Finite Group Databasebeta

← #7693272

Subgroups — #7693272

Order 512.

7468 conjugacy classes of subgroups.

The subgroup lattice has 1045 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3518C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#59652C213yesmaximal, complemented
4#59410C216yesmaximal, complemented
5#59056C213yesmaximal, complemented
6#59052C213yesmaximal, complemented
7#45101C216yesmaximal, complemented
8#44882C216yesmaximal, complemented
9#39381C216yesmaximal, complemented
10#39137C213yesmaximal, complemented
11#39136C213yesmaximal, complemented
12#36597C213yesmaximal, complemented
13Q8×#121C211yesmaximal, characteristic, complemented
14#36465C211yesmaximal, characteristic, complemented
15#36465C212yesmaximal, complemented
16#36455C211yesmaximal, characteristic, complemented
17#36150C213yesmaximal, complemented
18#35831C212yesmaximal, complemented
19#35771C212yesmaximal, complemented
20#34934C213yesmaximal, complemented
21#34312C212yesmaximal, complemented
22C4×Q82C211yesmaximal, characteristic, complemented
23C4×#548C211yesmaximal, characteristic, complemented
24#3522—216no—
25#3518—216no—
26C2×#559C2213yes—
27C2×Q82C2211yescharacteristic
28C2×#556C2216yes—
29C2×#556C2213yes—
30C2×#555C2213yes—
31C2×#554C2213yes—
32C2×#550C2211yescharacteristic
33C2×#550C2212yes—
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2212yes—
36C2×#548C2212yes—
37C2×#548C2212yes—
38C2×#548C2212yes—
39C2×#548C2211yescharacteristic
40C2×#548C2212yes—
41C2×#547C2216yes—
42C2×#542C2216yes—
43C2×#542C2216yes—
44C2×#533C2213yes—
45C2×#532C2213yes—
46C2×#529C2213yes—
47C2×#529C2213yes—
48C2×#520C2212yes—
49C2×#519C2212yes—
50C2×C4×#41C2211yescharacteristic
51C22×C4×Q8C2211yescharacteristic
52#2858C2213yes—
53#2858C2216yes—
54#2857C2213yes—
55#2856C2213yes—
56#2733C22112yes—
57#2732C22112yes—
58#2730C22112yes—
59#2727C22112yes—
60#2705C22112yes—
61#2705C22112yes—
62#2682C22112yes—
63#2620C2216yes—
64#2620C2216yes—
65#2554C2216yes—
66#2554C22112yes—
67#2554C22112yes—
68#2554C2216yes—
69#2552C2213yes—
70#2548C2213yes—
71#2546C2213yes—
72#2545C2216yes—
73#2544C2216yes—
74#2542C2216yes—
75#2542C2213yes—
76#2541C2216yes—
77#2541C2213yes—
78#2541C2213yes—
79#2541C2213yes—
80#2540C2216yes—
81#2540C2216yes—
82#2540C2216yes—
83#2540C2216yes—
84#2540C2216yes—
85#2540C2216yes—
86#2538C2213yes—
87#2538C2216yes—
88#2538C2213yes—
89#2537C2213yes—
90#2537C2216yes—
91#2512C2216yes—
92#2490C2213yes—
93#2490C2213yes—
94#2454C2216yes—
95#2448C2216yes—
96#2445C2216yes—
97#2441C2216yes—
98#2431C22112yes—
99#2429C2216yes—
100#2429C2216yes—
101#2428C2216yes—
102#2428C2216yes—
103#2428C2216yes—
104#2427C2216yes—
105#2426C22112yes—
106#2426C2216yes—
107#2426C2216yes—
108#2426C2211yescharacteristic
109#2426C2213yes—
110#2426C2216yes—
111#2423C22112yes—
112#2417C2216yes—
113#2417C2216yes—
114#2416C2216yes—
115#2415C2216yes—
116#2414C2216yes—
117#2414C2216yes—
118#2414C2216yes—
119#2407C2216yes—
120#2392C2216yes—
121#2392C2216yes—
122#2369C2216yes—
123#2369C2213yes—
124#2367C2216yes—
125#2367C2213yes—
126#2363C2216yes—
127#2363C2216yes—
128#2363C2216yes—
129#2362C2213yes—
130#2361C2213yes—
131#2360C2216yes—
132#2352C2216yes—
133#2352C2213yes—
134#2351C2211yescharacteristic
135Q8×C4⋊C4C2211yescharacteristic
136Q8×C4⋊C4C2212yes—
137Q8×C4⋊C4C2213yes—
138#2341C2212yes—
139#2341C2216yes—
140#2341C2211yescharacteristic
141Q8×C22⋊C4C2212yes—
142Q8×C22⋊C4C2211yescharacteristic
143#2324C2216yes—
144#2323C2216yes—
145C4×C4⋊Q8C2213yes—
146C4×C4⋊Q8C2216yes—
147C4×#127C2213yes—
148C4×#127C2216yes—
149C4×#124C2213yes—
150C4×#124C2216yes—
151C4×C22⋊Q8C2213yes—
152C4×#121C2213yes—
153C4×#121C2213yes—
154C4×#121C2213yes—
155#2293C2216yes—
156C42×Q8C2212yes—
157C42×Q8C2211yescharacteristic
158C42×Q8C2213yes—
159C42×D4C2213yes—
160C22×#41C2311yescharacteristic
161C22×#41C2312yes—
162C22×#41C2316yes—
163C23×Q8C2311yescharacteristic
164C23×Q8C2312yes—
165#559—224no—
166Q82D4116yescomplemented
167#556—248no—
168#556—224no—
169#555—224no—
170#554—224no—
171#550—28no—
172#550—48no—
173D4×Q8—28no—
174D4×Q8—48no—
175#548—216no—
176#548—216no—
177#548—216no—
178#548—28no—
179#548—48no—
180#547—248no—
181#542—248no—
182#542—248no—
183#533—224no—
184#532—224no—
185C2×C4⋊Q8C2313yes—
186C2×C4⋊Q8C2316yes—
187C2×C4⋊Q8C2313yes—
188C2×C4⋊Q8C2316yes—
189C2×#127C2313yes—
190C2×#127C2313yes—
191C2×#127C2316yes—
192C2×#127C2316yes—
193#529—224no—
194#529—224no—
195C2×#126C2316yes—
196C2×#126C2316yes—
197C2×#126C23112yes—
198C2×#125C2313yes—
199C2×#125C2313yes—
200C2×#124C2316yes—
201C2×#124C2313yes—
202C2×#124C2316yes—
203C2×#124C2316yes—
204C2×#124C2311yescharacteristic
205C2×#124C2313yes—
206C2×#124C2316yes—
207C2×#124C23112yes—
208C2×#124C2316yes—
209C2×#123C2316yes—
210C2×#123C2316yes—
211C2×#123C23112yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2313yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2316yes—
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2313yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C23112yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C2316yes—
223C2×C22⋊Q8C2316yes—
224C2×#121C2316yes—
225C2×#121C2313yes—
226C2×#121C2313yes—
227C2×#121C2313yes—
228C2×#121C2316yes—
229C2×#121C2316yes—
230C2×#121C2313yes—
231C2×#121C2316yes—
232C2×#121C2311yescharacteristic
233C2×#121C2316yes—
234C2×#121C2316yes—
235C2×#121C2316yes—
236C2×#121C2316yes—
237C2×#121C2316yes—
238C2×#121C23112yes—
239#520—216no—
240#519—216no—
241C4×#41—28no—
242C2×C4×Q8—28no—
243C2×C4×Q8C2316yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2316yes—
249C2×C4×Q8C2316yes—
250C2×C4×Q8C2313yes—
251C2×C4×Q8C2313yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2313yes—
254C2×C4×Q8C2316yes—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2313yes—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×D4C2313yes—
260C2×C4×D4C2316yes—
261C2×C4×D4C2316yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×C4×D4C2316yes—
266C2×C4×D4C2313yes—
267C2×C4×D4C2316yes—
268C2×C4×D4C2316yes—
269C2×C4×D4C2313yes—
270C2×C4×D4C2316yes—
271C2×C4×D4C2316yes—
272C2×C4×D4C2316yes—
273C2×C4×D4C2313yes—
274C2×C4×D4C2313yes—
275C2×#117C2316yes—
276C2×#117C2316yes—
277C2×#117C2313yes—
278C2×#117C2316yes—
279C2×#117C2316yes—
280C22×C4⋊C4C2316yes—
281C22×C4⋊C4C2313yes—
282C22×C42C2313yes—
283C22×C42C2313yes—
284#399C23112yes—
285#399C23112yes—
286#399C23112yes—
287#398C2316yes—
288#398C2316yes—
289#398C23112yes—
290#397C2316yes—
291#397C2316yes—
292#396C2316yes—
293#396C23112yes—
294#396C23112yes—
295#396C23112yes—
296#396C2312yes—
297#396C2316yes—
298#396C2316yes—
299#396C23112yes—
300#394C2316yes—
301#394C23112yes—
302#394C23112yes—
303#394C23112yes—
304#394C2312yes—
305#394C2316yes—
306#394C2316yes—
307#394C2316yes—
308#394C2316yes—
309#394C23112yes—
310#392C2316yes—
311#392C2316yes—
312#392C23112yes—
313#392C23112yes—
314#392C23112yes—
315#392C23112yes—
316#391C2316yes—
317#391C23112yes—
318#391C2316yes—
319#391C2316yes—
320#391C2313yes—
321#391C2313yes—
322#390C2311yescharacteristic
323#390C2312yes—
324#390C2316yes—
325#390C2313yes—
326#390C2316yes—
327#390C2316yes—
328#390C2316yes—
329#390C2316yes—
330#390C2316yes—
331#390C2316yes—
332#390C2316yes—
333#390C2316yes—
334#390C2316yes—
335#390C2316yes—
336#390C2313yes—
337#390C2316yes—
338#390C2313yes—
339#390C23112yes—
340#390C2313yes—
341#390C2316yes—
342#390C23112yes—
343#390C23112yes—
344#390C2316yes—
345#390C23112yes—
346#390C2316yes—
347#390C2313yes—
348#389C2316yes—
349#389C2316yes—
350#389C2316yes—
351#389C2316yes—
352#389C23112yes—
353#389C2313yes—
354#389C2316yes—
355#389C2313yes—
356#389C2316yes—
357#389C2316yes—
358#389C2316yes—
359#389C2313yes—
360#389C23112yes—
361#389C2311yescharacteristic
362#388C23112yes—
363#388C23112yes—
364#388C2316yes—
365#388C2316yes—
366#388C2316yes—
367#388C2316yes—
368#388C23112yes—
369#388C23112yes—
370#388C2316yes—
371#388C2316yes—
372#388C2312yes—
373#388C2316yes—
374#388C2316yes—
375#387C23112yes—
376#387C2316yes—
377#386C23112yes—
378#386C2316yes—
379#386C23112yes—
380#386C23112yes—
381#386C2316yes—
382#386C2316yes—
383#385C23112yes—
384#385C2316yes—
385#384C2316yes—
386#384C2313yes—
387#384C2313yes—
388#384C2316yes—
389#382C2313yes—
390#380C2316yes—
391#380C2316yes—
392#380C2313yes—
393#380C2316yes—
394#380C2313yes—
395#380C23112yes—
396#380C2313yes—
397#380C2313yes—
398C4×C4⋊C4C2316yes—
399C4×C4⋊C4C2313yes—
400C4×C4⋊C4C2313yes—
401C4×C4⋊C4C2316yes—
402C4×C4⋊C4C2316yes—
403C4×C4⋊C4C2316yes—
404C4×C4⋊C4C2313yes—
405C4×C4⋊C4C2313yes—
406C4×C4⋊C4C2313yes—
407C4×C4⋊C4C2316yes—
408C4×C4⋊C4C2313yes—
409C4×C4⋊C4C2313yes—
410C4×C4⋊C4C2313yes—
411C4×C4⋊C4C2316yes—
412C4×C4⋊C4C2313yes—
413C4×C22⋊C4C2313yes—
414C4×C22⋊C4C2316yes—
415C4×C22⋊C4C2313yes—
416C4×C22⋊C4C23112yes—
417C4×C22⋊C4C2316yes—
418C4×C22⋊C4C2313yes—
419C4×C22⋊C4C23112yes—
420C4×C22⋊C4C2313yes—
421C4×C22⋊C4C2316yes—
422C4×C22⋊C4C2313yes—
423C4×C22⋊C4C2311yescharacteristic
424C43C2313yes—
425C43C2316yes—
426C2×#41—24no—
427C2×#41—28no—
428C2×#41—224no—
429C2×#41—24no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—412no—
434C2×#41—86no—
435C22×Q8—24no—
436C22×Q8—28no—
437C22×Q8—24no—
438C22×Q8—28no—
439C22×Q8—28no—
440C22×Q8—24no—
441C22×Q8C2413yes—
442C22×Q8C2416yes—
443C22×Q8C2411yescharacteristic
444C22×Q8C2416yes—
445C22×Q8C2411yescharacteristic
446C22×D4C2411yescharacteristic
447C22×D4C2413yes—
448C22×D4C2413yes—
449C22×D4C2416yes—
450C22×D4C2413yes—
451C22×D4C2412yes—
452C22×D4C2416yes—
453C22×D4C2416yes—
454C22×D4C2416yes—
455C22×D4C2416yes—
456C22×D4C2416yes—
457C22×D4C2416yes—
458C22×D4C24112yes—
459C23×C4C2416yes—
460C23×C4C2413yes—
461C23×C4C2416yes—
462C23×C4C2413yes—
463C23×C4C2413yes—
464C23×C4C2411yescharacteristic
465C23×C4C2413yes—
466C23×C4C24112yes—
467C23×C4C2413yes—
468C4⋊Q8—212no—
469C4⋊Q8—412no—
470C4⋊Q8C2×D4124yes—
471C4⋊Q8C2×D4148yes—
472#127—212no—
473#127—46no—
474#127—412no—
475#127—412no—
476#126—224no—
477#126—224no—
478#126—248no—
479#125—212no—
480#125—212no—
481#124—24no—
482#124—212no—
483#124—224no—
484#124—248no—
485#124—224no—
486#124—224no—
487#124—224no—
488#124—212no—
489#124—412no—
490#123—224no—
491#123—224no—
492#123—248no—
493C22⋊Q8—24no—
494C22⋊Q8—212no—
495C22⋊Q8—224no—
496C22⋊Q8—248no—
497C22⋊Q8—224no—
498C22⋊Q8—224no—
499C22⋊Q8—224no—
500C22⋊Q8—224no—
501C22⋊Q8—212no—
502C22⋊Q8—412no—
503C22⋊Q8—412no—
504C22⋊Q8—412no—
505#121—212no—
506#121—212no—
507#121—224no—
508#121—224no—
509#121—224no—
510#121—212no—
511#121—224no—
512#121—24no—
513#121—212no—
514#121—412no—
515#121—412no—
516#121—412no—
517#121—412no—
518#121—86no—
519#121—812no—
520C4×Q8—24no—
521C4×Q8—24no—
522C4×Q8—224no—
523C4×Q8—24no—
524C4×Q8—28no—
525C4×Q8—212no—
526C4×Q8—224no—
527C4×Q8—24no—
528C4×Q8—212no—
529C4×Q8—224no—
530C4×Q8—46no—
531C4×Q8—86no—
532C4×Q8C2×D418yes—
533C4×Q8C2×D4116yes—
534C4×Q8C2×D4124yes—
535C4×Q8#4118yescomplemented
536C4×D4—212no—
537C4×D4—224no—
538C4×D4—224no—
539C4×D4—212no—
540C4×D4—224no—
541C4×D4—224no—
542C4×D4—224no—
543C4×D4—212no—
544C4×D4—212no—
545C4×D4—212no—
546C4×D4—224no—
547C4×D4—46no—
548C4×D4—412no—
549C4×D4—412no—
550C4×D4—412no—
551C4×D4—46no—
552#117—212no—
553#117—224no—
554#117—224no—
555#117—224no—
556#117—224no—
557C2×C4⋊C4—212no—
558C2×C4⋊C4—224no—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2412yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2416yes—
566C2×C4⋊C4C2416yes—
567C2×C4⋊C4C2411yescharacteristic
568C2×C4⋊C4C2416yes—
569C2×C4⋊C4C2416yes—
570C2×C4⋊C4C2413yes—
571C2×C4⋊C4C2416yes—
572C2×C4⋊C4C2413yes—
573C2×C4⋊C4C2416yes—
574C2×C4⋊C4C2413yes—
575C2×C4⋊C4C2416yes—
576C2×C4⋊C4C2412yes—
577C2×C4⋊C4C2412yes—
578C2×C4⋊C4C2416yes—
579C2×C4⋊C4C2416yes—
580C2×C4⋊C4C2413yes—
581C2×C4⋊C4C2413yes—
582C2×C4⋊C4C2416yes—
583C2×C4⋊C4C24112yes—
584C2×C4⋊C4C2416yes—
585C2×C4⋊C4C24112yes—
586C2×C4⋊C4C2416yes—
587C2×C4⋊C4C2413yes—
588C2×C4⋊C4C2413yes—
589C2×C4⋊C4C2416yes—
590C2×C4⋊C4C2413yes—
591C2×C4⋊C4C2411yescharacteristic
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2416yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C24112yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2412yes—
600C2×C22⋊C4C2411yescharacteristic
601C2×C22⋊C4C2411yescharacteristic
602C2×C22⋊C4C2412yes—
603C2×C22⋊C4C2416yes—
604C2×C22⋊C4C24112yes—
605C2×C22⋊C4C2416yes—
606C2×C22⋊C4C2416yes—
607C2×C22⋊C4C2416yes—
608C2×C22⋊C4C2413yes—
609C2×C22⋊C4C2416yes—
610C2×C22⋊C4C24112yes—
611C2×C22⋊C4C2416yes—
612C2×C22⋊C4C2416yes—
613C2×C22⋊C4C2412yes—
614C2×C22⋊C4C2412yes—
615C2×C22⋊C4C2416yes—
616C2×C22⋊C4C2416yes—
617C2×C22⋊C4C2416yes—
618C2×C22⋊C4C2416yes—
619C2×C22⋊C4C2416yes—
620C2×C22⋊C4C2413yes—
621C2×C22⋊C4C2413yes—
622C2×C22⋊C4C2413yes—
623C2×C22⋊C4C2416yes—
624C2×C22⋊C4C2416yes—
625C2×C22⋊C4C2416yes—
626C2×C22⋊C4C24112yes—
627C2×C22⋊C4C24112yes—
628C2×C42—212no—
629C2×C42—212no—
630C2×C42C2413yes—
631C2×C42C2413yes—
632C2×C42C24112yes—
633C2×C42C2413yes—
634C2×C42C2413yes—
635C2×C42C2413yes—
636C2×C42C2416yes—
637C2×C42C2413yes—
638C2×C42C2413yes—
639C2×C42C2411yescharacteristic
640C2×C42C2412yes—
641C2×C42C2411yescharacteristic
642C2×C42C2413yes—
643C2×C42C2413yes—
644C2×C42C2416yes—
645C2×C42C2416yes—
646C2×C42C2416yes—
647C2×C42C2416yes—
648C2×C42C2413yes—
649C2×C42C2413yes—
650#95C2413yes—
651#95C2411yescharacteristic
652#95C2411yescharacteristic
653#95C2416yes—
654#95C2412yes—
655#95C2416yes—
656#95C2413yes—
657#95C2413yes—
658#95C2413yes—
659#95C24112yes—
660#95C2416yes—
661#95C2416yes—
662#95C2416yes—
663#95C24112yes—
664#95C2416yes—
665#95C2416yes—
666#95C2416yes—
667#95C2416yes—
668C24C2513yes—
669C24C2512yes—
670C24C2516yes—
671C24C2511yescharacteristic
672#41—416no—
673#41—432no—
674#41—848no—
675C2×Q8—26no—
676C2×Q8—212no—
677C2×Q8—26no—
678C2×Q8—212no—
679C2×Q8—212no—
680C2×Q8—26no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—46no—
684C2×Q8—46no—
685C2×Q8—416no—
686C2×Q8—432no—
687C2×Q8C22×D414yes—
688C2×Q8C22×D4124yes—
689C2×Q8C22×D414yes—
690C2×Q8C2×#4114yes—
691C2×Q8H(5,𝔽2)14yes—
692C2×D4—26no—
693C2×D4—24no—
694C2×D4—212no—
695C2×D4—22no—
696C2×D4—26no—
697C2×D4—26no—
698C2×D4—212no—
699C2×D4—212no—
700C2×D4—212no—
701C2×D4—212no—
702C2×D4—26no—
703C2×D4—26no—
704C2×D4—212no—
705C2×D4—212no—
706C2×D4—212no—
707C2×D4—26no—
708C2×D4—24no—
709C2×D4—22no—
710C2×D4—26no—
711C2×D4—212no—
712C2×D4—26no—
713C2×D4—22no—
714C2×D4—42no—
715C2×D4—43no—
716C2×D4—46no—
717C2×D4—46no—
718C2×D4—46no—
719C2×D4—46no—
720C2×D4—46no—
721C2×D4—46no—
722C2×D4—46no—
723C2×D4—46no—
724C2×D4—46no—
725C2×D4—46no—
726C2×D4—46no—
727C2×D4—46no—
728C2×D4—412no—
729C2×D4—412no—
730C2×D4—412no—
731C22×C4—26no—
732C22×C4—22no—
733C22×C4—26no—
734C22×C4—26no—
735C22×C4—26no—
736C22×C4—26no—
737C22×C4—212no—
738C22×C4—212no—
739C22×C4—26no—
740C22×C4—212no—
741C22×C4—212no—
742C22×C4—26no—
743C22×C4—26no—
744C22×C4—212no—
745C22×C4—212no—
746C22×C4—26no—
747C22×C4—22no—
748C22×C4—26no—
749C22×C4—22no—
750C22×C4—26no—
751C22×C4—26no—
752C22×C4—224no—
753C22×C4—43no—
754C22×C4—43no—
755C22×C4—43no—
756C22×C4—412no—
757C22×C4—412no—
758C22×C4C2511yescharacteristic
759C22×C4C2513yes—
760C22×C4C2511yescharacteristic
761C22×C4C2513yes—
762C22×C4C2513yes—
763C22×C4C2516yes—
764C22×C4C2511yescharacteristic
765C22×C4C2511yescharacteristic
766C22×C4C2513yes—
767C22×C4C2516yes—
768C22×C4C2512yes—
769C22×C4C2513yes—
770C22×C4C2516yes—
771C22×C4C2512yes—
772C22×C4C2513yes—
773C22×C4C2511yescharacteristic
774C22×C4C2512yes—
775C22×C4C2513yes—
776C22×C4C2511yescharacteristic
777C4⋊C4—26no—
778C4⋊C4—212no—
779C4⋊C4—212no—
780C4⋊C4—26no—
781C4⋊C4—24no—
782C4⋊C4—26no—
783C4⋊C4—212no—
784C4⋊C4—212no—
785C4⋊C4—22no—
786C4⋊C4—212no—
787C4⋊C4—212no—
788C4⋊C4—212no—
789C4⋊C4—26no—
790C4⋊C4—212no—
791C4⋊C4—26no—
792C4⋊C4—212no—
793C4⋊C4—24no—
794C4⋊C4—26no—
795C4⋊C4—43no—
796C4⋊C4—43no—
797C4⋊C4—42no—
798C4⋊C4—46no—
799C4⋊C4—46no—
800C4⋊C4—46no—
801C4⋊C4—46no—
802C4⋊C4—412no—
803C4⋊C4—412no—
804C4⋊C4C22×D4112yes—
805C4⋊C4C22×D4124yes—
806C4⋊C4C22×D4112yes—
807C4⋊C4C22×D4124yes—
808C4⋊C4C2×#41112yes—
809C4⋊C42−1+414yes—
810C22⋊C4—22no—
811C22⋊C4—212no—
812C22⋊C4—24no—
813C22⋊C4—212no—
814C22⋊C4—212no—
815C22⋊C4—212no—
816C22⋊C4—224no—
817C22⋊C4—24no—
818C22⋊C4—24no—
819C22⋊C4—212no—
820C22⋊C4—224no—
821C22⋊C4—212no—
822C22⋊C4—212no—
823C22⋊C4—212no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—26no—
827C22⋊C4—212no—
828C22⋊C4—212no—
829C22⋊C4—224no—
830C22⋊C4—24no—
831C22⋊C4—212no—
832C22⋊C4—43no—
833C22⋊C4—43no—
834C22⋊C4—43no—
835C22⋊C4—42no—
836C22⋊C4—46no—
837C22⋊C4—46no—
838C22⋊C4—46no—
839C22⋊C4—46no—
840C22⋊C4—46no—
841C22⋊C4—412no—
842C22⋊C4—412no—
843C22⋊C4—46no—
844C22⋊C4—46no—
845C22⋊C4—46no—
846C42—22no—
847C42—26no—
848C42—26no—
849C42—26no—
850C42—26no—
851C42—26no—
852C42—224no—
853C42—26no—
854C42—212no—
855C42—24no—
856C42—22no—
857C42—26no—
858C42—43no—
859C42—46no—
860C42—43no—
861C42—46no—
862C42—46no—
863C42C22×D4112yes—
864C42C22×D4124yes—
865C42C2×#41112yes—
866C23—21no—
867C23—21no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—21no—
872C23—23no—
873C23—22no—
874C23—26no—
875C23—23no—
876C23—26no—
877C23—22no—
878C23—22no—
879C23—26no—
880C23—23no—
881C23—22no—
882C23—26no—
883C23—23no—
884C23—26no—
885C23—23no—
886C23—23no—
887C23—26no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—23no—
892C23—26no—
893C23#58512yes—
894C23C2611yescharacteristic
895Q8—28no—
896Q8—424no—
897Q8—412no—
898Q8—424no—
899Q8#550116yes—
900D4—48no—
901D4—412no—
902D4—424no—
903D4—412no—
904D4—424no—
905D4—44no—
906D4—412no—
907D4—812no—
908D4—812no—
909D4—812no—
910D4—812no—
911D4—812no—
912D4—1612no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—23no—
917C2×C4—22no—
918C2×C4—23no—
919C2×C4—22no—
920C2×C4—23no—
921C2×C4—26no—
922C2×C4—21no—
923C2×C4—23no—
924C2×C4—26no—
925C2×C4—21no—
926C2×C4—23no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—23no—
930C2×C4—26no—
931C2×C4—23no—
932C2×C4—22no—
933C2×C4—23no—
934C2×C4—26no—
935C2×C4—21no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—23no—
939C2×C4—26no—
940C2×C4—21no—
941C2×C4—22no—
942C2×C4—26no—
943C2×C4—23no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—23no—
947C2×C4—23no—
948C2×C4—21no—
949C2×C4—26no—
950C2×C4—21no—
951C2×C4—23no—
952C2×C4—21no—
953C2×C4—23no—
954C2×C4—23no—
955C2×C4—26no—
956C2×C4—21no—
957C2×C4—23no—
958C2×C4—412no—
959C2×C4—412no—
960C2×C4—424no—
961C2×C4—412no—
962C2×C4—424no—
963C2×C4—44no—
964C2×C4—412no—
965C2×C4—86no—
966C2×C4—824no—
967C2×C4C23×D416yes—
968C2×C4C23×D4112yes—
969C2×C4C23×D414yes—
970C2×C4C23×D416yes—
971C2×C4C23×D412yes—
972C2×C4C22×#4112yes—
973C2×C4C22×#4116yes—
974C2×C4C22×#4116yes—
975C2×C4C2×H(5,𝔽2)16yes—
976C2×C4C2×2−1+414yes—
977C2×C4C2×2−1+412yes—
978C2×C4#58512yes—
979C22—22no—
980C22—22no—
981C22—22no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—46no—
987C22—43no—
988C22—42no—
989C22—46no—
990C22—43no—
991C22—42no—
992C22—42no—
993C22—43no—
994C22—46no—
995C22—43no—
996C22—42no—
997C22—46no—
998C22—43no—
999C22—42no—
1000C22—46no—
1001C22—42no—
1002C22—46no—
1003C22—43no—
1004C22—42no—
1005C22—43no—
1006C22—46no—
1007C22C24×D411yescharacteristic
1008C22C23×#4111yescharacteristic
1009C22C22×H(5,𝔽2)11yescharacteristic
1010C22C22×2−1+411yescharacteristic
1011C22C2×#58511yescharacteristic
1012C22C2×#58511yescharacteristic
1013C22H(7,𝔽2)11yescharacteristic
1014C4—26no—
1015C4—212no—
1016C4—22no—
1017C4—24no—
1018C4—24no—
1019C4—26no—
1020C4—43no—
1021C4—41no—
1022C4—41no—
1023C4—41no—
1024C4—43no—
1025C4—43no—
1026C4—46no—
1027C4—41no—
1028C4—42no—
1029C4—43no—
1030C4—46no—
1031C4C2×#550112yes—
1032C4#349714yes—
1033C2—42no—
1034C2—86no—
1035C2—83no—
1036C2—82no—
1037C2C22×#55011yescharacteristic
1038C2C2×#349711yescharacteristic
1039C2#6281611yescharacteristic
1040C2#6292311yescharacteristic
1041C2#6298711yescharacteristic
1042C2#6299911yescharacteristic
1043C2#6301511yescharacteristic
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×#3518C2semidirect
2. C2×#3522C2semidirect
3. #59652C2semidirect
4. #59410C2semidirect
5. #59056C2semidirect
6. #59052C2semidirect
7. #45101C2semidirect
8. #44882C2semidirect
9. #39381C2semidirect
10. #39137C2semidirect
11. #39136C2semidirect
12. #36597C2semidirect
13. Q8×#121C2semidirect
14. #36465C2semidirect
15. #36465C2semidirect
16. #36455C2semidirect
17. #36150C2semidirect
18. #35831C2semidirect
19. #35771C2semidirect
20. #34934C2semidirect
21. #34312C2semidirect
22. C4×Q82C2semidirect
23. C4×#548C2semidirect
166. Q82D4semidirect
535. C4×Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35182
C2×#35222
#596522
#594102
#590562
#590522
#451012
#448822
#393812
#391372
#391362
#365972
Q8×#1212
#364652
#364552
#361502
#358312
#357712
#349342
#343122
C4×Q822
C4×#5482