Finite Group Databasebeta

← #8720556

Subgroups — #8720556

Order 512.

6088 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59406C216yesmaximal, complemented
2#58991C213yesmaximal, complemented
3#58987C211yesmaximal, characteristic, complemented
4#56344C211yesmaximal, characteristic, complemented
5#54892C216yesmaximal, complemented
6#53937C216yesmaximal, complemented
7#52912C213yesmaximal, complemented
8C2×#2736C211yesmaximal, characteristic, complemented
9#47182C213yesmaximal, complemented
10#47002C213yesmaximal, complemented
11#44241C213yesmaximal, complemented
12#43667C213yesmaximal, complemented
13#43244C213yesmaximal, complemented
14#41410C213yesmaximal, complemented
15#41204C213yesmaximal, complemented
16#40660C213yesmaximal, complemented
17#38132C216yesmaximal, complemented
18#37832C213yesmaximal, complemented
19#36078C213yesmaximal, complemented
20C22×2−1+4C2211yescharacteristic, complemented
21C2×#553C2213yescomplemented
22C2×#546C2216yescomplemented
23C2×#546C2213yescomplemented
24C22×#120C2213yes—
25#2852C2212yescomplemented
26#2846C2211yescharacteristic
27#2841C2213yescomplemented
28#2838C2216yescomplemented
29#2830C2216yescomplemented
30#2824C2213yescomplemented
31#2824C2216yescomplemented
32#2820C2213yescomplemented
33#2815C2213yescomplemented
34#2784C2216yescomplemented
35#2778C2216yescomplemented
36#2775C2216yescomplemented
37#2764C2213yescomplemented
38#2761C2216yescomplemented
39#2760C2213yescomplemented
40#2756C2216yescomplemented
41#2754C2216yescomplemented
42#2751C2216yescomplemented
43#2749C2216yescomplemented
44#2749C2216yescomplemented
45#2742C2213yescomplemented
46#2740C2216yescomplemented
47#2737C2216yescomplemented
48#2737C2216yescomplemented
49#2736C2211yescharacteristic
50#2736C2213yes—
51#2736C2213yescomplemented
52#2736C2216yescomplemented
53#2736C2213yescomplemented
54#2723C2216yescomplemented
55#2714C2216yescomplemented
56#2714C2216yescomplemented
57#2706C2216yescomplemented
58#2705C2216yescomplemented
59#2704C2216yescomplemented
60#2701C2216yescomplemented
61#2697C2216yescomplemented
62#2695C2216yescomplemented
63#2693C2213yescomplemented
64#2684C2216yescomplemented
65#2678C2216yes—
66#2678C2216yescomplemented
67#2678C2216yescomplemented
68#2678C2216yescomplemented
69#2670C2213yes—
70#2668C2213yes—
71#2668C2216yescomplemented
72#2656C2211yescharacteristic, complemented
73#2653C2216yescomplemented
74#2648C2216yescomplemented
75#2633C2213yescomplemented
76#2631C2213yescomplemented
77#2626C2213yescomplemented
78#2624C2213yescomplemented
79#2617C2213yescomplemented
80#2615C2213yescomplemented
81#2614C2213yescomplemented
82#2614C2213yescomplemented
83#2613C2213yescomplemented
84#2600C2213yescomplemented
85#2595C2216yescomplemented
86#2579C2216yescomplemented
87#2576C2216yescomplemented
88#2574C2216yescomplemented
89#2561C2213yes—
90#2560C2216yescomplemented
91#2558C2216yescomplemented
92#2543C2216yescomplemented
93#2539C2213yes—
94#2535C2213yescomplemented
95#2534C2213yes—
96#2534C2216yescomplemented
97#2534C2216yescomplemented
98#2523C2213yescomplemented
99#2521C2216yescomplemented
100#2510C2216yescomplemented
101#2504C2213yescomplemented
102#2493C2216yescomplemented
103#2483C2213yescomplemented
104#2482C2213yescomplemented
105#2480C2216yescomplemented
106#2476C2216yescomplemented
107#2472C2216yescomplemented
108#2464C2216yescomplemented
109#2459C2216yescomplemented
110#2457C2216yescomplemented
111#2456C2216yescomplemented
112#2444C2216yescomplemented
113#2437C2213yes—
114#2436C2213yescomplemented
115#2436C2216yescomplemented
116#2430C2213yescomplemented
117#2430C2216yescomplemented
118#2430C2213yescomplemented
119#2430C2216yescomplemented
120#2425C2216yescomplemented
121#2424C2216yes—
122#2424C2216yescomplemented
123#2419C2216yescomplemented
124#2419C2216yescomplemented
125#2418C2216yescomplemented
126#2418C2216yescomplemented
127#2412C2216yescomplemented
128#2412C2213yescomplemented
129#2410C2213yes—
130#2410C2216yescomplemented
131#2410C2216yescomplemented
132#2409C2213yescomplemented
133#2409C2216yescomplemented
134#2408C2216yescomplemented
135#2405C2213yes—
136#2404C2213yes—
137#2404C2216yescomplemented
138#2404C2213yescomplemented
139#2404C2216yescomplemented
140#2403C2213yes—
141C2×#397C2213yescomplemented
142#2388C2213yescomplemented
143C2×#393C2213yescomplemented
144C2×#393C2213yescomplemented
145#2359C2216yescomplemented
146#2358C2216yescomplemented
147#2358C2216yescomplemented
148#2339C2216yescomplemented
149#2339C2213yescomplemented
150D4×C22⋊C4C2216yes—
151D4×C22⋊C4C2213yescomplemented
152#2333C2216yescomplemented
153#2321C2213yescomplemented
154#2318C2213yescomplemented
155#2318C2216yescomplemented
156#2308C2213yescomplemented
157C4×#121C2216yescomplemented
158C2×#388C2216yescomplemented
159C2×#379C2213yes—
160C26C2311yescharacteristic
161C2×2−1+4—412no—
162C22×#41C2313yes—
163C22×#41C2313yes—
164C22×#41C2313yescomplemented
165C22×#41C2311yescharacteristic, complemented
166C23×Q8C2311yescharacteristic
167C23×Q8C2313yescomplemented
168C23×Q8C2311yescharacteristic, complemented
169C23×D4C2313yes—
170C23×D4C2313yes—
171C23×D4C2313yes—
172#553—412no—
173#546—412no—
174#546—424no—
175C2×#126C2316yescomplemented
176C2×#126C2312yescomplemented
177C2×#125C2313yescomplemented
178C2×#124C2313yes—
179C2×#124C2316yes—
180C2×#123C2316yes—
181C2×#123C2316yes—
182C2×#123C2313yes—
183C2×#123C2313yes—
184C2×#123C2316yes—
185C2×#123C2313yes—
186C2×#123C2316yescomplemented
187C2×C22⋊Q8C2316yes—
188C2×C22⋊Q8C2313yes—
189C2×#121C2316yes—
190C2×#121C2316yes—
191C2×#121C2316yes—
192C2×#121C2313yes—
193C2×#121C2313yes—
194C2×#121C2313yes—
195C2×#121C2313yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2313yescomplemented
199C2×#120—412no—
200C2×#120C2316yes—
201C2×#120C2313yes—
202C2×#120C2313yes—
203C2×#120C2313yes—
204C2×#120C2316yes—
205C2×#120C2316yes—
206C2×#120C2316yes—
207C2×#120C2316yes—
208C2×#120C2316yes—
209C2×#120C2311yescharacteristic
210C2×C4×D4C2313yes—
211C2×C4×D4C2316yes—
212C2×C4×D4C2313yes—
213C2×C4×D4C2316yes—
214C2×C4×D4C2316yes—
215C2×C4×D4C2316yes—
216C2×C4×D4C2313yescomplemented
217C2×C4×D4C2316yescomplemented
218C2×#117C2313yescomplemented
219C22×C4⋊C4C2313yes—
220C22×C22⋊C4C2313yes—
221C22×C22⋊C4C2313yes—
222C22×C22⋊C4C2313yes—
223C22×C22⋊C4C2316yes—
224C22×C22⋊C4C2313yes—
225C22×C22⋊C4C2316yes—
226C22×C22⋊C4C2313yes—
227C22×C22⋊C4C2316yes—
228C22×C22⋊C4C2313yes—
229C22×C22⋊C4C2313yes—
230C22×C42C2312yes—
231#401C2316yescomplemented
232#400C2316yescomplemented
233#400C2316yescomplemented
234#400C2316yescomplemented
235#400C2316yescomplemented
236#399C2313yes—
237#399C2313yes—
238#399C2316yes—
239#399C2313yescomplemented
240#399C2311yescharacteristic, complemented
241#398C2316yescomplemented
242#398C2316yescomplemented
243#398C2316yescomplemented
244#398C2316yescomplemented
245#397C2316yes—
246#397C2313yes—
247#397C2316yes—
248#397C2316yes—
249#397C2316yes—
250#397C2316yes—
251#397C2316yes—
252#397C2313yes—
253#397C2313yes—
254#397C2313yes—
255#397C2316yes—
256#397C2316yes—
257#397C2313yescomplemented
258#397C2316yescomplemented
259#397C2316yescomplemented
260#397C2316yescomplemented
261#397C2313yescomplemented
262#397C2313yescomplemented
263#397C2313yescomplemented
264#396C2316yes—
265#396C2316yes—
266#396C2316yes—
267#396C2316yes—
268#396C2316yescomplemented
269#396C2316yescomplemented
270#396C2316yescomplemented
271#395C2316yescomplemented
272#395C2316yescomplemented
273#395C2313yescomplemented
274#395C2313yescomplemented
275#395C2313yescomplemented
276#394C2316yes—
277#394C2316yes—
278#394C2316yes—
279#394C2316yes—
280#394C2316yes—
281#394C2316yes—
282#394C2316yes—
283#394C2316yes—
284#394C2316yes—
285#394C2316yes—
286#394C2316yes—
287#394C2316yes—
288#394C2316yes—
289#394C2316yescomplemented
290#394C2316yescomplemented
291#394C2313yescomplemented
292#393C2316yes—
293#393C2316yes—
294#393C2313yes—
295#393C2313yes—
296#393C2316yes—
297#393C2313yes—
298#393C2313yes—
299#393C2313yes—
300#393C2316yes—
301#393C2313yes—
302#393C2313yescomplemented
303#393C2313yescomplemented
304#393C2313yescomplemented
305#393C2316yescomplemented
306#393C2316yescomplemented
307#392C2313yes—
308#392C2313yes—
309#392C2313yes—
310#392C2316yes—
311#392C2316yes—
312#392C2313yes—
313#392C2316yes—
314#392C2316yes—
315#392C2316yes—
316#392C2316yes—
317#392C2313yescomplemented
318#392C2316yescomplemented
319#392C2311yescharacteristic, complemented
320#392C2313yescomplemented
321#391C2316yescomplemented
322#391C2316yescomplemented
323#391C2316yescomplemented
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yescomplemented
331#390C2316yescomplemented
332#389C2316yescomplemented
333#389C2316yescomplemented
334#388C2316yes—
335#388C2316yes—
336#388C2316yes—
337#388C2316yes—
338#388C2316yes—
339#388C2316yes—
340#388C2316yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C2316yes—
345#388C2316yes—
346#388C2316yes—
347#388C2316yes—
348#388C2316yes—
349#388C2316yes—
350#388C2316yescomplemented
351#388C2316yescomplemented
352#388C2316yescomplemented
353#388C2316yescomplemented
354#388C2316yescomplemented
355#387C2316yescomplemented
356#387C2316yescomplemented
357#387C2316yescomplemented
358#387C2316yescomplemented
359#387C2316yescomplemented
360#387C2316yescomplemented
361#387C2316yescomplemented
362#387C2316yescomplemented
363#387C2316yescomplemented
364#386C2316yes—
365#386C2316yes—
366#386C2316yes—
367#386C2316yes—
368#386C2316yes—
369#386C2316yes—
370#386C2316yes—
371#386C2316yes—
372#386C2316yes—
373#386C2316yes—
374#386C2316yes—
375#386C2313yes—
376#386C2316yes—
377#386C2316yes—
378#386C2316yes—
379#386C2316yes—
380#386C2316yes—
381#386C2316yes—
382#386C2316yes—
383#386C2316yes—
384#386C2316yes—
385#386C2316yes—
386#386C2316yescomplemented
387#386C2316yescomplemented
388#386C2316yescomplemented
389#386C2316yescomplemented
390#386C2316yescomplemented
391#386C2316yescomplemented
392#386C2316yescomplemented
393#385C2313yes—
394#385C2316yes—
395#385C2313yes—
396#385C2313yes—
397#385C2316yes—
398#385C2316yes—
399#385C2316yes—
400#385C2316yescomplemented
401#385C2316yescomplemented
402#385C2316yescomplemented
403#385C2316yescomplemented
404#385C2316yescomplemented
405#385C2316yescomplemented
406#383C2313yescomplemented
407#383C2316yescomplemented
408#383C2312yescomplemented
409#382C2313yescomplemented
410#382C2316yescomplemented
411#381C2313yes—
412#381C2313yes—
413#381C2313yes—
414#381C2313yes—
415#381C2316yes—
416#381C2313yescomplemented
417#381C2316yescomplemented
418#381C2316yescomplemented
419#381C2313yescomplemented
420#380C2316yes—
421#380C2316yes—
422#380C2316yes—
423#380C2313yes—
424#380C2313yescomplemented
425#380C2316yescomplemented
426#380C2313yescomplemented
427#380C2316yescomplemented
428#379C2311yescharacteristic
429#379C2313yes—
430#379C2313yes—
431#379C2313yes—
432#379C2313yes—
433#379C2316yes—
434#379C2313yes—
435#379C2313yes—
436#379C2313yes—
437#379C2316yes—
438#379C2316yes—
439C4×C4⋊C4C2316yescomplemented
440C4×C22⋊C4C2313yes—
441C4×C22⋊C4C2313yes—
442C4×C22⋊C4C2316yes—
443C4×C22⋊C4C2316yescomplemented
444C4×C22⋊C4C2316yescomplemented
445C4×C22⋊C4C2313yescomplemented
446C4×C22⋊C4C2316yescomplemented
447C2×#95C2311yescharacteristic
448C2×#95C2316yes—
449C2×#95C2313yes—
450C2×#95C2313yescomplemented
451C2×#95C2316yescomplemented
452C25—46no—
453C25—46no—
454C25—81no—
455C25C2413yes—
456C25C2411yescharacteristic
457C25C2413yes—
458C25C2413yes—
4592−1+4—464no—
460C2×#41—212no—
461C2×#41—224no—
462C2×#41—46no—
463C2×#41—46no—
464C2×#41—412no—
465C2×#41—46no—
466C2×#41—412no—
467C22×Q8—46no—
468C22×Q8—46no—
469C22×Q8—412no—
470C22×Q8—46no—
471C22×Q8C2413yes—
472C22×Q8C2413yes—
473C22×Q8C2413yes—
474C22×Q8C2411yescharacteristic
475C22×D4—212no—
476C22×D4—46no—
477C22×D4—46no—
478C22×D4—46no—
479C22×D4—412no—
480C22×D4—412no—
481C22×D4—83no—
482C22×D4C2413yes—
483C22×D4C2411yescharacteristic
484C22×D4C2416yes—
485C22×D4C2413yes—
486C22×D4C2413yes—
487C22×D4C2413yes—
488C22×D4C2416yes—
489C22×D4C2416yes—
490C22×D4C2413yes—
491C22×D4C2413yes—
492C22×D4C2416yes—
493C22×D4C2413yes—
494C22×D4C2413yes—
495C22×D4C2413yes—
496C22×D4C2416yes—
497C22×D4C2413yes—
498C23×C4C2413yes—
499C23×C4C2416yes—
500C23×C4C2416yes—
501C23×C4C2413yes—
502C23×C4C2413yes—
503C23×C4C2413yes—
504C23×C4C2413yes—
505C23×C4C2413yes—
506C23×C4C2413yes—
507C23×C4C2413yes—
508C23×C4C2416yes—
509C23×C4C2416yes—
510#126—412no—
511#126—82no—
512#125—46no—
513#124—46no—
514#124—412no—
515#123—412no—
516#123—412no—
517#123—412no—
518#123—412no—
519#123—46no—
520#123—46no—
521#123—83no—
522C22⋊Q8—412no—
523C22⋊Q8—46no—
524#121—224no—
525#121—412no—
526#121—412no—
527#121—46no—
528#121—412no—
529#121—46no—
530#121—46no—
531#121—46no—
532#121—46no—
533#121—86no—
534#120—224no—
535#120—412no—
536#120—412no—
537#120—412no—
538#120—46no—
539#120—46no—
540#120—46no—
541#120—412no—
542#120—412no—
543#120—81no—
544C4×D4—212no—
545C4×D4—46no—
546C4×D4—46no—
547C4×D4—412no—
548C4×D4—412no—
549C4×D4—412no—
550C4×D4—412no—
551C4×D4—86no—
552#117—46no—
553C2×C4⋊C4—46no—
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2416yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2416yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2413yes—
568C2×C4⋊C4C2413yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2416yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2416yes—
573C2×C22⋊C4—46no—
574C2×C22⋊C4—46no—
575C2×C22⋊C4—412no—
576C2×C22⋊C4—412no—
577C2×C22⋊C4—46no—
578C2×C22⋊C4—46no—
579C2×C22⋊C4—412no—
580C2×C22⋊C4—46no—
581C2×C22⋊C4—83no—
582C2×C22⋊C4—83no—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C2416yes—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2413yes—
591C2×C22⋊C4C2413yes—
592C2×C22⋊C4C2413yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C2413yes—
595C2×C22⋊C4C2413yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2416yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2413yes—
602C2×C22⋊C4C2413yes—
603C2×C22⋊C4C2413yes—
604C2×C22⋊C4C2416yes—
605C2×C22⋊C4C2413yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2413yes—
608C2×C22⋊C4C2416yes—
609C2×C22⋊C4C2413yes—
610C2×C22⋊C4C2413yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2413yes—
613C2×C22⋊C4C2416yes—
614C2×C22⋊C4C2416yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2413yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2416yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C2416yes—
627C2×C22⋊C4C2416yes—
628C2×C22⋊C4C2416yes—
629C2×C22⋊C4C2416yes—
630C2×C42—82no—
631C2×C42C2413yes—
632C2×C42C2416yes—
633C2×C42C2416yes—
634C2×C42C2416yes—
635C2×C42C2416yes—
636C2×C42C2412yes—
637#95C2413yes—
638#95C2416yes—
639#95C2411yescharacteristic
640#95C2416yes—
641#95C2413yes—
642#95C2416yes—
643#95C2413yes—
644#95C2416yes—
645#95C2416yes—
646#95C2416yes—
647#95C2413yes—
648#95C2416yes—
649#95C2416yes—
650#95C2416yes—
651#95C2413yes—
652#95C2416yes—
653#95C2413yes—
654#95C2416yes—
655#95C2416yes—
656#95C2416yes—
657#95C2416yes—
658#95C2416yes—
659#95C2416yes—
660#95C2413yes—
661#95C2416yes—
662#95C2416yes—
663#95C2416yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668#95C2416yes—
669C24—26no—
670C24—26no—
671C24—212no—
672C24—26no—
673C24—26no—
674C24—26no—
675C24—26no—
676C24—43no—
677C24—43no—
678C24—43no—
679C24—43no—
680C24—46no—
681C24—43no—
682C24—46no—
683C24—41no—
684C24—46no—
685C24—46no—
686C24—46no—
687C24—824no—
688C24—88no—
689C24—824no—
690C24C2513yes—
691C24C2513yes—
692C24C2511yescharacteristic
693C24C2513yes—
694C24C2513yes—
695C24C2511yescharacteristic
696#41—448no—
697#41—448no—
698#41—448no—
699#41—416no—
700C2×Q8—212no—
701C2×Q8—26no—
702C2×Q8—43no—
703C2×Q8—46no—
704C2×Q8—43no—
705C2×Q8—43no—
706C2×Q8—46no—
707C2×Q8—448no—
708C2×Q8—416no—
709C2×Q8—416no—
710C2×D4—212no—
711C2×D4—212no—
712C2×D4—212no—
713C2×D4—26no—
714C2×D4—212no—
715C2×D4—26no—
716C2×D4—26no—
717C2×D4—212no—
718C2×D4—212no—
719C2×D4—26no—
720C2×D4—212no—
721C2×D4—26no—
722C2×D4—212no—
723C2×D4—26no—
724C2×D4—46no—
725C2×D4—43no—
726C2×D4—46no—
727C2×D4—43no—
728C2×D4—43no—
729C2×D4—46no—
730C2×D4—46no—
731C2×D4—46no—
732C2×D4—46no—
733C2×D4—46no—
734C2×D4—43no—
735C2×D4—46no—
736C2×D4—46no—
737C2×D4—46no—
738C2×D4—46no—
739C2×D4—46no—
740C2×D4—46no—
741C2×D4—46no—
742C2×D4—43no—
743C2×D4—43no—
744C2×D4—46no—
745C2×D4—46no—
746C2×D4—824no—
747C2×D4—824no—
748C2×D4—824no—
749C2×D4H(5,𝔽2)112yes—
750C22×C4—26no—
751C22×C4—26no—
752C22×C4—212no—
753C22×C4—212no—
754C22×C4—26no—
755C22×C4—212no—
756C22×C4—26no—
757C22×C4—26no—
758C22×C4—212no—
759C22×C4—26no—
760C22×C4—26no—
761C22×C4—46no—
762C22×C4—46no—
763C22×C4—46no—
764C22×C4—46no—
765C22×C4—43no—
766C22×C4—43no—
767C22×C4—46no—
768C22×C4—46no—
769C22×C4—46no—
770C22×C4—46no—
771C22×C4—43no—
772C22×C4—46no—
773C22×C4—46no—
774C22×C4—46no—
775C22×C4—46no—
776C22×C4—46no—
777C22×C4—46no—
778C22×C4—46no—
779C22×C4C2516yes—
780C22×C4C2513yes—
781C22×C4C2516yes—
782C22×C4C2513yes—
783C22×C4C2513yes—
784C22×C4C2511yescharacteristic
785C22×C4C2516yes—
786C22×C4C2513yes—
787C22×C4C2513yes—
788C22×C4C2513yes—
789C22×C4C2516yes—
790C22×C4C2513yes—
791C22×C4C2513yes—
792C4⋊C4—26no—
793C4⋊C4—212no—
794C4⋊C4—43no—
795C4⋊C4—43no—
796C4⋊C4—46no—
797C4⋊C4—43no—
798C4⋊C4—46no—
799C4⋊C4—46no—
800C4⋊C4—43no—
801C4⋊C4—46no—
802C4⋊C4—46no—
803C4⋊C4—46no—
804C4⋊C4—46no—
805C4⋊C4—43no—
806C4⋊C4—46no—
807C4⋊C4—43no—
808C4⋊C4—46no—
809C4⋊C4—46no—
810C4⋊C4—46no—
811C22⋊C4—212no—
812C22⋊C4—212no—
813C22⋊C4—26no—
814C22⋊C4—26no—
815C22⋊C4—212no—
816C22⋊C4—212no—
817C22⋊C4—26no—
818C22⋊C4—212no—
819C22⋊C4—212no—
820C22⋊C4—212no—
821C22⋊C4—43no—
822C22⋊C4—46no—
823C22⋊C4—46no—
824C22⋊C4—46no—
825C22⋊C4—46no—
826C22⋊C4—46no—
827C22⋊C4—46no—
828C22⋊C4—43no—
829C22⋊C4—43no—
830C22⋊C4—46no—
831C22⋊C4—43no—
832C22⋊C4—46no—
833C22⋊C4—43no—
834C22⋊C4—46no—
835C22⋊C4—43no—
836C22⋊C4—43no—
837C22⋊C4—46no—
838C22⋊C4—43no—
839C22⋊C4—46no—
840C22⋊C4—43no—
841C22⋊C4—46no—
842C22⋊C4—43no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C22⋊C4—43no—
846C22⋊C4—46no—
847C22⋊C4—46no—
848C22⋊C4—46no—
849C22⋊C4—46no—
850C22⋊C4—46no—
851C22⋊C4—43no—
852C22⋊C4—43no—
853C22⋊C4—46no—
854C22⋊C4—46no—
855C22⋊C4—46no—
856C22⋊C4—46no—
857C22⋊C4—46no—
858C42—26no—
859C42—46no—
860C42—42no—
861C42—46no—
862C42—46no—
863C42—46no—
864C23—23no—
865C23—21no—
866C23—26no—
867C23—23no—
868C23—26no—
869C23—26no—
870C23—23no—
871C23—26no—
872C23—23no—
873C23—23no—
874C23—26no—
875C23—26no—
876C23—23no—
877C23—23no—
878C23—23no—
879C23—23no—
880C23—23no—
881C23—23no—
882C23—26no—
883C23—26no—
884C23—21no—
885C23—23no—
886C23—23no—
887C23—412no—
888C23—424no—
889C23—412no—
890C23—412no—
891C23—412no—
892C23—412no—
893C23—86no—
894C23—812no—
895C23—812no—
896C23—86no—
897C23—86no—
898C23—86no—
899C23—812no—
900C23—86no—
901C23—812no—
902C23—82no—
903C23—86no—
904C23—864no—
905C23—166no—
906C23C2×H(5,𝔽2)16yes—
907C23C2×H(5,𝔽2)16yes—
908C23#58516yes—
909C23C2611yescharacteristic
910Q8—412no—
911Q8—412no—
912Q8—412no—
913Q8—44no—
914D4—224no—
915D4—424no—
916D4—412no—
917D4—412no—
918D4—412no—
919D4—44no—
920D4—86no—
921D4—812no—
922D4—86no—
923D4—812no—
924D4—812no—
925D4—86no—
926D4—86no—
927D4—812no—
928D4—163no—
929D4—163no—
930C2×C4—26no—
931C2×C4—23no—
932C2×C4—23no—
933C2×C4—26no—
934C2×C4—23no—
935C2×C4—26no—
936C2×C4—26no—
937C2×C4—26no—
938C2×C4—23no—
939C2×C4—23no—
940C2×C4—26no—
941C2×C4—23no—
942C2×C4—26no—
943C2×C4—23no—
944C2×C4—26no—
945C2×C4—23no—
946C2×C4—26no—
947C2×C4—26no—
948C2×C4—26no—
949C2×C4—26no—
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—26no—
953C2×C4—26no—
954C2×C4—23no—
955C2×C4—26no—
956C2×C4—26no—
957C2×C4—23no—
958C2×C4—26no—
959C2×C4—424no—
960C2×C4—412no—
961C2×C4—412no—
962C2×C4—412no—
963C2×C4—86no—
964C2×C4—86no—
965C2×C4—86no—
966C2×C4—812no—
967C2×C4—86no—
968C2×C4—86no—
969C2×C4—166no—
970C2×C4—166no—
971C2×C4C2×H(5,𝔽2)16yes—
972C22—26no—
973C22—26no—
974C22—26no—
975C22—212no—
976C22—26no—
977C22—26no—
978C22—26no—
979C22—43no—
980C22—46no—
981C22—46no—
982C22—46no—
983C22—43no—
984C22—43no—
985C22—46no—
986C22—43no—
987C22—43no—
988C22—46no—
989C22—46no—
990C22—43no—
991C22—46no—
992C22—43no—
993C22—43no—
994C22—41no—
995C22—43no—
996C22—43no—
997C22—824no—
998C22—88no—
999C22—824no—
1000C22—1612no—
1001C22#353214yes—
1002C22C22×H(5,𝔽2)13yes—
1003C22C2×#58513yes—
1004C22H(7,𝔽2)11yescharacteristic
1005C4—26no—
1006C4—43no—
1007C4—46no—
1008C4—43no—
1009C4—43no—
1010C4—46no—
1011C4—46no—
1012C4—46no—
1013C4—43no—
1014C4—43no—
1015C4—43no—
1016C4—41no—
1017C4—43no—
1018C2—24no—
1019C2—46no—
1020C2—46no—
1021C2—81no—
1022C2—83no—
1023C2—83no—
1024C2C2×#353211yescharacteristic
1025C2#6291813yes—
1026C2#6301713yes—
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. #59406C2semidirect
2. #58991C2semidirect
3. #58987C2semidirect
4. #56344C2semidirect
5. #54892C2semidirect
6. #53937C2semidirect
7. #52912C2semidirect
8. C2×#2736C2semidirect
9. #47182C2semidirect
10. #47002C2semidirect
11. #44241C2semidirect
12. #43667C2semidirect
13. #43244C2semidirect
14. #41410C2semidirect
15. #41204C2semidirect
16. #40660C2semidirect
17. #38132C2semidirect
18. #37832C2semidirect
19. #36078C2semidirect
20. C22×2−1+4C22semidirect
21. C2×#553C22semidirect
22. C2×#546C22semidirect
23. C2×#546C22semidirect
25. #2852C22semidirect
27. #2841C22semidirect
28. #2838C22semidirect
29. #2830C22semidirect
30. #2824C22semidirect
31. #2824C22semidirect
32. #2820C22semidirect
33. #2815C22semidirect
34. #2784C22semidirect
35. #2778C22semidirect
36. #2775C22semidirect
37. #2764C22semidirect
38. #2761C22semidirect
39. #2760C22semidirect
40. #2756C22semidirect
41. #2754C22semidirect
42. #2751C22semidirect
43. #2749C22semidirect
44. #2749C22semidirect
45. #2742C22semidirect
46. #2740C22semidirect
47. #2737C22semidirect
48. #2737C22semidirect
51. #2736C22semidirect
52. #2736C22semidirect
53. #2736C22semidirect
54. #2723C22semidirect
55. #2714C22semidirect
56. #2714C22semidirect
57. #2706C22semidirect
58. #2705C22semidirect
59. #2704C22semidirect
60. #2701C22semidirect
61. #2697C22semidirect
62. #2695C22semidirect
63. #2693C22semidirect
64. #2684C22semidirect
66. #2678C22semidirect
67. #2678C22semidirect
68. #2678C22semidirect
71. #2668C22semidirect
72. #2656C22semidirect
73. #2653C22semidirect
74. #2648C22semidirect
75. #2633C22semidirect
76. #2631C22semidirect
77. #2626C22semidirect
78. #2624C22semidirect
79. #2617C22semidirect
80. #2615C22semidirect
81. #2614C22semidirect
82. #2614C22semidirect
83. #2613C22semidirect
84. #2600C22semidirect
85. #2595C22semidirect
86. #2579C22semidirect
87. #2576C22semidirect
88. #2574C22semidirect
90. #2560C22semidirect
91. #2558C22semidirect
92. #2543C22semidirect
94. #2535C22semidirect
96. #2534C22semidirect
97. #2534C22semidirect
98. #2523C22semidirect
99. #2521C22semidirect
100. #2510C22semidirect
101. #2504C22semidirect
102. #2493C22semidirect
103. #2483C22semidirect
104. #2482C22semidirect
105. #2480C22semidirect
106. #2476C22semidirect
107. #2472C22semidirect
108. #2464C22semidirect
109. #2459C22semidirect
110. #2457C22semidirect
111. #2456C22semidirect
112. #2444C22semidirect
114. #2436C22semidirect
115. #2436C22semidirect
116. #2430C22semidirect
117. #2430C22semidirect
118. #2430C22semidirect
119. #2430C22semidirect
120. #2425C22semidirect
122. #2424C22semidirect
123. #2419C22semidirect
124. #2419C22semidirect
125. #2418C22semidirect
126. #2418C22semidirect
127. #2412C22semidirect
128. #2412C22semidirect
130. #2410C22semidirect
131. #2410C22semidirect
132. #2409C22semidirect
133. #2409C22semidirect
134. #2408C22semidirect
137. #2404C22semidirect
138. #2404C22semidirect
139. #2404C22semidirect
141. C2×#397C22semidirect
142. #2388C22semidirect
143. C2×#393C22semidirect
144. C2×#393C22semidirect
145. #2359C22semidirect
146. #2358C22semidirect
147. #2358C22semidirect
148. #2339C22semidirect
149. #2339C22semidirect
151. D4×C22⋊C4C22semidirect
152. #2333C22semidirect
153. #2321C22semidirect
154. #2318C22semidirect
155. #2318C22semidirect
156. #2308C22semidirect
157. C4×#121C22semidirect
158. C2×#388C22semidirect
164. C22×#41C23semidirect
165. C22×#41C23semidirect
167. C23×Q8C23semidirect
168. C23×Q8C23semidirect
175. C2×#126C23semidirect
176. C2×#126C23semidirect
177. C2×#125C23semidirect
186. C2×#123C23semidirect
198. C2×#121C23semidirect
216. C2×C4×D4C23semidirect
217. C2×C4×D4C23semidirect
218. C2×#117C23semidirect
231. #401C23semidirect
232. #400C23semidirect
233. #400C23semidirect
234. #400C23semidirect
235. #400C23semidirect
239. #399C23semidirect
240. #399C23semidirect
241. #398C23semidirect
242. #398C23semidirect
243. #398C23semidirect
244. #398C23semidirect
257. #397C23semidirect
258. #397C23semidirect
259. #397C23semidirect
260. #397C23semidirect
261. #397C23semidirect
262. #397C23semidirect
263. #397C23semidirect
268. #396C23semidirect
269. #396C23semidirect
270. #396C23semidirect
271. #395C23semidirect
272. #395C23semidirect
273. #395C23semidirect
274. #395C23semidirect
275. #395C23semidirect
289. #394C23semidirect
290. #394C23semidirect
291. #394C23semidirect
302. #393C23semidirect
303. #393C23semidirect
304. #393C23semidirect
305. #393C23semidirect
306. #393C23semidirect
317. #392C23semidirect
318. #392C23semidirect
319. #392C23semidirect
320. #392C23semidirect
321. #391C23semidirect
322. #391C23semidirect
323. #391C23semidirect
330. #390C23semidirect
331. #390C23semidirect
332. #389C23semidirect
333. #389C23semidirect
350. #388C23semidirect
351. #388C23semidirect
352. #388C23semidirect
353. #388C23semidirect
354. #388C23semidirect
355. #387C23semidirect
356. #387C23semidirect
357. #387C23semidirect
358. #387C23semidirect
359. #387C23semidirect
360. #387C23semidirect
361. #387C23semidirect
362. #387C23semidirect
363. #387C23semidirect
386. #386C23semidirect
387. #386C23semidirect
388. #386C23semidirect
389. #386C23semidirect
390. #386C23semidirect
391. #386C23semidirect
392. #386C23semidirect
400. #385C23semidirect
401. #385C23semidirect
402. #385C23semidirect
403. #385C23semidirect
404. #385C23semidirect
405. #385C23semidirect
406. #383C23semidirect
407. #383C23semidirect
408. #383C23semidirect
409. #382C23semidirect
410. #382C23semidirect
416. #381C23semidirect
417. #381C23semidirect
418. #381C23semidirect
419. #381C23semidirect
424. #380C23semidirect
425. #380C23semidirect
426. #380C23semidirect
427. #380C23semidirect
439. C4×C4⋊C4C23semidirect
443. C4×C22⋊C4C23semidirect
444. C4×C22⋊C4C23semidirect
445. C4×C22⋊C4C23semidirect
446. C4×C22⋊C4C23semidirect
450. C2×#95C23semidirect
451. C2×#95C23semidirect

Maximal subgroups

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

subgroupindex
#594062
#589912
#589872
#563442
#548922
#539372
#529122
C2×#27362
#471822
#470022
#442412
#436672
#432442
#414102
#412042
#406602
#381322
#378322
#360782