Finite Group Databasebeta

← #7646188

Subgroups — #7646188

Order 512.

5432 conjugacy classes of subgroups.

The subgroup lattice has 1109 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42759C214yesmaximal, complemented
2#42719C214yesmaximal, complemented
3#42617C214yesmaximal, complemented
4#42533C214yesmaximal, complemented
5#40217C214yesmaximal, complemented
6#40126C214yesmaximal, complemented
7#39785C214yesmaximal, complemented
8#39212C214yesmaximal, complemented
9#37459C214yesmaximal, complemented
10#36759C214yesmaximal, complemented
11#36731C214yesmaximal, complemented
12#35618C212yesmaximal, complemented
13#35533C212yesmaximal, complemented
14#35256C212yesmaximal, complemented
15#35168C211yesmaximal, characteristic, complemented
16#35168C211yesmaximal, characteristic, complemented
17#35166C211yesmaximal, characteristic, complemented
18#35159C211yesmaximal, characteristic, complemented
19#35081C214yesmaximal, complemented
20#34744C212yesmaximal, complemented
21#34274C211yesmaximal, characteristic, complemented
22C2×#2357C211yesmaximal, characteristic, complemented
23C4×#537C211yesmaximal, characteristic, complemented
24C2×#537C2211yescharacteristic
25C2×#537C2211yescharacteristic
26C2×#537C2212yes—
27C2×#535C2212yes—
28C2×#535C2212yes—
29C2×#532C2212yes—
30C2×#520C2212yes—
31C2×C4×#41C2212yes—
32C22×C4×D4C2211yescharacteristic
33#2856C2214yes—
34#2856C2214yes—
35#2851C2214yes—
36#2850C2214yes—
37#2847C2214yes—
38#2847C2214yes—
39#2837C2218yescomplemented
40#2828C2218yescomplemented
41#2803C2218yescomplemented
42#2797C2218yescomplemented
43#2793C2218yescomplemented
44#2753C2218yescomplemented
45#2752C2218yescomplemented
46#2743C2218yescomplemented
47#2743C2218yescomplemented
48#2740C2218yescomplemented
49#2740C2218yescomplemented
50#2711C2218yescomplemented
51#2701C2218yescomplemented
52#2699C2218yescomplemented
53#2699C2218yescomplemented
54#2688C2218yescomplemented
55#2688C2218yescomplemented
56#2673C2218yescomplemented
57#2661C2218yescomplemented
58#2656C2214yes—
59#2651C2218yescomplemented
60#2649C2218yescomplemented
61#2648C2218yescomplemented
62#2648C2218yescomplemented
63#2646C2214yes—
64#2635C2218yescomplemented
65#2620C2214yes—
66#2619C2214yes—
67#2617C2214yes—
68#2617C2214yes—
69#2548C2214yes—
70#2545C2214yes—
71#2544C2214yes—
72#2542C2214yescomplemented
73#2541C2214yes—
74#2541C2214yescomplemented
75#2540C2214yescomplemented
76#2540C2214yescomplemented
77#2516C2218yescomplemented
78#2509C2214yescomplemented
79#2508C2214yescomplemented
80#2507C2214yescomplemented
81#2506C2214yescomplemented
82#2504C2214yescomplemented
83#2503C2214yescomplemented
84#2500C2214yescomplemented
85#2499C2214yescomplemented
86#2497C2214yescomplemented
87#2497C2214yescomplemented
88#2490C2214yescomplemented
89#2490C2214yescomplemented
90#2464C2218yescomplemented
91#2448C2212yescomplemented
92#2448C2212yescomplemented
93#2447C2212yescomplemented
94#2447C2212yescomplemented
95#2446C2212yescomplemented
96#2446C2212yescomplemented
97#2445C2212yescomplemented
98#2445C2212yescomplemented
99#2444C2214yes—
100#2444C2218yes—
101#2444C2218yes—
102#2444C2214yes—
103#2443C2214yes—
104#2443C2214yes—
105#2428C2214yes—
106#2428C2214yes—
107#2428C2214yes—
108#2428C2214yes—
109#2428C2214yes—
110#2428C2214yes—
111#2428C2214yescomplemented
112#2428C2214yescomplemented
113#2427C2214yes—
114#2427C2214yes—
115#2427C2214yes—
116#2427C2214yes—
117#2426C2214yes—
118#2426C2214yes—
119#2424C2218yes—
120#2424C2218yes—
121#2424C2218yes—
122#2424C2218yes—
123#2421C2214yescomplemented
124#2421C2214yescomplemented
125#2420C2214yescomplemented
126#2420C2214yescomplemented
127#2420C2214yescomplemented
128#2420C2214yescomplemented
129#2416C2214yes—
130#2416C2214yes—
131#2414C2214yes—
132#2414C2214yes—
133#2395C2214yescomplemented
134#2395C2214yescomplemented
135#2363C2214yescomplemented
136#2362C2214yescomplemented
137#2361C2214yescomplemented
138#2360C2214yescomplemented
139#2357C2214yes—
140#2357C2214yes—
141#2357C2214yes—
142#2357C2214yes—
143#2333C2218yescomplemented
144#2333C2218yescomplemented
145#2325C2214yes—
146#2325C2214yes—
147#2324C2214yescomplemented
148#2323C2214yescomplemented
149#2317C2212yes—
150#2316C2211yescharacteristic
151#2316C2211yescharacteristic
152#2311C2212yes—
153C4×C22⋊Q8C2214yescomplemented
154C4×#123C2214yescomplemented
155C4×#123C2214yescomplemented
156C4×#121C2214yes—
157C4×#121C2214yes—
158C4×#121C2214yescomplemented
159#2297C2212yes—
160#2297C2212yes—
161#2297C2212yes—
162#2296C2212yes—
163C2×#390C2211yescharacteristic
164C2×#390C2211yescharacteristic
165C2×#388C2212yes—
166C2×#388C2212yes—
167C2×#382C2211yescharacteristic
168C2×#381C2212yes—
169C2×C4×C4⋊C4C2211yescharacteristic
170C2×C4×C4⋊C4C2211yescharacteristic
171C2×C4×C4⋊C4C2211yescharacteristic
172C2×C4×C22⋊C4C2212yes—
173C22×#41C2312yes—
174C22×#41C2312yes—
175C23×D4C2311yescharacteristic
176C24×C4C2312yes—
177#537—28no—
178#537—28no—
179#537—48no—
180#535—48no—
181#535—48no—
182#532—48no—
183C2×C4⋊Q8C2312yes—
184C2×#127C2314yes—
185C2×#127C2312yes—
186C2×#127C2314yes—
187C2×#127C2314yes—
188C2×#125C2314yes—
189C2×#124C2314yes—
190C2×#124C2312yes—
191C2×#124C2312yes—
192C2×#124C2314yes—
193C2×#123C2314yes—
194C2×#123C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2318yes—
204C2×#121C2318yes—
205C2×#121C2314yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2318yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218C2×#121C2318yes—
219C2×#121C2318yes—
220C2×#120C2318yes—
221C2×#120C2318yes—
222#520—48no—
223C4×#41—48no—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×D4—28no—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2314yes—
232C2×C4×D4C2318yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×#117C2312yes—
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2314yes—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2314yes—
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2312yes—
255C22×C42C2311yescharacteristic
256C22×C42C2311yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2314yes—
259C22×C42C2312yes—
260C22×C42C2312yes—
261#400C2318yes—
262#400C2318yes—
263#400C2318yes—
264#400C2314yes—
265#400C2318yes—
266#400C2314yes—
267#399C2314yes—
268#399C2318yes—
269#399C2318yes—
270#399C2314yes—
271#398C2314yes—
272#398C2318yes—
273#398C2318yes—
274#398C2314yes—
275#397C2314yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#397C2318yes—
283#397C2318yes—
284#397C2314yes—
285#397C2314yes—
286#397C2314yes—
287#396C2318yes—
288#396C2318yes—
289#396C2318yes—
290#396C2318yes—
291#394C2314yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2314yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2314yes—
308#394C2314yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#392C2318yes—
313#392C2318yes—
314#392C2318yes—
315#392C2318yes—
316#392C2318yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2312yes—
324#390C2314yes—
325#390C2314yes—
326#390C2318yes—
327#390C2318yes—
328#390C2318yes—
329#390C2318yes—
330#390C2314yes—
331#390C2312yes—
332#390C2314yes—
333#390C2314yes—
334#390C2318yes—
335#390C2314yes—
336#390C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2318yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2314yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2314yes—
375#388C2314yes—
376#388C2314yes—
377#387C2318yes—
378#387C2318yes—
379#387C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2314yes—
384#387C2318yes—
385#387C2314yes—
386#387C2314yes—
387#386C2318yes—
388#386C2318yes—
389#386C2314yes—
390#386C2318yes—
391#386C2314yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2314yes—
400#386C2314yes—
401#386C2318yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#384C2314yes—
416#384C2314yes—
417#382C2314yes—
418#382C2314yes—
419#382C2314yes—
420#382C2314yes—
421#381C2314yes—
422#381C2318yes—
423#381C2318yes—
424#381C2318yes—
425#381C2318yes—
426#381C2314yes—
427#380C2314yes—
428#380C2314yes—
429#380C2314yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2314yes—
434#380C2314yes—
435C4×C4⋊C4C2314yes—
436C4×C4⋊C4C2314yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2312yes—
439C4×C4⋊C4C2312yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2314yes—
442C4×C4⋊C4C2314yes—
443C4×C4⋊C4C2314yes—
444C4×C4⋊C4C2314yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2314yes—
447C4×C22⋊C4C2314yes—
448C4×C22⋊C4C2314yes—
449C4×C22⋊C4C2318yes—
450C4×C22⋊C4C2318yes—
451C4×C22⋊C4C2314yes—
452C4×C22⋊C4C2314yes—
453C4×C22⋊C4C2314yes—
454C4×C22⋊C4C2314yes—
455C4×C22⋊C4C2314yes—
456C4×C22⋊C4C2314yes—
457C4×C22⋊C4C2314yes—
458C4×C22⋊C4C2314yes—
459C2×#95C2312yes—
460C2×#95C2312yes—
461C2×#95C2311yescharacteristic
462C2×#95C2312yes—
463C2×#95C2311yescharacteristic
464C2×#95C2312yes—
465C25C2412yes—
466C2×#41—28no—
467C2×#41—28no—
468C2×#41—28no—
469C2×#41—28no—
470C2×#41—28no—
471C2×#41—28no—
472C22×Q8C2412yes—
473C22×Q8C2412yes—
474C22×D4—24no—
475C22×D4—24no—
476C22×D4—24no—
477C22×D4C2414yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2412yes—
481C22×D4C2412yes—
482C22×D4C2414yes—
483C22×D4C2414yes—
484C22×D4C2414yes—
485C22×D4C2414yes—
486C22×D4C2418yes—
487C22×D4C2418yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2418yes—
491C23×C4—28no—
492C23×C4—82no—
493C23×C4—82no—
494C23×C4C2414yes—
495C23×C4C2414yes—
496C23×C4C2411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2412yes—
501C23×C4C2411yescharacteristic
502C23×C4C2412yes—
503C23×C4C2414yes—
504C23×C4C2414yes—
505C23×C4C2414yes—
506C23×C4C2411yescharacteristic
507C23×C4C2418yes—
508C23×C4C2414yes—
509C23×C4C2412yes—
510C23×C4C2411yescharacteristic
511C4⋊Q8—44no—
512#127—44no—
513#127—48no—
514#127—48no—
515#127—84no—
516#125—84no—
517#124—44no—
518#124—44no—
519#124—48no—
520#124—48no—
521#123—48no—
522#123—48no—
523C22⋊Q8—216no—
524C22⋊Q8—216no—
525C22⋊Q8—48no—
526C22⋊Q8—48no—
527#121—216no—
528#121—216no—
529#121—216no—
530#121—216no—
531#121—416no—
532#121—416no—
533#121—48no—
534#121—48no—
535#121—48no—
536#121—48no—
537#121—48no—
538#121—48no—
539#121—48no—
540#121—48no—
541#121—416no—
542#121—88no—
543#121—88no—
544#121—84no—
545#121—84no—
546#121—84no—
547#121—84no—
548#120—416no—
549#120—416no—
550C4×Q8—44no—
551C4×Q8—44no—
552C4×Q8—48no—
553C4×D4—216no—
554C4×D4—216no—
555C4×D4—44no—
556C4×D4—44no—
557C4×D4—48no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—48no—
561C4×D4—48no—
562C4×D4—416no—
563C4×D4—84no—
564C4×D4—84no—
565#117—28no—
566#117—28no—
567#117—48no—
568#117—48no—
569C2×C4⋊C4—24no—
570C2×C4⋊C4—24no—
571C2×C4⋊C4—42no—
572C2×C4⋊C4—42no—
573C2×C4⋊C4—48no—
574C2×C4⋊C4#4118yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2418yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2418yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2418yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C22⋊C4—28no—
605C2×C22⋊C4—44no—
606C2×C22⋊C4—44no—
607C2×C22⋊C4—82no—
608C2×C22⋊C4—82no—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2418yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2418yes—
632C2×C22⋊C4C2418yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C42—24no—
648C2×C42—24no—
649C2×C42—24no—
650C2×C42—48no—
651C2×C42—82no—
652C2×C42—82no—
653C2×C42C2412yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2418yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668#95C2411yescharacteristic
669#95C2411yescharacteristic
670#95C2411yescharacteristic
671#95C2411yescharacteristic
672#95C2414yes—
673#95C2414yes—
674#95C2412yes—
675#95C2412yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2414yes—
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2418yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2414yes—
690#95C2414yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2418yes—
695#95C2414yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2418yes—
700#95C2418yes—
701C24—24no—
702C24—24no—
703C24—24no—
704C24—42no—
705C24—42no—
706C24—42no—
707C24—42no—
708C24C2514yes—
709C24C2514yes—
710C24C2514yes—
711C24C2511yescharacteristic
712#41—432no—
713#41—432no—
714C2×Q8—24no—
715C2×Q8—24no—
716C2×Q8—24no—
717C2×Q8—24no—
718C2×Q8—24no—
719C2×Q8—24no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—24no—
728C2×D4—24no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—28no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—416no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—42no—
793C22×C4—42no—
794C22×C4—42no—
795C22×C4—42no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—816no—
811C22×C4C2×#4118yes—
812C22×C4C2×#4114yes—
813C22×C4H(5,𝔽2)14yes—
814C22×C4H(5,𝔽2)14yes—
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2514yes—
825C22×C4C2514yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—28no—
845C4⋊C4—42no—
846C4⋊C4—42no—
847C4⋊C4—48no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—48no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—44no—
861C4⋊C4—44no—
862C4⋊C4C2×#41116yes—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—216no—
866C22⋊C4—216no—
867C22⋊C4—216no—
868C22⋊C4—28no—
869C22⋊C4—28no—
870C22⋊C4—28no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—48no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—28no—
908C42—28no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—44no—
913C42—44no—
914C42—44no—
915C42—48no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—21no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—48no—
942C23—48no—
943C23—48no—
944C23—84no—
945C23—84no—
946C23—84no—
947C23—84no—
948C23C22×#4112yes—
949C23C2×H(5,𝔽2)12yes—
950C23C2×H(5,𝔽2)12yes—
951C23C2611yescharacteristic
952Q8—48no—
953Q8—48no—
954D4—416no—
955D4—416no—
956D4—416no—
957D4—48no—
958D4—48no—
959D4—88no—
960D4—88no—
961D4—88no—
962D4—88no—
963D4—168no—
964D4—168no—
965D4—168no—
966D4—168no—
967D4—168no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—24no—
985C2×C4—24no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—48no—
1020C2×C4—44no—
1021C2×C4—44no—
1022C2×C4—44no—
1023C2×C4—44no—
1024C2×C4—416no—
1025C2×C4—416no—
1026C2×C4—88no—
1027C2×C4—88no—
1028C2×C4—88no—
1029C2×C4—82no—
1030C2×C4—82no—
1031C2×C4—84no—
1032C2×C4—84no—
1033C2×C4—88no—
1034C2×C4—168no—
1035C2×C4#540116yes—
1036C2×C4C22×#4118yes—
1037C2×C4C22×#4114yes—
1038C2×C4C2×H(5,𝔽2)14yes—
1039C2×C4C2×H(5,𝔽2)14yes—
1040C2×C4#58512yes—
1041C2×C4#58512yes—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—44no—
1049C22—44no—
1050C22—44no—
1051C22—44no—
1052C22—44no—
1053C22—44no—
1054C22—44no—
1055C22—44no—
1056C22—44no—
1057C22—44no—
1058C22—44no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—816no—
1070C22C2×#54014yes—
1071C22C23×#4111yescharacteristic
1072C22C22×H(5,𝔽2)11yescharacteristic
1073C22C22×H(5,𝔽2)11yescharacteristic
1074C22C2×#58511yescharacteristic
1075C22C2×#58511yescharacteristic
1076C22H(7,𝔽2)11yescharacteristic
1077C22H(7,𝔽2)11yescharacteristic
1078C4—28no—
1079C4—22no—
1080C4—22no—
1081C4—42no—
1082C4—41no—
1083C4—41no—
1084C4—44no—
1085C4—44no—
1086C4—41no—
1087C4—41no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—44no—
1093C4—44no—
1094C4—44no—
1095C4—44no—
1096C4C2×#54018yes—
1097C2—24no—
1098C2—84no—
1099C2—84no—
1100C2—84no—
1101C2C22×#54011yescharacteristic
1102C2#6279311yescharacteristic
1103C2#6284611yescharacteristic
1104C2#6295711yescharacteristic
1105C2#6295711yescharacteristic
1106C2#6296111yescharacteristic
1107C2#6296111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42759C2semidirect
2. #42719C2semidirect
3. #42617C2semidirect
4. #42533C2semidirect
5. #40217C2semidirect
6. #40126C2semidirect
7. #39785C2semidirect
8. #39212C2semidirect
9. #37459C2semidirect
10. #36759C2semidirect
11. #36731C2semidirect
12. #35618C2semidirect
13. #35533C2semidirect
14. #35256C2semidirect
15. #35168C2semidirect
16. #35168C2semidirect
17. #35166C2semidirect
18. #35159C2semidirect
19. #35081C2semidirect
20. #34744C2semidirect
21. #34274C2semidirect
22. C2×#2357C2semidirect
23. C4×#537C2semidirect
39. #2837C22semidirect
40. #2828C22semidirect
41. #2803C22semidirect
42. #2797C22semidirect
43. #2793C22semidirect
44. #2753C22semidirect
45. #2752C22semidirect
46. #2743C22semidirect
47. #2743C22semidirect
48. #2740C22semidirect
49. #2740C22semidirect
50. #2711C22semidirect
51. #2701C22semidirect
52. #2699C22semidirect
53. #2699C22semidirect
54. #2688C22semidirect
55. #2688C22semidirect
56. #2673C22semidirect
57. #2661C22semidirect
59. #2651C22semidirect
60. #2649C22semidirect
61. #2648C22semidirect
62. #2648C22semidirect
64. #2635C22semidirect
72. #2542C22semidirect
74. #2541C22semidirect
75. #2540C22semidirect
76. #2540C22semidirect
77. #2516C22semidirect
78. #2509C22semidirect
79. #2508C22semidirect
80. #2507C22semidirect
81. #2506C22semidirect
82. #2504C22semidirect
83. #2503C22semidirect
84. #2500C22semidirect
85. #2499C22semidirect
86. #2497C22semidirect
87. #2497C22semidirect
88. #2490C22semidirect
89. #2490C22semidirect
90. #2464C22semidirect
91. #2448C22semidirect
92. #2448C22semidirect
93. #2447C22semidirect
94. #2447C22semidirect
95. #2446C22semidirect
96. #2446C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
111. #2428C22semidirect
112. #2428C22semidirect
123. #2421C22semidirect
124. #2421C22semidirect
125. #2420C22semidirect
126. #2420C22semidirect
127. #2420C22semidirect
128. #2420C22semidirect
133. #2395C22semidirect
134. #2395C22semidirect
135. #2363C22semidirect
136. #2362C22semidirect
137. #2361C22semidirect
138. #2360C22semidirect
143. #2333C22semidirect
144. #2333C22semidirect
147. #2324C22semidirect
148. #2323C22semidirect
153. C4×C22⋊Q8C22semidirect
154. C4×#123C22semidirect
155. C4×#123C22semidirect
158. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#427592
#427192
#426172
#425332
#402172
#401262
#397852
#392122
#374592
#367592
#367312
#356182
#355332
#352562
#351682
#351662
#351592
#350812
#347442
#342742
C2×#23572
C4×#5372