Finite Group Databasebeta

← #7647586

Subgroups — #7647586

Order 512.

5100 conjugacy classes of subgroups.

The subgroup lattice has 1175 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42661C214yesmaximal, complemented
2#42457C214yesmaximal, complemented
3#40664C218yesmaximal, complemented
4#39609C212yesmaximal, complemented
5#39351C212yesmaximal, complemented
6#39159C212yesmaximal, complemented
7#38941C212yesmaximal, complemented
8#38125C214yesmaximal, complemented
9#37704C214yesmaximal, complemented
10#37636C212yesmaximal, complemented
11#37631C212yesmaximal, complemented
12#37349C214yesmaximal, complemented
13#37340C214yesmaximal, complemented
14#35592C212yesmaximal, complemented
15#35545C212yesmaximal, complemented
16#35279C212yesmaximal, complemented
17#35273C211yesmaximal, characteristic
18#35255C212yesmaximal, complemented
19#35180C211yesmaximal, characteristic, complemented
20#35177C212yesmaximal, complemented
21#35170C212yesmaximal, complemented
22#34947C211yesmaximal, characteristic, complemented
23C2×#2551C211yesmaximal, characteristic, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34141C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27C2×#542C2214yes—
28C2×#537C2212yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×C4⋊Q8C2212yes—
32C22×C4⋊Q8C2212yes—
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2212yes—
35#2857C2214yes—
36#2857C2214yes—
37#2857C2212yes—
38#2856C2212yes—
39#2855C2214yes—
40#2854C2214yes—
41#2850C2214yes—
42#2838C2218yes—
43#2832C2218yes—
44#2801C2218yes—
45#2779C2218yes—
46#2777C2218yes—
47#2774C2218yes—
48#2758C2218yes—
49#2745C2218yes—
50#2742C2218yes—
51#2739C2218yes—
52#2737C2218yes—
53#2731C2218yes—
54#2729C2218yes—
55#2723C2218yes—
56#2716C2218yes—
57#2686C2218yes—
58#2674C2218yes—
59#2672C2218yes—
60#2665C2218yes—
61#2663C2218yes—
62#2650C2218yes—
63#2645C2214yes—
64#2640C2214yes—
65#2639C2214yes—
66#2632C2218yes—
67#2628C2214yes—
68#2628C2214yes—
69#2628C2214yes—
70#2625C2214yes—
71#2624C2214yes—
72#2624C2214yes—
73#2620C2214yes—
74#2592C2214yes—
75#2591C2218yes—
76#2568C2212yes—
77#2568C2211yescharacteristic
78#2568C2214yes—
79#2567C2211yescharacteristic
80#2567C2214yes—
81#2566C2212yes—
82#2565C2212yes—
83#2564C2214yes—
84#2563C2211yescharacteristic
85#2563C2212yes—
86#2563C2214yes—
87#2562C2214yes—
88#2551C2212yes—
89#2551C2212yes—
90#2551C2212yes—
91#2551C2214yes—
92#2551C2212yes—
93#2551C2214yes—
94#2548C2212yes—
95#2547C2212yes—
96#2542C2211yescharacteristic
97#2542C2214yes—
98#2538C2212yes—
99#2538C2212yes—
100#2537C2212yes—
101#2537C2212yes—
102#2521C2218yes—
103#2514C2214yes—
104#2513C2214yes—
105#2512C2214yes—
106#2511C2214yes—
107#2510C2218yes—
108#2509C2214yes—
109#2497C2214yes—
110#2496C2214yes—
111#2495C2214yes—
112#2495C2214yes—
113#2494C2214yes—
114#2492C2214yes—
115#2492C2214yes—
116#2492C2214yes—
117#2492C2214yes—
118#2492C2214yes—
119#2491C2214yes—
120#2491C2214yes—
121#2491C2214yes—
122#2491C2214yes—
123#2491C2214yes—
124#2487C2218yes—
125#2481C2218yes—
126#2465C2218yes—
127#2452C2214yes—
128#2451C2214yes—
129#2448C2214yes—
130#2444C2218yes—
131#2443C2218yes—
132#2436C2218yes—
133#2427C2214yes—
134#2423C2214yes—
135#2422C2214yes—
136#2421C2214yes—
137#2420C2214yes—
138#2417C2212yes—
139#2417C2212yes—
140#2416C2214yes—
141#2416C2214yes—
142#2409C2218yes—
143#2396C2214yes—
144C2×#395C2214yes—
145#2367C2212yes—
146#2367C2212yes—
147#2366C2211yescharacteristic
148#2366C2211yescharacteristic
149#2365C2211yescharacteristic
150#2365C2211yescharacteristic
151#2364C2214yes—
152#2361C2212yes—
153#2361C2212yes—
154#2360C2214yes—
155#2360C2214yes—
156#2355C2212yes—
157#2355C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160#2331C2214yes—
161#2330C2214yes—
162#2323C2214yes—
163#2320C2212yes—
164#2319C2212yes—
165#2319C2214yes—
166#2318C2214yes—
167#2317C2211yescharacteristic
168#2317C2211yescharacteristic
169#2317C2212yes—
170#2314C2212yes—
171#2314C2212yes—
172#2311C2211yescharacteristic
173#2311C2212yes—
174#2311C2211yescharacteristic
175#2311C2212yes—
176#2311C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2212yes—
181#2297C2212yes—
182#2297C2212yes—
183#2295C2212yes—
184#2293C2212yes—
185#2293C2212yes—
186C2×#389C2212yes—
187C2×#389C2212yes—
188#2290C2214yes—
189#2290C2214yes—
190#2285C2212yes—
191#2285C2212yes—
192C2×#384C2211yescharacteristic
193#2283C2212yes—
194#2274C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2312yes—
200C22×#41C2311yescharacteristic
201C23×Q8C2314yes—
202#542—416no—
203#537—48no—
204#533—28no—
205#532—28no—
206C2×C4⋊Q8—48no—
207C2×C4⋊Q8—48no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2318yes—
218C2×#127C2311yescharacteristic
219C2×#126C2318yes—
220C2×#125C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2318yes—
224C2×#124C2318yes—
225C2×#123C2318yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2318yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C4×#41—28no—
242C4×#41—48no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×#117C2311yescharacteristic
264C2×#117C2312yes—
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2312yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2314yes—
283C22×C42C2311yescharacteristic
284#401C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2318yes—
295#399C2314yes—
296#399C2318yes—
297#399C2318yes—
298#399C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2314yes—
310#396C2314yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#395C2314yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#393C2314yes—
329#393C2318yes—
330#393C2318yes—
331#393C2318yes—
332#393C2318yes—
333#393C2318yes—
334#393C2318yes—
335#393C2318yes—
336#391C2314yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2312yes—
344#391C2312yes—
345#391C2314yes—
346#391C2318yes—
347#391C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2318yes—
351#391C2312yes—
352#391C2312yes—
353#391C2318yes—
354#390C2312yes—
355#390C2314yes—
356#390C2314yes—
357#390C2314yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2318yes—
374#389C2312yes—
375#389C2318yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2314yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2314yes—
425#387C2314yes—
426#387C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2314yes—
435#386C2318yes—
436#386C2314yes—
437#386C2314yes—
438#386C2314yes—
439#385C2314yes—
440#385C2314yes—
441#385C2314yes—
442#385C2314yes—
443#385C2318yes—
444#385C2318yes—
445#385C2314yes—
446#385C2314yes—
447#384C2312yes—
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2314yes—
452#384C2312yes—
453#384C2312yes—
454#384C2312yes—
455#384C2312yes—
456#383C2314yes—
457#383C2318yes—
458#382C2312yes—
459#382C2312yes—
460#382C2314yes—
461#382C2314yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#381C2314yes—
466#381C2318yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521#376C2312yes—
522#376C2314yes—
523C2×#95C2312yes—
524C2×#95C2312yes—
525C2×#95C2314yes—
526C43C2312yes—
527C2×#41—24no—
528C2×#41—28no—
529C2×#41—28no—
530C2×#41—24no—
531C2×#41—28no—
532C2×#41—24no—
533C22×Q8—48no—
534C22×Q8—48no—
535C22×Q8—84no—
536C22×Q8C2412yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2418yes—
541C22×Q8C2418yes—
542C22×D4C2412yes—
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2411yescharacteristic
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2418yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2414yes—
559C23×C4C2414yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C4⋊Q8—216no—
564C4⋊Q8—24no—
565C4⋊Q8—24no—
566C4⋊Q8—24no—
567C4⋊Q8—48no—
568C4⋊Q8—48no—
569C4⋊Q8—48no—
570C4⋊Q8—48no—
571C4⋊Q8—48no—
572C4⋊Q8—416no—
573#127—24no—
574#126—416no—
575#125—28no—
576#124—28no—
577#124—48no—
578#124—416no—
579#124—88no—
580#123—416no—
581C22⋊Q8—28no—
582C22⋊Q8—28no—
583C22⋊Q8—28no—
584C22⋊Q8—28no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—416no—
588C22⋊Q8—88no—
589#121—28no—
590#121—28no—
591#121—48no—
592#121—48no—
593#121—48no—
594#121—416no—
595#121—84no—
596C4×Q8—24no—
597C4×Q8—24no—
598C4×Q8—28no—
599C4×Q8—28no—
600C4×Q8—44no—
601C4×Q8—44no—
602C4×Q8—48no—
603C4×Q8—84no—
604C4×D4—28no—
605C4×D4—28no—
606C4×D4—28no—
607C4×D4—28no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—28no—
611C4×D4—28no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—48no—
615C4×D4—48no—
616#117—24no—
617#117—28no—
618#117—24no—
619#117—24no—
620#117—28no—
621#117—48no—
622#117—48no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—44no—
629C2×C4⋊C4—48no—
630C2×C4⋊C4—48no—
631C2×C4⋊C4—82no—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C42—28no—
712C2×C42—28no—
713C2×C42—48no—
714C2×C42—44no—
715C2×C42#4118yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2414yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2418yes—
733C2×C42C2418yes—
734C2×C42C2414yes—
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#95C2412yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2414yes—
745#95C2412yes—
746#95C2418yes—
747#95C2418yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2418yes—
782C24C2512yes—
783C24C2514yes—
784C24C2511yescharacteristic
785#41—416no—
786#41—432no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—22no—
794C2×Q8—216no—
795C2×Q8—24no—
796C2×Q8—22no—
797C2×Q8—24no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—48no—
801C2×Q8—48no—
802C2×Q8—48no—
803C2×Q8—48no—
804C2×Q8—48no—
805C2×Q8—832no—
806C2×D4—24no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—28no—
812C2×D4—22no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—24no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—48no—
825C2×D4—48no—
826C2×D4—48no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—28no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—28no—
847C22×C4—28no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—41no—
851C22×C4—41no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—42no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—42no—
864C22×C4C2×#4114yes—
865C22×C4C2×#4114yes—
866C22×C4C2×#4114yes—
867C22×C4H(5,𝔽2)14yes—
868C22×C42−1+414yes—
869C22×C4C2512yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2512yes—
874C22×C4C2514yes—
875C22×C4C2512yes—
876C22×C4C2514yes—
877C22×C4C2514yes—
878C22×C4C2512yes—
879C22×C4C2512yes—
880C22×C4C2512yes—
881C22×C4C2514yes—
882C22×C4C2518yes—
883C22×C4C2512yes—
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2512yes—
888C22×C4C2512yes—
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—28no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—24no—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—28no—
911C4⋊C4—216no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—28no—
915C4⋊C4—24no—
916C4⋊C4—24no—
917C4⋊C4—24no—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—28no—
922C4⋊C4—48no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—48no—
936C4⋊C4—48no—
937C4⋊C4—44no—
938C4⋊C4—44no—
939C4⋊C4H(5,𝔽2)14yes—
940C4⋊C42−1+414yes—
941C22⋊C4—24no—
942C22⋊C4—28no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—24no—
946C22⋊C4—24no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—28no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—28no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—44no—
985C42—44no—
986C42—44no—
987C42—42no—
988C42—48no—
989C42—42no—
990C42—48no—
991C42C2×#4114yes—
992C42C2×#4114yes—
993C42C2×#4114yes—
994C42C2×#4114yes—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23C22×#4112yes—
1014C23C2×H(5,𝔽2)12yes—
1015C23C2×2−1+412yes—
1016C23C2611yescharacteristic
1017Q8—48no—
1018Q8—44no—
1019Q8—48no—
1020Q8—48no—
1021Q8—816no—
1022Q8—816no—
1023D4—48no—
1024D4—416no—
1025D4—44no—
1026D4—48no—
1027D4—48no—
1028D4—84no—
1029D4—168no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—28no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—28no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—48no—
1088C2×C4—48no—
1089C2×C4—48no—
1090C2×C4—48no—
1091C2×C4—416no—
1092C2×C4—48no—
1093C2×C4—48no—
1094C2×C4—84no—
1095C2×C4—88no—
1096C2×C4—88no—
1097C2×C4—88no—
1098C2×C4#542116yescomplemented
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C22×#4112yes—
1103C2×C4C22×#4112yes—
1104C2×C4C22×#4112yes—
1105C2×C4C2×H(5,𝔽2)14yes—
1106C2×C4C2×H(5,𝔽2)12yes—
1107C2×C4C2×H(5,𝔽2)12yes—
1108C2×C4C2×H(5,𝔽2)12yes—
1109C2×C4C2×2−1+414yes—
1110C2×C4C2×2−1+412yes—
1111C2×C4C2×2−1+412yes—
1112C2×C4C2×2−1+412yes—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—42no—
1120C22—44no—
1121C22—42no—
1122C22—44no—
1123C22—44no—
1124C22—42no—
1125C22—42no—
1126C22—44no—
1127C22—42no—
1128C22—44no—
1129C22—44no—
1130C22—42no—
1131C22—42no—
1132C22—44no—
1133C22C2×#54214yes—
1134C22C23×#4111yescharacteristic
1135C22C22×H(5,𝔽2)11yescharacteristic
1136C22C22×H(5,𝔽2)11yescharacteristic
1137C22C22×2−1+411yescharacteristic
1138C22C22×2−1+411yescharacteristic
1139C22H(7,𝔽2)11yescharacteristic
1140C222−1+611yescharacteristic
1141C4—22no—
1142C4—22no—
1143C4—22no—
1144C4—24no—
1145C4—24no—
1146C4—42no—
1147C4—44no—
1148C4—42no—
1149C4—44no—
1150C4—42no—
1151C4—44no—
1152C4—42no—
1153C4—48no—
1154C4—42no—
1155C4—44no—
1156C4—42no—
1157C4—44no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4C2×#54214yes—
1162C4C2×#54214yes—
1163C4#351114yes—
1164C2—24no—
1165C2—82no—
1166C2—84no—
1167C2C22×#54211yescharacteristic
1168C2C2×#351111yescharacteristic
1169C2#6285611yescharacteristic
1170C2#6291211yescharacteristic
1171C2#6291311yescharacteristic
1172C2#6294211yescharacteristic
1173C2#6294311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35273C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42661C2semidirect
2. #42457C2semidirect
3. #40664C2semidirect
4. #39609C2semidirect
5. #39351C2semidirect
6. #39159C2semidirect
7. #38941C2semidirect
8. #38125C2semidirect
9. #37704C2semidirect
10. #37636C2semidirect
11. #37631C2semidirect
12. #37349C2semidirect
13. #37340C2semidirect
14. #35592C2semidirect
15. #35545C2semidirect
16. #35279C2semidirect
18. #35255C2semidirect
19. #35180C2semidirect
20. #35177C2semidirect
21. #35170C2semidirect
22. #34947C2semidirect
23. C2×#2551C2semidirect
24. #34214C2semidirect
25. #34141C2semidirect
26. #34060C2semidirect
1098. C2×C4#542semidirect

Maximal subgroups

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

subgroupindex
#426612
#424572
#406642
#396092
#393512
#391592
#389412
#381252
#377042
#376362
#376312
#373492
#373402
#355922
#355452
#352792
#352732
#352552
#351802
#351772
#351702
#349472
C2×#25512
#342142
#341412
#340602