Finite Group Databasebeta

← #7339095

Subgroups — #7339095

Order 512.

1627 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59030C211yesmaximal, characteristic
2#45502C211yesmaximal, characteristic, complemented
3#32102C211yesmaximal, characteristic, complemented
4#31978C211yesmaximal, characteristic, complemented
5#31776C211yesmaximal, characteristic, complemented
6#31500C211yesmaximal, characteristic, complemented
7#31324C211yesmaximal, characteristic, complemented
8#31302C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#31302C211yesmaximal, characteristic, complemented
11#31134C211yesmaximal, characteristic, complemented
12#30970C211yesmaximal, characteristic, complemented
13#30805C211yesmaximal, characteristic, complemented
14#30799C211yesmaximal, characteristic, complemented
15#29950C211yesmaximal, characteristic, complemented
16#29689C211yesmaximal, characteristic, complemented
17#29109C211yesmaximal, characteristic, complemented
18#28960C211yesmaximal, characteristic, complemented
19#28085C211yesmaximal, characteristic, complemented
20#27783C211yesmaximal, characteristic, complemented
21#27541C211yesmaximal, characteristic, complemented
22#27262C211yesmaximal, characteristic, complemented
23#27113C211yesmaximal, characteristic, complemented
24#27049C211yesmaximal, characteristic, complemented
25#26763C211yesmaximal, characteristic, complemented
26#26476C211yesmaximal, characteristic, complemented
27#25950C211yesmaximal, characteristic, complemented
28#25881C211yesmaximal, characteristic
29#25678C211yesmaximal, characteristic, complemented
30#24033C211yesmaximal, characteristic
31#22367C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#481C2211yescharacteristic
38C2×#475C2211yescharacteristic, complemented
39C2×#476C2211yescharacteristic
40C2×#474C2211yescharacteristic, complemented
41C22×#102C2211yescharacteristic
42#2857C2211yescharacteristic, complemented
43#2857C2211yescharacteristic, complemented
44#2841—21no—
45#2774—21no—
46#2774—21no—
47#2729—21no—
48#2729—21no—
49#2691—21no—
50#2685—21no—
51#2683—21no—
52#2677—21no—
53#2563C2211yescharacteristic
54#2551C2211yescharacteristic, complemented
55#2551C2211yescharacteristic, complemented
56#2544C2211yescharacteristic
57#2534—21no—
58#2507C2211yescharacteristic, complemented
59#2507C2211yescharacteristic, complemented
60#2497C2211yescharacteristic, complemented
61#2497C2211yescharacteristic, complemented
62#2497C2211yescharacteristic, complemented
63#2497C2211yescharacteristic, complemented
64#2490C2211yescharacteristic
65#2487C2211yescharacteristic
66#2476—21no—
67#2454C2211yescharacteristic
68#2445C2211yescharacteristic
69#2440C2211yescharacteristic, complemented
70#2440C2211yescharacteristic, complemented
71#2435C2211yescharacteristic
72#2435C2211yescharacteristic
73#2426C2211yescharacteristic
74#2418—21no—
75#2417C2211yescharacteristic
76#2411—21no—
77#2405—21no—
78#2376—21no—
79#2367C2211yescharacteristic
80#2361C2211yescharacteristic
81D4×C22⋊C4—21no—
82D4×C22⋊C4C2211yescharacteristic
83C4×#123C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2093C2211yescharacteristic
86#2093C2211yescharacteristic
87#2093C2211yescharacteristic, complemented
88#2093C2211yescharacteristic, complemented
89#2087C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2084C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2076C2211yescharacteristic, complemented
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic, complemented
96#2071C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic, complemented
102#2067C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2042C2211yescharacteristic, complemented
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2036C2211yescharacteristic, complemented
118#2036C2211yescharacteristic, complemented
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2036C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2024C2211yescharacteristic, complemented
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#2023C2211yescharacteristic, complemented
132#2023C2211yescharacteristic, complemented
133#1992C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic, complemented
136#1982C2211yescharacteristic
137#1959C2211yescharacteristic
138#1959C2211yescharacteristic, complemented
139#1959C2211yescharacteristic, complemented
140#1954C2211yescharacteristic
141#1948C2211yescharacteristic, complemented
142#1944C2211yescharacteristic, complemented
143#1942C2211yescharacteristic, complemented
144#1940C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1936C2211yescharacteristic, complemented
151#1936C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1924C2211yescharacteristic, complemented
158#1924C2211yescharacteristic, complemented
159#1924C2211yescharacteristic, complemented
160#1924C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic, complemented
172#1865C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1862C2211yescharacteristic, complemented
177#1862C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1852C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1850C2211yescharacteristic, complemented
183#1824C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1808C2211yescharacteristic, complemented
186#1803C2211yescharacteristic, complemented
187#1802C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1797C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1749C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C23×C8C2311yescharacteristic
207D42—42no—
208D42—42no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215#529—42no—
216#529—42no—
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123D411yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#120—21no—
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250#501—42no—
251#489—42no—
252#486—42no—
253#481—42no—
254#476—42no—
255#475—42no—
256#474—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#102—42no—
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#395—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#393—21no—
358#393—21no—
359#391—21no—
360#391—21no—
361#391C2311yescharacteristic
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388D411yescharacteristic
402#388D411yescharacteristic
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387D411yescharacteristic
410#387D411yescharacteristic
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386D411yescharacteristic
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385D411yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#381D411yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—44no—
515C22×D4—44no—
516C22×D4—82no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C22×C8—41no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—82no—
548C4⋊Q8—82no—
549#127—22no—
550#127—41no—
551#126—44no—
552#125—22no—
553#125—41no—
554#124—22no—
555#124—22no—
556#124—41no—
557#124—41no—
558#124—41no—
559#124—41no—
560#123—24no—
561#123—44no—
562#123—82no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—82no—
568C22⋊Q8—82no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—44no—
575#121—41no—
576#120—44no—
577#120—44no—
578C4×Q8—22no—
579C4×Q8—41no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—44no—
589C4×D4—82no—
590#117—44no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4—82no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—22no—
712#106—22no—
713#106—22no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758#97—41no—
759#97—41no—
760#97—41no—
761#97—41no—
762C4×C8—41no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799C24—21no—
800C24—21no—
801C24—21no—
802C24—42no—
803C24—42no—
804C24—42no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—42no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—42no—
825C2×Q8—42no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×D4—24no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—44no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—81no—
877C2×D4—816no—
878C2×D4#13714yes—
879C2×D4H(5,𝔽2)12yes—
880C2×D42−1+412yes—
881C22×C4—21no—
882C22×C4—22no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—21no—
897C22×C4—21no—
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—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—41no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C2511yescharacteristic
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—82no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4H(5,𝔽2)12yes—
1024C22⋊C4—24no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—41no—
1078C42—41no—
1079C42—42no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—22no—
1097C23—22no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23—84no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23C2×#13712yes—
1132C23C2×#13712yes—
1133C23C23×D411yescharacteristic
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—162no—
1139Q8—162no—
1140Q8—162no—
1141D4—22no—
1142D4—22no—
1143D4—22no—
1144D4—22no—
1145D4—44no—
1146D4—48no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—84no—
1156D4—84no—
1157D4—84no—
1158D4—84no—
1159D4—162no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
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—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
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—82no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—82no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4C2×#13712yes—
1249C2×C4#57612yes—
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4C2×H(5,𝔽2)11yescharacteristic
1252C2×C4C2×2−1+411yescharacteristic
1253C2×C4#58511yescharacteristic
1254C2×C4#58511yescharacteristic
1255C2×C4#58511yescharacteristic
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—168no—
1300C22—168no—
1301C22#348411yescharacteristic
1302C22#348911yescharacteristic
1303C22#350011yescharacteristic
1304C22C22×#13711yescharacteristic
1305C22C2×#57611yescharacteristic
1306C22#358511yescharacteristic
1307C22#358511yescharacteristic
1308C4—22no—
1309C4—22no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4#353511yescharacteristic
1334C4#355111yescharacteristic
1335C4#356011yescharacteristic
1336C4#356111yescharacteristic
1337C2—42no—
1338C2—42no—
1339C2—82no—
1340C2—82no—
1341C2—161no—
1342C2#4795611yescharacteristic
1343C2#6157011yescharacteristic
1344C2#6161711yescharacteristic
1345C2#6212711yescharacteristic
1346C2#6223111yescharacteristic
1347C2#6258211yescharacteristic
1348C2#6261011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45502C2semidirect
3. #32102C2semidirect
4. #31978C2semidirect
5. #31776C2semidirect
6. #31500C2semidirect
7. #31324C2semidirect
8. #31302C2semidirect
9. #31302C2semidirect
10. #31302C2semidirect
11. #31134C2semidirect
12. #30970C2semidirect
13. #30805C2semidirect
14. #30799C2semidirect
15. #29950C2semidirect
16. #29689C2semidirect
17. #29109C2semidirect
18. #28960C2semidirect
19. #28085C2semidirect
20. #27783C2semidirect
21. #27541C2semidirect
22. #27262C2semidirect
23. #27113C2semidirect
24. #27049C2semidirect
25. #26763C2semidirect
26. #26476C2semidirect
27. #25950C2semidirect
29. #25678C2semidirect
31. #22367C2semidirect
34. C2×#501C22semidirect
35. C2×#489C22semidirect
38. C2×#475C22semidirect
40. C2×#474C22semidirect
42. #2857C22semidirect
43. #2857C22semidirect
54. #2551C22semidirect
55. #2551C22semidirect
58. #2507C22semidirect
59. #2507C22semidirect
60. #2497C22semidirect
61. #2497C22semidirect
62. #2497C22semidirect
63. #2497C22semidirect
69. #2440C22semidirect
70. #2440C22semidirect
87. #2093C22semidirect
88. #2093C22semidirect
89. #2087C22semidirect
90. #2086C22semidirect
91. #2084C22semidirect
92. #2076C22semidirect
93. #2076C22semidirect
95. #2071C22semidirect
96. #2071C22semidirect
97. #2068C22semidirect
101. #2067C22semidirect
102. #2067C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2059C22semidirect
106. #2059C22semidirect
107. #2057C22semidirect
110. #2042C22semidirect
111. #2042C22semidirect
112. #2042C22semidirect
113. #2042C22semidirect
116. #2036C22semidirect
117. #2036C22semidirect
118. #2036C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
121. #2036C22semidirect
128. #2024C22semidirect
131. #2023C22semidirect
132. #2023C22semidirect
133. #1992C22semidirect
135. #1983C22semidirect
138. #1959C22semidirect
139. #1959C22semidirect
141. #1948C22semidirect
142. #1944C22semidirect
143. #1942C22semidirect
144. #1940C22semidirect
148. #1936C22semidirect
149. #1936C22semidirect
150. #1936C22semidirect
151. #1936C22semidirect
152. #1933C22semidirect
153. #1928C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
157. #1924C22semidirect
158. #1924C22semidirect
159. #1924C22semidirect
160. #1924C22semidirect
161. #1921C22semidirect
162. #1920C22semidirect
163. #1919C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
168. #1892C22semidirect
169. #1872C22semidirect
171. #1865C22semidirect
172. #1865C22semidirect
175. #1862C22semidirect
176. #1862C22semidirect
177. #1862C22semidirect
178. #1862C22semidirect
179. #1852C22semidirect
180. #1852C22semidirect
181. #1852C22semidirect
182. #1850C22semidirect
183. #1824C22semidirect
184. #1824C22semidirect
185. #1808C22semidirect
186. #1803C22semidirect
187. #1802C22semidirect
188. #1802C22semidirect
189. #1797C22semidirect
197. #1776C22semidirect
198. #1771C22semidirect
199. #1762C22semidirect
201. #1752C22semidirect
202. #1749C22semidirect

Maximal subgroups

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

subgroupindex
#590302
#455022
#321022
#319782
#317762
#315002
#313242
#313022
#311342
#309702
#308052
#307992
#299502
#296892
#291092
#289602
#280852
#277832
#275412
#272622
#271132
#270492
#267632
#264762
#259502
#258812
#256782
#240332
#223672