Finite Group Databasebeta

← #8471056

Subgroups — #8471056

Order 512.

6911 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#59420C211yesmaximal, characteristic, complemented
2#59412C212yesmaximal, complemented
3#57213C214yesmaximal, complemented
4#53425C218yesmaximal, complemented
5#52969C214yesmaximal, complemented
6#47831C214yesmaximal, complemented
7#45604C214yesmaximal, complemented
8#44936C214yesmaximal, complemented
9#42483C214yesmaximal, complemented
10#42422C214yesmaximal, complemented
11#39745C212yesmaximal, complemented
12#39361C212yesmaximal, complemented
13#39336C214yesmaximal, complemented
14#37674C214yesmaximal, complemented
15#37626C211yesmaximal, characteristic, complemented
16#37332C214yesmaximal, complemented
17#36592C211yesmaximal, characteristic, complemented
18D4×#127C212yesmaximal, complemented
19#35197C212yesmaximal, complemented
20#34918C212yesmaximal, complemented
21C2×#559C2211yescharacteristic, complemented
22C2×#550C2212yescomplemented
23C2×#550C2214yescomplemented
24C2×#550C2212yescomplemented
25C2×#546C2214yescomplemented
26C2×D42C2211yescharacteristic
27C2×D42C2212yescomplemented
28C2×D42C2214yescomplemented
29C2×D42C2214yescomplemented
30C2×#535C2214yescomplemented
31C2×#534C2214yescomplemented
32C22×#127C2214yes—
33#2867C2212yescomplemented
34#2867C2211yescharacteristic, complemented
35#2856C2214yescomplemented
36#2854C2214yescomplemented
37#2850C2214yescomplemented
38#2828C2218yescomplemented
39#2828C2214yescomplemented
40#2815C2214yescomplemented
41#2815C2218yescomplemented
42#2812C2218yescomplemented
43#2797C2218yescomplemented
44#2752C2214yescomplemented
45#2703C2218yescomplemented
46#2703C2218yescomplemented
47#2699C2218yescomplemented
48#2697C2214yescomplemented
49#2688C2218yescomplemented
50#2688C2218yescomplemented
51#2688C2218yescomplemented
52#2678C2218yescomplemented
53#2673C2218yescomplemented
54#2673C2218yescomplemented
55#2673C2218yescomplemented
56#2673C2218yescomplemented
57#2673C2218yescomplemented
58#2673C2218yescomplemented
59#2671C2218yescomplemented
60#2669C2218yescomplemented
61#2669C2218yescomplemented
62#2669C2218yescomplemented
63#2669C2218yescomplemented
64#2669C2218yescomplemented
65#2669C2218yescomplemented
66#2668C2214yescomplemented
67#2668C2218yescomplemented
68#2668C2218yescomplemented
69#2657C2214yescomplemented
70#2648C2218yescomplemented
71#2635C2214yescomplemented
72#2624C2214yescomplemented
73#2619C2214yescomplemented
74#2619C2214yescomplemented
75#2617C2218yescomplemented
76#2615C2214yescomplemented
77#2613C2218yescomplemented
78#2597C2214yescomplemented
79#2595C2214yescomplemented
80#2592C2212yescomplemented
81#2580C2212yescomplemented
82#2571C2211yescharacteristic, complemented
83#2570C2212yescomplemented
84#2548C2212yescomplemented
85#2544C2212yes—
86#2544C2214yescomplemented
87#2541C2212yes—
88#2541C2214yescomplemented
89#2541C2212yescomplemented
90#2541C2214yescomplemented
91#2541C2214yescomplemented
92#2541C2214yescomplemented
93#2541C2214yescomplemented
94#2541C2212yescomplemented
95#2541C2214yescomplemented
96#2541C2214yescomplemented
97#2538C2212yescomplemented
98#2537C2211yescharacteristic, complemented
99#2535C2214yescomplemented
100#2534C2214yescomplemented
101#2516C2214yescomplemented
102#2513C2214yescomplemented
103#2513C2212yescomplemented
104#2511C2212yescomplemented
105#2458C2214yescomplemented
106#2457C2218yescomplemented
107#2447C2212yescomplemented
108#2445C2212yes—
109#2445C2214yescomplemented
110#2435C2214yescomplemented
111#2433C2214yes—
112#2433C2214yes—
113#2433C2218yescomplemented
114#2433C2218yescomplemented
115#2433C2214yescomplemented
116#2433C2214yescomplemented
117#2433C2214yescomplemented
118#2433C2214yescomplemented
119#2431C2214yescomplemented
120#2431C2214yescomplemented
121#2431C2214yescomplemented
122#2428C2214yescomplemented
123#2428C2214yescomplemented
124#2428C2214yescomplemented
125#2428C2214yescomplemented
126#2428C2214yescomplemented
127#2428C2214yescomplemented
128#2427C2214yescomplemented
129#2427C2214yescomplemented
130#2424C2218yescomplemented
131#2422C2214yescomplemented
132#2420C2214yescomplemented
133#2420C2214yescomplemented
134#2420C2214yescomplemented
135#2410C2218yescomplemented
136#2410C2218yescomplemented
137#2410C2218yescomplemented
138#2408C2214yescomplemented
139#2407C2214yescomplemented
140#2404C2214yescomplemented
141#2404C2218yescomplemented
142#2403C2214yescomplemented
143#2403C2218yescomplemented
144#2398C2214yescomplemented
145#2395C2214yescomplemented
146#2377C2214yescomplemented
147D4×C22⋊C4C2214yescomplemented
148D4×C22⋊C4C2214yescomplemented
149#2328C2214yescomplemented
150#2328C2214yescomplemented
151#2319C2214yescomplemented
152C4×#127C2212yes—
153C4×#127C2212yescomplemented
154C4×#127C2211yescharacteristic, complemented
155C4×#124C2212yescomplemented
156C4×#124C2212yescomplemented
157C4×#123C2214yescomplemented
158#2295C2212yescomplemented
159#2293C2212yescomplemented
160#2290C2214yescomplemented
161C42×Q8C2211yescharacteristic, complemented
162C42×D4C2212yescomplemented
163C22×#41C2314yes—
164C22×#41C2314yes—
165C23×D4C2314yes—
166C23×D4C2314yes—
167C23×D4C2318yes—
168C23×D4C2314yes—
169C23×D4C2318yes—
170#559—44no—
171#550—48no—
172#550—416no—
173#550—48no—
174#546—416no—
175D42—44no—
176D42—416no—
177D42—48no—
178D42—416no—
179#535—416no—
180#534—416no—
181C2×#127—416no—
182C2×#127C2312yes—
183C2×#127C2311yescharacteristic
184C2×#127C2312yes—
185C2×#127C2314yes—
186C2×#127C2314yes—
187C2×#127C2314yes—
188C2×#127C2314yes—
189C2×#127C2312yes—
190C2×#127C2314yes—
191C2×#127C2314yes—
192C2×#127C2314yes—
193C2×#127C2314yes—
194C2×#127C2314yes—
195C2×#127C2314yes—
196C2×#127C2318yes—
197C2×#127C2318yes—
198C2×#127C2312yes—
199C2×#127C2314yes—
200C2×#124C2312yes—
201C2×#124C2312yes—
202C2×#124C2314yes—
203C2×#124C2314yes—
204C2×#123C2314yes—
205C2×#123C2318yes—
206C2×#123C2314yes—
207C2×#123C2318yes—
208C2×C22⋊Q8C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2318yes—
218C2×#121C2318yes—
219C2×#121C2314yes—
220C2×#121C2314yes—
221C2×#121C2314yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2318yes—
225C2×#121C2318yes—
226C2×#121C2318yes—
227C2×#121C2318yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C2×#121C2318yes—
231C2×#121C2318yes—
232C2×#120C2318yes—
233C2×#120C2318yes—
234C2×#120C2318yes—
235C2×#120C2318yes—
236C2×#120C2318yes—
237C2×#120C2318yes—
238C2×#120C2318yes—
239C2×#120C2318yes—
240C2×#120C2318yes—
241C2×#120C2318yes—
242C2×#120C2314yes—
243C2×#120C2318yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×#117C2314yes—
261C22×C22⋊C4C2314yes—
262C22×C22⋊C4C2318yes—
263C22×C42C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#399C2314yes—
269#399C2314yes—
270#398C2314yes—
271#397C2318yes—
272#397C2318yes—
273#397C2318yes—
274#397C2314yes—
275#397C2314yes—
276#397C2314yes—
277#397C2314yes—
278#397C2314yes—
279#397C2318yes—
280#397C2318yes—
281#396C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2314yes—
287#394C2318yes—
288#394C2318yes—
289#394C2314yes—
290#394C2314yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2314yes—
299#394C2314yes—
300#394C2318yes—
301#393C2314yes—
302#393C2314yes—
303#392C2318yes—
304#392C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#392C2318yes—
313#392C2318yes—
314#392C2318yes—
315#392C2318yes—
316#392C2314yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#392C2318yes—
321#392C2318yes—
322#392C2318yes—
323#392C2314yes—
324#392C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#392C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2312yes—
334#390C2312yes—
335#390C2312yes—
336#390C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2318yes—
344#390C2314yes—
345#390C2314yes—
346#390C2312yes—
347#390C2314yes—
348#390C2314yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2318yes—
353#390C2312yes—
354#390C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#388C2314yes—
362#388C2314yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2318yes—
373#388C2314yes—
374#388C2314yes—
375#387C2314yes—
376#387C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2318yes—
391#386C2318yes—
392#386C2318yes—
393#386C2318yes—
394#386C2314yes—
395#386C2314yes—
396#386C2318yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2314yes—
402#386C2318yes—
403#385C2314yes—
404#385C2314yes—
405#385C2318yes—
406#385C2314yes—
407#384C2312yes—
408#384C2311yescharacteristic
409#382C2312yes—
410#382C2312yes—
411#382C2314yes—
412#381C2318yes—
413#381C2314yes—
414#381C2314yes—
415#381C2314yes—
416#380C2318yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#379C2318yes—
421#379C2318yes—
422#379C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440#376C2314yes—
441C43C2312yes—
442C43C2311yescharacteristic
443C25C2414yes—
444C25C2418yes—
445C2×#41—48no—
446C2×#41—48no—
447C2×#41—48no—
448C2×#41—416no—
449C2×#41—48no—
450C22×Q8C2411yescharacteristic
451C22×Q8C2412yes—
452C22×D4—216no—
453C22×D4—216no—
454C22×D4—48no—
455C22×D4—416no—
456C22×D4—48no—
457C22×D4—416no—
458C22×D4—48no—
459C22×D4—48no—
460C22×D4—48no—
461C22×D4—48no—
462C22×D4—48no—
463C22×D4—416no—
464C22×D4—416no—
465C22×D4—416no—
466C22×D4—88no—
467C22×D4C2414yes—
468C22×D4C2414yes—
469C22×D4C2412yes—
470C22×D4C2414yes—
471C22×D4C2414yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C22×D4C2414yes—
475C22×D4C2412yes—
476C22×D4C2418yes—
477C22×D4C2418yes—
478C22×D4C2418yes—
479C22×D4C2418yes—
480C22×D4C2414yes—
481C22×D4C2418yes—
482C22×D4C2418yes—
483C22×D4C2418yes—
484C22×D4C2414yes—
485C22×D4C2418yes—
486C22×D4C2418yes—
487C22×D4C2414yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2418yes—
491C22×D4C2418yes—
492C22×D4C2418yes—
493C23×C4C2414yes—
494C23×C4C2414yes—
495C23×C4C2414yes—
496C23×C4C2418yes—
497C23×C4C2414yes—
498C23×C4C2414yes—
499C23×C4C2414yes—
500C23×C4C2418yes—
501#127—28no—
502#127—216no—
503#127—216no—
504#127—28no—
505#127—24no—
506#127—48no—
507#127—48no—
508#127—48no—
509#127—48no—
510#127—48no—
511#127—48no—
512#127—48no—
513#127—44no—
514#127—48no—
515#127—416no—
516#127—416no—
517#127—84no—
518#127—82no—
519#124—28no—
520#124—28no—
521#124—48no—
522#124—48no—
523#123—216no—
524#123—416no—
525#123—416no—
526#123—48no—
527C22⋊Q8—48no—
528#121—216no—
529#121—48no—
530#121—416no—
531#121—416no—
532#121—416no—
533#121—416no—
534#121—416no—
535#121—416no—
536#121—416no—
537#121—416no—
538#121—48no—
539#121—48no—
540#121—48no—
541#121—48no—
542#121—48no—
543#121—48no—
544#121—48no—
545#121—416no—
546#121—48no—
547#121—48no—
548#121—416no—
549#121—416no—
550#121—88no—
551#120—416no—
552#120—416no—
553#120—416no—
554#120—48no—
555#120—416no—
556#120—416no—
557#120—416no—
558#120—416no—
559#120—416no—
560#120—416no—
561#120—416no—
562#120—88no—
563C4×Q8—24no—
564C4×Q8—28no—
565C4×Q8—28no—
566C4×D4—28no—
567C4×D4—28no—
568C4×D4—28no—
569C4×D4—216no—
570C4×D4—28no—
571C4×D4—216no—
572C4×D4—48no—
573C4×D4—48no—
574C4×D4—48no—
575C4×D4—48no—
576C4×D4—48no—
577C4×D4—48no—
578C4×D4—44no—
579#117—48no—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2412yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C22⋊C4—48no—
602C2×C22⋊C4—416no—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C42—48no—
645C2×C42C2412yes—
646C2×C42C2414yes—
647C2×C42C2412yes—
648C2×C42C2414yes—
649C2×C42C2412yes—
650C2×C42C2412yes—
651C2×C42C2412yes—
652C2×C42C2411yescharacteristic
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2411yescharacteristic
656C2×C42C2414yes—
657C2×C42C2414yes—
658C2×C42C2412yes—
659C2×C42C2411yescharacteristic
660#95C2414yes—
661#95C2414yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2414yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2414yes—
676#95C2414yes—
677#95C2412yes—
678#95C2412yes—
679#95C2411yescharacteristic
680#95C2411yescharacteristic
681#95C2414yes—
682#95C2414yes—
683#95C2414yes—
684#95C2418yes—
685#95C2414yes—
686#95C2418yes—
687C24—216no—
688C24—216no—
689C24—44no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—44no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—44no—
698C24—48no—
699C24C2514yes—
700C24C2518yes—
701C24C2514yes—
702C24C2514yes—
703#41—832no—
704#41—832no—
705C2×Q8—22no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—24no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—216no—
715C2×D4—216no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—24no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—24no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—28no—
734C2×D4—216no—
735C2×D4—24no—
736C2×D4—216no—
737C2×D4—216no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—42no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
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—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—42no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—44no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—44no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—832no—
785C2×D4—832no—
786C2×D4—832no—
787C2×D4—864no—
788C2×D4—864no—
789C2×D4H(5,𝔽2)18yes—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—28no—
799C22×C4—216no—
800C22×C4—28no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4C2514yes—
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2511yescharacteristic
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C4⋊C4—24no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—28no—
841C4⋊C4—28no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C4⋊C4—42no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4H(5,𝔽2)14yes—
850C22⋊C4—28no—
851C22⋊C4—28no—
852C22⋊C4—28no—
853C22⋊C4—28no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—28no—
860C22⋊C4—216no—
861C22⋊C4—216no—
862C22⋊C4—28no—
863C22⋊C4—28no—
864C22⋊C4—28no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—48no—
873C22⋊C4—44no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—44no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—48no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C42—24no—
892C42—28no—
893C42—24no—
894C42—24no—
895C42—28no—
896C42—24no—
897C42—22no—
898C42—24no—
899C42—24no—
900C42—44no—
901C42—44no—
902C42—42no—
903C42—41no—
904C42H(5,𝔽2)18yes—
905C42H(5,𝔽2)14yes—
906C23—24no—
907C23—24no—
908C23—24no—
909C23—24no—
910C23—24no—
911C23—24no—
912C23—24no—
913C23—24no—
914C23—28no—
915C23—28no—
916C23—24no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—28no—
921C23—28no—
922C23—28no—
923C23—28no—
924C23—24no—
925C23—28no—
926C23—28no—
927C23—24no—
928C23—24no—
929C23—28no—
930C23—24no—
931C23—416no—
932C23—816no—
933C23—816no—
934C23—816no—
935C23—816no—
936C23—816no—
937C23—816no—
938C23—816no—
939C23—164no—
940C23—168no—
941C23—164no—
942C23—168no—
943C23C2×H(5,𝔽2)18yes—
944C23C2611yescharacteristic
945Q8—28no—
946Q8—48no—
947D4—216no—
948D4—416no—
949D4—416no—
950D4—416no—
951D4—416no—
952D4—48no—
953D4—416no—
954D4—84no—
955D4—88no—
956D4—816no—
957D4—816no—
958D4—88no—
959D4—816no—
960D4—816no—
961D4—816no—
962D4—816no—
963D4—816no—
964D4—816no—
965D4—816no—
966D4—816no—
967D4—816no—
968D4—164no—
969D4—164no—
970D4—168no—
971D4—168no—
972D4—168no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—416no—
1011C2×C4—416no—
1012C2×C4—416no—
1013C2×C4—416no—
1014C2×C4—816no—
1015C2×C4—88no—
1016C2×C4—816no—
1017C2×C4—164no—
1018C2×C4C2×H(5,𝔽2)12yes—
1019C2×C4C2×H(5,𝔽2)14yes—
1020C2×C4C2×H(5,𝔽2)12yes—
1021C2×C4C2×H(5,𝔽2)14yes—
1022C2×C4C2×H(5,𝔽2)14yes—
1023C2×C4C2×H(5,𝔽2)14yes—
1024C2×C4C2×H(5,𝔽2)14yes—
1025C2×C4C2×H(5,𝔽2)14yes—
1026C22—28no—
1027C22—28no—
1028C22—28no—
1029C22—44no—
1030C22—44no—
1031C22—44no—
1032C22—44no—
1033C22—44no—
1034C22—48no—
1035C22—44no—
1036C22—48no—
1037C22—48no—
1038C22—44no—
1039C22—44no—
1040C22—48no—
1041C22—48no—
1042C22—44no—
1043C22—44no—
1044C22—44no—
1045C22—48no—
1046C22—48no—
1047C22—48no—
1048C22—44no—
1049C22—44no—
1050C22—48no—
1051C22—44no—
1052C22—1616no—
1053C22—1632no—
1054C22C22×H(5,𝔽2)11yescharacteristic
1055C22C22×H(5,𝔽2)12yes—
1056C22C22×H(5,𝔽2)12yes—
1057C22C22×H(5,𝔽2)11yescharacteristic
1058C22H(7,𝔽2)11yescharacteristic
1059C4—24no—
1060C4—22no—
1061C4—24no—
1062C4—24no—
1063C4—22no—
1064C4—44no—
1065C4—44no—
1066C4—44no—
1067C4—44no—
1068C4—41no—
1069C4—44no—
1070C4—44no—
1071C4—42no—
1072C4—42no—
1073C4—44no—
1074C4#354318yes—
1075C2—48no—
1076C2—88no—
1077C2—84no—
1078C2—84no—
1079C2C2×#354312yes—
1080C2#6283211yescharacteristic
1081C2#6291212yes—
1082C2#6291611yescharacteristic
1083C2#6301111yescharacteristic
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. #59420C2semidirect
2. #59412C2semidirect
3. #57213C2semidirect
4. #53425C2semidirect
5. #52969C2semidirect
6. #47831C2semidirect
7. #45604C2semidirect
8. #44936C2semidirect
9. #42483C2semidirect
10. #42422C2semidirect
11. #39745C2semidirect
12. #39361C2semidirect
13. #39336C2semidirect
14. #37674C2semidirect
15. #37626C2semidirect
16. #37332C2semidirect
17. #36592C2semidirect
18. D4×#127C2semidirect
19. #35197C2semidirect
20. #34918C2semidirect
21. C2×#559C22semidirect
22. C2×#550C22semidirect
23. C2×#550C22semidirect
24. C2×#550C22semidirect
25. C2×#546C22semidirect
27. C2×D42C22semidirect
28. C2×D42C22semidirect
29. C2×D42C22semidirect
30. C2×#535C22semidirect
31. C2×#534C22semidirect
33. #2867C22semidirect
34. #2867C22semidirect
35. #2856C22semidirect
36. #2854C22semidirect
37. #2850C22semidirect
38. #2828C22semidirect
39. #2828C22semidirect
40. #2815C22semidirect
41. #2815C22semidirect
42. #2812C22semidirect
43. #2797C22semidirect
44. #2752C22semidirect
45. #2703C22semidirect
46. #2703C22semidirect
47. #2699C22semidirect
48. #2697C22semidirect
49. #2688C22semidirect
50. #2688C22semidirect
51. #2688C22semidirect
52. #2678C22semidirect
53. #2673C22semidirect
54. #2673C22semidirect
55. #2673C22semidirect
56. #2673C22semidirect
57. #2673C22semidirect
58. #2673C22semidirect
59. #2671C22semidirect
60. #2669C22semidirect
61. #2669C22semidirect
62. #2669C22semidirect
63. #2669C22semidirect
64. #2669C22semidirect
65. #2669C22semidirect
66. #2668C22semidirect
67. #2668C22semidirect
68. #2668C22semidirect
69. #2657C22semidirect
70. #2648C22semidirect
71. #2635C22semidirect
72. #2624C22semidirect
73. #2619C22semidirect
74. #2619C22semidirect
75. #2617C22semidirect
76. #2615C22semidirect
77. #2613C22semidirect
78. #2597C22semidirect
79. #2595C22semidirect
80. #2592C22semidirect
81. #2580C22semidirect
82. #2571C22semidirect
83. #2570C22semidirect
84. #2548C22semidirect
86. #2544C22semidirect
88. #2541C22semidirect
89. #2541C22semidirect
90. #2541C22semidirect
91. #2541C22semidirect
92. #2541C22semidirect
93. #2541C22semidirect
94. #2541C22semidirect
95. #2541C22semidirect
96. #2541C22semidirect
97. #2538C22semidirect
98. #2537C22semidirect
99. #2535C22semidirect
100. #2534C22semidirect
101. #2516C22semidirect
102. #2513C22semidirect
103. #2513C22semidirect
104. #2511C22semidirect
105. #2458C22semidirect
106. #2457C22semidirect
107. #2447C22semidirect
109. #2445C22semidirect
110. #2435C22semidirect
113. #2433C22semidirect
114. #2433C22semidirect
115. #2433C22semidirect
116. #2433C22semidirect
117. #2433C22semidirect
118. #2433C22semidirect
119. #2431C22semidirect
120. #2431C22semidirect
121. #2431C22semidirect
122. #2428C22semidirect
123. #2428C22semidirect
124. #2428C22semidirect
125. #2428C22semidirect
126. #2428C22semidirect
127. #2428C22semidirect
128. #2427C22semidirect
129. #2427C22semidirect
130. #2424C22semidirect
131. #2422C22semidirect
132. #2420C22semidirect
133. #2420C22semidirect
134. #2420C22semidirect
135. #2410C22semidirect
136. #2410C22semidirect
137. #2410C22semidirect
138. #2408C22semidirect
139. #2407C22semidirect
140. #2404C22semidirect
141. #2404C22semidirect
142. #2403C22semidirect
143. #2403C22semidirect
144. #2398C22semidirect
145. #2395C22semidirect
146. #2377C22semidirect
147. D4×C22⋊C4C22semidirect
148. D4×C22⋊C4C22semidirect
149. #2328C22semidirect
150. #2328C22semidirect
151. #2319C22semidirect
153. C4×#127C22semidirect
154. C4×#127C22semidirect
155. C4×#124C22semidirect
156. C4×#124C22semidirect
157. C4×#123C22semidirect
158. #2295C22semidirect
159. #2293C22semidirect
160. #2290C22semidirect
161. C42×Q8C22semidirect
162. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#594202
#594122
#572132
#534252
#529692
#478312
#456042
#449362
#424832
#424222
#397452
#393612
#393362
#376742
#376262
#373322
#365922
D4×#1272
#351972
#349182