Finite Group Databasebeta

← #7720069

Subgroups — #7720069

Order 512.

4683 conjugacy classes of subgroups.

The subgroup lattice has 1075 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50717C214yesmaximal, complemented
2#50716C214yesmaximal, complemented
3#50664C214yesmaximal, complemented
4#50663C214yesmaximal, complemented
5#45433C214yesmaximal, complemented
6#45212C214yesmaximal, complemented
7#45126C214yesmaximal, complemented
8#45115C214yesmaximal, complemented
9#39439C214yesmaximal, complemented
10#39350C212yesmaximal, complemented
11#39071C214yesmaximal, complemented
12#38940C212yesmaximal, complemented
13#37432C212yesmaximal, complemented
14#37396C212yesmaximal, complemented
15#36586C212yesmaximal, complemented
16#36449C212yesmaximal, complemented
17#35331C212yesmaximal, complemented
18#35316C211yesmaximal, characteristic, complemented
19#35314C212yesmaximal, complemented
20#35289C211yesmaximal, characteristic, complemented
21#35192C211yesmaximal, characteristic, complemented
22#34609C211yesmaximal, characteristic
23#34371C211yesmaximal, characteristic, complemented
24#34367C211yesmaximal, characteristic, complemented
25#34121C211yesmaximal, characteristic, complemented
26C2×#542C2214yes—
27C2×#536C2212yes—
28C2×#532C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31#2864C2212yes—
32#2863C2214yes—
33#2862C2212yes—
34#2862C2212yes—
35#2858C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2850C2214yes—
39#2799C2218yes—
40#2797C2218yes—
41#2786C2218yes—
42#2775C2218yes—
43#2762C2218yes—
44#2759C2218yes—
45#2759C2218yes—
46#2754C2218yes—
47#2754C2218yes—
48#2752C2218yes—
49#2740C2218yes—
50#2740C2218yes—
51#2737C2218yes—
52#2737C2218yes—
53#2717C2218yes—
54#2716C2218yes—
55#2712C2218yes—
56#2698C2218yes—
57#2696C2218yes—
58#2693C2218yes—
59#2665C2214yes—
60#2640C2214yes—
61#2640C2214yes—
62#2635C2212yes—
63#2635C2212yes—
64#2632C2212yes—
65#2631C2212yes—
66#2628C2211yescharacteristic
67#2628C2211yescharacteristic
68#2625C2214yes—
69#2624C2212yes—
70#2621C2212yes—
71#2621C2212yes—
72#2619C2211yescharacteristic
73#2619C2211yescharacteristic
74#2615C2212yes—
75#2607C2218yes—
76#2605C2214yes—
77#2596C2218yes—
78#2578C2218yes—
79#2576C2218yes—
80#2572C2218yes—
81#2571C2212yes—
82#2563C2214yes—
83#2563C2214yes—
84#2560C2218yes—
85#2560C2218yes—
86#2557C2218yes—
87#2557C2218yes—
88#2557C2218yes—
89#2557C2218yes—
90#2554C2218yes—
91#2551C2212yes—
92#2547C2212yes—
93#2547C2212yes—
94#2547C2214yes—
95#2547C2212yes—
96#2547C2212yes—
97#2546C2212yes—
98#2546C2212yes—
99#2530C2218yes—
100#2524C2218yes—
101#2523C2218yes—
102#2523C2218yes—
103#2520C2218yes—
104#2517C2218yes—
105#2514C2214yes—
106#2510C2218yes—
107#2504C2214yes—
108#2496C2214yes—
109#2495C2214yes—
110#2495C2214yes—
111#2494C2214yes—
112#2492C2214yes—
113#2492C2218yes—
114#2487C2214yes—
115#2486C2212yes—
116#2486C2214yes—
117#2486C2212yes—
118#2486C2212yes—
119#2486C2212yes—
120#2485C2214yes—
121#2485C2214yes—
122#2451C2214yes—
123#2448C2214yes—
124#2447C2214yes—
125#2440C2214yes—
126#2439C2214yes—
127#2439C2214yes—
128#2439C2214yes—
129#2436C2214yes—
130#2427C2214yes—
131#2426C2214yes—
132#2421C2214yes—
133#2398C2212yes—
134#2397C2212yes—
135#2388C2212yes—
136#2388C2212yes—
137#2381C2214yes—
138#2377C2214yes—
139#2365C2212yes—
140#2365C2212yes—
141#2363C2214yes—
142#2357C2212yes—
143#2356C2212yes—
144#2355C2212yes—
145#2354C2212yes—
146#2354C2212yes—
147#2353C2212yes—
148#2353C2212yes—
149#2352C2212yes—
150#2352C2214yes—
151#2352C2214yes—
152#2352C2214yes—
153#2352C2212yes—
154D4×C4⋊C4C2212yes—
155#2347C2214yes—
156#2345C2214yes—
157#2345C2214yes—
158Q8×C22⋊C4C2214yes—
159#2337C2214yes—
160#2331C2212yes—
161#2331C2214yes—
162#2331C2214yes—
163#2328C2212yes—
164#2327C2212yes—
165#2327C2212yes—
166#2320C2214yes—
167#2313C2214yes—
168#2311C2214yes—
169#2311C2214yes—
170#2310C2212yes—
171C4×#124C2214yes—
172C4×C22⋊Q8C2214yes—
173C4×#121C2212yes—
174C4×#121C2212yes—
175#2298C2212yes—
176#2298C2212yes—
177#2297C2212yes—
178#2285C2211yescharacteristic
179#2285C2211yescharacteristic
180#2283C2211yescharacteristic
181#2283C2211yescharacteristic
182#2283C2211yescharacteristic
183C4×#117C2212yes—
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2312yes—
189C23×Q8C2312yes—
190#542—416no—
191#536—48no—
192#532—28no—
193C2×C4⋊Q8—28no—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×#127C2311yescharacteristic
203C2×#126C2318yes—
204C2×#124C2312yes—
205C2×#124C2314yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2318yes—
209C2×#123C2314yes—
210C2×#123C2314yes—
211C2×#123C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2314yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C4×#41—28no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2312yes—
241C2×#117C2314yes—
242C2×#117C2312yes—
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251#401C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2312yes—
256#400C2312yes—
257#400C2318yes—
258#400C2318yes—
259#399C2318yes—
260#399C2314yes—
261#399C2312yes—
262#399C2312yes—
263#398C2314yes—
264#398C2314yes—
265#398C2314yes—
266#398C2314yes—
267#398C2318yes—
268#398C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2314yes—
274#397C2314yes—
275#397C2314yes—
276#397C2314yes—
277#397C2314yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#396C2318yes—
286#396C2318yes—
287#395C2318yes—
288#395C2312yes—
289#395C2312yes—
290#395C2318yes—
291#394C2312yes—
292#394C2312yes—
293#394C2314yes—
294#394C2314yes—
295#394C2318yes—
296#394C2312yes—
297#394C2312yes—
298#394C2318yes—
299#393C2318yes—
300#393C2318yes—
301#393C2318yes—
302#393C2318yes—
303#393C2318yes—
304#393C2318yes—
305#393C2314yes—
306#393C2312yes—
307#393C2312yes—
308#392C2314yes—
309#392C2314yes—
310#392C2314yes—
311#392C2312yes—
312#392C2312yes—
313#392C2312yes—
314#392C2312yes—
315#391C2318yes—
316#391C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2318yes—
322#391C2318yes—
323#391C2318yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2318yes—
329#391C2318yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#390C2318yes—
334#390C2318yes—
335#390C2318yes—
336#390C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2314yes—
359#388C2318yes—
360#388C2314yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2314yes—
404#386C2314yes—
405#386C2314yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#384C2312yes—
410#384C2312yes—
411#383C2318yes—
412#383C2318yes—
413#383C2312yes—
414#383C2318yes—
415#383C2312yes—
416#383C2312yes—
417#382C2318yes—
418#382C2318yes—
419#382C2314yes—
420#382C2314yes—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2312yes—
424#382C2312yes—
425#382C2312yes—
426#382C2312yes—
427#381C2314yes—
428#381C2314yes—
429#381C2312yes—
430#381C2312yes—
431#381C2318yes—
432#381C2312yes—
433#380C2314yes—
434#380C2312yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2312yes—
441#380C2312yes—
442#380C2314yes—
443#380C2318yes—
444#380C2314yes—
445#380C2312yes—
446#380C2318yes—
447#380C2314yes—
448#380C2314yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2311yescharacteristic
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2318yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2314yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489#376C2312yes—
490#376C2312yes—
491#376C2312yes—
492#376C2312yes—
493#376C2312yes—
494C2×#95C2312yes—
495C43C2312yes—
496C43C2312yes—
497C2×#41—24no—
498C2×#41—28no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41—48no—
502C22×Q8—28no—
503C22×Q8—44no—
504C22×Q8—44no—
505C22×Q8C2414yes—
506C22×Q8C2411yescharacteristic
507C22×Q8C2414yes—
508C22×Q8C2412yes—
509C22×Q8C2418yes—
510C22×D4C2412yes—
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2414yes—
515C22×D4C2412yes—
516C22×D4C2414yes—
517C22×D4C2412yes—
518C22×D4C2414yes—
519C23×C4C2411yescharacteristic
520C23×C4C2414yes—
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C23×C4C2414yes—
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2418yes—
530C23×C4C2414yes—
531C23×C4C2411yescharacteristic
532C4⋊Q8—28no—
533C4⋊Q8—28no—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—48no—
538C4⋊Q8—48no—
539C4⋊Q8—48no—
540#127—24no—
541#126—416no—
542#124—28no—
543#124—48no—
544#124—48no—
545#124—48no—
546#124—416no—
547#123—48no—
548#123—416no—
549#123—48no—
550C22⋊Q8—216no—
551C22⋊Q8—416no—
552C22⋊Q8—48no—
553#121—28no—
554#121—28no—
555#121—28no—
556#121—44no—
557C4×Q8—24no—
558C4×Q8—24no—
559C4×Q8—48no—
560C4×Q8—48no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—24no—
564C4×D4—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—28no—
568C4×D4—28no—
569C4×D4—48no—
570C4×D4—48no—
571C4×D4—48no—
572#117—24no—
573#117—28no—
574#117—24no—
575#117—24no—
576#117—44no—
577#117—48no—
578#117—44no—
579#117—44no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—48no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C22⋊C4C2411yescharacteristic
619C2×C22⋊C4C2411yescharacteristic
620C2×C22⋊C4C2411yescharacteristic
621C2×C22⋊C4C2411yescharacteristic
622C2×C22⋊C4C2411yescharacteristic
623C2×C22⋊C4C2411yescharacteristic
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2414yes—
650C2×C42—24no—
651C2×C42—24no—
652C2×C42—44no—
653C2×C42#4118yes—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2418yes—
669C2×C42C2418yes—
670C2×C42C2418yes—
671C2×C42C2414yes—
672C2×C42C2414yes—
673C2×C42C2414yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678#95C2412yes—
679#95C2412yes—
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2412yes—
691#95C2412yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2418yes—
697#95C2418yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2412yes—
705#95C2412yes—
706#95C2414yes—
707#95C2414yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722C24C2511yescharacteristic
723C24C2514yes—
724C24C2511yescharacteristic
725C24C2511yescharacteristic
726#41—416no—
727#41—816no—
728C2×Q8—22no—
729C2×Q8—28no—
730C2×Q8—24no—
731C2×Q8—28no—
732C2×Q8—28no—
733C2×Q8—22no—
734C2×Q8—28no—
735C2×Q8—41no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—48no—
740C2×Q8—48no—
741C2×Q8—48no—
742C2×Q8—816no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—28no—
748C2×D4—28no—
749C2×D4—22no—
750C2×D4—24no—
751C2×D4—24no—
752C2×D4—24no—
753C2×D4—24no—
754C2×D4—22no—
755C2×D4—24no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—28no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—28no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—42no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4C2×#4114yes—
798C22×C4C2×#4114yes—
799C22×C4C2×#4114yes—
800C22×C4H(5,𝔽2)14yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2514yes—
804C22×C4C2514yes—
805C22×C4C2514yes—
806C22×C4C2514yes—
807C22×C4C2514yes—
808C22×C4C2511yescharacteristic
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2511yescharacteristic
812C22×C4C2518yes—
813C22×C4C2518yes—
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2511yescharacteristic
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—22no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—216no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—44no—
845C4⋊C4—48no—
846C4⋊C4—44no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—48no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—28no—
859C22⋊C4—216no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C42—22no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—22no—
893C42—22no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—48no—
905C42—44no—
906C42—48no—
907C42—48no—
908C42C2×#4114yes—
909C42C2×#4114yes—
910C42C2×#4114yes—
911C42C2×#4114yes—
912C23—21no—
913C23—21no—
914C23—22no—
915C23—22no—
916C23—21no—
917C23—21no—
918C23—22no—
919C23—22no—
920C23—21no—
921C23—24no—
922C23—24no—
923C23—21no—
924C23—24no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—21no—
929C23—24no—
930C23—22no—
931C23—24no—
932C23C22×#4112yes—
933C23C2×H(5,𝔽2)12yes—
934C23C2611yescharacteristic
935Q8—44no—
936Q8—416no—
937Q8—88no—
938Q8—84no—
939Q8—168no—
940D4—44no—
941D4—44no—
942D4—44no—
943D4—48no—
944D4—84no—
945D4—84no—
946D4—88no—
947D4—88no—
948D4—88no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—28no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—24no—
965C2×C4—28no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—28no—
971C2×C4—21no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—22no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—24no—
983C2×C4—28no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—44no—
998C2×C4—44no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—416no—
1002C2×C4—82no—
1003C2×C4—82no—
1004C2×C4—88no—
1005C2×C4—88no—
1006C2×C4—168no—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4112yes—
1009C2×C4C22×#4112yes—
1010C2×C4C22×#4112yes—
1011C2×C4C22×#4112yes—
1012C2×C4C22×#4112yes—
1013C2×C4C2×H(5,𝔽2)12yes—
1014C2×C4C2×H(5,𝔽2)12yes—
1015C2×C4#58512yes—
1016C2×C4#58514yes—
1017C22—22no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—24no—
1022C22—41no—
1023C22—41no—
1024C22—42no—
1025C22—42no—
1026C22—42no—
1027C22—41no—
1028C22—44no—
1029C22—44no—
1030C22—41no—
1031C22—41no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—42no—
1036C22—42no—
1037C22—44no—
1038C22—44no—
1039C22C23×#4111yescharacteristic
1040C22C22×H(5,𝔽2)11yescharacteristic
1041C22C2×#58511yescharacteristic
1042C22C2×#58512yes—
1043C222−1+612yes—
1044C4—22no—
1045C4—22no—
1046C4—22no—
1047C4—22no—
1048C4—22no—
1049C4—41no—
1050C4—48no—
1051C4—41no—
1052C4—41no—
1053C4—44no—
1054C4—41no—
1055C4—41no—
1056C4—44no—
1057C4—48no—
1058C4—44no—
1059C4—44no—
1060C4—44no—
1061C4—44no—
1062C4—44no—
1063C4#349414yes—
1064C4#351014yes—
1065C2—42no—
1066C2—42no—
1067C2—81no—
1068C2—84no—
1069C2C2×#349411yescharacteristic
1070C2C2×#351011yescharacteristic
1071C2#6286011yescharacteristic
1072C2#6293112yes—
1073C2#6293612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34609C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50717C2semidirect
2. #50716C2semidirect
3. #50664C2semidirect
4. #50663C2semidirect
5. #45433C2semidirect
6. #45212C2semidirect
7. #45126C2semidirect
8. #45115C2semidirect
9. #39439C2semidirect
10. #39350C2semidirect
11. #39071C2semidirect
12. #38940C2semidirect
13. #37432C2semidirect
14. #37396C2semidirect
15. #36586C2semidirect
16. #36449C2semidirect
17. #35331C2semidirect
18. #35316C2semidirect
19. #35314C2semidirect
20. #35289C2semidirect
21. #35192C2semidirect
23. #34371C2semidirect
24. #34367C2semidirect
25. #34121C2semidirect

Maximal subgroups

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

subgroupindex
#507172
#507162
#506642
#506632
#454332
#452122
#451262
#451152
#394392
#393502
#390712
#389402
#374322
#373962
#365862
#364492
#353312
#353162
#353142
#352892
#351922
#346092
#343712
#343672
#341212