Finite Group Databasebeta

← #7702855

Subgroups — #7702855

Order 512.

4820 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52306C212yesmaximal, complemented
2#52304C212yesmaximal, complemented
3#52298C218yesmaximal, complemented
4#46205C212yesmaximal, complemented
5#46199C212yesmaximal
6#46196C212yesmaximal, complemented
7#46190C212yesmaximal, complemented
8#46180C214yesmaximal, complemented
9#46174C214yesmaximal, complemented
10#46168C218yesmaximal, complemented
11#46158C212yesmaximal, complemented
12#46152C211yesmaximal, characteristic, complemented
13#46147C211yesmaximal, characteristic, complemented
14#46145C212yesmaximal, complemented
15#46136C212yesmaximal
16#36698C212yesmaximal, complemented
17#36640C212yesmaximal, complemented
18#34953C212yesmaximal, complemented
19#34814C214yesmaximal, complemented
20#34809C212yesmaximal
21#34739C214yesmaximal, complemented
22C4×#563C212yesmaximal, complemented
23C2×C4×#124C211yesmaximal, characteristic
24C2×#563C2212yes—
25C2×#533C2212yes—
26C22×#124C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2212yes—
30#2864C2214yescomplemented
31#2864C2214yescomplemented
32#2859C2212yescomplemented
33#2859C2212yescomplemented
34#2859C2212yescomplemented
35#2859C2212yescomplemented
36#2851C2214yes—
37#2851C2214yes—
38#2851C2214yes—
39#2851C2214yes—
40#2844C2212yescomplemented
41#2838C2218yescomplemented
42#2836C2218yescomplemented
43#2833C2214yescomplemented
44#2830C2214yes—
45#2822C2212yescomplemented
46#2820C2214yes—
47#2809C2212yescomplemented
48#2805C2214yescomplemented
49#2793C2218yescomplemented
50#2789C2214yescomplemented
51#2787C2218yescomplemented
52#2775C2218yescomplemented
53#2774C2218yescomplemented
54#2773C2218yescomplemented
55#2769C2214yescomplemented
56#2766C2218yescomplemented
57#2765C2218yescomplemented
58#2762C2218yescomplemented
59#2759C2218yescomplemented
60#2738C2218yescomplemented
61#2734C2212yescomplemented
62#2731C2214yes—
63#2727C2214yes—
64#2725C2218yescomplemented
65#2724C2212yes—
66#2723C2218yes—
67#2721C2218yescomplemented
68#2720C2218yescomplemented
69#2717C2214yes—
70#2715C2218yes—
71#2713C2218yescomplemented
72#2707C2218yes—
73#2698C2218yescomplemented
74#2690C2218yescomplemented
75#2683C2212yes—
76#2674C2218yes—
77#2584C2214yescomplemented
78#2584C2214yescomplemented
79#2583C2214yes—
80#2583C2214yes—
81#2567C2212yescomplemented
82#2567C2212yescomplemented
83#2546C2212yescomplemented
84#2546C2212yescomplemented
85#2502C2214yes—
86#2497C2214yescomplemented
87#2497C2214yescomplemented
88#2496C2214yescomplemented
89#2496C2214yescomplemented
90#2495C2214yescomplemented
91#2495C2214yescomplemented
92#2494C2214yescomplemented
93#2494C2214yescomplemented
94#2493C2218yes—
95#2493C2218yes—
96#2487C2212yes—
97#2487C2212yes—
98#2486C2212yes—
99#2486C2212yes—
100#2485C2214yes—
101#2485C2214yes—
102#2484C2214yes—
103#2483C2214yes—
104#2482C2214yes—
105#2480C2218yes—
106#2480C2218yes—
107#2442C2214yescomplemented
108#2442C2214yescomplemented
109#2441C2214yescomplemented
110#2441C2214yescomplemented
111#2440C2214yescomplemented
112#2440C2214yescomplemented
113#2439C2214yescomplemented
114#2439C2214yescomplemented
115#2438C2218yes—
116#2438C2218yes—
117#2437C2218yes—
118#2437C2218yes—
119#2434C2214yes—
120#2405C2214yes—
121#2401C2218yescomplemented
122#2401C2218yescomplemented
123#2399C2214yescomplemented
124#2399C2214yescomplemented
125#2396C2218yescomplemented
126#2396C2218yescomplemented
127#2395C2214yes—
128#2395C2214yes—
129#2383C2218yescomplemented
130#2382C2214yescomplemented
131#2381C2214yescomplemented
132#2379C2212yes—
133#2378C2218yescomplemented
134#2376C2214yes—
135C4×C4⋊Q8C2214yescomplemented
136C4×C4⋊Q8C2214yescomplemented
137C4×#125C2214yescomplemented
138C4×#125C2214yescomplemented
139C4×#125C2214yescomplemented
140C4×#125C2214yescomplemented
141C4×#126C2218yescomplemented
142C4×#126C2218yescomplemented
143C4×#124C2211yescharacteristic
144C4×#124C2211yescharacteristic
145C4×#124C2214yes—
146C4×#124C2211yescharacteristic
147C4×#124C2211yescharacteristic
148C4×#124C2211yescharacteristic
149C4×#124C2211yescharacteristic
150C4×#124C2214yes—
151C4×#124C2211yescharacteristic
152C4×#124C2211yescharacteristic
153C4×C22⋊Q8C2218yescomplemented
154C4×C22⋊Q8C2218yescomplemented
155C4×#123C2214yes—
156C4×#123C2214yes—
157#2296C2214yes—
158#2296C2214yes—
159#2296C2214yes—
160C2×#391C2211yescharacteristic
161C2×#390C2211yescharacteristic
162C2×#388C2214yes—
163#2285C2212yes—
164#2285C2212yes—
165C2×#382C2211yescharacteristic
166#2280C2214yes—
167#2280C2212yes—
168C4×#117C2212yes—
169C2×C4×C22⋊C4C2214yes—
170C2×C43C2211yescharacteristic
171C23×Q8C2311yescharacteristic
172C23×D4C2311yescharacteristic
173C24×C4C2312yes—
174#563—216no—
175#533—48no—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2314yes—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2312yes—
180C2×#126C2318yes—
181C2×#126C2318yes—
182C2×#125C2314yes—
183C2×#125C2314yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#125C2314yes—
187C2×#124—28no—
188C2×#124C2311yescharacteristic
189C2×#124C2314yes—
190C2×#124C2311yescharacteristic
191C2×#124C2311yescharacteristic
192C2×#124C2311yescharacteristic
193C2×#123C2314yes—
194C2×#123C2314yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×C4×Q8—44no—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2314yes—
202C2×C4×Q8C2312yes—
203C2×C4×Q8C2311yescharacteristic
204C2×C4×Q8C2312yes—
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2311yescharacteristic
208C2×C4×D4—44no—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2312yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2312yes—
213C2×C4×D4C2311yescharacteristic
214C2×C4×D4C2311yescharacteristic
215C2×#117—48no—
216C2×#117C2314yes—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C2×#117C2314yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C4⋊C4C2311yescharacteristic
226C22×C22⋊C4C2314yes—
227C22×C22⋊C4C2314yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2314yes—
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236C22×C42C2314yes—
237#401C2318yes—
238#401C2318yes—
239#400C2318yes—
240#400C2318yes—
241#400C2318yes—
242#400C2314yes—
243#400C2318yes—
244#400C2314yes—
245#400C2318yes—
246#400C2318yes—
247#400C2318yes—
248#400C2318yes—
249#399C2318yes—
250#399C2314yes—
251#399C2314yes—
252#399C2318yes—
253#398C2314yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2318yes—
259#398C2314yes—
260#398C2314yes—
261#398C2318yes—
262#398C2314yes—
263#398C2318yes—
264#398C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2314yes—
269#397C2318yes—
270#397C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#395C2318yes—
282#395C2314yes—
283#395C2314yes—
284#395C2314yes—
285#395C2314yes—
286#395C2318yes—
287#395C2318yes—
288#395C2318yes—
289#394C2318yes—
290#394C2318yes—
291#393C2318yes—
292#393C2318yes—
293#391C2314yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2311yescharacteristic
298#391C2318yes—
299#391C2311yescharacteristic
300#391C2318yes—
301#391C2314yes—
302#391C2311yescharacteristic
303#391C2311yescharacteristic
304#390C2311yescharacteristic
305#390C2311yescharacteristic
306#390C2311yescharacteristic
307#390C2314yes—
308#390C2311yescharacteristic
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2314yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2318yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2314yes—
342#388C2314yes—
343#388C2318yes—
344#388C2314yes—
345#388C2314yes—
346#388C2314yes—
347#388C2314yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#386C2314yes—
372#386C2314yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2314yes—
382#385C2318yes—
383#385C2318yes—
384#385C2314yes—
385#384C2314yes—
386#384C2314yes—
387#384C2312yes—
388#384C2312yes—
389#384C2312yes—
390#384C2312yes—
391#383C2318yes—
392#383C2318yes—
393#382C2314yes—
394#382C2314yes—
395#382C2314yes—
396#382C2314yes—
397#382C2311yescharacteristic
398#382C2314yes—
399#382C2314yes—
400#382C2311yescharacteristic
401#382C2314yes—
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381C2314yes—
405#381C2318yes—
406#381C2314yes—
407#381C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2318yes—
413#380C2318yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2312yes—
420#380C2312yes—
421#379C2318yes—
422#379C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2318yes—
427C4×C4⋊C4C2318yes—
428C4×C4⋊C4C2318yes—
429C4×C4⋊C4C2318yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2318yes—
433C4×C4⋊C4C2312yes—
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2318yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2314yes—
445C4×C22⋊C4C2314yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2314yes—
450#376C2314yes—
451C2×#95C2314yes—
452C2×#95C2314yes—
453C43C2314yes—
454C43C2311yescharacteristic
455C43C2312yes—
456C43C2311yescharacteristic
457C43C2311yescharacteristic
458C43C2312yes—
459C43C2311yescharacteristic
460C25C2412yes—
461C22×Q8—24no—
462C22×Q8—42no—
463C22×Q8—42no—
464C22×Q8C2412yes—
465C22×Q8C2411yescharacteristic
466C22×Q8C2414yes—
467C22×Q8C2414yes—
468C22×Q8C2411yescharacteristic
469C22×D4—24no—
470C22×D4—42no—
471C22×D4—42no—
472C22×D4C2412yes—
473C22×D4C2411yescharacteristic
474C22×D4C2411yescharacteristic
475C23×C4—28no—
476C23×C4—216no—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2411yescharacteristic
480C23×C4C2412yes—
481C23×C4C2412yes—
482C23×C4C2412yes—
483C23×C4C2412yes—
484C23×C4C2412yes—
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C23×C4C2414yes—
489C23×C4C2414yes—
490C23×C4C2411yescharacteristic
491C4⋊Q8—216no—
492C4⋊Q8—44no—
493C4⋊Q8—44no—
494C4⋊Q8—48no—
495#126—232no—
496#126—416no—
497#125—216no—
498#125—48no—
499#125—48no—
500#125—48no—
501#125—48no—
502#124—24no—
503#124—24no—
504#124—216no—
505#124—24no—
506#124#4118yes—
507#123—216no—
508#123—48no—
509C22⋊Q8—232no—
510C22⋊Q8—48no—
511C22⋊Q8—48no—
512C22⋊Q8—416no—
513C4×Q8—42no—
514C4×Q8—44no—
515C4×Q8—42no—
516C4×Q8—42no—
517C4×Q8—44no—
518C4×Q8—42no—
519C4×Q8—48no—
520C4×Q8—48no—
521C4×D4—42no—
522C4×D4—44no—
523C4×D4—42no—
524C4×D4—44no—
525C4×D4—42no—
526C4×D4—42no—
527#117—216no—
528#117—216no—
529#117—48no—
530#117—48no—
531#117—48no—
532C2×C4⋊C4—44no—
533C2×C4⋊C4—44no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—44no—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2411yescharacteristic
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2418yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C2414yes—
570C2×C4⋊C4C2414yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2418yes—
576C2×C4⋊C4C2418yes—
577C2×C22⋊C4—216no—
578C2×C22⋊C4—48no—
579C2×C22⋊C4—48no—
580C2×C22⋊C4—44no—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C42—24no—
604C2×C42—28no—
605C2×C42—28no—
606C2×C42—24no—
607C2×C42—48no—
608C2×C42—42no—
609C2×C42—44no—
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2411yescharacteristic
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2414yes—
620C2×C42C2412yes—
621C2×C42C2412yes—
622C2×C42C2418yes—
623C2×C42C2418yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2412yes—
630C2×C42C2418yes—
631C2×C42C2418yes—
632C2×C42C2414yes—
633C2×C42C2412yes—
634C2×C42C2411yescharacteristic
635C2×C42C2412yes—
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2418yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2418yes—
653#95C2418yes—
654#95C2418yes—
655#95C2414yes—
656#95C2418yes—
657#95C2418yes—
658#95C2418yes—
659#95C2418yes—
660#95C2418yes—
661#95C2418yes—
662#95C2418yes—
663#95C2418yes—
664#95C2418yes—
665#95C2418yes—
666#95C2418yes—
667#95C2418yes—
668#95C2418yes—
669#95C2418yes—
670#95C2418yes—
671#95C2418yes—
672C24—24no—
673C24—24no—
674C24—28no—
675C24—44no—
676C24—42no—
677C24C2512yes—
678C24C2512yes—
679C24C2511yescharacteristic
680C2×Q8—24no—
681C2×Q8—22no—
682C2×Q8—28no—
683C2×Q8—24no—
684C2×Q8—41no—
685C2×Q8—42no—
686C2×Q8—41no—
687C2×Q8—41no—
688C2×Q8—41no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—48no—
692C2×Q8—44no—
693C2×Q8—416no—
694C2×Q8C2×#4114yes—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—24no—
698C2×D4—41no—
699C2×D4—42no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—416no—
704C2×D4C2×#4114yes—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—24no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—28no—
726C22×C4—24no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—48no—
735C22×C4—44no—
736C22×C4—432no—
737C22×C4H(5,𝔽2)14yes—
738C22×C42−1+418yes—
739C22×C4C2512yes—
740C22×C4C2512yes—
741C22×C4C2512yes—
742C22×C4C2512yes—
743C22×C4C2518yes—
744C22×C4C2518yes—
745C22×C4C2512yes—
746C22×C4C2512yes—
747C22×C4C2518yes—
748C22×C4C2518yes—
749C22×C4C2511yescharacteristic
750C22×C4C2511yescharacteristic
751C22×C4C2512yes—
752C22×C4C2512yes—
753C22×C4C2512yes—
754C22×C4C2511yescharacteristic
755C22×C4C2512yes—
756C22×C4C2511yescharacteristic
757C22×C4C2511yescharacteristic
758C22×C4C2511yescharacteristic
759C4⋊C4—28no—
760C4⋊C4—216no—
761C4⋊C4—216no—
762C4⋊C4—216no—
763C4⋊C4—28no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—28no—
769C4⋊C4—216no—
770C4⋊C4—216no—
771C4⋊C4—28no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C4⋊C4—41no—
775C4⋊C4—42no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—42no—
779C4⋊C4—41no—
780C4⋊C4—42no—
781C4⋊C4—42no—
782C4⋊C4—42no—
783C4⋊C4—42no—
784C4⋊C4—48no—
785C4⋊C4—48no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—48no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C22⋊C4—28no—
800C22⋊C4—216no—
801C22⋊C4—28no—
802C22⋊C4—216no—
803C22⋊C4—216no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—48no—
811C22⋊C4—42no—
812C22⋊C4—42no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—48no—
816C22⋊C4—44no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4C2×#41116yes—
821C42—24no—
822C42—22no—
823C42—28no—
824C42—22no—
825C42—22no—
826C42—22no—
827C42—22no—
828C42—24no—
829C42—24no—
830C42—24no—
831C42—24no—
832C42—216no—
833C42—24no—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—216no—
838C42—24no—
839C42—24no—
840C42—24no—
841C42—41no—
842C42—42no—
843C42—41no—
844C42—42no—
845C42—48no—
846C42—48no—
847C42—44no—
848C42C2×#4114yes—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—24no—
854C23—24no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—22no—
861C23—48no—
862C23—416no—
863C23—48no—
864C23—88no—
865C23—84no—
866C23C22×#4114yes—
867C23C2×H(5,𝔽2)12yes—
868C23C2×2−1+414yes—
869C23C2611yescharacteristic
870Q8—44no—
871Q8—48no—
872Q8—44no—
873Q8—88no—
874Q8—88no—
875D4—44no—
876D4—48no—
877D4—44no—
878C2×C4—28no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—28no—
891C2×C4—22no—
892C2×C4—28no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—28no—
899C2×C4—28no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—28no—
905C2×C4—28no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—28no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—28no—
920C2×C4—28no—
921C2×C4—22no—
922C2×C4—48no—
923C2×C4—48no—
924C2×C4—48no—
925C2×C4—44no—
926C2×C4—48no—
927C2×C4—48no—
928C2×C4—48no—
929C2×C4—48no—
930C2×C4—48no—
931C2×C4—84no—
932C2×C4—88no—
933C2×C4—88no—
934C2×C4#563116yescomplemented
935C2×C4C22×#4114yes—
936C2×C4C22×#4114yes—
937C2×C4C22×#4112yes—
938C2×C4C2×H(5,𝔽2)12yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C2×C4C2×2−1+414yes—
941C2×C4C2×2−1+414yes—
942C2×C4#58514yes—
943C2×C4#58512yes—
944C22—24no—
945C22—22no—
946C22—22no—
947C22—24no—
948C22—24no—
949C22—28no—
950C22—44no—
951C22—42no—
952C22—42no—
953C22—44no—
954C22—42no—
955C22—42no—
956C22—44no—
957C22—42no—
958C22—816no—
959C22C2×#56314yes—
960C22C23×#4111yescharacteristic
961C22C22×H(5,𝔽2)11yescharacteristic
962C22C22×2−1+412yes—
963C22C2×#58511yescharacteristic
964C22C2×#58512yes—
965C4—24no—
966C4—22no—
967C4—22no—
968C4—24no—
969C4—24no—
970C4—48no—
971C4—42no—
972C4—41no—
973C4—41no—
974C4—42no—
975C4—48no—
976C4—42no—
977C4—42no—
978C4—48no—
979C4—48no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4C2×#56314yes—
984C4C2×#56314yes—
985C2—24no—
986C2—44no—
987C2—82no—
988C2C22×#56311yescharacteristic
989C2#6275212yes—
990C2#6275911yescharacteristic
991C2#6277311yescharacteristic
992C2#6280512yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52306C2semidirect
2. #52304C2semidirect
3. #52298C2semidirect
4. #46205C2semidirect
6. #46196C2semidirect
7. #46190C2semidirect
8. #46180C2semidirect
9. #46174C2semidirect
10. #46168C2semidirect
11. #46158C2semidirect
12. #46152C2semidirect
13. #46147C2semidirect
14. #46145C2semidirect
16. #36698C2semidirect
17. #36640C2semidirect
18. #34953C2semidirect
19. #34814C2semidirect
21. #34739C2semidirect
22. C4×#563C2semidirect
30. #2864C22semidirect
31. #2864C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2859C22semidirect
40. #2844C22semidirect
41. #2838C22semidirect
42. #2836C22semidirect
43. #2833C22semidirect
45. #2822C22semidirect
47. #2809C22semidirect
48. #2805C22semidirect
49. #2793C22semidirect
50. #2789C22semidirect
51. #2787C22semidirect
52. #2775C22semidirect
53. #2774C22semidirect
54. #2773C22semidirect
55. #2769C22semidirect
56. #2766C22semidirect
57. #2765C22semidirect
58. #2762C22semidirect
59. #2759C22semidirect
60. #2738C22semidirect
61. #2734C22semidirect
64. #2725C22semidirect
67. #2721C22semidirect
68. #2720C22semidirect
71. #2713C22semidirect
73. #2698C22semidirect
74. #2690C22semidirect
77. #2584C22semidirect
78. #2584C22semidirect
81. #2567C22semidirect
82. #2567C22semidirect
83. #2546C22semidirect
84. #2546C22semidirect
86. #2497C22semidirect
87. #2497C22semidirect
88. #2496C22semidirect
89. #2496C22semidirect
90. #2495C22semidirect
91. #2495C22semidirect
92. #2494C22semidirect
93. #2494C22semidirect
107. #2442C22semidirect
108. #2442C22semidirect
109. #2441C22semidirect
110. #2441C22semidirect
111. #2440C22semidirect
112. #2440C22semidirect
113. #2439C22semidirect
114. #2439C22semidirect
121. #2401C22semidirect
122. #2401C22semidirect
123. #2399C22semidirect
124. #2399C22semidirect
125. #2396C22semidirect
126. #2396C22semidirect
129. #2383C22semidirect
130. #2382C22semidirect
131. #2381C22semidirect
133. #2378C22semidirect
135. C4×C4⋊Q8C22semidirect
136. C4×C4⋊Q8C22semidirect
137. C4×#125C22semidirect
138. C4×#125C22semidirect
139. C4×#125C22semidirect
140. C4×#125C22semidirect
141. C4×#126C22semidirect
142. C4×#126C22semidirect
153. C4×C22⋊Q8C22semidirect
154. C4×C22⋊Q8C22semidirect
934. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#523062
#523042
#522982
#462052
#461992
#461962
#461902
#461802
#461742
#461682
#461582
#461522
#461472
#461452
#461362
#366982
#366402
#349532
#348142
#348092
#347392
C4×#5632
C2×C4×#1242