Finite Group Databasebeta

← #6990346

Subgroups — #6990346

Order 512.

1581 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36314C211yesmaximal, characteristic, complemented
2#35131C211yesmaximal, characteristic
3#32822C211yesmaximal, characteristic, complemented
4#32822C211yesmaximal, characteristic, complemented
5#31316C211yesmaximal, characteristic, complemented
6#31314C211yesmaximal, characteristic
7#31296C211yesmaximal, characteristic, complemented
8#31294C211yesmaximal, characteristic, complemented
9#31006C211yesmaximal, characteristic, complemented
10#31004C211yesmaximal, characteristic
11#30998C211yesmaximal, characteristic, complemented
12#30996C211yesmaximal, characteristic, complemented
13#30225C211yesmaximal, characteristic, complemented
14#30221C211yesmaximal, characteristic, complemented
15#29801C211yesmaximal, characteristic, complemented
16#29797C211yesmaximal, characteristic, complemented
17#29692C211yesmaximal, characteristic, complemented
18#29563C211yesmaximal, characteristic, complemented
19#29557C211yesmaximal, characteristic, complemented
20#28436C211yesmaximal, characteristic, complemented
21#28424C211yesmaximal, characteristic, complemented
22#27761C211yesmaximal, characteristic, complemented
23#27759C211yesmaximal, characteristic, complemented
24#25864C211yesmaximal, characteristic, complemented
25#25286C211yesmaximal, characteristic, complemented
26#25284C211yesmaximal, characteristic, complemented
27#24741C211yesmaximal, characteristic, complemented
28#24739C211yesmaximal, characteristic, complemented
29#24217C211yesmaximal, characteristic, complemented
30#23578C211yesmaximal, characteristic, complemented
31#22634C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#477C2211yescharacteristic, complemented
37C2×#476C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#464C2211yescharacteristic, complemented
42C2×#462C2211yescharacteristic, complemented
43C2×#460C2211yescharacteristic
44C2×#451C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#441C2211yescharacteristic, complemented
47C2×#440C2211yescharacteristic, complemented
48#2864C2211yescharacteristic, complemented
49#2864C2211yescharacteristic, complemented
50#2861C2211yescharacteristic
51#2861C2211yescharacteristic
52#2858C2211yescharacteristic
53#2858C2211yescharacteristic
54#2857C2211yescharacteristic
55#2662—21no—
56#2662—21no—
57#2610—21no—
58#2610—21no—
59#2571C2211yescharacteristic, complemented
60#2568C2211yescharacteristic, complemented
61#2545C2211yescharacteristic
62#2545C2211yescharacteristic
63#2544C2211yescharacteristic
64#2544C2211yescharacteristic
65#2533—21no—
66#2533—21no—
67#2530—21no—
68#2530—21no—
69#2511—21no—
70#2499—21no—
71#2495C2211yescharacteristic
72#2495C2211yescharacteristic
73#2436C2211yescharacteristic
74#2435C2211yescharacteristic
75#2434C2211yescharacteristic
76#2433C2211yescharacteristic
77#2421C2211yescharacteristic
78#2421C2211yescharacteristic
79#2411—21no—
80#2411—21no—
81#2365C2211yescharacteristic, complemented
82#2362—21no—
83#2356—21no—
84Q8×C4⋊C4C2211yescharacteristic, complemented
85#2321—21no—
86#2321—21no—
87C4×C22⋊Q8C2211yescharacteristic
88#2295C2211yescharacteristic, complemented
89#2295C2211yescharacteristic, complemented
90C4×#117C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2066C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic, complemented
123#2042C2211yescharacteristic, complemented
124#2042C2211yescharacteristic, complemented
125#2042C2211yescharacteristic, complemented
126#2042C2211yescharacteristic, complemented
127#2042C2211yescharacteristic, complemented
128#2041C2211yescharacteristic
129#2041C2211yescharacteristic
130#2041C2211yescharacteristic
131#2036C2211yescharacteristic
132#2035C2211yescharacteristic
133#2035C2211yescharacteristic
134#2034C2211yescharacteristic
135#2033C2211yescharacteristic
136#2033C2211yescharacteristic
137#2026C2211yescharacteristic, complemented
138#2016C2211yescharacteristic, complemented
139#2015C2211yescharacteristic
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2001C2211yescharacteristic
146#2000C2211yescharacteristic
147#1983C2211yescharacteristic
148#1983C2211yescharacteristic
149#1983C2211yescharacteristic
150#1983C2211yescharacteristic, complemented
151#1982C2211yescharacteristic
152#1981C2211yescharacteristic, complemented
153#1973C2211yescharacteristic
154#1971C2211yescharacteristic, complemented
155#1969C2211yescharacteristic, complemented
156#1968C2211yescharacteristic
157#1961C2211yescharacteristic
158#1961C2211yescharacteristic
159#1960C2211yescharacteristic, complemented
160#1960C2211yescharacteristic, complemented
161#1959C2211yescharacteristic
162#1959C2211yescharacteristic
163#1958C2211yescharacteristic
164#1958C2211yescharacteristic
165#1958C2211yescharacteristic, complemented
166#1958C2211yescharacteristic, complemented
167#1940C2211yescharacteristic, complemented
168#1940C2211yescharacteristic, complemented
169#1936C2211yescharacteristic
170#1935C2211yescharacteristic, complemented
171#1934C2211yescharacteristic
172#1933C2211yescharacteristic, complemented
173#1928C2211yescharacteristic, complemented
174#1927C2211yescharacteristic, complemented
175#1926C2211yescharacteristic
176#1925C2211yescharacteristic
177#1924C2211yescharacteristic
178#1924C2211yescharacteristic
179#1923C2211yescharacteristic
180#1923C2211yescharacteristic
181#1880C2211yescharacteristic
182#1880C2211yescharacteristic
183#1878C2211yescharacteristic, complemented
184#1878C2211yescharacteristic, complemented
185#1831C2211yescharacteristic, complemented
186#1831C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1797C2211yescharacteristic
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1787C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200#1749C2211yescharacteristic
201#1745C2211yescharacteristic, complemented
202#1744C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216#529—42no—
217#529—42no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—42no—
223C2×#124—42no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#123—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117D411yescharacteristic
249C2×#117D411yescharacteristic
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C42C2311yescharacteristic
253#489—42no—
254#489—42no—
255#477—42no—
256#476—42no—
257#464—42no—
258#464—42no—
259#464—42no—
260#464—42no—
261#462—42no—
262#460—42no—
263#451—42no—
264#450—42no—
265#441—42no—
266#440—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395—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#392—21no—
360#392—21no—
361#391—21no—
362#391—21no—
363#391—21no—
364#391—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
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#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#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384—21no—
440#384C2311yescharacteristic
441#383—21no—
442#383—21no—
443#382—21no—
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#382C2311yescharacteristic
448#380—21no—
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4D411yescharacteristic
459C4×C4⋊C4D411yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4D411yescharacteristic
467C4×C22⋊C4D411yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376—21no—
471#376—21no—
472#376D411yescharacteristic
473#376D411yescharacteristic
474C43C2311yescharacteristic
475C43C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561#127—41no—
562#127—41no—
563#127—41no—
564#127—41no—
565#126—44no—
566#125—41no—
567#125—41no—
568#124—22no—
569#124—22no—
570#124—22no—
571#124—22no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—44no—
579#124—44no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#123—44no—
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—44no—
594#121—41no—
595#121—41no—
596#120—44no—
597#120—44no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—44no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—44no—
610#117—42no—
611#117—44no—
612#117—42no—
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—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⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—44no—
684C2×C22⋊C4—44no—
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—22no—
690C2×C42—22no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#107—41no—
715#107—41no—
716#107—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
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#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774#97—22no—
775#97—22no—
776#97—41no—
777#97—41no—
778C4×C8—41no—
779C4×C8—41no—
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#95—21no—
816#95—21no—
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—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
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—42no—
860C2×Q8—42no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—82no—
866C2×Q8—82no—
867C2×Q8—82no—
868C2×Q8—82no—
869C2×Q8H(5,𝔽2)12yes—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
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—21no—
887C2×D4—21no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—82no—
910C22×C4—22no—
911C22×C4—21no—
912C22×C4—22no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—22no—
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—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C2511yescharacteristic
955Q16—44no—
956Q16—82no—
957Q16—82no—
958SD16—44no—
959SD16—82no—
960SD16—82no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
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—
985C4⋊C4—22no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
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—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—41no—
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—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
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—
1067C22⋊C4—81no—
1068C42—22no—
1069C42—22no—
1070C42—22no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—41no—
1082C42—41no—
1083C42—41no—
1084C42—41no—
1085C42—41no—
1086C42—41no—
1087C42—41no—
1088C42—42no—
1089C42—42no—
1090C42—42no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42H(5,𝔽2)12yes—
1096C42H(5,𝔽2)12yes—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
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—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—84no—
1125C23—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23#57512yes—
1132C23C23×D411yescharacteristic
1133Q8—22no—
1134Q8—22no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—84no—
1150Q8—84no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—84no—
1164D4—84no—
1165D4—162no—
1166D4—162no—
1167D4—162no—
1168D4—162no—
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—21no—
1190C2×C4—22no—
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—21no—
1205C2×C4—21no—
1206C2×C4—44no—
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—82no—
1250C2×C4—84no—
1251C2×C4—84no—
1252C2×C4#53512yes—
1253C2×C4#53512yes—
1254C2×C4#57512yes—
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4#58511yescharacteristic
1259C2×C4#58511yescharacteristic
1260C2×C4#58511yescharacteristic
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
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—168no—
1298C22C2×#53511yescharacteristic
1299C22#348811yescharacteristic
1300C22#350011yescharacteristic
1301C22C2×#57511yescharacteristic
1302C22C2×#57511yescharacteristic
1303C22#358411yescharacteristic
1304C22#358611yescharacteristic
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—42no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4#354211yescharacteristic
1332C4#354211yescharacteristic
1333C4#355111yescharacteristic
1334C4#355111yescharacteristic
1335C2—42no—
1336C2—161no—
1337C2—161no—
1338C2—161no—
1339C2#4296211yescharacteristic
1340C2#6080511yescharacteristic
1341C2#6081611yescharacteristic
1342C2#6197211yescharacteristic
1343C2#6199211yescharacteristic
1344C2#6254811yescharacteristic
1345C2#6258511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36314C2semidirect
3. #32822C2semidirect
4. #32822C2semidirect
5. #31316C2semidirect
7. #31296C2semidirect
8. #31294C2semidirect
9. #31006C2semidirect
11. #30998C2semidirect
12. #30996C2semidirect
13. #30225C2semidirect
14. #30221C2semidirect
15. #29801C2semidirect
16. #29797C2semidirect
17. #29692C2semidirect
18. #29563C2semidirect
19. #29557C2semidirect
20. #28436C2semidirect
21. #28424C2semidirect
22. #27761C2semidirect
23. #27759C2semidirect
24. #25864C2semidirect
25. #25286C2semidirect
26. #25284C2semidirect
27. #24741C2semidirect
28. #24739C2semidirect
29. #24217C2semidirect
30. #23578C2semidirect
31. #22634C2semidirect
36. C2×#477C22semidirect
37. C2×#476C22semidirect
41. C2×#464C22semidirect
42. C2×#462C22semidirect
46. C2×#441C22semidirect
47. C2×#440C22semidirect
48. #2864C22semidirect
49. #2864C22semidirect
59. #2571C22semidirect
60. #2568C22semidirect
81. #2365C22semidirect
84. Q8×C4⋊C4C22semidirect
88. #2295C22semidirect
89. #2295C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
99. #2068C22semidirect
100. #2068C22semidirect
103. #2066C22semidirect
104. #2066C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
122. #2042C22semidirect
123. #2042C22semidirect
124. #2042C22semidirect
125. #2042C22semidirect
126. #2042C22semidirect
127. #2042C22semidirect
137. #2026C22semidirect
138. #2016C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
150. #1983C22semidirect
152. #1981C22semidirect
154. #1971C22semidirect
155. #1969C22semidirect
159. #1960C22semidirect
160. #1960C22semidirect
165. #1958C22semidirect
166. #1958C22semidirect
167. #1940C22semidirect
168. #1940C22semidirect
170. #1935C22semidirect
172. #1933C22semidirect
173. #1928C22semidirect
174. #1927C22semidirect
183. #1878C22semidirect
184. #1878C22semidirect
185. #1831C22semidirect
186. #1831C22semidirect
187. #1803C22semidirect
188. #1802C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1763C22semidirect
199. #1762C22semidirect
201. #1745C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#363142
#351312
#328222
#313162
#313142
#312962
#312942
#310062
#310042
#309982
#309962
#302252
#302212
#298012
#297972
#296922
#295632
#295572
#284362
#284242
#277612
#277592
#258642
#252862
#252842
#247412
#247392
#242172
#235782
#226342