Finite Group Databasebeta

← #7238690

Subgroups — #7238690

Order 512.

1587 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40124C211yesmaximal, characteristic, complemented
2#38918C211yesmaximal, characteristic
3#32744C211yesmaximal, characteristic, complemented
4#32103C211yesmaximal, characteristic, complemented
5#31990C211yesmaximal, characteristic, complemented
6#31677C211yesmaximal, characteristic, complemented
7#31586C211yesmaximal, characteristic, complemented
8#31494C211yesmaximal, characteristic, complemented
9#31316C211yesmaximal, characteristic, complemented
10#31287C211yesmaximal, characteristic, complemented
11#31013C211yesmaximal, characteristic, complemented
12#30990C211yesmaximal, characteristic, complemented
13#30901C211yesmaximal, characteristic, complemented
14#30654C211yesmaximal, characteristic, complemented
15#30407C211yesmaximal, characteristic, complemented
16#29479C211yesmaximal, characteristic, complemented
17#27756C211yesmaximal, characteristic, complemented
18#27523C211yesmaximal, characteristic, complemented
19#27265C211yesmaximal, characteristic, complemented
20#26979C211yesmaximal, characteristic, complemented
21#26934C211yesmaximal, characteristic, complemented
22#26840C211yesmaximal, characteristic, complemented
23#26181C211yesmaximal, characteristic, complemented
24#25864C211yesmaximal, characteristic, complemented
25#25089C211yesmaximal, characteristic, complemented
26#24921C211yesmaximal, characteristic, complemented
27#24743C211yesmaximal, characteristic, complemented
28#24259C211yesmaximal, characteristic
29#24217C211yesmaximal, characteristic, complemented
30#24037C211yesmaximal, characteristic
31#22371C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#467C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#462C2211yescharacteristic, complemented
42C2×#452C2211yescharacteristic
43C2×#451C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#416C2211yescharacteristic
48#2857C2211yescharacteristic
49#2855C2211yescharacteristic
50#2809—21no—
51#2775—21no—
52#2744—21no—
53#2717—21no—
54#2717—21no—
55#2694—21no—
56#2686—21no—
57#2686—21no—
58#2664—21no—
59#2622—21no—
60#2560—21no—
61#2556—21no—
62#2552C2211yescharacteristic, complemented
63#2547C2211yescharacteristic
64#2547C2211yescharacteristic
65#2538C2211yescharacteristic
66#2506C2211yescharacteristic, complemented
67#2496C2211yescharacteristic, complemented
68#2495C2211yescharacteristic
69#2485C2211yescharacteristic
70#2483—21no—
71#2451C2211yescharacteristic, complemented
72#2447C2211yescharacteristic
73#2447C2211yescharacteristic
74#2439C2211yescharacteristic, complemented
75#2434C2211yescharacteristic
76#2432C2211yescharacteristic
77#2432C2211yescharacteristic
78#2427C2211yescharacteristic
79#2427C2211yescharacteristic
80#2423C2211yescharacteristic
81#2423C2211yescharacteristic, complemented
82#2412—21no—
83#2409C2211yescharacteristic
84#2362C2211yescharacteristic, complemented
85#2351C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2336—21no—
88#2315—21no—
89C4×C22⋊Q8C2211yescharacteristic
90C4×#123C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2087C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2073C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic, complemented
128#2036C2211yescharacteristic, complemented
129#2035C2211yescharacteristic
130#2035C2211yescharacteristic, complemented
131#2033C2211yescharacteristic
132#2024C2211yescharacteristic, complemented
133#2016C2211yescharacteristic, complemented
134#2015C2211yescharacteristic
135#2015C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic, complemented
138#2000C2211yescharacteristic
139#1983C2211yescharacteristic
140#1983C2211yescharacteristic
141#1981C2211yescharacteristic, complemented
142#1971C2211yescharacteristic, complemented
143#1969C2211yescharacteristic, complemented
144#1960C2211yescharacteristic, complemented
145#1959C2211yescharacteristic
146#1959C2211yescharacteristic
147#1959C2211yescharacteristic
148#1956C2211yescharacteristic, complemented
149#1955C2211yescharacteristic
150#1943C2211yescharacteristic, complemented
151#1940C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1935C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1935C2211yescharacteristic, complemented
156#1935C2211yescharacteristic, complemented
157#1935C2211yescharacteristic, complemented
158#1934C2211yescharacteristic
159#1928C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic, complemented
164#1923C2211yescharacteristic
165#1923C2211yescharacteristic, complemented
166#1919C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1893C2211yescharacteristic
170#1892C2211yescharacteristic, complemented
171#1880C2211yescharacteristic
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1873C2211yescharacteristic, complemented
178#1873C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1850C2211yescharacteristic, complemented
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1797C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1770C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—42no—
213#546—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—42no—
223C2×#124—42no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123D411yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C42C2311yescharacteristic
253#489—42no—
254#489—42no—
255#482—42no—
256#467—42no—
257#464—42no—
258#464—42no—
259#464—42no—
260#462—42no—
261#452—42no—
262#451—42no—
263#450—42no—
264#440—42no—
265#440—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278#416—42no—
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#400—21no—
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#395—21no—
357#395—21no—
358#395—21no—
359#395—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#393—21no—
368#393—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388D411yescharacteristic
405#388D411yescharacteristic
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387D411yescharacteristic
418#387D411yescharacteristic
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386D411yescharacteristic
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385D411yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#383—21no—
441#382—21no—
442#382C2311yescharacteristic
443#381—21no—
444#381—21no—
445#381—21no—
446#381D411yescharacteristic
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×Q16—22no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568#126—82no—
569#125—44no—
570#125—82no—
571#124—22no—
572#124—22no—
573#124—22no—
574#124—22no—
575#124—22no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—44no—
582#124—44no—
583#123—42no—
584#123—44no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—82no—
596#121—22no—
597#121—41no—
598#121—44no—
599#120—44no—
600C4×Q8—22no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614#117—41no—
615#117—41no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
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—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—44no—
691C2×C22⋊C4—44no—
692C2×C22⋊C4—44no—
693C2×C22⋊C4—44no—
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#106—41no—
723#106—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774#97—41no—
775#97—41no—
776#97—41no—
777#97—41no—
778C4×C8—41no—
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#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#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—24no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836#41—44no—
837#41—82no—
838#41—82no—
839#41—82no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
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—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—42no—
864C2×Q8—42no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—82no—
870C2×Q8—82no—
871C2×Q8—82no—
872C2×Q8—82no—
873C2×Q8H(5,𝔽2)12yes—
874C2×D4—24no—
875C2×D4—22no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4H(5,𝔽2)12yes—
901C2×D4H(5,𝔽2)12yes—
902C22×C4—21no—
903C22×C4—22no—
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—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C2511yescharacteristic
962Q16—82no—
963Q16—82no—
964Q16—82no—
965SD16—44no—
966SD16—44no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
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—82no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
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—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—41no—
1095C42—41no—
1096C42—42no—
1097C42—42no—
1098C42—42no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—22no—
1111C23—22no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—48no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—84no—
1131C23—84no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23#57812yes—
1137C23C23×D411yescharacteristic
1138Q8—22no—
1139Q8—22no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—84no—
1155Q8—162no—
1156D4—22no—
1157D4—22no—
1158D4—22no—
1159D4—22no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—82no—
1165D4—84no—
1166D4—84no—
1167D4—162no—
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—21no—
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—22no—
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—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
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—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—82no—
1254C2×C4—82no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4#57512yes—
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C2×C4#58511yescharacteristic
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—42no—
1285C22—42no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—41no—
1294C22—42no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—168no—
1304C22#348411yescharacteristic
1305C22#348811yescharacteristic
1306C22#350011yescharacteristic
1307C22C2×#57511yescharacteristic
1308C22C2×#57811yescharacteristic
1309C22#358511yescharacteristic
1310C22#358611yescharacteristic
1311C4—22no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4#353311yescharacteristic
1338C4#353411yescharacteristic
1339C4#353411yescharacteristic
1340C4#356011yescharacteristic
1341C2—42no—
1342C2—81no—
1343C2—82no—
1344C2—82no—
1345C2#4636211yescharacteristic
1346C2#6159511yescharacteristic
1347C2#6164711yescharacteristic
1348C2#6197511yescharacteristic
1349C2#6202011yescharacteristic
1350C2#6258511yescharacteristic
1351C2#6260411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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
1. #40124C2semidirect
3. #32744C2semidirect
4. #32103C2semidirect
5. #31990C2semidirect
6. #31677C2semidirect
7. #31586C2semidirect
8. #31494C2semidirect
9. #31316C2semidirect
10. #31287C2semidirect
11. #31013C2semidirect
12. #30990C2semidirect
13. #30901C2semidirect
14. #30654C2semidirect
15. #30407C2semidirect
16. #29479C2semidirect
17. #27756C2semidirect
18. #27523C2semidirect
19. #27265C2semidirect
20. #26979C2semidirect
21. #26934C2semidirect
22. #26840C2semidirect
23. #26181C2semidirect
24. #25864C2semidirect
25. #25089C2semidirect
26. #24921C2semidirect
27. #24743C2semidirect
29. #24217C2semidirect
31. #22371C2semidirect
37. C2×#467C22semidirect
41. C2×#462C22semidirect
62. #2552C22semidirect
66. #2506C22semidirect
67. #2496C22semidirect
71. #2451C22semidirect
74. #2439C22semidirect
81. #2423C22semidirect
84. #2362C22semidirect
85. #2351C22semidirect
91. #2097C22semidirect
92. #2095C22semidirect
94. #2087C22semidirect
95. #2087C22semidirect
96. #2083C22semidirect
101. #2072C22semidirect
102. #2072C22semidirect
103. #2072C22semidirect
104. #2068C22semidirect
105. #2068C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
108. #2068C22semidirect
109. #2066C22semidirect
111. #2057C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2043C22semidirect
127. #2036C22semidirect
128. #2036C22semidirect
130. #2035C22semidirect
132. #2024C22semidirect
133. #2016C22semidirect
137. #2001C22semidirect
141. #1981C22semidirect
142. #1971C22semidirect
143. #1969C22semidirect
144. #1960C22semidirect
148. #1956C22semidirect
150. #1943C22semidirect
151. #1940C22semidirect
153. #1935C22semidirect
154. #1935C22semidirect
155. #1935C22semidirect
156. #1935C22semidirect
157. #1935C22semidirect
159. #1928C22semidirect
160. #1927C22semidirect
163. #1924C22semidirect
165. #1923C22semidirect
166. #1919C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
170. #1892C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
177. #1873C22semidirect
178. #1873C22semidirect
180. #1865C22semidirect
186. #1850C22semidirect
199. #1770C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#401242
#389182
#327442
#321032
#319902
#316772
#315862
#314942
#313162
#312872
#310132
#309902
#309012
#306542
#304072
#294792
#277562
#275232
#272652
#269792
#269342
#268402
#261812
#258642
#250892
#249212
#247432
#242592
#242172
#240372
#223712