Finite Group Databasebeta

← #7647484

Subgroups — #7647484

Order 512.

4932 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42453C214yesmaximal, complemented
2#42447C214yesmaximal, complemented
3#40649C218yesmaximal, complemented
4#39628C212yesmaximal, complemented
5#39608C212yesmaximal, complemented
6#39374C212yesmaximal, complemented
7#39351C212yesmaximal, complemented
8#39185C212yesmaximal, complemented
9#39148C212yesmaximal, complemented
10#38972C212yesmaximal, complemented
11#38931C212yesmaximal, complemented
12#37511C214yesmaximal, complemented
13#36833C214yesmaximal, complemented
14#36832C214yesmaximal, complemented
15#35553C214yesmaximal, complemented
16#35292C211yesmaximal, characteristic, complemented
17#35230C214yesmaximal, complemented
18#35195C214yesmaximal, complemented
19#35192C211yesmaximal, characteristic, complemented
20#34977C211yesmaximal, characteristic, complemented
21#34909C211yesmaximal, characteristic, complemented
22#34236C211yesmaximal, characteristic, complemented
23C4⋊C4×#41C211yesmaximal, characteristic, complemented
24#34060C211yesmaximal, characteristic, complemented
25C2×#542C2214yes—
26C2×#532C2211yescharacteristic
27C2×C4×#41C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2212yes—
30#2864C2212yes—
31#2862C2212yes—
32#2857C2212yes—
33#2856C2212yes—
34#2852C2218yes—
35#2850C2218yes—
36#2827C2218yes—
37#2824C2218yes—
38#2804C2218yes—
39#2796C2218yes—
40#2775C2218yes—
41#2773C2218yes—
42#2763C2218yes—
43#2758C2218yes—
44#2749C2218yes—
45#2732C2218yes—
46#2723C2218yes—
47#2714C2218yes—
48#2710C2218yes—
49#2698C2218yes—
50#2692C2218yes—
51#2689C2218yes—
52#2688C2218yes—
53#2672C2218yes—
54#2665C2214yes—
55#2651C2218yes—
56#2650C2218yes—
57#2647C2214yes—
58#2644C2214yes—
59#2638C2218yes—
60#2636C2218yes—
61#2636C2218yes—
62#2631C2218yes—
63#2628C2214yes—
64#2624C2214yes—
65#2624C2212yes—
66#2615C2212yes—
67#2610C2214yes—
68#2605C2214yes—
69#2600C2214yes—
70#2599C2212yes—
71#2598C2212yes—
72#2592C2212yes—
73#2581C2211yescharacteristic
74#2580C2212yes—
75#2580C2211yescharacteristic
76#2575C2218yes—
77#2571C2212yes—
78#2570C2214yes—
79#2567C2211yescharacteristic
80#2563C2211yescharacteristic
81#2563C2214yes—
82#2560C2218yes—
83#2551C2212yes—
84#2548C2211yescharacteristic
85#2542C2214yes—
86#2541C2211yescharacteristic
87#2540C2212yes—
88#2536C2211yescharacteristic
89#2535C2211yescharacteristic
90#2535C2212yes—
91#2535C2214yes—
92#2521C2218yes—
93#2517C2218yes—
94#2515C2218yes—
95#2512C2214yes—
96#2508C2214yes—
97#2508C2214yes—
98#2504C2214yes—
99#2500C2212yes—
100#2497C2214yes—
101#2496C2214yes—
102#2496C2214yes—
103#2495C2214yes—
104#2491C2214yes—
105#2488C2218yes—
106#2487C2214yes—
107#2485C2212yes—
108#2477C2218yes—
109#2471C2218yes—
110#2467C2218yes—
111#2463C2218yes—
112#2456C2218yes—
113#2452C2214yes—
114#2452C2214yes—
115#2450C2218yes—
116#2450C2218yes—
117#2448C2214yes—
118#2444C2218yes—
119#2440C2214yes—
120#2439C2214yes—
121#2439C2214yes—
122#2431C2212yes—
123#2428C2214yes—
124#2422C2214yes—
125#2421C2214yes—
126#2420C2214yes—
127#2420C2214yes—
128#2416C2214yes—
129#2414C2214yes—
130#2414C2214yes—
131#2407C2212yes—
132#2407C2214yes—
133#2395C2212yes—
134#2388C2212yes—
135#2388C2214yes—
136#2369C2212yes—
137#2366C2212yes—
138#2361C2214yes—
139#2357C2212yes—
140#2351C2212yes—
141Q8×C4⋊C4C2212yes—
142#2349C2212yes—
143#2349C2214yes—
144#2349C2212yes—
145D4×C4⋊C4C2212yes—
146D4×C4⋊C4C2214yes—
147#2339C2214yes—
148#2337C2214yes—
149#2331C2214yes—
150#2328C2214yes—
151#2324C2214yes—
152#2324C2214yes—
153#2320C2212yes—
154#2320C2214yes—
155#2319C2212yes—
156#2319C2212yes—
157#2318C2214yes—
158#2317C2212yes—
159#2314C2212yes—
160#2314C2212yes—
161#2311C2212yes—
162C4×#127C2212yes—
163C4×#124C2212yes—
164C4×C22⋊Q8C2212yes—
165C4×#121C2212yes—
166C4×#121C2214yes—
167C4×#121C2214yes—
168#2296C2212yes—
169#2296C2214yes—
170#2295C2212yes—
171#2293C2212yes—
172#2290C2214yes—
173#2290C2214yes—
174#2285C2212yes—
175#2285C2211yescharacteristic
176#2285C2212yes—
177#2283C2212yes—
178#2283C2211yescharacteristic
179#2275C2212yes—
180C4×#117C2211yescharacteristic
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×C4×C4⋊C4C2212yes—
183C22×#41C2311yescharacteristic
184C22×#41C2311yescharacteristic
185C22×#41C2312yes—
186#542—416no—
187#532—28no—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2314yes—
190C2×C4⋊Q8C2314yes—
191C2×#127C2312yes—
192C2×#127C2311yescharacteristic
193C2×#126C2318yes—
194C2×#126C2318yes—
195C2×#124C2312yes—
196C2×#124C2312yes—
197C2×#124C2318yes—
198C2×#123C2318yes—
199C2×C22⋊Q8C2312yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2318yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2314yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2312yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2314yes—
212C4×#41—28no—
213C4×#41—28no—
214C4×#41—48no—
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2312yes—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2312yes—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2318yes—
237C2×#117C2312yes—
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2312yes—
244C2×#117C2314yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2314yes—
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2314yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2312yes—
259#400C2318yes—
260#399C2318yes—
261#399C2312yes—
262#399C2314yes—
263#399C2318yes—
264#399C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2312yes—
268#398C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2314yes—
273#397C2318yes—
274#397C2314yes—
275#397C2312yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#395C2314yes—
285#395C2312yes—
286#395C2318yes—
287#395C2318yes—
288#394C2318yes—
289#394C2314yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2312yes—
294#394C2314yes—
295#394C2314yes—
296#394C2318yes—
297#394C2318yes—
298#393C2318yes—
299#393C2314yes—
300#393C2318yes—
301#393C2318yes—
302#393C2318yes—
303#393C2314yes—
304#393C2312yes—
305#392C2318yes—
306#392C2312yes—
307#392C2314yes—
308#392C2314yes—
309#392C2314yes—
310#392C2318yes—
311#392C2318yes—
312#391C2318yes—
313#391C2314yes—
314#391C2312yes—
315#391C2312yes—
316#391C2318yes—
317#391C2314yes—
318#391C2318yes—
319#391C2318yes—
320#390C2318yes—
321#390C2312yes—
322#390C2318yes—
323#390C2312yes—
324#390C2318yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2312yes—
333#390C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2314yes—
349#389C2318yes—
350#389C2314yes—
351#388C2314yes—
352#388C2314yes—
353#388C2318yes—
354#388C2314yes—
355#388C2314yes—
356#388C2314yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2314yes—
366#388C2318yes—
367#387C2318yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2314yes—
372#387C2318yes—
373#387C2318yes—
374#387C2314yes—
375#387C2318yes—
376#387C2318yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2314yes—
381#387C2318yes—
382#386C2318yes—
383#386C2314yes—
384#386C2314yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2314yes—
397#386C2314yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2314yes—
405#385C2318yes—
406#385C2314yes—
407#385C2318yes—
408#385C2314yes—
409#385C2318yes—
410#385C2318yes—
411#384C2312yes—
412#384C2312yes—
413#384C2312yes—
414#384C2314yes—
415#384C2312yes—
416#383C2314yes—
417#383C2318yes—
418#383C2312yes—
419#382C2318yes—
420#382C2312yes—
421#382C2312yes—
422#382C2312yes—
423#382C2314yes—
424#382C2314yes—
425#382C2314yes—
426#382C2318yes—
427#382C2311yescharacteristic
428#382C2312yes—
429#382C2311yescharacteristic
430#382C2314yes—
431#381C2314yes—
432#381C2314yes—
433#381C2318yes—
434#381C2312yes—
435#380C2312yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2312yes—
440#380C2312yes—
441#380C2312yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2312yes—
446#380C2312yes—
447#380C2314yes—
448#380C2312yes—
449#380C2312yes—
450#380C2312yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2312yes—
479#376C2312yes—
480#376C2312yes—
481#376C2314yes—
482C2×#95C2312yes—
483C2×#95C2314yes—
484C2×#95C2314yes—
485C43C2312yes—
486C2×#41—24no—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—24no—
490C2×#41—28no—
491C2×#41—44no—
492C2×#41—84no—
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2412yes—
496C22×Q8C2418yes—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2412yes—
500C22×D4C2411yescharacteristic
501C22×D4C2414yes—
502C22×D4C2412yes—
503C22×D4C2411yescharacteristic
504C22×D4C2414yes—
505C22×D4C2418yes—
506C22×D4C2412yes—
507C22×D4C2418yes—
508C23×C4C2412yes—
509C23×C4C2412yes—
510C23×C4C2412yes—
511C23×C4C2412yes—
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2412yes—
515C23×C4C2414yes—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2418yes—
519C23×C4C2418yes—
520C23×C4C2411yescharacteristic
521C4⋊Q8—24no—
522C4⋊Q8—48no—
523C4⋊Q8—48no—
524#127—28no—
525#127—24no—
526#126—416no—
527#126—88no—
528#124—28no—
529#124—28no—
530#124—416no—
531#123—416no—
532C22⋊Q8—28no—
533C22⋊Q8—416no—
534C22⋊Q8—88no—
535C22⋊Q8—88no—
536C22⋊Q8—84no—
537#121—28no—
538#121—28no—
539#121—28no—
540#121—48no—
541#121—48no—
542#121—48no—
543#121—88no—
544#121—84no—
545C4×Q8—216no—
546C4×Q8—24no—
547C4×Q8—24no—
548C4×Q8—24no—
549C4×Q8—24no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—28no—
553C4×D4—28no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—24no—
557C4×D4—24no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—48no—
561C4×D4—48no—
562C4×D4—416no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—88no—
566C4×D4—88no—
567#117—24no—
568#117—24no—
569#117—28no—
570#117—28no—
571#117—48no—
572#117—44no—
573#117—44no—
574#117—48no—
575C2×C4⋊C4—44no—
576C2×C4⋊C4—48no—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2412yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C42—28no—
647C2×C42—28no—
648C2×C42—44no—
649C2×C42—48no—
650C2×C42#4118yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2418yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2418yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2414yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2418yes—
690#95C2414yes—
691#95C2412yes—
692#95C2414yes—
693#95C2418yes—
694#95C2412yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2418yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2418yes—
704#95C2414yes—
705#95C2414yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712C24C2512yes—
713C24C2514yes—
714C24C2511yescharacteristic
715C24C2512yes—
716#41—232no—
717#41—416no—
718#41—816no—
719C2×Q8—22no—
720C2×Q8—22no—
721C2×Q8—24no—
722C2×Q8—22no—
723C2×Q8—42no—
724C2×Q8—44no—
725C2×Q8—48no—
726C2×Q8—48no—
727C2×Q8—48no—
728C2×Q8H(5,𝔽2)14yes—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—216no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—22no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—28no—
745C2×D4—48no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D42−1+414yes—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—24no—
769C22×C4—28no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—28no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—48no—
778C22×C4—44no—
779C22×C4—48no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—48no—
783C22×C4—42no—
784C22×C4—48no—
785C22×C4—42no—
786C22×C4—48no—
787C22×C4—48no—
788C22×C4—48no—
789C22×C4C2×#4114yes—
790C22×C4C2×#4114yes—
791C22×C4C2×#4114yes—
792C22×C4C2514yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2512yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2518yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2512yes—
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—216no—
824C4⋊C4—24no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—24no—
829C4⋊C4—28no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—44no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—44no—
840C4⋊C4—48no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C22⋊C4—24no—
849C22⋊C4—24no—
850C22⋊C4—28no—
851C22⋊C4—24no—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—24no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—216no—
859C22⋊C4—44no—
860C22⋊C4—48no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—48no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—48no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—216no—
889C42—24no—
890C42—24no—
891C42—28no—
892C42—42no—
893C42—42no—
894C42—44no—
895C42—44no—
896C42—44no—
897C42—48no—
898C42C2×#4114yes—
899C42C2×#4114yes—
900C42C2×#4114yes—
901C42C2×#4114yes—
902C23—22no—
903C23—21no—
904C23—22no—
905C23—21no—
906C23—22no—
907C23—24no—
908C23—24no—
909C23—22no—
910C23—22no—
911C23—24no—
912C23—22no—
913C23—24no—
914C23—22no—
915C23—24no—
916C23—28no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—22no—
922C23C22×#4112yes—
923C23C2×2−1+414yes—
924C23C2611yescharacteristic
925Q8—28no—
926Q8—44no—
927Q8—84no—
928Q8—168no—
929D4—216no—
930D4—28no—
931D4—44no—
932D4—48no—
933D4—416no—
934D4—48no—
935D4—48no—
936D4—84no—
937D4—88no—
938D4—816no—
939D4—168no—
940C2×C4—216no—
941C2×C4—22no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—28no—
949C2×C4—28no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—28no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—28no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—28no—
985C2×C4—24no—
986C2×C4—44no—
987C2×C4—48no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—84no—
991C2×C4—84no—
992C2×C4—88no—
993C2×C4—88no—
994C2×C4—816no—
995C2×C4—168no—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C22×#4112yes—
1002C2×C4C2×H(5,𝔽2)14yes—
1003C2×C4C2×H(5,𝔽2)12yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4#58514yes—
1006C22—22no—
1007C22—24no—
1008C22—22no—
1009C22—22no—
1010C22—28no—
1011C22—42no—
1012C22—42no—
1013C22—44no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—44no—
1018C22—44no—
1019C22—42no—
1020C22—48no—
1021C22—42no—
1022C22—42no—
1023C22—42no—
1024C22—44no—
1025C22—42no—
1026C22—48no—
1027C22—42no—
1028C22C23×#4111yescharacteristic
1029C22C22×H(5,𝔽2)11yescharacteristic
1030C22C22×2−1+411yescharacteristic
1031C22C2×#58512yes—
1032C22H(7,𝔽2)12yes—
1033C4—22no—
1034C4—24no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—44no—
1042C4—44no—
1043C4—44no—
1044C4—48no—
1045C4—44no—
1046C4—44no—
1047C4—42no—
1048C4—42no—
1049C4—44no—
1050C4—44no—
1051C4#345514yes—
1052C4#349214yes—
1053C2—42no—
1054C2—44no—
1055C2—82no—
1056C2—84no—
1057C2C2×#345511yescharacteristic
1058C2C2×#349211yescharacteristic
1059C2#6285511yescharacteristic
1060C2#6292312yes—
1061C2#6295112yes—
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. #42453C2semidirect
2. #42447C2semidirect
3. #40649C2semidirect
4. #39628C2semidirect
5. #39608C2semidirect
6. #39374C2semidirect
7. #39351C2semidirect
8. #39185C2semidirect
9. #39148C2semidirect
10. #38972C2semidirect
11. #38931C2semidirect
12. #37511C2semidirect
13. #36833C2semidirect
14. #36832C2semidirect
15. #35553C2semidirect
16. #35292C2semidirect
17. #35230C2semidirect
18. #35195C2semidirect
19. #35192C2semidirect
20. #34977C2semidirect
21. #34909C2semidirect
22. #34236C2semidirect
23. C4⋊C4×#41C2semidirect
24. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#424532
#424472
#406492
#396282
#396082
#393742
#393512
#391852
#391482
#389722
#389312
#375112
#368332
#368322
#355532
#352922
#352302
#351952
#351922
#349772
#349092
#342362
C4⋊C4×#412
#340602