Finite Group Databasebeta

← #7549149

Subgroups — #7549149

Order 512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45092C211yesmaximal, characteristic
2#35759C211yesmaximal, characteristic, complemented
3#32058C211yesmaximal, characteristic, complemented
4#32004C211yesmaximal, characteristic, complemented
5#31941C211yesmaximal, characteristic, complemented
6#31789C211yesmaximal, characteristic, complemented
7#28787C211yesmaximal, characteristic, complemented
8#27705C211yesmaximal, characteristic, complemented
9#27334C211yesmaximal, characteristic, complemented
10#27166C211yesmaximal, characteristic, complemented
11#26416C211yesmaximal, characteristic, complemented
12#26343C211yesmaximal, characteristic, complemented
13#26222C211yesmaximal, characteristic, complemented
14#26154C211yesmaximal, characteristic, complemented
15#25962C211yesmaximal, characteristic, complemented
16#25551C211yesmaximal, characteristic, complemented
17#25542C211yesmaximal, characteristic, complemented
18#25208C211yesmaximal, characteristic, complemented
19#25111C211yesmaximal, characteristic, complemented
20#24891C211yesmaximal, characteristic, complemented
21#24779C211yesmaximal, characteristic, complemented
22#24566C211yesmaximal, characteristic, complemented
23#24393C211yesmaximal, characteristic, complemented
24#24131C211yesmaximal, characteristic, complemented
25#23041C211yesmaximal, characteristic, complemented
26#22862C211yesmaximal, characteristic, complemented
27#22843C211yesmaximal, characteristic, complemented
28#22704C211yesmaximal, characteristic, complemented
29#22488C211yesmaximal, characteristic, complemented
30#20915C211yesmaximal, characteristic, complemented
31#20849C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#537C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×C8×D4C2211yescharacteristic
45C2×C8×D4C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C2×#427C2211yescharacteristic
48C2×#417C2211yescharacteristic
49C2×#416C2211yescharacteristic
50C2×#408C2211yescharacteristic
51C2×#408C2211yescharacteristic
52#2703—21no—
53#2699—21no—
54#2689—21no—
55#2688—21no—
56#2636—21no—
57#2616C2211yescharacteristic
58#2604—21no—
59#2581—21no—
60#2559—21no—
61#2535C2211yescharacteristic
62#2503C2211yescharacteristic
63#2503C2211yescharacteristic
64#2489C2211yescharacteristic
65#2488—21no—
66#2487C2211yescharacteristic
67#2466—21no—
68#2466—21no—
69#2459—21no—
70#2459—21no—
71#2444—21no—
72#2442C2211yescharacteristic
73#2439C2211yescharacteristic
74#2439C2211yescharacteristic
75#2420—21no—
76#2420C2211yescharacteristic
77#2415C2211yescharacteristic
78#2415C2211yescharacteristic
79#2415C2211yescharacteristic
80#2415C2211yescharacteristic
81#2407C2211yescharacteristic
82#2398—21no—
83#2388C2211yescharacteristic
84#2363C2211yescharacteristic
85#2360C2211yescharacteristic
86#2360C2211yescharacteristic
87#2352C2211yescharacteristic
88#2352C2211yescharacteristic
89#2352C2211yescharacteristic
90#2346C2211yescharacteristic
91#2339C2211yescharacteristic
92#2311C2211yescharacteristic
93#2101C2211yescharacteristic
94#2101C2211yescharacteristic
95#2097C2211yescharacteristic
96#2092C2211yescharacteristic
97#2088C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2074C2211yescharacteristic
104#2074C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2059C2211yescharacteristic
110#2057C2211yescharacteristic
111#2056C2211yescharacteristic
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic
121#2024C2211yescharacteristic
122#2001C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1993C2211yescharacteristic
126#1991C2211yescharacteristic
127#1989C2211yescharacteristic
128#1969C2211yescharacteristic
129#1968C2211yescharacteristic
130#1955C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1943C2211yescharacteristic
134#1942C2211yescharacteristic
135#1935C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1927C2211yescharacteristic
140#1926C2211yescharacteristic
141#1923C2211yescharacteristic
142#1923C2211yescharacteristic
143#1920C2211yescharacteristic
144#1920C2211yescharacteristic
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1893C2211yescharacteristic
148#1893C2211yescharacteristic
149#1892C2211yescharacteristic
150#1878C2211yescharacteristic
151#1877C2211yescharacteristic
152#1875C2211yescharacteristic
153#1875C2211yescharacteristic
154#1875C2211yescharacteristic
155#1874C2211yescharacteristic
156#1874C2211yescharacteristic
157#1873C2211yescharacteristic
158#1873C2211yescharacteristic
159#1873C2211yescharacteristic
160#1873C2211yescharacteristic
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic
163#1872C2211yescharacteristic
164#1870C2211yescharacteristic
165#1870C2211yescharacteristic
166#1869C2211yescharacteristic
167#1865C2211yescharacteristic
168#1864C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1850C2211yescharacteristic
184#1850C2211yescharacteristic
185#1835C2211yescharacteristic
186#1825C2211yescharacteristic
187#1824C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic
192#1804C2211yescharacteristic
193#1788C2211yescharacteristic
194C4×#107C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1735C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#556—42no—
213#556—42no—
214#553—24no—
215#553—42no—
216#537—24no—
217#537—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#123—21no—
225C2×C22⋊Q8—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×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240#520—42no—
241#520—42no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265#485—42no—
266#483—42no—
267#476—42no—
268#468—24no—
269#467—42no—
270#467—42no—
271#452—24no—
272#440—42no—
273C8×D4—24no—
274C8×D4—42no—
275#428—42no—
276#427—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294#417—42no—
295#416—42no—
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316#408—24no—
317#408—42no—
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
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×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#399—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395D411yescharacteristic
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#394D411yescharacteristic
362#394D411yescharacteristic
363#394D411yescharacteristic
364#393—21no—
365#393—21no—
366#393D411yescharacteristic
367#392—21no—
368#392—21no—
369#392D411yescharacteristic
370#392D411yescharacteristic
371#392D411yescharacteristic
372#391—21no—
373#391—21no—
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#381—21no—
440#381—21no—
441#381—21no—
442#381—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
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
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C22×Q8—21no—
515C22×Q8C2×D411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
525C22×D4C2×D411yescharacteristic
526C22×D4C2×D411yescharacteristic
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×Q16—22no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—22no—
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
570C4⋊Q8—22no—
571C4⋊Q8—41no—
572#126—44no—
573#126—44no—
574#126—44no—
575#125—22no—
576#125—41no—
577#124—44no—
578#123—44no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—44no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—44no—
598#121—41no—
599#121—41no—
600#121—44no—
601#121—44no—
602#121—44no—
603#121#4114yes—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—44no—
607C4×Q8—44no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4—44no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—22no—
627#117—22no—
628#117—41no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—41no—
634C2×C4⋊C4—22no—
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—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#107—22no—
738#107—22no—
739#107—22no—
740#107—41no—
741#107—41no—
742#107—41no—
743#107—41no—
744#106—22no—
745#106—22no—
746#106—41no—
747#106—41no—
748#106—41no—
749#106—41no—
750#106—41no—
751C4⋊C8—22no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—41no—
772#102—41no—
773#102—41no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8#4114yes—
785#97—41no—
786C4×C8—22no—
787C4×C8—41no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
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#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836#41—44no—
837#41—44no—
838#41—44no—
839#41—44no—
840#41—44no—
841#41—44no—
842#41—82no—
843#41—82no—
844C2×Q8—22no—
845C2×Q8—22no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
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—41no—
859C2×Q8—42no—
860C2×Q8—42no—
861C2×Q8—81no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—24no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4C2×#4112yes—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
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—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
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×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
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×C4C22×D411yescharacteristic
967C22×C4C2×#4112yes—
968C22×C4C2×#4112yes—
969C22×C4H(5,𝔽2)12yes—
970C22×C42−1+412yes—
971C22×C4C2511yescharacteristic
972Q16—82no—
973SD16—44no—
974M16—44no—
975M16—82no—
976C2×C8—21no—
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—44no—
999C2×C8—82no—
1000C2×C8—82no—
1001C2×C8C2×#4112yes—
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—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
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—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4C2×#4112yes—
1052C4⋊C4H(5,𝔽2)12yes—
1053C4⋊C4H(5,𝔽2)12yes—
1054C22⋊C4—24no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—24no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
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—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
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—
1096C42—24no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—42no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
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—22no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23#54612yes—
1146C23#54712yes—
1147C23C23×D411yescharacteristic
1148Q8—44no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—84no—
1158D4—22no—
1159D4—22no—
1160D4—44no—
1161D4—44no—
1162D4—44no—
1163D4—44no—
1164D4—44no—
1165D4—41no—
1166D4—41no—
1167D4—84no—
1168D4—82no—
1169D4—84no—
1170D4—162no—
1171D4—162no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
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—84no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4#54612yes—
1270C2×C4#54712yes—
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×2−1+411yescharacteristic
1277C8—22no—
1278C8—22no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—42no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—42no—
1315C22—41no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22C2×#54611yescharacteristic
1321C22C2×#54711yescharacteristic
1322C22#348411yescharacteristic
1323C22#358411yescharacteristic
1324C22#358411yescharacteristic
1325C22#358411yescharacteristic
1326C22#358611yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—42no—
1338C4—41no—
1339C4—42no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4#348111yescharacteristic
1353C4#351911yescharacteristic
1354C4#352011yescharacteristic
1355C4#353611yescharacteristic
1356C2—42no—
1357C2—42no—
1358C2—81no—
1359C2—81no—
1360C2—82no—
1361C2#5909011yescharacteristic
1362C2#6116911yescharacteristic
1363C2#6120711yescharacteristic
1364C2#6126111yescharacteristic
1365C2#6128011yescharacteristic
1366C2#6162611yescharacteristic
1367C2#6166611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45092C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35759C2semidirect
3. #32058C2semidirect
4. #32004C2semidirect
5. #31941C2semidirect
6. #31789C2semidirect
7. #28787C2semidirect
8. #27705C2semidirect
9. #27334C2semidirect
10. #27166C2semidirect
11. #26416C2semidirect
12. #26343C2semidirect
13. #26222C2semidirect
14. #26154C2semidirect
15. #25962C2semidirect
16. #25551C2semidirect
17. #25542C2semidirect
18. #25208C2semidirect
19. #25111C2semidirect
20. #24891C2semidirect
21. #24779C2semidirect
22. #24566C2semidirect
23. #24393C2semidirect
24. #24131C2semidirect
25. #23041C2semidirect
26. #22862C2semidirect
27. #22843C2semidirect
28. #22704C2semidirect
29. #22488C2semidirect
30. #20915C2semidirect
31. #20849C2semidirect

Maximal subgroups

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

subgroupindex
#450922
#357592
#320582
#320042
#319412
#317892
#287872
#277052
#273342
#271662
#264162
#263432
#262222
#261542
#259622
#255512
#255422
#252082
#251112
#248912
#247792
#245662
#243932
#241312
#230412
#228622
#228432
#227042
#224882
#209152
#208492