Finite Group Databasebeta

← #7643464

Subgroups — #7643464

Order 512.

5796 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40009C214yesmaximal, complemented
2#40008C214yesmaximal, complemented
3#39189C214yesmaximal, complemented
4#38974C214yesmaximal, complemented
5#38488C218yesmaximal, complemented
6#38120C218yesmaximal, complemented
7#37431C214yesmaximal, complemented
8#37393C212yesmaximal, complemented
9#37317C212yesmaximal, complemented
10#36624C211yesmaximal, characteristic, complemented
11C2×#2851C211yesmaximal, characteristic, complemented
12#35649C212yesmaximal, complemented
13#35618C212yesmaximal, complemented
14#35564C212yesmaximal, complemented
15#35545C212yesmaximal, complemented
16#35251C212yesmaximal, complemented
17#35086C212yesmaximal, complemented
18#35081C212yesmaximal, complemented
19#35023C214yesmaximal, complemented
20#34202C212yesmaximal, complemented
21C2×#2297C211yesmaximal, characteristic, complemented
22C23×#41C2211yescharacteristic
23C2×#537C2212yes—
24C2×#537C2212yes—
25C2×#532C2211yescharacteristic, complemented
26C22×#125C2211yescharacteristic, complemented
27C2×#525C2212yes—
28C2×#520C2212yescomplemented
29C22×#117C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic, complemented
33#2856C2211yescharacteristic
34#2856C2211yescharacteristic, complemented
35#2854C2214yescomplemented
36#2851C2212yes—
37#2851C2214yes—
38#2851C2212yes—
39#2851C2212yescomplemented
40#2851C2212yescomplemented
41#2851C2214yescomplemented
42#2850C2212yes—
43#2850C2212yescomplemented
44#2848C2214yes—
45#2847C2214yes—
46#2847C2214yes—
47#2803C2218yescomplemented
48#2800C2218yescomplemented
49#2797C2218yescomplemented
50#2797C2218yescomplemented
51#2781C2218yescomplemented
52#2779C2218yescomplemented
53#2778C2218yescomplemented
54#2775C2218yescomplemented
55#2774C2218yescomplemented
56#2753C2218yescomplemented
57#2751C2218yescomplemented
58#2749C2218yescomplemented
59#2745C2218yescomplemented
60#2714C2218yescomplemented
61#2714C2218yescomplemented
62#2688C2218yescomplemented
63#2652C2218yescomplemented
64#2648C2218yescomplemented
65#2643C2218yes—
66#2622C2218yes—
67#2616C2214yes—
68#2615C2214yes—
69#2597C2218yescomplemented
70#2595C2218yescomplemented
71#2591C2218yescomplemented
72#2578C2218yescomplemented
73#2576C2218yescomplemented
74#2543C2218yescomplemented
75#2514C2214yescomplemented
76#2513C2214yescomplemented
77#2512C2214yescomplemented
78#2511C2214yescomplemented
79#2510C2218yescomplemented
80#2505C2218yes—
81#2504C2214yescomplemented
82#2504C2218yescomplemented
83#2503C2214yescomplemented
84#2500C2214yescomplemented
85#2499C2214yescomplemented
86#2497C2214yescomplemented
87#2496C2214yescomplemented
88#2495C2214yescomplemented
89#2494C2214yescomplemented
90#2490C2214yescomplemented
91#2490C2214yescomplemented
92#2490C2214yescomplemented
93#2490C2214yescomplemented
94#2489C2214yescomplemented
95#2489C2214yescomplemented
96#2489C2214yescomplemented
97#2489C2214yescomplemented
98#2481C2218yescomplemented
99#2480C2218yes—
100#2444C2218yes—
101#2444C2218yescomplemented
102#2444C2218yescomplemented
103#2430C2218yes—
104#2429C2214yescomplemented
105#2428C2214yescomplemented
106#2427C2214yescomplemented
107#2426C2214yescomplemented
108#2424C2218yes—
109#2421C2214yescomplemented
110#2421C2214yescomplemented
111#2420C2214yescomplemented
112#2420C2214yescomplemented
113#2417C2214yescomplemented
114#2416C2214yescomplemented
115#2416C2218yescomplemented
116#2415C2214yescomplemented
117#2414C2214yescomplemented
118#2410C2218yes—
119#2409C2214yes—
120#2408C2214yes—
121#2407C2214yes—
122#2407C2214yes—
123#2359C2218yescomplemented
124#2358C2218yes—
125#2354C2214yescomplemented
126#2352C2214yes—
127#2352C2214yescomplemented
128D4×C4⋊C4C2214yes—
129#2334C2218yescomplemented
130#2333C2218yescomplemented
131#2324C2214yescomplemented
132#2323C2214yescomplemented
133#2321C2218yes—
134#2318C2218yes—
135#2317C2212yescomplemented
136#2311C2212yes—
137#2311C2212yes—
138#2311C2212yescomplemented
139C4×C22⋊Q8C2214yes—
140C4×#121C2214yes—
141C4×#121C2214yes—
142C4×#121C2214yescomplemented
143#2297C2212yes—
144#2297C2212yes—
145#2297C2212yes—
146#2297C2212yes—
147#2297C2212yes—
148#2297C2214yes—
149#2297C2212yes—
150#2297C2212yescomplemented
151C2×#391C2212yes—
152C2×#390C2212yes—
153C2×#389C2212yescomplemented
154C2×#387C2214yescomplemented
155C2×#386C2214yes—
156C2×#385C2214yes—
157#2285C2211yescharacteristic, complemented
158C2×#382C2211yescharacteristic, complemented
159C2×#380C2212yes—
160#2274C2212yescomplemented
161C2×C4×C22⋊C4C2212yes—
162C2×C4×C22⋊C4C2212yes—
163C22×#41—28no—
164C22×#41—44no—
165C22×#41—44no—
166C22×#41C2312yes—
167C22×#41C2312yes—
168C22×#41C2312yes—
169C22×#41C2312yes—
170C22×#41C2312yes—
171C23×Q8C2311yescharacteristic
172C23×D4C2311yescharacteristic
173C23×D4C2312yes—
174C24×C4C2311yescharacteristic
175C24×C4C2312yes—
176C24×C4C2312yes—
177#537—48no—
178#537—48no—
179#532—44no—
180C2×C4⋊Q8C2311yescharacteristic
181C2×#127C2311yescharacteristic
182C2×#126C2318yes—
183C2×#125—44no—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#124C2312yes—
188#525—216no—
189C2×#123C2314yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2312yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×#121C2312yes—
197C2×#121C2312yes—
198C2×#121C2318yes—
199C2×#121C2318yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C2×#120C2314yes—
209C2×#120C2318yes—
210#520—48no—
211C2×C4×Q8C2314yes—
212C2×C4×D4C2314yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2318yes—
217C2×C4×D4C2314yes—
218C2×#117—44no—
219C2×#117C2312yes—
220C2×#117C2312yes—
221C2×#117C2312yes—
222C2×#117C2314yes—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2312yes—
226C22×C4⋊C4C2312yes—
227C22×C4⋊C4C2312yes—
228C22×C4⋊C4C2314yes—
229C22×C4⋊C4C2312yes—
230C22×C4⋊C4C2314yes—
231C22×C4⋊C4C2314yes—
232C22×C22⋊C4C2314yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2314yes—
235C22×C22⋊C4C2314yes—
236C22×C42—44no—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2311yescharacteristic
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245C22×C42C2312yes—
246C22×C42C2312yes—
247#401C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#398C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#397C2318yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#396C2318yes—
269#396C2318yes—
270#396C2318yes—
271#395C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#394C2318yes—
277#394C2318yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#393C2318yes—
283#392C2318yes—
284#392C2318yes—
285#392C2318yes—
286#392C2318yes—
287#391C2314yes—
288#391C2314yes—
289#391C2314yes—
290#391C2312yes—
291#391C2312yes—
292#391C2312yes—
293#391C2312yes—
294#391C2312yes—
295#391C2312yes—
296#391C2314yes—
297#391C2314yes—
298#390C2314yes—
299#390C2314yes—
300#390C2314yes—
301#390C2318yes—
302#390C2318yes—
303#390C2318yes—
304#390C2314yes—
305#390C2318yes—
306#390C2312yes—
307#390C2312yes—
308#390C2314yes—
309#390C2312yes—
310#390C2312yes—
311#390C2314yes—
312#390C2312yes—
313#390C2312yes—
314#390C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2318yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#388C2318yes—
326#388C2318yes—
327#388C2314yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2314yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2314yes—
342#388C2314yes—
343#388C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2314yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2314yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2314yes—
379#386C2314yes—
380#386C2314yes—
381#385C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#384C2314yes—
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#383C2318yes—
395#382C2314yes—
396#382C2318yes—
397#382C2318yes—
398#382C2312yes—
399#382C2312yes—
400#382C2312yes—
401#382C2314yes—
402#381C2318yes—
403#381C2318yes—
404#380C2314yes—
405#380C2314yes—
406#380C2314yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2318yes—
411#380C2314yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#379C2318yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2318yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2318yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C2×#95C2314yes—
439C2×#95C2314yes—
440C2×#95C2314yes—
441C2×#95C2314yes—
442C2×#95C2314yes—
443C25C2411yescharacteristic
444C25C2412yes—
445C2×#41—28no—
446C2×#41—28no—
447C2×#41—28no—
448C2×#41—28no—
449C2×#41—28no—
450C2×#41—28no—
451C2×#41—28no—
452C2×#41—28no—
453C2×#41—28no—
454C2×#41—44no—
455C2×#41—44no—
456C2×#41—44no—
457C2×#41—44no—
458C2×#41—44no—
459C2×#41—44no—
460C2×#41—464no—
461C22×Q8—24no—
462C22×Q8—42no—
463C22×Q8—42no—
464C22×Q8C2412yes—
465C22×Q8C2412yes—
466C22×Q8C2412yes—
467C22×D4—28no—
468C22×D4—24no—
469C22×D4—42no—
470C22×D4—42no—
471C22×D4—44no—
472C22×D4—44no—
473C22×D4C2414yes—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2414yes—
477C22×D4C2412yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2412yes—
482C22×D4C2418yes—
483C22×D4C2418yes—
484C23×C4—24no—
485C23×C4—24no—
486C23×C4—28no—
487C23×C4—44no—
488C23×C4—44no—
489C23×C4—44no—
490C23×C4—44no—
491C23×C4—44no—
492C23×C4#4118yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2412yes—
496C23×C4C2412yes—
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C23×C4C2411yescharacteristic
502C23×C4C2414yes—
503C23×C4C2412yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2412yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2418yes—
511C23×C4C2412yes—
512C23×C4C2411yescharacteristic
513C4⋊Q8—42no—
514#127—42no—
515#126—416no—
516#125—44no—
517#125—48no—
518#125—44no—
519#124—44no—
520#123—216no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8—48no—
524C22⋊Q8—48no—
525C22⋊Q8—48no—
526C22⋊Q8—48no—
527#121—28no—
528#121—28no—
529#121—416no—
530#121—48no—
531#121—48no—
532#121—48no—
533#121—48no—
534#121—48no—
535#121—48no—
536#121—48no—
537#121—416no—
538#121—416no—
539#120—216no—
540#120—416no—
541C4×Q8—48no—
542C4×D4—216no—
543C4×D4—216no—
544C4×D4—48no—
545C4×D4—48no—
546C4×D4—416no—
547C4×D4—416no—
548#117—28no—
549#117—28no—
550#117—44no—
551#117—44no—
552#117—42no—
553#117—42no—
554#117—48no—
555C2×C4⋊C4—28no—
556C2×C4⋊C4—28no—
557C2×C4⋊C4—48no—
558C2×C4⋊C4—44no—
559C2×C4⋊C4—48no—
560C2×C4⋊C4—48no—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2412yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2414yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2418yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2418yes—
584C2×C22⋊C4—48no—
585C2×C22⋊C4—48no—
586C2×C22⋊C4—44no—
587C2×C22⋊C4—48no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2414yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C42—24no—
624C2×C42—24no—
625C2×C42—44no—
626C2×C42—44no—
627C2×C42—44no—
628C2×C42—42no—
629C2×C42—42no—
630C2×C42—42no—
631C2×C42—42no—
632C2×C42—44no—
633C2×C42C2414yes—
634C2×C42C2414yes—
635C2×C42C2412yes—
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2411yescharacteristic
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2418yes—
644C2×C42C2418yes—
645C2×C42C2418yes—
646C2×C42C2412yes—
647C2×C42C2412yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650#95C2414yes—
651#95C2414yes—
652#95C2414yes—
653#95C2414yes—
654#95C2414yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2418yes—
673#95C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2418yes—
680C24—22no—
681C24—22no—
682C24—24no—
683C24—24no—
684C24—28no—
685C24—42no—
686C24—44no—
687C24—42no—
688C24—42no—
689C24C2×#4114yes—
690C24C2514yes—
691C24C2514yes—
692C24C2511yescharacteristic
693C24C2511yescharacteristic
694C24C2511yescharacteristic
695#41—432no—
696#41—432no—
697#41—432no—
698#41—432no—
699#41—432no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—24no—
703C2×Q8—24no—
704C2×Q8—24no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—42no—
708C2×Q8—42no—
709C2×Q8—416no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—24no—
722C2×D4—24no—
723C2×D4—24no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—28no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—416no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—432no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—232no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—432no—
799C22×C4—432no—
800C22×C4C2×#4114yes—
801C22×C4C2×#4114yes—
802C22×C4C2×#4114yes—
803C22×C4C2×#4114yes—
804C22×C4C2×#4114yes—
805C22×C4C2×#4114yes—
806C22×C4H(5,𝔽2)14yes—
807C22×C4H(5,𝔽2)14yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2514yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2518yes—
816C22×C4C2518yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2512yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—216no—
835C4⋊C4—28no—
836C4⋊C4—48no—
837C4⋊C4—44no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—28no—
850C22⋊C4—28no—
851C22⋊C4—216no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—44no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—42no—
864C22⋊C4—42no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C42—28no—
883C42—24no—
884C42—22no—
885C42—24no—
886C42—22no—
887C42—22no—
888C42—22no—
889C42—28no—
890C42—42no—
891C42—42no—
892C42—42no—
893C42—42no—
894C42—42no—
895C42—42no—
896C42—48no—
897C42—48no—
898C42—48no—
899C23—21no—
900C23—21no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—28no—
909C23—28no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—44no—
925C23—48no—
926C23—48no—
927C23—48no—
928C23—48no—
929C23—48no—
930C23—88no—
931C23—88no—
932C23C22×#4112yes—
933C23C22×#4112yes—
934C23C22×#4112yes—
935C23C2×H(5,𝔽2)12yes—
936C23C2×H(5,𝔽2)12yes—
937C23#58514yes—
938C23C2611yescharacteristic
939Q8—48no—
940Q8—48no—
941Q8—48no—
942D4—48no—
943D4—416no—
944D4—416no—
945D4—416no—
946D4—416no—
947D4—48no—
948D4—48no—
949D4—88no—
950D4—88no—
951D4—168no—
952D4—168no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—28no—
960C2×C4—28no—
961C2×C4—28no—
962C2×C4—28no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—28no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—28no—
996C2×C4—22no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—416no—
1001C2×C4—48no—
1002C2×C4—48no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—88no—
1008C2×C4—88no—
1009C2×C4—88no—
1010C2×C4—168no—
1011C2×C4#538116yes—
1012C2×C4C22×#4112yes—
1013C2×C4C22×#4112yes—
1014C2×C4C22×#4112yes—
1015C2×C4C22×#4112yes—
1016C2×C4C2×H(5,𝔽2)12yes—
1017C2×C4C2×H(5,𝔽2)12yes—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4C2×H(5,𝔽2)12yes—
1020C2×C4#58514yes—
1021C22—22no—
1022C22—22no—
1023C22—22no—
1024C22—24no—
1025C22—24no—
1026C22—24no—
1027C22—24no—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—416no—
1033C22—42no—
1034C22—42no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22—44no—
1047C22—44no—
1048C22—44no—
1049C22—816no—
1050C22C2×#53814yes—
1051C22#351214yes—
1052C22C23×#4111yescharacteristic
1053C22C22×H(5,𝔽2)11yescharacteristic
1054C22C22×H(5,𝔽2)11yescharacteristic
1055C22C2×#58512yes—
1056C22C2×#58512yes—
1057C4—24no—
1058C4—22no—
1059C4—22no—
1060C4—44no—
1061C4—44no—
1062C4—42no—
1063C4—42no—
1064C4—42no—
1065C4—48no—
1066C4—44no—
1067C4—44no—
1068C4—48no—
1069C4—44no—
1070C4—44no—
1071C4C2×#53814yes—
1072C4C2×#53814yes—
1073C2—24no—
1074C2—24no—
1075C2—42no—
1076C2—84no—
1077C2—84no—
1078C2C22×#53811yescharacteristic
1079C2C2×#351211yescharacteristic
1080C2#6281511yescharacteristic
1081C2#6282112yes—
1082C2#6283012yes—
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. #40009C2semidirect
2. #40008C2semidirect
3. #39189C2semidirect
4. #38974C2semidirect
5. #38488C2semidirect
6. #38120C2semidirect
7. #37431C2semidirect
8. #37393C2semidirect
9. #37317C2semidirect
10. #36624C2semidirect
11. C2×#2851C2semidirect
12. #35649C2semidirect
13. #35618C2semidirect
14. #35564C2semidirect
15. #35545C2semidirect
16. #35251C2semidirect
17. #35086C2semidirect
18. #35081C2semidirect
19. #35023C2semidirect
20. #34202C2semidirect
21. C2×#2297C2semidirect
25. C2×#532C22semidirect
26. C22×#125C22semidirect
28. C2×#520C22semidirect
32. #2857C22semidirect
34. #2856C22semidirect
35. #2854C22semidirect
39. #2851C22semidirect
40. #2851C22semidirect
41. #2851C22semidirect
43. #2850C22semidirect
47. #2803C22semidirect
48. #2800C22semidirect
49. #2797C22semidirect
50. #2797C22semidirect
51. #2781C22semidirect
52. #2779C22semidirect
53. #2778C22semidirect
54. #2775C22semidirect
55. #2774C22semidirect
56. #2753C22semidirect
57. #2751C22semidirect
58. #2749C22semidirect
59. #2745C22semidirect
60. #2714C22semidirect
61. #2714C22semidirect
62. #2688C22semidirect
63. #2652C22semidirect
64. #2648C22semidirect
69. #2597C22semidirect
70. #2595C22semidirect
71. #2591C22semidirect
72. #2578C22semidirect
73. #2576C22semidirect
74. #2543C22semidirect
75. #2514C22semidirect
76. #2513C22semidirect
77. #2512C22semidirect
78. #2511C22semidirect
79. #2510C22semidirect
81. #2504C22semidirect
82. #2504C22semidirect
83. #2503C22semidirect
84. #2500C22semidirect
85. #2499C22semidirect
86. #2497C22semidirect
87. #2496C22semidirect
88. #2495C22semidirect
89. #2494C22semidirect
90. #2490C22semidirect
91. #2490C22semidirect
92. #2490C22semidirect
93. #2490C22semidirect
94. #2489C22semidirect
95. #2489C22semidirect
96. #2489C22semidirect
97. #2489C22semidirect
98. #2481C22semidirect
101. #2444C22semidirect
102. #2444C22semidirect
104. #2429C22semidirect
105. #2428C22semidirect
106. #2427C22semidirect
107. #2426C22semidirect
109. #2421C22semidirect
110. #2421C22semidirect
111. #2420C22semidirect
112. #2420C22semidirect
113. #2417C22semidirect
114. #2416C22semidirect
115. #2416C22semidirect
116. #2415C22semidirect
117. #2414C22semidirect
123. #2359C22semidirect
125. #2354C22semidirect
127. #2352C22semidirect
129. #2334C22semidirect
130. #2333C22semidirect
131. #2324C22semidirect
132. #2323C22semidirect
135. #2317C22semidirect
138. #2311C22semidirect
142. C4×#121C22semidirect
150. #2297C22semidirect
153. C2×#389C22semidirect
154. C2×#387C22semidirect
157. #2285C22semidirect
158. C2×#382C22semidirect
160. #2274C22semidirect

Maximal subgroups

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

subgroupindex
#400092
#400082
#391892
#389742
#384882
#381202
#374312
#373932
#373172
#366242
C2×#28512
#356492
#356182
#355642
#355452
#352512
#350862
#350812
#350232
#342022
C2×#22972