Finite Group Databasebeta

← #7673868

Subgroups — #7673868

Order 512.

5130 conjugacy classes of subgroups.

The subgroup lattice has 1085 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45201C214yesmaximal, complemented
2#45168C214yesmaximal, complemented
3#45043C214yesmaximal, complemented
4#44986C214yesmaximal, complemented
5#39807C214yesmaximal, complemented
6#39804C214yesmaximal, complemented
7#39768C214yesmaximal, complemented
8#39764C214yesmaximal, complemented
9#39275C214yesmaximal, complemented
10#39274C214yesmaximal, complemented
11#39269C214yesmaximal, complemented
12#39268C214yesmaximal, complemented
13#35618C212yesmaximal, complemented
14#35592C212yesmaximal, complemented
15#35255C212yesmaximal, complemented
16#35180C211yesmaximal, characteristic, complemented
17#35166C211yesmaximal, characteristic
18#34637C211yesmaximal, characteristic, complemented
19#34267C212yesmaximal, complemented
20#34213C211yesmaximal, characteristic, complemented
21#34206C211yesmaximal, characteristic, complemented
22C2×#2331C211yesmaximal, characteristic, complemented
23#34070C211yesmaximal, characteristic, complemented
24C2×#537C2212yes—
25C2×#537C2212yes—
26C2×#533C2211yescharacteristic
27C2×#532C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2212yes—
31C2×C4×#41C2212yes—
32#2856C2214yes—
33#2855C2214yes—
34#2854C2214yes—
35#2850C2214yes—
36#2808C2218yes—
37#2804C2218yes—
38#2803C2218yes—
39#2798C2218yes—
40#2798C2218yes—
41#2797C2218yes—
42#2796C2218yes—
43#2794C2218yes—
44#2771C2218yes—
45#2754C2218yes—
46#2751C2218yes—
47#2751C2218yes—
48#2751C2218yes—
49#2712C2218yes—
50#2710C2218yes—
51#2709C2218yes—
52#2656C2214yes—
53#2642C2212yes—
54#2641C2212yes—
55#2640C2212yes—
56#2640C2212yes—
57#2639C2212yes—
58#2639C2212yes—
59#2639C2212yes—
60#2639C2212yes—
61#2639C2214yes—
62#2625C2214yes—
63#2624C2214yes—
64#2607C2218yes—
65#2600C2218yes—
66#2597C2218yes—
67#2596C2218yes—
68#2595C2218yes—
69#2592C2218yes—
70#2592C2214yes—
71#2591C2218yes—
72#2589C2218yes—
73#2575C2218yes—
74#2568C2212yes—
75#2563C2212yes—
76#2562C2214yes—
77#2557C2218yes—
78#2548C2212yes—
79#2547C2212yes—
80#2544C2218yes—
81#2542C2212yes—
82#2542C2212yes—
83#2541C2212yes—
84#2541C2212yes—
85#2540C2214yes—
86#2540C2214yes—
87#2516C2218yes—
88#2511C2218yes—
89#2504C2214yes—
90#2503C2214yes—
91#2500C2214yes—
92#2499C2214yes—
93#2492C2214yes—
94#2492C2214yes—
95#2492C2214yes—
96#2492C2214yes—
97#2491C2214yes—
98#2491C2214yes—
99#2491C2214yes—
100#2491C2214yes—
101#2459C2218yes—
102#2459C2218yes—
103#2458C2218yes—
104#2447C2218yes—
105#2444C2218yes—
106#2444C2218yes—
107#2444C2218yes—
108#2443C2218yes—
109#2436C2218yes—
110#2423C2214yes—
111#2422C2214yes—
112#2421C2214yes—
113#2421C2214yes—
114#2421C2214yes—
115#2420C2214yes—
116#2420C2214yes—
117#2420C2214yes—
118#2398C2214yes—
119#2398C2214yes—
120#2370C2214yes—
121#2369C2212yes—
122#2367C2214yes—
123#2366C2212yes—
124#2365C2212yes—
125#2365C2212yes—
126#2364C2218yes—
127#2363C2214yes—
128#2362C2214yes—
129#2361C2218yes—
130#2361C2214yes—
131#2360C2214yes—
132#2355C2212yes—
133#2355C2214yes—
134#2354C2212yes—
135#2352C2214yes—
136Q8×C4⋊C4C2212yes—
137D4×C4⋊C4C2212yes—
138#2331C2214yes—
139#2331C2214yes—
140#2331C2214yes—
141#2331C2214yes—
142#2329C2214yes—
143#2328C2212yes—
144#2327C2212yes—
145#2326C2212yes—
146#2326C2212yes—
147#2325C2212yes—
148#2325C2212yes—
149#2325C2212yes—
150#2325C2212yes—
151#2325C2214yes—
152#2324C2214yes—
153#2323C2214yes—
154#2317C2212yes—
155#2311C2212yes—
156#2311C2212yes—
157#2311C2212yes—
158C4×C22⋊Q8C2214yes—
159C4×C22⋊Q8C2214yes—
160C4×#121C2214yes—
161C4×#121C2214yes—
162#2297C2212yes—
163#2297C2212yes—
164#2297C2212yes—
165C2×#391C2212yes—
166C2×#391C2212yes—
167C2×#389C2211yescharacteristic
168C2×#389C2211yescharacteristic
169#2290C2214yes—
170#2290C2214yes—
171C2×#387C2212yes—
172C2×#387C2212yes—
173#2285C2211yescharacteristic
174C2×#382C2211yescharacteristic
175#2274C2212yes—
176C2×C4×C4⋊C4C2211yescharacteristic
177C2×C4×C4⋊C4C2211yescharacteristic
178C2×#376C2211yescharacteristic
179C22×#41C2312yes—
180C22×#41C2312yes—
181C23×Q8C2312yes—
182#537—216no—
183#537—48no—
184#533—28no—
185#532—28no—
186#532—28no—
187C2×C4⋊Q8—28no—
188C2×C4⋊Q8C2311yescharacteristic
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2311yescharacteristic
193C2×C4⋊Q8C2311yescharacteristic
194C2×#127C2311yescharacteristic
195C2×#127C2311yescharacteristic
196C2×#127C2314yes—
197C2×#125C2312yes—
198C2×#124C2312yes—
199C2×#124C2312yes—
200C2×#124C2318yes—
201C2×#124C2314yes—
202C2×#124C2318yes—
203C2×#123C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2314yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2312yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2312yes—
217C2×#121C2314yes—
218C2×#121C2318yes—
219C2×#121C2314yes—
220#520—48no—
221C4×#41—48no—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2318yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2314yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2314yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254C22×C42C2314yes—
255C22×C42C2312yes—
256C22×C42C2312yes—
257C22×C42C2311yescharacteristic
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2314yes—
262#400C2318yes—
263#400C2314yes—
264#400C2314yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#399C2318yes—
269#399C2318yes—
270#399C2318yes—
271#398C2318yes—
272#397C2314yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2314yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#394C2314yes—
291#394C2314yes—
292#394C2314yes—
293#394C2318yes—
294#394C2318yes—
295#393C2318yes—
296#393C2318yes—
297#393C2314yes—
298#393C2314yes—
299#393C2318yes—
300#393C2314yes—
301#393C2314yes—
302#393C2318yes—
303#393C2318yes—
304#392C2318yes—
305#392C2318yes—
306#391C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2318yes—
314#391C2318yes—
315#391C2318yes—
316#391C2318yes—
317#391C2318yes—
318#391C2318yes—
319#391C2318yes—
320#391C2314yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2318yes—
330#390C2312yes—
331#390C2312yes—
332#390C2318yes—
333#390C2314yes—
334#390C2318yes—
335#390C2314yes—
336#390C2314yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#388C2318yes—
351#388C2318yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2314yes—
396#386C2314yes—
397#386C2314yes—
398#386C2318yes—
399#386C2314yes—
400#386C2318yes—
401#386C2318yes—
402#386C2314yes—
403#386C2318yes—
404#386C2314yes—
405#386C2314yes—
406#386C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2314yes—
410#385C2314yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#384C2314yes—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2314yes—
420#382C2314yes—
421#382C2314yes—
422#382C2312yes—
423#382C2314yes—
424#382C2314yes—
425#381C2318yes—
426#381C2318yes—
427#381C2318yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2312yes—
435#380C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2314yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2312yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2312yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2314yes—
459C4×C22⋊C4C2314yes—
460C4×C22⋊C4C2314yes—
461C4×C22⋊C4C2314yes—
462C4×C22⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464#376C2312yes—
465#376C2312yes—
466#376C2312yes—
467#376C2312yes—
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2312yes—
473C2×#95C2312yes—
474C2×#95C2312yes—
475C2×#95C2312yes—
476C2×#95C2312yes—
477C2×#95C2312yes—
478C2×#41—28no—
479C2×#41—28no—
480C2×#41—28no—
481C2×#41—28no—
482C2×#41—28no—
483C2×#41—28no—
484C22×Q8—28no—
485C22×Q8—82no—
486C22×Q8—82no—
487C22×Q8C2412yes—
488C22×Q8C2412yes—
489C22×Q8C2412yes—
490C22×Q8C2412yes—
491C22×Q8C2418yes—
492C22×D4C2414yes—
493C22×D4C2414yes—
494C22×D4C2412yes—
495C22×D4C2412yes—
496C22×D4C2412yes—
497C22×D4C2418yes—
498C22×D4C2412yes—
499C22×D4C2412yes—
500C22×D4C2412yes—
501C22×D4C2418yes—
502C23×C4C2414yes—
503C23×C4C2414yes—
504C23×C4C2412yes—
505C23×C4C2411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C23×C4C2418yes—
512C23×C4C2414yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C4⋊Q8—216no—
519C4⋊Q8—216no—
520C4⋊Q8—24no—
521C4⋊Q8—24no—
522C4⋊Q8—24no—
523C4⋊Q8—24no—
524#127—24no—
525#127—24no—
526#127—84no—
527#125—28no—
528#124—28no—
529#124—28no—
530#124—84no—
531#124—88no—
532#124—88no—
533#123—88no—
534C22⋊Q8—28no—
535C22⋊Q8—28no—
536C22⋊Q8—216no—
537C22⋊Q8—216no—
538C22⋊Q8—48no—
539C22⋊Q8—48no—
540#121—28no—
541#121—28no—
542#121—28no—
543#121—28no—
544#121—232no—
545#121—216no—
546#121—216no—
547#121—48no—
548#121—48no—
549#121—416no—
550C4×Q8—28no—
551C4×Q8—28no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—48no—
555C4×Q8—84no—
556C4×D4—28no—
557C4×D4—28no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—44no—
561C4×D4—44no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—416no—
566C4×D4—84no—
567C4×D4—88no—
568#117—28no—
569#117—28no—
570#117—48no—
571#117—48no—
572C2×C4⋊C4—28no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—48no—
577C2×C4⋊C4—82no—
578C2×C4⋊C4—82no—
579C2×C4⋊C4#4118yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2418yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C42—24no—
646C2×C42—24no—
647C2×C42—48no—
648C2×C42—82no—
649C2×C42—82no—
650C2×C42#4118yes—
651C2×C42C2414yes—
652C2×C42C2412yes—
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2418yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2418yes—
661C2×C42C2414yes—
662C2×C42C2418yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#95C2412yes—
671#95C2412yes—
672#95C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2412yes—
676#95C2412yes—
677#95C2412yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2418yes—
685#95C2418yes—
686#95C2414yes—
687#95C2414yes—
688#95C2418yes—
689#95C2414yes—
690#95C2418yes—
691#95C2418yes—
692#95C2418yes—
693#95C2414yes—
694#95C2414yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710C24C2514yes—
711C24C2514yes—
712C24C2511yescharacteristic
713#41—432no—
714#41—432no—
715C2×Q8—24no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—24no—
719C2×Q8—24no—
720C2×Q8—24no—
721C2×Q8—216no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—42no—
725C2×Q8—42no—
726C2×Q8—42no—
727C2×Q8—48no—
728C2×Q8—48no—
729C2×Q8—42no—
730C2×Q8—816no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—24no—
738C2×D4—24no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—24no—
744C2×D4—24no—
745C2×D4—216no—
746C2×D4—24no—
747C2×D4—24no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—48no—
751C2×D4—42no—
752C2×D4—48no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—24no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—24no—
768C22×C4—28no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—41no—
775C22×C4—41no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—41no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—42no—
789C22×C4—42no—
790C22×C4—41no—
791C22×C4—41no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—41no—
795C22×C4—41no—
796C22×C4—42no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—42no—
800C22×C4—48no—
801C22×C4—48no—
802C22×C4—48no—
803C22×C4C2×#4114yes—
804C22×C4C2×#4114yes—
805C22×C4C2×#4118yes—
806C22×C4C2×#4114yes—
807C22×C4C2×#4114yes—
808C22×C4H(5,𝔽2)14yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2512yes—
812C22×C4C2512yes—
813C22×C4C2514yes—
814C22×C4C2514yes—
815C22×C4C2514yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2511yescharacteristic
823C22×C4C2511yescharacteristic
824C22×C4C2511yescharacteristic
825C22×C4C2511yescharacteristic
826C22×C4C2514yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C4⋊C4—216no—
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—216no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—48no—
850C4⋊C4—48no—
851C4⋊C4—48no—
852C4⋊C4—42no—
853C4⋊C4—42no—
854C4⋊C4—48no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4C2×#4118yes—
862C4⋊C4C2×#4118yes—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—28no—
869C22⋊C4—216no—
870C22⋊C4—216no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C42—24no—
895C42—24no—
896C42—28no—
897C42—24no—
898C42—24no—
899C42—28no—
900C42—44no—
901C42—44no—
902C42—44no—
903C42—44no—
904C42—44no—
905C42—44no—
906C42—48no—
907C42—48no—
908C42—48no—
909C42C2×#4114yes—
910C42C2×#4114yes—
911C42C2×#4114yes—
912C42C2×#4114yes—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23C22×#4112yes—
932C23C22×#4112yes—
933C23C2×H(5,𝔽2)12yes—
934C23C2611yescharacteristic
935Q8—48no—
936Q8—48no—
937Q8—48no—
938Q8—84no—
939Q8—816no—
940D4—48no—
941D4—416no—
942D4—416no—
943D4—48no—
944D4—48no—
945D4—816no—
946D4—84no—
947D4—84no—
948D4—84no—
949D4—168no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—24no—
954C2×C4—21no—
955C2×C4—24no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—44no—
1000C2×C4—44no—
1001C2×C4—48no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—44no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—82no—
1008C2×C4—82no—
1009C2×C4—84no—
1010C2×C4—84no—
1011C2×C4—88no—
1012C2×C4—88no—
1013C2×C4—168no—
1014C2×C4#559116yes—
1015C2×C4C22×#4112yes—
1016C2×C4C22×#4112yes—
1017C2×C4C22×#4112yes—
1018C2×C4C22×#4112yes—
1019C2×C4C22×#4118yes—
1020C2×C4C22×#4112yes—
1021C2×C4C22×#4112yes—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4112yes—
1024C2×C4C2×H(5,𝔽2)12yes—
1025C2×C4C2×H(5,𝔽2)12yes—
1026C22—22no—
1027C22—22no—
1028C22—22no—
1029C22—22no—
1030C22—22no—
1031C22—22no—
1032C22—44no—
1033C22—44no—
1034C22—44no—
1035C22—44no—
1036C22—44no—
1037C22—44no—
1038C22—44no—
1039C22—44no—
1040C22—44no—
1041C22—44no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—44no—
1046C22C2×#55914yes—
1047C22C23×#4111yescharacteristic
1048C22C23×#4111yescharacteristic
1049C22C22×H(5,𝔽2)11yescharacteristic
1050C22H(7,𝔽2)11yescharacteristic
1051C22H(7,𝔽2)11yescharacteristic
1052C222−1+611yescharacteristic
1053C222−1+611yescharacteristic
1054C4—28no—
1055C4—22no—
1056C4—22no—
1057C4—22no—
1058C4—22no—
1059C4—44no—
1060C4—42no—
1061C4—42no—
1062C4—44no—
1063C4—44no—
1064C4—44no—
1065C4—42no—
1066C4—42no—
1067C4—44no—
1068C4—44no—
1069C4—44no—
1070C4—44no—
1071C4—44no—
1072C4C2×#55914yes—
1073C4C2×#55914yes—
1074C2—24no—
1075C2—84no—
1076C2—84no—
1077C2C22×#55911yescharacteristic
1078C2#6284611yescharacteristic
1079C2#6285011yescharacteristic
1080C2#6285611yescharacteristic
1081C2#6285611yescharacteristic
1082C2#6287811yescharacteristic
1083C2#6287811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35166C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45201C2semidirect
2. #45168C2semidirect
3. #45043C2semidirect
4. #44986C2semidirect
5. #39807C2semidirect
6. #39804C2semidirect
7. #39768C2semidirect
8. #39764C2semidirect
9. #39275C2semidirect
10. #39274C2semidirect
11. #39269C2semidirect
12. #39268C2semidirect
13. #35618C2semidirect
14. #35592C2semidirect
15. #35255C2semidirect
16. #35180C2semidirect
18. #34637C2semidirect
19. #34267C2semidirect
20. #34213C2semidirect
21. #34206C2semidirect
22. C2×#2331C2semidirect
23. #34070C2semidirect

Maximal subgroups

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

subgroupindex
#452012
#451682
#450432
#449862
#398072
#398042
#397682
#397642
#392752
#392742
#392692
#392682
#356182
#355922
#352552
#351802
#351662
#346372
#342672
#342132
#342062
C2×#23312
#340702