Finite Group Databasebeta

← C22×#35906 #72324719

Subgroups — C22×#35906 #72324719

Order 1024.

103081 conjugacy classes of subgroups.

The subgroup lattice has 1788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#553C211yesmaximal, characteristic, complemented
2C23×#546C211yesmaximal, characteristic, complemented
3C2×#35906C2196yesmaximal, direct product factor
4C22×#2610C211yesmaximal, characteristic, complemented
5C22×#2603C211yesmaximal, characteristic, complemented
6C22×#2583C211yesmaximal, characteristic, complemented
7C22×#2558C212yesmaximal, complemented
8C22×#2559C212yesmaximal, complemented
9C22×#2543C211yesmaximal, characteristic, complemented
10C22×#2430C211yesmaximal, characteristic, complemented
11C22×#2445C212yesmaximal, complemented
12C22×#2428C212yesmaximal, complemented
13C22×#2433C211yesmaximal, characteristic, complemented
14C22×#2424C212yesmaximal, complemented
15C22×#2424C212yesmaximal, complemented
16C22×#2662C211yesmaximal, characteristic, complemented
17C22×#2661C211yesmaximal, characteristic, complemented
18C22×#2639C211yesmaximal, characteristic, complemented
19C22×#2392C211yesmaximal, characteristic, complemented
20C22×#2388C211yesmaximal, characteristic, complemented
21C23×#394C211yesmaximal, characteristic, complemented
22C22×#2358C212yesmaximal, complemented
23C22×#2358C212yesmaximal, complemented
24C22×#2275C211yesmaximal, characteristic, complemented
25C24×#41C2211yescharacteristic
26C25×D4C2211yescharacteristic
27C22×#553—232no—
28C22×#553C22148yescomplemented
29C22×#546—232no—
30C22×#546C22148yescomplemented
31C23×#127C2212yes—
32C23×#126C2211yescharacteristic, complemented
33C23×#126C2211yescharacteristic, complemented
34C23×#125C2211yescharacteristic, complemented
35C23×#124C2211yescharacteristic
36C23×#123C2212yes—
37C23×#123C2211yescharacteristic, complemented
38C23×#123C2211yescharacteristic, complemented
39C23×C22⋊Q8C2211yescharacteristic
40C23×#121C2211yescharacteristic
41C23×#121C2211yescharacteristic
42C23×#121C2211yescharacteristic
43C23×#121C2212yes—
44C23×#121C2211yescharacteristic
45C23×#121C2211yescharacteristic, complemented
46C23×#121C2212yescomplemented
47C23×#121C2212yescomplemented
48C23×#120C2212yes—
49C23×#120C2212yes—
50C23×#120C2212yes—
51C23×C4×D4C2212yes—
52C23×C4×D4C2211yescharacteristic
53C23×C4×D4C2211yescharacteristic
54C23×C4×D4C2211yescharacteristic
55C23×C4×D4C2211yescharacteristic
56C23×C4×D4C2211yescharacteristic, complemented
57C23×C4×D4C2212yescomplemented
58C23×C4×D4C2212yescomplemented
59C23×#117C2211yescharacteristic, complemented
60C24×C4⋊C4C2211yescharacteristic
61C24×C22⋊C4C2212yes—
62C24×C22⋊C4C2212yes—
63C24×C22⋊C4C2212yes—
64#35906C2211024yesdirect product factor
65C2×#2610C22148yescomplemented
66C2×#2603C22148yescomplemented
67C2×#2583C22148yescomplemented
68C2×#2558C22196yescomplemented
69C2×#2559C22196yescomplemented
70C2×#2543C22148yescomplemented
71C2×#2430C22148yescomplemented
72C2×#2445C22196yescomplemented
73C2×#2428C22196yescomplemented
74C2×#2433C22148yescomplemented
75C2×#2424C22196yescomplemented
76C2×#2424C22196yescomplemented
77C2×#2662C22148yescomplemented
78C2×#2661C22148yescomplemented
79C2×#2639C22148yescomplemented
80C22×#400C2212yescomplemented
81C2×#2392C22148yescomplemented
82C22×#398C2211yescharacteristic, complemented
83C22×#398C2211yescharacteristic, complemented
84C22×#397C2211yescharacteristic, complemented
85C22×#397C2211yescharacteristic, complemented
86C22×#396C2212yescomplemented
87C22×#396C2212yescomplemented
88C2×#2388C22148yescomplemented
89C22×#395C2211yescharacteristic, complemented
90C22×#395C2211yescharacteristic, complemented
91C22×#394C2211yescharacteristic
92C22×#394C2212yes—
93C22×#394C2212yes—
94C22×#394C2211yescharacteristic
95C22×#394C2211yescharacteristic
96C22×#394C2211yescharacteristic
97C22×#394C22148yescomplemented
98C22×#394C2212yescomplemented
99C22×#394C2212yescomplemented
100C22×#394C2212yescomplemented
101C22×#394C2212yescomplemented
102C22×#394C2212yescomplemented
103C22×#393C2211yescharacteristic, complemented
104C22×#393C2211yescharacteristic, complemented
105C22×#392C2211yescharacteristic
106C22×#392C2211yescharacteristic
107C22×#392C2211yescharacteristic
108C22×#392C2211yescharacteristic
109C22×#392C2212yescomplemented
110C22×#392C2212yescomplemented
111C2×#2358C22196yescomplemented
112C2×#2358C22196yescomplemented
113C22×#390C2212yes—
114C22×#390C2212yescomplemented
115C22×#390C2212yescomplemented
116C22×#390C2212yescomplemented
117C22×#390C2212yescomplemented
118C22×#389C2212yescomplemented
119C22×#389C2212yescomplemented
120C22×#388C2212yescomplemented
121C22×#388C2212yescomplemented
122C22×#388C2212yescomplemented
123C22×#388C2212yescomplemented
124C22×#388C2212yescomplemented
125C22×#388C2212yescomplemented
126C22×#386C2212yes—
127C22×#386C2212yes—
128C22×#386C2212yescomplemented
129C22×#386C2212yescomplemented
130C22×#386C2212yescomplemented
131C22×#386C2212yescomplemented
132C22×#386C2212yescomplemented
133C22×#386C2212yescomplemented
134C22×#385C2212yes—
135C22×#385C2212yes—
136C22×#385C2212yescomplemented
137C22×#385C2212yescomplemented
138C2×#2275C22148yescomplemented
139C22×C4×C4⋊C4C2212yescomplemented
140C22×C4×C4⋊C4C2211yescharacteristic, complemented
141C22×C4×C22⋊C4C2211yescharacteristic
142C22×C4×C22⋊C4C2212yes—
143C22×C4×C22⋊C4C2212yescomplemented
144C22×C4×C22⋊C4C2212yescomplemented
145C22×C4×C22⋊C4C2212yescomplemented
146C22×C4×C22⋊C4C2211yescharacteristic, complemented
147C22×#376C2211yescharacteristic, complemented
148C23×#95C2211yescharacteristic
149C23×#95C2211yescharacteristic, complemented
150C27C2312yes—
151C23×#41—216no—
152C23×#41—416no—
153C23×#41C23124yes—
154C24×Q8C2311yescharacteristic
155C24×D4—216no—
156C24×D4—416no—
157C24×D4C2311yescharacteristic
158C24×D4C2311yescharacteristic
159C24×D4C2311yescharacteristic
160C24×D4C2312yes—
161C24×D4C2312yes—
162C24×D4C2312yes—
163C24×D4C2312yes—
164C24×D4C2311yescharacteristic
165C24×D4C2311yescharacteristic
166C24×D4C23124yes—
167C24×D4C2311yescharacteristic
168C24×D4C2312yes—
169C24×D4C2312yes—
170C24×D4C2312yes—
171C24×D4C2311yescharacteristic
172C24×D4C2311yescharacteristic
173C25×C4C2312yes—
174C25×C4C2311yescharacteristic
175C25×C4C2311yescharacteristic
176C25×C4C2311yescharacteristic
177C25×C4C2312yes—
178C25×C4C2312yes—
179C25×C4C2311yescharacteristic
180C25×C4C2312yes—
181C25×C4C2311yescharacteristic
182C25×C4C2311yescharacteristic
183C2×#553—2768no—
184C2×#553C231256yescomplemented
185C2×#546—2768no—
186C2×#546C231256yescomplemented
187C22×#127—416no—
188C22×#127C23148yes—
189C22×#126—216no—
190C22×#126—216no—
191C22×#126C23124yescomplemented
192C22×#126C23124yescomplemented
193C22×#125—216no—
194C22×#125C23124yescomplemented
195C22×#124—216no—
196C22×#124C23124yes—
197C22×#123—216no—
198C22×#123—232no—
199C22×#123—216no—
200C22×#123C23148yes—
201C22×#123C23124yescomplemented
202C22×#123C23124yescomplemented
203C22×C22⋊Q8—216no—
204C22×C22⋊Q8C23124yes—
205C22×#121—216no—
206C22×#121—216no—
207C22×#121—216no—
208C22×#121—216no—
209C22×#121—232no—
210C22×#121—216no—
211C22×#121—416no—
212C22×#121—416no—
213C22×#121C23124yes—
214C22×#121C23124yes—
215C22×#121C23148yes—
216C22×#121C23124yes—
217C22×#121C23124yes—
218C22×#121C23124yescomplemented
219C22×#121C23148yescomplemented
220C22×#121C23148yescomplemented
221C22×#120—232no—
222C22×#120—232no—
223C22×#120—232no—
224C22×#120C23148yes—
225C22×#120C23148yes—
226C22×#120C23148yes—
227C22×C4×D4—216no—
228C22×C4×D4—216no—
229C22×C4×D4—216no—
230C22×C4×D4—216no—
231C22×C4×D4—232no—
232C22×C4×D4—416no—
233C22×C4×D4—416no—
234C22×C4×D4D4132yescomplemented
235C22×C4×D4C23124yes—
236C22×C4×D4C23124yes—
237C22×C4×D4C23124yes—
238C22×C4×D4C23148yes—
239C22×C4×D4C23124yes—
240C22×C4×D4C23124yescomplemented
241C22×C4×D4C23148yescomplemented
242C22×C4×D4C23148yescomplemented
243C22×#117—216no—
244C22×#117C23124yescomplemented
245C23×C4⋊C4—216no—
246C23×C4⋊C4C23124yes—
247C23×C4⋊C4C2311yescharacteristic
248C23×C4⋊C4C2311yescharacteristic
249C23×C4⋊C4C2311yescharacteristic
250C23×C4⋊C4C2311yescharacteristic
251C23×C4⋊C4C2311yescharacteristic
252C23×C4⋊C4C2311yescharacteristic
253C23×C4⋊C4C2311yescharacteristic
254C23×C4⋊C4C2312yes—
255C23×C4⋊C4C2311yescharacteristic
256C23×C4⋊C4C2312yes—
257C23×C4⋊C4C2312yes—
258C23×C4⋊C4C2311yescharacteristic
259C23×C4⋊C4C2311yescharacteristic
260C23×C4⋊C4C2312yes—
261C23×C4⋊C4C2312yes—
262C23×C4⋊C4C2312yes—
263C23×C4⋊C4C2311yescharacteristic
264C23×C22⋊C4—232no—
265C23×C22⋊C4—416no—
266C23×C22⋊C4—416no—
267C23×C22⋊C4C23148yes—
268C23×C22⋊C4C2312yes—
269C23×C22⋊C4C2312yes—
270C23×C22⋊C4C2312yes—
271C23×C22⋊C4C2312yes—
272C23×C22⋊C4C2312yes—
273C23×C22⋊C4C2312yes—
274C23×C22⋊C4C2312yes—
275C23×C22⋊C4C2311yescharacteristic
276C23×C22⋊C4C2311yescharacteristic
277C23×C22⋊C4C2312yes—
278C23×C22⋊C4C2311yescharacteristic
279C23×C22⋊C4C2311yescharacteristic
280C23×C22⋊C4C2312yes—
281C23×C22⋊C4C2311yescharacteristic
282C23×C22⋊C4C2311yescharacteristic
283C23×C22⋊C4C2312yes—
284C23×C22⋊C4C2312yes—
285C23×C22⋊C4C2312yes—
286C23×C22⋊C4C2312yes—
287C23×C22⋊C4C2312yes—
288C23×C22⋊C4C2311yescharacteristic
289C23×C22⋊C4C2311yescharacteristic
290C23×C22⋊C4C23148yes—
291C23×C22⋊C4C23148yes—
292C23×C22⋊C4C2312yes—
293C23×C22⋊C4C2312yes—
294C23×C22⋊C4C2312yes—
295C23×C22⋊C4C2312yes—
296C23×C22⋊C4C2312yes—
297C23×C22⋊C4C2312yes—
298C23×C22⋊C4C2312yes—
299C23×C22⋊C4C2312yes—
300C23×C22⋊C4C2311yescharacteristic
301C23×C22⋊C4C2311yescharacteristic
302C23×C22⋊C4C2312yes—
303C23×C42C2311yescharacteristic
304C23×C42C2311yescharacteristic
305C23×C42C2312yes—
306C23×C42C2312yes—
307C23×C42C2312yes—
308C23×C42C2312yes—
309C23×C42C2311yescharacteristic
310#2662C231256yescomplemented
311#2661C231256yescomplemented
312#2639C231256yescomplemented
313#2610C231256yescomplemented
314#2603C231256yescomplemented
315#2583C231256yescomplemented
316#2559C231512yescomplemented
317#2558C231512yescomplemented
318#2543C231256yescomplemented
319#2445C231512yescomplemented
320#2433C231256yescomplemented
321#2430C231256yescomplemented
322#2428C231512yescomplemented
323#2424C231512yescomplemented
324#2424C231512yescomplemented
325C2×#400C23148yescomplemented
326#2392C231256yescomplemented
327C2×#398C23124yescomplemented
328C2×#398C23124yescomplemented
329C2×#397C23124yescomplemented
330C2×#397C23124yescomplemented
331C2×#396C23148yescomplemented
332C2×#396C23148yescomplemented
333#2388C231256yescomplemented
334C2×#395C23124yescomplemented
335C2×#395C23124yescomplemented
336C2×#394C23124yes—
337C2×#394C23148yes—
338C2×#394C23148yes—
339C2×#394C23124yes—
340C2×#394C23124yes—
341C2×#394C23124yes—
342C2×#394C231256yescomplemented
343C2×#394C23148yescomplemented
344C2×#394C23148yescomplemented
345C2×#394C23148yescomplemented
346C2×#394C23148yescomplemented
347C2×#394C23148yescomplemented
348C2×#393C23124yescomplemented
349C2×#393C23124yescomplemented
350C2×#392C23124yes—
351C2×#392C23124yes—
352C2×#392C23124yes—
353C2×#392C23124yes—
354C2×#392C23148yescomplemented
355C2×#392C23148yescomplemented
356#2358C231512yescomplemented
357#2358C231512yescomplemented
358C2×#390C23148yes—
359C2×#390C23148yescomplemented
360C2×#390C23148yescomplemented
361C2×#390C23148yescomplemented
362C2×#390C23148yescomplemented
363C2×#389C23148yescomplemented
364C2×#389C23148yescomplemented
365C2×#388C23148yescomplemented
366C2×#388C23148yescomplemented
367C2×#388C23148yescomplemented
368C2×#388C23148yescomplemented
369C2×#388C23148yescomplemented
370C2×#388C23148yescomplemented
371C2×#386C23148yes—
372C2×#386C23148yes—
373C2×#386C23148yescomplemented
374C2×#386C23148yescomplemented
375C2×#386C23148yescomplemented
376C2×#386C23148yescomplemented
377C2×#386C23148yescomplemented
378C2×#386C23148yescomplemented
379C2×#385C23148yes—
380C2×#385C23148yes—
381C2×#385C23148yescomplemented
382C2×#385C23148yescomplemented
383#2275C231256yescomplemented
384C2×C4×C4⋊C4C23148yescomplemented
385C2×C4×C4⋊C4C23124yescomplemented
386C2×C4×C22⋊C4C23124yes—
387C2×C4×C22⋊C4C23148yes—
388C2×C4×C22⋊C4C23148yescomplemented
389C2×C4×C22⋊C4C23148yescomplemented
390C2×C4×C22⋊C4C23148yescomplemented
391C2×C4×C22⋊C4C23124yescomplemented
392C2×#376C23124yescomplemented
393C22×#95C23124yes—
394C22×#95C2311yescharacteristic
395C22×#95C2311yescharacteristic
396C22×#95C2312yes—
397C22×#95C2312yes—
398C22×#95C2311yescharacteristic
399C22×#95C2312yes—
400C22×#95C2311yescharacteristic
401C22×#95C2312yes—
402C22×#95C2312yes—
403C22×#95C2312yes—
404C22×#95C2312yes—
405C22×#95C2312yes—
406C22×#95C2312yes—
407C22×#95C2312yes—
408C22×#95C2312yes—
409C22×#95C23124yescomplemented
410C26—216no—
411C26—216no—
412C26—216no—
413C26—216no—
414C26—48no—
415C26—48no—
416C26—48no—
417C26C2411yescharacteristic
418C26C2411yescharacteristic
419C26C2412yes—
420C26C2411yescharacteristic
421C26C2412yes—
422C26C24124yes—
423C26C2411yescharacteristic
424C22×#41—2192no—
425C22×#41—4192no—
426C22×#41—4256no—
427C22×#41C24164yes—
428C23×Q8—28no—
429C23×Q8—48no—
430C23×Q8C24112yes—
431C23×D4—216no—
432C23×D4—216no—
433C23×D4—216no—
434C23×D4—28no—
435C23×D4—28no—
436C23×D4—28no—
437C23×D4—216no—
438C23×D4—216no—
439C23×D4—216no—
440C23×D4—216no—
441C23×D4—216no—
442C23×D4—216no—
443C23×D4—216no—
444C23×D4—28no—
445C23×D4—28no—
446C23×D4—216no—
447C23×D4—28no—
448C23×D4—2192no—
449C23×D4—28no—
450C23×D4—216no—
451C23×D4—216no—
452C23×D4—216no—
453C23×D4—216no—
454C23×D4—28no—
455C23×D4—48no—
456C23×D4—48no—
457C23×D4—48no—
458C23×D4—44no—
459C23×D4—48no—
460C23×D4—48no—
461C23×D4—48no—
462C23×D4—48no—
463C23×D4—48no—
464C23×D4—48no—
465C23×D4—48no—
466C23×D4—48no—
467C23×D4—48no—
468C23×D4—48no—
469C23×D4—4192no—
470C23×D4—4256no—
471C23×D4C2×D4116yes—
472C23×D4C24112yes—
473C23×D4C24112yes—
474C23×D4C24112yes—
475C23×D4C24124yes—
476C23×D4C24124yes—
477C23×D4C24124yes—
478C23×D4C24124yes—
479C23×D4C24112yes—
480C23×D4C24112yes—
481C23×D4C24112yes—
482C23×D4C24164yes—
483C23×D4C24124yes—
484C23×D4C24124yes—
485C23×D4C24112yes—
486C23×D4C24124yes—
487C23×D4C24112yes—
488C24×C4—28no—
489C24×C4—216no—
490C24×C4—28no—
491C24×C4—216no—
492C24×C4—216no—
493C24×C4—28no—
494C24×C4—28no—
495C24×C4—28no—
496C24×C4—216no—
497C24×C4—28no—
498C24×C4—216no—
499C24×C4—44no—
500C24×C4—44no—
501C24×C4—48no—
502C24×C4—48no—
503C24×C4—48no—
504C24×C4—48no—
505C24×C4—48no—
506C24×C4—48no—
507C24×C4—48no—
508C24×C4—48no—
509C24×C4—48no—
510C24×C4—48no—
511C24×C4—48no—
512C24×C4C2×D4116yes—
513C24×C4C2×D4116yes—
514C24×C4C2411yescharacteristic
515C24×C4C2412yes—
516C24×C4C2412yes—
517C24×C4C2411yescharacteristic
518C24×C4C2412yes—
519C24×C4C2412yes—
520C24×C4C2411yescharacteristic
521C24×C4C2411yescharacteristic
522C24×C4C2411yescharacteristic
523C24×C4C24124yes—
524C24×C4C24112yes—
525C24×C4C24112yes—
526C24×C4C2411yescharacteristic
527C24×C4C2411yescharacteristic
528C24×C4C2411yescharacteristic
529C24×C4C2411yescharacteristic
530C24×C4C2411yescharacteristic
531C24×C4C2412yes—
532C24×C4C2412yes—
533C24×C4C2411yescharacteristic
534C24×C4C24112yes—
535C24×C4C24124yes—
536C24×C4C24124yes—
537C24×C4C24112yes—
538C24×C4C24124yes—
539C24×C4C24112yes—
540C24×C4C24112yes—
541#553—22048no—
542#546—22048no—
543C2×#127—4192no—
544C2×#127C241128yes—
545C2×#126—2192no—
546C2×#126—2192no—
547C2×#126C24164yescomplemented
548C2×#126C24164yescomplemented
549C2×#125—2192no—
550C2×#125C24164yescomplemented
551C2×#124—2192no—
552C2×#124C24164yes—
553C2×#123—2192no—
554C2×#123—2384no—
555C2×#123—2192no—
556C2×#123C241128yes—
557C2×#123C24164yescomplemented
558C2×#123C24164yescomplemented
559C2×C22⋊Q8—2192no—
560C2×C22⋊Q8C24164yes—
561C2×#121—2192no—
562C2×#121—2192no—
563C2×#121—2192no—
564C2×#121—2192no—
565C2×#121—2384no—
566C2×#121—2192no—
567C2×#121—4192no—
568C2×#121—4192no—
569C2×#121C24164yes—
570C2×#121C24164yes—
571C2×#121C24164yes—
572C2×#121C24164yes—
573C2×#121C241128yes—
574C2×#121C24164yescomplemented
575C2×#121C241128yescomplemented
576C2×#121C241128yescomplemented
577C2×#120—2384no—
578C2×#120—2384no—
579C2×#120—2384no—
580C2×#120C241128yes—
581C2×#120C241128yes—
582C2×#120C241128yes—
583C2×C4×D4—2192no—
584C2×C4×D4—2192no—
585C2×C4×D4—2192no—
586C2×C4×D4—2384no—
587C2×C4×D4—2192no—
588C2×C4×D4—4192no—
589C2×C4×D4—4192no—
590C2×C4×D4C2×D41384yescomplemented
591C2×C4×D4C24164yes—
592C2×C4×D4C24164yes—
593C2×C4×D4C24164yes—
594C2×C4×D4C241128yes—
595C2×C4×D4C24164yes—
596C2×C4×D4C24164yescomplemented
597C2×C4×D4C241128yescomplemented
598C2×C4×D4C241128yescomplemented
599C2×#117—2192no—
600C2×#117C24164yescomplemented
601C22×C4⋊C4—28no—
602C22×C4⋊C4—28no—
603C22×C4⋊C4—28no—
604C22×C4⋊C4—28no—
605C22×C4⋊C4—2192no—
606C22×C4⋊C4—28no—
607C22×C4⋊C4—28no—
608C22×C4⋊C4—28no—
609C22×C4⋊C4—28no—
610C22×C4⋊C4—216no—
611C22×C4⋊C4—28no—
612C22×C4⋊C4—28no—
613C22×C4⋊C4—216no—
614C22×C4⋊C4—216no—
615C22×C4⋊C4—48no—
616C22×C4⋊C4—48no—
617C22×C4⋊C4—48no—
618C22×C4⋊C4C2×D4116yes—
619C22×C4⋊C4C24164yes—
620C22×C4⋊C4C24112yes—
621C22×C4⋊C4C24112yes—
622C22×C4⋊C4C24112yes—
623C22×C4⋊C4C24112yes—
624C22×C4⋊C4C24124yes—
625C22×C4⋊C4C24124yes—
626C22×C4⋊C4C24112yes—
627C22×C4⋊C4C24112yes—
628C22×C4⋊C4C24124yes—
629C22×C4⋊C4C24112yes—
630C22×C4⋊C4C24112yes—
631C22×C4⋊C4C24112yes—
632C22×C4⋊C4C24112yes—
633C22×C4⋊C4C24124yes—
634C22×C4⋊C4C24124yes—
635C22×C4⋊C4C24124yes—
636C22×C4⋊C4C24112yes—
637C22×C22⋊C4—216no—
638C22×C22⋊C4—28no—
639C22×C22⋊C4—28no—
640C22×C22⋊C4—216no—
641C22×C22⋊C4—216no—
642C22×C22⋊C4—216no—
643C22×C22⋊C4—216no—
644C22×C22⋊C4—28no—
645C22×C22⋊C4—28no—
646C22×C22⋊C4—216no—
647C22×C22⋊C4—28no—
648C22×C22⋊C4—28no—
649C22×C22⋊C4—28no—
650C22×C22⋊C4—216no—
651C22×C22⋊C4—28no—
652C22×C22⋊C4—216no—
653C22×C22⋊C4—216no—
654C22×C22⋊C4—216no—
655C22×C22⋊C4—216no—
656C22×C22⋊C4—216no—
657C22×C22⋊C4—216no—
658C22×C22⋊C4—216no—
659C22×C22⋊C4—2384no—
660C22×C22⋊C4—4192no—
661C22×C22⋊C4—4192no—
662C22×C22⋊C4—48no—
663C22×C22⋊C4—48no—
664C22×C22⋊C4—48no—
665C22×C22⋊C4—48no—
666C22×C22⋊C4—48no—
667C22×C22⋊C4—48no—
668C22×C22⋊C4—48no—
669C22×C22⋊C4—48no—
670C22×C22⋊C4C2×D4116yes—
671C22×C22⋊C4C2×D4116yes—
672C22×C22⋊C4#41132yescomplemented
673C22×C22⋊C4C241128yes—
674C22×C22⋊C4C24112yes—
675C22×C22⋊C4C24112yes—
676C22×C22⋊C4C24124yes—
677C22×C22⋊C4C24124yes—
678C22×C22⋊C4C24124yes—
679C22×C22⋊C4C24124yes—
680C22×C22⋊C4C24124yes—
681C22×C22⋊C4C24124yes—
682C22×C22⋊C4C24124yes—
683C22×C22⋊C4C24124yes—
684C22×C22⋊C4C24124yes—
685C22×C22⋊C4C24112yes—
686C22×C22⋊C4C24112yes—
687C22×C22⋊C4C24112yes—
688C22×C22⋊C4C24112yes—
689C22×C22⋊C4C24124yes—
690C22×C22⋊C4C24124yes—
691C22×C22⋊C4C24124yes—
692C22×C22⋊C4C24124yes—
693C22×C22⋊C4C24124yes—
694C22×C22⋊C4C24112yes—
695C22×C22⋊C4C24112yes—
696C22×C22⋊C4C241128yes—
697C22×C22⋊C4C241128yes—
698C22×C22⋊C4C24124yes—
699C22×C22⋊C4C24124yes—
700C22×C22⋊C4C24124yes—
701C22×C22⋊C4C24124yes—
702C22×C22⋊C4C24124yes—
703C22×C22⋊C4C24124yes—
704C22×C22⋊C4C24124yes—
705C22×C22⋊C4C24124yes—
706C22×C22⋊C4C24112yes—
707C22×C22⋊C4C24112yes—
708C22×C22⋊C4C24124yes—
709C22×C42—28no—
710C22×C42—28no—
711C22×C42—216no—
712C22×C42—48no—
713C22×C42—48no—
714C22×C42—48no—
715C22×C42C2×D4116yes—
716C22×C42C24112yes—
717C22×C42C24112yes—
718C22×C42C24124yes—
719C22×C42C24124yes—
720C22×C42C24124yes—
721C22×C42C24124yes—
722C22×C42C24112yes—
723#400C241128yescomplemented
724#398C24164yescomplemented
725#398C24164yescomplemented
726#397C24164yescomplemented
727#397C24164yescomplemented
728#396C241128yescomplemented
729#396C241128yescomplemented
730#395C24164yescomplemented
731#395C24164yescomplemented
732#394C24164yes—
733#394C24164yes—
734#394C24164yes—
735#394C24164yes—
736#394C241128yes—
737#394C241128yes—
738#394C241128yescomplemented
739#394C241128yescomplemented
740#394C241128yescomplemented
741#394C241128yescomplemented
742#394C241128yescomplemented
743#393C24164yescomplemented
744#393C24164yescomplemented
745#392C24164yes—
746#392C24164yes—
747#392C24164yes—
748#392C24164yes—
749#392C241128yescomplemented
750#392C241128yescomplemented
751#390C241128yes—
752#390C241128yescomplemented
753#390C241128yescomplemented
754#390C241128yescomplemented
755#390C241128yescomplemented
756#389C241128yescomplemented
757#389C241128yescomplemented
758#388C241128yescomplemented
759#388C241128yescomplemented
760#388C241128yescomplemented
761#388C241128yescomplemented
762#388C241128yescomplemented
763#388C241128yescomplemented
764#386C241128yes—
765#386C241128yes—
766#386C241128yescomplemented
767#386C241128yescomplemented
768#386C241128yescomplemented
769#386C241128yescomplemented
770#386C241128yescomplemented
771#386C241128yescomplemented
772#385C241128yes—
773#385C241128yes—
774#385C241128yescomplemented
775#385C241128yescomplemented
776C4×C4⋊C4C24164yescomplemented
777C4×C4⋊C4C241128yescomplemented
778C4×C22⋊C4C24164yes—
779C4×C22⋊C4C241128yes—
780C4×C22⋊C4C241128yescomplemented
781C4×C22⋊C4C241128yescomplemented
782C4×C22⋊C4C24164yescomplemented
783C4×C22⋊C4C241128yescomplemented
784#376C24164yescomplemented
785C2×#95C24164yes—
786C2×#95C24112yes—
787C2×#95C24112yes—
788C2×#95C24124yes—
789C2×#95C24124yes—
790C2×#95C24112yes—
791C2×#95C24112yes—
792C2×#95C24124yes—
793C2×#95C24124yes—
794C2×#95C24124yes—
795C2×#95C24124yes—
796C2×#95C24124yes—
797C2×#95C24124yes—
798C2×#95C24124yes—
799C2×#95C24124yes—
800C2×#95C24124yes—
801C2×#95C24164yescomplemented
802C25—24no—
803C25—28no—
804C25—24no—
805C25—28no—
806C25—28no—
807C25—28no—
808C25—28no—
809C25—28no—
810C25—28no—
811C25—24no—
812C25—28no—
813C25—28no—
814C25—24no—
815C25—24no—
816C25—24no—
817C25—28no—
818C25—28no—
819C25—28no—
820C25—28no—
821C25—28no—
822C25—28no—
823C25—24no—
824C25—24no—
825C25—296no—
826C25—28no—
827C25—28no—
828C25—28no—
829C25—28no—
830C25—24no—
831C25—24no—
832C25—28no—
833C25—296no—
834C25—296no—
835C25—296no—
836C25—448no—
837C25—448no—
838C25—448no—
839C25—4128no—
840C25—4128no—
841C25—4128no—
842C25—4128no—
843C25—864no—
844C25—864no—
845C25—864no—
846C25C22×D418yes—
847C25C22×D418yes—
848C25C2×#41116yes—
849C25H(5,𝔽2)116yes—
850C25C25112yes—
851C25C2516yes—
852C25C2516yes—
853C25C2516yes—
854C25C25112yes—
855C25C25132yes—
856C25C2516yes—
857C25C2511yescharacteristic
858C2×#41—2256no—
859C2×#41—4256no—
860C2×#41—41536no—
861C22×Q8—248no—
862C22×Q8—448no—
863C22×Q8—464no—
864C22×Q8C25116yes—
865C22×D4—2128no—
866C22×D4—2128no—
867C22×D4—296no—
868C22×D4—296no—
869C22×D4—248no—
870C22×D4—248no—
871C22×D4—248no—
872C22×D4—296no—
873C22×D4—296no—
874C22×D4—296no—
875C22×D4—296no—
876C22×D4—296no—
877C22×D4—296no—
878C22×D4—296no—
879C22×D4—296no—
880C22×D4—248no—
881C22×D4—248no—
882C22×D4—296no—
883C22×D4—248no—
884C22×D4—2256no—
885C22×D4—248no—
886C22×D4—296no—
887C22×D4—296no—
888C22×D4—296no—
889C22×D4—296no—
890C22×D4—248no—
891C22×D4—448no—
892C22×D4—448no—
893C22×D4—448no—
894C22×D4—448no—
895C22×D4—424no—
896C22×D4—448no—
897C22×D4—464no—
898C22×D4—4128no—
899C22×D4—4128no—
900C22×D4—4128no—
901C22×D4—464no—
902C22×D4—448no—
903C22×D4—448no—
904C22×D4—448no—
905C22×D4—448no—
906C22×D4—448no—
907C22×D4—448no—
908C22×D4—448no—
909C22×D4—448no—
910C22×D4—4256no—
911C22×D4—41536no—
912C22×D4—4128no—
913C22×D4—464no—
914C22×D4—464no—
915C22×D4—832no—
916C22×D4—864no—
917C22×D4—864no—
918C22×D4—832no—
919C22×D4—864no—
920C22×D4C22×D4196yes—
921C22×D4C25116yes—
922C22×D4C25116yes—
923C22×D4C25116yes—
924C22×D4C25132yes—
925C22×D4C25132yes—
926C22×D4C25116yes—
927C22×D4C25132yes—
928C22×D4C25132yes—
929C22×D4C25116yes—
930C22×D4C25132yes—
931C22×D4C25132yes—
932C22×D4C25132yes—
933C22×D4C25116yes—
934C22×D4C25116yes—
935C22×D4C25116yes—
936C23×C4—24no—
937C23×C4—28no—
938C23×C4—28no—
939C23×C4—28no—
940C23×C4—28no—
941C23×C4—28no—
942C23×C4—24no—
943C23×C4—28no—
944C23×C4—28no—
945C23×C4—28no—
946C23×C4—24no—
947C23×C4—24no—
948C23×C4—24no—
949C23×C4—28no—
950C23×C4—28no—
951C23×C4—24no—
952C23×C4—24no—
953C23×C4—24no—
954C23×C4—24no—
955C23×C4—248no—
956C23×C4—28no—
957C23×C4—28no—
958C23×C4—28no—
959C23×C4—28no—
960C23×C4—28no—
961C23×C4—28no—
962C23×C4—28no—
963C23×C4—28no—
964C23×C4—28no—
965C23×C4—28no—
966C23×C4—24no—
967C23×C4—28no—
968C23×C4—28no—
969C23×C4—28no—
970C23×C4—296no—
971C23×C4—24no—
972C23×C4—28no—
973C23×C4—248no—
974C23×C4—296no—
975C23×C4—296no—
976C23×C4—248no—
977C23×C4—248no—
978C23×C4—248no—
979C23×C4—296no—
980C23×C4—248no—
981C23×C4—296no—
982C23×C4—464no—
983C23×C4—464no—
984C23×C4—424no—
985C23×C4—424no—
986C23×C4—448no—
987C23×C4—448no—
988C23×C4—448no—
989C23×C4—464no—
990C23×C4—448no—
991C23×C4—448no—
992C23×C4—448no—
993C23×C4—448no—
994C23×C4—448no—
995C23×C4—448no—
996C23×C4—448no—
997C23×C4—448no—
998C23×C4—464no—
999C23×C4—4128no—
1000C23×C4—832no—
1001C23×C4—864no—
1002C23×C4—864no—
1003C23×C4—832no—
1004C23×C4—864no—
1005C23×C4C22×D418yes—
1006C23×C4C22×D418yes—
1007C23×C4C22×D418yes—
1008C23×C4C22×D418yes—
1009C23×C4C22×D418yes—
1010C23×C4C22×D4196yes—
1011C23×C4C22×D4196yes—
1012C23×C4C2×#41116yes—
1013C23×C4C2×#41116yes—
1014C23×C4H(5,𝔽2)18yes—
1015C23×C4C2516yes—
1016C23×C4C25112yes—
1017C23×C4C2516yes—
1018C23×C4C2516yes—
1019C23×C4C2516yes—
1020C23×C4C25112yes—
1021C23×C4C2516yes—
1022C23×C4C25112yes—
1023C23×C4C25112yes—
1024C23×C4C25116yes—
1025C23×C4C25132yes—
1026C23×C4C25116yes—
1027C23×C4C2516yes—
1028C23×C4C2516yes—
1029C23×C4C2516yes—
1030C23×C4C2516yes—
1031C23×C4C2516yes—
1032C23×C4C25112yes—
1033C23×C4C25112yes—
1034C23×C4C2516yes—
1035C23×C4C25116yes—
1036C23×C4C25132yes—
1037C23×C4C25132yes—
1038C23×C4C25116yes—
1039C23×C4C25132yes—
1040C23×C4C25116yes—
1041C23×C4C25116yes—
1042#127—4256no—
1043#126—2256no—
1044#126—2256no—
1045#125—2256no—
1046#124—2256no—
1047#123—2256no—
1048#123—2512no—
1049#123—2256no—
1050C22⋊Q8—2256no—
1051#121—2256no—
1052#121—2256no—
1053#121—2256no—
1054#121—2256no—
1055#121—2512no—
1056#121—2256no—
1057#121—4256no—
1058#121—4256no—
1059#120—2512no—
1060#120—2512no—
1061#120—2512no—
1062C4×D4—2256no—
1063C4×D4—2256no—
1064C4×D4—2256no—
1065C4×D4—2512no—
1066C4×D4—2256no—
1067C4×D4—4256no—
1068C4×D4—4256no—
1069C4×D4C22×D41512yescomplemented
1070#117—2256no—
1071C2×C4⋊C4—248no—
1072C2×C4⋊C4—248no—
1073C2×C4⋊C4—248no—
1074C2×C4⋊C4—248no—
1075C2×C4⋊C4—2256no—
1076C2×C4⋊C4—248no—
1077C2×C4⋊C4—248no—
1078C2×C4⋊C4—248no—
1079C2×C4⋊C4—248no—
1080C2×C4⋊C4—296no—
1081C2×C4⋊C4—248no—
1082C2×C4⋊C4—248no—
1083C2×C4⋊C4—296no—
1084C2×C4⋊C4—296no—
1085C2×C4⋊C4—448no—
1086C2×C4⋊C4—448no—
1087C2×C4⋊C4—448no—
1088C2×C4⋊C4C22×D4196yes—
1089C2×C4⋊C4C25116yes—
1090C2×C4⋊C4C25116yes—
1091C2×C4⋊C4C25116yes—
1092C2×C4⋊C4C25116yes—
1093C2×C4⋊C4C25116yes—
1094C2×C4⋊C4C25116yes—
1095C2×C4⋊C4C25116yes—
1096C2×C4⋊C4C25116yes—
1097C2×C4⋊C4C25132yes—
1098C2×C4⋊C4C25132yes—
1099C2×C4⋊C4C25132yes—
1100C2×C4⋊C4C25116yes—
1101C2×C4⋊C4C25116yes—
1102C2×C4⋊C4C25132yes—
1103C2×C4⋊C4C25132yes—
1104C2×C4⋊C4C25132yes—
1105C2×C4⋊C4C25116yes—
1106C2×C22⋊C4—296no—
1107C2×C22⋊C4—248no—
1108C2×C22⋊C4—248no—
1109C2×C22⋊C4—296no—
1110C2×C22⋊C4—296no—
1111C2×C22⋊C4—296no—
1112C2×C22⋊C4—296no—
1113C2×C22⋊C4—248no—
1114C2×C22⋊C4—248no—
1115C2×C22⋊C4—296no—
1116C2×C22⋊C4—248no—
1117C2×C22⋊C4—248no—
1118C2×C22⋊C4—248no—
1119C2×C22⋊C4—296no—
1120C2×C22⋊C4—248no—
1121C2×C22⋊C4—296no—
1122C2×C22⋊C4—296no—
1123C2×C22⋊C4—296no—
1124C2×C22⋊C4—296no—
1125C2×C22⋊C4—296no—
1126C2×C22⋊C4—296no—
1127C2×C22⋊C4—296no—
1128C2×C22⋊C4—2512no—
1129C2×C22⋊C4—4256no—
1130C2×C22⋊C4—4256no—
1131C2×C22⋊C4—448no—
1132C2×C22⋊C4—448no—
1133C2×C22⋊C4—448no—
1134C2×C22⋊C4—448no—
1135C2×C22⋊C4—448no—
1136C2×C22⋊C4—448no—
1137C2×C22⋊C4—448no—
1138C2×C22⋊C4—448no—
1139C2×C22⋊C4C22×D4196yes—
1140C2×C22⋊C4C22×D4196yes—
1141C2×C22⋊C4C2×#411192yescomplemented
1142C2×C22⋊C4C25132yes—
1143C2×C22⋊C4C25132yes—
1144C2×C22⋊C4C25132yes—
1145C2×C22⋊C4C25132yes—
1146C2×C22⋊C4C25132yes—
1147C2×C22⋊C4C25132yes—
1148C2×C22⋊C4C25132yes—
1149C2×C22⋊C4C25116yes—
1150C2×C22⋊C4C25116yes—
1151C2×C22⋊C4C25132yes—
1152C2×C22⋊C4C25116yes—
1153C2×C22⋊C4C25116yes—
1154C2×C22⋊C4C25132yes—
1155C2×C22⋊C4C25116yes—
1156C2×C22⋊C4C25116yes—
1157C2×C22⋊C4C25132yes—
1158C2×C22⋊C4C25132yes—
1159C2×C22⋊C4C25132yes—
1160C2×C22⋊C4C25132yes—
1161C2×C22⋊C4C25132yes—
1162C2×C22⋊C4C25116yes—
1163C2×C22⋊C4C25116yes—
1164C2×C22⋊C4C25132yes—
1165C2×C22⋊C4C25132yes—
1166C2×C22⋊C4C25132yes—
1167C2×C22⋊C4C25132yes—
1168C2×C22⋊C4C25132yes—
1169C2×C22⋊C4C25132yes—
1170C2×C22⋊C4C25132yes—
1171C2×C22⋊C4C25132yes—
1172C2×C22⋊C4C25116yes—
1173C2×C22⋊C4C25116yes—
1174C2×C22⋊C4C25132yes—
1175C2×C42—248no—
1176C2×C42—248no—
1177C2×C42—296no—
1178C2×C42—448no—
1179C2×C42—448no—
1180C2×C42—448no—
1181C2×C42C22×D4196yes—
1182C2×C42C25116yes—
1183C2×C42C25116yes—
1184C2×C42C25132yes—
1185C2×C42C25132yes—
1186C2×C42C25132yes—
1187C2×C42C25132yes—
1188C2×C42C25116yes—
1189#95C25116yes—
1190#95C25116yes—
1191#95C25132yes—
1192#95C25132yes—
1193#95C25116yes—
1194#95C25132yes—
1195#95C25116yes—
1196#95C25132yes—
1197#95C25132yes—
1198#95C25132yes—
1199#95C25132yes—
1200#95C25132yes—
1201#95C25132yes—
1202#95C25132yes—
1203#95C25132yes—
1204C24—212no—
1205C24—224no—
1206C24—212no—
1207C24—232no—
1208C24—232no—
1209C24—264no—
1210C24—264no—
1211C24—224no—
1212C24—224no—
1213C24—224no—
1214C24—224no—
1215C24—224no—
1216C24—224no—
1217C24—212no—
1218C24—224no—
1219C24—224no—
1220C24—212no—
1221C24—232no—
1222C24—264no—
1223C24—232no—
1224C24—232no—
1225C24—264no—
1226C24—264no—
1227C24—212no—
1228C24—212no—
1229C24—224no—
1230C24—224no—
1231C24—224no—
1232C24—224no—
1233C24—224no—
1234C24—224no—
1235C24—212no—
1236C24—212no—
1237C24—264no—
1238C24—224no—
1239C24—224no—
1240C24—224no—
1241C24—224no—
1242C24—212no—
1243C24—212no—
1244C24—224no—
1245C24—264no—
1246C24—264no—
1247C24—264no—
1248C24—432no—
1249C24—432no—
1250C24—432no—
1251C24—4384no—
1252C24—4384no—
1253C24—4384no—
1254C24—432no—
1255C24—432no—
1256C24—432no—
1257C24—432no—
1258C24—432no—
1259C24—432no—
1260C24—416no—
1261C24—416no—
1262C24—4384no—
1263C24—432no—
1264C24—416no—
1265C24—432no—
1266C24—416no—
1267C24—416no—
1268C24—416no—
1269C24—432no—
1270C24—432no—
1271C24—432no—
1272C24—432no—
1273C24—432no—
1274C24—432no—
1275C24—432no—
1276C24—432no—
1277C24—432no—
1278C24—8192no—
1279C24—8192no—
1280C24—8192no—
1281C24—81024no—
1282C24#532164yes—
1283C24C23×D4124yes—
1284C24C23×D4124yes—
1285C24C23×D414yes—
1286C24C22×#41148yes—
1287C24C22×#4118yes—
1288C24C2×H(5,𝔽2)148yes—
1289C24C2×H(5,𝔽2)18yes—
1290C24C2×H(5,𝔽2)14yes—
1291C24#58514yes—
1292C24C2618yes—
1293C24C2614yes—
1294C24C2614yes—
1295C24C2614yes—
1296C24C2618yes—
1297C24C2614yes—
1298C24C2613yes—
1299#41—41024no—
1300C2×Q8—232no—
1301C2×Q8—432no—
1302C2×Q8—4192no—
1303C2×D4—2384no—
1304C2×D4—264no—
1305C2×D4—264no—
1306C2×D4—2384no—
1307C2×D4—232no—
1308C2×D4—232no—
1309C2×D4—232no—
1310C2×D4—264no—
1311C2×D4—264no—
1312C2×D4—264no—
1313C2×D4—264no—
1314C2×D4—264no—
1315C2×D4—264no—
1316C2×D4—264no—
1317C2×D4—264no—
1318C2×D4—232no—
1319C2×D4—232no—
1320C2×D4—264no—
1321C2×D4—232no—
1322C2×D4—232no—
1323C2×D4—264no—
1324C2×D4—264no—
1325C2×D4—264no—
1326C2×D4—264no—
1327C2×D4—232no—
1328C2×D4—432no—
1329C2×D4—432no—
1330C2×D4—432no—
1331C2×D4—432no—
1332C2×D4—416no—
1333C2×D4—432no—
1334C2×D4—4384no—
1335C2×D4—4384no—
1336C2×D4—4192no—
1337C2×D4—4384no—
1338C2×D4—4192no—
1339C2×D4—432no—
1340C2×D4—432no—
1341C2×D4—432no—
1342C2×D4—432no—
1343C2×D4—432no—
1344C2×D4—432no—
1345C2×D4—432no—
1346C2×D4—432no—
1347C2×D4—41024no—
1348C2×D4—4384no—
1349C2×D4—4192no—
1350C2×D4—4192no—
1351C2×D4—896no—
1352C2×D4—8192no—
1353C2×D4—8192no—
1354C2×D4—896no—
1355C2×D4—8192no—
1356C2×D4C23×D4164yes—
1357C22×C4—212no—
1358C22×C4—224no—
1359C22×C4—224no—
1360C22×C4—212no—
1361C22×C4—224no—
1362C22×C4—224no—
1363C22×C4—224no—
1364C22×C4—224no—
1365C22×C4—224no—
1366C22×C4—224no—
1367C22×C4—212no—
1368C22×C4—212no—
1369C22×C4—232no—
1370C22×C4—232no—
1371C22×C4—232no—
1372C22×C4—232no—
1373C22×C4—232no—
1374C22×C4—232no—
1375C22×C4—264no—
1376C22×C4—264no—
1377C22×C4—212no—
1378C22×C4—212no—
1379C22×C4—212no—
1380C22×C4—212no—
1381C22×C4—224no—
1382C22×C4—224no—
1383C22×C4—212no—
1384C22×C4—232no—
1385C22×C4—224no—
1386C22×C4—224no—
1387C22×C4—224no—
1388C22×C4—224no—
1389C22×C4—224no—
1390C22×C4—224no—
1391C22×C4—224no—
1392C22×C4—224no—
1393C22×C4—224no—
1394C22×C4—224no—
1395C22×C4—212no—
1396C22×C4—224no—
1397C22×C4—224no—
1398C22×C4—224no—
1399C22×C4—264no—
1400C22×C4—212no—
1401C22×C4—224no—
1402C22×C4—232no—
1403C22×C4—264no—
1404C22×C4—264no—
1405C22×C4—232no—
1406C22×C4—232no—
1407C22×C4—232no—
1408C22×C4—264no—
1409C22×C4—232no—
1410C22×C4—264no—
1411C22×C4—4192no—
1412C22×C4—4192no—
1413C22×C4—416no—
1414C22×C4—416no—
1415C22×C4—432no—
1416C22×C4—432no—
1417C22×C4—432no—
1418C22×C4—4192no—
1419C22×C4—432no—
1420C22×C4—432no—
1421C22×C4—432no—
1422C22×C4—432no—
1423C22×C4—432no—
1424C22×C4—432no—
1425C22×C4—432no—
1426C22×C4—432no—
1427C22×C4—4192no—
1428C22×C4—4384no—
1429C22×C4—416no—
1430C22×C4—416no—
1431C22×C4—432no—
1432C22×C4—416no—
1433C22×C4—416no—
1434C22×C4—416no—
1435C22×C4—432no—
1436C22×C4—432no—
1437C22×C4—432no—
1438C22×C4—896no—
1439C22×C4—8192no—
1440C22×C4—8192no—
1441C22×C4—896no—
1442C22×C4—8192no—
1443C22×C4C23×D4124yes—
1444C22×C4C23×D4124yes—
1445C22×C4C23×D4124yes—
1446C22×C4C23×D4124yes—
1447C22×C4C23×D4124yes—
1448C22×C4C23×D4164yes—
1449C22×C4C23×D4164yes—
1450C22×C4C22×#41148yes—
1451C22×C4C22×#41148yes—
1452C22×C4C2×H(5,𝔽2)124yes—
1453C22×C4C2618yes—
1454C22×C4C2618yes—
1455C22×C4C2614yes—
1456C22×C4C2614yes—
1457C22×C4C2618yes—
1458C22×C4C2618yes—
1459C22×C4C2614yes—
1460C22×C4C2614yes—
1461C22×C4C2614yes—
1462C22×C4C2614yes—
1463C22×C4C2614yes—
1464C22×C4C2614yes—
1465C22×C4C2614yes—
1466C22×C4C2614yes—
1467C22×C4C2618yes—
1468C22×C4C2618yes—
1469C22×C4C2614yes—
1470C4⋊C4—232no—
1471C4⋊C4—232no—
1472C4⋊C4—232no—
1473C4⋊C4—232no—
1474C4⋊C4—232no—
1475C4⋊C4—232no—
1476C4⋊C4—232no—
1477C4⋊C4—232no—
1478C4⋊C4—264no—
1479C4⋊C4—232no—
1480C4⋊C4—232no—
1481C4⋊C4—264no—
1482C4⋊C4—264no—
1483C4⋊C4—432no—
1484C4⋊C4—432no—
1485C4⋊C4—432no—
1486C4⋊C4C23×D4164yes—
1487C22⋊C4—264no—
1488C22⋊C4—232no—
1489C22⋊C4—232no—
1490C22⋊C4—264no—
1491C22⋊C4—264no—
1492C22⋊C4—264no—
1493C22⋊C4—264no—
1494C22⋊C4—232no—
1495C22⋊C4—232no—
1496C22⋊C4—264no—
1497C22⋊C4—232no—
1498C22⋊C4—232no—
1499C22⋊C4—232no—
1500C22⋊C4—264no—
1501C22⋊C4—232no—
1502C22⋊C4—264no—
1503C22⋊C4—264no—
1504C22⋊C4—264no—
1505C22⋊C4—264no—
1506C22⋊C4—264no—
1507C22⋊C4—264no—
1508C22⋊C4—264no—
1509C22⋊C4—432no—
1510C22⋊C4—432no—
1511C22⋊C4—432no—
1512C22⋊C4—432no—
1513C22⋊C4—432no—
1514C22⋊C4—432no—
1515C22⋊C4—432no—
1516C22⋊C4—432no—
1517C22⋊C4C23×D4164yes—
1518C22⋊C4C23×D4164yes—
1519C22⋊C4C22×#411128yescomplemented
1520C42—232no—
1521C42—232no—
1522C42—264no—
1523C42—432no—
1524C42—432no—
1525C42—432no—
1526C42C23×D4164yes—
1527C23—248no—
1528C23—296no—
1529C23—296no—
1530C23—2256no—
1531C23—248no—
1532C23—24no—
1533C23—28no—
1534C23—24no—
1535C23—296no—
1536C23—248no—
1537C23—296no—
1538C23—296no—
1539C23—248no—
1540C23—28no—
1541C23—28no—
1542C23—28no—
1543C23—28no—
1544C23—28no—
1545C23—28no—
1546C23—24no—
1547C23—28no—
1548C23—28no—
1549C23—24no—
1550C23—248no—
1551C23—24no—
1552C23—24no—
1553C23—28no—
1554C23—28no—
1555C23—28no—
1556C23—28no—
1557C23—28no—
1558C23—28no—
1559C23—24no—
1560C23—24no—
1561C23—28no—
1562C23—28no—
1563C23—28no—
1564C23—28no—
1565C23—24no—
1566C23—24no—
1567C23—28no—
1568C23—4128no—
1569C23—4128no—
1570C23—4128no—
1571C23—448no—
1572C23—448no—
1573C23—448no—
1574C23—448no—
1575C23—4128no—
1576C23—4256no—
1577C23—448no—
1578C23—448no—
1579C23—424no—
1580C23—448no—
1581C23—424no—
1582C23—448no—
1583C23—448no—
1584C23—448no—
1585C23—448no—
1586C23—448no—
1587C23—448no—
1588C23—448no—
1589C23—448no—
1590C23—424no—
1591C23—424no—
1592C23—448no—
1593C23—424no—
1594C23—424no—
1595C23—4128no—
1596C23—448no—
1597C23—864no—
1598C23—864no—
1599C23—864no—
1600C23—81536no—
1601C23—864no—
1602C23—864no—
1603C23—8128no—
1604C23C2×#532196yes—
1605C23C2×#532116yes—
1606C23#3484116yes—
1607C23#3488116yes—
1608C23#3513132yes—
1609C23#3519132yes—
1610C23C24×D418yes—
1611C23C24×D418yes—
1612C23C24×D416yes—
1613C23C23×#41116yes—
1614C23C23×#41112yes—
1615C23C22×H(5,𝔽2)116yes—
1616C23C22×H(5,𝔽2)112yes—
1617C23C22×H(5,𝔽2)16yes—
1618C23C2×#58516yes—
1619C23C2711yescharacteristic
1620Q8—464no—
1621D4—2128no—
1622D4—2128no—
1623D4—4128no—
1624D4—4128no—
1625D4—464no—
1626D4—4128no—
1627D4—464no—
1628D4—4128no—
1629D4—464no—
1630D4—464no—
1631D4—832no—
1632D4—864no—
1633D4—864no—
1634D4—832no—
1635D4—864no—
1636C2×C4—248no—
1637C2×C4—248no—
1638C2×C4—248no—
1639C2×C4—296no—
1640C2×C4—296no—
1641C2×C4—248no—
1642C2×C4—248no—
1643C2×C4—24no—
1644C2×C4—28no—
1645C2×C4—28no—
1646C2×C4—24no—
1647C2×C4—28no—
1648C2×C4—28no—
1649C2×C4—28no—
1650C2×C4—28no—
1651C2×C4—28no—
1652C2×C4—28no—
1653C2×C4—24no—
1654C2×C4—24no—
1655C2×C4—248no—
1656C2×C4—24no—
1657C2×C4—24no—
1658C2×C4—24no—
1659C2×C4—24no—
1660C2×C4—28no—
1661C2×C4—28no—
1662C2×C4—24no—
1663C2×C4—28no—
1664C2×C4—28no—
1665C2×C4—28no—
1666C2×C4—28no—
1667C2×C4—28no—
1668C2×C4—28no—
1669C2×C4—28no—
1670C2×C4—28no—
1671C2×C4—28no—
1672C2×C4—28no—
1673C2×C4—24no—
1674C2×C4—28no—
1675C2×C4—28no—
1676C2×C4—28no—
1677C2×C4—24no—
1678C2×C4—28no—
1679C2×C4—464no—
1680C2×C4—464no—
1681C2×C4—464no—
1682C2×C4—464no—
1683C2×C4—4128no—
1684C2×C4—448no—
1685C2×C4—424no—
1686C2×C4—424no—
1687C2×C4—448no—
1688C2×C4—448no—
1689C2×C4—424no—
1690C2×C4—448no—
1691C2×C4—424no—
1692C2×C4—424no—
1693C2×C4—832no—
1694C2×C4—864no—
1695C2×C4—864no—
1696C2×C4—832no—
1697C2×C4—864no—
1698C2×C4C24×D418yes—
1699C2×C4C24×D418yes—
1700C2×C4C24×D418yes—
1701C2×C4C24×D418yes—
1702C2×C4C24×D418yes—
1703C2×C4C23×#41116yes—
1704C2×C4C23×#41116yes—
1705C2×C4C22×H(5,𝔽2)18yes—
1706C22—28no—
1707C22—216no—
1708C22—216no—
1709C22—28no—
1710C22—2192no—
1711C22—28no—
1712C22—216no—
1713C22—28no—
1714C22—216no—
1715C22—216no—
1716C22—28no—
1717C22—48no—
1718C22—48no—
1719C22—48no—
1720C22—48no—
1721C22—48no—
1722C22—48no—
1723C22—496no—
1724C22—4192no—
1725C22—44no—
1726C22—44no—
1727C22—48no—
1728C22—44no—
1729C22—48no—
1730C22—44no—
1731C22—48no—
1732C22—48no—
1733C22—48no—
1734C22—48no—
1735C22—48no—
1736C22—48no—
1737C22—48no—
1738C22—48no—
1739C22—44no—
1740C22—44no—
1741C22—48no—
1742C22—8256no—
1743C22—848no—
1744C22—848no—
1745C22—896no—
1746C22#35906164yesdirect product factor
1747C22C22×#532116yes—
1748C22C22×#532112yes—
1749C22C2×#3484112yes—
1750C22C2×#3513124yes—
1751C22C2×#3519124yes—
1752C22C2×#3488112yes—
1753C22C25×D411yescharacteristic
1754C22C24×#4112yes—
1755C22C23×H(5,𝔽2)12yes—
1756C22C23×H(5,𝔽2)11yescharacteristic
1757C22C22×#58511yescharacteristic
1758C4—28no—
1759C4—28no—
1760C4—28no—
1761C4—28no—
1762C4—216no—
1763C4—216no—
1764C4—28no—
1765C4—28no—
1766C4—44no—
1767C4—44no—
1768C4—48no—
1769C4—44no—
1770C4—44no—
1771C4—48no—
1772C4—48no—
1773C4—44no—
1774C4—48no—
1775C2—216no—
1776C2—48no—
1777C2—416no—
1778C2—84no—
1779C2—84no—
1780C2—88no—
1781C2C2×#35906124yesdirect product factor
1782C2C23×#53211yescharacteristic
1783C2C22×#348411yescharacteristic
1784C2C22×#351312yes—
1785C2C22×#351912yes—
1786C2C22×#348811yescharacteristic
subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC23C27
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×#553C2semidirect
2. C23×#546C2semidirect
3. C2×#35906C2direct (N × H)
4. C22×#2610C2semidirect
5. C22×#2603C2semidirect
6. C22×#2583C2semidirect
7. C22×#2558C2semidirect
8. C22×#2559C2semidirect
9. C22×#2543C2semidirect
10. C22×#2430C2semidirect
11. C22×#2445C2semidirect
12. C22×#2428C2semidirect
13. C22×#2433C2semidirect
14. C22×#2424C2semidirect
15. C22×#2424C2semidirect
16. C22×#2662C2semidirect
17. C22×#2661C2semidirect
18. C22×#2639C2semidirect
19. C22×#2392C2semidirect
20. C22×#2388C2semidirect
21. C23×#394C2semidirect
22. C22×#2358C2semidirect
23. C22×#2358C2semidirect
24. C22×#2275C2semidirect
28. C22×#553C22semidirect
30. C22×#546C22semidirect
32. C23×#126C22semidirect
33. C23×#126C22semidirect
34. C23×#125C22semidirect
37. C23×#123C22semidirect
38. C23×#123C22semidirect
45. C23×#121C22semidirect
46. C23×#121C22semidirect
47. C23×#121C22semidirect
56. C23×C4×D4C22semidirect
57. C23×C4×D4C22semidirect
58. C23×C4×D4C22semidirect
59. C23×#117C22semidirect
64. #35906C22direct (N × H)
65. C2×#2610C22semidirect
66. C2×#2603C22semidirect
67. C2×#2583C22semidirect
68. C2×#2558C22semidirect
69. C2×#2559C22semidirect
70. C2×#2543C22semidirect
71. C2×#2430C22semidirect
72. C2×#2445C22semidirect
73. C2×#2428C22semidirect
74. C2×#2433C22semidirect
75. C2×#2424C22semidirect
76. C2×#2424C22semidirect
77. C2×#2662C22semidirect
78. C2×#2661C22semidirect
79. C2×#2639C22semidirect
80. C22×#400C22semidirect
81. C2×#2392C22semidirect
82. C22×#398C22semidirect
83. C22×#398C22semidirect
84. C22×#397C22semidirect
85. C22×#397C22semidirect
86. C22×#396C22semidirect
87. C22×#396C22semidirect
88. C2×#2388C22semidirect
89. C22×#395C22semidirect
90. C22×#395C22semidirect
97. C22×#394C22semidirect
98. C22×#394C22semidirect
99. C22×#394C22semidirect
100. C22×#394C22semidirect
101. C22×#394C22semidirect
102. C22×#394C22semidirect
103. C22×#393C22semidirect
104. C22×#393C22semidirect
109. C22×#392C22semidirect
110. C22×#392C22semidirect
111. C2×#2358C22semidirect
112. C2×#2358C22semidirect
114. C22×#390C22semidirect
115. C22×#390C22semidirect
116. C22×#390C22semidirect
117. C22×#390C22semidirect
118. C22×#389C22semidirect
119. C22×#389C22semidirect
120. C22×#388C22semidirect
121. C22×#388C22semidirect
122. C22×#388C22semidirect
123. C22×#388C22semidirect
124. C22×#388C22semidirect
125. C22×#388C22semidirect
128. C22×#386C22semidirect
129. C22×#386C22semidirect
130. C22×#386C22semidirect
131. C22×#386C22semidirect
132. C22×#386C22semidirect
133. C22×#386C22semidirect
136. C22×#385C22semidirect
137. C22×#385C22semidirect
138. C2×#2275C22semidirect
139. C22×C4×C4⋊C4C22semidirect
140. C22×C4×C4⋊C4C22semidirect
143. C22×C4×C22⋊C4C22semidirect
144. C22×C4×C22⋊C4C22semidirect
145. C22×C4×C22⋊C4C22semidirect
146. C22×C4×C22⋊C4C22semidirect
147. C22×#376C22semidirect
149. C23×#95C22semidirect
184. C2×#553C23semidirect
186. C2×#546C23semidirect
191. C22×#126C23semidirect
192. C22×#126C23semidirect
194. C22×#125C23semidirect
201. C22×#123C23semidirect
202. C22×#123C23semidirect
218. C22×#121C23semidirect
219. C22×#121C23semidirect
220. C22×#121C23semidirect
234. C22×C4×D4D4semidirect
240. C22×C4×D4C23semidirect
241. C22×C4×D4C23semidirect
242. C22×C4×D4C23semidirect
244. C22×#117C23semidirect
310. #2662C23semidirect
311. #2661C23semidirect
312. #2639C23semidirect
313. #2610C23semidirect
314. #2603C23semidirect
315. #2583C23semidirect
316. #2559C23semidirect
317. #2558C23semidirect
318. #2543C23semidirect
319. #2445C23semidirect
320. #2433C23semidirect
321. #2430C23semidirect
322. #2428C23semidirect
323. #2424C23semidirect
324. #2424C23semidirect
325. C2×#400C23semidirect
326. #2392C23semidirect
327. C2×#398C23semidirect
328. C2×#398C23semidirect
329. C2×#397C23semidirect
330. C2×#397C23semidirect
331. C2×#396C23semidirect
332. C2×#396C23semidirect
333. #2388C23semidirect
334. C2×#395C23semidirect
335. C2×#395C23semidirect
342. C2×#394C23semidirect
343. C2×#394C23semidirect
344. C2×#394C23semidirect
345. C2×#394C23semidirect
346. C2×#394C23semidirect
347. C2×#394C23semidirect
348. C2×#393C23semidirect
349. C2×#393C23semidirect
354. C2×#392C23semidirect
355. C2×#392C23semidirect
356. #2358C23semidirect
357. #2358C23semidirect
359. C2×#390C23semidirect
360. C2×#390C23semidirect
361. C2×#390C23semidirect
362. C2×#390C23semidirect
363. C2×#389C23semidirect
364. C2×#389C23semidirect
365. C2×#388C23semidirect
366. C2×#388C23semidirect
367. C2×#388C23semidirect
368. C2×#388C23semidirect
369. C2×#388C23semidirect
370. C2×#388C23semidirect
373. C2×#386C23semidirect
374. C2×#386C23semidirect
375. C2×#386C23semidirect
376. C2×#386C23semidirect
377. C2×#386C23semidirect
378. C2×#386C23semidirect
381. C2×#385C23semidirect
382. C2×#385C23semidirect
383. #2275C23semidirect
384. C2×C4×C4⋊C4C23semidirect
385. C2×C4×C4⋊C4C23semidirect
388. C2×C4×C22⋊C4C23semidirect
389. C2×C4×C22⋊C4C23semidirect
390. C2×C4×C22⋊C4C23semidirect
391. C2×C4×C22⋊C4C23semidirect
392. C2×#376C23semidirect
409. C22×#95C23semidirect
547. C2×#126C24semidirect
548. C2×#126C24semidirect
550. C2×#125C24semidirect
557. C2×#123C24semidirect
558. C2×#123C24semidirect
574. C2×#121C24semidirect
575. C2×#121C24semidirect
576. C2×#121C24semidirect
590. C2×C4×D4C2×D4semidirect
596. C2×C4×D4C24semidirect
597. C2×C4×D4C24semidirect
598. C2×C4×D4C24semidirect
600. C2×#117C24semidirect
672. C22×C22⋊C4#41semidirect
723. #400C24semidirect
724. #398C24semidirect
725. #398C24semidirect
726. #397C24semidirect
727. #397C24semidirect
728. #396C24semidirect
729. #396C24semidirect
730. #395C24semidirect
731. #395C24semidirect
738. #394C24semidirect
739. #394C24semidirect
740. #394C24semidirect
741. #394C24semidirect
742. #394C24semidirect
743. #393C24semidirect
744. #393C24semidirect
749. #392C24semidirect
750. #392C24semidirect
752. #390C24semidirect
753. #390C24semidirect
754. #390C24semidirect
755. #390C24semidirect
756. #389C24semidirect
757. #389C24semidirect
758. #388C24semidirect
759. #388C24semidirect
760. #388C24semidirect
761. #388C24semidirect
762. #388C24semidirect
763. #388C24semidirect
766. #386C24semidirect
767. #386C24semidirect
768. #386C24semidirect
769. #386C24semidirect
770. #386C24semidirect
771. #386C24semidirect
774. #385C24semidirect
775. #385C24semidirect
776. C4×C4⋊C4C24semidirect
777. C4×C4⋊C4C24semidirect
780. C4×C22⋊C4C24semidirect
781. C4×C22⋊C4C24semidirect
782. C4×C22⋊C4C24semidirect
783. C4×C22⋊C4C24semidirect
784. #376C24semidirect
801. C2×#95C24semidirect
1069. C4×D4C22×D4semidirect
1141. C2×C22⋊C4C2×#41semidirect
1519. C22⋊C4C22×#41semidirect
1746. C22#35906direct (N × H)
1781. C2C2×#35906direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5532
C23×#5462
C2×#359062
C22×#26102
C22×#26032
C22×#25832
C22×#25582
C22×#25592
C22×#25432
C22×#24302
C22×#24452
C22×#24282
C22×#24332
C22×#24242
C22×#26622
C22×#26612
C22×#26392
C22×#23922
C22×#23882
C23×#3942
C22×#23582
C22×#22752