95C24124yes—
777C2×#95C24124yes—
778C2×#95C24124yes—
779C2×#95C24124yes—
780C2×#95C24124yes—
781C2×#95C24124yes—
782C2×#95C24124yes—
783C2×#95C241128yescomplemented
784C25—24no—
785C25—28no—
786C25—24no—
787C25—28no—
788C25—28no—
789C25—2128no—
790C25—2128no—
791C25—248no—
792C25—24no—
793C25—24no—
794C25—24no—
795C25—28no—
796C25—296no—
797C25—28no—
798C25—28no—
799C25—248no—
800C25—24no—
801C25—24no—
802C25—24no—
803C25—28no—
804C25—28no—
805C25—28no—
806C25—2128no—
807C25—248no—
808C25—248no—
809C25—24no—
810C25—24no—
811C25—28no—
812C25—24no—
813C25—28no—
814C25—464no—
815C25—448no—
816C25—464no—
817C25—448no—
818C25—464no—
819C25—448no—
820C25—4128no—
821C25—4128no—
822C25—864no—
823C25—864no—
824C25C22×D418yes—
825C25C22×D418yes—
826C25C22×D418yes—
827C25C22×D4196yes—
828C25C22×D418yes—
829C25C22×D418yes—
830C25C22×D4196yes—
831C25C2×#4118yes—
832C25H(5,𝔽2)116yes—
833C252−1+418yes—
834C25C2516yes—
835C25C2516yes—
836C25C2516yes—
837C25C2516yes—
838C25C25116yes—
839C25C2516yes—
840C25C2516yes—
841C25C25116yes—
842C25C2511yescharacteristic
843C2×#41—2256no—
844C2×#41—4256no—
845C2×#41—41536no—
846C22×Q8—248no—
847C22×Q8—448no—
848C22×Q8—464no—
849C22×Q8C25116yes—
850C22×D4—2128no—
851C22×D4—2128no—
852C22×D4—296no—
853C22×D4—296no—
854C22×D4—248no—
855C22×D4—248no—
856C22×D4—248no—
857C22×D4—248no—
858C22×D4—296no—
859C22×D4—248no—
860C22×D4—248no—
861C22×D4—248no—
862C22×D4—464no—
863C22×D4—464no—
864C22×D4—448no—
865C22×D4—448no—
866C22×D4—448no—
867C22×D4—448no—
868C22×D4—448no—
869C22×D4—41536no—
870C22×D4—4256no—
871C22×D4—464no—
872C22×D4—464no—
873C22×D4—464no—
874C22×D4—832no—
875C22×D4—832no—
876C22×D4C22×D4196yes—
877C22×D4C22×D4196yes—
878C22×D4C22×D4196yes—
879C22×D4C22×D4196yes—
880C22×D4C22×D41512yes—
881C22×D4C25116yes—
882C22×D4C25116yes—
883C22×D4C25116yes—
884C22×D4C25116yes—
885C22×D4C25116yes—
886C22×D4C25116yes—
887C22×D4C25116yes—
888C22×D4C25116yes—
889C22×D4C25116yes—
890C23×C4—28no—
891C23×C4—28no—
892C23×C4—28no—
893C23×C4—28no—
894C23×C4—248no—
895C23×C4—248no—
896C23×C4—28no—
897C23×C4—28no—
898C23×C4—24no—
899C23×C4—24no—
900C23×C4—24no—
901C23×C4—24no—
902C23×C4—24no—
903C23×C4—24no—
904C23×C4—24no—
905C23×C4—248no—
906C23×C4—248no—
907C23×C4—28no—
908C23×C4—28no—
909C23×C4—248no—
910C23×C4—248no—
911C23×C4—296no—
912C23×C4—2256no—
913C23×C4—296no—
914C23×C4—28no—
915C23×C4—28no—
916C23×C4—28no—
917C23×C4—24no—
918C23×C4—248no—
919C23×C4—28no—
920C23×C4—28no—
921C23×C4—28no—
922C23×C4—28no—
923C23×C4—28no—
924C23×C4—296no—
925C23×C4—296no—
926C23×C4—28no—
927C23×C4—28no—
928C23×C4—28no—
929C23×C4—28no—
930C23×C4—296no—
931C23×C4—28no—
932C23×C4—296no—
933C23×C4—28no—
934C23×C4—248no—
935C23×C4—28no—
936C23×C4—24no—
937C23×C4—28no—
938C23×C4—28no—
939C23×C4—28no—
940C23×C4—28no—
941C23×C4—28no—
942C23×C4—28no—
943C23×C4—28no—
944C23×C4—28no—
945C23×C4—248no—
946C23×C4—248no—
947C23×C4—248no—
948C23×C4—296no—
949C23×C4—296no—
950C23×C4—448no—
951C23×C4—448no—
952C23×C4—448no—
953C23×C4—448no—
954C23×C4—4256no—
955C23×C4—464no—
956C23×C4—448no—
957C23×C4—448no—
958C23×C4—448no—
959C23×C4—448no—
960C23×C4—448no—
961C23×C4—448no—
962C23×C4—448no—
963C23×C4—448no—
964C23×C4—448no—
965C23×C4—4128no—
966C23×C4—464no—
967C23×C4—464no—
968C23×C4—464no—
969C23×C4—464no—
970C23×C4—41536no—
971C23×C4—4128no—
972C23×C4—464no—
973C23×C4—4128no—
974C23×C4—464no—
975C23×C4—464no—
976C23×C4—864no—
977C23×C4—832no—
978C23×C4—832no—
979C23×C4C22×D418yes—
980C23×C4C22×D418yes—
981C23×C4C22×D4196yes—
982C23×C4C2×#41116yes—
983C23×C4C25112yes—
984C23×C4C25112yes—
985C23×C4C25112yes—
986C23×C4C25112yes—
987C23×C4C25112yes—
988C23×C4C2516yes—
989C23×C4C25116yes—
990C23×C4C2516yes—
991C23×C4C2516yes—
992C23×C4C25112yes—
993C23×C4C25112yes—
994C23×C4C2516yes—
995C23×C4C2516yes—
996C23×C4C2516yes—
997C23×C4C2516yes—
998C23×C4C25116yes—
999C23×C4C25132yes—
1000C23×C4C25132yes—
1001C23×C4C2516yes—
1002C23×C4C2516yes—
1003C23×C4C25112yes—
1004C23×C4C25116yes—
1005C23×C4C25116yes—
1006C23×C4C25116yes—
1007C23×C4C25116yes—
1008C23×C4C25116yes—
1009C23×C4C25132yes—
1010C23×C4C25116yes—
1011C23×C4C25116yes—
1012C23×C4C25132yes—
1013C23×C4C25116yes—
1014#124—2256no—
1015#123—2512no—
1016#123—2512no—
1017#123—2512no—
1018#123—2512no—
1019#123—2256no—
1020#123—2256no—
1021#123—2256no—
1022#123—4256no—
1023C22⋊Q8—2256no—
1024#121—2256no—
1025#121—2256no—
1026#121—2256no—
1027#120—2256no—
1028#120—2256no—
1029C4×D4—2256no—
1030C4×D4—2256no—
1031C4×D4—4256no—
1032C2×C4⋊C4—296no—
1033C2×C4⋊C4—296no—
1034C2×C4⋊C4—296no—
1035C2×C4⋊C4—296no—
1036C2×C4⋊C4—2256no—
1037C2×C4⋊C4—2256no—
1038C2×C4⋊C4—248no—
1039C2×C4⋊C4—248no—
1040C2×C4⋊C4—248no—
1041C2×C4⋊C4—248no—
1042C2×C4⋊C4—296no—
1043C2×C4⋊C4—448no—
1044C2×C4⋊C4—448no—
1045C2×C4⋊C4—448no—
1046C2×C4⋊C4—448no—
1047C2×C4⋊C4—4256no—
1048C2×C4⋊C4—448no—
1049C2×C4⋊C4—448no—
1050C2×C4⋊C4—448no—
1051C2×C4⋊C4—448no—
1052C2×C4⋊C4—448no—
1053C2×C4⋊C4—448no—
1054C2×C4⋊C4C25132yes—
1055C2×C4⋊C4C25132yes—
1056C2×C4⋊C4C25132yes—
1057C2×C4⋊C4C25132yes—
1058C2×C4⋊C4C25116yes—
1059C2×C4⋊C4C25116yes—
1060C2×C4⋊C4C25116yes—
1061C2×C4⋊C4C25116yes—
1062C2×C4⋊C4C25132yes—
1063C2×C4⋊C4C25132yes—
1064C2×C4⋊C4C25132yes—
1065C2×C4⋊C4C25132yes—
1066C2×C4⋊C4C25132yes—
1067C2×C4⋊C4C25132yes—
1068C2×C4⋊C4C25132yes—
1069C2×C4⋊C4C25132yes—
1070C2×C4⋊C4C25132yes—
1071C2×C4⋊C4C25132yes—
1072C2×C4⋊C4C25132yes—
1073C2×C22⋊C4—248no—
1074C2×C22⋊C4—248no—
1075C2×C22⋊C4—248no—
1076C2×C22⋊C4—248no—
1077C2×C22⋊C4—248no—
1078C2×C22⋊C4—248no—
1079C2×C22⋊C4—248no—
1080C2×C22⋊C4—296no—
1081C2×C22⋊C4—2256no—
1082C2×C22⋊C4—296no—
1083C2×C22⋊C4—296no—
1084C2×C22⋊C4—296no—
1085C2×C22⋊C4—296no—
1086C2×C22⋊C4—296no—
1087C2×C22⋊C4—2256no—
1088C2×C22⋊C4—2256no—
1089C2×C22⋊C4—2256no—
1090C2×C22⋊C4—2256no—
1091C2×C22⋊C4—248no—
1092C2×C22⋊C4—248no—
1093C2×C22⋊C4—248no—
1094C2×C22⋊C4—248no—
1095C2×C22⋊C4—248no—
1096C2×C22⋊C4—248no—
1097C2×C22⋊C4—296no—
1098C2×C22⋊C4—248no—
1099C2×C22⋊C4—248no—
1100C2×C22⋊C4—296no—
1101C2×C22⋊C4—296no—
1102C2×C22⋊C4—296no—
1103C2×C22⋊C4—2256no—
1104C2×C22⋊C4—2256no—
1105C2×C22⋊C4—448no—
1106C2×C22⋊C4—448no—
1107C2×C22⋊C4—448no—
1108C2×C22⋊C4—448no—
1109C2×C22⋊C4—448no—
1110C2×C22⋊C4—448no—
1111C2×C22⋊C4C2×#41196yescomplemented
1112C2×C22⋊C4C25116yes—
1113C2×C22⋊C4C25116yes—
1114C2×C22⋊C4C25116yes—
1115C2×C22⋊C4C25116yes—
1116C2×C22⋊C4C25116yes—
1117C2×C22⋊C4C25116yes—
1118C2×C22⋊C4C25116yes—
1119C2×C22⋊C4C25132yes—
1120C2×C22⋊C4C25132yes—
1121C2×C22⋊C4C25132yes—
1122C2×C22⋊C4C25132yes—
1123C2×C22⋊C4C25132yes—
1124C2×C22⋊C4C25132yes—
1125C2×C22⋊C4C25116yes—
1126C2×C22⋊C4C25116yes—
1127C2×C22⋊C4C25132yes—
1128C2×C22⋊C4C25132yes—
1129C2×C22⋊C4C25116yes—
1130C2×C22⋊C4C25116yes—
1131C2×C22⋊C4C25116yes—
1132C2×C22⋊C4C25132yes—
1133C2×C22⋊C4C25116yes—
1134C2×C22⋊C4C25116yes—
1135C2×C22⋊C4C25132yes—
1136C2×C22⋊C4C25116yes—
1137C2×C22⋊C4C25132yes—
1138C2×C22⋊C4C25132yes—
1139C2×C22⋊C4C25132yes—
1140C2×C22⋊C4C25132yes—
1141C2×C22⋊C4C25132yes—
1142C2×C22⋊C4C25132yes—
1143C2×C22⋊C4C25116yes—
1144C2×C42—248no—
1145C2×C42—448no—
1146C2×C42C25116yes—
1147C2×C42C25132yes—
1148#95C25132yes—
1149#95C25132yes—
1150#95C25132yes—
1151#95C25132yes—
1152#95C25132yes—
1153#95C25132yes—
1154#95C25132yes—
1155#95C25132yes—
1156#95C25132yes—
1157#95C25132yes—
1158#95C25132yes—
1159#95C25132yes—
1160#95C25132yes—
1161#95C25132yes—
1162#95C25132yes—
1163#95C25132yes—
1164#95C25132yes—
1165#95C25132yes—
1166#95C25132yes—
1167#95C25132yes—
1168C24—212no—
1169C24—224no—
1170C24—212no—
1171C24—224no—
1172C24—224no—
1173C24—232no—
1174C24—232no—
1175C24—232no—
1176C24—232no—
1177C24—264no—
1178C24—264no—
1179C24—264no—
1180C24—264no—
1181C24—232no—
1182C24—212no—
1183C24—212no—
1184C24—212no—
1185C24—224no—
1186C24—264no—
1187C24—224no—
1188C24—224no—
1189C24—232no—
1190C24—212no—
1191C24—212no—
1192C24—212no—
1193C24—224no—
1194C24—224no—
1195C24—224no—
1196C24—2384no—
1197C24—232no—
1198C24—232no—
1199C24—232no—
1200C24—2384no—
1201C24—232no—
1202C24—232no—
1203C24—232no—
1204C24—232no—
1205C24—232no—
1206C24—232no—
1207C24—232no—
1208C24—232no—
1209C24—2384no—
1210C24—212no—
1211C24—212no—
1212C24—224no—
1213C24—212no—
1214C24—224no—
1215C24—4192no—
1216C24—432no—
1217C24—4192no—
1218C24—432no—
1219C24—4192no—
1220C24—432no—
1221C24—4384no—
1222C24—4384no—
1223C24—41024no—
1224C24—432no—
1225C24—432no—
1226C24—432no—
1227C24—432no—
1228C24—432no—
1229C24—432no—
1230C24—416no—
1231C24—416no—
1232C24—416no—
1233C24—432no—
1234C24—432no—
1235C24—8192no—
1236C24—8192no—
1237C24—8512no—
1238C24#534164yes—
1239C24#547164yes—
1240C24C23×D4124yes—
1241C24C23×D4124yes—
1242C24C23×D4124yes—
1243C24C23×D4164yes—
1244C24C23×D4124yes—
1245C24C23×D4124yes—
1246C24C23×D4164yes—
1247C24C23×D414yes—
1248C24C22×#41124yes—
1249C24C22×#4114yes—
1250C24C2×H(5,𝔽2)148yes—
1251C24C2×H(5,𝔽2)18yes—
1252C24C2×2−1+4124yes—
1253C24C2×2−1+414yes—
1254C24#58518yes—
1255C24C2614yes—
1256C24C2614yes—
1257C24C2614yes—
1258C24C2614yes—
1259C24C2614yes—
1260C24C2614yes—
1261C24C2613yes—
1262#41—41024no—
1263C2×Q8—232no—
1264C2×Q8—432no—
1265C2×Q8—4192no—
1266C2×D4—264no—
1267C2×D4—264no—
1268C2×D4—2384no—
1269C2×D4—2384no—
1270C2×D4—232no—
1271C2×D4—232no—
1272C2×D4—232no—
1273C2×D4—232no—
1274C2×D4—264no—
1275C2×D4—232no—
1276C2×D4—232no—
1277C2×D4—232no—
1278C2×D4—4192no—
1279C2×D4—4192no—
1280C2×D4—432no—
1281C2×D4—432no—
1282C2×D4—432no—
1283C2×D4—432no—
1284C2×D4—432no—
1285C2×D4—41024no—
1286C2×D4—4192no—
1287C2×D4—4192no—
1288C2×D4—4192no—
1289C2×D4—896no—
1290C2×D4—896no—
1291C2×D4C23×D4164yes—
1292C2×D4C23×D4164yes—
1293C2×D4C23×D4164yes—
1294C2×D4C23×D4164yes—
1295C22×C4—224no—
1296C22×C4—224no—
1297C22×C4—224no—
1298C22×C4—224no—
1299C22×C4—232no—
1300C22×C4—232no—
1301C22×C4—264no—
1302C22×C4—212no—
1303C22×C4—212no—
1304C22×C4—232no—
1305C22×C4—224no—
1306C22×C4—232no—
1307C22×C4—224no—
1308C22×C4—212no—
1309C22×C4—212no—
1310C22×C4—212no—
1311C22×C4—212no—
1312C22×C4—212no—
1313C22×C4—232no—
1314C22×C4—232no—
1315C22×C4—224no—
1316C22×C4—224no—
1317C22×C4—232no—
1318C22×C4—232no—
1319C22×C4—264no—
1320C22×C4—264no—
1321C22×C4—224no—
1322C22×C4—224no—
1323C22×C4—224no—
1324C22×C4—212no—
1325C22×C4—232no—
1326C22×C4—224no—
1327C22×C4—224no—
1328C22×C4—224no—
1329C22×C4—224no—
1330C22×C4—224no—
1331C22×C4—264no—
1332C22×C4—264no—
1333C22×C4—224no—
1334C22×C4—224no—
1335C22×C4—224no—
1336C22×C4—224no—
1337C22×C4—264no—
1338C22×C4—224no—
1339C22×C4—264no—
1340C22×C4—224no—
1341C22×C4—232no—
1342C22×C4—224no—
1343C22×C4—212no—
1344C22×C4—224no—
1345C22×C4—224no—
1346C22×C4—224no—
1347C22×C4—224no—
1348C22×C4—224no—
1349C22×C4—224no—
1350C22×C4—224no—
1351C22×C4—224no—
1352C22×C4—232no—
1353C22×C4—232no—
1354C22×C4—232no—
1355C22×C4—264no—
1356C22×C4—264no—
1357C22×C4—432no—
1358C22×C4—432no—
1359C22×C4—432no—
1360C22×C4—432no—
1361C22×C4—4192no—
1362C22×C4—432no—
1363C22×C4—432no—
1364C22×C4—432no—
1365C22×C4—432no—
1366C22×C4—432no—
1367C22×C4—432no—
1368C22×C4—432no—
1369C22×C4—432no—
1370C22×C4—432no—
1371C22×C4—4384no—
1372C22×C4—4192no—
1373C22×C4—4192no—
1374C22×C4—4192no—
1375C22×C4—4192no—
1376C22×C4—41024no—
1377C22×C4—4384no—
1378C22×C4—4192no—
1379C22×C4—4384no—
1380C22×C4—416no—
1381C22×C4—432no—
1382C22×C4—432no—
1383C22×C4—416no—
1384C22×C4—416no—
1385C22×C4—4192no—
1386C22×C4—4192no—
1387C22×C4—432no—
1388C22×C4—416no—
1389C22×C4—432no—
1390C22×C4—416no—
1391C22×C4—416no—
1392C22×C4—416no—
1393C22×C4—432no—
1394C22×C4—432no—
1395C22×C4—432no—
1396C22×C4—8192no—
1397C22×C4—896no—
1398C22×C4—896no—
1399C22×C4C23×D4124yes—
1400C22×C4C23×D4124yes—
1401C22×C4C23×D4164yes—
1402C22×C4C22×#41148yes—
1403C22×C4C2618yes—
1404C22×C4C2614yes—
1405C22×C4C2614yes—
1406C22×C4C2618yes—
1407C22×C4C2618yes—
1408C22×C4C2618yes—
1409C22×C4C2614yes—
1410C22×C4C2614yes—
1411C22×C4C2618yes—
1412C22×C4C2614yes—
1413C22×C4C2618yes—
1414C22×C4C2618yes—
1415C22×C4C2614yes—
1416C22×C4C2614yes—
1417C22×C4C2614yes—
1418C22×C4C2614yes—
1419C22×C4C2618yes—
1420C4⋊C4—264no—
1421C4⋊C4—264no—
1422C4⋊C4—264no—
1423C4⋊C4—264no—
1424C4⋊C4—232no—
1425C4⋊C4—232no—
1426C4⋊C4—232no—
1427C4⋊C4—232no—
1428C4⋊C4—264no—
1429C4⋊C4—432no—
1430C4⋊C4—432no—
1431C4⋊C4—432no—
1432C4⋊C4—432no—
1433C4⋊C4—432no—
1434C4⋊C4—432no—
1435C4⋊C4—432no—
1436C4⋊C4—432no—
1437C4⋊C4—432no—
1438C4⋊C4—432no—
1439C22⋊C4—232no—
1440C22⋊C4—232no—
1441C22⋊C4—232no—
1442C22⋊C4—232no—
1443C22⋊C4—232no—
1444C22⋊C4—232no—
1445C22⋊C4—232no—
1446C22⋊C4—264no—
1447C22⋊C4—264no—
1448C22⋊C4—264no—
1449C22⋊C4—264no—
1450C22⋊C4—264no—
1451C22⋊C4—264no—
1452C22⋊C4—232no—
1453C22⋊C4—232no—
1454C22⋊C4—232no—
1455C22⋊C4—232no—
1456C22⋊C4—232no—
1457C22⋊C4—232no—
1458C22⋊C4—264no—
1459C22⋊C4—232no—
1460C22⋊C4—232no—
1461C22⋊C4—264no—
1462C22⋊C4—264no—
1463C22⋊C4—264no—
1464C22⋊C4—432no—
1465C22⋊C4—432no—
1466C22⋊C4—432no—
1467C22⋊C4—432no—
1468C22⋊C4—432no—
1469C22⋊C4—432no—
1470C22⋊C4C22×#41164yescomplemented
1471C42—232no—
1472C42—432no—
1473C23—296no—
1474C23—296no—
1475C23—296no—
1476C23—296no—
1477C23—248no—
1478C23—248no—
1479C23—24no—
1480C23—28no—
1481C23—24no—
1482C23—28no—
1483C23—28no—
1484C23—2256no—
1485C23—2256no—
1486C23—248no—
1487C23—248no—
1488C23—248no—
1489C23—248no—
1490C23—248no—
1491C23—24no—
1492C23—24no—
1493C23—24no—
1494C23—28no—
1495C23—28no—
1496C23—28no—
1497C23—24no—
1498C23—24no—
1499C23—24no—
1500C23—28no—
1501C23—28no—
1502C23—28no—
1503C23—2128no—
1504C23—248no—
1505C23—248no—
1506C23—248no—
1507C23—2128no—
1508C23—248no—
1509C23—248no—
1510C23—248no—
1511C23—2128no—
1512C23—24no—
1513C23—24no—
1514C23—28no—
1515C23—24no—
1516C23—28no—
1517C23—464no—
1518C23—464no—
1519C23—464no—
1520C23—4128no—
1521C23—4128no—
1522C23—41536no—
1523C23—448no—
1524C23—448no—
1525C23—448no—
1526C23—448no—
1527C23—448no—
1528C23—448no—
1529C23—4128no—
1530C23—4128no—
1531C23—4128no—
1532C23—448no—
1533C23—448no—
1534C23—424no—
1535C23—424no—
1536C23—424no—
1537C23—864no—
1538C23—864no—
1539C23—8768no—
1540C23—864no—
1541C23C2×#534196yes—
1542C23C2×#534116yes—
1543C23C2×#547196yes—
1544C23C2×#547116yes—
1545C23#3485116yes—
1546C23#3513132yes—
1547C23#3535132yes—
1548C23C24×D418yes—
1549C23C24×D418yes—
1550C23C24×D418yes—
1551C23C24×D418yes—
1552C23C24×D418yes—
1553C23C24×D416yes—
1554C23C23×#4118yes—
1555C23C23×#4116yes—
1556C23C22×H(5,𝔽2)116yes—
1557C23C22×H(5,𝔽2)112yes—
1558C23C22×2−1+418yes—
1559C23C22×2−1+416yes—
1560C23C2×#585112yes—
1561C23C2711yescharacteristic
1562Q8—464no—
1563D4—2128no—
1564D4—2128no—
1565D4—464no—
1566D4—464no—
1567D4—464no—
1568D4—464no—
1569D4—464no—
1570D4—832no—
1571D4—832no—
1572C2×C4—296no—
1573C2×C4—28no—
1574C2×C4—28no—
1575C2×C4—28no—
1576C2×C4—28no—
1577C2×C4—248no—
1578C2×C4—248no—
1579C2×C4—24no—
1580C2×C4—24no—
1581C2×C4—28no—
1582C2×C4—28no—
1583C2×C4—24no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—28no—
1589C2×C4—28no—
1590C2×C4—28no—
1591C2×C4—28no—
1592C2×C4—28no—
1593C2×C4—24no—
1594C2×C4—28no—
1595C2×C4—28no—
1596C2×C4—28no—
1597C2×C4—28no—
1598C2×C4—28no—
1599C2×C4—28no—
1600C2×C4—28no—
1601C2×C4—28no—
1602C2×C4—28no—
1603C2×C4—28no—
1604C2×C4—28no—
1605C2×C4—28no—
1606C2×C4—24no—
1607C2×C4—28no—
1608C2×C4—28no—
1609C2×C4—28no—
1610C2×C4—28no—
1611C2×C4—28no—
1612C2×C4—28no—
1613C2×C4—28no—
1614C2×C4—28no—
1615C2×C4—464no—
1616C2×C4—4128no—
1617C2×C4—464no—
1618C2×C4—464no—
1619C2×C4—464no—
1620C2×C4—464no—
1621C2×C4—4128no—
1622C2×C4—464no—
1623C2×C4—448no—
1624C2×C4—448no—
1625C2×C4—448no—
1626C2×C4—448no—
1627C2×C4—424no—
1628C2×C4—424no—
1629C2×C4—424no—
1630C2×C4—4128no—
1631C2×C4—424no—
1632C2×C4—448no—
1633C2×C4—448no—
1634C2×C4—424no—
1635C2×C4—424no—
1636C2×C4—464no—
1637C2×C4—464no—
1638C2×C4—448no—
1639C2×C4—424no—
1640C2×C4—864no—
1641C2×C4—832no—
1642C2×C4—832no—
1643C2×C4C24×D418yes—
1644C2×C4C24×D418yes—
1645C2×C4C23×#41116yes—
1646C22—216no—
1647C22—216no—
1648C22—28no—
1649C22—28no—
1650C22—216no—
1651C22—216no—
1652C22—28no—
1653C22—28no—
1654C22—2192no—
1655C22—2192no—
1656C22—28no—
1657C22—28no—
1658C22—28no—
1659C22—28no—
1660C22—28no—
1661C22—28no—
1662C22—28no—
1663C22—28no—
1664C22—28no—
1665C22—4256no—
1666C22—48no—
1667C22—48no—
1668C22—48no—
1669C22—48no—
1670C22—48no—
1671C22—48no—
1672C22—496no—
1673C22—496no—
1674C22—496no—
1675C22—48no—
1676C22—44no—
1677C22—44no—
1678C22—48no—
1679C22—44no—
1680C22—8128no—
1681C22—848no—
1682C22#38038164yesdirect product factor
1683C22C22×#534116yes—
1684C22C22×#534112yes—
1685C22C22×#547116yes—
1686C22C22×#547112yes—
1687C22C2×#3535124yes—
1688C22C2×#3513124yes—
1689C22C2×#3485112yes—
1690C22C25×D411yescharacteristic
1691C22C24×#4111yescharacteristic
1692C22C23×H(5,𝔽2)12yes—
1693C22C23×2−1+411yescharacteristic
1694C22C22×#58512yes—
1695C4—28no—
1696C4—28no—
1697C4—216no—
1698C4—48no—
1699C4—44no—
1700C4—48no—
1701C4—48no—
1702C4—44no—
1703C4—44no—
1704C4—48no—
1705C4—44no—
1706C4—48no—
1707C4—48no—
1708C4—48no—
1709C4—44no—
1710C4—44no—
1711C4—44no—
1712C2—216no—
1713C2—216no—
1714C2—48no—
1715C2—48no—
1716C2—48no—
1717C2—84no—
1718C2C2×#38038124yesdirect product factor
1719C2C23×#53411yescharacteristic
1720C2C23×#54711yescharacteristic
1721C2C22×#351312yes—
1722C2C22×#348511yescharacteristic
1723C2C22×#353512yes—
subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC23C27
prime radicalC23×#546C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C24×#123C2semidirect
3. C2×#38038C2direct (N × H)
4. C22×#2724C2semidirect
5. C22×#2717C2semidirect
6. C22×#2708C2semidirect
7. C22×#2701C2semidirect
8. C22×#2849C2semidirect
9. C22×#2583C2semidirect
10. C22×#2579C2semidirect
11. C22×#2486C2semidirect
12. C22×#2483C2semidirect
13. C22×#2483C2semidirect
14. C22×#2406C2semidirect
15. C22×#2425C2semidirect
16. C22×#2419C2semidirect
17. C22×#2412C2semidirect
18. C22×#2412C2semidirect
19. C22×#2627C2semidirect
20. C22×#2622C2semidirect
21. C22×D4×C22⋊C4C2semidirect
22. C22×#2322C2semidirect
23. C22×#2315C2semidirect
24. C23×#385C2semidirect
39. C23×#123C22semidirect
40. C23×#123C22semidirect
52. C24×C4⋊C4C22semidirect
60. C2×#2724C22semidirect
61. C2×#2717C22semidirect
62. C2×#2708C22semidirect
63. C2×#2701C22semidirect
64. #38038C22direct (N × H)
65. C2×#2849C22semidirect
66. C2×#2583C22semidirect
67. C2×#2579C22semidirect
68. C2×#2486C22semidirect
69. C2×#2483C22semidirect
70. C2×#2483C22semidirect
71. C2×#2406C22semidirect
72. C2×#2425C22semidirect
73. C2×#2419C22semidirect
74. C2×#2412C22semidirect
75. C2×#2412C22semidirect
76. C2×#2627C22semidirect
77. C2×#2622C22semidirect
78. C22×#400C22semidirect
79. C22×#398C22semidirect
80. C22×#398C22semidirect
81. C22×#398C22semidirect
82. C22×#398C22semidirect
83. C22×#397C22semidirect
84. C22×#397C22semidirect
85. C22×#397C22semidirect
86. C22×#397C22semidirect
87. C22×#397C22semidirect
88. C22×#397C22semidirect
89. C22×#397C22semidirect
90. C22×#397C22semidirect
91. C22×#396C22semidirect
92. C22×#395C22semidirect
93. C22×#395C22semidirect
94. C22×#394C22semidirect
95. C22×#394C22semidirect
96. C22×#394C22semidirect
97. C22×#394C22semidirect
98. C2×D4×C22⋊C4C22semidirect
99. C2×#2322C22semidirect
100. C2×#2315C22semidirect
102. C22×#389C22semidirect
103. C22×#389C22semidirect
104. C22×#389C22semidirect
105. C22×#388C22semidirect
106. C22×#387C22semidirect
107. C22×#387C22semidirect
113. C22×#386C22semidirect
114. C22×#386C22semidirect
115. C22×#386C22semidirect
125. C22×#385C22semidirect
126. C22×#385C22semidirect
127. C22×#385C22semidirect
128. C22×#385C22semidirect
129. C22×#385C22semidirect
130. C22×#385C22semidirect
131. C22×#385C22semidirect
132. C22×#385C22semidirect
133. C22×#385C22semidirect
134. C22×#385C22semidirect
138. C22×#381C22semidirect
139. C22×#381C22semidirect
140. C22×#381C22semidirect
142. C22×#380C22semidirect
143. C22×#380C22semidirect
144. C22×#380C22semidirect
145. C22×#380C22semidirect
149. C23×#95C22semidirect
205. C22×#123C23semidirect
206. C22×#123C23semidirect
249. C23×C4⋊C4C23semidirect
298. #2849C23semidirect
299. #2724C23semidirect
300. #2717C23semidirect
301. #2708C23semidirect
302. #2701C23semidirect
303. #2627C23semidirect
304. #2622C23semidirect
305. #2583C23semidirect
306. #2579C23semidirect
307. #2486C23semidirect
308. #2483C23semidirect
309. #2483C23semidirect
310. #2425C23semidirect
311. #2419C23semidirect
312. #2412C23semidirect
313. #2412C23semidirect
314. #2406C23semidirect
315. C2×#400C23semidirect
316. C2×#398C23semidirect
317. C2×#398C23semidirect
318. C2×#398C23semidirect
319. C2×#398C23semidirect
320. C2×#397C23semidirect
321. C2×#397C23semidirect
322. C2×#397C23semidirect
323. C2×#397C23semidirect
324. C2×#397C23semidirect
325. C2×#397C23semidirect
326. C2×#397C23semidirect
327. C2×#397C23semidirect
328. C2×#396C23semidirect
329. C2×#395C23semidirect
330. C2×#395C23semidirect
331. C2×#394C23semidirect
332. C2×#394C23semidirect
333. C2×#394C23semidirect
334. C2×#394C23semidirect
335. D4×C22⋊C4C23semidirect
336. #2322C23semidirect
337. #2315C23semidirect
339. C2×#389C23semidirect
340. C2×#389C23semidirect
341. C2×#389C23semidirect
342. C2×#388C23semidirect
343. C2×#387C23semidirect
344. C2×#387C23semidirect
350. C2×#386C23semidirect
351. C2×#386C23semidirect
352. C2×#386C23semidirect
362. C2×#385C23semidirect
363. C2×#385C23semidirect
364. C2×#385C23semidirect
365. C2×#385C23semidirect
366. C2×#385C23semidirect
367. C2×#385C23semidirect
368. C2×#385C23semidirect
369. C2×#385C23semidirect
370. C2×#385C23semidirect
371. C2×#385C23semidirect
375. C2×#381C23semidirect
376. C2×#381C23semidirect
377. C2×#381C23semidirect
379. C2×#380C23semidirect
380. C2×#380C23semidirect
381. C2×#380C23semidirect
382. C2×#380C23semidirect
406. C22×#95C23semidirect
551. C2×#123C24semidirect
613. C22×C4⋊C4C24semidirect
652. C22×C22⋊C4#41semidirect
696. #400C24semidirect
697. #398C24semidirect
698. #398C24semidirect
699. #398C24semidirect
700. #398C24semidirect
701. #397C24semidirect
702. #397C24semidirect
703. #397C24semidirect
704. #397C24semidirect
705. #397C24semidirect
706. #397C24semidirect
707. #397C24semidirect
708. #397C24semidirect
709. #396C24semidirect
710. #395C24semidirect
711. #395C24semidirect
712. #394C24semidirect
713. #394C24semidirect
714. #394C24semidirect
715. #394C24semidirect
717. #389C24semidirect
718. #389C24semidirect
719. #389C24semidirect
720. #388C24semidirect
721. #387C24semidirect
722. #387C24semidirect
728. #386C24semidirect
729. #386C24semidirect
730. #386C24semidirect
740. #385C24semidirect
741. #385C24semidirect
742. #385C24semidirect
743. #385C24semidirect
744. #385C24semidirect
745. #385C24semidirect
746. #385C24semidirect
747. #385C24semidirect
748. #385C24semidirect
752. #381C24semidirect
753. #381C24semidirect
754. #381C24semidirect
756. #380C24semidirect
757. #380C24semidirect
758. #380C24semidirect
759. #380C24semidirect
783. C2×#95C24semidirect
1111. C2×C22⋊C4C2×#41semidirect
1470. C22⋊C4C22×#41semidirect
1682. C22#38038direct (N × H)
1718. C2C2×#38038direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5462
C24×#1232
C2×#380382
C22×#27242
C22×#27172
C22×#27082
C22×#27012
C22×#28492
C22×#25832
C22×#25792
C22×#24862
C22×#24832
C22×#24062
C22×#24252
C22×#24192
C22×#24122
C22×#26272
C22×#26222
C22×D4×C22⋊C42
C22×#23222
C22×#23152
C23×#3852