Finite Group Databasebeta

← #6767463

Subgroups — #6767463

Order 512.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38213C211yesmaximal, characteristic, complemented
2#35538C211yesmaximal, characteristic, complemented
3#32917C211yesmaximal, characteristic, complemented
4#31966C211yesmaximal, characteristic, complemented
5#31878C211yesmaximal, characteristic, complemented
6#31630C211yesmaximal, characteristic, complemented
7#31486C211yesmaximal, characteristic, complemented
8#31209C211yesmaximal, characteristic, complemented
9#31162C211yesmaximal, characteristic, complemented
10#30859C211yesmaximal, characteristic, complemented
11#30603C211yesmaximal, characteristic, complemented
12#30126C211yesmaximal, characteristic, complemented
13#30024C211yesmaximal, characteristic, complemented
14#29537C211yesmaximal, characteristic, complemented
15#29428C211yesmaximal, characteristic, complemented
16#29249C211yesmaximal, characteristic, complemented
17#28586C211yesmaximal, characteristic, complemented
18#28552C211yesmaximal, characteristic, complemented
19#26417C211yesmaximal, characteristic, complemented
20#26366C211yesmaximal, characteristic, complemented
21#25507C211yesmaximal, characteristic, complemented
22#25132C211yesmaximal, characteristic, complemented
23#25112C211yesmaximal, characteristic, complemented
24#25093C211yesmaximal, characteristic, complemented
25#25076C211yesmaximal, characteristic, complemented
26#24795C211yesmaximal, characteristic, complemented
27#24162C211yesmaximal, characteristic, complemented
28#22701C211yesmaximal, characteristic, complemented
29#22199C211yesmaximal, characteristic, complemented
30#22147C211yesmaximal, characteristic, complemented
31#20876C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#478C2211yescharacteristic, complemented
35C2×#469C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic, complemented
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#459C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#436C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic
48C2×#428C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2860C2211yescharacteristic, complemented
52#2797—21no—
53#2790—21no—
54#2779—21no—
55#2761—21no—
56#2625C2211yescharacteristic, complemented
57#2620C2211yescharacteristic
58#2603—21no—
59#2602—21no—
60#2539—21no—
61#2529—21no—
62#2512—21no—
63#2507C2211yescharacteristic, complemented
64#2496C2211yescharacteristic, complemented
65#2468—21no—
66#2456—21no—
67#2455—21no—
68#2454C2211yescharacteristic
69#2447C2211yescharacteristic, complemented
70#2445C2211yescharacteristic
71#2441C2211yescharacteristic
72#2433C2211yescharacteristic
73#2428C2211yescharacteristic
74#2426C2211yescharacteristic, complemented
75#2424—21no—
76#2422C2211yescharacteristic
77#2418—21no—
78#2417C2211yescharacteristic
79#2414—21no—
80#2414C2211yescharacteristic
81#2414C2211yescharacteristic
82#2411—21no—
83#2408C2211yescharacteristic
84#2362C2211yescharacteristic
85#2361C2211yescharacteristic
86#2324C2211yescharacteristic
87#2324C2211yescharacteristic
88#2324C2211yescharacteristic, complemented
89#2317C2211yescharacteristic
90C4×#127C2211yescharacteristic
91#2295C2211yescharacteristic, complemented
92#2293C2211yescharacteristic
93#2293C2211yescharacteristic
94#2100C2211yescharacteristic, complemented
95#2094C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2087C2211yescharacteristic, complemented
100#2086C2211yescharacteristic, complemented
101#2083C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic, complemented
113#2065C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic, complemented
120#2042C2211yescharacteristic, complemented
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2033C2211yescharacteristic, complemented
127#2026C2211yescharacteristic, complemented
128#2014C2211yescharacteristic
129#2012C2211yescharacteristic, complemented
130#2011C2211yescharacteristic
131#2000C2211yescharacteristic
132#1999C2211yescharacteristic
133#1999C2211yescharacteristic, complemented
134#1989C2211yescharacteristic, complemented
135#1982C2211yescharacteristic
136#1982C2211yescharacteristic
137#1970C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1948C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1939C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic, complemented
147#1934C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1893C2211yescharacteristic
159#1893C2211yescharacteristic, complemented
160#1893C2211yescharacteristic, complemented
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic, complemented
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1874C2211yescharacteristic
173#1873C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1864C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic
187#1853C2211yescharacteristic
188#1851C2211yescharacteristic
189#1851C2211yescharacteristic, complemented
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic, complemented
192#1831C2211yescharacteristic, complemented
193#1809C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1802C2211yescharacteristic
196#1802C2211yescharacteristic
197#1798C2211yescharacteristic
198#1798C2211yescharacteristic, complemented
199C4×C4⋊C8C2211yescharacteristic, complemented
200#1735C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#540—42no—
215#540—42no—
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#125C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×#120—21no—
240#518—42no—
241#518—42no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263#478—42no—
264#469—24no—
265#468—42no—
266#468—42no—
267#466—42no—
268#465—42no—
269#463—42no—
270#463—42no—
271#460—24no—
272#459—42no—
273#450—42no—
274#447—42no—
275#436—42no—
276C8×D4—42no—
277#428—42no—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296#418—24no—
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102—42no—
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#400—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390D411yescharacteristic
380#390D411yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#389—21no—
391#389—21no—
392#389D411yescharacteristic
393#389D411yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388D411yescharacteristic
421#388D411yescharacteristic
422#388D411yescharacteristic
423#388D411yescharacteristic
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#382—21no—
450#381—21no—
451#380—21no—
452#380—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467#376—21no—
468C43C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—22no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570#127—22no—
571#127—22no—
572#127—41no—
573#127—41no—
574#126—82no—
575#126—82no—
576#125—22no—
577#125—41no—
578#124—41no—
579#124—41no—
580#123—44no—
581#123—44no—
582#123—82no—
583#123—82no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—44no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—44no—
602#121—82no—
603#120—82no—
604#120—82no—
605#120—82no—
606C4×Q8—22no—
607C4×Q8—41no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—82no—
625C4×D4—82no—
626C4×D4—82no—
627#117—22no—
628#117—22no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635#117—82no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—44no—
719C2×C22⋊C4—44no—
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#107—22no—
746#107—22no—
747#107—41no—
748#107—41no—
749#107—41no—
750#106—22no—
751#106—41no—
752#106—41no—
753#106—41no—
754#106—41no—
755C4⋊C8—22no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763#103—22no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102#4114yes—
791C22⋊C8—22no—
792C22⋊C8—22no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C4×C8—41no—
796C4×C8—41no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—42no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×D4—28no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—41no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4C2×#4112yes—
910C2×D4H(5,𝔽2)12yes—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—24no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4H(5,𝔽2)12yes—
967C22×C42−1+412yes—
968C22×C4C2511yescharacteristic
969SD16—82no—
970SD16—82no—
971SD16—82no—
972D8—82no—
973D8—82no—
974D8—82no—
975M16—44no—
976M16—82no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—82no—
1001C2×C8—82no—
1002C2×C8C2×#4112yes—
1003C4⋊C4—22no—
1004C4⋊C4—22no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4C2×#4112yes—
1053C4⋊C4H(5,𝔽2)12yes—
1054C22⋊C4—24no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C42—22no—
1105C42—22no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—41no—
1117C42—41no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C42—81no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—21no—
1135C23—22no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—48no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—162no—
1167C23—162no—
1168C23—162no—
1169C23—162no—
1170C23—162no—
1171C23—162no—
1172C23#53712yes—
1173C23C23×D411yescharacteristic
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178D4—22no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—44no—
1183D4—48no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—84no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4#53712yes—
1291C2×C4#57612yes—
1292C2×C4#57712yes—
1293C2×C4C22×#4111yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4C2×2−1+411yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—22no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—42no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—168no—
1350C22C2×#53711yescharacteristic
1351C22D4×#4111yescharacteristic
1352C22#348411yescharacteristic
1353C22C2×#57611yescharacteristic
1354C22C2×#57711yescharacteristic
1355C22#358411yescharacteristic
1356C22#358511yescharacteristic
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—41no—
1361C4—42no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—42no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4#349211yescharacteristic
1382C4#351911yescharacteristic
1383C4#353411yescharacteristic
1384C4#354111yescharacteristic
1385C2—42no—
1386C2—81no—
1387C2—82no—
1388C2—82no—
1389C2—161no—
1390C2—161no—
1391C2#3835711yescharacteristic
1392C2#6092211yescharacteristic
1393C2#6093511yescharacteristic
1394C2#6149811yescharacteristic
1395C2#6154811yescharacteristic
1396C2#6165711yescharacteristic
1397C2#6168911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #38213C2semidirect
2. #35538C2semidirect
3. #32917C2semidirect
4. #31966C2semidirect
5. #31878C2semidirect
6. #31630C2semidirect
7. #31486C2semidirect
8. #31209C2semidirect
9. #31162C2semidirect
10. #30859C2semidirect
11. #30603C2semidirect
12. #30126C2semidirect
13. #30024C2semidirect
14. #29537C2semidirect
15. #29428C2semidirect
16. #29249C2semidirect
17. #28586C2semidirect
18. #28552C2semidirect
19. #26417C2semidirect
20. #26366C2semidirect
21. #25507C2semidirect
22. #25132C2semidirect
23. #25112C2semidirect
24. #25093C2semidirect
25. #25076C2semidirect
26. #24795C2semidirect
27. #24162C2semidirect
28. #22701C2semidirect
29. #22199C2semidirect
30. #22147C2semidirect
31. #20876C2semidirect
34. C2×#478C22semidirect
37. C2×#468C22semidirect
51. #2860C22semidirect
56. #2625C22semidirect
63. #2507C22semidirect
64. #2496C22semidirect
69. #2447C22semidirect
74. #2426C22semidirect
88. #2324C22semidirect
91. #2295C22semidirect
94. #2100C22semidirect
95. #2094C22semidirect
96. #2088C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
99. #2087C22semidirect
100. #2086C22semidirect
101. #2083C22semidirect
102. #2076C22semidirect
103. #2071C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
108. #2067C22semidirect
109. #2067C22semidirect
112. #2065C22semidirect
113. #2065C22semidirect
114. #2059C22semidirect
119. #2054C22semidirect
120. #2042C22semidirect
123. #2035C22semidirect
126. #2033C22semidirect
127. #2026C22semidirect
129. #2012C22semidirect
133. #1999C22semidirect
134. #1989C22semidirect
139. #1968C22semidirect
140. #1948C22semidirect
141. #1942C22semidirect
142. #1939C22semidirect
143. #1939C22semidirect
146. #1934C22semidirect
147. #1934C22semidirect
148. #1928C22semidirect
151. #1925C22semidirect
152. #1919C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
159. #1893C22semidirect
160. #1893C22semidirect
166. #1879C22semidirect
169. #1877C22semidirect
174. #1865C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1864C22semidirect
189. #1851C22semidirect
191. #1850C22semidirect
192. #1831C22semidirect
193. #1809C22semidirect
194. #1803C22semidirect
198. #1798C22semidirect
199. C4×C4⋊C8C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#382132
#355382
#329172
#319662
#318782
#316302
#314862
#312092
#311622
#308592
#306032
#301262
#300242
#295372
#294282
#292492
#285862
#285522
#264172
#263662
#255072
#251322
#251122
#250932
#250762
#247952
#241622
#227012
#221992
#221472
#208762