Finite Group Databasebeta

← #7657395

Subgroups — #7657395

Order 512.

6546 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42584C214yesmaximal, complemented
2#42578C214yesmaximal, complemented
3#40730C218yesmaximal, complemented
4#40690C218yesmaximal, complemented
5#39735C212yesmaximal, complemented
6#39507C211yesmaximal, characteristic, complemented
7#39386C211yesmaximal, characteristic, complemented
8#37893C212yesmaximal, complemented
9#37694C212yesmaximal, complemented
10#37662C214yesmaximal, complemented
11#37626C212yesmaximal, complemented
12#37493C214yesmaximal, complemented
13#36165C211yesmaximal, characteristic, complemented
14D4×#127C211yesmaximal, characteristic, complemented
15D4×#121C212yesmaximal, complemented
16#35713C214yesmaximal, complemented
17#35691C214yesmaximal, complemented
18#35278C211yesmaximal, characteristic, complemented
19#35261C212yesmaximal, complemented
20#34621C211yesmaximal, characteristic, complemented
21C2×#2619C212yesmaximal, complemented
22#34310C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic, complemented
24C2×D42C2212yes—
25C2×D42C2214yes—
26C2×D42C2214yes—
27C2×#540C2212yescomplemented
28C2×#540C2212yescomplemented
29C22×#127C2212yescomplemented
30C22×#121C2214yescomplemented
31C2×#518C2214yes—
32C22×C4×D4C2211yescharacteristic
33C22×#117C2212yescomplemented
34#2867C2211yescharacteristic, complemented
35#2859C2211yescharacteristic, complemented
36#2856C2212yescomplemented
37#2856C2212yescomplemented
38#2851C2212yescomplemented
39#2847C2214yescomplemented
40#2829C2218yescomplemented
41#2828C2218yescomplemented
42#2828C2218yescomplemented
43#2803C2218yescomplemented
44#2761C2218yescomplemented
45#2753C2218yescomplemented
46#2753C2218yescomplemented
47#2709C2218yescomplemented
48#2703C2218yescomplemented
49#2703C2218yescomplemented
50#2699C2218yescomplemented
51#2688C2218yescomplemented
52#2673C2218yescomplemented
53#2673C2218yescomplemented
54#2671C2218yescomplemented
55#2661C2218yescomplemented
56#2651C2214yescomplemented
57#2648C2214yescomplemented
58#2648C2218yescomplemented
59#2647C2211yescharacteristic, complemented
60#2644C2212yescomplemented
61#2641C2211yescharacteristic, complemented
62#2641C2212yescomplemented
63#2635C2218yescomplemented
64#2629C2211yescharacteristic, complemented
65#2624C2212yescomplemented
66#2624C2214yescomplemented
67#2624C2214yescomplemented
68#2622C2218yescomplemented
69#2619C2211yescharacteristic
70#2619C2212yescomplemented
71#2619C2218yescomplemented
72#2619C2214yescomplemented
73#2619C2212yescomplemented
74#2619C2218yescomplemented
75#2619C2214yescomplemented
76#2619C2212yescomplemented
77#2619C2214yescomplemented
78#2617C2218yescomplemented
79#2571C2212yescomplemented
80#2543C2218yescomplemented
81#2541C2212yescomplemented
82#2541C2214yescomplemented
83#2541C2214yescomplemented
84#2541C2212yescomplemented
85#2537C2212yescomplemented
86#2535C2214yescomplemented
87#2513C2214yescomplemented
88#2508C2214yescomplemented
89#2505C2218yescomplemented
90#2500C2214yescomplemented
91#2490C2214yescomplemented
92#2485C2214yescomplemented
93#2476C2218yescomplemented
94#2471C2218yescomplemented
95#2445C2214yescomplemented
96#2445C2214yescomplemented
97#2445C2214yescomplemented
98#2445C2214yescomplemented
99#2444C2218yescomplemented
100#2443C2218yescomplemented
101#2442C2214yescomplemented
102#2433C2218yescomplemented
103#2433C2214yescomplemented
104#2428C2214yescomplemented
105#2428C2214yescomplemented
106#2428C2214yescomplemented
107#2428C2214yescomplemented
108#2428C2214yescomplemented
109#2428C2214yescomplemented
110#2424C2218yescomplemented
111#2424C2218yescomplemented
112#2424C2218yescomplemented
113#2422C2214yescomplemented
114#2420C2214yescomplemented
115#2420C2214yescomplemented
116#2418C2218yescomplemented
117#2418C2218yescomplemented
118#2416C2214yescomplemented
119#2416C2214yescomplemented
120#2414C2214yescomplemented
121#2414C2214yescomplemented
122#2412C2218yescomplemented
123#2410C2218yescomplemented
124#2410C2218yescomplemented
125#2410C2218yescomplemented
126#2408C2218yescomplemented
127#2408C2214yescomplemented
128#2405C2218yescomplemented
129#2395C2214yescomplemented
130#2392C2214yescomplemented
131C2×#394C2218yescomplemented
132C2×#392C2218yescomplemented
133#2366C2212yescomplemented
134#2363C2214yescomplemented
135#2361C2214yescomplemented
136#2358C2218yescomplemented
137#2354C2212yescomplemented
138#2354C2212yescomplemented
139#2352C2214yescomplemented
140#2349C2214yes—
141D4×C4⋊C4C2212yes—
142D4×C4⋊C4C2212yes—
143#2344C2212yescomplemented
144#2342C2214yescomplemented
145D4×C22⋊C4C2214yes—
146D4×C22⋊C4C2212yes—
147D4×C22⋊C4C2214yes—
148D4×C22⋊C4C2214yescomplemented
149#2328C2212yescomplemented
150#2324C2214yescomplemented
151#2324C2214yescomplemented
152#2321C2218yescomplemented
153#2314C2212yescomplemented
154C4×#127C2212yescomplemented
155C4×#127C2211yescharacteristic, complemented
156C4×#125C2211yescharacteristic, complemented
157C4×#121C2214yescomplemented
158C4×#121C2212yescomplemented
159#2293C2212yescomplemented
160#2293C2211yescharacteristic, complemented
161#2293C2211yescharacteristic, complemented
162C2×#390C2214yescomplemented
163#2290C2212yescomplemented
164#2290C2212yescomplemented
165#2285C2211yescharacteristic, complemented
166C2×#382C2212yescomplemented
167#2280C2212yescomplemented
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic, complemented
171C23×D4C2311yescharacteristic
172C23×D4C2314yes—
173C23×D4C2314yes—
174C23×D4C2318yes—
175C23×D4C2318yes—
176C24×C4C2312yes—
177D42—216no—
178D42—416no—
179D42—416no—
180#540—48no—
181#540—48no—
182C2×#127—48no—
183C2×#127C2312yes—
184C2×#127C2311yescharacteristic
185C2×#127C2312yes—
186C2×#127C2312yes—
187C2×#127C2314yes—
188C2×#127C2318yes—
189C2×#127C2314yes—
190C2×#127C2314yes—
191C2×#127C2314yes—
192C2×#125C2311yescharacteristic
193C2×#125C2312yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×#121—416no—
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2312yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#121C2318yes—
206C2×#121C2314yes—
207C2×#121C2318yes—
208C2×#121C2318yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2314yes—
212C2×#121C2314yes—
213C2×#121C2318yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2318yes—
217C2×#121C2318yes—
218C2×#120C2318yes—
219C2×#120C2318yes—
220C2×#120C2318yes—
221C2×#120C2318yes—
222C2×#120C2318yes—
223#518—416no—
224C2×C4×D4—28no—
225C2×C4×D4C2312yes—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2312yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2312yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2314yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2318yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2311yescharacteristic
244C2×#117—48no—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2312yes—
249C2×#117C2314yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2312yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2314yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2318yes—
259C22×C22⋊C4C2314yes—
260C22×C22⋊C4C2318yes—
261C22×C22⋊C4C2318yes—
262C22×C22⋊C4C2318yes—
263C22×C42C2312yes—
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266#400C2318yes—
267#400C2318yes—
268#400C2314yes—
269#399C2318yes—
270#399C2314yes—
271#398C2318yes—
272#398C2314yes—
273#398C2314yes—
274#397C2314yes—
275#397C2318yes—
276#397C2318yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#397C2314yes—
283#396C2314yes—
284#396C2318yes—
285#396C2314yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#394C2318yes—
307#394C2314yes—
308#394C2314yes—
309#394C2314yes—
310#394C2314yes—
311#392C2318yes—
312#392C2318yes—
313#392C2318yes—
314#392C2318yes—
315#392C2318yes—
316#392C2318yes—
317#392C2318yes—
318#392C2318yes—
319#392C2318yes—
320#392C2314yes—
321#392C2318yes—
322#392C2318yes—
323#392C2318yes—
324#392C2318yes—
325#392C2318yes—
326#390C2314yes—
327#390C2314yes—
328#390C2314yes—
329#390C2312yes—
330#390C2314yes—
331#390C2318yes—
332#390C2318yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2314yes—
337#390C2314yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2318yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2318yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2318yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2318yes—
375#387C2314yes—
376#387C2318yes—
377#387C2314yes—
378#387C2318yes—
379#387C2314yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#386C2318yes—
390#386C2314yes—
391#386C2314yes—
392#386C2318yes—
393#386C2318yes—
394#386C2318yes—
395#386C2318yes—
396#386C2314yes—
397#386C2318yes—
398#386C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2314yes—
404#385C2314yes—
405#385C2318yes—
406#384C2311yescharacteristic
407#384C2312yes—
408#384C2312yes—
409#382C2311yescharacteristic
410#382C2312yes—
411#382C2314yes—
412#382C2314yes—
413#382C2312yes—
414#382C2318yes—
415#381C2314yes—
416#381C2318yes—
417#380C2314yes—
418#380C2312yes—
419#380C2314yes—
420#380C2314yes—
421#380C2312yes—
422#380C2314yes—
423#380C2312yes—
424#380C2314yes—
425#380C2318yes—
426#380C2314yes—
427#379C2318yes—
428#379C2314yes—
429#379C2318yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2312yes—
437C4×C4⋊C4C2312yes—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2312yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2314yes—
444C4×C22⋊C4C2312yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2314yes—
447C4×C22⋊C4C2318yes—
448C4×C22⋊C4C2312yes—
449C4×C22⋊C4C2312yes—
450C4×C22⋊C4C2312yes—
451#376C2311yescharacteristic
452#376C2311yescharacteristic
453C2×#95C2318yes—
454C43C2311yescharacteristic
455C43C2311yescharacteristic
456C25C2412yes—
457C25C2418yes—
458C22×D4—24no—
459C22×D4—216no—
460C22×D4—216no—
461C22×D4—28no—
462C22×D4—216no—
463C22×D4—216no—
464C22×D4—48no—
465C22×D4—48no—
466C22×D4—416no—
467C22×D4—416no—
468C22×D4—416no—
469C22×D4—416no—
470C22×D4—88no—
471C22×D4—88no—
472C22×D4C2412yes—
473C22×D4C2418yes—
474C22×D4C2411yescharacteristic
475C22×D4C2414yes—
476C22×D4C2414yes—
477C22×D4C2412yes—
478C22×D4C2414yes—
479C22×D4C2414yes—
480C22×D4C2414yes—
481C22×D4C2418yes—
482C22×D4C2418yes—
483C22×D4C2418yes—
484C22×D4C2418yes—
485C22×D4C2418yes—
486C22×D4C2418yes—
487C22×D4C2418yes—
488C22×D4C2418yes—
489C22×D4C2418yes—
490C22×D4C2411yescharacteristic
491C23×C4—28no—
492C23×C4—28no—
493C23×C4—44no—
494C23×C4C2411yescharacteristic
495C23×C4C2414yes—
496C23×C4C2412yes—
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2414yes—
500C23×C4C2412yes—
501C23×C4C2412yes—
502C23×C4C2411yescharacteristic
503C23×C4C2414yes—
504C23×C4C2418yes—
505C23×C4C2411yescharacteristic
506C23×C4C2418yes—
507C23×C4C2418yes—
508#127—28no—
509#127—24no—
510#127—28no—
511#127—48no—
512#127—416no—
513#127—44no—
514#127—48no—
515#127—48no—
516#127—84no—
517#125—24no—
518#125—44no—
519#123—416no—
520#123—416no—
521#123—88no—
522#121—216no—
523#121—28no—
524#121—216no—
525#121—216no—
526#121—416no—
527#121—416no—
528#121—416no—
529#121—48no—
530#121—48no—
531#121—48no—
532#121—48no—
533#121—48no—
534#121—48no—
535#121—48no—
536#121—416no—
537#121—416no—
538#121—416no—
539#121—88no—
540#121—88no—
541#121—84no—
542#120—232no—
543#120—416no—
544#120—416no—
545#120—416no—
546#120—416no—
547C4×D4—24no—
548C4×D4—28no—
549C4×D4—216no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—24no—
553C4×D4—28no—
554C4×D4—24no—
555C4×D4—28no—
556C4×D4—48no—
557C4×D4—48no—
558C4×D4—48no—
559C4×D4—48no—
560C4×D4—48no—
561C4×D4—48no—
562C4×D4—416no—
563C4×D4—416no—
564C4×D4—84no—
565C4×D4#4118yes—
566#117—24no—
567#117—24no—
568#117—28no—
569#117—44no—
570#117—44no—
571#117—48no—
572#117—48no—
573#117—48no—
574#117—48no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—48no—
577C2×C4⋊C4—48no—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2412yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2418yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2414yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—28no—
605C2×C22⋊C4—48no—
606C2×C22⋊C4—416no—
607C2×C22⋊C4—416no—
608C2×C22⋊C4—416no—
609C2×C22⋊C4—88no—
610C2×C22⋊C4C2412yes—
611C2×C22⋊C4C2414yes—
612C2×C22⋊C4C2414yes—
613C2×C22⋊C4C2414yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2412yes—
616C2×C22⋊C4C2412yes—
617C2×C22⋊C4C2412yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2412yes—
620C2×C22⋊C4C2414yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2418yes—
623C2×C22⋊C4C2414yes—
624C2×C22⋊C4C2418yes—
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⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2414yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2412yes—
653C2×C42—24no—
654C2×C42—28no—
655C2×C42—44no—
656C2×C42C2411yescharacteristic
657C2×C42C2412yes—
658C2×C42C2412yes—
659C2×C42C2412yes—
660C2×C42C2414yes—
661C2×C42C2411yescharacteristic
662C2×C42C2414yes—
663C2×C42C2411yescharacteristic
664C2×C42C2412yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674#95C2414yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2412yes—
679#95C2412yes—
680#95C2412yes—
681#95C2412yes—
682#95C2414yes—
683#95C2414yes—
684#95C2414yes—
685#95C2412yes—
686#95C2412yes—
687#95C2414yes—
688#95C2414yes—
689#95C2414yes—
690#95C2418yes—
691#95C2414yes—
692#95C2414yes—
693#95C2414yes—
694#95C2414yes—
695#95C2418yes—
696#95C2414yes—
697#95C2418yes—
698#95C2418yes—
699C24—24no—
700C24—24no—
701C24—28no—
702C24—216no—
703C24—216no—
704C24—216no—
705C24—42no—
706C24—44no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24C2514yes—
712C24C2512yes—
713C24C2518yes—
714C24C2511yescharacteristic
715C24C2512yes—
716C2×D4—24no—
717C2×D4—216no—
718C2×D4—216no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—216no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—216no—
729C2×D4—28no—
730C2×D4—28no—
731C2×D4—28no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—24no—
737C2×D4—216no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
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—44no—
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—416no—
769C2×D4—464no—
770C2×D4—832no—
771C2×D4—864no—
772C2×D4—864no—
773C2×D4C2×#4114yes—
774C2×D4H(5,𝔽2)18yes—
775C22×C4—22no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—22no—
779C22×C4—24no—
780C22×C4—28no—
781C22×C4—24no—
782C22×C4—28no—
783C22×C4—216no—
784C22×C4—22no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—28no—
793C22×C4—24no—
794C22×C4—28no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—22no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—44no—
802C22×C4—432no—
803C22×C4—44no—
804C22×C4—48no—
805C22×C4—44no—
806C22×C4—48no—
807C22×C4—42no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4C2×#4118yes—
815C22×C4H(5,𝔽2)14yes—
816C22×C4C2514yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2518yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—24no—
835C4⋊C4—22no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—28no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—28no—
847C4⋊C4—44no—
848C4⋊C4—44no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—44no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4C2×#4114yes—
860C22⋊C4—24no—
861C22⋊C4—28no—
862C22⋊C4—216no—
863C22⋊C4—24no—
864C22⋊C4—28no—
865C22⋊C4—24no—
866C22⋊C4—24no—
867C22⋊C4—28no—
868C22⋊C4—216no—
869C22⋊C4—24no—
870C22⋊C4—28no—
871C22⋊C4—28no—
872C22⋊C4—216no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—48no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4C2×#4118yes—
903C42—22no—
904C42—22no—
905C42—22no—
906C42—28no—
907C42—24no—
908C42—22no—
909C42—24no—
910C42—22no—
911C42—22no—
912C42—24no—
913C42—28no—
914C42—24no—
915C42—44no—
916C42—48no—
917C42—42no—
918C42—42no—
919C42C2×#4114yes—
920C42H(5,𝔽2)14yes—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—21no—
925C23—21no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—24no—
930C23—28no—
931C23—22no—
932C23—28no—
933C23—24no—
934C23—24no—
935C23—28no—
936C23—24no—
937C23—28no—
938C23—24no—
939C23—28no—
940C23—22no—
941C23—24no—
942C23—24no—
943C23—28no—
944C23—24no—
945C23—28no—
946C23—24no—
947C23—48no—
948C23—416no—
949C23—48no—
950C23—432no—
951C23—84no—
952C23—88no—
953C23—816no—
954C23—816no—
955C23—816no—
956C23—816no—
957C23—816no—
958C23—816no—
959C23C22×#4114yes—
960C23C2×H(5,𝔽2)12yes—
961C23C2×H(5,𝔽2)18yes—
962C23C2611yescharacteristic
963D4—416no—
964D4—416no—
965D4—48no—
966D4—432no—
967D4—44no—
968D4—416no—
969D4—416no—
970D4—48no—
971D4—88no—
972D4—816no—
973D4—816no—
974D4—816no—
975D4—816no—
976D4—816no—
977D4—816no—
978D4—816no—
979D4—168no—
980D4—168no—
981D4#540116yescomplemented
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—28no—
990C2×C4—216no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—28no—
1008C2×C4—24no—
1009C2×C4—28no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—48no—
1026C2×C4—48no—
1027C2×C4—48no—
1028C2×C4—416no—
1029C2×C4—44no—
1030C2×C4—416no—
1031C2×C4—48no—
1032C2×C4—82no—
1033C2×C4—88no—
1034C2×C4—816no—
1035C2×C4—168no—
1036C2×C4—168no—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4114yes—
1039C2×C4C22×#4112yes—
1040C2×C4C22×#4112yes—
1041C2×C4C2×H(5,𝔽2)14yes—
1042C2×C4C2×H(5,𝔽2)12yes—
1043C2×C4C2×H(5,𝔽2)14yes—
1044C2×C4C2×H(5,𝔽2)12yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C22—24no—
1047C22—24no—
1048C22—28no—
1049C22—28no—
1050C22—22no—
1051C22—24no—
1052C22—41no—
1053C22—42no—
1054C22—41no—
1055C22—42no—
1056C22—44no—
1057C22—48no—
1058C22—48no—
1059C22—42no—
1060C22—44no—
1061C22—48no—
1062C22—48no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—48no—
1068C22—48no—
1069C22—44no—
1070C22—44no—
1071C22—44no—
1072C22—42no—
1073C22—48no—
1074C22—816no—
1075C22—1632no—
1076C22C2×#54018yes—
1077C22C23×#4111yescharacteristic
1078C22C22×H(5,𝔽2)11yescharacteristic
1079C22C22×H(5,𝔽2)11yescharacteristic
1080C22C22×H(5,𝔽2)12yes—
1081C22H(7,𝔽2)12yes—
1082C4—22no—
1083C4—24no—
1084C4—22no—
1085C4—24no—
1086C4—42no—
1087C4—41no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C4—44no—
1092C4—48no—
1093C4—42no—
1094C4—44no—
1095C4—42no—
1096C4—41no—
1097C4—44no—
1098C4C2×#54014yes—
1099C4#351914yes—
1100C2—28no—
1101C2—42no—
1102C2—82no—
1103C2—88no—
1104C2—84no—
1105C2C22×#54011yescharacteristic
1106C2C2×#351911yescharacteristic
1107C2#6285811yescharacteristic
1108C2#6291212yes—
1109C2#6291212yes—
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. #42584C2semidirect
2. #42578C2semidirect
3. #40730C2semidirect
4. #40690C2semidirect
5. #39735C2semidirect
6. #39507C2semidirect
7. #39386C2semidirect
8. #37893C2semidirect
9. #37694C2semidirect
10. #37662C2semidirect
11. #37626C2semidirect
12. #37493C2semidirect
13. #36165C2semidirect
14. D4×#127C2semidirect
15. D4×#121C2semidirect
16. #35713C2semidirect
17. #35691C2semidirect
18. #35278C2semidirect
19. #35261C2semidirect
20. #34621C2semidirect
21. C2×#2619C2semidirect
22. #34310C2semidirect
23. D4×#117C2semidirect
27. C2×#540C22semidirect
28. C2×#540C22semidirect
29. C22×#127C22semidirect
30. C22×#121C22semidirect
33. C22×#117C22semidirect
34. #2867C22semidirect
35. #2859C22semidirect
36. #2856C22semidirect
37. #2856C22semidirect
38. #2851C22semidirect
39. #2847C22semidirect
40. #2829C22semidirect
41. #2828C22semidirect
42. #2828C22semidirect
43. #2803C22semidirect
44. #2761C22semidirect
45. #2753C22semidirect
46. #2753C22semidirect
47. #2709C22semidirect
48. #2703C22semidirect
49. #2703C22semidirect
50. #2699C22semidirect
51. #2688C22semidirect
52. #2673C22semidirect
53. #2673C22semidirect
54. #2671C22semidirect
55. #2661C22semidirect
56. #2651C22semidirect
57. #2648C22semidirect
58. #2648C22semidirect
59. #2647C22semidirect
60. #2644C22semidirect
61. #2641C22semidirect
62. #2641C22semidirect
63. #2635C22semidirect
64. #2629C22semidirect
65. #2624C22semidirect
66. #2624C22semidirect
67. #2624C22semidirect
68. #2622C22semidirect
70. #2619C22semidirect
71. #2619C22semidirect
72. #2619C22semidirect
73. #2619C22semidirect
74. #2619C22semidirect
75. #2619C22semidirect
76. #2619C22semidirect
77. #2619C22semidirect
78. #2617C22semidirect
79. #2571C22semidirect
80. #2543C22semidirect
81. #2541C22semidirect
82. #2541C22semidirect
83. #2541C22semidirect
84. #2541C22semidirect
85. #2537C22semidirect
86. #2535C22semidirect
87. #2513C22semidirect
88. #2508C22semidirect
89. #2505C22semidirect
90. #2500C22semidirect
91. #2490C22semidirect
92. #2485C22semidirect
93. #2476C22semidirect
94. #2471C22semidirect
95. #2445C22semidirect
96. #2445C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
99. #2444C22semidirect
100. #2443C22semidirect
101. #2442C22semidirect
102. #2433C22semidirect
103. #2433C22semidirect
104. #2428C22semidirect
105. #2428C22semidirect
106. #2428C22semidirect
107. #2428C22semidirect
108. #2428C22semidirect
109. #2428C22semidirect
110. #2424C22semidirect
111. #2424C22semidirect
112. #2424C22semidirect
113. #2422C22semidirect
114. #2420C22semidirect
115. #2420C22semidirect
116. #2418C22semidirect
117. #2418C22semidirect
118. #2416C22semidirect
119. #2416C22semidirect
120. #2414C22semidirect
121. #2414C22semidirect
122. #2412C22semidirect
123. #2410C22semidirect
124. #2410C22semidirect
125. #2410C22semidirect
126. #2408C22semidirect
127. #2408C22semidirect
128. #2405C22semidirect
129. #2395C22semidirect
130. #2392C22semidirect
131. C2×#394C22semidirect
132. C2×#392C22semidirect
133. #2366C22semidirect
134. #2363C22semidirect
135. #2361C22semidirect
136. #2358C22semidirect
137. #2354C22semidirect
138. #2354C22semidirect
139. #2352C22semidirect
143. #2344C22semidirect
144. #2342C22semidirect
148. D4×C22⋊C4C22semidirect
149. #2328C22semidirect
150. #2324C22semidirect
151. #2324C22semidirect
152. #2321C22semidirect
153. #2314C22semidirect
154. C4×#127C22semidirect
155. C4×#127C22semidirect
156. C4×#125C22semidirect
157. C4×#121C22semidirect
158. C4×#121C22semidirect
159. #2293C22semidirect
160. #2293C22semidirect
161. #2293C22semidirect
162. C2×#390C22semidirect
163. #2290C22semidirect
164. #2290C22semidirect
165. #2285C22semidirect
166. C2×#382C22semidirect
167. #2280C22semidirect
170. C4×#117C22semidirect
981. D4#540semidirect

Maximal subgroups

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

subgroupindex
#425842
#425782
#407302
#406902
#397352
#395072
#393862
#378932
#376942
#376622
#376262
#374932
#361652
D4×#1272
D4×#1212
#357132
#356912
#352782
#352612
#346212
C2×#26192
#343102
D4×#1172