Finite Group Databasebeta

← #7720525

Subgroups — #7720525

Order 512.

5022 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51428C218yesmaximal, complemented
2#50878C214yesmaximal, complemented
3#50660C214yesmaximal, complemented
4#45428C212yesmaximal, complemented
5#45421C212yesmaximal, complemented
6#45299C212yesmaximal, complemented
7#45097C214yesmaximal, complemented
8#45070C212yesmaximal, complemented
9#44961C214yesmaximal, complemented
10#39046C214yesmaximal, complemented
11#39042C214yesmaximal, complemented
12#38987C212yesmaximal, complemented
13#38985C212yesmaximal, complemented
14#37292C214yesmaximal, complemented
15#36469C212yesmaximal, complemented
16#36463C212yesmaximal, complemented
17#35285C211yesmaximal, characteristic, complemented
18#35272C211yesmaximal, characteristic
19#35271C214yesmaximal, complemented
20#35200C211yesmaximal, characteristic, complemented
21#34625C211yesmaximal, characteristic, complemented
22#34394C211yesmaximal, characteristic, complemented
23#34364C211yesmaximal, characteristic, complemented
24#34123C211yesmaximal, characteristic, complemented
25C2×#559C2214yescomplemented
26C2×#535C2212yes—
27C2×#533C2211yescharacteristic
28C22×#127C2211yescharacteristic
29C2×C4×#41C2211yescharacteristic
30#2858C2212yes—
31#2858C2212yes—
32#2856C2214yes—
33#2854C2214yescomplemented
34#2854C2214yescomplemented
35#2851C2214yescomplemented
36#2786C2218yescomplemented
37#2761C2218yescomplemented
38#2761C2218yescomplemented
39#2757C2218yescomplemented
40#2749C2218yescomplemented
41#2740C2218yescomplemented
42#2737C2218yescomplemented
43#2737C2218yescomplemented
44#2735C2218yes—
45#2735C2218yes—
46#2723C2218yescomplemented
47#2715C2218yescomplemented
48#2706C2218yescomplemented
49#2701C2218yescomplemented
50#2700C2218yescomplemented
51#2697C2218yes—
52#2691C2218yescomplemented
53#2686C2218yescomplemented
54#2684C2218yes—
55#2672C2218yescomplemented
56#2667C2212yes—
57#2666C2214yescomplemented
58#2665C2212yes—
59#2660C2212yescomplemented
60#2647C2212yescomplemented
61#2644C2214yescomplemented
62#2644C2214yescomplemented
63#2641C2212yes—
64#2641C2212yes—
65#2638C2214yes—
66#2629C2212yes—
67#2628C2212yes—
68#2619C2214yes—
69#2603C2218yescomplemented
70#2602C2218yescomplemented
71#2599C2214yescomplemented
72#2597C2218yescomplemented
73#2592C2214yescomplemented
74#2592C2214yescomplemented
75#2567C2211yescharacteristic, complemented
76#2563C2211yescharacteristic, complemented
77#2561C2218yes—
78#2557C2218yescomplemented
79#2557C2218yescomplemented
80#2548C2212yes—
81#2548C2212yes—
82#2548C2212yes—
83#2548C2212yes—
84#2548C2214yes—
85#2547C2214yescomplemented
86#2547C2211yescharacteristic, complemented
87#2546C2211yescharacteristic, complemented
88#2545C2214yescomplemented
89#2544C2214yescomplemented
90#2541C2212yes—
91#2541C2212yes—
92#2538C2214yescomplemented
93#2534C2218yes—
94#2531C2218yescomplemented
95#2531C2218yescomplemented
96#2531C2218yescomplemented
97#2526C2218yescomplemented
98#2526C2218yescomplemented
99#2513C2214yescomplemented
100#2513C2214yescomplemented
101#2512C2214yescomplemented
102#2512C2214yescomplemented
103#2499C2212yes—
104#2491C2214yescomplemented
105#2490C2214yescomplemented
106#2485C2214yes—
107#2480C2218yes—
108#2461C2218yescomplemented
109#2459C2218yescomplemented
110#2454C2214yescomplemented
111#2452C2214yescomplemented
112#2448C2214yescomplemented
113#2447C2214yescomplemented
114#2447C2214yescomplemented
115#2445C2214yescomplemented
116#2444C2218yescomplemented
117#2444C2218yescomplemented
118#2435C2214yes—
119#2435C2212yes—
120#2435C2212yes—
121#2432C2212yes—
122#2425C2218yescomplemented
123#2425C2218yescomplemented
124#2422C2214yescomplemented
125#2420C2214yescomplemented
126#2418C2218yes—
127#2408C2212yes—
128#2408C2212yes—
129#2408C2214yes—
130#2402C2212yescomplemented
131#2399C2212yescomplemented
132#2396C2214yes—
133#2380C2214yes—
134#2378C2214yes—
135#2369C2212yescomplemented
136#2367C2214yescomplemented
137#2366C2212yes—
138#2366C2212yes—
139#2366C2214yescomplemented
140#2365C2212yescomplemented
141#2357C2214yescomplemented
142#2356C2212yescomplemented
143#2356C2211yescharacteristic, complemented
144#2356C2211yescharacteristic, complemented
145#2353C2212yes—
146#2353C2212yes—
147#2351C2212yescomplemented
148#2349C2211yescharacteristic, complemented
149#2349C2211yescharacteristic, complemented
150#2347C2212yes—
151#2346C2212yes—
152#2346C2212yes—
153#2343C2214yescomplemented
154#2339C2212yes—
155D4×C22⋊C4C2214yes—
156D4×C22⋊C4C2214yes—
157#2330C2214yescomplemented
158#2328C2212yes—
159#2328C2212yes—
160#2328C2214yes—
161#2327C2212yescomplemented
162#2326C2212yescomplemented
163#2323C2214yes—
164#2320C2214yescomplemented
165#2319C2214yescomplemented
166#2319C2214yescomplemented
167#2309C2214yes—
168#2309C2212yes—
169#2308C2214yes—
170C4×C4⋊Q8C2212yescomplemented
171C4×#125C2212yescomplemented
172C4×#121C2214yescomplemented
173C4×#121C2214yescomplemented
174#2295C2212yescomplemented
175#2290C2214yes—
176#2285C2211yescharacteristic
177#2283C2211yescharacteristic
178#2283C2211yescharacteristic
179#2283C2212yescomplemented
180C42×D4C2212yescomplemented
181C4×#117C2211yescharacteristic
182C2×#376C2212yescomplemented
183C22×#41C2311yescharacteristic
184C23×D4C2312yes—
185C23×D4C2312yes—
186C23×D4C2312yes—
187#559—416no—
188#535—48no—
189#533—28no—
190C2×C4⋊Q8C2311yescharacteristic
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×#127—28no—
195C2×#127C2312yes—
196C2×#127C2312yes—
197C2×#127C2312yes—
198C2×#127C2312yes—
199C2×#127C2314yes—
200C2×#126C2318yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#124C2312yes—
204C2×#124C2314yes—
205C2×#124C2314yes—
206C2×#124C2314yes—
207C2×#124C2318yes—
208C2×#124C2314yes—
209C2×#124C2314yes—
210C2×#123C2318yes—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2318yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2318yes—
219C2×#121C2318yes—
220C2×#120C2314yes—
221C2×#120C2314yes—
222C4×#41—28no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2318yes—
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C22×C22⋊C4C2318yes—
247C22×C42C2312yes—
248C22×C42C2314yes—
249C22×C42C2311yescharacteristic
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#399C2314yes—
254#399C2318yes—
255#398C2314yes—
256#398C2314yes—
257#398C2314yes—
258#398C2314yes—
259#398C2314yes—
260#398C2314yes—
261#398C2314yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2318yes—
268#397C2314yes—
269#397C2318yes—
270#397C2318yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C2318yes—
276#396C2314yes—
277#396C2314yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#395C2314yes—
284#395C2314yes—
285#395C2314yes—
286#395C2314yes—
287#394C2314yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2314yes—
292#394C2318yes—
293#394C2314yes—
294#394C2314yes—
295#394C2318yes—
296#394C2318yes—
297#394C2314yes—
298#394C2314yes—
299#394C2318yes—
300#394C2318yes—
301#393C2314yes—
302#393C2318yes—
303#393C2314yes—
304#393C2318yes—
305#392C2318yes—
306#392C2314yes—
307#392C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2318yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#390C2312yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2318yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2318yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2318yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2312yes—
351#389C2312yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2314yes—
370#388C2318yes—
371#388C2318yes—
372#387C2314yes—
373#387C2314yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2318yes—
406#384C2312yes—
407#384C2312yes—
408#384C2312yes—
409#383C2312yes—
410#383C2314yes—
411#383C2312yes—
412#383C2312yes—
413#383C2312yes—
414#382C2312yes—
415#382C2312yes—
416#382C2312yes—
417#382C2314yes—
418#382C2312yes—
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2314yes—
422#381C2318yes—
423#381C2318yes—
424#381C2312yes—
425#381C2312yes—
426#381C2318yes—
427#381C2314yes—
428#380C2314yes—
429#380C2318yes—
430#380C2318yes—
431#380C2312yes—
432#380C2312yes—
433#380C2314yes—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2312yes—
437#380C2312yes—
438#380C2312yes—
439#380C2318yes—
440#379C2314yes—
441#379C2318yes—
442#379C2318yes—
443#379C2314yes—
444#379C2318yes—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2312yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C22⋊C4C2318yes—
464C4×C22⋊C4C2312yes—
465C4×C22⋊C4C2312yes—
466C4×C22⋊C4C2312yes—
467C4×C22⋊C4C2314yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2318yes—
472C4×C22⋊C4C2314yes—
473#376C2314yes—
474#376C2314yes—
475#376C2312yes—
476#376C2312yes—
477#376C2314yes—
478#376C2312yes—
479#376C2312yes—
480#376C2311yescharacteristic
481#376C2311yescharacteristic
482C2×#95C2314yes—
483C2×#95C2312yes—
484C2×#95C2312yes—
485C43C2312yes—
486C25C2414yes—
487C2×#41—24no—
488C2×#41—24no—
489C2×#41—42no—
490C22×Q8C2412yes—
491C22×Q8C2411yescharacteristic
492C22×Q8C2412yes—
493C22×Q8C2414yes—
494C22×D4—28no—
495C22×D4—28no—
496C22×D4—28no—
497C22×D4—44no—
498C22×D4—48no—
499C22×D4—44no—
500C22×D4—84no—
501C22×D4C2414yes—
502C22×D4C2414yes—
503C22×D4C2412yes—
504C22×D4C2411yescharacteristic
505C22×D4C2418yes—
506C22×D4C2418yes—
507C22×D4C2414yes—
508C22×D4C2414yes—
509C22×D4C2414yes—
510C22×D4C2414yes—
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2414yes—
516C23×C4C2412yes—
517C23×C4C2418yes—
518C23×C4C2418yes—
519C23×C4C2414yes—
520C23×C4C2411yescharacteristic
521C4⋊Q8—24no—
522C4⋊Q8—24no—
523C4⋊Q8—44no—
524C4⋊Q8—44no—
525#127—216no—
526#127—28no—
527#127—28no—
528#127—28no—
529#127—28no—
530#126—88no—
531#125—28no—
532#125—44no—
533#124—28no—
534#124—48no—
535#124—48no—
536#124—48no—
537#124—416no—
538#124—84no—
539#124—84no—
540#123—416no—
541#123—416no—
542#123—88no—
543C22⋊Q8—28no—
544C22⋊Q8—28no—
545C22⋊Q8—88no—
546#121—48no—
547#121—48no—
548#121—416no—
549#121—88no—
550#120—48no—
551#120—48no—
552C4×Q8—24no—
553C4×Q8—24no—
554C4×Q8—28no—
555C4×Q8—28no—
556C4×Q8—48no—
557C4×Q8—48no—
558C4×D4—28no—
559C4×D4—28no—
560C4×D4—28no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—44no—
567C4×D4—48no—
568C4×D4—416no—
569C4×D4—88no—
570#117—24no—
571#117—28no—
572#117—28no—
573#117—44no—
574#117—44no—
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2418yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C22⋊C4—88no—
611C2×C22⋊C4C2412yes—
612C2×C22⋊C4C2412yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2418yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2412yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2418yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C42—28no—
646C2×C42—48no—
647C2×C42#4118yes—
648C2×C42C2412yes—
649C2×C42C2414yes—
650C2×C42C2414yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2418yes—
661C2×C42C2418yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670#95C2411yescharacteristic
671#95C2412yes—
672#95C2411yescharacteristic
673#95C2414yes—
674#95C2414yes—
675#95C2412yes—
676#95C2414yes—
677#95C2412yes—
678#95C2414yes—
679#95C2414yes—
680#95C2412yes—
681#95C2412yes—
682#95C2411yescharacteristic
683#95C2411yescharacteristic
684#95C2412yes—
685#95C2414yes—
686#95C2418yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2412yes—
694#95C2418yes—
695#95C2418yes—
696#95C2414yes—
697#95C2412yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701#95C2414yes—
702#95C2414yes—
703#95C2414yes—
704#95C2414yes—
705#95C2414yes—
706#95C2412yes—
707#95C2412yes—
708#95C2418yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712C24—28no—
713C24—48no—
714C24—44no—
715C24—48no—
716C24—44no—
717C24C2518yes—
718C24C2511yescharacteristic
719C24C2512yes—
720#41—416no—
721C2×Q8—22no—
722C2×Q8—24no—
723C2×Q8—24no—
724C2×Q8—24no—
725C2×Q8—22no—
726C2×Q8—24no—
727C2×Q8—22no—
728C2×Q8—44no—
729C2×Q8—44no—
730C2×Q8—44no—
731C2×Q8—44no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—216no—
735C2×D4—216no—
736C2×D4—22no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—28no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—22no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—42no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—816no—
760C2×D4—816no—
761C2×D4—816no—
762C2×D4H(5,𝔽2)14yes—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—22no—
766C22×C4—24no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—48no—
781C22×C4—48no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C4—48no—
785C22×C4—48no—
786C22×C4C2×#4114yes—
787C22×C4C2×#4114yes—
788C22×C4C2×#4114yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2512yes—
793C22×C4C2514yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2514yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2512yes—
802C22×C4C2514yes—
803C22×C4C2512yes—
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C22×C4C2511yescharacteristic
810C4⋊C4—22no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—24no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—42no—
827C4⋊C4—42no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C4⋊C4—44no—
833C4⋊C4—48no—
834C4⋊C4—44no—
835C4⋊C4—44no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C22⋊C4—24no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—216no—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—42no—
856C22⋊C4—42no—
857C22⋊C4—42no—
858C22⋊C4—42no—
859C22⋊C4—48no—
860C22⋊C4—48no—
861C22⋊C4—44no—
862C22⋊C4—48no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4—48no—
870C22⋊C4—48no—
871C22⋊C4—48no—
872C22⋊C4—48no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C42—24no—
880C42—24no—
881C42—24no—
882C42—28no—
883C42—28no—
884C42—24no—
885C42—24no—
886C42—24no—
887C42—28no—
888C42—24no—
889C42—24no—
890C42—24no—
891C42—44no—
892C42—44no—
893C42—48no—
894C42—48no—
895C42—42no—
896C42—42no—
897C42C2×#4114yes—
898C42C2×#4114yes—
899C42C2×#4114yes—
900C42C2×#4114yes—
901C23—22no—
902C23—21no—
903C23—22no—
904C23—22no—
905C23—24no—
906C23—21no—
907C23—22no—
908C23—24no—
909C23—28no—
910C23—28no—
911C23—28no—
912C23—28no—
913C23—28no—
914C23—28no—
915C23—28no—
916C23—416no—
917C23—88no—
918C23—88no—
919C23—168no—
920C23—168no—
921C23C22×#4112yes—
922C23C2×H(5,𝔽2)14yes—
923C23C2611yescharacteristic
924Q8—48no—
925Q8—44no—
926Q8—84no—
927Q8—88no—
928D4—28no—
929D4—48no—
930D4—416no—
931D4—416no—
932D4—88no—
933D4—88no—
934D4—88no—
935D4—88no—
936D4—816no—
937D4—816no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—28no—
944C2×C4—28no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—24no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—28no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—84no—
991C2×C4—88no—
992C2×C4—88no—
993C2×C4—168no—
994C2×C4—168no—
995C2×C4C22×#4112yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4112yes—
998C2×C4C22×#4112yes—
999C2×C4C22×#4112yes—
1000C2×C4C22×#4112yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4#58512yes—
1003C2×C4#58514yes—
1004C22—22no—
1005C22—24no—
1006C22—22no—
1007C22—22no—
1008C22—28no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—44no—
1013C22—42no—
1014C22—48no—
1015C22—48no—
1016C22—48no—
1017C22—48no—
1018C22—48no—
1019C22—48no—
1020C22—48no—
1021C22—1616no—
1022C22C23×#4111yescharacteristic
1023C22C22×H(5,𝔽2)11yescharacteristic
1024C22C2×#58511yescharacteristic
1025C22C2×#58512yes—
1026C22H(7,𝔽2)12yes—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—22no—
1031C4—42no—
1032C4—44no—
1033C4—42no—
1034C4—42no—
1035C4—44no—
1036C4—42no—
1037C4—44no—
1038C4—44no—
1039C4—44no—
1040C4—44no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—44no—
1045C4—44no—
1046C4#349414yes—
1047C4#351014yes—
1048C2—44no—
1049C2—42no—
1050C2—88no—
1051C2C2×#349411yescharacteristic
1052C2C2×#351011yescharacteristic
1053C2#6285511yescharacteristic
1054C2#6292012yes—
1055C2#6296612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35272C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51428C2semidirect
2. #50878C2semidirect
3. #50660C2semidirect
4. #45428C2semidirect
5. #45421C2semidirect
6. #45299C2semidirect
7. #45097C2semidirect
8. #45070C2semidirect
9. #44961C2semidirect
10. #39046C2semidirect
11. #39042C2semidirect
12. #38987C2semidirect
13. #38985C2semidirect
14. #37292C2semidirect
15. #36469C2semidirect
16. #36463C2semidirect
17. #35285C2semidirect
19. #35271C2semidirect
20. #35200C2semidirect
21. #34625C2semidirect
22. #34394C2semidirect
23. #34364C2semidirect
24. #34123C2semidirect
25. C2×#559C22semidirect
33. #2854C22semidirect
34. #2854C22semidirect
35. #2851C22semidirect
36. #2786C22semidirect
37. #2761C22semidirect
38. #2761C22semidirect
39. #2757C22semidirect
40. #2749C22semidirect
41. #2740C22semidirect
42. #2737C22semidirect
43. #2737C22semidirect
46. #2723C22semidirect
47. #2715C22semidirect
48. #2706C22semidirect
49. #2701C22semidirect
50. #2700C22semidirect
52. #2691C22semidirect
53. #2686C22semidirect
55. #2672C22semidirect
57. #2666C22semidirect
59. #2660C22semidirect
60. #2647C22semidirect
61. #2644C22semidirect
62. #2644C22semidirect
69. #2603C22semidirect
70. #2602C22semidirect
71. #2599C22semidirect
72. #2597C22semidirect
73. #2592C22semidirect
74. #2592C22semidirect
75. #2567C22semidirect
76. #2563C22semidirect
78. #2557C22semidirect
79. #2557C22semidirect
85. #2547C22semidirect
86. #2547C22semidirect
87. #2546C22semidirect
88. #2545C22semidirect
89. #2544C22semidirect
92. #2538C22semidirect
94. #2531C22semidirect
95. #2531C22semidirect
96. #2531C22semidirect
97. #2526C22semidirect
98. #2526C22semidirect
99. #2513C22semidirect
100. #2513C22semidirect
101. #2512C22semidirect
102. #2512C22semidirect
104. #2491C22semidirect
105. #2490C22semidirect
108. #2461C22semidirect
109. #2459C22semidirect
110. #2454C22semidirect
111. #2452C22semidirect
112. #2448C22semidirect
113. #2447C22semidirect
114. #2447C22semidirect
115. #2445C22semidirect
116. #2444C22semidirect
117. #2444C22semidirect
122. #2425C22semidirect
123. #2425C22semidirect
124. #2422C22semidirect
125. #2420C22semidirect
130. #2402C22semidirect
131. #2399C22semidirect
135. #2369C22semidirect
136. #2367C22semidirect
139. #2366C22semidirect
140. #2365C22semidirect
141. #2357C22semidirect
142. #2356C22semidirect
143. #2356C22semidirect
144. #2356C22semidirect
147. #2351C22semidirect
148. #2349C22semidirect
149. #2349C22semidirect
153. #2343C22semidirect
157. #2330C22semidirect
161. #2327C22semidirect
162. #2326C22semidirect
164. #2320C22semidirect
165. #2319C22semidirect
166. #2319C22semidirect
170. C4×C4⋊Q8C22semidirect
171. C4×#125C22semidirect
172. C4×#121C22semidirect
173. C4×#121C22semidirect
174. #2295C22semidirect
179. #2283C22semidirect
180. C42×D4C22semidirect
182. C2×#376C22semidirect

Maximal subgroups

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

subgroupindex
#514282
#508782
#506602
#454282
#454212
#452992
#450972
#450702
#449612
#390462
#390422
#389872
#389852
#372922
#364692
#364632
#352852
#352722
#352712
#352002
#346252
#343942
#343642
#341232