Finite Group Databasebeta

← #7722054

Subgroups — #7722054

Order 512.

8252 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3505C211yesmaximal, characteristic, complemented
2C22×#537C211yesmaximal, characteristic, complemented
3#51523C218yesmaximal, complemented
4#46427C214yesmaximal, complemented
5#46358C214yesmaximal, complemented
6#45092C214yesmaximal, complemented
7#45091C214yesmaximal, complemented
8#39466C212yesmaximal, complemented
9#38917C212yesmaximal, complemented
10#38037C214yesmaximal, complemented
11#37840C214yesmaximal, complemented
12#37784C214yesmaximal, complemented
13#37656C214yesmaximal, complemented
14#37453C211yesmaximal, characteristic, complemented
15#37117C212yesmaximal, complemented
16#36715C212yesmaximal, complemented
17#36213C212yesmaximal, complemented
18#36163C212yesmaximal, complemented
19#35540C212yesmaximal, complemented
20#35351C212yesmaximal, complemented
21#35305C211yesmaximal, characteristic, complemented
22#35084C211yesmaximal, characteristic, complemented
23#34736C211yesmaximal, characteristic, complemented
24#34363C211yesmaximal, characteristic, complemented
25C23×#41C2211yescharacteristic
26C23×#41C2211yescharacteristic, complemented
27#3505—216no—
28C2×#553C2212yescomplemented
29C2×#553C2214yescomplemented
30C2×#552C2212yes—
31C2×#551C2214yes—
32C2×#548C2212yescomplemented
33C2×#547C2214yescomplemented
34C2×#546C2212yes—
35C2×#539C2212yescomplemented
36C2×#538C2212yescomplemented
37C2×#537—216no—
38C2×#537C2214yes—
39C2×#537C2214yes—
40C2×#537C2214yescomplemented
41C2×#537C2214yescomplemented
42C2×#536C2212yescomplemented
43C2×#534C2212yes—
44C2×#529C2212yescomplemented
45C2×#525C2212yescomplemented
46C2×#525C2212yescomplemented
47C22×C22⋊Q8C2211yescharacteristic
48C22×C22⋊Q8C2211yescharacteristic
49C22×C22⋊Q8C2211yescharacteristic, complemented
50C22×C22⋊Q8C2212yescomplemented
51C22×#121C2212yes—
52C22×#121C2212yes—
53C22×#121C2211yescharacteristic
54C22×#121C2211yescharacteristic, complemented
55C22×#121C2212yescomplemented
56C2×#518C2212yes—
57C22×C4×D4C2211yescharacteristic
58C23×C4⋊C4C2211yescharacteristic, complemented
59#2855C2212yescomplemented
60#2849C2214yes—
61#2849C2214yes—
62#2848C2212yescomplemented
63#2848C2212yescomplemented
64#2848C2212yescomplemented
65#2817C2214yescomplemented
66#2723C2218yescomplemented
67#2720C2218yescomplemented
68#2708C2218yescomplemented
69#2708C2218yescomplemented
70#2703C2218yescomplemented
71#2701C2218yescomplemented
72#2699C2218yescomplemented
73#2698C2218yescomplemented
74#2691C2218yescomplemented
75#2689C2218yescomplemented
76#2688C2218yescomplemented
77#2688C2218yescomplemented
78#2682C2218yescomplemented
79#2680C2218yescomplemented
80#2678C2218yescomplemented
81#2674C2218yescomplemented
82#2672C2218yescomplemented
83#2671C2218yescomplemented
84#2671C2218yescomplemented
85#2668C2218yescomplemented
86#2638C2214yescomplemented
87#2627C2214yescomplemented
88#2627C2214yescomplemented
89#2623C2214yes—
90#2621C2214yescomplemented
91#2616C2214yescomplemented
92#2613C2214yes—
93#2583C2212yescomplemented
94#2561C2212yescomplemented
95#2559C2218yescomplemented
96#2555C2218yescomplemented
97#2542C2214yescomplemented
98#2535C2214yescomplemented
99#2503C2212yescomplemented
100#2503C2212yescomplemented
101#2489C2214yescomplemented
102#2488C2218yescomplemented
103#2486C2212yes—
104#2484C2214yescomplemented
105#2483C2212yes—
106#2483C2212yes—
107#2483C2212yes—
108#2483C2214yescomplemented
109#2482C2214yescomplemented
110#2481C2218yescomplemented
111#2476C2218yescomplemented
112#2473C2218yescomplemented
113#2464C2218yescomplemented
114#2449C2218yescomplemented
115#2444C2218yescomplemented
116#2444C2218yescomplemented
117#2443C2218yescomplemented
118#2443C2218yescomplemented
119#2442C2214yescomplemented
120#2440C2218yescomplemented
121#2438C2218yescomplemented
122#2435C2212yescomplemented
123#2434C2212yescomplemented
124#2434C2212yescomplemented
125#2434C2212yescomplemented
126#2432C2214yescomplemented
127#2432C2214yescomplemented
128#2430C2218yescomplemented
129#2429C2214yescomplemented
130#2427C2214yescomplemented
131#2422C2218yescomplemented
132#2422C2218yescomplemented
133#2420C2214yescomplemented
134#2420C2218yescomplemented
135#2420C2218yescomplemented
136#2417C2214yescomplemented
137#2415C2214yescomplemented
138#2415C2214yescomplemented
139#2413C2214yes—
140#2412C2214yes—
141#2411C2214yes—
142#2410C2214yes—
143#2409C2212yes—
144#2409C2212yes—
145#2408C2212yes—
146#2407C2214yescomplemented
147#2407C2214yescomplemented
148#2407C2214yescomplemented
149#2406C2212yescomplemented
150#2406C2218yescomplemented
151#2406C2214yescomplemented
152#2405C2212yes—
153#2405C2211yescharacteristic
154#2405C2212yes—
155#2405C2211yescharacteristic
156#2405C2212yes—
157#2405C2214yescomplemented
158#2404C2212yescomplemented
159#2403C2211yescharacteristic
160#2403C2211yescharacteristic
161#2388C2214yescomplemented
162#2377C2214yescomplemented
163#2363C2214yescomplemented
164#2360C2214yescomplemented
165#2352C2214yescomplemented
166#2344C2212yescomplemented
167#2342C2214yescomplemented
168#2339C2214yescomplemented
169D4×C22⋊C4C2212yescomplemented
170#2333C2214yescomplemented
171#2324C2214yescomplemented
172#2322C2214yes—
173#2317C2214yescomplemented
174#2311C2212yescomplemented
175#2309C2212yes—
176#2308C2212yes—
177#2308C2214yescomplemented
178C4×#120C2212yes—
179C4×#120C2212yes—
180#2297C2212yescomplemented
181C2×#385C2214yescomplemented
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2214yescomplemented
185C22×#41—28no—
186C22×#41—28no—
187C22×#41—48no—
188C22×#41—48no—
189C22×#41C2312yes—
190C22×#41C2312yes—
191C22×#41C2314yes—
192C22×#41C2312yes—
193C22×#41C2312yes—
194C22×#41C2314yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×Q8C2311yescharacteristic
199C23×D4C2312yes—
200C23×D4C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C23×D4C2312yes—
204C23×D4C2311yescharacteristic
205C23×D4C2312yes—
206C23×D4C2311yescharacteristic
207C24×C4C2311yescharacteristic
208C24×C4C2311yescharacteristic
209C24×C4C2312yes—
210C24×C4C2311yescharacteristic
211C24×C4C2312yes—
212C24×C4C2311yescharacteristic
213#553—216no—
214#553—232no—
215#552—216no—
216#551—232no—
217#548—216no—
218#547—416no—
219#546—216no—
220#539—216no—
221#538—216no—
222#537—232no—
223#537—232no—
224#537—232no—
225#537—232no—
226#536—48no—
227#534—216no—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2314yes—
230#529—216no—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#126C2314yes—
234C2×#125C2312yes—
235C2×#125C2314yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239#525—216no—
240#525—48no—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×#123C2314yes—
247C2×#123C2318yes—
248C2×#123C2312yes—
249C2×#123C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2318yes—
253C2×C22⋊Q8—28no—
254C2×C22⋊Q8—28no—
255C2×C22⋊Q8—28no—
256C2×C22⋊Q8—216no—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2312yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2314yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2318yes—
268C2×C22⋊Q8C2318yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×#121—216no—
276C2×#121—216no—
277C2×#121—28no—
278C2×#121—216no—
279C2×#121D4116yescomplemented
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2318yes—
283C2×#121C2318yes—
284C2×#121C2318yes—
285C2×#121C2318yes—
286C2×#121C2318yes—
287C2×#121C2318yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2314yes—
292C2×#121C2314yes—
293C2×#121C2318yes—
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×#120C2314yes—
299C2×#120C2314yes—
300C2×#120C2312yes—
301C2×#120C2312yes—
302C2×#120C2312yes—
303C2×#120C2312yes—
304#518—216no—
305C2×C4×Q8C2312yes—
306C2×C4×D4—28no—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×#117C2314yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2314yes—
324C2×#117C2312yes—
325C2×#117C2312yes—
326C22×C4⋊C4—28no—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2312yes—
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2314yes—
336C22×C4⋊C4C2318yes—
337C22×C4⋊C4C2311yescharacteristic
338C22×C22⋊C4C2311yescharacteristic
339C22×C22⋊C4C2314yes—
340C22×C22⋊C4C2311yescharacteristic
341C22×C22⋊C4C2312yes—
342C22×C22⋊C4C2312yes—
343C22×C22⋊C4C2312yes—
344C22×C22⋊C4C2312yes—
345C22×C22⋊C4C2314yes—
346C22×C22⋊C4C2312yes—
347C22×C42C2311yescharacteristic
348#400C2318yes—
349#400C2318yes—
350#400C2318yes—
351#400C2318yes—
352#399C2318yes—
353#399C2318yes—
354#398C2314yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#397C2314yes—
361#397C2318yes—
362#397C2318yes—
363#397C2318yes—
364#397C2318yes—
365#397C2318yes—
366#397C2318yes—
367#397C2318yes—
368#397C2318yes—
369#396C2318yes—
370#396C2318yes—
371#395C2318yes—
372#395C2318yes—
373#395C2314yes—
374#395C2318yes—
375#395C2314yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#394C2318yes—
380#394C2318yes—
381#394C2318yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2318yes—
386#394C2318yes—
387#394C2318yes—
388#394C2318yes—
389#394C2318yes—
390#393C2314yes—
391#393C2314yes—
392#392C2318yes—
393#392C2318yes—
394#392C2314yes—
395#392C2314yes—
396#392C2314yes—
397#392C2318yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#390C2318yes—
404#390C2318yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2318yes—
409#389C2318yes—
410#389C2318yes—
411#389C2318yes—
412#389C2314yes—
413#389C2314yes—
414#389C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2318yes—
436#386C2312yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2312yes—
443#386C2312yes—
444#386C2312yes—
445#386C2312yes—
446#386C2312yes—
447#386C2314yes—
448#386C2314yes—
449#386C2318yes—
450#385C2312yes—
451#385C2314yes—
452#385C2314yes—
453#385C2314yes—
454#385C2318yes—
455#385C2318yes—
456#385C2314yes—
457#385C2314yes—
458#385C2314yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2314yes—
465#385C2314yes—
466#385C2314yes—
467#385C2312yes—
468#385C2314yes—
469#385C2318yes—
470#385C2314yes—
471#385C2318yes—
472#385C2318yes—
473#384C2318yes—
474#382C2318yes—
475#382C2314yes—
476#381C2314yes—
477#381C2312yes—
478#381C2314yes—
479#381C2314yes—
480#381C2314yes—
481#381C2318yes—
482#381C2314yes—
483#381C2314yes—
484#381C2314yes—
485#381C2312yes—
486#381C2318yes—
487#380C2314yes—
488#380C2314yes—
489#380C2312yes—
490#380C2312yes—
491#380C2314yes—
492#380C2312yes—
493#380C2312yes—
494#380C2318yes—
495#380C2318yes—
496#380C2318yes—
497#379C2314yes—
498#379C2311yescharacteristic
499#379C2312yes—
500#379C2312yes—
501#379C2314yes—
502#379C2311yescharacteristic
503#379C2314yes—
504#379C2314yes—
505#379C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C2×#95C2318yes—
517C25C2411yescharacteristic
518C25C2411yescharacteristic
519C25C2412yes—
520C25C2411yescharacteristic
521C25C2411yescharacteristic
522C2×#41—216no—
523C2×#41—216no—
524C2×#41—28no—
525C2×#41—28no—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—216no—
532C2×#41—44no—
533C2×#41—44no—
534C2×#41—48no—
535C2×#41—44no—
536C2×#41—44no—
537C2×#41—48no—
538C2×#41—48no—
539C2×#41—44no—
540C2×#41—44no—
541C2×#41—48no—
542C2×#41—464no—
543C2×#41—464no—
544C22×Q8—24no—
545C22×Q8—24no—
546C22×Q8—24no—
547C22×Q8—44no—
548C22×Q8—44no—
549C22×Q8—44no—
550C22×Q8C2412yes—
551C22×Q8C2412yes—
552C22×Q8C2412yes—
553C22×Q8C2412yes—
554C22×Q8C2412yes—
555C22×Q8C2412yes—
556C22×D4—24no—
557C22×D4—24no—
558C22×D4—24no—
559C22×D4—28no—
560C22×D4—28no—
561C22×D4—24no—
562C22×D4—44no—
563C22×D4—44no—
564C22×D4—48no—
565C22×D4—48no—
566C22×D4—44no—
567C22×D4—44no—
568C22×D4—44no—
569C22×D4—48no—
570C22×D4C2×D4116yes—
571C22×D4C2×D418yes—
572C22×D4C2412yes—
573C22×D4C2412yes—
574C22×D4C2412yes—
575C22×D4C2412yes—
576C22×D4C2418yes—
577C22×D4C2412yes—
578C22×D4C2412yes—
579C22×D4C2412yes—
580C22×D4C2412yes—
581C22×D4C2412yes—
582C22×D4C2414yes—
583C22×D4C2414yes—
584C22×D4C2414yes—
585C22×D4C2418yes—
586C22×D4C2414yes—
587C22×D4C2414yes—
588C22×D4C2414yes—
589C22×D4C2412yes—
590C23×C4—24no—
591C23×C4—28no—
592C23×C4—28no—
593C23×C4—24no—
594C23×C4—28no—
595C23×C4—24no—
596C23×C4—44no—
597C23×C4—48no—
598C23×C4—44no—
599C23×C4—44no—
600C23×C4—48no—
601C23×C4C2×D418yes—
602C23×C4C2412yes—
603C23×C4C2411yescharacteristic
604C23×C4C2412yes—
605C23×C4C2412yes—
606C23×C4C2412yes—
607C23×C4C2418yes—
608C23×C4C2412yes—
609C23×C4C2411yescharacteristic
610C23×C4C2411yescharacteristic
611C23×C4C2411yescharacteristic
612C23×C4C2412yes—
613C23×C4C2412yes—
614C23×C4C2411yescharacteristic
615C23×C4C2411yescharacteristic
616C23×C4C2414yes—
617C23×C4C2412yes—
618C23×C4C2411yescharacteristic
619C23×C4C2412yes—
620C23×C4C2414yes—
621C23×C4C2418yes—
622C23×C4C2411yescharacteristic
623C23×C4C2412yes—
624C23×C4C2412yes—
625C23×C4C2418yes—
626C23×C4C2411yescharacteristic
627C23×C4C2411yescharacteristic
628C23×C4C2411yescharacteristic
629C4⋊Q8—48no—
630C4⋊Q8—48no—
631#126—216no—
632#126—216no—
633#126—216no—
634#125—28no—
635#125—216no—
636#124—28no—
637#124—216no—
638#124—48no—
639#123—216no—
640#123—216no—
641#123—216no—
642#123—216no—
643#123—216no—
644#123—44no—
645#123—48no—
646#123—416no—
647#123—416no—
648#123—48no—
649#123—44no—
650#123—48no—
651C22⋊Q8—28no—
652C22⋊Q8—28no—
653C22⋊Q8—28no—
654C22⋊Q8—28no—
655C22⋊Q8—28no—
656C22⋊Q8—28no—
657C22⋊Q8—28no—
658C22⋊Q8—28no—
659C22⋊Q8—216no—
660C22⋊Q8—216no—
661C22⋊Q8—216no—
662C22⋊Q8—28no—
663C22⋊Q8—232no—
664C22⋊Q8—232no—
665C22⋊Q8—216no—
666C22⋊Q8—48no—
667C22⋊Q8—48no—
668C22⋊Q8—48no—
669#121—216no—
670#121—216no—
671#121—232no—
672#121—232no—
673#121—232no—
674#121—232no—
675#121—28no—
676#121—216no—
677#121—216no—
678#121—216no—
679#121—232no—
680#121—232no—
681#121—48no—
682#121—416no—
683#121C2×D4116yes—
684#121C2×D4116yes—
685#121C2×D4116yes—
686#121C2×D4116yes—
687#120—216no—
688#120—216no—
689#120—44no—
690#120—44no—
691#120—44no—
692#120—44no—
693C4×Q8—28no—
694C4×D4—216no—
695C4×D4—216no—
696C4×D4—216no—
697C4×D4—216no—
698C4×D4—28no—
699C4×D4—28no—
700C4×D4—28no—
701C4×D4—28no—
702C4×D4—28no—
703C4×D4—216no—
704C4×D4—216no—
705C4×D4—48no—
706C4×D4—48no—
707#117—216no—
708#117—28no—
709#117—216no—
710#117—44no—
711#117—48no—
712#117—44no—
713C2×C4⋊C4—28no—
714C2×C4⋊C4—24no—
715C2×C4⋊C4—24no—
716C2×C4⋊C4—28no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—24no—
719C2×C4⋊C4—28no—
720C2×C4⋊C4—216no—
721C2×C4⋊C4—216no—
722C2×C4⋊C4—416no—
723C2×C4⋊C4C2×D418yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2418yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2418yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2418yes—
744C2×C4⋊C4C2418yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2418yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2418yes—
749C2×C4⋊C4C2418yes—
750C2×C4⋊C4C2418yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C22⋊C4—24no—
754C2×C22⋊C4—28no—
755C2×C22⋊C4—216no—
756C2×C22⋊C4—28no—
757C2×C22⋊C4—28no—
758C2×C22⋊C4—24no—
759C2×C22⋊C4—28no—
760C2×C22⋊C4—48no—
761C2×C22⋊C4C2×D4116yes—
762C2×C22⋊C4C2412yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2412yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2412yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2412yes—
772C2×C22⋊C4C2414yes—
773C2×C22⋊C4C2418yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2412yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2418yes—
784C2×C22⋊C4C2418yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2418yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C42—24no—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2412yes—
810C2×C42C2414yes—
811C2×C42C2412yes—
812C2×C42C2414yes—
813C2×C42C2418yes—
814#95C2414yes—
815#95C2418yes—
816#95C2418yes—
817#95C2418yes—
818#95C2414yes—
819#95C2418yes—
820#95C2414yes—
821#95C2418yes—
822#95C2418yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2418yes—
827#95C2414yes—
828#95C2414yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836C24—22no—
837C24—24no—
838C24—28no—
839C24—24no—
840C24—22no—
841C24—24no—
842C24—22no—
843C24—24no—
844C24—42no—
845C24—42no—
846C24—44no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—44no—
851C24—42no—
852C24—42no—
853C24—42no—
854C24C22×D414yes—
855C24C22×D418yes—
856C24C2512yes—
857C24C2512yes—
858C24C2511yescharacteristic
859C24C2511yescharacteristic
860C24C2514yes—
861C24C2512yes—
862C24C2511yescharacteristic
863#41—432no—
864#41—432no—
865#41—464no—
866#41—432no—
867#41—432no—
868#41—464no—
869#41—816no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—28no—
877C2×Q8—24no—
878C2×Q8—28no—
879C2×Q8—24no—
880C2×Q8—42no—
881C2×Q8—42no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—416no—
885C2×Q8—416no—
886C2×Q8—88no—
887C2×D4—24no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—24no—
892C2×D4—216no—
893C2×D4—24no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—216no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—216no—
904C2×D4—28no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—28no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—416no—
911C2×D4—432no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—48no—
925C2×D4—42no—
926C2×D4—416no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—44no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—48no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—48no—
936C2×D4—416no—
937C2×D4—416no—
938C2×D4—416no—
939C2×D4—432no—
940C2×D4—816no—
941C2×D4C22×D418yes—
942C2×D4C22×D4116yes—
943C2×D4C22×D4116yes—
944C2×D4C22×D418yes—
945C22×C4—232no—
946C22×C4—22no—
947C22×C4—24no—
948C22×C4—28no—
949C22×C4—24no—
950C22×C4—24no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—22no—
958C22×C4—24no—
959C22×C4—22no—
960C22×C4—24no—
961C22×C4—216no—
962C22×C4—28no—
963C22×C4—22no—
964C22×C4—24no—
965C22×C4—22no—
966C22×C4—24no—
967C22×C4—28no—
968C22×C4—28no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—216no—
973C22×C4—28no—
974C22×C4—24no—
975C22×C4—24no—
976C22×C4—216no—
977C22×C4—24no—
978C22×C4—416no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—44no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—48no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—48no—
989C22×C4—48no—
990C22×C4—48no—
991C22×C4—44no—
992C22×C4—42no—
993C22×C4—44no—
994C22×C4—48no—
995C22×C4—48no—
996C22×C4—48no—
997C22×C4—42no—
998C22×C4—48no—
999C22×C4—44no—
1000C22×C4—432no—
1001C22×C4—416no—
1002C22×C4—88no—
1003C22×C4—816no—
1004C22×C4C22×D414yes—
1005C22×C4C22×D418yes—
1006C22×C4C22×D414yes—
1007C22×C4C22×D414yes—
1008C22×C4C22×D414yes—
1009C22×C4C22×D414yes—
1010C22×C4C22×D414yes—
1011C22×C4H(5,𝔽2)18yes—
1012C22×C4C2514yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2518yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2514yes—
1025C22×C4C2511yescharacteristic
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C4⋊C4—216no—
1030C4⋊C4—24no—
1031C4⋊C4—24no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—24no—
1036C4⋊C4—28no—
1037C4⋊C4—28no—
1038C4⋊C4—216no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—216no—
1047C4⋊C4—28no—
1048C4⋊C4—48no—
1049C4⋊C4—48no—
1050C4⋊C4—48no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—48no—
1054C4⋊C4—48no—
1055C4⋊C4—48no—
1056C4⋊C4C22×D418yes—
1057C4⋊C4C22×D418yes—
1058C22⋊C4—24no—
1059C22⋊C4—28no—
1060C22⋊C4—24no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—216no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—216no—
1071C22⋊C4—24no—
1072C22⋊C4—28no—
1073C22⋊C4—24no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—216no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—48no—
1081C22⋊C4—44no—
1082C22⋊C4—48no—
1083C22⋊C4—48no—
1084C22⋊C4—48no—
1085C22⋊C4—42no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—48no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—48no—
1098C22⋊C4—48no—
1099C22⋊C4—48no—
1100C22⋊C4C22×D4116yes—
1101C22⋊C4C22×D4116yes—
1102C42—24no—
1103C42—24no—
1104C42—28no—
1105C42—28no—
1106C42—28no—
1107C42—48no—
1108C42—44no—
1109C23—22no—
1110C23—22no—
1111C23—28no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—28no—
1116C23—22no—
1117C23—24no—
1118C23—24no—
1119C23—24no—
1120C23—22no—
1121C23—22no—
1122C23—24no—
1123C23—22no—
1124C23—22no—
1125C23—28no—
1126C23—28no—
1127C23—216no—
1128C23—22no—
1129C23—22no—
1130C23—24no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—24no—
1135C23—22no—
1136C23—24no—
1137C23—24no—
1138C23—44no—
1139C23—48no—
1140C23—44no—
1141C23—48no—
1142C23—416no—
1143C23—44no—
1144C23—44no—
1145C23—44no—
1146C23—44no—
1147C23—44no—
1148C23—44no—
1149C23—82no—
1150C23—816no—
1151C23—88no—
1152C23—88no—
1153C23—82no—
1154C23—88no—
1155C23C23×D412yes—
1156C23C23×D418yes—
1157C23C23×D412yes—
1158C23C23×D412yes—
1159C23C2×H(5,𝔽2)14yes—
1160C23#58514yes—
1161C23C2611yescharacteristic
1162Q8—48no—
1163Q8—48no—
1164Q8—48no—
1165Q8—48no—
1166Q8—48no—
1167Q8—84no—
1168D4—216no—
1169D4—416no—
1170D4—416no—
1171D4—48no—
1172D4—48no—
1173D4—48no—
1174D4—48no—
1175D4—48no—
1176D4—48no—
1177D4—48no—
1178D4—432no—
1179D4—48no—
1180D4—48no—
1181D4—88no—
1182D4—88no—
1183D4—816no—
1184D4—88no—
1185D4—88no—
1186C2×C4—28no—
1187C2×C4—216no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—24no—
1194C2×C4—24no—
1195C2×C4—216no—
1196C2×C4—28no—
1197C2×C4—216no—
1198C2×C4—28no—
1199C2×C4—28no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—22no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—28no—
1211C2×C4—24no—
1212C2×C4—28no—
1213C2×C4—22no—
1214C2×C4—28no—
1215C2×C4—22no—
1216C2×C4—24no—
1217C2×C4—28no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—28no—
1221C2×C4—22no—
1222C2×C4—28no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—28no—
1226C2×C4—24no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—432no—
1231C2×C4—48no—
1232C2×C4—44no—
1233C2×C4—48no—
1234C2×C4—44no—
1235C2×C4—48no—
1236C2×C4—48no—
1237C2×C4—48no—
1238C2×C4—84no—
1239C2×C4—816no—
1240C2×C4—82no—
1241C2×C4—88no—
1242C2×C4—84no—
1243C2×C4—82no—
1244C2×C4—84no—
1245C2×C4—88no—
1246C2×C4—816no—
1247C2×C4C23×D418yes—
1248C2×C4C23×D412yes—
1249C2×C4C23×D412yes—
1250C2×C4C23×D412yes—
1251C2×C4C23×D412yes—
1252C2×C4C2×H(5,𝔽2)14yes—
1253C2×C4C2×H(5,𝔽2)14yes—
1254C22—22no—
1255C22—22no—
1256C22—28no—
1257C22—24no—
1258C22—22no—
1259C22—22no—
1260C22—28no—
1261C22—22no—
1262C22—22no—
1263C22—28no—
1264C22—22no—
1265C22—28no—
1266C22—22no—
1267C22—28no—
1268C22—416no—
1269C22—42no—
1270C22—42no—
1271C22—48no—
1272C22—44no—
1273C22—44no—
1274C22—48no—
1275C22—44no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—816no—
1287C22—88no—
1288C22—88no—
1289C22—88no—
1290C22#348514yes—
1291C22C24×D411yescharacteristic
1292C22C22×H(5,𝔽2)12yes—
1293C22C2×#58512yes—
1294C222−1+612yes—
1295C4—22no—
1296C4—24no—
1297C4—22no—
1298C4—22no—
1299C4—28no—
1300C4—42no—
1301C4—44no—
1302C4—42no—
1303C4—44no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—48no—
1309C4—44no—
1310C4—44no—
1311C4#348414yes—
1312C2—24no—
1313C2—44no—
1314C2—42no—
1315C2—48no—
1316C2—42no—
1317C2—82no—
1318C2—82no—
1319C2C2×#348411yescharacteristic
1320C2C2×#348511yescharacteristic
1321C2#6285911yescharacteristic
1322C2#6292714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3505C2semidirect
2. C22×#537C2semidirect
3. #51523C2semidirect
4. #46427C2semidirect
5. #46358C2semidirect
6. #45092C2semidirect
7. #45091C2semidirect
8. #39466C2semidirect
9. #38917C2semidirect
10. #38037C2semidirect
11. #37840C2semidirect
12. #37784C2semidirect
13. #37656C2semidirect
14. #37453C2semidirect
15. #37117C2semidirect
16. #36715C2semidirect
17. #36213C2semidirect
18. #36163C2semidirect
19. #35540C2semidirect
20. #35351C2semidirect
21. #35305C2semidirect
22. #35084C2semidirect
23. #34736C2semidirect
24. #34363C2semidirect
26. C23×#41C22semidirect
28. C2×#553C22semidirect
29. C2×#553C22semidirect
32. C2×#548C22semidirect
33. C2×#547C22semidirect
35. C2×#539C22semidirect
36. C2×#538C22semidirect
40. C2×#537C22semidirect
41. C2×#537C22semidirect
42. C2×#536C22semidirect
44. C2×#529C22semidirect
45. C2×#525C22semidirect
46. C2×#525C22semidirect
49. C22×C22⋊Q8C22semidirect
50. C22×C22⋊Q8C22semidirect
54. C22×#121C22semidirect
55. C22×#121C22semidirect
58. C23×C4⋊C4C22semidirect
59. #2855C22semidirect
62. #2848C22semidirect
63. #2848C22semidirect
64. #2848C22semidirect
65. #2817C22semidirect
66. #2723C22semidirect
67. #2720C22semidirect
68. #2708C22semidirect
69. #2708C22semidirect
70. #2703C22semidirect
71. #2701C22semidirect
72. #2699C22semidirect
73. #2698C22semidirect
74. #2691C22semidirect
75. #2689C22semidirect
76. #2688C22semidirect
77. #2688C22semidirect
78. #2682C22semidirect
79. #2680C22semidirect
80. #2678C22semidirect
81. #2674C22semidirect
82. #2672C22semidirect
83. #2671C22semidirect
84. #2671C22semidirect
85. #2668C22semidirect
86. #2638C22semidirect
87. #2627C22semidirect
88. #2627C22semidirect
90. #2621C22semidirect
91. #2616C22semidirect
93. #2583C22semidirect
94. #2561C22semidirect
95. #2559C22semidirect
96. #2555C22semidirect
97. #2542C22semidirect
98. #2535C22semidirect
99. #2503C22semidirect
100. #2503C22semidirect
101. #2489C22semidirect
102. #2488C22semidirect
104. #2484C22semidirect
108. #2483C22semidirect
109. #2482C22semidirect
110. #2481C22semidirect
111. #2476C22semidirect
112. #2473C22semidirect
113. #2464C22semidirect
114. #2449C22semidirect
115. #2444C22semidirect
116. #2444C22semidirect
117. #2443C22semidirect
118. #2443C22semidirect
119. #2442C22semidirect
120. #2440C22semidirect
121. #2438C22semidirect
122. #2435C22semidirect
123. #2434C22semidirect
124. #2434C22semidirect
125. #2434C22semidirect
126. #2432C22semidirect
127. #2432C22semidirect
128. #2430C22semidirect
129. #2429C22semidirect
130. #2427C22semidirect
131. #2422C22semidirect
132. #2422C22semidirect
133. #2420C22semidirect
134. #2420C22semidirect
135. #2420C22semidirect
136. #2417C22semidirect
137. #2415C22semidirect
138. #2415C22semidirect
146. #2407C22semidirect
147. #2407C22semidirect
148. #2407C22semidirect
149. #2406C22semidirect
150. #2406C22semidirect
151. #2406C22semidirect
157. #2405C22semidirect
158. #2404C22semidirect
161. #2388C22semidirect
162. #2377C22semidirect
163. #2363C22semidirect
164. #2360C22semidirect
165. #2352C22semidirect
166. #2344C22semidirect
167. #2342C22semidirect
168. #2339C22semidirect
169. D4×C22⋊C4C22semidirect
170. #2333C22semidirect
171. #2324C22semidirect
173. #2317C22semidirect
174. #2311C22semidirect
177. #2308C22semidirect
180. #2297C22semidirect
181. C2×#385C22semidirect
184. #2280C22semidirect
279. C2×#121D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35052
C22×#5372
#515232
#464272
#463582
#450922
#450912
#394662
#389172
#380372
#378402
#377842
#376562
#374532
#371172
#367152
#362132
#361632
#355402
#353512
#353052
#350842
#347362
#343632