Finite Group Databasebeta

← #8095498

Subgroups — #8095498

Order 512.

6068 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53065C214yesmaximal, complemented
2#53046C214yesmaximal, complemented
3#53005C214yesmaximal, complemented
4#52967C214yesmaximal, complemented
5#52753C214yesmaximal, complemented
6#52410C214yesmaximal, complemented
7#46031C218yesmaximal, complemented
8#45667C214yesmaximal, complemented
9#45645C214yesmaximal, complemented
10#45601C214yesmaximal, complemented
11#45509C214yesmaximal, complemented
12#35649C211yesmaximal, characteristic, complemented
13#35649C211yesmaximal, characteristic, complemented
14#35542C212yesmaximal, complemented
15#35542C212yesmaximal, complemented
16#35251C212yesmaximal, complemented
17#35251C212yesmaximal, complemented
18#35158C212yesmaximal, complemented
19C2×#2562C211yesmaximal, characteristic, complemented
20#34736C212yesmaximal, complemented
21C23×#41C2212yescomplemented
22C2×#544C2212yescomplemented
23C2×#537C2211yescharacteristic
24C2×#537C2211yescharacteristic
25C2×#537C2212yes—
26C22×#125C2211yescharacteristic, complemented
27C2×#525C2212yes—
28C2×#525C2212yes—
29C22×C4×D4C2211yescharacteristic
30#2850C2218yescomplemented
31#2848C2214yescomplemented
32#2848C2214yescomplemented
33#2847C2214yescomplemented
34#2847C2214yescomplemented
35#2844C2214yescomplemented
36#2835C2218yescomplemented
37#2832C2218yescomplemented
38#2832C2218yescomplemented
39#2828C2214yescomplemented
40#2828C2218yescomplemented
41#2828C2214yescomplemented
42#2828C2218yescomplemented
43#2824C2218yescomplemented
44#2824C2218yescomplemented
45#2819C2214yescomplemented
46#2812C2218yescomplemented
47#2804C2214yescomplemented
48#2785C2218yescomplemented
49#2782C2214yes—
50#2782C2218yescomplemented
51#2782C2214yescomplemented
52#2782C2218yescomplemented
53#2763C2218yescomplemented
54#2763C2218yescomplemented
55#2753C2218yescomplemented
56#2753C2218yescomplemented
57#2753C2218yescomplemented
58#2753C2218yescomplemented
59#2753C2218yescomplemented
60#2753C2218yescomplemented
61#2736C2218yescomplemented
62#2733C2218yescomplemented
63#2712C2218yescomplemented
64#2684C2218yes—
65#2684C2218yescomplemented
66#2679C2214yes—
67#2670C2218yescomplemented
68#2670C2218yescomplemented
69#2639C2218yescomplemented
70#2616C2214yescomplemented
71#2616C2214yescomplemented
72#2615C2214yescomplemented
73#2615C2214yescomplemented
74#2591C2214yescomplemented
75#2591C2214yescomplemented
76#2563C2214yescomplemented
77#2563C2214yescomplemented
78#2562C2214yes—
79#2562C2214yescomplemented
80#2562C2214yescomplemented
81#2562C2214yescomplemented
82#2562C2214yescomplemented
83#2562C2214yescomplemented
84#2562C2214yescomplemented
85#2562C2214yescomplemented
86#2547C2214yescomplemented
87#2547C2214yescomplemented
88#2504C2214yescomplemented
89#2504C2214yescomplemented
90#2492C2214yescomplemented
91#2492C2214yescomplemented
92#2492C2214yescomplemented
93#2492C2214yescomplemented
94#2491C2214yescomplemented
95#2491C2214yescomplemented
96#2491C2214yescomplemented
97#2491C2214yescomplemented
98#2490C2214yescomplemented
99#2490C2214yescomplemented
100#2490C2214yescomplemented
101#2490C2214yescomplemented
102#2490C2214yescomplemented
103#2490C2214yescomplemented
104#2490C2214yescomplemented
105#2490C2214yescomplemented
106#2489C2214yescomplemented
107#2489C2214yescomplemented
108#2489C2214yescomplemented
109#2489C2214yescomplemented
110#2489C2214yescomplemented
111#2489C2214yescomplemented
112#2489C2214yescomplemented
113#2489C2214yescomplemented
114#2488C2218yescomplemented
115#2488C2218yescomplemented
116#2472C2218yescomplemented
117#2472C2218yescomplemented
118#2430C2218yescomplemented
119#2430C2218yescomplemented
120#2410C2218yescomplemented
121#2410C2218yescomplemented
122#2409C2212yes—
123#2409C2212yescomplemented
124#2409C2214yescomplemented
125#2409C2214yescomplemented
126#2408C2212yes—
127#2408C2214yescomplemented
128#2408C2214yescomplemented
129#2408C2212yescomplemented
130#2407C2212yes—
131#2407C2212yes—
132#2407C2214yescomplemented
133#2407C2214yescomplemented
134#2407C2212yescomplemented
135#2407C2214yescomplemented
136#2407C2214yescomplemented
137#2407C2212yescomplemented
138#2406C2214yescomplemented
139#2405C2214yescomplemented
140#2404C2214yes—
141#2403C2214yes—
142C2×#400C2212yescomplemented
143#2388C2214yes—
144#2388C2214yescomplemented
145C2×#394C2212yes—
146#2379C2218yescomplemented
147#2375C2218yescomplemented
148#2311C2212yescomplemented
149#2311C2212yescomplemented
150#2311C2212yescomplemented
151#2311C2212yescomplemented
152C4×#120C2214yes—
153C4×#120C2214yescomplemented
154#2297C2212yescomplemented
155#2297C2212yescomplemented
156C2×#388C2214yescomplemented
157#2280C2212yescomplemented
158C2×#380C2212yescomplemented
159C2×#380C2212yescomplemented
160#2274C2211yescharacteristic, complemented
161#2274C2211yescharacteristic, complemented
162C2×C4×C4⋊C4C2211yescharacteristic, complemented
163C22×#41—48no—
164C22×#41—48no—
165C22×#41—48no—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2314yes—
169C22×#41C2314yes—
170C22×#41C2312yes—
171C22×#41C2312yes—
172C23×Q8C2312yes—
173C23×D4C2314yes—
174C23×D4C2312yes—
175C23×D4C2311yescharacteristic
176C24×C4C2312yes—
177C24×C4C2314yes—
178#544—48no—
179#537—44no—
180#537—44no—
181#537—48no—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2314yes—
184C2×#125—44no—
185C2×#125C2314yes—
186C2×#125C2314yes—
187C2×#125C2314yes—
188C2×#125C2314yes—
189C2×#124C2318yes—
190C2×#124C2318yes—
191C2×#124C2318yes—
192#525—48no—
193#525—48no—
194C2×#123C2314yes—
195C2×#123C2314yes—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2312yes—
204C2×C22⋊Q8C2312yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2312yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2318yes—
214C2×#121C2312yes—
215C2×#121C2312yes—
216C2×#120C2318yes—
217C2×#120C2314yes—
218C2×#120C2314yes—
219C2×#120C2314yes—
220C2×#120C2314yes—
221C2×#120C2318yes—
222C2×C4×D4—44no—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×#117C2312yes—
232C2×#117C2312yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2312yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2314yes—
242C22×C42C2311yescharacteristic
243C22×C42C2312yes—
244#400C2318yes—
245#400C2314yes—
246#400C2314yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#400C2318yes—
253#400C2314yes—
254#400C2318yes—
255#400C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#395C2314yes—
267#395C2318yes—
268#395C2314yes—
269#395C2318yes—
270#394C2314yes—
271#394C2314yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2314yes—
278#394C2318yes—
279#394C2314yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2314yes—
285#394C2314yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2314yes—
290#394C2318yes—
291#394C2314yes—
292#394C2314yes—
293#394C2314yes—
294#393C2318yes—
295#393C2318yes—
296#393C2318yes—
297#393C2318yes—
298#393C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2314yes—
302#393C2318yes—
303#393C2314yes—
304#392C2314yes—
305#392C2318yes—
306#392C2314yes—
307#392C2318yes—
308#392C2314yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#392C2314yes—
313#392C2318yes—
314#392C2314yes—
315#392C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2318yes—
322#391C2318yes—
323#391C2312yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#390C2318yes—
328#390C2318yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2314yes—
336#390C2318yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2312yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2314yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2314yes—
370#386C2314yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2314yes—
379#386C2314yes—
380#386C2314yes—
381#385C2314yes—
382#385C2318yes—
383#385C2314yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2314yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#382C2318yes—
394#382C2318yes—
395#382C2314yes—
396#382C2314yes—
397#382C2318yes—
398#382C2318yes—
399#381C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2312yes—
405#380C2314yes—
406#380C2314yes—
407#380C2312yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2312yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2312yes—
418#380C2314yes—
419#380C2314yes—
420#379C2318yes—
421#379C2318yes—
422#379C2314yes—
423#379C2314yes—
424#379C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C2×#95C2312yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C25C2412yes—
443C25C2414yes—
444C2×#41—28no—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—48no—
451C2×#41—48no—
452C2×#41—48no—
453C2×#41—48no—
454C2×#41—48no—
455C2×#41—48no—
456C2×#41—44no—
457C2×#41—44no—
458C2×#41—44no—
459C2×#41—44no—
460C2×#41—44no—
461C2×#41—44no—
462C2×#41—4128no—
463C22×Q8—44no—
464C22×Q8—44no—
465C22×Q8—44no—
466C22×Q8C2412yes—
467C22×Q8C2412yes—
468C22×Q8C2418yes—
469C22×Q8C2414yes—
470C22×D4—44no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4—42no—
474C22×D4—44no—
475C22×D4—48no—
476C22×D4—48no—
477C22×D4—48no—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2411yescharacteristic
483C22×D4C2412yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2411yescharacteristic
487C22×D4C2414yes—
488C22×D4C2414yes—
489C22×D4C2418yes—
490C22×D4C2414yes—
491C22×D4C2414yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2414yes—
495C23×C4—28no—
496C23×C4—28no—
497C23×C4—28no—
498C23×C4—48no—
499C23×C4—48no—
500C23×C4—48no—
501C23×C4C2412yes—
502C23×C4C2412yes—
503C23×C4C2412yes—
504C23×C4C2412yes—
505C23×C4C2412yes—
506C23×C4C2414yes—
507C23×C4C2414yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C23×C4C2414yes—
512C23×C4C2411yescharacteristic
513C23×C4C2414yes—
514C23×C4C2414yes—
515C23×C4C2414yes—
516C23×C4C2411yescharacteristic
517C4⋊Q8—48no—
518C4⋊Q8—48no—
519#125—48no—
520#125—48no—
521#125—48no—
522#125—48no—
523#124—416no—
524#124—88no—
525#124—88no—
526#123—48no—
527#123—48no—
528C22⋊Q8—416no—
529C22⋊Q8—44no—
530C22⋊Q8—44no—
531C22⋊Q8—44no—
532C22⋊Q8—44no—
533C22⋊Q8—48no—
534C22⋊Q8—48no—
535C22⋊Q8—48no—
536C22⋊Q8—48no—
537#121—44no—
538#121—44no—
539#121—44no—
540#121—44no—
541#121—48no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—48no—
546#121—48no—
547#121—416no—
548#120—416no—
549#120—48no—
550#120—48no—
551#120—48no—
552#120—48no—
553#120—88no—
554C4×D4—44no—
555C4×D4—44no—
556C4×D4—44no—
557C4×D4—44no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—48no—
561C4×D4—48no—
562#117—28no—
563#117—28no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—28no—
567C2×C4⋊C4—42no—
568C2×C4⋊C4—44no—
569C2×C4⋊C4—44no—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2412yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2418yes—
594C2×C22⋊C4—48no—
595C2×C22⋊C4—44no—
596C2×C22⋊C4—84no—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2412yes—
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2412yes—
604C2×C22⋊C4C2412yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C42—24no—
640C2×C42—82no—
641C2×C42C2414yes—
642C2×C42C2414yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2414yes—
646C2×C42C2418yes—
647C2×C42C2418yes—
648C2×C42C2414yes—
649#95C2414yes—
650#95C2414yes—
651#95C2418yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2414yes—
656#95C2418yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674#95C2418yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678C24—24no—
679C24—24no—
680C24—24no—
681C24—24no—
682C24—28no—
683C24—42no—
684C24—44no—
685C24—44no—
686C24—44no—
687C24—42no—
688C24—42no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24C2512yes—
693C24C2514yes—
694C24C2514yes—
695C24C2512yes—
696C24C2511yescharacteristic
697#41—464no—
698#41—432no—
699#41—432no—
700#41—464no—
701#41—432no—
702#41—432no—
703C2×Q8—24no—
704C2×Q8—24no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×Q8—44no—
712C2×Q8—48no—
713C2×Q8—48no—
714C2×Q8—48no—
715C2×Q8—432no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—41no—
733C2×D4—42no—
734C2×D4—41no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—48no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—48no—
763C2×D4—44no—
764C2×D4—416no—
765C2×D4—464no—
766C2×D4—432no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—41no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—41no—
804C22×C4—42no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—464no—
811C22×C4—432no—
812C22×C4H(5,𝔽2)14yes—
813C22×C4H(5,𝔽2)18yes—
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2518yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—41no—
838C4⋊C4—42no—
839C4⋊C4—41no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—216no—
856C22⋊C4—28no—
857C22⋊C4—48no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4—42no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C42—24no—
896C42—24no—
897C42—28no—
898C42—28no—
899C42—48no—
900C42—44no—
901C42—48no—
902C42—44no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—22no—
927C23—22no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—22no—
932C23—24no—
933C23—48no—
934C23—48no—
935C23—48no—
936C23—416no—
937C23—48no—
938C23—84no—
939C23—84no—
940C23—84no—
941C23—88no—
942C23—88no—
943C23—88no—
944C23—88no—
945C23—88no—
946C23—88no—
947C23C2×H(5,𝔽2)14yes—
948C23C2×H(5,𝔽2)12yes—
949C23#58514yes—
950C23C2611yescharacteristic
951Q8—416no—
952Q8—48no—
953Q8—48no—
954Q8—168no—
955D4—44no—
956D4—48no—
957D4—44no—
958D4—416no—
959D4—416no—
960D4—416no—
961D4—416no—
962D4—416no—
963D4—48no—
964D4—48no—
965D4—88no—
966D4—88no—
967D4—88no—
968D4—88no—
969D4—164no—
970D4—164no—
971D4—168no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—21no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—28no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—44no—
1012C2×C4—44no—
1013C2×C4—416no—
1014C2×C4—416no—
1015C2×C4—416no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—48no—
1019C2×C4—48no—
1020C2×C4—48no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—84no—
1024C2×C4—84no—
1025C2×C4—88no—
1026C2×C4H(3,𝔽4)116yes—
1027C2×C4C2×H(5,𝔽2)14yes—
1028C2×C4C2×H(5,𝔽2)14yes—
1029C2×C4C2×H(5,𝔽2)14yes—
1030C22—22no—
1031C22—22no—
1032C22—24no—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—42no—
1046C22—44no—
1047C22—42no—
1048C22—44no—
1049C22—44no—
1050C22—42no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—42no—
1056C22—42no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—42no—
1062C22—816no—
1063C22—832no—
1064C22C2×H(3,𝔽4)14yes—
1065C22C22×H(5,𝔽2)11yescharacteristic
1066C22C22×H(5,𝔽2)12yes—
1067C22C2×#58512yes—
1068C22H(7,𝔽2)11yescharacteristic
1069C222−1+611yescharacteristic
1070C4—41no—
1071C4—41no—
1072C4—44no—
1073C4—42no—
1074C4—44no—
1075C4—44no—
1076C4—44no—
1077C4—42no—
1078C4—42no—
1079C4—44no—
1080C4—44no—
1081C4—48no—
1082C4—44no—
1083C4—44no—
1084C4C2×H(3,𝔽4)18yes—
1085C2—24no—
1086C2—44no—
1087C2—82no—
1088C2—84no—
1089C2—84no—
1090C2C22×H(3,𝔽4)11yescharacteristic
1091C2#6282111yescharacteristic
1092C2#6287511yescharacteristic
1093C2#6292712yes—
1094C2#6295712yes—
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. #53065C2semidirect
2. #53046C2semidirect
3. #53005C2semidirect
4. #52967C2semidirect
5. #52753C2semidirect
6. #52410C2semidirect
7. #46031C2semidirect
8. #45667C2semidirect
9. #45645C2semidirect
10. #45601C2semidirect
11. #45509C2semidirect
12. #35649C2semidirect
13. #35649C2semidirect
14. #35542C2semidirect
15. #35542C2semidirect
16. #35251C2semidirect
17. #35251C2semidirect
18. #35158C2semidirect
19. C2×#2562C2semidirect
20. #34736C2semidirect
21. C23×#41C22semidirect
22. C2×#544C22semidirect
26. C22×#125C22semidirect
30. #2850C22semidirect
31. #2848C22semidirect
32. #2848C22semidirect
33. #2847C22semidirect
34. #2847C22semidirect
35. #2844C22semidirect
36. #2835C22semidirect
37. #2832C22semidirect
38. #2832C22semidirect
39. #2828C22semidirect
40. #2828C22semidirect
41. #2828C22semidirect
42. #2828C22semidirect
43. #2824C22semidirect
44. #2824C22semidirect
45. #2819C22semidirect
46. #2812C22semidirect
47. #2804C22semidirect
48. #2785C22semidirect
50. #2782C22semidirect
51. #2782C22semidirect
52. #2782C22semidirect
53. #2763C22semidirect
54. #2763C22semidirect
55. #2753C22semidirect
56. #2753C22semidirect
57. #2753C22semidirect
58. #2753C22semidirect
59. #2753C22semidirect
60. #2753C22semidirect
61. #2736C22semidirect
62. #2733C22semidirect
63. #2712C22semidirect
65. #2684C22semidirect
67. #2670C22semidirect
68. #2670C22semidirect
69. #2639C22semidirect
70. #2616C22semidirect
71. #2616C22semidirect
72. #2615C22semidirect
73. #2615C22semidirect
74. #2591C22semidirect
75. #2591C22semidirect
76. #2563C22semidirect
77. #2563C22semidirect
79. #2562C22semidirect
80. #2562C22semidirect
81. #2562C22semidirect
82. #2562C22semidirect
83. #2562C22semidirect
84. #2562C22semidirect
85. #2562C22semidirect
86. #2547C22semidirect
87. #2547C22semidirect
88. #2504C22semidirect
89. #2504C22semidirect
90. #2492C22semidirect
91. #2492C22semidirect
92. #2492C22semidirect
93. #2492C22semidirect
94. #2491C22semidirect
95. #2491C22semidirect
96. #2491C22semidirect
97. #2491C22semidirect
98. #2490C22semidirect
99. #2490C22semidirect
100. #2490C22semidirect
101. #2490C22semidirect
102. #2490C22semidirect
103. #2490C22semidirect
104. #2490C22semidirect
105. #2490C22semidirect
106. #2489C22semidirect
107. #2489C22semidirect
108. #2489C22semidirect
109. #2489C22semidirect
110. #2489C22semidirect
111. #2489C22semidirect
112. #2489C22semidirect
113. #2489C22semidirect
114. #2488C22semidirect
115. #2488C22semidirect
116. #2472C22semidirect
117. #2472C22semidirect
118. #2430C22semidirect
119. #2430C22semidirect
120. #2410C22semidirect
121. #2410C22semidirect
123. #2409C22semidirect
124. #2409C22semidirect
125. #2409C22semidirect
127. #2408C22semidirect
128. #2408C22semidirect
129. #2408C22semidirect
132. #2407C22semidirect
133. #2407C22semidirect
134. #2407C22semidirect
135. #2407C22semidirect
136. #2407C22semidirect
137. #2407C22semidirect
138. #2406C22semidirect
139. #2405C22semidirect
142. C2×#400C22semidirect
144. #2388C22semidirect
146. #2379C22semidirect
147. #2375C22semidirect
148. #2311C22semidirect
149. #2311C22semidirect
150. #2311C22semidirect
151. #2311C22semidirect
153. C4×#120C22semidirect
154. #2297C22semidirect
155. #2297C22semidirect
156. C2×#388C22semidirect
157. #2280C22semidirect
158. C2×#380C22semidirect
159. C2×#380C22semidirect
160. #2274C22semidirect
161. #2274C22semidirect
162. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#530652
#530462
#530052
#529672
#527532
#524102
#460312
#456672
#456452
#456012
#455092
#356492
#355422
#352512
#351582
C2×#25622
#347362