Finite Group Databasebeta

← #7633914

Subgroups — #7633914

Order 512.

4884 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37631C212yesmaximal, complemented
2#37630C212yesmaximal, complemented
3#37629C212yesmaximal, complemented
4#37625C212yesmaximal, complemented
5#37581C214yesmaximal, complemented
6#37572C214yesmaximal, complemented
7#37505C214yesmaximal, complemented
8#37494C214yesmaximal, complemented
9#37487C218yesmaximal, complemented
10#36693C214yesmaximal, complemented
11#34969C214yesmaximal, complemented
12#34955C211yesmaximal, characteristic, complemented
13#34952C211yesmaximal, characteristic, complemented
14#34938C211yesmaximal, characteristic, complemented
15#34937C211yesmaximal, characteristic
16#34745C212yesmaximal, complemented
17#34744C212yesmaximal, complemented
18#34639C212yesmaximal, complemented
19#34637C212yesmaximal, complemented
20#34619C214yesmaximal, complemented
21#34596C214yesmaximal, complemented
22C4×#532C211yesmaximal, characteristic, complemented
23#34026C211yesmaximal, characteristic, complemented
24C2×#2295C211yesmaximal, characteristic, complemented
25C2×#533C2212yes—
26C2×#532C2211yescharacteristic
27C2×#532C2212yes—
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2212yes—
30C22×C4×Q8C2211yescharacteristic
31#2839C2218yes—
32#2838C2218yes—
33#2838C2218yes—
34#2837C2218yes—
35#2832C2218yes—
36#2831C2218yes—
37#2830C2218yes—
38#2829C2218yes—
39#2665C2218yes—
40#2663C2218yes—
41#2655C2218yes—
42#2654C2218yes—
43#2653C2218yes—
44#2653C2218yes—
45#2652C2218yes—
46#2650C2218yes—
47#2650C2218yes—
48#2649C2218yes—
49#2647C2214yes—
50#2645C2214yes—
51#2645C2214yes—
52#2645C2214yes—
53#2644C2214yes—
54#2644C2214yes—
55#2644C2214yes—
56#2643C2218yes—
57#2643C2218yes—
58#2642C2214yes—
59#2641C2214yes—
60#2640C2214yes—
61#2640C2214yes—
62#2640C2214yes—
63#2639C2218yes—
64#2639C2218yes—
65#2638C2218yes—
66#2630C2218yes—
67#2628C2214yes—
68#2625C2214yes—
69#2624C2214yes—
70#2620C2214yes—
71#2592C2214yes—
72#2591C2214yes—
73#2582C2212yes—
74#2581C2212yes—
75#2580C2212yes—
76#2579C2214yes—
77#2568C2212yes—
78#2552C2212yes—
79#2551C2212yes—
80#2550C2214yes—
81#2549C2214yes—
82#2548C2211yescharacteristic
83#2548C2212yes—
84#2547C2211yescharacteristic
85#2546C2211yescharacteristic
86#2545C2212yes—
87#2544C2212yes—
88#2543C2214yes—
89#2541C2211yescharacteristic
90#2538C2212yes—
91#2530C2218yes—
92#2527C2218yes—
93#2511C2214yes—
94#2509C2214yes—
95#2504C2212yes—
96#2494C2214yes—
97#2492C2214yes—
98#2487C2212yes—
99#2477C2218yes—
100#2470C2218yes—
101#2454C2214yes—
102#2453C2214yes—
103#2452C2214yes—
104#2452C2214yes—
105#2451C2214yes—
106#2450C2218yes—
107#2449C2218yes—
108#2448C2214yes—
109#2447C2214yes—
110#2447C2214yes—
111#2446C2214yes—
112#2445C2214yes—
113#2444C2218yes—
114#2443C2218yes—
115#2440C2214yes—
116#2436C2212yes—
117#2427C2214yes—
118#2422C2214yes—
119#2416C2214yes—
120#2409C2212yes—
121#2401C2218yes—
122#2401C2218yes—
123#2399C2214yes—
124#2398C2218yes—
125#2398C2214yes—
126#2398C2218yes—
127#2396C2214yes—
128#2396C2218yes—
129#2395C2218yes—
130#2392C2214yes—
131C4×C4⋊Q8C2214yes—
132C4×C4⋊Q8C2212yes—
133C4×#127C2212yes—
134C4×#124C2214yes—
135C4×#124C2214yes—
136C4×C22⋊Q8C2218yes—
137C4×C22⋊Q8C2214yes—
138C4×#123C2218yes—
139C4×#121C2214yes—
140C4×#121C2214yes—
141C4×#121C2214yes—
142#2298C2212yes—
143#2298C2212yes—
144#2297C2211yescharacteristic
145#2297C2212yes—
146#2297C2212yes—
147#2297C2212yes—
148#2297C2212yes—
149#2297C2212yes—
150#2297C2211yescharacteristic
151#2296C2211yescharacteristic
152#2296C2212yes—
153#2296C2212yes—
154#2296C2211yescharacteristic
155#2295C2212yes—
156#2295C2212yes—
157#2295C2212yes—
158#2295C2212yes—
159#2295C2214yes—
160#2295C2212yes—
161#2295C2212yes—
162#2295C2212yes—
163#2295C2212yes—
164C2×#391C2212yes—
165#2293C2212yes—
166#2293C2212yes—
167#2293C2212yes—
168#2293C2212yes—
169C2×#389C2212yes—
170#2290C2214yes—
171#2290C2214yes—
172C2×#387C2214yes—
173#2285C2211yescharacteristic
174C42×D4C2212yes—
175C42×D4C2212yes—
176C4×#117C2212yes—
177C4×#117C2211yescharacteristic
178C4×#117C2212yes—
179C2×C4×C4⋊C4C2211yescharacteristic
180C2×C4×C4⋊C4C2212yes—
181C2×#376C2212yes—
182C2×C43C2211yescharacteristic
183C22×#41C2311yescharacteristic
184C22×#41C2312yes—
185C23×Q8C2311yescharacteristic
186#533—48no—
187#532—28no—
188#532—48no—
189C2×C4⋊Q8C2311yescharacteristic
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2314yes—
192C2×C4⋊Q8C2312yes—
193C2×#127C2311yescharacteristic
194C2×#127C2312yes—
195C2×#125C2314yes—
196C2×#124C2312yes—
197C2×#124C2314yes—
198C2×#124C2312yes—
199C2×#124C2312yes—
200C2×#123C2318yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2318yes—
204C2×#121C2312yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C4×#41—28no—
209C4×#41—48no—
210C2×C4×Q8—28no—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2312yes—
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2318yes—
218C2×C4×Q8C2314yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2312yes—
222C2×C4×D4C2312yes—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2312yes—
225C2×C4×D4C2314yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2318yes—
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2314yes—
236C2×#117C2314yes—
237C2×#117C2314yes—
238C22×C4⋊C4C2312yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2314yes—
242C22×C42C2312yes—
243C22×C42C2311yescharacteristic
244C22×C42C2312yes—
245C22×C42C2312yes—
246C22×C42C2311yescharacteristic
247C22×C42C2314yes—
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2311yescharacteristic
251#401C2318yes—
252#401C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2318yes—
267#399C2318yes—
268#399C2314yes—
269#399C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2314yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2314yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#396C2318yes—
296#396C2318yes—
297#396C2318yes—
298#395C2318yes—
299#395C2314yes—
300#395C2318yes—
301#395C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2314yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#393C2314yes—
315#393C2318yes—
316#393C2318yes—
317#393C2318yes—
318#392C2314yes—
319#391C2314yes—
320#391C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2318yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#390C2314yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2314yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2318yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#388C2314yes—
372#388C2318yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2314yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2314yes—
390#387C2314yes—
391#387C2318yes—
392#387C2314yes—
393#387C2318yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#386C2314yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#386C2314yes—
405#386C2318yes—
406#386C2314yes—
407#386C2318yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2314yes—
418#385C2318yes—
419#385C2314yes—
420#384C2312yes—
421#384C2314yes—
422#382C2314yes—
423#382C2312yes—
424#381C2318yes—
425#380C2312yes—
426#380C2314yes—
427#380C2314yes—
428#380C2318yes—
429#380C2312yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2314yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2314yes—
439C4×C4⋊C4C2314yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2318yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2312yes—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C22⋊C4C2312yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2312yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2312yes—
462C4×C22⋊C4C2312yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2314yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2312yes—
469#376C2314yes—
470#376C2314yes—
471#376C2314yes—
472#376C2312yes—
473#376C2314yes—
474#376C2314yes—
475#376C2314yes—
476C2×#95C2314yes—
477C2×#95C2314yes—
478C2×#95C2314yes—
479C2×#95C2312yes—
480C43C2312yes—
481C43C2312yes—
482C43C2311yescharacteristic
483C43C2311yescharacteristic
484C43C2311yescharacteristic
485C43C2311yescharacteristic
486C43C2312yes—
487C2×#41—24no—
488C2×#41—28no—
489C2×#41—28no—
490C2×#41—24no—
491C2×#41—24no—
492C2×#41—28no—
493C22×Q8—24no—
494C22×Q8—44no—
495C22×Q8C2412yes—
496C22×Q8C2411yescharacteristic
497C22×Q8C2412yes—
498C22×Q8C2412yes—
499C22×Q8C2418yes—
500C22×D4C2412yes—
501C22×D4C2412yes—
502C22×D4C2414yes—
503C22×D4C2411yescharacteristic
504C22×D4C2412yes—
505C22×D4C2412yes—
506C22×D4C2418yes—
507C23×C4C2412yes—
508C23×C4C2412yes—
509C23×C4C2414yes—
510C23×C4C2412yes—
511C23×C4C2411yescharacteristic
512C23×C4C2412yes—
513C23×C4C2414yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2418yes—
517C23×C4C2412yes—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C4⋊Q8—24no—
521C4⋊Q8—48no—
522C4⋊Q8—48no—
523C4⋊Q8—44no—
524#127—24no—
525#127—44no—
526#125—48no—
527#124—28no—
528#124—48no—
529#124—44no—
530#124—44no—
531#123—416no—
532C22⋊Q8—416no—
533C22⋊Q8—416no—
534C22⋊Q8—48no—
535#121—28no—
536#121—28no—
537#121—48no—
538#121—416no—
539C4×Q8—28no—
540C4×Q8—28no—
541C4×Q8—28no—
542C4×Q8—28no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8—416no—
546C4×Q8—48no—
547C4×D4—28no—
548C4×D4—28no—
549C4×D4—24no—
550C4×D4—24no—
551C4×D4—28no—
552C4×D4—28no—
553C4×D4—48no—
554C4×D4—48no—
555C4×D4—48no—
556C4×D4—416no—
557C4×D4—416no—
558#117—24no—
559#117—28no—
560#117—24no—
561#117—24no—
562#117—28no—
563#117—48no—
564#117—48no—
565#117—48no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—28no—
568C2×C4⋊C4—44no—
569C2×C4⋊C4—48no—
570C2×C4⋊C4C2412yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2412yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2414yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2418yes—
604C2×C4⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2412yes—
607C2×C22⋊C4C2412yes—
608C2×C22⋊C4C2412yes—
609C2×C22⋊C4C2412yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C42—28no—
631C2×C42—24no—
632C2×C42—28no—
633C2×C42—24no—
634C2×C42—28no—
635C2×C42—48no—
636C2×C42—44no—
637C2×C42—44no—
638C2×C42#4118yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2414yes—
642C2×C42C2412yes—
643C2×C42C2412yes—
644C2×C42C2412yes—
645C2×C42C2412yes—
646C2×C42C2412yes—
647C2×C42C2414yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2411yescharacteristic
652C2×C42C2414yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2414yes—
662C2×C42C2418yes—
663C2×C42C2412yes—
664C2×C42C2412yes—
665C2×C42C2412yes—
666C2×C42C2412yes—
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2412yes—
683#95C2412yes—
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#95C2414yes—
697#95C2414yes—
698#95C2418yes—
699#95C2418yes—
700#95C2418yes—
701#95C2418yes—
702#95C2418yes—
703#95C2418yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712C24C2512yes—
713C24C2514yes—
714C24C2511yescharacteristic
715#41—416no—
716#41—432no—
717C2×Q8—24no—
718C2×Q8—24no—
719C2×Q8—22no—
720C2×Q8—24no—
721C2×Q8—24no—
722C2×Q8—22no—
723C2×Q8—22no—
724C2×Q8—24no—
725C2×Q8—24no—
726C2×Q8—24no—
727C2×Q8—44no—
728C2×Q8—48no—
729C2×Q8—48no—
730C2×Q8—48no—
731C2×Q8—416no—
732C2×D4—24no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—28no—
738C2×D4—22no—
739C2×D4—24no—
740C2×D4—24no—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—24no—
746C2×D4—28no—
747C2×D4—44no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—28no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—24no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—24no—
763C22×C4—24no—
764C22×C4—28no—
765C22×C4—24no—
766C22×C4—28no—
767C22×C4—216no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—48no—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4C2×#4114yes—
782C22×C4H(5,𝔽2)14yes—
783C22×C42−1+414yes—
784C22×C4C2512yes—
785C22×C4C2512yes—
786C22×C4C2514yes—
787C22×C4C2512yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2518yes—
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2511yescharacteristic
801C22×C4C2512yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C4⋊C4—24no—
806C4⋊C4—24no—
807C4⋊C4—28no—
808C4⋊C4—28no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—28no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—44no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—48no—
831C4⋊C4—44no—
832C4⋊C4—48no—
833C4⋊C4—48no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—48no—
839C4⋊C4—48no—
840C22⋊C4—24no—
841C22⋊C4—28no—
842C22⋊C4—24no—
843C22⋊C4—24no—
844C22⋊C4—24no—
845C22⋊C4—24no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—28no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—48no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C42—24no—
866C42—24no—
867C42—24no—
868C42—28no—
869C42—28no—
870C42—22no—
871C42—22no—
872C42—24no—
873C42—28no—
874C42—24no—
875C42—24no—
876C42—28no—
877C42—24no—
878C42—22no—
879C42—22no—
880C42—24no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—24no—
885C42—24no—
886C42—28no—
887C42—42no—
888C42—42no—
889C42—42no—
890C42—42no—
891C42—48no—
892C42—44no—
893C42C2×#4114yes—
894C42C2×#4114yes—
895C42C2×#4114yes—
896C42C2×#4114yes—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—24no—
901C23—24no—
902C23—22no—
903C23—22no—
904C23—24no—
905C23—24no—
906C23—28no—
907C23—24no—
908C23—28no—
909C23C22×#4112yes—
910C23C2×H(5,𝔽2)12yes—
911C23C2×2−1+412yes—
912C23C2611yescharacteristic
913Q8—48no—
914Q8—44no—
915Q8—48no—
916Q8—48no—
917Q8—816no—
918D4—48no—
919D4—48no—
920D4—416no—
921D4—44no—
922D4—48no—
923D4—48no—
924D4—816no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—28no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—28no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—28no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—44no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—48no—
975C2×C4—48no—
976C2×C4—48no—
977C2×C4—48no—
978C2×C4—416no—
979C2×C4—48no—
980C2×C4—816no—
981C2×C4—88no—
982C2×C4#542116yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4112yes—
985C2×C4C22×#4112yes—
986C2×C4C22×#4112yes—
987C2×C4C22×#4112yes—
988C2×C4C22×#4112yes—
989C2×C4C2×H(5,𝔽2)12yes—
990C2×C4C2×H(5,𝔽2)12yes—
991C2×C4C2×2−1+412yes—
992C2×C4C2×2−1+412yes—
993C2×C4#58514yes—
994C2×C4#58514yes—
995C22—24no—
996C22—24no—
997C22—22no—
998C22—22no—
999C22—48no—
1000C22—44no—
1001C22—44no—
1002C22—48no—
1003C22—42no—
1004C22—44no—
1005C22—42no—
1006C22—44no—
1007C22—42no—
1008C22—44no—
1009C22C2×#54214yes—
1010C22C23×#4111yescharacteristic
1011C22C22×H(5,𝔽2)11yescharacteristic
1012C22C22×2−1+411yescharacteristic
1013C22C2×#58512yes—
1014C22C2×#58512yes—
1015C4—24no—
1016C4—22no—
1017C4—22no—
1018C4—22no—
1019C4—42no—
1020C4—44no—
1021C4—48no—
1022C4—44no—
1023C4—44no—
1024C4—44no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—44no—
1029C4—42no—
1030C4—44no—
1031C4—42no—
1032C4—44no—
1033C4C2×#54214yes—
1034C4C2×#54214yes—
1035C4#345514yes—
1036C2—24no—
1037C2—84no—
1038C2—82no—
1039C2C22×#54211yescharacteristic
1040C2C2×#345511yescharacteristic
1041C2#6268611yescharacteristic
1042C2#6274812yes—
1043C2#6276112yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
prime radical#34937C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37631C2semidirect
2. #37630C2semidirect
3. #37629C2semidirect
4. #37625C2semidirect
5. #37581C2semidirect
6. #37572C2semidirect
7. #37505C2semidirect
8. #37494C2semidirect
9. #37487C2semidirect
10. #36693C2semidirect
11. #34969C2semidirect
12. #34955C2semidirect
13. #34952C2semidirect
14. #34938C2semidirect
16. #34745C2semidirect
17. #34744C2semidirect
18. #34639C2semidirect
19. #34637C2semidirect
20. #34619C2semidirect
21. #34596C2semidirect
22. C4×#532C2semidirect
23. #34026C2semidirect
24. C2×#2295C2semidirect

Maximal subgroups

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

subgroupindex
#376312
#376302
#376292
#376252
#375812
#375722
#375052
#374942
#374872
#366932
#349692
#349552
#349522
#349382
#349372
#347452
#347442
#346392
#346372
#346192
#345962
C4×#5322
#340262
C2×#22952