Finite Group Databasebeta

← #7715975

Subgroups — #7715975

Order 512.

7304 conjugacy classes of subgroups.

The subgroup lattice has 1105 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3536C212yesmaximal, complemented
2#49565C218yesmaximal, complemented
3#47857C218yesmaximal, complemented
4#45095C214yesmaximal, complemented
5#45091C214yesmaximal, complemented
6#44875C214yesmaximal, complemented
7#44869C214yesmaximal, complemented
8#39614C212yesmaximal, complemented
9#39486C212yesmaximal, complemented
10#39486C214yesmaximal, complemented
11#37860C214yesmaximal, complemented
12#36740C214yesmaximal, complemented
13#36561C212yesmaximal, complemented
14#36153C212yesmaximal, complemented
15#35306C212yesmaximal, complemented
16#35011C211yesmaximal, characteristic, complemented
17#35003C212yesmaximal, complemented
18#35002C212yesmaximal, complemented
19#34575C211yesmaximal, characteristic, complemented
20C2×#2363C211yesmaximal, characteristic, complemented
21#3536—232no—
22C2×#562C2218yes—
23C2×#554C2214yes—
24C2×#548C2214yes—
25C2×#547C2214yes—
26C2×#547C2212yescomplemented
27C2×#546C2214yes—
28C2×#546C2218yes—
29C2×#543C2214yes—
30C2×#542C2214yes—
31C2×#539C2214yes—
32C2×#538C2214yes—
33C2×#537C2214yes—
34C2×#537C2214yes—
35C2×#536C2212yescomplemented
36C2×#525C2212yes—
37C22×C22⋊Q8C2212yes—
38C22×#121C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×#117C2211yescharacteristic
41#2857C2212yes—
42#2857C2214yes—
43#2857C2212yes—
44#2857C2214yes—
45#2850C2214yes—
46#2847C2214yes—
47#2726C2214yescomplemented
48#2724C2218yescomplemented
49#2724C2214yescomplemented
50#2717C2218yescomplemented
51#2708C2218yescomplemented
52#2704C2218yescomplemented
53#2701C2218yescomplemented
54#2701C2218yescomplemented
55#2701C2218yescomplemented
56#2700C2218yescomplemented
57#2698C2218yescomplemented
58#2689C2218yescomplemented
59#2687C2218yescomplemented
60#2686C2218yescomplemented
61#2683C2214yescomplemented
62#2682C2218yescomplemented
63#2682C2214yescomplemented
64#2681C2218yescomplemented
65#2680C2218yescomplemented
66#2674C2218yescomplemented
67#2672C2218yescomplemented
68#2671C2218yescomplemented
69#2663C2214yescomplemented
70#2661C2214yescomplemented
71#2659C2211yescharacteristic
72#2659C2212yes—
73#2659C2212yes—
74#2659C2214yes—
75#2656C2211yescharacteristic
76#2639C2212yes—
77#2621C2214yescomplemented
78#2620C2214yescomplemented
79#2617C2212yes—
80#2617C2212yes—
81#2617C2214yes—
82#2583C2218yescomplemented
83#2564C2218yes—
84#2556C2218yescomplemented
85#2555C2218yescomplemented
86#2553C2218yescomplemented
87#2551C2212yescomplemented
88#2549C2218yescomplemented
89#2549C2218yescomplemented
90#2547C2212yescomplemented
91#2542C2212yescomplemented
92#2537C2212yescomplemented
93#2521C2218yescomplemented
94#2506C2214yescomplemented
95#2502C2214yescomplemented
96#2492C2214yescomplemented
97#2486C2214yescomplemented
98#2464C2218yescomplemented
99#2452C2214yescomplemented
100#2451C2214yescomplemented
101#2447C2214yescomplemented
102#2447C2218yescomplemented
103#2443C2218yescomplemented
104#2440C2218yescomplemented
105#2440C2214yescomplemented
106#2440C2218yescomplemented
107#2434C2214yescomplemented
108#2432C2214yescomplemented
109#2432C2218yescomplemented
110#2430C2218yescomplemented
111#2429C2214yescomplemented
112#2427C2214yescomplemented
113#2425C2218yescomplemented
114#2422C2218yescomplemented
115#2422C2214yescomplemented
116#2419C2218yescomplemented
117#2417C2214yes—
118#2417C2218yes—
119#2417C2214yes—
120#2417C2214yescomplemented
121#2416C2214yescomplemented
122#2415C2214yescomplemented
123#2415C2214yescomplemented
124#2413C2218yescomplemented
125#2412C2218yes—
126#2412C2218yes—
127#2412C2218yes—
128#2407C2214yescomplemented
129#2407C2218yescomplemented
130#2406C2218yescomplemented
131#2395C2214yescomplemented
132#2388C2214yescomplemented
133#2365C2212yescomplemented
134#2363C2214yes—
135#2363C2214yes—
136#2363C2218yes—
137#2360C2214yescomplemented
138D4×C4⋊C4C2212yescomplemented
139D4×C4⋊C4C2212yescomplemented
140#2339C2214yescomplemented
141#2325C2214yes—
142#2317C2212yescomplemented
143#2315C2214yes—
144#2315C2212yes—
145#2315C2212yes—
146#2311C2212yescomplemented
147#2310C2212yescomplemented
148C4×#121C2212yes—
149C4×#121C2212yes—
150C4×#121C2214yes—
151C2×#390C2212yes—
152C2×#390C2211yescharacteristic
153C2×#389C2211yescharacteristic
154C2×#388C2212yes—
155C2×#386C2212yes—
156C2×#380C2214yes—
157C2×C4×C4⋊C4C2211yescharacteristic
158C2×C4×C22⋊C4C2211yescharacteristic
159C2×C4×C22⋊C4C2212yes—
160C22×#41C2312yes—
161C22×#41C2314yes—
162C22×#41C2318yes—
163C23×Q8C2312yes—
164C23×D4C2311yescharacteristic
165C23×D4C2312yes—
166C24×C4C2312yes—
167C24×C4C2311yescharacteristic
168#562—264no—
169#554—232no—
170#548—232no—
171#547—232no—
172#547—48no—
173#546—264no—
174#546—232no—
175#543—232no—
176#542—232no—
177#539—232no—
178#538—232no—
179#537—232no—
180#537—232no—
181#536—48no—
182C2×C4⋊Q8C2314yes—
183C2×C4⋊Q8C2312yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2312yes—
186C2×C4⋊Q8C2314yes—
187C2×#126C2318yes—
188C2×#125C2318yes—
189C2×#124C2318yes—
190C2×#124C2314yes—
191C2×#124C2318yes—
192C2×#124C2314yes—
193#525—216no—
194C2×#123C2314yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×#123C2318yes—
198C2×#123C2318yes—
199C2×#123C2318yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×C22⋊Q8—216no—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2314yes—
206C2×C22⋊Q8C2312yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2318yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2318yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2318yes—
216C2×C22⋊Q8C2318yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2318yes—
219C2×#121D4116yescomplemented
220C2×#121C2312yes—
221C2×#121C2312yes—
222C2×#121C2312yes—
223C2×#121C2312yes—
224C2×#121C2318yes—
225C2×#121C2314yes—
226C2×#121C2318yes—
227C2×#121C2318yes—
228C2×#121C2318yes—
229C2×#121C2318yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#120C2318yes—
235C2×#120C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×D4—44no—
238C2×C4×D4C2318yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2318yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×#117—44no—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C2×#117C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C22⋊C4C2311yescharacteristic
264C22×C22⋊C4C2312yes—
265C22×C22⋊C4C2311yescharacteristic
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2318yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2312yes—
270C22×C22⋊C4C2312yes—
271C22×C22⋊C4C2312yes—
272C22×C42C2312yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2312yes—
276#400C2318yes—
277#400C2314yes—
278#399C2318yes—
279#399C2314yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#397C2314yes—
290#397C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2314yes—
307#395C2318yes—
308#395C2318yes—
309#394C2314yes—
310#394C2314yes—
311#394C2314yes—
312#394C2314yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#393C2318yes—
323#393C2314yes—
324#392C2314yes—
325#392C2314yes—
326#392C2318yes—
327#392C2314yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2314yes—
335#391C2318yes—
336#391C2318yes—
337#390C2314yes—
338#390C2314yes—
339#390C2318yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2312yes—
344#390C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2318yes—
361#389C2314yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#386C2314yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2314yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#385C2318yes—
397#385C2318yes—
398#385C2318yes—
399#384C2314yes—
400#384C2312yes—
401#384C2312yes—
402#384C2314yes—
403#382C2314yes—
404#381C2318yes—
405#381C2318yes—
406#381C2318yes—
407#380C2314yes—
408#380C2318yes—
409#380C2314yes—
410#380C2314yes—
411#380C2314yes—
412#380C2312yes—
413#380C2314yes—
414#380C2318yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2312yes—
419#380C2318yes—
420#380C2318yes—
421#380C2314yes—
422#380C2314yes—
423C4×C4⋊C4C2312yes—
424C4×C4⋊C4C2312yes—
425C4×C4⋊C4C2312yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2312yes—
428C4×C4⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2318yes—
435C4×C22⋊C4C2318yes—
436C2×#95C2312yes—
437C2×#95C2312yes—
438C2×#95C2318yes—
439C2×#95C2311yescharacteristic
440C2×#95C2311yescharacteristic
441C25C2411yescharacteristic
442C25C2412yes—
443C2×#41—232no—
444C2×#41—216no—
445C2×#41—28no—
446C2×#41—44no—
447C2×#41—44no—
448C2×#41—48no—
449C2×#41—48no—
450C2×#41—88no—
451C2×#41—88no—
452C22×Q8—28no—
453C22×Q8—44no—
454C22×Q8—44no—
455C22×Q8C2414yes—
456C22×Q8C2412yes—
457C22×Q8C2418yes—
458C22×Q8C2414yes—
459C22×D4—42no—
460C22×D4—42no—
461C22×D4—82no—
462C22×D4—82no—
463C22×D4C2×D418yes—
464C22×D4C2×D4116yes—
465C22×D4C2414yes—
466C22×D4C2412yes—
467C22×D4C2412yes—
468C22×D4C2414yes—
469C22×D4C2412yes—
470C22×D4C2418yes—
471C22×D4C2418yes—
472C22×D4C2414yes—
473C22×D4C2412yes—
474C22×D4C2412yes—
475C22×D4C2418yes—
476C23×C4—28no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—44no—
480C23×C4—82no—
481C23×C4C2×D418yes—
482C23×C4C2414yes—
483C23×C4C2412yes—
484C23×C4C2414yes—
485C23×C4C2411yescharacteristic
486C23×C4C2412yes—
487C23×C4C2411yescharacteristic
488C23×C4C2412yes—
489C23×C4C2411yescharacteristic
490C23×C4C2414yes—
491C23×C4C2414yes—
492C23×C4C2418yes—
493C23×C4C2418yes—
494C23×C4C2418yes—
495C23×C4C2414yes—
496C23×C4C2411yescharacteristic
497C23×C4C2412yes—
498C23×C4C2412yes—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C4⋊Q8—216no—
502C4⋊Q8—48no—
503C4⋊Q8—44no—
504C4⋊Q8—44no—
505C4⋊Q8—84no—
506#126—232no—
507#125—232no—
508#124—216no—
509#124—232no—
510#124—232no—
511#124—48no—
512#123—232no—
513#123—232no—
514#123—232no—
515#123—216no—
516#123—232no—
517#123—416no—
518#123—416no—
519#123—88no—
520C22⋊Q8—216no—
521C22⋊Q8—216no—
522C22⋊Q8—216no—
523C22⋊Q8—216no—
524C22⋊Q8—28no—
525C22⋊Q8—28no—
526C22⋊Q8—232no—
527C22⋊Q8—216no—
528C22⋊Q8—232no—
529C22⋊Q8—216no—
530C22⋊Q8—232no—
531C22⋊Q8—232no—
532C22⋊Q8—232no—
533C22⋊Q8—232no—
534C22⋊Q8—48no—
535C22⋊Q8—88no—
536#121—216no—
537#121—232no—
538#121—232no—
539#121—232no—
540#121—232no—
541#121—28no—
542#121—28no—
543#121—28no—
544#121—28no—
545#121—232no—
546#121—48no—
547#121—84no—
548#121C2×D4132yes—
549#121C2×D4132yes—
550#120—216no—
551#120—232no—
552C4×Q8—216no—
553C4×D4—232no—
554C4×D4—216no—
555C4×D4—216no—
556C4×D4—216no—
557C4×D4—232no—
558C4×D4—28no—
559C4×D4—44no—
560C4×D4—44no—
561C4×D4—44no—
562C4×D4—48no—
563C4×D4—84no—
564#117—28no—
565#117—28no—
566#117—48no—
567#117—44no—
568C2×C4⋊C4—216no—
569C2×C4⋊C4—28no—
570C2×C4⋊C4—216no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—42no—
573C2×C4⋊C4—48no—
574C2×C4⋊C4—84no—
575C2×C4⋊C4—82no—
576C2×C4⋊C4C2×D418yes—
577C2×C4⋊C4C2414yes—
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2418yes—
582C2×C4⋊C4C2418yes—
583C2×C4⋊C4C2418yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2418yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2418yes—
592C2×C4⋊C4C2418yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2418yes—
601C2×C4⋊C4C2418yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2418yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C22⋊C4—216no—
616C2×C22⋊C4—232no—
617C2×C22⋊C4—28no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—44no—
621C2×C22⋊C4—44no—
622C2×C22⋊C4—82no—
623C2×C22⋊C4C2×D4116yes—
624C2×C22⋊C4C2418yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2418yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2418yes—
638C2×C22⋊C4C2414yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2414yes—
650C2×C22⋊C4C2414yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2418yes—
655C2×C42—44no—
656C2×C42—42no—
657C2×C42—42no—
658C2×C42—82no—
659C2×C42C2414yes—
660C2×C42C2414yes—
661C2×C42C2412yes—
662C2×C42C2418yes—
663C2×C42C2412yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2412yes—
669#95C2414yes—
670#95C2414yes—
671#95C2418yes—
672#95C2414yes—
673#95C2414yes—
674#95C2414yes—
675#95C2418yes—
676#95C2418yes—
677#95C2418yes—
678#95C2418yes—
679#95C2414yes—
680#95C2418yes—
681#95C2414yes—
682#95C2414yes—
683#95C2418yes—
684#95C2414yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2418yes—
689#95C2418yes—
690#95C2418yes—
691#95C2418yes—
692C24—22no—
693C24—22no—
694C24—24no—
695C24—24no—
696C24—41no—
697C24—42no—
698C24—42no—
699C24—41no—
700C24—42no—
701C24—42no—
702C24—41no—
703C24—41no—
704C24C22×D418yes—
705C24C22×D414yes—
706C24C2514yes—
707C24C2512yes—
708C24C2514yes—
709C24C2511yescharacteristic
710#41—816no—
711#41—832no—
712#41—864no—
713C2×Q8—28no—
714C2×Q8—24no—
715C2×Q8—28no—
716C2×Q8—216no—
717C2×Q8—28no—
718C2×Q8—28no—
719C2×Q8—48no—
720C2×Q8—44no—
721C2×Q8—42no—
722C2×Q8—48no—
723C2×Q8—44no—
724C2×Q8—42no—
725C2×Q8—816no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—28no—
730C2×D4—216no—
731C2×D4—28no—
732C2×D4—216no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—24no—
736C2×D4—24no—
737C2×D4—24no—
738C2×D4—416no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—42no—
748C2×D4—48no—
749C2×D4—42no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—816no—
758C2×D4C22×D418yes—
759C2×D4C22×D4132yes—
760C2×D4C22×D418yes—
761C22×C4—22no—
762C22×C4—24no—
763C22×C4—22no—
764C22×C4—24no—
765C22×C4—28no—
766C22×C4—24no—
767C22×C4—28no—
768C22×C4—216no—
769C22×C4—216no—
770C22×C4—22no—
771C22×C4—24no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—24no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—216no—
780C22×C4—28no—
781C22×C4—416no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—41no—
797C22×C4—42no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—42no—
801C22×C4—48no—
802C22×C4—41no—
803C22×C4—48no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—44no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—816no—
813C22×C4C22×D418yes—
814C22×C4C22×D414yes—
815C22×C4C22×D414yes—
816C22×C4C22×D418yes—
817C22×C4C22×D418yes—
818C22×C42−1+414yes—
819C22×C42−1+414yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2518yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2518yes—
829C22×C4C2512yes—
830C22×C4C2514yes—
831C22×C4C2511yescharacteristic
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2512yes—
835C22×C4C2511yescharacteristic
836C4⋊C4—28no—
837C4⋊C4—216no—
838C4⋊C4—216no—
839C4⋊C4—216no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—216no—
844C4⋊C4—28no—
845C4⋊C4—28no—
846C4⋊C4—216no—
847C4⋊C4—216no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—216no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—44no—
857C4⋊C4—42no—
858C4⋊C4—44no—
859C4⋊C4—48no—
860C4⋊C4—48no—
861C4⋊C4—42no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—42no—
871C4⋊C4C22×D418yes—
872C4⋊C4C22×D418yes—
873C4⋊C4H(5,𝔽2)14yes—
874C22⋊C4—216no—
875C22⋊C4—28no—
876C22⋊C4—216no—
877C22⋊C4—216no—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—216no—
882C22⋊C4—216no—
883C22⋊C4—28no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—216no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4C22×D4132yes—
905C42—28no—
906C42—216no—
907C42—28no—
908C42—24no—
909C42—24no—
910C42—42no—
911C42—44no—
912C42—42no—
913C42—44no—
914C42—44no—
915C23—21no—
916C23—21no—
917C23—21no—
918C23—21no—
919C23—22no—
920C23—24no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—22no—
931C23—28no—
932C23—216no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—44no—
941C23—48no—
942C23—44no—
943C23—48no—
944C23—84no—
945C23—82no—
946C23—82no—
947C23—84no—
948C23—82no—
949C23—84no—
950C23—82no—
951C23—84no—
952C23C23×D418yes—
953C23C23×D414yes—
954C23C23×D412yes—
955C23C2×2−1+412yes—
956C23C2×2−1+412yes—
957C23C2611yescharacteristic
958Q8—416no—
959Q8—88no—
960Q8—84no—
961Q8—816no—
962D4—216no—
963D4—48no—
964D4—432no—
965D4—48no—
966D4—416no—
967D4—416no—
968D4—84no—
969D4—84no—
970D4—88no—
971D4—816no—
972D4—816no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—28no—
986C2×C4—216no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—28no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—22no—
995C2×C4—28no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—28no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—28no—
1012C2×C4—28no—
1013C2×C4—24no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—48no—
1018C2×C4—44no—
1019C2×C4—416no—
1020C2×C4—48no—
1021C2×C4—416no—
1022C2×C4—416no—
1023C2×C4—88no—
1024C2×C4—816no—
1025C2×C4—82no—
1026C2×C4—84no—
1027C2×C4—82no—
1028C2×C4—88no—
1029C2×C4—816no—
1030C2×C4—816no—
1031C2×C4C23×D418yes—
1032C2×C4C23×D412yes—
1033C2×C4C23×D414yes—
1034C2×C4C23×D412yes—
1035C2×C4C2×H(5,𝔽2)14yes—
1036C2×C4C2×H(5,𝔽2)12yes—
1037C2×C4C2×2−1+414yes—
1038C2×C4C2×2−1+414yes—
1039C2×C4#58512yes—
1040C22—22no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—24no—
1047C22—28no—
1048C22—24no—
1049C22—28no—
1050C22—24no—
1051C22—28no—
1052C22—44no—
1053C22—42no—
1054C22—42no—
1055C22—44no—
1056C22—42no—
1057C22—44no—
1058C22—42no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—88no—
1068C22—816no—
1069C22#349914yes—
1070C22C24×D411yescharacteristic
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C22×2−1+411yescharacteristic
1073C22C22×2−1+411yescharacteristic
1074C22C2×#58511yescharacteristic
1075C22H(7,𝔽2)11yescharacteristic
1076C22H(7,𝔽2)11yescharacteristic
1077C4—22no—
1078C4—24no—
1079C4—28no—
1080C4—24no—
1081C4—24no—
1082C4—24no—
1083C4—44no—
1084C4—48no—
1085C4—44no—
1086C4—48no—
1087C4—44no—
1088C4—42no—
1089C4—42no—
1090C4—44no—
1091C4—42no—
1092C4#349614yes—
1093C2—24no—
1094C2—44no—
1095C2—48no—
1096C2—84no—
1097C2C2×#349611yescharacteristic
1098C2C2×#349911yescharacteristic
1099C2#6284211yescharacteristic
1100C2#6289411yescharacteristic
1101C2#6290211yescharacteristic
1102C2#6291711yescharacteristic
1103C2#6292911yescharacteristic
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. C2×#3536C2semidirect
2. #49565C2semidirect
3. #47857C2semidirect
4. #45095C2semidirect
5. #45091C2semidirect
6. #44875C2semidirect
7. #44869C2semidirect
8. #39614C2semidirect
9. #39486C2semidirect
10. #39486C2semidirect
11. #37860C2semidirect
12. #36740C2semidirect
13. #36561C2semidirect
14. #36153C2semidirect
15. #35306C2semidirect
16. #35011C2semidirect
17. #35003C2semidirect
18. #35002C2semidirect
19. #34575C2semidirect
20. C2×#2363C2semidirect
26. C2×#547C22semidirect
35. C2×#536C22semidirect
47. #2726C22semidirect
48. #2724C22semidirect
49. #2724C22semidirect
50. #2717C22semidirect
51. #2708C22semidirect
52. #2704C22semidirect
53. #2701C22semidirect
54. #2701C22semidirect
55. #2701C22semidirect
56. #2700C22semidirect
57. #2698C22semidirect
58. #2689C22semidirect
59. #2687C22semidirect
60. #2686C22semidirect
61. #2683C22semidirect
62. #2682C22semidirect
63. #2682C22semidirect
64. #2681C22semidirect
65. #2680C22semidirect
66. #2674C22semidirect
67. #2672C22semidirect
68. #2671C22semidirect
69. #2663C22semidirect
70. #2661C22semidirect
77. #2621C22semidirect
78. #2620C22semidirect
82. #2583C22semidirect
84. #2556C22semidirect
85. #2555C22semidirect
86. #2553C22semidirect
87. #2551C22semidirect
88. #2549C22semidirect
89. #2549C22semidirect
90. #2547C22semidirect
91. #2542C22semidirect
92. #2537C22semidirect
93. #2521C22semidirect
94. #2506C22semidirect
95. #2502C22semidirect
96. #2492C22semidirect
97. #2486C22semidirect
98. #2464C22semidirect
99. #2452C22semidirect
100. #2451C22semidirect
101. #2447C22semidirect
102. #2447C22semidirect
103. #2443C22semidirect
104. #2440C22semidirect
105. #2440C22semidirect
106. #2440C22semidirect
107. #2434C22semidirect
108. #2432C22semidirect
109. #2432C22semidirect
110. #2430C22semidirect
111. #2429C22semidirect
112. #2427C22semidirect
113. #2425C22semidirect
114. #2422C22semidirect
115. #2422C22semidirect
116. #2419C22semidirect
120. #2417C22semidirect
121. #2416C22semidirect
122. #2415C22semidirect
123. #2415C22semidirect
124. #2413C22semidirect
128. #2407C22semidirect
129. #2407C22semidirect
130. #2406C22semidirect
131. #2395C22semidirect
132. #2388C22semidirect
133. #2365C22semidirect
137. #2360C22semidirect
138. D4×C4⋊C4C22semidirect
139. D4×C4⋊C4C22semidirect
140. #2339C22semidirect
142. #2317C22semidirect
146. #2311C22semidirect
147. #2310C22semidirect
219. C2×#121D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35362
#495652
#478572
#450952
#450912
#448752
#448692
#396142
#394862
#378602
#367402
#365612
#361532
#353062
#350112
#350032
#350022
#345752
C2×#23632