Finite Group Databasebeta

← #7674599

Subgroups — #7674599

Order 512.

4642 conjugacy classes of subgroups.

The subgroup lattice has 1053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43576C218yesmaximal, complemented
2#43151C218yesmaximal, complemented
3#39803C214yesmaximal, complemented
4#39802C214yesmaximal, complemented
5#39801C214yesmaximal, complemented
6#39800C214yesmaximal, complemented
7#37963C214yesmaximal, complemented
8#37962C214yesmaximal, complemented
9#37961C214yesmaximal, complemented
10#37960C214yesmaximal, complemented
11#35629C211yesmaximal, characteristic, complemented
12#35629C211yesmaximal, characteristic, complemented
13#35557C211yesmaximal, characteristic, complemented
14#35557C211yesmaximal, characteristic, complemented
15#35341C211yesmaximal, characteristic
16#35334C211yesmaximal, characteristic, complemented
17#35289C211yesmaximal, characteristic
18#35280C211yesmaximal, characteristic, complemented
19C2×#2660C211yesmaximal, characteristic, complemented
20#34217C211yesmaximal, characteristic, complemented
21#34216C211yesmaximal, characteristic, complemented
22#34189C211yesmaximal, characteristic, complemented
23#34188C211yesmaximal, characteristic, complemented
24#34074C211yesmaximal, characteristic, complemented
25#34070C211yesmaximal, characteristic
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2862C2212yes—
33#2861C2212yes—
34#2861C2212yes—
35#2858C2212yes—
36#2857C2214yes—
37#2851C2214yes—
38#2789C2218yes—
39#2788C2218yes—
40#2787C2218yes—
41#2786C2218yes—
42#2783C2218yes—
43#2777C2218yes—
44#2775C2218yes—
45#2767C2218yes—
46#2762C2218yes—
47#2759C2218yes—
48#2758C2218yes—
49#2745C2218yes—
50#2740C2218yes—
51#2715C2218yes—
52#2700C2218yes—
53#2689C2218yes—
54#2660C2212yes—
55#2660C2212yes—
56#2660C2212yes—
57#2660C2212yes—
58#2660C2214yes—
59#2660C2214yes—
60#2642C2212yes—
61#2641C2212yes—
62#2640C2212yes—
63#2640C2212yes—
64#2629C2214yes—
65#2628C2214yes—
66#2605C2218yes—
67#2604C2218yes—
68#2601C2218yes—
69#2599C2218yes—
70#2594C2218yes—
71#2591C2214yes—
72#2591C2214yes—
73#2588C2218yes—
74#2582C2214yes—
75#2581C2214yes—
76#2580C2214yes—
77#2577C2218yes—
78#2564C2218yes—
79#2563C2214yes—
80#2562C2214yes—
81#2562C2214yes—
82#2560C2218yes—
83#2547C2214yes—
84#2538C2214yes—
85#2532C2218yes—
86#2528C2218yes—
87#2524C2218yes—
88#2521C2218yes—
89#2514C2214yes—
90#2514C2214yes—
91#2513C2214yes—
92#2513C2214yes—
93#2512C2214yes—
94#2512C2214yes—
95#2511C2214yes—
96#2511C2214yes—
97#2510C2218yes—
98#2510C2218yes—
99#2504C2214yes—
100#2497C2214yes—
101#2497C2214yes—
102#2496C2214yes—
103#2496C2214yes—
104#2495C2214yes—
105#2495C2214yes—
106#2494C2214yes—
107#2494C2214yes—
108#2481C2218yes—
109#2481C2218yes—
110#2478C2218yes—
111#2474C2218yes—
112#2469C2218yes—
113#2465C2218yes—
114#2436C2214yes—
115#2417C2218yes—
116C2×#398C2214yes—
117C2×#395C2214yes—
118#2370C2214yes—
119#2370C2214yes—
120#2369C2214yes—
121#2365C2214yes—
122#2357C2214yes—
123#2356C2214yes—
124#2355C2214yes—
125#2354C2214yes—
126#2353C2218yes—
127#2352C2218yes—
128#2345C2214yes—
129#2345C2214yes—
130#2345C2214yes—
131Q8×C22⋊C4C2214yes—
132#2331C2212yes—
133#2331C2212yes—
134#2331C2214yes—
135#2330C2212yes—
136#2330C2212yes—
137#2330C2214yes—
138#2329C2214yes—
139#2329C2214yes—
140#2328C2212yes—
141#2327C2212yes—
142#2326C2212yes—
143#2326C2212yes—
144#2325C2214yes—
145#2325C2214yes—
146#2316C2211yescharacteristic
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2316C2211yescharacteristic
150#2314C2214yes—
151#2314C2214yes—
152#2311C2211yescharacteristic
153#2311C2211yescharacteristic
154#2311C2211yescharacteristic
155#2311C2211yescharacteristic
156#2311C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160C4×C4⋊Q8C2214yes—
161C4×#125C2214yes—
162#2297C2211yescharacteristic
163#2297C2211yescharacteristic
164#2296C2211yescharacteristic
165#2296C2211yescharacteristic
166#2295C2214yes—
167#2295C2214yes—
168#2290C2212yes—
169#2290C2212yes—
170#2290C2212yes—
171#2290C2212yes—
172#2285C2211yescharacteristic
173#2285C2211yescharacteristic
174#2285C2214yes—
175C2×#384C2211yescharacteristic
176C2×#384C2211yescharacteristic
177#2283C2214yes—
178C2×#382C2211yescharacteristic
179C2×#382C2211yescharacteristic
180#2274C2211yescharacteristic
181#2274C2211yescharacteristic
182#2274C2211yescharacteristic
183#2274C2211yescharacteristic
184C4×#117C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×#376C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2312yes—
190#533—28no—
191#532—28no—
192C2×C4⋊Q8—28no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×#127C2311yescharacteristic
200C2×#126C2318yes—
201C2×#126C2318yes—
202C2×#125—28no—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2312yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#124C2311yescharacteristic
209C2×#124C2311yescharacteristic
210C2×#124C2318yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2318yes—
213C2×#121C2312yes—
214C2×#121C2312yes—
215C4×#41—28no—
216C4×#41—28no—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2318yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2314yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2312yes—
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2312yes—
232C2×#117C2312yes—
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2318yes—
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2314yes—
245C22×C42C2312yes—
246C22×C42C2312yes—
247C22×C42C2311yescharacteristic
248C22×C42C2311yescharacteristic
249C22×C42C2311yescharacteristic
250#401C2318yes—
251#401C2318yes—
252#400C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#399C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2318yes—
267#398C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#395C2318yes—
281#395C2318yes—
282#395C2318yes—
283#395C2318yes—
284#395C2318yes—
285#394C2318yes—
286#394C2318yes—
287#393C2318yes—
288#393C2318yes—
289#393C2318yes—
290#391C2314yes—
291#391C2318yes—
292#391C2312yes—
293#391C2312yes—
294#391C2312yes—
295#391C2312yes—
296#391C2312yes—
297#391C2312yes—
298#391C2312yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2318yes—
303#391C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2318yes—
307#391C2318yes—
308#391C2318yes—
309#390C2318yes—
310#390C2312yes—
311#390C2312yes—
312#390C2312yes—
313#390C2312yes—
314#390C2312yes—
315#390C2312yes—
316#390C2312yes—
317#390C2312yes—
318#390C2312yes—
319#390C2312yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2318yes—
325#389C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2318yes—
339#389C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2318yes—
350#388C2318yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2314yes—
368#387C2318yes—
369#387C2318yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#387C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#386C2314yes—
389#386C2314yes—
390#386C2314yes—
391#386C2314yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2314yes—
396#386C2314yes—
397#386C2314yes—
398#386C2314yes—
399#386C2314yes—
400#386C2314yes—
401#386C2314yes—
402#385C2318yes—
403#385C2318yes—
404#385C2314yes—
405#385C2314yes—
406#385C2314yes—
407#385C2314yes—
408#385C2314yes—
409#385C2314yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#384C2314yes—
414#384C2312yes—
415#384C2312yes—
416#384C2312yes—
417#384C2314yes—
418#383C2318yes—
419#383C2318yes—
420#383C2318yes—
421#382C2312yes—
422#382C2318yes—
423#382C2312yes—
424#382C2312yes—
425#382C2314yes—
426#382C2318yes—
427#382C2312yes—
428#382C2312yes—
429#382C2312yes—
430#382C2314yes—
431#381C2318yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2314yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2318yes—
445#380C2312yes—
446#380C2312yes—
447#380C2314yes—
448#380C2318yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2312yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C22⋊C4C2318yes—
471C4×C22⋊C4C2312yes—
472C4×C22⋊C4C2312yes—
473C4×C22⋊C4C2312yes—
474C4×C22⋊C4C2312yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483#376C2312yes—
484#376C2312yes—
485#376C2312yes—
486#376C2311yescharacteristic
487#376C2311yescharacteristic
488#376C2312yes—
489#376C2311yescharacteristic
490#376C2311yescharacteristic
491#376C2318yes—
492C2×#95C2314yes—
493C2×#95C2312yes—
494C2×#95C2312yes—
495C2×#95C2314yes—
496C43C2312yes—
497C43C2312yes—
498C2×#41—24no—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41—24no—
502C2×#41—24no—
503C2×#41—24no—
504C22×Q8—28no—
505C22×Q8—84no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×Q8C2414yes—
511C22×D4C2412yes—
512C22×D4C2412yes—
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2412yes—
516C22×D4C2412yes—
517C23×C4C2412yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2411yescharacteristic
527C23×C4C2412yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C4⋊Q8—28no—
531C4⋊Q8—28no—
532C4⋊Q8—28no—
533C4⋊Q8—28no—
534C4⋊Q8—24no—
535C4⋊Q8—28no—
536#127—24no—
537#126—88no—
538#126—88no—
539#125—28no—
540#125—28no—
541#125—28no—
542#125—28no—
543#125—28no—
544#124—24no—
545#124—24no—
546#124—88no—
547C22⋊Q8—216no—
548C22⋊Q8—88no—
549#121—28no—
550#121—28no—
551C4×Q8—28no—
552C4×Q8—28no—
553C4×Q8—216no—
554C4×Q8—88no—
555C4×D4—216no—
556C4×D4—216no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—28no—
561#117—24no—
562#117—24no—
563#117—24no—
564#117—24no—
565#117—24no—
566#117—24no—
567#117—28no—
568#117—28no—
569#117—88no—
570C2×C4⋊C4—28no—
571C2×C4⋊C4—28no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—28no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—24no—
577C2×C4⋊C4—84no—
578C2×C4⋊C4—84no—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2414yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2412yes—
627C2×C22⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2412yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2418yes—
646C2×C42—24no—
647C2×C42—28no—
648C2×C42—28no—
649C2×C42#4118yes—
650C2×C42#4118yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2412yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2418yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677#95C2412yes—
678#95C2412yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2412yes—
683#95C2412yes—
684#95C2412yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721C24C2512yes—
722C24C2512yes—
723C24C2511yescharacteristic
724#41—416no—
725#41—416no—
726C2×Q8—22no—
727C2×Q8—22no—
728C2×Q8—22no—
729C2×Q8—22no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—28no—
733C2×Q8—22no—
734C2×Q8—22no—
735C2×Q8—48no—
736C2×Q8—44no—
737C2×Q8—48no—
738C2×Q8—44no—
739C2×Q8—816no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—24no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—24no—
751C2×D4—24no—
752C2×D4—22no—
753C2×D4—22no—
754C2×D4—44no—
755C2×D4—44no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—24no—
761C22×C4—24no—
762C22×C4—24no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—44no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4C2×#4114yes—
784C22×C4C2×#4114yes—
785C22×C4C2×#4118yes—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C42−1+414yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2514yes—
798C22×C4C2514yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2514yes—
802C22×C4C2514yes—
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2512yes—
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2511yescharacteristic
810C22×C4C2511yescharacteristic
811C4⋊C4—28no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—28no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—28no—
828C4⋊C4—28no—
829C4⋊C4—24no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—28no—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C22⋊C4—24no—
855C22⋊C4—24no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—24no—
863C22⋊C4—24no—
864C22⋊C4—24no—
865C22⋊C4—24no—
866C22⋊C4—44no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—44no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C42—24no—
879C42—24no—
880C42—28no—
881C42—28no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—22no—
886C42—22no—
887C42—24no—
888C42—24no—
889C42—44no—
890C42—44no—
891C42—48no—
892C42—48no—
893C42—48no—
894C42—44no—
895C42—48no—
896C42—44no—
897C42C2×#4114yes—
898C42C2×#4114yes—
899C42C2×#4118yes—
900C42C2×#4114yes—
901C42C2×#4114yes—
902C42C2×#4114yes—
903C42C2×#4114yes—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—24no—
916C23C22×#4112yes—
917C23C22×#4112yes—
918C23C2×2−1+412yes—
919C23C2611yescharacteristic
920Q8—416no—
921Q8—44no—
922Q8—44no—
923Q8—88no—
924Q8—88no—
925D4—48no—
926D4—48no—
927D4—44no—
928D4—44no—
929D4—84no—
930D4—84no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—28no—
963C2×C4—24no—
964C2×C4—28no—
965C2×C4—28no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—48no—
978C2×C4—44no—
979C2×C4—44no—
980C2×C4—416no—
981C2×C4—48no—
982C2×C4—48no—
983C2×C4—48no—
984C2×C4—88no—
985C2×C4—84no—
986C2×C4—84no—
987C2×C4—84no—
988C2×C4—84no—
989C2×C4#556116yes—
990C2×C4C22×#4114yes—
991C2×C4C22×#4114yes—
992C2×C4C22×#4112yes—
993C2×C4C22×#4112yes—
994C2×C4C22×#4112yes—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C2×2−1+412yes—
1001C2×C4C2×2−1+412yes—
1002C22—22no—
1003C22—24no—
1004C22—22no—
1005C22—24no—
1006C22—42no—
1007C22—42no—
1008C22—44no—
1009C22—44no—
1010C22—42no—
1011C22—42no—
1012C22—44no—
1013C22—44no—
1014C22—42no—
1015C22—42no—
1016C22C2×#55614yes—
1017C22C23×#4111yescharacteristic
1018C22C23×#4111yescharacteristic
1019C22C22×2−1+411yescharacteristic
1020C22H(7,𝔽2)12yes—
1021C222−1+612yes—
1022C4—22no—
1023C4—22no—
1024C4—24no—
1025C4—24no—
1026C4—22no—
1027C4—22no—
1028C4—44no—
1029C4—44no—
1030C4—44no—
1031C4—44no—
1032C4—44no—
1033C4—44no—
1034C4—44no—
1035C4—44no—
1036C4—44no—
1037C4—44no—
1038C4—42no—
1039C4—42no—
1040C4—42no—
1041C4—42no—
1042C4C2×#55614yes—
1043C4C2×#55614yes—
1044C2—24no—
1045C2—82no—
1046C2—82no—
1047C2C22×#55611yescharacteristic
1048C2#6285511yescharacteristic
1049C2#6285612yes—
1050C2#6286011yescharacteristic
1051C2#6287712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43576C2semidirect
2. #43151C2semidirect
3. #39803C2semidirect
4. #39802C2semidirect
5. #39801C2semidirect
6. #39800C2semidirect
7. #37963C2semidirect
8. #37962C2semidirect
9. #37961C2semidirect
10. #37960C2semidirect
11. #35629C2semidirect
12. #35629C2semidirect
13. #35557C2semidirect
14. #35557C2semidirect
16. #35334C2semidirect
18. #35280C2semidirect
19. C2×#2660C2semidirect
20. #34217C2semidirect
21. #34216C2semidirect
22. #34189C2semidirect
23. #34188C2semidirect
24. #34074C2semidirect

Maximal subgroups

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

subgroupindex
#435762
#431512
#398032
#398022
#398012
#398002
#379632
#379622
#379612
#379602
#356292
#355572
#353412
#353342
#352892
#352802
C2×#26602
#342172
#342162
#341892
#341882
#340742
#340702