Finite Group Databasebeta

← #7642993

Subgroups — #7642993

Order 512.

4706 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39765C212yesmaximal, complemented
2#39761C212yesmaximal, complemented
3#39760C212yesmaximal, complemented
4#39637C212yesmaximal, complemented
5#39633C212yesmaximal, complemented
6#39632C212yesmaximal, complemented
7#39504C212yesmaximal, complemented
8#39376C212yesmaximal, complemented
9#38980C214yesmaximal, complemented
10#38976C212yesmaximal, complemented
11#38975C212yesmaximal, complemented
12#37896C214yesmaximal, complemented
13#37708C214yesmaximal, complemented
14#37143C214yesmaximal, complemented
15#37142C214yesmaximal, complemented
16#36645C211yesmaximal, characteristic, complemented
17#36631C211yesmaximal, characteristic
18#35599C214yesmaximal, complemented
19#35596C214yesmaximal, complemented
20#35270C214yesmaximal, complemented
21#35247C212yesmaximal, complemented
22#35015C212yesmaximal, complemented
23#35006C212yesmaximal
24#34243C212yesmaximal, complemented
25C2×#2295C211yesmaximal, characteristic, complemented
26C2×#539C2214yes—
27C2×#533C2212yes—
28C2×#529C2212yes—
29C22×C4×Q8C2211yescharacteristic
30#2868C2211yescharacteristic
31#2868C2211yescharacteristic
32#2862C2212yes—
33#2861C2212yes—
34#2860C2212yes—
35#2860C2212yes—
36#2859C2211yescharacteristic
37#2859C2212yes—
38#2859C2212yes—
39#2858C2211yescharacteristic
40#2857C2211yescharacteristic
41#2857C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2857C2212yes—
45#2856C2211yescharacteristic
46#2855C2214yes—
47#2854C2212yes—
48#2854C2212yes—
49#2854C2214yes—
50#2850C2212yes—
51#2809C2214yes—
52#2808C2214yes—
53#2808C2214yes—
54#2806C2214yes—
55#2805C2214yes—
56#2804C2214yes—
57#2793C2218yes—
58#2790C2218yes—
59#2788C2218yes—
60#2783C2218yes—
61#2766C2218yes—
62#2761C2218yes—
63#2759C2218yes—
64#2729C2218yes—
65#2726C2214yes—
66#2724C2214yes—
67#2719C2218yes—
68#2716C2218yes—
69#2707C2218yes—
70#2689C2218yes—
71#2647C2214yes—
72#2646C2214yes—
73#2645C2214yes—
74#2644C2214yes—
75#2640C2214yes—
76#2639C2214yes—
77#2637C2218yes—
78#2627C2214yes—
79#2618C2214yes—
80#2597C2218yes—
81#2594C2218yes—
82#2592C2214yes—
83#2590C2218yes—
84#2588C2218yes—
85#2585C2218yes—
86#2584C2214yes—
87#2582C2212yes—
88#2582C2212yes—
89#2573C2218yes—
90#2560C2218yes—
91#2558C2218yes—
92#2538C2212yes—
93#2538C2212yes—
94#2532C2218yes—
95#2530C2218yes—
96#2529C2218yes—
97#2527C2218yes—
98#2514C2214yes—
99#2512C2214yes—
100#2511C2214yes—
101#2511C2214yes—
102#2510C2218yes—
103#2508C2214yes—
104#2507C2214yes—
105#2506C2214yes—
106#2506C2214yes—
107#2502C2214yes—
108#2499C2214yes—
109#2497C2214yes—
110#2496C2214yes—
111#2492C2214yes—
112#2492C2214yes—
113#2488C2218yes—
114#2486C2214yes—
115#2486C2214yes—
116#2485C2214yes—
117#2469C2218yes—
118#2458C2218yes—
119#2453C2218yes—
120#2452C2214yes—
121#2451C2214yes—
122#2450C2218yes—
123#2446C2214yes—
124#2445C2214yes—
125#2440C2214yes—
126#2439C2214yes—
127#2421C2218yes—
128#2419C2218yes—
129#2417C2214yes—
130#2415C2214yes—
131#2413C2218yes—
132#2409C2214yes—
133#2370C2214yes—
134#2367C2214yes—
135#2359C2218yes—
136#2355C2212yes—
137#2354C2212yes—
138#2352C2214yes—
139Q8×C4⋊C4C2212yes—
140D4×C4⋊C4C2212yes—
141D4×C4⋊C4C2214yes—
142#2334C2218yes—
143#2331C2214yes—
144#2329C2214yes—
145#2326C2214yes—
146#2325C2214yes—
147#2323C2214yes—
148#2323C2214yes—
149#2320C2214yes—
150#2319C2214yes—
151#2314C2214yes—
152#2313C2214yes—
153C4×C4⋊Q8C2212yes—
154C4×C4⋊Q8C2212yes—
155C4×C4⋊Q8C2211yescharacteristic
156C4×C4⋊Q8C2212yes—
157C4×C4⋊Q8C2212yes—
158C4×#127C2211yescharacteristic
159C4×#124C2212yes—
160C4×C22⋊Q8C2214yes—
161C4×#121C2212yes—
162C4×#121C2212yes—
163C4×#121C2214yes—
164#2295C2212yes—
165#2295C2212yes—
166#2295C2212yes—
167#2295C2212yes—
168#2295C2212yes—
169#2295C2212yes—
170#2295C2212yes—
171#2295C2212yes—
172C2×#391C2211yescharacteristic
173C2×#391C2211yescharacteristic
174#2293C2212yes—
175#2293C2212yes—
176C2×#389C2211yescharacteristic
177C2×#389C2211yescharacteristic
178C2×#387C2212yes—
179C2×#387C2212yes—
180#2285C2212yes—
181#2285C2212yes—
182#2274C2214yes—
183C2×C4×C4⋊C4C2212yes—
184C2×C4×C4⋊C4C2211yescharacteristic
185C2×#376C2212yes—
186C2×C43C2211yescharacteristic
187C23×Q8C2311yescharacteristic
188#539—416no—
189#533—48no—
190C2×C4⋊Q8C2312yes—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×#127C2311yescharacteristic
198#529—216no—
199C2×#126C2314yes—
200C2×#126C2318yes—
201C2×#125C2312yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#123C2314yes—
207C2×#123C2318yes—
208C2×#123C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2312yes—
218C2×C4×Q8—28no—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×#117C2314yes—
234C2×#117C2314yes—
235C2×#117C2314yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2312yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2314yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252#401C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#395C2318yes—
285#395C2318yes—
286#394C2318yes—
287#394C2318yes—
288#393C2318yes—
289#393C2318yes—
290#393C2318yes—
291#393C2318yes—
292#391C2314yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2314yes—
299#391C2314yes—
300#391C2314yes—
301#391C2318yes—
302#391C2318yes—
303#391C2318yes—
304#391C2312yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2312yes—
314#390C2312yes—
315#390C2312yes—
316#390C2312yes—
317#390C2312yes—
318#390C2314yes—
319#390C2314yes—
320#390C2312yes—
321#390C2312yes—
322#390C2312yes—
323#390C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2312yes—
330#389C2312yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2318yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2312yes—
347#389C2312yes—
348#389C2318yes—
349#389C2318yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#386C2318yes—
411#386C2318yes—
412#386C2314yes—
413#386C2314yes—
414#386C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#384C2311yescharacteristic
423#384C2312yes—
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#383C2318yes—
434#382C2314yes—
435#382C2318yes—
436#382C2312yes—
437#382C2314yes—
438#382C2314yes—
439#381C2318yes—
440#381C2318yes—
441#380C2312yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2318yes—
446#380C2314yes—
447#380C2314yes—
448#380C2312yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C22⋊C4C2318yes—
473C4×C22⋊C4C2318yes—
474C4×C22⋊C4C2318yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477#376C2314yes—
478#376C2314yes—
479#376C2314yes—
480#376C2314yes—
481C2×#95C2312yes—
482C2×#95C2312yes—
483C2×#95C2312yes—
484C2×#95C2312yes—
485C2×#95C2312yes—
486C2×#95C2312yes—
487C2×#95C2312yes—
488C43C2311yescharacteristic
489C43C2311yescharacteristic
490C43C2311yescharacteristic
491C43C2311yescharacteristic
492C43C2311yescharacteristic
493C43C2311yescharacteristic
494C43C2311yescharacteristic
495C43C2311yescharacteristic
496C22×Q8—24no—
497C22×Q8—42no—
498C22×Q8—42no—
499C22×Q8C2412yes—
500C22×Q8C2412yes—
501C22×Q8C2412yes—
502C22×Q8C2414yes—
503C22×Q8C2414yes—
504C22×D4C2414yes—
505C22×D4C2412yes—
506C22×D4C2412yes—
507C22×D4C2412yes—
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2412yes—
518C23×C4C2418yes—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C4⋊Q8—28no—
522C4⋊Q8—44no—
523C4⋊Q8—44no—
524C4⋊Q8—44no—
525C4⋊Q8—44no—
526C4⋊Q8—42no—
527C4⋊Q8—44no—
528#127—42no—
529#126—216no—
530#126—416no—
531#125—28no—
532#125—48no—
533#125—416no—
534#124—28no—
535#124—28no—
536#123—216no—
537#123—416no—
538#123—416no—
539C22⋊Q8—28no—
540C22⋊Q8—216no—
541C22⋊Q8—48no—
542C22⋊Q8—416no—
543C22⋊Q8—48no—
544C22⋊Q8—48no—
545#121—28no—
546#121—28no—
547#121—28no—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—48no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×D4—216no—
557C4×D4—28no—
558C4×D4—48no—
559C4×D4—44no—
560C4×D4—44no—
561C4×D4—416no—
562#117—216no—
563#117—48no—
564#117—48no—
565C2×C4⋊C4—24no—
566C2×C4⋊C4—28no—
567C2×C4⋊C4—28no—
568C2×C4⋊C4—28no—
569C2×C4⋊C4—42no—
570C2×C4⋊C4—48no—
571C2×C4⋊C4—42no—
572C2×C4⋊C4C2412yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2418yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C42—28no—
637C2×C42—24no—
638C2×C42—24no—
639C2×C42—24no—
640C2×C42—42no—
641C2×C42—42no—
642C2×C42—44no—
643C2×C42—42no—
644C2×C42#4118yes—
645C2×C42C2414yes—
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2414yes—
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2414yes—
652C2×C42C2414yes—
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2418yes—
667C2×C42C2418yes—
668C2×C42C2418yes—
669C2×C42C2418yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2414yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2414yes—
711#95C2414yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720C24C2514yes—
721C24C2511yescharacteristic
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—28no—
726C2×Q8—24no—
727C2×Q8—28no—
728C2×Q8—24no—
729C2×Q8—24no—
730C2×Q8—24no—
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—416no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—22no—
759C22×C4—24no—
760C22×C4—22no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—41no—
770C22×C4—41no—
771C22×C4—41no—
772C22×C4—41no—
773C22×C4—41no—
774C22×C4—41no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—48no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C4C2×#4114yes—
785C22×C4C2×#4114yes—
786C22×C4C2×#4114yes—
787C22×C4H(5,𝔽2)14yes—
788C22×C42−1+414yes—
789C22×C4C2511yescharacteristic
790C22×C4C2514yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C2511yescharacteristic
794C22×C4C2514yes—
795C22×C4C2518yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2518yes—
800C22×C4C2511yescharacteristic
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C22×C4C2511yescharacteristic
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—216no—
825C4⋊C4—28no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—48no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—42no—
843C4⋊C4—42no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C22⋊C4—28no—
858C22⋊C4—216no—
859C22⋊C4—28no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C42—28no—
877C42—28no—
878C42—28no—
879C42—22no—
880C42—22no—
881C42—22no—
882C42—22no—
883C42—22no—
884C42—22no—
885C42—22no—
886C42—22no—
887C42—22no—
888C42—22no—
889C42—22no—
890C42—22no—
891C42—22no—
892C42—28no—
893C42—22no—
894C42—22no—
895C42—22no—
896C42—22no—
897C42—41no—
898C42—41no—
899C42—41no—
900C42—41no—
901C42—41no—
902C42—41no—
903C42—44no—
904C42—48no—
905C42—48no—
906C42—48no—
907C42—48no—
908C42C2×#4114yes—
909C42C2×#4114yes—
910C42C2×#4114yes—
911C42C2×#4114yes—
912C422−1+414yes—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23C22×#4112yes—
925C23C2×H(5,𝔽2)12yes—
926C23C2×2−1+412yes—
927C23C2611yescharacteristic
928Q8—48no—
929Q8—48no—
930Q8—48no—
931Q8—88no—
932Q8—88no—
933D4—416no—
934D4—48no—
935D4—84no—
936D4—84no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—28no—
958C2×C4—28no—
959C2×C4—28no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—21no—
966C2×C4—28no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—28no—
970C2×C4—24no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—28no—
979C2×C4—24no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—28no—
987C2×C4—28no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—44no—
994C2×C4—44no—
995C2×C4—44no—
996C2×C4—44no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—416no—
1000C2×C4—84no—
1001C2×C4—84no—
1002C2×C4—168no—
1003C2×C4C22×#4112yes—
1004C2×C4C22×#4112yes—
1005C2×C4C22×#4112yes—
1006C2×C4C22×#4112yes—
1007C2×C4C22×#4112yes—
1008C2×C4C22×#4112yes—
1009C2×C4C2×H(5,𝔽2)12yes—
1010C2×C4C2×H(5,𝔽2)12yes—
1011C2×C4C2×2−1+412yes—
1012C2×C4C2×2−1+412yes—
1013C2×C4C2×2−1+412yes—
1014C2×C4C2×2−1+412yes—
1015C2×C4C2×2−1+412yes—
1016C2×C4#58512yes—
1017C2×C4#58512yes—
1018C2×C4#58512yes—
1019C22—22no—
1020C22—22no—
1021C22—22no—
1022C22—22no—
1023C22—22no—
1024C22—22no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22#351114yes—
1033C22C23×#4111yescharacteristic
1034C22C22×H(5,𝔽2)11yescharacteristic
1035C22C22×2−1+411yescharacteristic
1036C22C22×2−1+411yescharacteristic
1037C22C2×#58511yescharacteristic
1038C22C2×#58511yescharacteristic
1039C22C2×#58511yescharacteristic
1040C4—22no—
1041C4—22no—
1042C4—22no—
1043C4—22no—
1044C4—22no—
1045C4—22no—
1046C4—22no—
1047C4—22no—
1048C4—22no—
1049C4—22no—
1050C4—44no—
1051C4—44no—
1052C4—44no—
1053C4—44no—
1054C4—48no—
1055C4—44no—
1056C4—41no—
1057C4—48no—
1058C4—41no—
1059C4—44no—
1060C4—44no—
1061C4#345514yes—
1062C4#350714yes—
1063C2—24no—
1064C2—84no—
1065C2C2×#345511yescharacteristic
1066C2C2×#350711yescharacteristic
1067C2C2×#351111yescharacteristic
1068C2#6282211yescharacteristic
1069C2#6282311yescharacteristic
1070C2#6283511yescharacteristic
1071C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39765C2semidirect
2. #39761C2semidirect
3. #39760C2semidirect
4. #39637C2semidirect
5. #39633C2semidirect
6. #39632C2semidirect
7. #39504C2semidirect
8. #39376C2semidirect
9. #38980C2semidirect
10. #38976C2semidirect
11. #38975C2semidirect
12. #37896C2semidirect
13. #37708C2semidirect
14. #37143C2semidirect
15. #37142C2semidirect
16. #36645C2semidirect
18. #35599C2semidirect
19. #35596C2semidirect
20. #35270C2semidirect
21. #35247C2semidirect
22. #35015C2semidirect
24. #34243C2semidirect
25. C2×#2295C2semidirect

Maximal subgroups

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

subgroupindex
#397652
#397612
#397602
#396372
#396332
#396322
#395042
#393762
#389802
#389762
#389752
#378962
#377082
#371432
#371422
#366452
#366312
#355992
#355962
#352702
#352472
#350152
#350062
#342432
C2×#22952