Finite Group Databasebeta

← #7651257

Subgroups — #7651257

Order 512.

4628 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42781C214yesmaximal, complemented
2#42717C214yesmaximal, complemented
3#42692C214yesmaximal, complemented
4#42513C214yesmaximal, complemented
5#40691C218yesmaximal, complemented
6#40203C214yesmaximal, complemented
7#40001C214yesmaximal, complemented
8#39535C214yesmaximal, complemented
9#38978C214yesmaximal, complemented
10#38139C218yesmaximal, complemented
11#35662C211yesmaximal, characteristic, complemented
12#35661C211yesmaximal, characteristic
13#35644C211yesmaximal, characteristic, complemented
14#35629C211yesmaximal, characteristic, complemented
15#35619C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17#35330C211yesmaximal, characteristic, complemented
18#35312C211yesmaximal, characteristic, complemented
19#35151C211yesmaximal, characteristic, complemented
20#34814C211yesmaximal, characteristic, complemented
21#34813C211yesmaximal, characteristic
22C2×#2499C211yesmaximal, characteristic, complemented
23#34254C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34201C211yesmaximal, characteristic
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C22×#117C2211yescharacteristic
35#2862C2212yescomplemented
36#2862C2212yescomplemented
37#2861C2212yescomplemented
38#2859C2212yescomplemented
39#2855C2214yes—
40#2838C2218yes—
41#2830C2218yes—
42#2799C2218yescomplemented
43#2777C2218yes—
44#2777C2218yescomplemented
45#2775C2218yescomplemented
46#2774C2218yescomplemented
47#2772C2218yes—
48#2772C2218yes—
49#2772C2218yescomplemented
50#2766C2218yescomplemented
51#2762C2218yescomplemented
52#2759C2218yes—
53#2757C2218yes—
54#2754C2218yescomplemented
55#2751C2218yes—
56#2723C2218yes—
57#2700C2218yes—
58#2660C2212yescomplemented
59#2660C2212yescomplemented
60#2655C2218yescomplemented
61#2652C2218yescomplemented
62#2651C2218yes—
63#2650C2218yes—
64#2644C2218yes—
65#2642C2212yescomplemented
66#2640C2212yescomplemented
67#2637C2218yes—
68#2626C2214yes—
69#2582C2214yescomplemented
70#2581C2214yescomplemented
71#2567C2212yescomplemented
72#2566C2212yescomplemented
73#2565C2212yescomplemented
74#2561C2214yes—
75#2550C2214yescomplemented
76#2550C2214yescomplemented
77#2549C2218yes—
78#2542C2212yescomplemented
79#2538C2214yes—
80#2536C2214yes—
81#2532C2218yes—
82#2527C2218yescomplemented
83#2520C2218yescomplemented
84#2514C2214yescomplemented
85#2513C2214yescomplemented
86#2510C2218yes—
87#2509C2218yescomplemented
88#2503C2214yes—
89#2503C2212yescomplemented
90#2502C2212yescomplemented
91#2499C2214yes—
92#2499C2214yes—
93#2499C2214yes—
94#2499C2214yes—
95#2499C2212yescomplemented
96#2499C2212yescomplemented
97#2497C2212yes—
98#2496C2212yes—
99#2495C2212yes—
100#2495C2214yescomplemented
101#2494C2212yes—
102#2494C2214yescomplemented
103#2493C2214yes—
104#2492C2214yes—
105#2492C2214yes—
106#2492C2212yes—
107#2492C2214yescomplemented
108#2491C2212yes—
109#2490C2212yes—
110#2489C2214yes—
111#2489C2214yes—
112#2489C2212yes—
113#2489C2214yescomplemented
114#2488C2218yes—
115#2488C2214yes—
116#2480C2214yes—
117#2472C2214yes—
118#2465C2218yescomplemented
119#2453C2214yescomplemented
120#2451C2214yescomplemented
121#2449C2218yes—
122#2448C2218yes—
123#2447C2214yescomplemented
124#2446C2214yescomplemented
125#2441C2214yes—
126#2441C2214yes—
127#2441C2214yescomplemented
128#2440C2214yescomplemented
129#2439C2214yes—
130#2439C2214yes—
131#2438C2218yes—
132#2429C2214yes—
133#2426C2214yes—
134#2419C2218yes—
135#2413C2214yes—
136#2411C2214yes—
137#2401C2214yes—
138#2398C2214yes—
139C2×#397C2214yes—
140#2363C2214yes—
141#2362C2214yes—
142#2360C2218yes—
143#2356C2214yescomplemented
144#2355C2214yescomplemented
145#2355C2214yescomplemented
146#2354C2214yes—
147#2352C2214yes—
148Q8×C4⋊C4C2214yescomplemented
149#2343C2218yes—
150#2332C2218yescomplemented
151#2330C2214yescomplemented
152#2321C2214yes—
153#2320C2214yescomplemented
154#2320C2218yescomplemented
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2211yescharacteristic
158#2317C2211yescharacteristic
159#2316C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2310C2211yescharacteristic
163#2310C2211yescharacteristic
164C4×C4⋊Q8C2214yescomplemented
165C4×#126C2214yes—
166C4×#124C2214yes—
167C4×#123C2214yes—
168#2297C2211yescharacteristic
169#2297C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2295C2214yescomplemented
173C2×#391C2211yescharacteristic
174C2×#391C2211yescharacteristic
175C2×#387C2214yes—
176#2285C2211yescharacteristic
177C2×#384C2211yescharacteristic
178C2×#382C2211yescharacteristic
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181#2280C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C24×C4C2311yescharacteristic
190#544—44no—
191#544—44no—
192#536—44no—
193#533—28no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#126C2314yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208#525—28no—
209C2×#123C2312yes—
210C2×#123C2314yes—
211C2×C22⋊Q8—44no—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×#121C2312yes—
222C2×#120C2312yes—
223#520—44no—
224#519—28no—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2318yes—
229C2×C4×Q8C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×#117—44no—
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2314yes—
241C2×#117C2314yes—
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2314yes—
250C22×C4⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256C22×C42C2312yes—
257#401C2318yes—
258#401C2314yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2318yes—
270#400C2314yes—
271#399C2318yes—
272#399C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2318yes—
287#397C2318yes—
288#397C2314yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2314yes—
295#396C2318yes—
296#396C2314yes—
297#396C2318yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#394C2314yes—
306#394C2318yes—
307#394C2314yes—
308#393C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2314yes—
312#393C2314yes—
313#391C2318yes—
314#391C2311yescharacteristic
315#391C2312yes—
316#391C2314yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2311yescharacteristic
324#391C2314yes—
325#391C2312yes—
326#391C2318yes—
327#391C2314yes—
328#391C2318yes—
329#391C2318yes—
330#391C2318yes—
331#391C2312yes—
332#391C2318yes—
333#391C2318yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#390C2311yescharacteristic
339#390C2312yes—
340#390C2312yes—
341#390C2318yes—
342#390C2311yescharacteristic
343#390C2314yes—
344#390C2318yes—
345#390C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2318yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2312yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2318yes—
408#386C2314yes—
409#386C2314yes—
410#385C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2314yes—
418#384C2312yes—
419#384C2312yes—
420#384C2312yes—
421#384C2312yes—
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#383C2314yes—
428#383C2318yes—
429#383C2318yes—
430#382C2312yes—
431#382C2312yes—
432#382C2312yes—
433#382C2312yes—
434#382C2318yes—
435#382C2318yes—
436#382C2318yes—
437#382C2311yescharacteristic
438#382C2312yes—
439#382C2311yescharacteristic
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#381C2314yes—
444#381C2314yes—
445#381C2318yes—
446#381C2312yes—
447#381C2312yes—
448#381C2312yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2312yes—
456#380C2312yes—
457#380C2312yes—
458#380C2312yes—
459#379C2312yes—
460#379C2312yes—
461#379C2312yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C22⋊C4C2312yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492#376C2312yes—
493#376C2318yes—
494#376C2312yes—
495C2×#95C2314yes—
496C2×#95C2314yes—
497C2×#95C2314yes—
498C2×#95C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2411yescharacteristic
502C2×#41—24no—
503C2×#41—24no—
504C2×#41—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8—24no—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2414yes—
512C22×Q8C2414yes—
513C22×Q8C2414yes—
514C22×D4C2412yes—
515C22×D4C2411yescharacteristic
516C22×D4C2414yes—
517C23×C4—24no—
518C23×C4—24no—
519C23×C4—24no—
520C23×C4C2412yes—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C4⋊Q8—28no—
533C4⋊Q8—44no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538#126—48no—
539#125—28no—
540#125—44no—
541#125—44no—
542#125—44no—
543#125—44no—
544#124—44no—
545#124—48no—
546#123—28no—
547#123—48no—
548C22⋊Q8—28no—
549C22⋊Q8—216no—
550C22⋊Q8—48no—
551C22⋊Q8—48no—
552C22⋊Q8—416no—
553C22⋊Q8—48no—
554C22⋊Q8—48no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557#121—28no—
558#120—28no—
559C4×Q8—216no—
560C4×Q8—216no—
561C4×Q8—216no—
562C4×Q8—416no—
563C4×Q8—44no—
564C4×D4—216no—
565C4×D4—44no—
566C4×D4—48no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—24no—
573#117—216no—
574#117—48no—
575#117—48no—
576#117—44no—
577#117#4118yes—
578C2×C4⋊C4—24no—
579C2×C4⋊C4—24no—
580C2×C4⋊C4—24no—
581C2×C4⋊C4—48no—
582C2×C4⋊C4—44no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2418yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2418yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C22⋊C4—44no—
629C2×C22⋊C4—44no—
630C2×C22⋊C4—44no—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2414yes—
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2418yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2412yes—
661C2×C42—24no—
662C2×C42—24no—
663C2×C42—44no—
664C2×C42C2412yes—
665C2×C42C2418yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2414yes—
672C2×C42C2412yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2418yes—
681C2×C42C2418yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685C2×C42C2412yes—
686#95C2418yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2418yes—
692#95C2418yes—
693#95C2418yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729C24—22no—
730C24—22no—
731C24—22no—
732C24—42no—
733C24—42no—
734C24C2512yes—
735C24C2512yes—
736C24C2511yescharacteristic
737#41—416no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—28no—
741C2×Q8—22no—
742C2×Q8—22no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—24no—
747C2×Q8—22no—
748C2×Q8—28no—
749C2×Q8—44no—
750C2×Q8—44no—
751C2×Q8—44no—
752C2×Q8—48no—
753C2×Q8—48no—
754C2×Q8—416no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—24no—
758C2×D4—22no—
759C2×D4—28no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—44no—
763C2×D4—44no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—24no—
769C22×C4—22no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
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—24no—
784C22×C4—24no—
785C22×C4—42no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—42no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—416no—
794C22×C4C2×#4114yes—
795C22×C4H(5,𝔽2)14yes—
796C22×C42−1+414yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2512yes—
806C22×C4C2512yes—
807C22×C4C2514yes—
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C4⋊C4—24no—
820C4⋊C4—216no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—24no—
839C4⋊C4—216no—
840C4⋊C4—28no—
841C4⋊C4—48no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4C2×#4118yes—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—24no—
868C22⋊C4—24no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—28no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—44no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4C2×#4118yes—
893C42—24no—
894C42—22no—
895C42—22no—
896C42—24no—
897C42—216no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—24no—
902C42—24no—
903C42—22no—
904C42—22no—
905C42—24no—
906C42—28no—
907C42—48no—
908C42—44no—
909C42—44no—
910C42—44no—
911C42—48no—
912C42—48no—
913C42—44no—
914C42C2×#4118yes—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—24no—
925C23—22no—
926C23—24no—
927C23—22no—
928C23—22no—
929C23—44no—
930C23—44no—
931C23—44no—
932C23—84no—
933C23—84no—
934C23C22×#4112yes—
935C23C2×H(5,𝔽2)12yes—
936C23C2×2−1+412yes—
937C23C2611yescharacteristic
938Q8—416no—
939Q8—48no—
940Q8—48no—
941Q8—44no—
942Q8—164no—
943Q8—164no—
944D4—48no—
945D4—44no—
946D4—88no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—28no—
996C2×C4—48no—
997C2×C4—44no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4—48no—
1001C2×C4—48no—
1002C2×C4—84no—
1003C2×C4—84no—
1004C2×C4—84no—
1005C2×C4—84no—
1006C2×C4—164no—
1007C2×C4#542116yes—
1008C2×C4C22×#4118yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C2×H(5,𝔽2)12yes—
1012C2×C4C2×H(5,𝔽2)12yes—
1013C2×C4C2×2−1+412yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4#58514yes—
1016C22—24no—
1017C22—22no—
1018C22—22no—
1019C22—24no—
1020C22—42no—
1021C22—44no—
1022C22—42no—
1023C22—42no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—44no—
1030C22—42no—
1031C22—42no—
1032C22—88no—
1033C22C2×#54214yes—
1034C22C23×#4111yescharacteristic
1035C22C22×H(5,𝔽2)11yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C22C2×#58512yes—
1038C222−1+612yes—
1039C4—24no—
1040C4—28no—
1041C4—44no—
1042C4—42no—
1043C4—44no—
1044C4—42no—
1045C4—44no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—44no—
1051C4—42no—
1052C4—42no—
1053C4—42no—
1054C4—42no—
1055C4—44no—
1056C4—44no—
1057C4—42no—
1058C4—42no—
1059C4C2×#54214yes—
1060C4C2×#54214yes—
1061C2—24no—
1062C2—82no—
1063C2—82no—
1064C2C22×#54211yescharacteristic
1065C2#6283611yescharacteristic
1066C2#6288711yescharacteristic
1067C2#6295912yes—
1068C2#6299312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42781C2semidirect
2. #42717C2semidirect
3. #42692C2semidirect
4. #42513C2semidirect
5. #40691C2semidirect
6. #40203C2semidirect
7. #40001C2semidirect
8. #39535C2semidirect
9. #38978C2semidirect
10. #38139C2semidirect
11. #35662C2semidirect
13. #35644C2semidirect
14. #35629C2semidirect
15. #35619C2semidirect
16. #35532C2semidirect
17. #35330C2semidirect
18. #35312C2semidirect
19. #35151C2semidirect
20. #34814C2semidirect
22. C2×#2499C2semidirect
23. #34254C2semidirect
24. #34214C2semidirect
35. #2862C22semidirect
36. #2862C22semidirect
37. #2861C22semidirect
38. #2859C22semidirect
42. #2799C22semidirect
44. #2777C22semidirect
45. #2775C22semidirect
46. #2774C22semidirect
49. #2772C22semidirect
50. #2766C22semidirect
51. #2762C22semidirect
54. #2754C22semidirect
58. #2660C22semidirect
59. #2660C22semidirect
60. #2655C22semidirect
61. #2652C22semidirect
65. #2642C22semidirect
66. #2640C22semidirect
69. #2582C22semidirect
70. #2581C22semidirect
71. #2567C22semidirect
72. #2566C22semidirect
73. #2565C22semidirect
75. #2550C22semidirect
76. #2550C22semidirect
78. #2542C22semidirect
82. #2527C22semidirect
83. #2520C22semidirect
84. #2514C22semidirect
85. #2513C22semidirect
87. #2509C22semidirect
89. #2503C22semidirect
90. #2502C22semidirect
95. #2499C22semidirect
96. #2499C22semidirect
100. #2495C22semidirect
102. #2494C22semidirect
107. #2492C22semidirect
113. #2489C22semidirect
118. #2465C22semidirect
119. #2453C22semidirect
120. #2451C22semidirect
123. #2447C22semidirect
124. #2446C22semidirect
127. #2441C22semidirect
128. #2440C22semidirect
143. #2356C22semidirect
144. #2355C22semidirect
145. #2355C22semidirect
148. Q8×C4⋊C4C22semidirect
150. #2332C22semidirect
151. #2330C22semidirect
153. #2320C22semidirect
154. #2320C22semidirect
164. C4×C4⋊Q8C22semidirect
172. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#427812
#427172
#426922
#425132
#406912
#402032
#400012
#395352
#389782
#381392
#356622
#356612
#356442
#356292
#356192
#355322
#353302
#353122
#351512
#348142
#348132
C2×#24992
#342542
#342142
#342012