Finite Group Databasebeta

← #7657603

Subgroups — #7657603

Order 512.

5989 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42736C214yesmaximal, complemented
2#42730C214yesmaximal, complemented
3#40723C218yesmaximal, complemented
4#40698C218yesmaximal, complemented
5#39770C211yesmaximal, characteristic, complemented
6#39763C211yesmaximal, characteristic, complemented
7#38942C212yesmaximal, complemented
8#38056C214yesmaximal, complemented
9#37706C212yesmaximal, complemented
10#37694C212yesmaximal, complemented
11#37625C212yesmaximal, complemented
12#37493C214yesmaximal, complemented
13#36258C212yesmaximal, complemented
14D4×#127C211yesmaximal, characteristic, complemented
15D4×#125C211yesmaximal, characteristic, complemented
16#35761C214yesmaximal, complemented
17#35713C214yesmaximal, complemented
18#35278C211yesmaximal, characteristic, complemented
19#35271C212yesmaximal, complemented
20#34621C211yesmaximal, characteristic, complemented
21C2×#2641C212yesmaximal, complemented
22#34310C212yesmaximal, complemented
23#34123C211yesmaximal, characteristic, complemented
24C2×#546C2214yes—
25C2×D42C2212yes—
26C2×D42C2214yes—
27C2×#540C2212yescomplemented
28C22×#127C2212yes—
29C22×#125C2212yescomplemented
30C2×#518C2214yes—
31C2×C4×#41C2211yescharacteristic
32#2867C2211yescharacteristic
33#2859C2211yescharacteristic, complemented
34#2856C2212yes—
35#2856C2212yescomplemented
36#2854C2214yescomplemented
37#2851C2212yescomplemented
38#2829C2218yescomplemented
39#2829C2218yescomplemented
40#2828C2218yescomplemented
41#2800C2218yescomplemented
42#2756C2218yescomplemented
43#2756C2218yescomplemented
44#2753C2218yescomplemented
45#2749C2218yescomplemented
46#2711C2218yescomplemented
47#2709C2218yescomplemented
48#2709C2218yescomplemented
49#2707C2218yescomplemented
50#2706C2218yescomplemented
51#2699C2218yescomplemented
52#2673C2218yescomplemented
53#2661C2218yescomplemented
54#2651C2214yescomplemented
55#2648C2214yescomplemented
56#2648C2218yescomplemented
57#2647C2211yescharacteristic, complemented
58#2644C2212yescomplemented
59#2644C2214yescomplemented
60#2641C2211yescharacteristic
61#2641C2212yes—
62#2641C2218yescomplemented
63#2641C2214yescomplemented
64#2641C2212yescomplemented
65#2641C2214yescomplemented
66#2641C2212yescomplemented
67#2641C2218yescomplemented
68#2630C2218yescomplemented
69#2629C2211yescharacteristic, complemented
70#2624C2212yescomplemented
71#2624C2214yescomplemented
72#2622C2218yescomplemented
73#2620C2214yescomplemented
74#2619C2211yescharacteristic
75#2619C2212yescomplemented
76#2617C2218yescomplemented
77#2552C2212yescomplemented
78#2548C2212yescomplemented
79#2544C2214yescomplemented
80#2541C2212yes—
81#2541C2214yes—
82#2538C2212yescomplemented
83#2537C2214yescomplemented
84#2534C2218yescomplemented
85#2531C2218yescomplemented
86#2526C2218yescomplemented
87#2513C2214yescomplemented
88#2506C2214yescomplemented
89#2500C2214yescomplemented
90#2490C2214yescomplemented
91#2485C2214yescomplemented
92#2473C2218yescomplemented
93#2454C2214yescomplemented
94#2445C2214yescomplemented
95#2445C2214yescomplemented
96#2445C2214yescomplemented
97#2445C2214yescomplemented
98#2445C2214yescomplemented
99#2444C2218yescomplemented
100#2443C2218yescomplemented
101#2442C2214yescomplemented
102#2433C2218yes—
103#2433C2214yes—
104#2428C2214yescomplemented
105#2428C2214yescomplemented
106#2428C2214yescomplemented
107#2427C2214yescomplemented
108#2426C2214yescomplemented
109#2425C2218yescomplemented
110#2424C2218yescomplemented
111#2424C2218yescomplemented
112#2422C2214yescomplemented
113#2420C2214yescomplemented
114#2418C2218yescomplemented
115#2418C2218yescomplemented
116#2416C2218yescomplemented
117#2416C2214yescomplemented
118#2415C2214yescomplemented
119#2414C2214yescomplemented
120#2414C2214yescomplemented
121#2412C2218yescomplemented
122#2412C2218yescomplemented
123#2411C2218yescomplemented
124#2410C2218yescomplemented
125#2408C2214yescomplemented
126#2405C2218yescomplemented
127#2395C2214yescomplemented
128#2392C2214yescomplemented
129C2×#394C2218yescomplemented
130C2×#394C2218yescomplemented
131#2366C2212yescomplemented
132#2363C2214yescomplemented
133#2361C2214yescomplemented
134#2358C2218yescomplemented
135#2356C2212yescomplemented
136#2354C2212yescomplemented
137#2353C2214yescomplemented
138#2349C2212yes—
139D4×C4⋊C4C2212yes—
140D4×C4⋊C4C2214yes—
141#2346C2212yescomplemented
142#2343C2214yescomplemented
143#2339C2212yes—
144D4×C22⋊C4C2214yes—
145D4×C22⋊C4C2214yes—
146D4×C22⋊C4C2214yescomplemented
147#2330C2212yescomplemented
148#2328C2212yescomplemented
149#2328C2212yescomplemented
150#2324C2214yescomplemented
151#2321C2218yescomplemented
152#2319C2214yescomplemented
153C4×#127C2211yescharacteristic
154C4×#127C2212yescomplemented
155C4×#125C2211yescharacteristic, complemented
156C4×#121C2214yescomplemented
157C4×#121C2212yescomplemented
158#2295C2211yescharacteristic, complemented
159#2295C2211yescharacteristic, complemented
160#2293C2212yescomplemented
161C2×#390C2214yescomplemented
162C2×#390C2214yescomplemented
163#2290C2212yescomplemented
164#2290C2212yescomplemented
165#2283C2211yescharacteristic, complemented
166#2283C2212yescomplemented
167C42×D4C2211yescharacteristic
168C42×D4C2211yescharacteristic
169C4×#117C2211yescharacteristic, complemented
170C2×#376C2212yescomplemented
171C22×#41C2311yescharacteristic
172C23×D4C2314yes—
173C23×D4C2314yes—
174C23×D4C2318yes—
175#546—416no—
176D42—216no—
177D42—416no—
178#540—48no—
179C2×#127—48no—
180C2×#127C2311yescharacteristic
181C2×#127C2312yes—
182C2×#127C2312yes—
183C2×#127C2312yes—
184C2×#127C2314yes—
185C2×#127C2318yes—
186C2×#127C2314yes—
187C2×#127C2314yes—
188C2×#125—48no—
189C2×#125C2311yescharacteristic
190C2×#125C2312yes—
191C2×#125C2314yes—
192C2×#125C2318yes—
193C2×#124C2314yes—
194C2×#123C2318yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×C22⋊Q8C2314yes—
199C2×#121C2314yes—
200C2×#121C2314yes—
201C2×#121C2318yes—
202C2×#121C2314yes—
203C2×#121C2314yes—
204C2×#121C2318yes—
205C2×#121C2312yes—
206C2×#121C2314yes—
207C2×#121C2314yes—
208C2×#121C2318yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#120C2318yes—
212C2×#120C2318yes—
213C2×#120C2318yes—
214C2×#120C2318yes—
215#518—416no—
216C4×#41—28no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4C2312yes—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2314yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2318yes—
231C2×C4×D4C2318yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2311yescharacteristic
236C2×#117C2312yes—
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2314yes—
240C2×#117C2314yes—
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2314yes—
243C22×C4⋊C4C2318yes—
244C22×C22⋊C4C2318yes—
245C22×C22⋊C4C2318yes—
246C22×C22⋊C4C2318yes—
247C22×C22⋊C4C2318yes—
248C22×C22⋊C4C2318yes—
249C22×C42C2312yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252C22×C42C2312yes—
253#400C2318yes—
254#400C2314yes—
255#399C2314yes—
256#399C2318yes—
257#398C2318yes—
258#398C2318yes—
259#398C2314yes—
260#398C2314yes—
261#397C2318yes—
262#397C2318yes—
263#397C2318yes—
264#397C2318yes—
265#397C2318yes—
266#397C2318yes—
267#397C2314yes—
268#397C2314yes—
269#397C2314yes—
270#397C2314yes—
271#396C2318yes—
272#396C2318yes—
273#396C2318yes—
274#396C2318yes—
275#396C2314yes—
276#396C2314yes—
277#394C2314yes—
278#394C2318yes—
279#394C2318yes—
280#394C2318yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2318yes—
285#394C2318yes—
286#394C2318yes—
287#394C2318yes—
288#394C2318yes—
289#394C2318yes—
290#394C2314yes—
291#394C2318yes—
292#394C2314yes—
293#394C2318yes—
294#394C2314yes—
295#394C2314yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#394C2318yes—
306#392C2318yes—
307#392C2318yes—
308#392C2318yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#392C2314yes—
313#391C2312yes—
314#391C2312yes—
315#390C2312yes—
316#390C2314yes—
317#390C2314yes—
318#390C2314yes—
319#390C2314yes—
320#390C2318yes—
321#390C2314yes—
322#390C2314yes—
323#390C2318yes—
324#390C2314yes—
325#390C2314yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2314yes—
330#390C2318yes—
331#390C2314yes—
332#390C2314yes—
333#390C2312yes—
334#390C2312yes—
335#390C2314yes—
336#390C2318yes—
337#390C2314yes—
338#390C2318yes—
339#390C2318yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2312yes—
353#388C2314yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#388C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2314yes—
367#388C2318yes—
368#387C2314yes—
369#387C2314yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2314yes—
374#387C2314yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2314yes—
387#386C2314yes—
388#386C2318yes—
389#386C2314yes—
390#386C2318yes—
391#386C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2314yes—
396#385C2314yes—
397#385C2318yes—
398#385C2318yes—
399#384C2311yescharacteristic
400#384C2312yes—
401#384C2314yes—
402#383C2312yes—
403#383C2314yes—
404#382C2311yescharacteristic
405#382C2312yes—
406#382C2314yes—
407#382C2312yes—
408#381C2318yes—
409#381C2314yes—
410#381C2312yes—
411#380C2318yes—
412#380C2314yes—
413#380C2314yes—
414#380C2314yes—
415#380C2312yes—
416#380C2318yes—
417#380C2314yes—
418#380C2312yes—
419#380C2318yes—
420#379C2318yes—
421#379C2318yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2312yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2312yes—
440C4×C22⋊C4C2318yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2312yes—
443#376C2312yes—
444#376C2311yescharacteristic
445#376C2312yes—
446#376C2314yes—
447#376C2314yes—
448#376C2311yescharacteristic
449#376C2312yes—
450C2×#95C2314yes—
451C2×#95C2314yes—
452C43C2311yescharacteristic
453C43C2311yescharacteristic
454C25C2418yes—
455C2×#41—24no—
456C2×#41—28no—
457C22×Q8C2411yescharacteristic
458C22×D4—216no—
459C22×D4—216no—
460C22×D4—216no—
461C22×D4—216no—
462C22×D4—48no—
463C22×D4—416no—
464C22×D4—48no—
465C22×D4—416no—
466C22×D4—88no—
467C22×D4C2412yes—
468C22×D4C2418yes—
469C22×D4C2414yes—
470C22×D4C2414yes—
471C22×D4C2412yes—
472C22×D4C2414yes—
473C22×D4C2414yes—
474C22×D4C2418yes—
475C22×D4C2418yes—
476C22×D4C2414yes—
477C22×D4C2418yes—
478C22×D4C2418yes—
479C22×D4C2418yes—
480C22×D4C2418yes—
481C22×D4C2411yescharacteristic
482C23×C4C2412yes—
483C23×C4C2414yes—
484C23×C4C2411yescharacteristic
485C23×C4C2411yescharacteristic
486C23×C4C2414yes—
487C23×C4C2412yes—
488C23×C4C2418yes—
489C23×C4C2414yes—
490C23×C4C2412yes—
491C23×C4C2411yescharacteristic
492C23×C4C2418yes—
493C23×C4C2418yes—
494#127—28no—
495#127—24no—
496#127—28no—
497#127—48no—
498#127—416no—
499#127—44no—
500#127—48no—
501#127—84no—
502#125—24no—
503#125—28no—
504#125—48no—
505#125—416no—
506#124—48no—
507#123—416no—
508#123—416no—
509#123—88no—
510#123—88no—
511C22⋊Q8—48no—
512#121—216no—
513#121—216no—
514#121—416no—
515#121—44no—
516#121—48no—
517#121—48no—
518#121—48no—
519#121—48no—
520#121—416no—
521#121—416no—
522#121—84no—
523#121—88no—
524#120—232no—
525#120—416no—
526#120—416no—
527#120—416no—
528C4×Q8—24no—
529C4×Q8—24no—
530C4×D4—24no—
531C4×D4—28no—
532C4×D4—216no—
533C4×D4—28no—
534C4×D4—28no—
535C4×D4—28no—
536C4×D4—28no—
537C4×D4—48no—
538C4×D4—48no—
539C4×D4—48no—
540C4×D4—48no—
541C4×D4—48no—
542C4×D4—48no—
543C4×D4—416no—
544C4×D4—416no—
545C4×D4—84no—
546C4×D4#4118yes—
547#117—24no—
548#117—28no—
549#117—24no—
550#117—42no—
551#117—48no—
552#117—48no—
553C2×C4⋊C4—48no—
554C2×C4⋊C4—416no—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2412yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2411yescharacteristic
583C2×C22⋊C4—416no—
584C2×C22⋊C4—416no—
585C2×C22⋊C4—416no—
586C2×C22⋊C4—88no—
587C2×C22⋊C4—88no—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2412yes—
593C2×C22⋊C4C2414yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2414yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2418yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2418yes—
610C2×C22⋊C4C2418yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2414yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2418yes—
618C2×C22⋊C4C2418yes—
619C2×C22⋊C4C2418yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2418yes—
622C2×C22⋊C4C2414yes—
623C2×C22⋊C4C2418yes—
624C2×C22⋊C4C2414yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2412yes—
628C2×C42—28no—
629C2×C42—24no—
630C2×C42—28no—
631C2×C42—44no—
632C2×C42C2412yes—
633C2×C42C2412yes—
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2414yes—
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2412yes—
642C2×C42C2412yes—
643C2×C42C2411yescharacteristic
644C2×C42C2412yes—
645C2×C42C2414yes—
646C2×C42C2411yescharacteristic
647C2×C42C2418yes—
648C2×C42C2412yes—
649C2×C42C2412yes—
650C2×C42C2414yes—
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653#95C2412yes—
654#95C2412yes—
655#95C2414yes—
656#95C2414yes—
657#95C2414yes—
658#95C2414yes—
659#95C2414yes—
660#95C2414yes—
661#95C2412yes—
662#95C2412yes—
663#95C2414yes—
664#95C2412yes—
665#95C2412yes—
666#95C2414yes—
667#95C2414yes—
668#95C2414yes—
669#95C2418yes—
670#95C2414yes—
671#95C2414yes—
672#95C2414yes—
673#95C2414yes—
674#95C2418yes—
675#95C2414yes—
676#95C2414yes—
677#95C2414yes—
678#95C2414yes—
679#95C2418yes—
680#95C2418yes—
681#95C2418yes—
682C24—216no—
683C24—216no—
684C24—216no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24C2514yes—
690C24C2518yes—
691C24C2511yescharacteristic
692C24C2512yes—
693#41—416no—
694C2×Q8—22no—
695C2×Q8—24no—
696C2×D4—24no—
697C2×D4—216no—
698C2×D4—216no—
699C2×D4—28no—
700C2×D4—216no—
701C2×D4—24no—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—216no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—24no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—464no—
738C2×D4—832no—
739C2×D4—864no—
740C2×D4C2×#4114yes—
741C2×D4H(5,𝔽2)18yes—
742C22×C4—24no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—24no—
748C22×C4—28no—
749C22×C4—216no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—48no—
765C22×C4—48no—
766C22×C4—42no—
767C22×C4—48no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4—48no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4C2×#4118yes—
774C22×C4C2511yescharacteristic
775C22×C4C2512yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C22×C4C2512yes—
782C22×C4C2511yescharacteristic
783C22×C4C2512yes—
784C22×C4C2512yes—
785C22×C4C2514yes—
786C22×C4C2518yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2511yescharacteristic
792C22×C4C2511yescharacteristic
793C4⋊C4—22no—
794C4⋊C4—24no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—28no—
798C4⋊C4—24no—
799C4⋊C4—28no—
800C4⋊C4—216no—
801C4⋊C4—24no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—48no—
807C4⋊C4—48no—
808C4⋊C4—48no—
809C4⋊C4—42no—
810C4⋊C4—44no—
811C4⋊C4—44no—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—48no—
816C4⋊C4—48no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C4⋊C4C2×#4114yes—
821C22⋊C4—24no—
822C22⋊C4—28no—
823C22⋊C4—216no—
824C22⋊C4—28no—
825C22⋊C4—24no—
826C22⋊C4—28no—
827C22⋊C4—216no—
828C22⋊C4—24no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—44no—
839C22⋊C4—44no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C22⋊C4—48no—
844C22⋊C4—48no—
845C22⋊C4—48no—
846C22⋊C4—42no—
847C22⋊C4—48no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—48no—
855C22⋊C4—44no—
856C22⋊C4—48no—
857C22⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—48no—
860C22⋊C4C2×#4118yes—
861C42—22no—
862C42—24no—
863C42—22no—
864C42—22no—
865C42—24no—
866C42—24no—
867C42—28no—
868C42—24no—
869C42—22no—
870C42—24no—
871C42—28no—
872C42—24no—
873C42—22no—
874C42—24no—
875C42—22no—
876C42—44no—
877C42—48no—
878C42—42no—
879C42—42no—
880C42C2×#4114yes—
881C42H(5,𝔽2)14yes—
882C23—22no—
883C23—22no—
884C23—24no—
885C23—21no—
886C23—24no—
887C23—28no—
888C23—21no—
889C23—24no—
890C23—24no—
891C23—28no—
892C23—28no—
893C23—22no—
894C23—28no—
895C23—24no—
896C23—21no—
897C23—28no—
898C23—24no—
899C23—24no—
900C23—28no—
901C23—24no—
902C23—22no—
903C23—28no—
904C23—432no—
905C23—816no—
906C23—816no—
907C23—816no—
908C23—816no—
909C23—816no—
910C23—816no—
911C23C22×#4114yes—
912C23C2×H(5,𝔽2)18yes—
913C23C2611yescharacteristic
914Q8—44no—
915D4—416no—
916D4—432no—
917D4—48no—
918D4—416no—
919D4—416no—
920D4—48no—
921D4—88no—
922D4—816no—
923D4—816no—
924D4—88no—
925D4—816no—
926D4—816no—
927D4—168no—
928D4—168no—
929D4#540116yescomplemented
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—216no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—24no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—24no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—28no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—416no—
975C2×C4—48no—
976C2×C4—416no—
977C2×C4—44no—
978C2×C4—44no—
979C2×C4—82no—
980C2×C4—84no—
981C2×C4—816no—
982C2×C4—88no—
983C2×C4—168no—
984C2×C4—168no—
985C2×C4C22×#4114yes—
986C2×C4C22×#4112yes—
987C2×C4C22×#4112yes—
988C2×C4C22×#4112yes—
989C2×C4C2×H(5,𝔽2)14yes—
990C2×C4C2×H(5,𝔽2)14yes—
991C2×C4C2×H(5,𝔽2)12yes—
992C2×C4#58512yes—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—41no—
998C22—44no—
999C22—48no—
1000C22—41no—
1001C22—48no—
1002C22—44no—
1003C22—48no—
1004C22—44no—
1005C22—44no—
1006C22—48no—
1007C22—42no—
1008C22—48no—
1009C22—42no—
1010C22—44no—
1011C22—48no—
1012C22—44no—
1013C22—41no—
1014C22—44no—
1015C22—48no—
1016C22—1632no—
1017C22C2×#54018yes—
1018C22C23×#4111yescharacteristic
1019C22C22×H(5,𝔽2)11yescharacteristic
1020C22C22×H(5,𝔽2)12yes—
1021C22C2×#58511yescharacteristic
1022C22H(7,𝔽2)12yes—
1023C4—24no—
1024C4—22no—
1025C4—24no—
1026C4—41no—
1027C4—42no—
1028C4—41no—
1029C4—44no—
1030C4—44no—
1031C4—48no—
1032C4—42no—
1033C4—42no—
1034C4—44no—
1035C4—44no—
1036C4—42no—
1037C4—41no—
1038C4—44no—
1039C4—42no—
1040C4C2×#54014yes—
1041C4#351414yes—
1042C2—28no—
1043C2—81no—
1044C2—88no—
1045C2—84no—
1046C2C22×#54011yescharacteristic
1047C2C2×#351411yescharacteristic
1048C2#6285811yescharacteristic
1049C2#6291212yes—
1050C2#6292012yes—
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. #42736C2semidirect
2. #42730C2semidirect
3. #40723C2semidirect
4. #40698C2semidirect
5. #39770C2semidirect
6. #39763C2semidirect
7. #38942C2semidirect
8. #38056C2semidirect
9. #37706C2semidirect
10. #37694C2semidirect
11. #37625C2semidirect
12. #37493C2semidirect
13. #36258C2semidirect
14. D4×#127C2semidirect
15. D4×#125C2semidirect
16. #35761C2semidirect
17. #35713C2semidirect
18. #35278C2semidirect
19. #35271C2semidirect
20. #34621C2semidirect
21. C2×#2641C2semidirect
22. #34310C2semidirect
23. #34123C2semidirect
27. C2×#540C22semidirect
29. C22×#125C22semidirect
33. #2859C22semidirect
35. #2856C22semidirect
36. #2854C22semidirect
37. #2851C22semidirect
38. #2829C22semidirect
39. #2829C22semidirect
40. #2828C22semidirect
41. #2800C22semidirect
42. #2756C22semidirect
43. #2756C22semidirect
44. #2753C22semidirect
45. #2749C22semidirect
46. #2711C22semidirect
47. #2709C22semidirect
48. #2709C22semidirect
49. #2707C22semidirect
50. #2706C22semidirect
51. #2699C22semidirect
52. #2673C22semidirect
53. #2661C22semidirect
54. #2651C22semidirect
55. #2648C22semidirect
56. #2648C22semidirect
57. #2647C22semidirect
58. #2644C22semidirect
59. #2644C22semidirect
62. #2641C22semidirect
63. #2641C22semidirect
64. #2641C22semidirect
65. #2641C22semidirect
66. #2641C22semidirect
67. #2641C22semidirect
68. #2630C22semidirect
69. #2629C22semidirect
70. #2624C22semidirect
71. #2624C22semidirect
72. #2622C22semidirect
73. #2620C22semidirect
75. #2619C22semidirect
76. #2617C22semidirect
77. #2552C22semidirect
78. #2548C22semidirect
79. #2544C22semidirect
82. #2538C22semidirect
83. #2537C22semidirect
84. #2534C22semidirect
85. #2531C22semidirect
86. #2526C22semidirect
87. #2513C22semidirect
88. #2506C22semidirect
89. #2500C22semidirect
90. #2490C22semidirect
91. #2485C22semidirect
92. #2473C22semidirect
93. #2454C22semidirect
94. #2445C22semidirect
95. #2445C22semidirect
96. #2445C22semidirect
97. #2445C22semidirect
98. #2445C22semidirect
99. #2444C22semidirect
100. #2443C22semidirect
101. #2442C22semidirect
104. #2428C22semidirect
105. #2428C22semidirect
106. #2428C22semidirect
107. #2427C22semidirect
108. #2426C22semidirect
109. #2425C22semidirect
110. #2424C22semidirect
111. #2424C22semidirect
112. #2422C22semidirect
113. #2420C22semidirect
114. #2418C22semidirect
115. #2418C22semidirect
116. #2416C22semidirect
117. #2416C22semidirect
118. #2415C22semidirect
119. #2414C22semidirect
120. #2414C22semidirect
121. #2412C22semidirect
122. #2412C22semidirect
123. #2411C22semidirect
124. #2410C22semidirect
125. #2408C22semidirect
126. #2405C22semidirect
127. #2395C22semidirect
128. #2392C22semidirect
129. C2×#394C22semidirect
130. C2×#394C22semidirect
131. #2366C22semidirect
132. #2363C22semidirect
133. #2361C22semidirect
134. #2358C22semidirect
135. #2356C22semidirect
136. #2354C22semidirect
137. #2353C22semidirect
141. #2346C22semidirect
142. #2343C22semidirect
146. D4×C22⋊C4C22semidirect
147. #2330C22semidirect
148. #2328C22semidirect
149. #2328C22semidirect
150. #2324C22semidirect
151. #2321C22semidirect
152. #2319C22semidirect
154. C4×#127C22semidirect
155. C4×#125C22semidirect
156. C4×#121C22semidirect
157. C4×#121C22semidirect
158. #2295C22semidirect
159. #2295C22semidirect
160. #2293C22semidirect
161. C2×#390C22semidirect
162. C2×#390C22semidirect
163. #2290C22semidirect
164. #2290C22semidirect
165. #2283C22semidirect
166. #2283C22semidirect
169. C4×#117C22semidirect
170. C2×#376C22semidirect
929. D4#540semidirect

Maximal subgroups

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

subgroupindex
#427362
#427302
#407232
#406982
#397702
#397632
#389422
#380562
#377062
#376942
#376252
#374932
#362582
D4×#1272
D4×#1252
#357612
#357132
#352782
#352712
#346212
C2×#26412
#343102
#341232