Finite Group Databasebeta

← #7695087

Subgroups — #7695087

Order 512.

10973 conjugacy classes of subgroups.

The subgroup lattice has 1007 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C212yesmaximal, complemented
2C2×#3487C212yesmaximal, complemented
3#59815C213yesmaximal, complemented
4#59002C216yesmaximal, complemented
5#52103C213yesmaximal, complemented
6#45241C216yesmaximal, complemented
7#44892C216yesmaximal, complemented
8#44886C216yesmaximal, complemented
9#39356C213yesmaximal, complemented
10#39355C213yesmaximal, complemented
11#37658C216yesmaximal, complemented
12#37649C216yesmaximal, complemented
13#36465C211yesmaximal, characteristic, complemented
14#36429C212yesmaximal, complemented
15#35831C212yesmaximal, complemented
16#35771C212yesmaximal, complemented
17#35687C212yesmaximal, complemented
18#34313C211yesmaximal, characteristic, complemented
19#34311C211yesmaximal, characteristic, complemented
20C22×2−1+4C2212yes—
21C23×#41C2212yescomplemented
22#3489—232no—
23#3487—232no—
24C2×#550C2212yes—
25C2×#550C2211yescharacteristic
26C2×#550C2211yescharacteristic
27C2×#550C2216yescomplemented
28C2×#550C2216yescomplemented
29C2×D4×Q8C2211yescharacteristic
30C2×D4×Q8C2212yescomplemented
31C2×D4×Q8C2211yescharacteristic, complemented
32C2×#548C2212yes—
33C2×#548C2216yescomplemented
34C2×#548C2212yescomplemented
35C2×#548C2212yescomplemented
36C2×#548C2216yescomplemented
37C2×#548C2212yescomplemented
38C2×#547C2216yes—
39C2×#547C2216yescomplemented
40C2×#546C2216yes—
41C2×#546C2216yescomplemented
42C2×#537C2216yes—
43C2×#536C2216yescomplemented
44C2×#535C2216yescomplemented
45C2×#535C2216yescomplemented
46C2×#525C2216yes—
47C2×#525C2216yescomplemented
48C2×#525C2216yescomplemented
49C22×C22⋊Q8C2216yescomplemented
50C2×#520C2212yescomplemented
51C2×#519C2212yescomplemented
52#2858C2213yescomplemented
53#2847C2216yescomplemented
54#2683C2216yescomplemented
55#2683C2213yescomplemented
56#2682C2211yescharacteristic
57#2682C2216yescomplemented
58#2682C2213yescomplemented
59#2682C2216yescomplemented
60#2682C2216yescomplemented
61#2681C2216yescomplemented
62#2681C2216yescomplemented
63#2680C2216yescomplemented
64#2679C2216yes—
65#2679C2213yes—
66#2678C2216yes—
67#2678C2216yescomplemented
68#2676C22112yescomplemented
69#2673C22112yescomplemented
70#2672C22112yescomplemented
71#2669C22112yescomplemented
72#2669C2216yescomplemented
73#2620C2216yescomplemented
74#2620C2216yescomplemented
75#2616C2216yescomplemented
76#2545C2216yescomplemented
77#2544C2216yescomplemented
78#2542C2213yescomplemented
79#2541C2213yescomplemented
80#2541C2216yescomplemented
81#2540C2216yescomplemented
82#2540C2216yescomplemented
83#2538C2216yescomplemented
84#2537C2216yescomplemented
85#2461C22112yescomplemented
86#2461C22112yescomplemented
87#2449C22112yescomplemented
88#2445C22112yescomplemented
89#2443C22112yescomplemented
90#2434C2216yescomplemented
91#2433C2216yescomplemented
92#2432C2216yescomplemented
93#2432C2216yescomplemented
94#2431C2216yescomplemented
95#2431C2216yescomplemented
96#2429C2216yescomplemented
97#2428C2216yescomplemented
98#2427C2216yescomplemented
99#2426C2216yescomplemented
100#2424C22112yescomplemented
101#2424C22112yescomplemented
102#2424C22112yescomplemented
103#2418C22112yescomplemented
104#2417C2216yescomplemented
105#2416C2216yescomplemented
106#2416C22112yescomplemented
107#2415C2216yescomplemented
108#2414C2216yescomplemented
109#2409C2216yescomplemented
110#2408C2216yescomplemented
111#2407C2216yescomplemented
112#2407C2216yescomplemented
113#2407C2216yescomplemented
114#2407C2216yescomplemented
115#2392C2216yescomplemented
116#2392C2216yescomplemented
117#2388C2216yescomplemented
118#2366C2213yescomplemented
119#2365C2213yescomplemented
120#2362C2216yescomplemented
121#2361C2216yescomplemented
122#2354C2213yes—
123Q8×C4⋊C4C2211yescharacteristic, complemented
124Q8×C4⋊C4C2211yescharacteristic, complemented
125D4×C4⋊C4C2213yescomplemented
126D4×C4⋊C4C2216yescomplemented
127#2341C2212yescomplemented
128#2341C2212yescomplemented
129Q8×C22⋊C4C2212yescomplemented
130Q8×C22⋊C4C2212yescomplemented
131#2324C2216yescomplemented
132#2323C2216yescomplemented
133C4×C4⋊Q8C2213yescomplemented
134C4×#127C2213yescomplemented
135C4×#127C2213yescomplemented
136C4×#120C2216yescomplemented
137#2293C2213yes—
138#2293C2213yescomplemented
139C42×Q8C2211yescharacteristic, complemented
140C2×2−1+4—216no—
141C2×2−1+4—216no—
142C2×2−1+4—48no—
143C22×#41—216no—
144C22×#41—216no—
145C22×#41—48no—
146C22×#41C2312yes—
147C22×#41C2316yes—
148C22×#41C2316yes—
149C22×#41C2316yes—
150C22×#41C2316yes—
151C22×#41C2316yes—
152C22×#41C2312yes—
153C23×Q8C2312yes—
154C23×Q8C2316yes—
155C23×Q8C2312yes—
156C23×D4C2316yes—
157C24×C4C2316yes—
158#550—216no—
159#550—248no—
160#550—248no—
161#550—44no—
162#550D4116yescomplemented
163D4×Q8—216no—
164D4×Q8—44no—
165D4×Q8D4116yescomplemented
166#548—216no—
167#548—216no—
168#548—248no—
169#548—216no—
170#548—216no—
171#548—248no—
172#547—248no—
173#547—248no—
174#546—248no—
175#546—248no—
176#537—248no—
177#536—248no—
178#535—248no—
179#535—248no—
180C2×C4⋊Q8C2316yes—
181C2×C4⋊Q8C2313yes—
182C2×C4⋊Q8C2313yes—
183C2×#127C23112yes—
184C2×#127C2316yes—
185C2×#127C2313yes—
186C2×#127C2313yes—
187C2×#127C2313yes—
188C2×#124C2316yes—
189C2×#124C2316yes—
190C2×#124C23112yes—
191C2×#124C2316yes—
192C2×#124C2316yes—
193#525—248no—
194#525—248no—
195#525—248no—
196C2×#123C2316yes—
197C2×#123C2316yes—
198C2×#123C2316yes—
199C2×#123C2312yes—
200C2×#123C23112yes—
201C2×#123C23112yes—
202C2×C22⋊Q8—248no—
203C2×C22⋊Q8C2316yes—
204C2×C22⋊Q8C2316yes—
205C2×C22⋊Q8C2316yes—
206C2×C22⋊Q8C2316yes—
207C2×C22⋊Q8C2316yes—
208C2×C22⋊Q8C2316yes—
209C2×C22⋊Q8C23112yes—
210C2×C22⋊Q8C2316yes—
211C2×C22⋊Q8C2316yes—
212C2×C22⋊Q8C2316yes—
213C2×C22⋊Q8C2316yes—
214C2×C22⋊Q8C2316yes—
215C2×C22⋊Q8C2316yes—
216C2×#121C2316yes—
217C2×#121C2316yes—
218C2×#121C2316yes—
219C2×#121C2316yes—
220C2×#121C2312yes—
221C2×#121C2316yes—
222C2×#121C2316yes—
223C2×#121C2316yes—
224C2×#121C23112yes—
225C2×#121C2316yes—
226C2×#121C23112yes—
227C2×#121C23112yes—
228C2×#121C2316yes—
229C2×#121C23112yes—
230C2×#121C2316yes—
231C2×#121C23112yes—
232C2×#121C2316yes—
233C2×#120C2316yes—
234C2×#120C2316yes—
235C2×#120C23112yes—
236C2×#120C2316yes—
237C2×#120C2316yes—
238C2×#120C2316yes—
239C2×#120C23112yes—
240#520—216no—
241#519—216no—
242C2×C4×Q8C2316yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2316yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×D4C2316yes—
250C2×C4×D4C2316yes—
251C2×C4×D4C2316yes—
252C2×C4×D4C23112yes—
253C2×C4×D4C2316yes—
254C2×C4×D4C2316yes—
255C2×C4×D4C2316yes—
256C2×C4×D4C2316yes—
257C2×C4×D4C2316yes—
258C2×C4×D4C23112yes—
259C2×C4×D4C2316yes—
260C2×C4×D4C2313yes—
261C2×C4×D4C2313yes—
262C2×C4×D4C2316yes—
263C2×C4×D4C2313yes—
264C2×C4×D4C2313yes—
265C2×#117C2316yes—
266C2×#117C2316yes—
267C2×#117C2316yes—
268C22×C4⋊C4C2316yes—
269C22×C4⋊C4C23112yes—
270C22×C22⋊C4C23112yes—
271#399C23112yes—
272#398C2316yes—
273#398C2316yes—
274#397C2316yes—
275#397C2316yes—
276#396C2316yes—
277#396C23112yes—
278#396C23112yes—
279#396C23112yes—
280#396C2312yes—
281#396C2316yes—
282#396C2316yes—
283#395C23112yes—
284#395C2316yes—
285#394C2316yes—
286#394C23112yes—
287#394C23112yes—
288#394C2316yes—
289#394C23112yes—
290#394C23112yes—
291#394C23112yes—
292#394C2316yes—
293#394C2316yes—
294#394C2312yes—
295#394C2316yes—
296#394C2316yes—
297#394C2316yes—
298#394C2316yes—
299#394C23112yes—
300#393C2316yes—
301#392C2312yes—
302#392C2316yes—
303#392C2316yes—
304#392C2316yes—
305#392C2316yes—
306#392C23112yes—
307#392C23112yes—
308#392C23112yes—
309#392C23112yes—
310#391C2316yes—
311#391C2316yes—
312#391C2316yes—
313#391C2316yes—
314#390C2311yescharacteristic
315#390C2313yes—
316#390C2316yes—
317#390C2316yes—
318#390C2313yes—
319#390C2316yes—
320#390C2316yes—
321#390C2316yes—
322#390C2316yes—
323#390C2316yes—
324#390C2316yes—
325#390C2316yes—
326#390C2316yes—
327#390C2313yes—
328#390C2313yes—
329#390C23112yes—
330#390C2311yescharacteristic
331#389C2313yes—
332#389C2316yes—
333#389C2316yes—
334#389C2316yes—
335#389C2313yes—
336#389C23112yes—
337#389C2313yes—
338#389C2311yescharacteristic
339#388C2316yes—
340#388C23112yes—
341#388C2316yes—
342#388C2316yes—
343#388C2316yes—
344#388C23112yes—
345#388C23112yes—
346#387C23112yes—
347#386C23112yes—
348#386C2316yes—
349#386C23112yes—
350#386C23112yes—
351#386C23112yes—
352#386C2316yes—
353#386C23112yes—
354#386C23112yes—
355#386C2316yes—
356#385C23112yes—
357#385C2316yes—
358#385C23112yes—
359#385C2316yes—
360#385C23112yes—
361#385C23112yes—
362#385C2312yes—
363#384C2313yes—
364#384C2313yes—
365#384C2313yes—
366#380C2316yes—
367#380C2316yes—
368#380C2316yes—
369#380C2316yes—
370#380C23112yes—
371#379C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2313yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C22⋊C4C2316yes—
380C4×C22⋊C4C2316yes—
381C4×C22⋊C4C2316yes—
382C4×C22⋊C4C2316yes—
383C43C2313yes—
384C25C2416yes—
3852−1+4—4128no—
386C2×#41—28no—
387C2×#41—224no—
388C2×#41—224no—
389C2×#41—224no—
390C2×#41—28no—
391C2×#41—28no—
392C2×#41—28no—
393C2×#41—28no—
394C2×#41—224no—
395C2×#41—224no—
396C2×#41—224no—
397C2×#41—224no—
398C2×#41—224no—
399C2×#41—224no—
400C2×#41—224no—
401C2×#41—412no—
402C2×#41—412no—
403C2×#41—412no—
404C2×#41—412no—
405C2×#41—412no—
406C2×#41—4128no—
407C2×#41C2×D4116yes—
408C22×Q8—28no—
409C22×Q8—28no—
410C22×Q8—224no—
411C22×Q8—28no—
412C22×Q8—28no—
413C22×Q8—28no—
414C22×Q8—224no—
415C22×Q8—412no—
416C22×Q8C2×D4116yes—
417C22×Q8C2416yes—
418C22×Q8C2416yes—
419C22×Q8C2416yes—
420C22×Q8C2411yescharacteristic
421C22×D4—224no—
422C22×D4—224no—
423C22×D4—412no—
424C22×D4C2416yes—
425C22×D4C2416yes—
426C22×D4C2412yes—
427C22×D4C2416yes—
428C22×D4C24112yes—
429C22×D4C2416yes—
430C22×D4C2412yes—
431C22×D4C2411yescharacteristic
432C22×D4C2416yes—
433C22×D4C24112yes—
434C22×D4C2416yes—
435C22×D4C2413yes—
436C22×D4C2416yes—
437C22×D4C2416yes—
438C22×D4C2416yes—
439C22×D4C2416yes—
440C22×D4C2411yescharacteristic
441C22×D4C2413yes—
442C22×D4C2416yes—
443C23×C4—224no—
444C23×C4—224no—
445C23×C4—412no—
446C23×C4C2416yes—
447C23×C4C2416yes—
448C23×C4C24112yes—
449C23×C4C2416yes—
450C23×C4C2416yes—
451C23×C4C2412yes—
452C23×C4C2416yes—
453C23×C4C2416yes—
454C23×C4C24112yes—
455C4⋊Q8—224no—
456C4⋊Q8—46no—
457C4⋊Q8C2×D4124yes—
458#127—248no—
459#127—224no—
460#127—46no—
461#127—46no—
462#127C2×D4124yes—
463#124—224no—
464#124—224no—
465#124—248no—
466#124—224no—
467#124—224no—
468#123—28no—
469#123—224no—
470#123—248no—
471#123—248no—
472#123—224no—
473#123—224no—
474C22⋊Q8—224no—
475C22⋊Q8—224no—
476C22⋊Q8—224no—
477C22⋊Q8—224no—
478C22⋊Q8—248no—
479C22⋊Q8—224no—
480C22⋊Q8—224no—
481C22⋊Q8—224no—
482C22⋊Q8—224no—
483C22⋊Q8—224no—
484C22⋊Q8—224no—
485C22⋊Q8—412no—
486C22⋊Q8C2×D4148yes—
487#121—28no—
488#121—224no—
489#121—224no—
490#121—224no—
491#121—248no—
492#121—248no—
493#121—224no—
494#121—224no—
495#121—224no—
496#121—248no—
497#121—224no—
498#121—224no—
499#121—224no—
500#121—248no—
501#121—412no—
502#121—812no—
503#121C2×D4148yes—
504#120—248no—
505#120—224no—
506#120—224no—
507#120—224no—
508#120—224no—
509#120—412no—
510#120—812no—
511C4×Q8—28no—
512C4×Q8—28no—
513C4×Q8—24no—
514C4×Q8—224no—
515C4×Q8—224no—
516C4×Q8C2×D418yes—
517C4×Q8C2×D418yes—
518C4×D4—248no—
519C4×D4—224no—
520C4×D4—224no—
521C4×D4—224no—
522C4×D4—224no—
523C4×D4—224no—
524C4×D4—248no—
525C4×D4—224no—
526C4×D4—224no—
527C4×D4—224no—
528C4×D4—412no—
529C4×D4—46no—
530C4×D4—46no—
531C4×D4—86no—
532C4×D4C2×D4124yes—
533C4×D4C2×D4124yes—
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⋊C4C2416yes—
543C2×C4⋊C4C24112yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2416yes—
546C2×C4⋊C4C2416yes—
547C2×C4⋊C4C2416yes—
548C2×C4⋊C4C2416yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2416yes—
551C2×C4⋊C4C2416yes—
552C2×C4⋊C4C2413yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2413yes—
555C2×C4⋊C4C2413yes—
556C2×C4⋊C4C2416yes—
557C2×C4⋊C4C2416yes—
558C2×C4⋊C4C2416yes—
559C2×C4⋊C4C2413yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2411yescharacteristic
562C2×C4⋊C4C2413yes—
563C2×C4⋊C4C2416yes—
564C2×C4⋊C4C2413yes—
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2413yes—
567C2×C22⋊C4—248no—
568C2×C22⋊C4C2416yes—
569C2×C22⋊C4C24112yes—
570C2×C22⋊C4C24112yes—
571C2×C22⋊C4C2416yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2416yes—
574C2×C22⋊C4C2416yes—
575C2×C22⋊C4C2416yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2416yes—
581C2×C22⋊C4C24112yes—
582C2×C22⋊C4C2416yes—
583C2×C22⋊C4C2416yes—
584C2×C22⋊C4C24112yes—
585C2×C22⋊C4C2416yes—
586C2×C22⋊C4C2416yes—
587C2×C22⋊C4C2416yes—
588C2×C22⋊C4C2416yes—
589C2×C22⋊C4C2412yes—
590C2×C22⋊C4C24112yes—
591C2×C22⋊C4C2416yes—
592C2×C22⋊C4C2416yes—
593C2×C22⋊C4C2416yes—
594C2×C22⋊C4C24112yes—
595C2×C22⋊C4C2416yes—
596C2×C22⋊C4C2416yes—
597C2×C22⋊C4C2412yes—
598C2×C22⋊C4C2416yes—
599C2×C22⋊C4C2416yes—
600C2×C22⋊C4C2416yes—
601C2×C22⋊C4C2416yes—
602C2×C42C2416yes—
603C2×C42C2416yes—
604C2×C42C24112yes—
605C2×C42C2413yes—
606C2×C42C2413yes—
607C2×C42C2413yes—
608C2×C42C2411yescharacteristic
609C2×C42C2413yes—
610C2×C42C2413yes—
611C2×C42C2413yes—
612#95C2412yes—
613#95C2412yes—
614#95C2416yes—
615#95C2416yes—
616#95C2416yes—
617#95C2416yes—
618#95C2416yes—
619#95C2416yes—
620#95C2416yes—
621#95C24112yes—
622#95C2416yes—
623#95C2416yes—
624#95C24112yes—
625C24—212no—
626C24—212no—
627C24—46no—
628C24—46no—
629C24—46no—
630C24—46no—
631C24—46no—
632C24C2516yes—
633C24C2512yes—
634C24C2512yes—
635C24C2516yes—
636#41—264no—
637#41—496no—
638#41—496no—
639#41—496no—
640#41—496no—
641#41—496no—
642#41—432no—
643C2×Q8—264no—
644C2×Q8—212no—
645C2×Q8—212no—
646C2×Q8—212no—
647C2×Q8—212no—
648C2×Q8—212no—
649C2×Q8—212no—
650C2×Q8—212no—
651C2×Q8—46no—
652C2×Q8—496no—
653C2×Q8—432no—
654C2×Q8C22×D4124yes—
655C2×Q8C22×D414yes—
656C2×Q8C22×D414yes—
657C2×Q8H(5,𝔽2)14yes—
658C2×D4—24no—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—24no—
662C2×D4—224no—
663C2×D4—212no—
664C2×D4—212no—
665C2×D4—212no—
666C2×D4—224no—
667C2×D4—212no—
668C2×D4—212no—
669C2×D4—24no—
670C2×D4—212no—
671C2×D4—224no—
672C2×D4—212no—
673C2×D4—212no—
674C2×D4—212no—
675C2×D4—212no—
676C2×D4—212no—
677C2×D4—212no—
678C2×D4—22no—
679C2×D4—26no—
680C2×D4—496no—
681C2×D4—41no—
682C2×D4—46no—
683C2×D4—43no—
684C2×D4—412no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—43no—
688C2×D4—46no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—46no—
694C2×D4—46no—
695C2×D4—43no—
696C2×D4—46no—
697C2×D4—46no—
698C2×D4—46no—
699C2×D4—412no—
700C2×D4—46no—
701C2×D4—46no—
702C2×D4—46no—
703C2×D4—46no—
704C2×D4—46no—
705C2×D4—43no—
706C2×D4—46no—
707C2×D4—412no—
708C2×D4—46no—
709C2×D4—46no—
710C2×D4—46no—
711C2×D4—46no—
712C2×D4C22×D4124yes—
713C2×D4C22×D4124yes—
714C2×D4C22×D414yes—
715C2×D4C22×D4112yes—
716C22×C4—212no—
717C22×C4—212no—
718C22×C4—212no—
719C22×C4—212no—
720C22×C4—224no—
721C22×C4—212no—
722C22×C4—24no—
723C22×C4—224no—
724C22×C4—212no—
725C22×C4—212no—
726C22×C4—212no—
727C22×C4—212no—
728C22×C4—212no—
729C22×C4—212no—
730C22×C4—212no—
731C22×C4—24no—
732C22×C4—212no—
733C22×C4—212no—
734C22×C4—224no—
735C22×C4—42no—
736C22×C4—46no—
737C22×C4—46no—
738C22×C4—412no—
739C22×C4—496no—
740C22×C4—412no—
741C22×C4—412no—
742C22×C4C22×D4124yes—
743C22×C4C22×D4124yes—
744C22×C4C2513yes—
745C22×C4C2512yes—
746C22×C4C2512yes—
747C22×C4C2516yes—
748C22×C4C2516yes—
749C22×C4C2516yes—
750C22×C4C2512yes—
751C22×C4C2513yes—
752C22×C4C2513yes—
753C22×C4C2516yes—
754C22×C4C2512yes—
755C22×C4C2511yescharacteristic
756C22×C4C2511yescharacteristic
757C22×C4C2511yescharacteristic
758C22×C4C2513yes—
759C4⋊C4—212no—
760C4⋊C4—212no—
761C4⋊C4—212no—
762C4⋊C4—212no—
763C4⋊C4—224no—
764C4⋊C4—24no—
765C4⋊C4—212no—
766C4⋊C4—212no—
767C4⋊C4—212no—
768C4⋊C4—212no—
769C4⋊C4—24no—
770C4⋊C4—212no—
771C4⋊C4—212no—
772C4⋊C4—26no—
773C4⋊C4—41no—
774C4⋊C4—43no—
775C4⋊C4—41no—
776C4⋊C4—46no—
777C4⋊C4—41no—
778C4⋊C4—43no—
779C4⋊C4—43no—
780C4⋊C4—46no—
781C4⋊C4—46no—
782C4⋊C4C22×D4112yes—
783C4⋊C4C22×D4124yes—
784C4⋊C4C22×D4112yes—
785C4⋊C4C22×D414yes—
786C4⋊C4C22×D4112yes—
787C22⋊C4—212no—
788C22⋊C4—212no—
789C22⋊C4—24no—
790C22⋊C4—224no—
791C22⋊C4—212no—
792C22⋊C4—224no—
793C22⋊C4—224no—
794C22⋊C4—212no—
795C22⋊C4—24no—
796C22⋊C4—212no—
797C22⋊C4—212no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—212no—
802C22⋊C4—224no—
803C22⋊C4—212no—
804C22⋊C4—212no—
805C22⋊C4—212no—
806C22⋊C4—212no—
807C22⋊C4—212no—
808C22⋊C4—24no—
809C22⋊C4—46no—
810C22⋊C4—42no—
811C22⋊C4—46no—
812C22⋊C4—46no—
813C22⋊C4—46no—
814C22⋊C4—412no—
815C22⋊C4—46no—
816C22⋊C4—46no—
817C22⋊C4—412no—
818C22⋊C4—46no—
819C22⋊C4C22×D4124yes—
820C22⋊C4C22×D4124yes—
821C42—212no—
822C42—224no—
823C42—212no—
824C42—26no—
825C42—26no—
826C42—43no—
827C42—41no—
828C42—43no—
829C42C22×D4112yes—
830C42C22×D4112yes—
831C23—22no—
832C23—26no—
833C23—22no—
834C23—26no—
835C23—26no—
836C23—22no—
837C23—22no—
838C23—26no—
839C23—26no—
840C23—26no—
841C23—22no—
842C23—22no—
843C23—26no—
844C23—22no—
845C23—26no—
846C23—22no—
847C23—22no—
848C23—26no—
849C23—26no—
850C23—22no—
851C23—22no—
852C23—26no—
853C23—22no—
854C23—26no—
855C23—22no—
856C23—26no—
857C23—424no—
858C23—424no—
859C23—812no—
860C23—812no—
861C23—812no—
862C23—812no—
863C23—812no—
864C23C23×D414yes—
865C23C23×D4112yes—
866C23C2611yescharacteristic
867Q8—248no—
868Q8—424no—
869Q8—424no—
870Q8D42116yes—
871D4—248no—
872D4—424no—
873D4—44no—
874D4—412no—
875D4—448no—
876D4—48no—
877D4—424no—
878D4—44no—
879D4—424no—
880D4—48no—
881D4—424no—
882D4—812no—
883D4—812no—
884D4—86no—
885D4—812no—
886D4—812no—
887D4—812no—
888D4—824no—
889D4—166no—
890C2×C4—26no—
891C2×C4—22no—
892C2×C4—21no—
893C2×C4—22no—
894C2×C4—26no—
895C2×C4—23no—
896C2×C4—23no—
897C2×C4—21no—
898C2×C4—23no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—23no—
903C2×C4—21no—
904C2×C4—248no—
905C2×C4—248no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—26no—
909C2×C4—26no—
910C2×C4—26no—
911C2×C4—22no—
912C2×C4—26no—
913C2×C4—22no—
914C2×C4—23no—
915C2×C4—22no—
916C2×C4—26no—
917C2×C4—22no—
918C2×C4—26no—
919C2×C4—23no—
920C2×C4—26no—
921C2×C4—26no—
922C2×C4—23no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—26no—
927C2×C4—424no—
928C2×C4—48no—
929C2×C4—424no—
930C2×C4—448no—
931C2×C4—424no—
932C2×C4—424no—
933C2×C4—824no—
934C2×C4C23×D416yes—
935C2×C4C23×D412yes—
936C2×C4C23×D412yes—
937C2×C4C23×D416yes—
938C2×C4C23×D414yes—
939C2×C4C23×D4112yes—
940C2×C4C23×D416yes—
941C2×C4C23×D416yes—
942C2×C4C2×H(5,𝔽2)16yes—
943C2×C4#58512yes—
944C22—212no—
945C22—24no—
946C22—24no—
947C22—212no—
948C22—24no—
949C22—212no—
950C22—42no—
951C22—46no—
952C22—46no—
953C22—42no—
954C22—46no—
955C22—42no—
956C22—46no—
957C22—42no—
958C22—42no—
959C22—46no—
960C22—42no—
961C22—46no—
962C22—46no—
963C22—42no—
964C22—42no—
965C22—46no—
966C22—42no—
967C22—46no—
968C22—42no—
969C22—46no—
970C22—42no—
971C22—46no—
972C22—848no—
973C22C24×D411yescharacteristic
974C22C24×D411yescharacteristic
975C22C22×H(5,𝔽2)11yescharacteristic
976C22C2×#58511yescharacteristic
977C22H(7,𝔽2)11yescharacteristic
978C222−1+611yescharacteristic
979C222−1+611yescharacteristic
980C4—26no—
981C4—26no—
982C4—22no—
983C4—22no—
984C4—22no—
985C4—24no—
986C4—212no—
987C4—42no—
988C4—46no—
989C4—43no—
990C4—42no—
991C4—46no—
992C4—42no—
993C4—46no—
994C4C2×D42112yes—
995C2—412no—
996C2—44no—
997C2—82no—
998C2—86no—
999C2C22×D4211yescharacteristic
1000C2#6284811yescharacteristic
1001C2#6285311yescharacteristic
1002C2#6289711yescharacteristic
1003C2#6298811yescharacteristic
1004C2#6300311yescharacteristic
1005C2#6305211yescharacteristic
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×#3487C2semidirect
3. #59815C2semidirect
4. #59002C2semidirect
5. #52103C2semidirect
6. #45241C2semidirect
7. #44892C2semidirect
8. #44886C2semidirect
9. #39356C2semidirect
10. #39355C2semidirect
11. #37658C2semidirect
12. #37649C2semidirect
13. #36465C2semidirect
14. #36429C2semidirect
15. #35831C2semidirect
16. #35771C2semidirect
17. #35687C2semidirect
18. #34313C2semidirect
19. #34311C2semidirect
21. C23×#41C22semidirect
27. C2×#550C22semidirect
28. C2×#550C22semidirect
30. C2×D4×Q8C22semidirect
31. C2×D4×Q8C22semidirect
33. C2×#548C22semidirect
34. C2×#548C22semidirect
35. C2×#548C22semidirect
36. C2×#548C22semidirect
37. C2×#548C22semidirect
39. C2×#547C22semidirect
41. C2×#546C22semidirect
43. C2×#536C22semidirect
44. C2×#535C22semidirect
45. C2×#535C22semidirect
47. C2×#525C22semidirect
48. C2×#525C22semidirect
49. C22×C22⋊Q8C22semidirect
50. C2×#520C22semidirect
51. C2×#519C22semidirect
52. #2858C22semidirect
53. #2847C22semidirect
54. #2683C22semidirect
55. #2683C22semidirect
57. #2682C22semidirect
58. #2682C22semidirect
59. #2682C22semidirect
60. #2682C22semidirect
61. #2681C22semidirect
62. #2681C22semidirect
63. #2680C22semidirect
67. #2678C22semidirect
68. #2676C22semidirect
69. #2673C22semidirect
70. #2672C22semidirect
71. #2669C22semidirect
72. #2669C22semidirect
73. #2620C22semidirect
74. #2620C22semidirect
75. #2616C22semidirect
76. #2545C22semidirect
77. #2544C22semidirect
78. #2542C22semidirect
79. #2541C22semidirect
80. #2541C22semidirect
81. #2540C22semidirect
82. #2540C22semidirect
83. #2538C22semidirect
84. #2537C22semidirect
85. #2461C22semidirect
86. #2461C22semidirect
87. #2449C22semidirect
88. #2445C22semidirect
89. #2443C22semidirect
90. #2434C22semidirect
91. #2433C22semidirect
92. #2432C22semidirect
93. #2432C22semidirect
94. #2431C22semidirect
95. #2431C22semidirect
96. #2429C22semidirect
97. #2428C22semidirect
98. #2427C22semidirect
99. #2426C22semidirect
100. #2424C22semidirect
101. #2424C22semidirect
102. #2424C22semidirect
103. #2418C22semidirect
104. #2417C22semidirect
105. #2416C22semidirect
106. #2416C22semidirect
107. #2415C22semidirect
108. #2414C22semidirect
109. #2409C22semidirect
110. #2408C22semidirect
111. #2407C22semidirect
112. #2407C22semidirect
113. #2407C22semidirect
114. #2407C22semidirect
115. #2392C22semidirect
116. #2392C22semidirect
117. #2388C22semidirect
118. #2366C22semidirect
119. #2365C22semidirect
120. #2362C22semidirect
121. #2361C22semidirect
123. Q8×C4⋊C4C22semidirect
124. Q8×C4⋊C4C22semidirect
125. D4×C4⋊C4C22semidirect
126. D4×C4⋊C4C22semidirect
127. #2341C22semidirect
128. #2341C22semidirect
129. Q8×C22⋊C4C22semidirect
130. Q8×C22⋊C4C22semidirect
131. #2324C22semidirect
132. #2323C22semidirect
133. C4×C4⋊Q8C22semidirect
134. C4×#127C22semidirect
135. C4×#127C22semidirect
136. C4×#120C22semidirect
138. #2293C22semidirect
139. C42×Q8C22semidirect
162. #550D4semidirect
165. D4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#34872
#598152
#590022
#521032
#452412
#448922
#448862
#393562
#393552
#376582
#376492
#364652
#364292
#358312
#357712
#356872
#343132
#343112