Finite Group Databasebeta

← #7696420

Subgroups — #7696420

Order 512.

10745 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C212yesmaximal, complemented
2C2×#3486C212yesmaximal, complemented
3#59818C213yesmaximal, complemented
4#59000C213yesmaximal, complemented
5#58998C213yesmaximal, complemented
6#52103C213yesmaximal, complemented
7#45332C216yesmaximal, complemented
8#45134C216yesmaximal, complemented
9#45091C216yesmaximal, complemented
10#39360C216yesmaximal, complemented
11#37656C216yesmaximal, complemented
12#37651C216yesmaximal, complemented
13Q8×#127C211yesmaximal, characteristic, complemented
14Q8×#120C211yesmaximal, characteristic, complemented
15#36428C211yesmaximal, characteristic, complemented
16#35737C212yesmaximal, complemented
17#35700C212yesmaximal, complemented
18#35687C212yesmaximal, complemented
19#34312C212yesmaximal, complemented
20C22×2−1+4C2212yes—
21C23×#41C2211yescharacteristic, complemented
22C24×Q8C2211yescharacteristic, complemented
23#3489—232no—
24#3486—232no—
25C2×D4×Q8C2212yes—
26C2×D4×Q8C2211yescharacteristic
27C2×D4×Q8C2216yescomplemented
28C2×D4×Q8C2216yescomplemented
29C2×D4×Q8C2212yescomplemented
30C2×D4×Q8C2212yescomplemented
31C2×D4×Q8C2212yescomplemented
32C2×D4×Q8C2211yescharacteristic, complemented
33C2×#548C2212yes—
34C2×#548C2212yes—
35C2×#548C2216yescomplemented
36C2×#548C2216yescomplemented
37C2×#548C2212yescomplemented
38C2×#547C2216yes—
39C2×#547C2216yescomplemented
40C2×#546C2216yes—
41C2×#546C2216yescomplemented
42C2×#537C2216yes—
43C2×#536C2216yescomplemented
44C2×#536C2216yescomplemented
45C2×#536C2216yescomplemented
46C2×#525C2216yes—
47C2×#525C2216yescomplemented
48C2×#525C2216yescomplemented
49C22×C22⋊Q8C2216yescomplemented
50C2×#520C2212yescomplemented
51C2×#519C2212yescomplemented
52#2868C2213yescomplemented
53#2848C2213yescomplemented
54#2848C2213yescomplemented
55#2683C2213yes—
56#2682C2216yescomplemented
57#2681C2216yes—
58#2681C2216yescomplemented
59#2680C22112yescomplemented
60#2680C22112yescomplemented
61#2680C2216yescomplemented
62#2680C2216yescomplemented
63#2679C2213yes—
64#2678C2216yes—
65#2678C2216yescomplemented
66#2677C2216yescomplemented
67#2674C22112yescomplemented
68#2672C22112yescomplemented
69#2671C22112yescomplemented
70#2669C2211yescharacteristic
71#2669C2213yes—
72#2668C2216yescomplemented
73#2621C2216yescomplemented
74#2621C2216yescomplemented
75#2616C2216yescomplemented
76#2555C2216yescomplemented
77#2547C2216yescomplemented
78#2546C2216yescomplemented
79#2542C2213yes—
80#2542C2216yescomplemented
81#2542C2216yescomplemented
82#2542C2213yescomplemented
83#2536C2216yescomplemented
84#2535C2216yescomplemented
85#2472C22112yescomplemented
86#2464C22112yescomplemented
87#2455C2216yescomplemented
88#2449C22112yescomplemented
89#2443C22112yescomplemented
90#2440C22112yescomplemented
91#2440C22112yescomplemented
92#2437C2216yescomplemented
93#2435C2213yescomplemented
94#2434C2213yescomplemented
95#2434C2216yescomplemented
96#2434C2216yescomplemented
97#2432C2216yescomplemented
98#2432C2216yescomplemented
99#2432C2216yescomplemented
100#2429C2216yescomplemented
101#2429C2216yescomplemented
102#2427C2216yescomplemented
103#2427C2216yescomplemented
104#2422C22112yescomplemented
105#2422C22112yescomplemented
106#2418C22112yes—
107#2417C2216yescomplemented
108#2417C2216yescomplemented
109#2415C2216yes—
110#2415C2216yescomplemented
111#2409C2216yes—
112#2409C2213yes—
113#2409C2216yescomplemented
114#2408C2213yes—
115#2407C2216yes—
116#2407C2216yescomplemented
117#2407C2216yescomplemented
118#2392C2216yes—
119#2392C2216yescomplemented
120#2388C2216yescomplemented
121#2367C2216yescomplemented
122#2363C2216yescomplemented
123#2360C2216yescomplemented
124#2358C2216yes—
125#2352C2216yescomplemented
126#2351C2212yescomplemented
127#2341C2212yescomplemented
128Q8×C22⋊C4C2212yescomplemented
129Q8×C22⋊C4C2211yescharacteristic, complemented
130Q8×C22⋊C4C2212yescomplemented
131Q8×C22⋊C4C2211yescharacteristic, complemented
132#2324C2216yescomplemented
133#2323C2216yescomplemented
134C4×#127C2213yes—
135C4×#124C2216yescomplemented
136C4×#120C2213yes—
137C4×#120C2213yes—
138#2293C2216yescomplemented
139C42×Q8C2211yescharacteristic, complemented
140C2×2−1+4—216no—
141C2×2−1+4—216no—
142C2×2−1+4—48no—
143C22×#41—216no—
144C22×#41—44no—
145C22×#41C2316yes—
146C22×#41C2316yes—
147C22×#41C2316yes—
148C22×#41C2316yes—
149C22×#41C2312yes—
150C23×Q8—216no—
151C23×Q8—44no—
152C23×Q8C2311yescharacteristic
153C23×Q8C2311yescharacteristic
154C23×Q8C2312yes—
155C23×Q8C2316yes—
156C23×Q8C2313yes—
157C23×Q8C2316yes—
158C23×Q8C2312yes—
159C23×D4C2313yes—
160C24×C4C2313yes—
161C24×C4C2313yes—
162D4×Q8—216no—
163D4×Q8—216no—
164D4×Q8—248no—
165D4×Q8—216no—
166D4×Q8—216no—
167D4×Q8—248no—
168D4×Q8—44no—
169D4×Q8—44no—
170#548—216no—
171#548—216no—
172#548—248no—
173#548—248no—
174#548D4132yescomplemented
175#547—248no—
176#547—248no—
177#546—248no—
178#546—248no—
179#537—248no—
180#536—248no—
181#536—248no—
182#536—248no—
183C2×C4⋊Q8C2316yes—
184C2×C4⋊Q8C2316yes—
185C2×C4⋊Q8C23112yes—
186C2×C4⋊Q8C2316yes—
187C2×C4⋊Q8C2316yes—
188C2×C4⋊Q8C2313yes—
189C2×C4⋊Q8C2313yes—
190C2×#127C2311yescharacteristic
191C2×#124C23112yes—
192C2×#124C2316yes—
193C2×#124C2316yes—
194C2×#124C2316yes—
195#525—248no—
196#525—248no—
197#525—248no—
198C2×#123C2316yes—
199C2×#123C2316yes—
200C2×#123C23112yes—
201C2×#123C2316yes—
202C2×#123C2316yes—
203C2×#123C23112yes—
204C2×#123C23112yes—
205C2×C22⋊Q8—248no—
206C2×C22⋊Q8C2316yes—
207C2×C22⋊Q8C2316yes—
208C2×C22⋊Q8C2316yes—
209C2×C22⋊Q8C2316yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C23112yes—
215C2×C22⋊Q8C2316yes—
216C2×C22⋊Q8C2316yes—
217C2×C22⋊Q8C2316yes—
218C2×C22⋊Q8C2316yes—
219C2×C22⋊Q8C2316yes—
220C2×C22⋊Q8C23112yes—
221C2×C22⋊Q8C2316yes—
222C2×C22⋊Q8C23112yes—
223C2×C22⋊Q8C2313yes—
224C2×C22⋊Q8C2313yes—
225C2×C22⋊Q8C2316yes—
226C2×C22⋊Q8C2316yes—
227C2×#121C2316yes—
228C2×#121C2316yes—
229C2×#121C2312yes—
230C2×#121C2316yes—
231C2×#121C2316yes—
232C2×#121C2316yes—
233C2×#121C23112yes—
234C2×#121C23112yes—
235C2×#121C2316yes—
236C2×#120C2313yes—
237C2×#120C2316yes—
238C2×#120C2316yes—
239C2×#120C2316yes—
240C2×#120C2312yes—
241C2×#120C2311yescharacteristic
242#520—216no—
243#519—216no—
244C2×C4×Q8C2316yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2316yes—
249C2×C4×Q8C2312yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C2316yes—
253C2×C4×D4C23112yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C2316yes—
259C2×C4×D4C23112yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×#117C2316yes—
264C2×#117C2316yes—
265C2×#117C2316yes—
266C22×C4⋊C4C2316yes—
267C22×C4⋊C4C23112yes—
268C22×C22⋊C4C23112yes—
269#399C2316yes—
270#399C23112yes—
271#399C2316yes—
272#398C2316yes—
273#398C23112yes—
274#398C23112yes—
275#398C23112yes—
276#398C2316yes—
277#397C2316yes—
278#397C23112yes—
279#397C23112yes—
280#397C23112yes—
281#397C2316yes—
282#396C2316yes—
283#396C2316yes—
284#396C2316yes—
285#396C2316yes—
286#395C23112yes—
287#395C2316yes—
288#395C23112yes—
289#395C2316yes—
290#394C2316yes—
291#394C23112yes—
292#394C23112yes—
293#394C2316yes—
294#394C2316yes—
295#394C2316yes—
296#394C2316yes—
297#394C2316yes—
298#394C2312yes—
299#394C2316yes—
300#394C2316yes—
301#394C23112yes—
302#394C2316yes—
303#393C2316yes—
304#393C2316yes—
305#392C2312yes—
306#392C2316yes—
307#392C2316yes—
308#392C2312yes—
309#392C2316yes—
310#392C2316yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#391C2316yes—
315#391C2316yes—
316#391C2316yes—
317#390C2313yes—
318#390C2316yes—
319#390C2316yes—
320#390C2313yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#389C2316yes—
326#389C2316yes—
327#389C2316yes—
328#389C2316yes—
329#389C23112yes—
330#389C23112yes—
331#388C23112yes—
332#388C23112yes—
333#388C2316yes—
334#388C23112yes—
335#388C2316yes—
336#388C2312yes—
337#388C2316yes—
338#388C23112yes—
339#387C23112yes—
340#386C23112yes—
341#386C2313yes—
342#386C23112yes—
343#386C2316yes—
344#386C23112yes—
345#386C2316yes—
346#386C2311yescharacteristic
347#386C23112yes—
348#385C23112yes—
349#385C2313yes—
350#385C23112yes—
351#385C23112yes—
352#385C2316yes—
353#385C23112yes—
354#385C23112yes—
355#385C23112yes—
356#385C2316yes—
357#385C2316yes—
358#385C2313yes—
359#384C2313yes—
360#384C2316yes—
361#384C23112yes—
362#382C2316yes—
363#380C2316yes—
364#380C2316yes—
365#380C2313yes—
366#380C2313yes—
367#380C2316yes—
368#380C23112yes—
369#380C23112yes—
370#379C2313yes—
371#379C2316yes—
372#379C2313yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C22⋊C4C2316yes—
377C4×C22⋊C4C2316yes—
378C4×C22⋊C4C2313yes—
379C4×C22⋊C4C2313yes—
380C4×C22⋊C4C2316yes—
381C4×C22⋊C4C23112yes—
382C4×C22⋊C4C23112yes—
383C43C2313yes—
384C25C2413yes—
385C25C2411yescharacteristic
3862−1+4—4128no—
387C2×#41—28no—
388C2×#41—224no—
389C2×#41—28no—
390C2×#41—224no—
391C2×#41—224no—
392C2×#41—224no—
393C2×#41—224no—
394C2×#41—224no—
395C2×#41—224no—
396C2×#41—224no—
397C2×#41—412no—
398C2×#41—412no—
399C2×#41—412no—
400C2×#41—412no—
401C2×#41—464no—
402C2×#41C2×D4116yes—
403C22×Q8—28no—
404C22×Q8—28no—
405C22×Q8—224no—
406C22×Q8—224no—
407C22×Q8—224no—
408C22×Q8—28no—
409C22×Q8—28no—
410C22×Q8—28no—
411C22×Q8—28no—
412C22×Q8—24no—
413C22×Q8—24no—
414C22×Q8—28no—
415C22×Q8—224no—
416C22×Q8—224no—
417C22×Q8—412no—
418C22×Q8—46no—
419C22×Q8—412no—
420C22×Q8—464no—
421C22×Q8C2×D4116yes—
422C22×Q8C2413yes—
423C22×Q8C2416yes—
424C22×Q8C2413yes—
425C22×Q8C2416yes—
426C22×Q8C2416yes—
427C22×Q8C2416yes—
428C22×Q8C2411yescharacteristic
429C22×D4—224no—
430C22×D4—46no—
431C22×D4C2412yes—
432C22×D4C2412yes—
433C22×D4C2416yes—
434C22×D4C2412yes—
435C22×D4C2416yes—
436C22×D4C2412yes—
437C22×D4C2416yes—
438C22×D4C2416yes—
439C22×D4C2416yes—
440C22×D4C2412yes—
441C22×D4C2411yescharacteristic
442C22×D4C2416yes—
443C22×D4C2416yes—
444C22×D4C2411yescharacteristic
445C23×C4—224no—
446C23×C4—224no—
447C23×C4—46no—
448C23×C4—46no—
449C23×C4C2413yes—
450C23×C4C2416yes—
451C23×C4C2413yes—
452C23×C4C24112yes—
453C23×C4C2416yes—
454C23×C4C2413yes—
455C23×C4C2416yes—
456C23×C4C2411yescharacteristic
457C23×C4C2416yes—
458C23×C4C2416yes—
459C23×C4C24112yes—
460C4⋊Q8—224no—
461C4⋊Q8—224no—
462C4⋊Q8—248no—
463C4⋊Q8—224no—
464C4⋊Q8—224no—
465C4⋊Q8—46no—
466C4⋊Q8—46no—
467#127—24no—
468#124—224no—
469#124—224no—
470#124—248no—
471#124C2×D4148yes—
472#123—224no—
473#123—224no—
474#123—248no—
475#123—224no—
476#123—224no—
477#123—248no—
478#123—248no—
479C22⋊Q8—224no—
480C22⋊Q8—224no—
481C22⋊Q8—224no—
482C22⋊Q8—224no—
483C22⋊Q8—224no—
484C22⋊Q8—224no—
485C22⋊Q8—224no—
486C22⋊Q8—224no—
487C22⋊Q8—224no—
488C22⋊Q8—224no—
489C22⋊Q8—224no—
490C22⋊Q8—224no—
491C22⋊Q8—248no—
492C22⋊Q8—224no—
493C22⋊Q8—224no—
494C22⋊Q8—248no—
495C22⋊Q8—248no—
496C22⋊Q8—46no—
497C22⋊Q8—46no—
498C22⋊Q8—412no—
499C22⋊Q8C2×D4148yes—
500#121—224no—
501#121—224no—
502#121—224no—
503#121—248no—
504#121—224no—
505#121—28no—
506#121—224no—
507#121—248no—
508#121C2×D4148yes—
509#120—224no—
510#120—224no—
511#120—24no—
512#120—212no—
513#120—28no—
514#120—224no—
515C4×Q8—28no—
516C4×Q8—28no—
517C4×Q8—24no—
518C4×Q8—224no—
519C4×Q8—224no—
520C4×Q8C2×D4116yes—
521C4×D4—248no—
522C4×D4—224no—
523C4×D4—224no—
524C4×D4—224no—
525C4×D4—224no—
526C4×D4—224no—
527C4×D4—248no—
528C4×D4—224no—
529C4×D4—224no—
530C4×D4—224no—
531C4×D4—46no—
532C4×D4—46no—
533C4×D4C2×D4148yes—
534#117—224no—
535#117—224no—
536#117—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—248no—
539C2×C4⋊C4C2416yes—
540C2×C4⋊C4C2416yes—
541C2×C4⋊C4C2416yes—
542C2×C4⋊C4C24112yes—
543C2×C4⋊C4C24112yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2416yes—
546C2×C4⋊C4C2416yes—
547C2×C4⋊C4C2416yes—
548C2×C4⋊C4C24112yes—
549C2×C4⋊C4C2416yes—
550C2×C4⋊C4C2416yes—
551C2×C4⋊C4C24112yes—
552C2×C4⋊C4C2416yes—
553C2×C4⋊C4C2416yes—
554C2×C4⋊C4C2416yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2413yes—
557C2×C4⋊C4C2413yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2416yes—
560C2×C4⋊C4C2416yes—
561C2×C4⋊C4C2416yes—
562C2×C4⋊C4C2416yes—
563C2×C4⋊C4C2416yes—
564C2×C22⋊C4—248no—
565C2×C22⋊C4C2416yes—
566C2×C22⋊C4C2416yes—
567C2×C22⋊C4C24112yes—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2416yes—
571C2×C22⋊C4C2416yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2416yes—
574C2×C22⋊C4C2416yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2416yes—
577C2×C22⋊C4C2416yes—
578C2×C22⋊C4C2416yes—
579C2×C22⋊C4C2416yes—
580C2×C22⋊C4C24112yes—
581C2×C22⋊C4C2416yes—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2411yescharacteristic
586C2×C22⋊C4C2413yes—
587C2×C22⋊C4C2413yes—
588C2×C22⋊C4C2413yes—
589C2×C22⋊C4C2416yes—
590C2×C22⋊C4C2411yescharacteristic
591C2×C22⋊C4C2412yes—
592C2×C22⋊C4C2413yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C24112yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C24112yes—
598C2×C22⋊C4C2412yes—
599C2×C22⋊C4C2416yes—
600C2×C42C2416yes—
601C2×C42C2416yes—
602C2×C42C24112yes—
603C2×C42C2413yes—
604C2×C42C2411yescharacteristic
605C2×C42C2413yes—
606C2×C42C2416yes—
607C2×C42C2416yes—
608#95C2412yes—
609#95C2416yes—
610#95C2416yes—
611#95C2416yes—
612#95C2416yes—
613#95C2416yes—
614#95C24112yes—
615#95C24112yes—
616#95C2416yes—
617#95C2416yes—
618#95C2416yes—
619#95C2416yes—
620#95C2412yes—
621#95C2416yes—
622#95C24112yes—
623#95C2416yes—
624C24—24no—
625C24—22no—
626C24—212no—
627C24—26no—
628C24—41no—
629C24—42no—
630C24—41no—
631C24—43no—
632C24—46no—
633C24—43no—
634C24C2512yes—
635C24C2512yes—
636C24C2516yes—
637C24C2511yescharacteristic
638C24C2511yescharacteristic
639#41—264no—
640#41—496no—
641#41—496no—
642#41—496no—
643#41—496no—
644C2×Q8—264no—
645C2×Q8—212no—
646C2×Q8—212no—
647C2×Q8—224no—
648C2×Q8—212no—
649C2×Q8—212no—
650C2×Q8—212no—
651C2×Q8—212no—
652C2×Q8—212no—
653C2×Q8—212no—
654C2×Q8—26no—
655C2×Q8—212no—
656C2×Q8—26no—
657C2×Q8—46no—
658C2×Q8—46no—
659C2×Q8—496no—
660C2×Q8—496no—
661C2×Q8—448no—
662C2×Q8—416no—
663C2×Q8—416no—
664C2×Q8—432no—
665C2×Q8C22×D4124yes—
666C2×Q8C22×D418yes—
667C2×Q8H(5,𝔽2)14yes—
668C2×D4—24no—
669C2×D4—212no—
670C2×D4—24no—
671C2×D4—212no—
672C2×D4—212no—
673C2×D4—24no—
674C2×D4—224no—
675C2×D4—212no—
676C2×D4—24no—
677C2×D4—212no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—212no—
681C2×D4—212no—
682C2×D4—24no—
683C2×D4—24no—
684C2×D4—212no—
685C2×D4—24no—
686C2×D4—212no—
687C2×D4—22no—
688C2×D4—41no—
689C2×D4—41no—
690C2×D4—46no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—41no—
695C2×D4—46no—
696C2×D4—46no—
697C2×D4—42no—
698C2×D4—46no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—46no—
703C2×D4—46no—
704C2×D4—46no—
705C2×D4—46no—
706C2×D4—448no—
707C2×D4C22×D4124yes—
708C2×D4C22×D4124yes—
709C2×D42−1+414yescomplemented
710C22×C4—212no—
711C22×C4—212no—
712C22×C4—212no—
713C22×C4—212no—
714C22×C4—212no—
715C22×C4—224no—
716C22×C4—212no—
717C22×C4—224no—
718C22×C4—212no—
719C22×C4—212no—
720C22×C4—212no—
721C22×C4—212no—
722C22×C4—212no—
723C22×C4—212no—
724C22×C4—24no—
725C22×C4—212no—
726C22×C4—26no—
727C22×C4—26no—
728C22×C4—212no—
729C22×C4—224no—
730C22×C4—41no—
731C22×C4—43no—
732C22×C4—46no—
733C22×C4—46no—
734C22×C4—412no—
735C22×C4—448no—
736C22×C4—448no—
737C22×C4—412no—
738C22×C4—412no—
739C22×C4C22×D4124yes—
740C22×C4C22×D4124yes—
741C22×C4C2516yes—
742C22×C4C2513yes—
743C22×C4C2512yes—
744C22×C4C2516yes—
745C22×C4C2512yes—
746C22×C4C2513yes—
747C22×C4C2516yes—
748C22×C4C2513yes—
749C22×C4C2512yes—
750C22×C4C2516yes—
751C22×C4C2516yes—
752C22×C4C2512yes—
753C22×C4C2511yescharacteristic
754C22×C4C2513yes—
755C4⋊C4—212no—
756C4⋊C4—212no—
757C4⋊C4—212no—
758C4⋊C4—224no—
759C4⋊C4—224no—
760C4⋊C4—24no—
761C4⋊C4—212no—
762C4⋊C4—212no—
763C4⋊C4—212no—
764C4⋊C4—212no—
765C4⋊C4—224no—
766C4⋊C4—212no—
767C4⋊C4—224no—
768C4⋊C4—212no—
769C4⋊C4—212no—
770C4⋊C4—212no—
771C4⋊C4—26no—
772C4⋊C4—46no—
773C4⋊C4—46no—
774C4⋊C4—43no—
775C4⋊C4—43no—
776C4⋊C4—46no—
777C4⋊C4—46no—
778C4⋊C4C22×D4124yes—
779C4⋊C4C22×D4124yes—
780C22⋊C4—224no—
781C22⋊C4—212no—
782C22⋊C4—212no—
783C22⋊C4—212no—
784C22⋊C4—212no—
785C22⋊C4—224no—
786C22⋊C4—26no—
787C22⋊C4—22no—
788C22⋊C4—212no—
789C22⋊C4—212no—
790C22⋊C4—212no—
791C22⋊C4—24no—
792C22⋊C4—212no—
793C22⋊C4—212no—
794C22⋊C4—24no—
795C22⋊C4—212no—
796C22⋊C4—24no—
797C22⋊C4—212no—
798C22⋊C4—212no—
799C22⋊C4—212no—
800C22⋊C4—24no—
801C22⋊C4—212no—
802C22⋊C4—46no—
803C22⋊C4—412no—
804C22⋊C4—46no—
805C22⋊C4—42no—
806C22⋊C4—46no—
807C22⋊C4—41no—
808C22⋊C4—43no—
809C22⋊C4—43no—
810C22⋊C4—46no—
811C22⋊C4—43no—
812C22⋊C4C22×D4148yes—
813C22⋊C4C22×D418yes—
814C22⋊C4C22×D4124yes—
815C42—212no—
816C42—224no—
817C42—212no—
818C42—26no—
819C42—22no—
820C42—43no—
821C42—46no—
822C42C22×D4124yes—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—26no—
827C23—21no—
828C23—21no—
829C23—22no—
830C23—26no—
831C23—22no—
832C23—26no—
833C23—22no—
834C23—21no—
835C23—26no—
836C23—26no—
837C23—21no—
838C23—26no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—44no—
851C23—48no—
852C23—412no—
853C23—424no—
854C23—48no—
855C23—44no—
856C23—44no—
857C23—812no—
858C23—86no—
859C23—86no—
860C23C23×D4112yes—
861C23C23×D414yes—
862C23C2×2−1+412yes—
863C23C2×2−1+412yes—
864C23C2611yescharacteristic
865Q8—248no—
866Q8—424no—
867Q8—424no—
868Q8—412no—
869Q8—424no—
870Q8—412no—
871Q8D42116yes—
872D4—248no—
873D4—424no—
874D4—44no—
875D4—48no—
876D4—48no—
877D4—48no—
878D4—424no—
879D4—44no—
880D4—424no—
881D4—48no—
882D4—424no—
883D4—424no—
884D4—48no—
885D4—812no—
886C2×C4—26no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—26no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—21no—
894C2×C4—26no—
895C2×C4—26no—
896C2×C4—248no—
897C2×C4—248no—
898C2×C4—22no—
899C2×C4—26no—
900C2×C4—22no—
901C2×C4—26no—
902C2×C4—26no—
903C2×C4—26no—
904C2×C4—26no—
905C2×C4—26no—
906C2×C4—23no—
907C2×C4—23no—
908C2×C4—26no—
909C2×C4—23no—
910C2×C4—22no—
911C2×C4—26no—
912C2×C4—26no—
913C2×C4—22no—
914C2×C4—26no—
915C2×C4—26no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—26no—
919C2×C4—44no—
920C2×C4—412no—
921C2×C4—424no—
922C2×C4—424no—
923C2×C4—448no—
924C2×C4—412no—
925C2×C4—412no—
926C2×C4—424no—
927C2×C4—824no—
928C2×C4C23×D4112yes—
929C2×C4C23×D414yes—
930C2×C4C23×D4112yes—
931C2×C4C23×D414yes—
932C2×C4C23×D4112yes—
933C2×C4C2×H(5,𝔽2)16yes—
934C2×C4C2×2−1+412yes—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—212no—
939C22—24no—
940C22—212no—
941C22—22no—
942C22—22no—
943C22—24no—
944C22—212no—
945C22—416no—
946C22—42no—
947C22—46no—
948C22—41no—
949C22—42no—
950C22—46no—
951C22—41no—
952C22—46no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—46no—
958C22—41no—
959C22—41no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—824no—
968C22C24×D412yes—
969C22C22×H(5,𝔽2)11yescharacteristic
970C22C22×2−1+411yescharacteristic
971C222−1+612yes—
972C222−1+611yescharacteristic
973C4—24no—
974C4—212no—
975C4—22no—
976C4—24no—
977C4—212no—
978C4—42no—
979C4—46no—
980C4—43no—
981C4—46no—
982C4—42no—
983C4—43no—
984C4—46no—
985C4—43no—
986C4C2×D42112yes—
987C2—42no—
988C2—44no—
989C2—412no—
990C2—42no—
991C2—82no—
992C2C22×D4211yescharacteristic
993C2#6285912yes—
994C2#6289311yescharacteristic
995C2D4×2−1+412yes—
996C2#6304411yescharacteristic
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×#3489C2semidirect
2. C2×#3486C2semidirect
3. #59818C2semidirect
4. #59000C2semidirect
5. #58998C2semidirect
6. #52103C2semidirect
7. #45332C2semidirect
8. #45134C2semidirect
9. #45091C2semidirect
10. #39360C2semidirect
11. #37656C2semidirect
12. #37651C2semidirect
13. Q8×#127C2semidirect
14. Q8×#120C2semidirect
15. #36428C2semidirect
16. #35737C2semidirect
17. #35700C2semidirect
18. #35687C2semidirect
19. #34312C2semidirect
21. C23×#41C22semidirect
22. C24×Q8C22semidirect
27. C2×D4×Q8C22semidirect
28. C2×D4×Q8C22semidirect
29. C2×D4×Q8C22semidirect
30. C2×D4×Q8C22semidirect
31. C2×D4×Q8C22semidirect
32. C2×D4×Q8C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#548C22semidirect
39. C2×#547C22semidirect
41. C2×#546C22semidirect
43. C2×#536C22semidirect
44. C2×#536C22semidirect
45. C2×#536C22semidirect
47. C2×#525C22semidirect
48. C2×#525C22semidirect
49. C22×C22⋊Q8C22semidirect
50. C2×#520C22semidirect
51. C2×#519C22semidirect
52. #2868C22semidirect
53. #2848C22semidirect
54. #2848C22semidirect
56. #2682C22semidirect
58. #2681C22semidirect
59. #2680C22semidirect
60. #2680C22semidirect
61. #2680C22semidirect
62. #2680C22semidirect
65. #2678C22semidirect
66. #2677C22semidirect
67. #2674C22semidirect
68. #2672C22semidirect
69. #2671C22semidirect
72. #2668C22semidirect
73. #2621C22semidirect
74. #2621C22semidirect
75. #2616C22semidirect
76. #2555C22semidirect
77. #2547C22semidirect
78. #2546C22semidirect
80. #2542C22semidirect
81. #2542C22semidirect
82. #2542C22semidirect
83. #2536C22semidirect
84. #2535C22semidirect
85. #2472C22semidirect
86. #2464C22semidirect
87. #2455C22semidirect
88. #2449C22semidirect
89. #2443C22semidirect
90. #2440C22semidirect
91. #2440C22semidirect
92. #2437C22semidirect
93. #2435C22semidirect
94. #2434C22semidirect
95. #2434C22semidirect
96. #2434C22semidirect
97. #2432C22semidirect
98. #2432C22semidirect
99. #2432C22semidirect
100. #2429C22semidirect
101. #2429C22semidirect
102. #2427C22semidirect
103. #2427C22semidirect
104. #2422C22semidirect
105. #2422C22semidirect
107. #2417C22semidirect
108. #2417C22semidirect
110. #2415C22semidirect
113. #2409C22semidirect
116. #2407C22semidirect
117. #2407C22semidirect
119. #2392C22semidirect
120. #2388C22semidirect
121. #2367C22semidirect
122. #2363C22semidirect
123. #2360C22semidirect
125. #2352C22semidirect
126. #2351C22semidirect
127. #2341C22semidirect
128. Q8×C22⋊C4C22semidirect
129. Q8×C22⋊C4C22semidirect
130. Q8×C22⋊C4C22semidirect
131. Q8×C22⋊C4C22semidirect
132. #2324C22semidirect
133. #2323C22semidirect
135. C4×#124C22semidirect
138. #2293C22semidirect
139. C42×Q8C22semidirect
174. #548D4semidirect
709. C2×D42−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#34862
#598182
#590002
#589982
#521032
#453322
#451342
#450912
#393602
#376562
#376512
Q8×#1272
Q8×#1202
#364282
#357372
#357002
#356872
#343122