Finite Group Databasebeta

← #7652624

Subgroups — #7652624

Order 512.

4652 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42902C214yesmaximal, complemented
2#42845C214yesmaximal, complemented
3#42837C214yesmaximal, complemented
4#42830C214yesmaximal, complemented
5#42010C218yesmaximal, complemented
6#40191C214yesmaximal, complemented
7#40105C214yesmaximal, complemented
8#39782C214yesmaximal, complemented
9#39219C214yesmaximal, complemented
10#38469C218yesmaximal, complemented
11#35679C211yesmaximal, characteristic
12#35679C211yesmaximal, characteristic
13#35674C211yesmaximal, characteristic, complemented
14#35668C211yesmaximal, characteristic, complemented
15#35626C211yesmaximal, characteristic
16#35529C211yesmaximal, characteristic
17#35313C211yesmaximal, characteristic, complemented
18#35266C211yesmaximal, characteristic
19#35154C211yesmaximal, characteristic, complemented
20C2×#2545C211yesmaximal, characteristic
21#34815C211yesmaximal, characteristic, complemented
22#34815C211yesmaximal, characteristic, complemented
23#34249C211yesmaximal, characteristic, complemented
24#34211C211yesmaximal, characteristic
25#34209C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C2×#519C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2863C2214yescomplemented
36#2860C2214yes—
37#2855C2214yes—
38#2838C2218yescomplemented
39#2836C2218yescomplemented
40#2807C2218yescomplemented
41#2798C2218yescomplemented
42#2793C2218yescomplemented
43#2790C2218yescomplemented
44#2787C2218yescomplemented
45#2783C2218yescomplemented
46#2783C2218yescomplemented
47#2777C2218yescomplemented
48#2775C2218yescomplemented
49#2773C2218yescomplemented
50#2771C2218yescomplemented
51#2765C2218yescomplemented
52#2744C2218yescomplemented
53#2721C2218yescomplemented
54#2720C2218yescomplemented
55#2689C2218yescomplemented
56#2667C2218yescomplemented
57#2664C2218yescomplemented
58#2654C2218yescomplemented
59#2654C2218yescomplemented
60#2652C2218yescomplemented
61#2650C2218yescomplemented
62#2645C2214yescomplemented
63#2644C2214yes—
64#2627C2214yes—
65#2596C2218yescomplemented
66#2594C2218yescomplemented
67#2577C2218yescomplemented
68#2575C2218yescomplemented
69#2573C2218yescomplemented
70#2568C2212yescomplemented
71#2567C2212yescomplemented
72#2566C2212yes—
73#2566C2212yes—
74#2565C2212yescomplemented
75#2565C2212yescomplemented
76#2563C2212yes—
77#2556C2218yescomplemented
78#2545C2214yes—
79#2545C2214yes—
80#2545C2214yes—
81#2545C2214yes—
82#2542C2212yes—
83#2514C2214yescomplemented
84#2513C2214yes—
85#2512C2214yes—
86#2511C2214yescomplemented
87#2509C2212yescomplemented
88#2509C2212yescomplemented
89#2508C2212yescomplemented
90#2508C2212yescomplemented
91#2507C2212yescomplemented
92#2507C2212yescomplemented
93#2506C2212yescomplemented
94#2506C2212yescomplemented
95#2505C2214yes—
96#2505C2214yes—
97#2493C2218yes—
98#2484C2218yes—
99#2483C2214yes—
100#2483C2214yes—
101#2482C2214yes—
102#2482C2218yes—
103#2482C2214yes—
104#2480C2218yes—
105#2473C2214yes—
106#2473C2214yes—
107#2454C2214yes—
108#2453C2214yescomplemented
109#2453C2214yescomplemented
110#2453C2214yescomplemented
111#2452C2214yes—
112#2451C2214yescomplemented
113#2451C2214yescomplemented
114#2451C2214yescomplemented
115#2448C2214yes—
116#2448C2214yes—
117#2448C2214yes—
118#2448C2214yes—
119#2448C2214yes—
120#2448C2214yes—
121#2448C2214yes—
122#2448C2214yes—
123#2447C2214yes—
124#2447C2214yes—
125#2447C2214yes—
126#2447C2214yes—
127#2446C2214yescomplemented
128#2446C2214yescomplemented
129#2446C2214yescomplemented
130#2446C2214yescomplemented
131#2438C2218yes—
132#2437C2218yes—
133#2402C2214yescomplemented
134#2402C2214yescomplemented
135C2×#396C2214yes—
136#2367C2214yes—
137#2367C2214yes—
138#2365C2214yescomplemented
139#2365C2214yescomplemented
140#2351C2214yescomplemented
141#2351C2214yescomplemented
142Q8×C4⋊C4C2214yescomplemented
143Q8×C4⋊C4C2214yescomplemented
144#2344C2218yes—
145#2342C2218yes—
146#2334C2218yescomplemented
147#2332C2218yescomplemented
148#2327C2212yescomplemented
149#2327C2212yescomplemented
150#2326C2212yes—
151#2326C2212yes—
152#2317C2214yes—
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2316C2211yescharacteristic
156#2310C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2211yescharacteristic
159#2310C2211yescharacteristic
160#2310C2211yescharacteristic
161#2309C2211yescharacteristic
162#2309C2211yescharacteristic
163#2309C2211yescharacteristic
164C4×C4⋊Q8C2212yescomplemented
165C4×C4⋊Q8C2212yescomplemented
166C4×#125C2214yescomplemented
167C4×#125C2214yescomplemented
168C4×#124C2212yes—
169C4×#124C2212yes—
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2296C2214yes—
173#2296C2211yescharacteristic
174#2296C2211yescharacteristic
175#2296C2211yescharacteristic
176#2296C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179C2×#391C2211yescharacteristic
180C2×#390C2211yescharacteristic
181C2×#388C2214yes—
182#2285C2211yescharacteristic
183#2285C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188C23×Q8C2311yescharacteristic
189C23×D4C2311yescharacteristic
190#544—44no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#126C2318yes—
198C2×#125C2314yes—
199C2×#125C2314yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#124—28no—
203C2×#124—44no—
204C2×#124C2312yes—
205C2×#124C2314yes—
206C2×#124C2312yes—
207C2×#124C2314yes—
208C2×#124C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2314yes—
211#519—28no—
212#519—44no—
213#519—44no—
214#518—44no—
215C2×C4×Q8—44no—
216C2×C4×Q8C2314yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2314yes—
241C2×#117C2314yes—
242C2×#117C2314yes—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C22⋊C4C2314yes—
248C22×C22⋊C4C2314yes—
249C22×C22⋊C4C2312yes—
250C22×C22⋊C4C2314yes—
251C22×C22⋊C4C2312yes—
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255C22×C42C2312yes—
256#401C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2314yes—
261#400C2314yes—
262#400C2318yes—
263#400C2314yes—
264#400C2318yes—
265#400C2314yes—
266#400C2318yes—
267#400C2318yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#399C2318yes—
273#399C2318yes—
274#399C2318yes—
275#399C2318yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2314yes—
280#398C2314yes—
281#398C2318yes—
282#398C2314yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#395C2318yes—
310#395C2318yes—
311#393C2318yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2318yes—
329#391C2318yes—
330#391C2314yes—
331#390C2312yes—
332#390C2312yes—
333#390C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2312yes—
341#390C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2318yes—
356#389C2312yes—
357#389C2318yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2318yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2312yes—
421#385C2312yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2312yes—
426#385C2312yes—
427#385C2312yes—
428#385C2312yes—
429#385C2318yes—
430#385C2314yes—
431#385C2314yes—
432#385C2314yes—
433#385C2314yes—
434#385C2312yes—
435#385C2312yes—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2318yes—
443#383C2318yes—
444#382C2314yes—
445#382C2314yes—
446#382C2311yescharacteristic
447#382C2312yes—
448#382C2311yescharacteristic
449#382C2312yes—
450#382C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2318yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#381C2314yes—
458#381C2318yes—
459#381C2318yes—
460#380C2318yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#379C2314yes—
465#379C2314yes—
466#379C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2318yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2318yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495#376C2312yes—
496#376C2312yes—
497C2×#95C2314yes—
498C2×#95C2312yes—
499C43C2312yes—
500C43C2312yes—
501C25C2412yes—
502C22×Q8—24no—
503C22×Q8—24no—
504C22×Q8—24no—
505C22×Q8—24no—
506C22×Q8—24no—
507C22×Q8#4118yes—
508C22×Q8C2412yes—
509C22×Q8C2412yes—
510C22×Q8C2412yes—
511C22×Q8C2412yes—
512C22×Q8C2414yes—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4—24no—
516C22×D4C2412yes—
517C22×D4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2411yescharacteristic
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2411yescharacteristic
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—216no—
531C4⋊Q8—44no—
532C4⋊Q8—44no—
533#126—416no—
534#125—48no—
535#125—44no—
536#125—44no—
537#125—48no—
538#124—28no—
539#124—216no—
540#124—28no—
541#124—48no—
542#124—48no—
543C22⋊Q8—48no—
544C22⋊Q8—416no—
545C4×Q8—216no—
546C4×Q8—216no—
547C4×Q8—48no—
548C4×Q8—48no—
549C4×Q8—44no—
550C4×Q8—44no—
551C4×Q8—44no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—44no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×D4—44no—
558C4×D4—44no—
559C4×D4—44no—
560C4×D4—44no—
561#117—216no—
562#117—24no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—48no—
571#117—48no—
572C2×C4⋊C4—216no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—44no—
575C2×C4⋊C4—44no—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2418yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
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⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C22⋊C4—216no—
629C2×C22⋊C4—48no—
630C2×C22⋊C4—48no—
631C2×C22⋊C4—44no—
632C2×C22⋊C4—44no—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C42—24no—
656C2×C42—24no—
657C2×C42—24no—
658C2×C42—44no—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2418yes—
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2414yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2414yes—
678C2×C42C2414yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2418yes—
682C2×C42C2414yes—
683C2×C42C2414yes—
684C2×C42C2414yes—
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2418yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2418yes—
703#95C2414yes—
704#95C2414yes—
705#95C2418yes—
706#95C2418yes—
707#95C2414yes—
708#95C2414yes—
709#95C2418yes—
710#95C2418yes—
711#95C2414yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728C24—24no—
729C24—24no—
730C24—24no—
731C24—44no—
732C24—44no—
733C24C2514yes—
734C24C2511yescharacteristic
735C2×Q8—232no—
736C2×Q8—24no—
737C2×Q8—24no—
738C2×Q8—24no—
739C2×Q8—24no—
740C2×Q8—24no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—24no—
745C2×Q8—24no—
746C2×Q8—44no—
747C2×Q8—48no—
748C2×Q8—416no—
749C2×Q8C2×#4118yes—
750C2×Q8C2×#4118yes—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—24no—
755C2×D4—24no—
756C2×D4—24no—
757C2×D4—416no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—44no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4C2×#4118yes—
780C22×C4C2×#4114yes—
781C22×C4H(5,𝔽2)14yes—
782C22×C42−1+414yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2512yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C4⋊C4—216no—
807C4⋊C4—216no—
808C4⋊C4—216no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—42no—
829C4⋊C4—42no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—44no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—48no—
857C4⋊C4—48no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—216no—
867C22⋊C4—216no—
868C22⋊C4—216no—
869C22⋊C4—48no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C42—22no—
881C42—22no—
882C42—24no—
883C42—22no—
884C42—24no—
885C42—22no—
886C42—216no—
887C42—24no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—28no—
898C42—48no—
899C42—44no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—44no—
905C42—44no—
906C23—22no—
907C23—22no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—28no—
912C23—28no—
913C23—48no—
914C23—88no—
915C23—84no—
916C23—84no—
917C23—88no—
918C23C22×#4112yes—
919C23C2×H(5,𝔽2)12yes—
920C23C2×2−1+412yes—
921C23C2611yescharacteristic
922Q8—216no—
923Q8—216no—
924Q8—48no—
925Q8—48no—
926Q8—164no—
927D4—48no—
928D4—48no—
929C2×C4—22no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—22no—
933C2×C4—216no—
934C2×C4—24no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—28no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—48no—
983C2×C4—44no—
984C2×C4—44no—
985C2×C4—48no—
986C2×C4—84no—
987C2×C4—84no—
988C2×C4—164no—
989C2×C4—164no—
990C2×C4#539116yes—
991C2×C4C22×#4118yes—
992C2×C4C22×#4112yes—
993C2×C4C22×#4112yes—
994C2×C4C2×H(5,𝔽2)12yes—
995C2×C4C2×H(5,𝔽2)12yes—
996C2×C4C2×2−1+412yes—
997C2×C4C2×2−1+412yes—
998C2×C4#58514yes—
999C22—24no—
1000C22—22no—
1001C22—22no—
1002C22—24no—
1003C22—48no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—48no—
1008C22—168no—
1009C22C2×#53914yes—
1010C22C23×#4111yescharacteristic
1011C22C22×H(5,𝔽2)11yescharacteristic
1012C22C22×2−1+411yescharacteristic
1013C22C2×#58512yes—
1014C222−1+612yes—
1015C4—24no—
1016C4—28no—
1017C4—44no—
1018C4—44no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—44no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4C2×#53914yes—
1037C4C2×#53914yes—
1038C2—24no—
1039C2—84no—
1040C2C22×#53911yescharacteristic
1041C2#6283611yescharacteristic
1042C2#6288711yescharacteristic
1043C2#6293212yes—
1044C2#6300512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42902C2semidirect
2. #42845C2semidirect
3. #42837C2semidirect
4. #42830C2semidirect
5. #42010C2semidirect
6. #40191C2semidirect
7. #40105C2semidirect
8. #39782C2semidirect
9. #39219C2semidirect
10. #38469C2semidirect
13. #35674C2semidirect
14. #35668C2semidirect
17. #35313C2semidirect
19. #35154C2semidirect
21. #34815C2semidirect
22. #34815C2semidirect
23. #34249C2semidirect
25. #34209C2semidirect
35. #2863C22semidirect
38. #2838C22semidirect
39. #2836C22semidirect
40. #2807C22semidirect
41. #2798C22semidirect
42. #2793C22semidirect
43. #2790C22semidirect
44. #2787C22semidirect
45. #2783C22semidirect
46. #2783C22semidirect
47. #2777C22semidirect
48. #2775C22semidirect
49. #2773C22semidirect
50. #2771C22semidirect
51. #2765C22semidirect
52. #2744C22semidirect
53. #2721C22semidirect
54. #2720C22semidirect
55. #2689C22semidirect
56. #2667C22semidirect
57. #2664C22semidirect
58. #2654C22semidirect
59. #2654C22semidirect
60. #2652C22semidirect
61. #2650C22semidirect
62. #2645C22semidirect
65. #2596C22semidirect
66. #2594C22semidirect
67. #2577C22semidirect
68. #2575C22semidirect
69. #2573C22semidirect
70. #2568C22semidirect
71. #2567C22semidirect
74. #2565C22semidirect
75. #2565C22semidirect
77. #2556C22semidirect
83. #2514C22semidirect
86. #2511C22semidirect
87. #2509C22semidirect
88. #2509C22semidirect
89. #2508C22semidirect
90. #2508C22semidirect
91. #2507C22semidirect
92. #2507C22semidirect
93. #2506C22semidirect
94. #2506C22semidirect
108. #2453C22semidirect
109. #2453C22semidirect
110. #2453C22semidirect
112. #2451C22semidirect
113. #2451C22semidirect
114. #2451C22semidirect
127. #2446C22semidirect
128. #2446C22semidirect
129. #2446C22semidirect
130. #2446C22semidirect
133. #2402C22semidirect
134. #2402C22semidirect
138. #2365C22semidirect
139. #2365C22semidirect
140. #2351C22semidirect
141. #2351C22semidirect
142. Q8×C4⋊C4C22semidirect
143. Q8×C4⋊C4C22semidirect
146. #2334C22semidirect
147. #2332C22semidirect
148. #2327C22semidirect
149. #2327C22semidirect
164. C4×C4⋊Q8C22semidirect
165. C4×C4⋊Q8C22semidirect
166. C4×#125C22semidirect
167. C4×#125C22semidirect

Maximal subgroups

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

subgroupindex
#429022
#428452
#428372
#428302
#420102
#401912
#401052
#397822
#392192
#384692
#356792
#356742
#356682
#356262
#355292
#353132
#352662
#351542
C2×#25452
#348152
#342492
#342112
#342092