Finite Group Databasebeta

← #7549028

Subgroups — #7549028

Order 512.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59020C211yesmaximal, characteristic
2#36234C211yesmaximal, characteristic, complemented
3#32055C211yesmaximal, characteristic, complemented
4#32003C211yesmaximal, characteristic, complemented
5#31957C211yesmaximal, characteristic, complemented
6#31788C211yesmaximal, characteristic, complemented
7#28786C211yesmaximal, characteristic, complemented
8#27716C211yesmaximal, characteristic, complemented
9#27355C211yesmaximal, characteristic, complemented
10#27166C211yesmaximal, characteristic, complemented
11#26434C211yesmaximal, characteristic, complemented
12#26345C211yesmaximal, characteristic, complemented
13#26217C211yesmaximal, characteristic, complemented
14#26133C211yesmaximal, characteristic, complemented
15#25972C211yesmaximal, characteristic, complemented
16#25541C211yesmaximal, characteristic, complemented
17#25532C211yesmaximal, characteristic, complemented
18#25201C211yesmaximal, characteristic, complemented
19#25119C211yesmaximal, characteristic, complemented
20#24879C211yesmaximal, characteristic, complemented
21#24779C211yesmaximal, characteristic, complemented
22#24561C211yesmaximal, characteristic, complemented
23#24383C211yesmaximal, characteristic, complemented
24#24137C211yesmaximal, characteristic, complemented
25#23033C211yesmaximal, characteristic, complemented
26#22862C211yesmaximal, characteristic, complemented
27#22846C211yesmaximal, characteristic, complemented
28#22709C211yesmaximal, characteristic, complemented
29#22488C211yesmaximal, characteristic, complemented
30#20910C211yesmaximal, characteristic, complemented
31#20843C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#483C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic, complemented
39C2×#467C2211yescharacteristic
40C2×#467C2211yescharacteristic, complemented
41C2×#465C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#440C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic
46C2×#427C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C2×#417C2211yescharacteristic
49C2×#417C2211yescharacteristic
50C2×#407C2211yescharacteristic
51C22×C22⋊C8C2211yescharacteristic
52#2851—21no—
53#2848C2211yescharacteristic
54#2697—21no—
55#2668—21no—
56#2611—21no—
57#2609—21no—
58#2553—21no—
59#2537C2211yescharacteristic
60#2499C2211yescharacteristic
61#2499C2211yescharacteristic
62#2489C2211yescharacteristic
63#2485C2211yescharacteristic
64#2480—21no—
65#2478—21no—
66#2470—21no—
67#2466—21no—
68#2457—21no—
69#2442C2211yescharacteristic
70#2441C2211yescharacteristic
71#2441C2211yescharacteristic
72#2420—21no—
73#2420C2211yescharacteristic
74#2419—21no—
75#2418—21no—
76#2417C2211yescharacteristic
77#2417C2211yescharacteristic
78#2415C2211yescharacteristic
79#2415C2211yescharacteristic
80#2407C2211yescharacteristic
81#2364—21no—
82#2363C2211yescharacteristic
83#2362C2211yescharacteristic
84#2360C2211yescharacteristic
85#2352C2211yescharacteristic
86#2352C2211yescharacteristic
87D4×C4⋊C4C2211yescharacteristic
88#2346C2211yescharacteristic
89#2339C2211yescharacteristic
90C4×#120C2211yescharacteristic
91#2290—21no—
92#2280C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2100C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2094C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2074C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic, complemented
117#2035C2211yescharacteristic, complemented
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic, complemented
120#2026C2211yescharacteristic, complemented
121#2026C2211yescharacteristic, complemented
122#2001C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic, complemented
125#1992C2211yescharacteristic, complemented
126#1991C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1973C2211yescharacteristic, complemented
129#1969C2211yescharacteristic, complemented
130#1955C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1947C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1928C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1926C2211yescharacteristic, complemented
141#1924C2211yescharacteristic
142#1923C2211yescharacteristic
143#1920C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1893C2211yescharacteristic
148#1893C2211yescharacteristic, complemented
149#1892C2211yescharacteristic
150#1878C2211yescharacteristic, complemented
151#1877C2211yescharacteristic, complemented
152#1875C2211yescharacteristic
153#1875C2211yescharacteristic
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1874C2211yescharacteristic, complemented
157#1873C2211yescharacteristic
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1873C2211yescharacteristic
162#1873C2211yescharacteristic
163#1872C2211yescharacteristic, complemented
164#1870C2211yescharacteristic
165#1869C2211yescharacteristic
166#1869C2211yescharacteristic
167#1865C2211yescharacteristic, complemented
168#1864C2211yescharacteristic, complemented
169#1864C2211yescharacteristic, complemented
170#1862C2211yescharacteristic, complemented
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic
185#1836C2211yescharacteristic, complemented
186#1825C2211yescharacteristic
187#1824C2211yescharacteristic, complemented
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1808C2211yescharacteristic, complemented
191#1804C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic, complemented
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#553—24no—
213#553—42no—
214#552—42no—
215#552—42no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221#525—24no—
222#525—42no—
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120D411yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117—21no—
252C2×#117—21no—
253C2×#117—42no—
254C2×#117—42no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—21no—
267C22×C42—21no—
268#485—42no—
269#483—42no—
270#478—42no—
271#467—42no—
272#467—42no—
273#465—24no—
274#452—24no—
275#440—42no—
276#435—24no—
277C8×D4—42no—
278#427—42no—
279#427—42no—
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297#417—42no—
298#417—42no—
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319#407—42no—
320C2×C22⋊C8—24no—
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335#400—21no—
336#400—21no—
337#399—21no—
338#399—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—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#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#386D411yescharacteristic
415#386D411yescharacteristic
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385D411yescharacteristic
425#385D411yescharacteristic
426#385D411yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382—21no—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452#379D411yescharacteristic
453C4×C4⋊C4—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#376—21no—
467C2×#95—21no—
468#340C2311yescharacteristic
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#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25C2×D411yescharacteristic
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—22no—
520C23×C4—22no—
521C23×C4—22no—
522C23×C4—22no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C22×C8—22no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568#126—44no—
569#126—44no—
570#125—22no—
571#125—22no—
572#125—41no—
573#125—41no—
574#125—44no—
575#123—44no—
576#123—44no—
577#123—44no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—41no—
596#121—41no—
597#121—44no—
598#121—44no—
599#121#4114yes—
600#120—42no—
601#120—44no—
602C4×Q8—22no—
603C4×Q8—41no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—44no—
615C4×D4—44no—
616C4×D4—44no—
617C4×D4—44no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—44no—
626#117—44no—
627#117—44no—
628#117—41no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117—41no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
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—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
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—44no—
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—44no—
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—41no—
747#107—41no—
748#107—41no—
749#107—41no—
750#107—41no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758C4⋊C8—22no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—41no—
779#102—41no—
780#102—41no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8#4114yes—
792#97—22no—
793#97—41no—
794C4×C8—41no—
795#95—21no—
796#95—21no—
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#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834C24—21no—
835C24—22no—
836C24—22no—
837C24—41no—
838C24—41no—
839C24—41no—
840C24—41no—
841C24—41no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846#41—44no—
847#41—44no—
848#41—82no—
849#41—82no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—24no—
867C2×D4—22no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4C2×#4112yes—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
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—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
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×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C2×#4112yes—
969C22×C4C2×#4112yes—
970C22×C4H(5,𝔽2)12yes—
971C22×C42−1+412yes—
972C22×C4C2511yescharacteristic
973Q16—82no—
974SD16—44no—
975M16—82no—
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—44no—
1000C2×C8—44no—
1001C2×C8—82no—
1002C2×C8C2×#4112yes—
1003C2×C8C2×#4112yes—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
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—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
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—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4C2×#4112yes—
1057C4⋊C4H(5,𝔽2)12yes—
1058C4⋊C4H(5,𝔽2)12yes—
1059C22⋊C4—24no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—24no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
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—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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—
1102C42—24no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—22no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—44no—
1146C23—44no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—82no—
1154C23—82no—
1155C23—82no—
1156C23—82no—
1157C23—82no—
1158C23#54612yes—
1159C23#54712yes—
1160C23#57512yes—
1161C23C23×D411yescharacteristic
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170D4—22no—
1171D4—22no—
1172D4—44no—
1173D4—44no—
1174D4—41no—
1175D4—41no—
1176D4—82no—
1177D4—84no—
1178D4—84no—
1179D4—84no—
1180D4—84no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
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—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—84no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4—162no—
1280C2×C4#54612yes—
1281C2×C4#54712yes—
1282C2×C4C22×#4111yescharacteristic
1283C2×C4C22×#4111yescharacteristic
1284C2×C4C2×H(5,𝔽2)11yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4C2×2−1+411yescharacteristic
1288C8—22no—
1289C8—22no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—42no—
1327C22—88no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22C2×#54611yescharacteristic
1333C22C2×#54711yescharacteristic
1334C22#348411yescharacteristic
1335C22C2×#57511yescharacteristic
1336C22#358411yescharacteristic
1337C22#358411yescharacteristic
1338C22#358611yescharacteristic
1339C4—22no—
1340C4—22no—
1341C4—41no—
1342C4—42no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
1347C4—41no—
1348C4—42no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4#348111yescharacteristic
1365C4#351911yescharacteristic
1366C4#352011yescharacteristic
1367C4#353611yescharacteristic
1368C2—42no—
1369C2—42no—
1370C2—42no—
1371C2—81no—
1372C2—82no—
1373C2#5909011yescharacteristic
1374C2#6114111yescharacteristic
1375C2#6118811yescharacteristic
1376C2#6125311yescharacteristic
1377C2#6126111yescharacteristic
1378C2#6160611yescharacteristic
1379C2#6162611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59020C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36234C2semidirect
3. #32055C2semidirect
4. #32003C2semidirect
5. #31957C2semidirect
6. #31788C2semidirect
7. #28786C2semidirect
8. #27716C2semidirect
9. #27355C2semidirect
10. #27166C2semidirect
11. #26434C2semidirect
12. #26345C2semidirect
13. #26217C2semidirect
14. #26133C2semidirect
15. #25972C2semidirect
16. #25541C2semidirect
17. #25532C2semidirect
18. #25201C2semidirect
19. #25119C2semidirect
20. #24879C2semidirect
21. #24779C2semidirect
22. #24561C2semidirect
23. #24383C2semidirect
24. #24137C2semidirect
25. #23033C2semidirect
26. #22862C2semidirect
27. #22846C2semidirect
28. #22709C2semidirect
29. #22488C2semidirect
30. #20910C2semidirect
31. #20843C2semidirect
37. C2×#483C22semidirect
38. C2×#478C22semidirect
40. C2×#467C22semidirect
43. C2×#440C22semidirect
93. #2101C22semidirect
94. #2100C22semidirect
95. #2097C22semidirect
96. #2094C22semidirect
97. #2088C22semidirect
98. #2085C22semidirect
99. #2083C22semidirect
101. #2077C22semidirect
103. #2074C22semidirect
104. #2072C22semidirect
105. #2067C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2059C22semidirect
110. #2059C22semidirect
111. #2056C22semidirect
113. #2036C22semidirect
116. #2035C22semidirect
117. #2035C22semidirect
119. #2033C22semidirect
120. #2026C22semidirect
121. #2026C22semidirect
124. #2000C22semidirect
125. #1992C22semidirect
126. #1991C22semidirect
127. #1989C22semidirect
128. #1973C22semidirect
129. #1969C22semidirect
131. #1949C22semidirect
132. #1947C22semidirect
133. #1944C22semidirect
134. #1942C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
137. #1928C22semidirect
138. #1928C22semidirect
139. #1927C22semidirect
140. #1926C22semidirect
143. #1920C22semidirect
144. #1919C22semidirect
148. #1893C22semidirect
150. #1878C22semidirect
151. #1877C22semidirect
156. #1874C22semidirect
163. #1872C22semidirect
167. #1865C22semidirect
168. #1864C22semidirect
169. #1864C22semidirect
170. #1862C22semidirect
179. #1853C22semidirect
182. #1852C22semidirect
185. #1836C22semidirect
187. #1824C22semidirect
190. #1808C22semidirect
191. #1804C22semidirect
192. #1803C22semidirect
194. #1776C22semidirect
195. C4×#102C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#590202
#362342
#320552
#320032
#319572
#317882
#287862
#277162
#273552
#271662
#264342
#263452
#262172
#261332
#259722
#255412
#255322
#252012
#251192
#248792
#247792
#245612
#243832
#241372
#230332
#228622
#228462
#227092
#224882
#209102
#208432