Finite Group Databasebeta

← #7658021

Subgroups — #7658021

Order 512.

5494 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42641C214yesmaximal, complemented
2#42633C214yesmaximal, complemented
3#40894C218yesmaximal, complemented
4#40889C218yesmaximal, complemented
5#39606C212yesmaximal, complemented
6#39513C211yesmaximal, characteristic, complemented
7#39378C211yesmaximal, characteristic, complemented
8#37883C212yesmaximal, complemented
9#37851C214yesmaximal, complemented
10#37706C212yesmaximal, complemented
11#37627C212yesmaximal, complemented
12#37502C214yesmaximal, complemented
13#36179C211yesmaximal, characteristic, complemented
14#36153C212yesmaximal, complemented
15D4×#125C211yesmaximal, characteristic, complemented
16#35998C214yesmaximal, complemented
17#35821C214yesmaximal, complemented
18#35284C211yesmaximal, characteristic, complemented
19#35261C212yesmaximal, complemented
20#34621C211yesmaximal, characteristic, complemented
21C2×#2629C212yesmaximal, complemented
22#34308C212yesmaximal, complemented
23D4×#117C211yesmaximal, characteristic, complemented
24C2×#547C2212yes—
25C2×#547C2214yes—
26C2×#546C2214yes—
27C2×#540C2212yescomplemented
28C22×#125C2212yescomplemented
29C2×#520C2214yes—
30C22×C4×D4C2211yescharacteristic
31C22×#117C2212yes—
32#2868C2211yescharacteristic, complemented
33#2859C2211yescharacteristic, complemented
34#2857C2212yes—
35#2856C2212yescomplemented
36#2851C2212yescomplemented
37#2847C2214yes—
38#2837C2218yescomplemented
39#2837C2218yescomplemented
40#2836C2218yescomplemented
41#2793C2218yescomplemented
42#2793C2218yescomplemented
43#2791C2218yescomplemented
44#2768C2218yescomplemented
45#2748C2218yes—
46#2748C2218yescomplemented
47#2743C2218yes—
48#2741C2218yescomplemented
49#2740C2218yes—
50#2711C2218yescomplemented
51#2707C2218yescomplemented
52#2701C2218yescomplemented
53#2667C2218yescomplemented
54#2651C2214yescomplemented
55#2651C2218yescomplemented
56#2649C2218yescomplemented
57#2648C2214yes—
58#2647C2211yescharacteristic, complemented
59#2647C2212yescomplemented
60#2644C2212yescomplemented
61#2641C2211yescharacteristic, complemented
62#2629C2211yescharacteristic
63#2629C2218yes—
64#2629C2214yes—
65#2629C2212yes—
66#2629C2212yescomplemented
67#2629C2214yescomplemented
68#2629C2218yescomplemented
69#2629C2212yescomplemented
70#2625C2214yescomplemented
71#2624C2212yes—
72#2624C2214yescomplemented
73#2623C2218yescomplemented
74#2620C2214yes—
75#2619C2211yescharacteristic
76#2618C2218yes—
77#2552C2212yescomplemented
78#2547C2212yes—
79#2545C2214yes—
80#2542C2214yescomplemented
81#2542C2212yescomplemented
82#2538C2214yes—
83#2537C2212yes—
84#2534C2218yes—
85#2507C2214yescomplemented
86#2507C2214yescomplemented
87#2506C2214yescomplemented
88#2502C2214yescomplemented
89#2501C2214yescomplemented
90#2501C2218yescomplemented
91#2498C2218yescomplemented
92#2497C2214yes—
93#2497C2214yescomplemented
94#2497C2214yescomplemented
95#2490C2214yescomplemented
96#2486C2214yes—
97#2486C2214yescomplemented
98#2484C2218yescomplemented
99#2476C2218yescomplemented
100#2473C2218yescomplemented
101#2471C2218yes—
102#2454C2214yescomplemented
103#2446C2214yescomplemented
104#2446C2214yescomplemented
105#2443C2218yescomplemented
106#2443C2218yescomplemented
107#2442C2214yescomplemented
108#2429C2214yes—
109#2427C2214yes—
110#2426C2214yes—
111#2425C2218yes—
112#2425C2218yes—
113#2424C2218yes—
114#2423C2214yescomplemented
115#2423C2214yescomplemented
116#2420C2214yescomplemented
117#2419C2218yescomplemented
118#2419C2218yescomplemented
119#2417C2214yes—
120#2417C2214yes—
121#2416C2214yes—
122#2416C2218yes—
123#2416C2214yes—
124#2413C2218yes—
125#2412C2218yes—
126#2411C2218yes—
127#2395C2214yescomplemented
128#2392C2214yes—
129C2×#398C2218yescomplemented
130C2×#396C2218yes—
131#2365C2212yescomplemented
132#2361C2214yescomplemented
133#2360C2214yescomplemented
134#2359C2218yescomplemented
135#2354C2212yes—
136#2352C2214yes—
137D4×C4⋊C4C2212yes—
138D4×C4⋊C4C2214yes—
139D4×C4⋊C4C2212yes—
140D4×C4⋊C4C2212yescomplemented
141#2344C2212yes—
142#2344C2214yescomplemented
143#2342C2214yes—
144#2339C2214yes—
145#2339C2214yes—
146D4×C22⋊C4C2212yes—
147#2330C2212yescomplemented
148#2324C2214yes—
149#2323C2214yescomplemented
150#2322C2218yescomplemented
151#2314C2212yes—
152#2314C2212yescomplemented
153C4×C4⋊Q8C2212yescomplemented
154C4×#127C2211yescharacteristic, complemented
155C4×#125C2211yescharacteristic, complemented
156C4×#121C2212yes—
157C4×#121C2214yescomplemented
158#2293C2211yescharacteristic
159#2293C2211yescharacteristic
160#2293C2212yescomplemented
161C2×#389C2214yescomplemented
162#2290C2212yes—
163#2290C2212yes—
164#2285C2211yescharacteristic
165C2×#384C2212yescomplemented
166#2280C2212yes—
167C2×#380C2214yes—
168C42×D4C2211yescharacteristic
169C42×D4C2211yescharacteristic
170C4×#117C2211yescharacteristic
171C22×#41C2314yes—
172C23×D4C2311yescharacteristic
173C24×C4C2312yes—
174#547—216no—
175#547—416no—
176#546—416no—
177#540—48no—
178C2×C4⋊Q8C2312yes—
179C2×C4⋊Q8C2314yes—
180C2×#127C2311yescharacteristic
181C2×#125—48no—
182C2×#125C2311yescharacteristic
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#125C2318yes—
186C2×#124C2314yes—
187C2×#123C2318yes—
188C2×#123C2318yes—
189C2×#123C2318yes—
190C2×#123C2318yes—
191C2×#123C2318yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×#121C2312yes—
197C2×#121C2314yes—
198C2×#121C2314yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#121C2314yes—
202C2×#121C2318yes—
203C2×#120C2318yes—
204#520—416no—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×D4—28no—
208C2×C4×D4C2312yes—
209C2×C4×D4C2312yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2314yes—
220C2×C4×D4C2318yes—
221C2×C4×D4C2314yes—
222C2×C4×D4C2311yescharacteristic
223C2×#117—48no—
224C2×#117C2311yescharacteristic
225C2×#117C2312yes—
226C2×#117C2311yescharacteristic
227C2×#117C2314yes—
228C2×#117C2312yes—
229C2×#117C2314yes—
230C2×#117C2318yes—
231C2×#117C2314yes—
232C2×#117C2312yes—
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2314yes—
235C22×C4⋊C4C2318yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2314yes—
238C22×C4⋊C4C2318yes—
239C22×C4⋊C4C2314yes—
240C22×C4⋊C4C2318yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2314yes—
243C22×C22⋊C4C2318yes—
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2312yes—
247#400C2318yes—
248#400C2318yes—
249#400C2318yes—
250#400C2318yes—
251#400C2314yes—
252#399C2318yes—
253#399C2318yes—
254#399C2318yes—
255#399C2318yes—
256#399C2318yes—
257#399C2314yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2318yes—
266#398C2314yes—
267#398C2318yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2318yes—
272#398C2314yes—
273#397C2314yes—
274#397C2318yes—
275#397C2318yes—
276#397C2314yes—
277#397C2318yes—
278#397C2318yes—
279#397C2318yes—
280#397C2314yes—
281#397C2314yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#396C2314yes—
288#396C2318yes—
289#396C2314yes—
290#396C2318yes—
291#396C2318yes—
292#396C2318yes—
293#396C2318yes—
294#396C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2314yes—
302#394C2314yes—
303#394C2314yes—
304#394C2314yes—
305#394C2314yes—
306#392C2314yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#390C2312yes—
312#390C2314yes—
313#390C2314yes—
314#390C2318yes—
315#390C2312yes—
316#390C2312yes—
317#390C2318yes—
318#390C2312yes—
319#390C2312yes—
320#390C2312yes—
321#390C2318yes—
322#389C2312yes—
323#389C2314yes—
324#389C2314yes—
325#389C2318yes—
326#389C2314yes—
327#389C2314yes—
328#389C2318yes—
329#389C2314yes—
330#389C2318yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2314yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2318yes—
355#388C2314yes—
356#388C2318yes—
357#388C2318yes—
358#387C2314yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2314yes—
365#387C2318yes—
366#387C2318yes—
367#387C2314yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#386C2318yes—
372#386C2318yes—
373#386C2318yes—
374#386C2318yes—
375#386C2318yes—
376#386C2314yes—
377#386C2314yes—
378#386C2318yes—
379#386C2318yes—
380#386C2314yes—
381#386C2318yes—
382#385C2318yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2314yes—
388#385C2314yes—
389#385C2318yes—
390#385C2318yes—
391#384C2311yescharacteristic
392#384C2312yes—
393#384C2312yes—
394#384C2312yes—
395#384C2312yes—
396#384C2314yes—
397#384C2314yes—
398#384C2314yes—
399#384C2318yes—
400#382C2311yescharacteristic
401#382C2312yes—
402#382C2312yes—
403#381C2318yes—
404#381C2318yes—
405#381C2314yes—
406#381C2318yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411#380C2312yes—
412#380C2314yes—
413#380C2312yes—
414#380C2314yes—
415#380C2314yes—
416#380C2318yes—
417#380C2314yes—
418#380C2312yes—
419#380C2318yes—
420#380C2314yes—
421#380C2314yes—
422#380C2318yes—
423#380C2318yes—
424#379C2314yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2312yes—
431C4×C4⋊C4C2312yes—
432C4×C4⋊C4C2312yes—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2312yes—
435C4×C4⋊C4C2312yes—
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2312yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441C4×C22⋊C4C2312yes—
442C4×C22⋊C4C2314yes—
443C4×C22⋊C4C2312yes—
444C4×C22⋊C4C2318yes—
445C4×C22⋊C4C2312yes—
446C4×C22⋊C4C2312yes—
447C4×C22⋊C4C2312yes—
448#376C2311yescharacteristic
449#376C2311yescharacteristic
450C2×#95C2318yes—
451C2×#95C2318yes—
452C43C2311yescharacteristic
453C43C2311yescharacteristic
454C25C2412yes—
455C2×#41—216no—
456C2×#41—216no—
457C2×#41—216no—
458C22×Q8C2414yes—
459C22×D4—24no—
460C22×D4—28no—
461C22×D4C2412yes—
462C22×D4C2418yes—
463C22×D4C2412yes—
464C22×D4C2411yescharacteristic
465C22×D4C2414yes—
466C22×D4C2414yes—
467C22×D4C2418yes—
468C22×D4C2411yescharacteristic
469C23×C4—28no—
470C23×C4—28no—
471C23×C4—44no—
472C23×C4C2418yes—
473C23×C4C2414yes—
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2412yes—
478C23×C4C2412yes—
479C23×C4C2412yes—
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2418yes—
484C23×C4C2414yes—
485C23×C4C2418yes—
486C4⋊Q8—28no—
487C4⋊Q8—48no—
488#127—24no—
489#125—24no—
490#125—28no—
491#125—48no—
492#125—416no—
493#124—48no—
494#123—232no—
495#123—416no—
496#123—416no—
497#123—416no—
498#123—416no—
499C22⋊Q8—216no—
500C22⋊Q8—48no—
501C22⋊Q8—48no—
502C22⋊Q8—48no—
503#121—216no—
504#121—28no—
505#121—416no—
506#121—48no—
507#121—48no—
508#121—416no—
509#121—416no—
510#120—416no—
511C4×Q8—48no—
512C4×Q8—48no—
513C4×D4—24no—
514C4×D4—28no—
515C4×D4—216no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—24no—
519C4×D4—28no—
520C4×D4—24no—
521C4×D4—28no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—416no—
526C4×D4—416no—
527C4×D4#4118yes—
528#117—24no—
529#117—24no—
530#117—28no—
531#117—44no—
532#117—44no—
533#117—48no—
534#117—48no—
535#117—48no—
536#117—416no—
537C2×C4⋊C4—216no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—48no—
540C2×C4⋊C4—48no—
541C2×C4⋊C4—48no—
542C2×C4⋊C4—416no—
543C2×C4⋊C4—416no—
544C2×C4⋊C4—416no—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2412yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2411yescharacteristic
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2412yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2412yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2418yes—
575C2×C4⋊C4C2414yes—
576C2×C4⋊C4C2414yes—
577C2×C4⋊C4C2418yes—
578C2×C4⋊C4C2418yes—
579C2×C4⋊C4C2414yes—
580C2×C4⋊C4C2414yes—
581C2×C4⋊C4C2414yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2411yescharacteristic
584C2×C22⋊C4—28no—
585C2×C22⋊C4—48no—
586C2×C22⋊C4—416no—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C2412yes—
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2414yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2412yes—
595C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2414yes—
608C2×C22⋊C4C2418yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C22⋊C4C2418yes—
613C2×C22⋊C4C2418yes—
614C2×C22⋊C4C2418yes—
615C2×C22⋊C4C2414yes—
616C2×C22⋊C4C2414yes—
617C2×C22⋊C4C2414yes—
618C2×C22⋊C4C2414yes—
619C2×C22⋊C4C2414yes—
620C2×C22⋊C4C2412yes—
621C2×C42—24no—
622C2×C42—28no—
623C2×C42—44no—
624C2×C42C2411yescharacteristic
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2414yes—
629C2×C42C2414yes—
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2412yes—
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2414yes—
637C2×C42C2418yes—
638C2×C42C2418yes—
639C2×C42C2412yes—
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643#95C2414yes—
644#95C2414yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2412yes—
652#95C2412yes—
653#95C2412yes—
654#95C2412yes—
655#95C2414yes—
656#95C2414yes—
657#95C2412yes—
658#95C2412yes—
659#95C2414yes—
660#95C2414yes—
661#95C2418yes—
662#95C2414yes—
663#95C2414yes—
664#95C2414yes—
665#95C2418yes—
666#95C2418yes—
667#95C2414yes—
668#95C2414yes—
669#95C2414yes—
670#95C2418yes—
671#95C2418yes—
672#95C2418yes—
673#95C2418yes—
674C24—24no—
675C24—24no—
676C24—28no—
677C24—42no—
678C24—44no—
679C24C2512yes—
680C24C2514yes—
681C24C2511yescharacteristic
682C24C2512yes—
683#41—464no—
684C2×Q8—28no—
685C2×Q8—28no—
686C2×Q8—28no—
687C2×D4—24no—
688C2×D4—216no—
689C2×D4—216no—
690C2×D4—216no—
691C2×D4—28no—
692C2×D4—28no—
693C2×D4—22no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—28no—
698C2×D4—24no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—416no—
707C2×D4C2×#4114yes—
708C2×D4H(5,𝔽2)18yes—
709C22×C4—22no—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—24no—
713C22×C4—216no—
714C22×C4—24no—
715C22×C4—216no—
716C22×C4—216no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—216no—
720C22×C4—28no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—28no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—22no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—44no—
739C22×C4—432no—
740C22×C4—44no—
741C22×C4—48no—
742C22×C4—42no—
743C22×C4—44no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4C2×#4118yes—
749C22×C42−1+414yes—
750C22×C4C2511yescharacteristic
751C22×C4C2512yes—
752C22×C4C2514yes—
753C22×C4C2512yes—
754C22×C4C2512yes—
755C22×C4C2514yes—
756C22×C4C2518yes—
757C22×C4C2512yes—
758C22×C4C2518yes—
759C22×C4C2511yescharacteristic
760C22×C4C2514yes—
761C22×C4C2514yes—
762C22×C4C2514yes—
763C22×C4C2511yescharacteristic
764C22×C4C2512yes—
765C22×C4C2512yes—
766C22×C4C2511yescharacteristic
767C22×C4C2511yescharacteristic
768C22×C4C2511yescharacteristic
769C4⋊C4—24no—
770C4⋊C4—24no—
771C4⋊C4—22no—
772C4⋊C4—28no—
773C4⋊C4—216no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—216no—
783C4⋊C4—24no—
784C4⋊C4—24no—
785C4⋊C4—24no—
786C4⋊C4—44no—
787C4⋊C4—48no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C4⋊C4—48no—
794C4⋊C4—48no—
795C4⋊C4—48no—
796C4⋊C4—48no—
797C4⋊C4—48no—
798C4⋊C4—48no—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—48no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—48no—
806C4⋊C4—48no—
807C4⋊C4C2×#4114yes—
808C22⋊C4—24no—
809C22⋊C4—28no—
810C22⋊C4—216no—
811C22⋊C4—28no—
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—24no—
815C22⋊C4—28no—
816C22⋊C4—216no—
817C22⋊C4—24no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—44no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—44no—
827C22⋊C4—44no—
828C22⋊C4—44no—
829C22⋊C4—44no—
830C22⋊C4—44no—
831C22⋊C4—44no—
832C22⋊C4—44no—
833C22⋊C4—44no—
834C22⋊C4—48no—
835C22⋊C4—44no—
836C22⋊C4—44no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4C2×#4118yes—
842C42—22no—
843C42—22no—
844C42—22no—
845C42—28no—
846C42—24no—
847C42—22no—
848C42—24no—
849C42—24no—
850C42—28no—
851C42—24no—
852C42—22no—
853C42—22no—
854C42—44no—
855C42—42no—
856C42—42no—
857C42—48no—
858C42—48no—
859C42C2×#4114yes—
860C42H(5,𝔽2)14yes—
861C23—22no—
862C23—22no—
863C23—24no—
864C23—21no—
865C23—21no—
866C23—22no—
867C23—22no—
868C23—24no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—22no—
877C23—24no—
878C23—24no—
879C23—24no—
880C23—48no—
881C23—416no—
882C23—48no—
883C23—84no—
884C23—88no—
885C23C22×#4114yes—
886C23C2×H(5,𝔽2)18yes—
887C23C2×2−1+412yes—
888C23C2611yescharacteristic
889Q8—416no—
890D4—48no—
891D4—432no—
892D4—44no—
893D4—48no—
894D4—88no—
895D4—88no—
896D4—168no—
897D4#540116yescomplemented
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—28no—
906C2×C4—216no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—22no—
918C2×C4—24no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—28no—
922C2×C4—28no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—28no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—28no—
944C2×C4—48no—
945C2×C4—416no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—432no—
949C2×C4—44no—
950C2×C4—416no—
951C2×C4—48no—
952C2×C4—82no—
953C2×C4—88no—
954C2×C4—816no—
955C2×C4—168no—
956C2×C4C22×#4112yes—
957C2×C4C22×#4114yes—
958C2×C4C22×#4112yes—
959C2×C4C22×#4112yes—
960C2×C4C2×H(5,𝔽2)14yes—
961C2×C4C2×H(5,𝔽2)14yes—
962C2×C4C2×H(5,𝔽2)12yes—
963C2×C4C2×2−1+412yes—
964C2×C4C2×2−1+412yes—
965C22—24no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—22no—
970C22—24no—
971C22—41no—
972C22—42no—
973C22—41no—
974C22—42no—
975C22—44no—
976C22—44no—
977C22—42no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—44no—
985C22—42no—
986C22—816no—
987C22C2×#54018yes—
988C22C23×#4111yescharacteristic
989C22C22×H(5,𝔽2)11yescharacteristic
990C22C22×H(5,𝔽2)12yes—
991C22C22×2−1+411yescharacteristic
992C222−1+612yes—
993C4—22no—
994C4—24no—
995C4—22no—
996C4—24no—
997C4—42no—
998C4—41no—
999C4—44no—
1000C4—42no—
1001C4—44no—
1002C4—44no—
1003C4—48no—
1004C4—42no—
1005C4—42no—
1006C4—44no—
1007C4—44no—
1008C4—41no—
1009C4—48no—
1010C4C2×#54014yes—
1011C4#352014yes—
1012C2—28no—
1013C2—42no—
1014C2—84no—
1015C2—82no—
1016C2C22×#54011yescharacteristic
1017C2C2×#352011yescharacteristic
1018C2#6286111yescharacteristic
1019C2#6291412yes—
1020C2#6291512yes—
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. #42641C2semidirect
2. #42633C2semidirect
3. #40894C2semidirect
4. #40889C2semidirect
5. #39606C2semidirect
6. #39513C2semidirect
7. #39378C2semidirect
8. #37883C2semidirect
9. #37851C2semidirect
10. #37706C2semidirect
11. #37627C2semidirect
12. #37502C2semidirect
13. #36179C2semidirect
14. #36153C2semidirect
15. D4×#125C2semidirect
16. #35998C2semidirect
17. #35821C2semidirect
18. #35284C2semidirect
19. #35261C2semidirect
20. #34621C2semidirect
21. C2×#2629C2semidirect
22. #34308C2semidirect
23. D4×#117C2semidirect
27. C2×#540C22semidirect
28. C22×#125C22semidirect
32. #2868C22semidirect
33. #2859C22semidirect
35. #2856C22semidirect
36. #2851C22semidirect
38. #2837C22semidirect
39. #2837C22semidirect
40. #2836C22semidirect
41. #2793C22semidirect
42. #2793C22semidirect
43. #2791C22semidirect
44. #2768C22semidirect
46. #2748C22semidirect
48. #2741C22semidirect
50. #2711C22semidirect
51. #2707C22semidirect
52. #2701C22semidirect
53. #2667C22semidirect
54. #2651C22semidirect
55. #2651C22semidirect
56. #2649C22semidirect
58. #2647C22semidirect
59. #2647C22semidirect
60. #2644C22semidirect
61. #2641C22semidirect
66. #2629C22semidirect
67. #2629C22semidirect
68. #2629C22semidirect
69. #2629C22semidirect
70. #2625C22semidirect
72. #2624C22semidirect
73. #2623C22semidirect
77. #2552C22semidirect
80. #2542C22semidirect
81. #2542C22semidirect
85. #2507C22semidirect
86. #2507C22semidirect
87. #2506C22semidirect
88. #2502C22semidirect
89. #2501C22semidirect
90. #2501C22semidirect
91. #2498C22semidirect
93. #2497C22semidirect
94. #2497C22semidirect
95. #2490C22semidirect
97. #2486C22semidirect
98. #2484C22semidirect
99. #2476C22semidirect
100. #2473C22semidirect
102. #2454C22semidirect
103. #2446C22semidirect
104. #2446C22semidirect
105. #2443C22semidirect
106. #2443C22semidirect
107. #2442C22semidirect
114. #2423C22semidirect
115. #2423C22semidirect
116. #2420C22semidirect
117. #2419C22semidirect
118. #2419C22semidirect
127. #2395C22semidirect
129. C2×#398C22semidirect
131. #2365C22semidirect
132. #2361C22semidirect
133. #2360C22semidirect
134. #2359C22semidirect
140. D4×C4⋊C4C22semidirect
142. #2344C22semidirect
147. #2330C22semidirect
149. #2323C22semidirect
150. #2322C22semidirect
152. #2314C22semidirect
153. C4×C4⋊Q8C22semidirect
154. C4×#127C22semidirect
155. C4×#125C22semidirect
157. C4×#121C22semidirect
160. #2293C22semidirect
161. C2×#389C22semidirect
165. C2×#384C22semidirect
897. D4#540semidirect

Maximal subgroups

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

subgroupindex
#426412
#426332
#408942
#408892
#396062
#395132
#393782
#378832
#378512
#377062
#376272
#375022
#361792
#361532
D4×#1252
#359982
#358212
#352842
#352612
#346212
C2×#26292
#343082
D4×#1172