Finite Group Databasebeta

← #7090020

Subgroups — #7090020

Order 512.

1723 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59843C211yesmaximal, characteristic, complemented
2#39024C211yesmaximal, characteristic, complemented
3#32666C211yesmaximal, characteristic, complemented
4#32614C211yesmaximal, characteristic, complemented
5#32412C211yesmaximal, characteristic, complemented
6#31933C211yesmaximal, characteristic, complemented
7#31681C211yesmaximal, characteristic, complemented
8#31306C211yesmaximal, characteristic, complemented
9#31044C211yesmaximal, characteristic, complemented
10#30607C211yesmaximal, characteristic, complemented
11#29445C211yesmaximal, characteristic, complemented
12#29429C211yesmaximal, characteristic, complemented
13#28847C211yesmaximal, characteristic, complemented
14#28194C211yesmaximal, characteristic, complemented
15#27534C211yesmaximal, characteristic, complemented
16#27518C211yesmaximal, characteristic, complemented
17#26966C211yesmaximal, characteristic, complemented
18#26929C211yesmaximal, characteristic, complemented
19#26617C211yesmaximal, characteristic, complemented
20#26549C211yesmaximal, characteristic, complemented
21#25305C211yesmaximal, characteristic, complemented
22#25242C211yesmaximal, characteristic, complemented
23#25218C211yesmaximal, characteristic, complemented
24#24901C211yesmaximal, characteristic, complemented
25#24355C211yesmaximal, characteristic, complemented
26#24272C211yesmaximal, characteristic
27#23680C211yesmaximal, characteristic, complemented
28#23206C211yesmaximal, characteristic, complemented
29#23143C211yesmaximal, characteristic, complemented
30C22⋊C4×D8C211yesmaximal, characteristic, complemented
31#22155C211yesmaximal, characteristic, complemented
32C23×D8C2211yescharacteristic
33C2×#551—21no—
34C2×#484C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic, complemented
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#446C2211yescharacteristic, complemented
42C2×C4×SD16C2211yescharacteristic, complemented
43C2×C4×D8C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45C2×#435C2211yescharacteristic
46#2860C2211yescharacteristic, complemented
47#2756—21no—
48#2735—21no—
49#2728—21no—
50#2702—21no—
51#2697—21no—
52#2685—21no—
53#2648—21no—
54#2609—21no—
55#2592C2211yescharacteristic, complemented
56#2538C2211yescharacteristic, complemented
57#2538C2211yescharacteristic, complemented
58#2538C2211yescharacteristic, complemented
59#2518—21no—
60#2500C2211yescharacteristic, complemented
61#2496C2211yescharacteristic
62#2496C2211yescharacteristic
63#2495C2211yescharacteristic
64#2486C2211yescharacteristic
65#2480—21no—
66#2480—21no—
67#2472—21no—
68#2457—21no—
69#2457—21no—
70#2435C2211yescharacteristic
71#2427C2211yescharacteristic, complemented
72#2426C2211yescharacteristic, complemented
73#2423C2211yescharacteristic
74#2422C2211yescharacteristic, complemented
75#2422C2211yescharacteristic, complemented
76#2415C2211yescharacteristic
77#2408C2211yescharacteristic
78#2408C2211yescharacteristic
79#2363C2211yescharacteristic, complemented
80#2361C2211yescharacteristic, complemented
81#2361C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85#2312—21no—
86C4×#124C2211yescharacteristic
87C4×#124C2211yescharacteristic, complemented
88#2293C2211yescharacteristic, complemented
89#2293C2211yescharacteristic, complemented
90#2096C2211yescharacteristic, complemented
91#2094C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2065C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2034C2211yescharacteristic, complemented
123#2034C2211yescharacteristic, complemented
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#2000C2211yescharacteristic, complemented
128#1999C2211yescharacteristic
129#1999C2211yescharacteristic
130#1985C2211yescharacteristic, complemented
131#1983C2211yescharacteristic, complemented
132#1973C2211yescharacteristic, complemented
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1970C2211yescharacteristic
136#1970C2211yescharacteristic
137#1959C2211yescharacteristic, complemented
138#1955C2211yescharacteristic
139#1949C2211yescharacteristic, complemented
140#1947C2211yescharacteristic, complemented
141#1944C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1936C2211yescharacteristic, complemented
144#1936C2211yescharacteristic, complemented
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic, complemented
150#1934C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1926C2211yescharacteristic, complemented
153#1926C2211yescharacteristic, complemented
154#1925C2211yescharacteristic, complemented
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic
157#1923C2211yescharacteristic, complemented
158#1923C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1894C2211yescharacteristic, complemented
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1877C2211yescharacteristic, complemented
172#1875C2211yescharacteristic, complemented
173#1874C2211yescharacteristic, complemented
174#1874C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic, complemented
177#1864C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1862C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1851C2211yescharacteristic, complemented
183#1850C2211yescharacteristic
184#1834C2211yescharacteristic, complemented
185#1808C2211yescharacteristic
186#1807C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1802C2211yescharacteristic, complemented
189#1802C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1767C2211yescharacteristic, complemented
196C4×C4⋊C8C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8—24no—
208C22×D8—42no—
209C22×D8—42no—
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#551—48no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#126—21no—
220C2×#124D411yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255#484—42no—
256#482—42no—
257#469—24no—
258#469—42no—
259#463—24no—
260#463—42no—
261#450—42no—
262#446—42no—
263C4×SD16—42no—
264C4×D8—42no—
265C4×D8—42no—
266#435—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#400—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#394—21no—
346#394—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#393—21no—
357#392—21no—
358#392—21no—
359#391D411yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#390—21no—
363#390—21no—
364#390D411yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
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#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388D411yescharacteristic
409#388D411yescharacteristic
410#388D411yescharacteristic
411#388D411yescharacteristic
412#387—21no—
413#387—21no—
414#387—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#382D411yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450#379—21no—
451#379—21no—
452#379—21no—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C43C2311yescharacteristic
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#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
494C25—21no—
495C25—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—416no—
548C2×D8#4114yes—
549C2×M16—22no—
550C2×M16—41no—
551C2×M16—41no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563#126—44no—
564#126—44no—
565#126—82no—
566#124—24no—
567#124—22no—
568#124—41no—
569#124—41no—
570#124—41no—
571#123—44no—
572#123—44no—
573#123—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—82no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#120—44no—
590#120—82no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—44no—
610C4×D4—44no—
611#117—44no—
612#117—44no—
613#117—41no—
614#117—41no—
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—41no—
636C2×C4⋊C4—41no—
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×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
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—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4—44no—
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—41no—
732#106—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#103—22no—
743#103—22no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
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—22no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776#97—41no—
777#97—41no—
778#97—41no—
779C4×C8—22no—
780C4×C8—41no—
781C4×C8—41no—
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#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—42no—
820C24—42no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C2×Q8—22no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—41no—
844C2×D4—22no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—82no—
885C2×D4—82no—
886C2×D4—82no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4C2×#4112yes—
895C2×D4C2×#4112yes—
896C2×D4H(5,𝔽2)12yes—
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—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—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
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
955SD16—44no—
956SD16—82no—
957D8—28no—
958D8—44no—
959D8—44no—
960D8—44no—
961M16—82no—
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—44no—
985C2×C8C2×#4112yes—
986C2×C8H(5,𝔽2)12yes—
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—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
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—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
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—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—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
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—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4AGL(1,ℤ/8)14yes—
1090C42—22no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—41no—
1102C42—41no—
1103C42—41no—
1104C42—42no—
1105C42—42no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—22no—
1120C23—21no—
1121C23—22no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—84no—
1151C23—84no—
1152C23—84no—
1153C23—84no—
1154C23—84no—
1155C23—162no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23C2×AGL(1,ℤ/8)12yes—
1165C23C23×D411yescharacteristic
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—82no—
1171D4—22no—
1172D4—22no—
1173D4—22no—
1174D4—22no—
1175D4—22no—
1176D4—22no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—82no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
1192D4—162no—
1193D4—162no—
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—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4C2×AGL(1,ℤ/8)12yes—
1280C2×C4C2×AGL(1,ℤ/8)12yes—
1281C2×C4C22×#4111yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C2×C4#58511yescharacteristic
1287C8—22no—
1288C8—22no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—41no—
1304C22—41no—
1305C22—42no—
1306C22—41no—
1307C22—42no—
1308C22—42no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—41no—
1317C22—42no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—168no—
1338C22—168no—
1339C22D4×#4111yescharacteristic
1340C22#348811yescharacteristic
1341C22#349611yescharacteristic
1342C22C22×AGL(1,ℤ/8)11yescharacteristic
1343C22#358411yescharacteristic
1344C22#358411yescharacteristic
1345C22#358511yescharacteristic
1346C4—22no—
1347C4—22no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4#349011yescharacteristic
1371C4#352111yescharacteristic
1372C4#353311yescharacteristic
1373C4#356211yescharacteristic
1374C2—42no—
1375C2—81no—
1376C2—82no—
1377C2—82no—
1378C2—82no—
1379C2—161no—
1380C2#4422611yescharacteristic
1381C2#6143711yescharacteristic
1382C2#6152911yescharacteristic
1383C2#6198911yescharacteristic
1384C2#6202411yescharacteristic
1385C2#6229911yescharacteristic
1386C2#6233011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24272C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59843C2semidirect
2. #39024C2semidirect
3. #32666C2semidirect
4. #32614C2semidirect
5. #32412C2semidirect
6. #31933C2semidirect
7. #31681C2semidirect
8. #31306C2semidirect
9. #31044C2semidirect
10. #30607C2semidirect
11. #29445C2semidirect
12. #29429C2semidirect
13. #28847C2semidirect
14. #28194C2semidirect
15. #27534C2semidirect
16. #27518C2semidirect
17. #26966C2semidirect
18. #26929C2semidirect
19. #26617C2semidirect
20. #26549C2semidirect
21. #25305C2semidirect
22. #25242C2semidirect
23. #25218C2semidirect
24. #24901C2semidirect
25. #24355C2semidirect
27. #23680C2semidirect
28. #23206C2semidirect
29. #23143C2semidirect
30. C22⋊C4×D8C2semidirect
31. #22155C2semidirect
34. C2×#484C22semidirect
35. C2×#482C22semidirect
41. C2×#446C22semidirect
42. C2×C4×SD16C22semidirect
46. #2860C22semidirect
55. #2592C22semidirect
56. #2538C22semidirect
57. #2538C22semidirect
58. #2538C22semidirect
60. #2500C22semidirect
71. #2427C22semidirect
72. #2426C22semidirect
74. #2422C22semidirect
75. #2422C22semidirect
79. #2363C22semidirect
80. #2361C22semidirect
81. #2361C22semidirect
87. C4×#124C22semidirect
88. #2293C22semidirect
89. #2293C22semidirect
90. #2096C22semidirect
91. #2094C22semidirect
92. #2094C22semidirect
93. #2088C22semidirect
94. #2087C22semidirect
95. #2087C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2084C22semidirect
103. #2073C22semidirect
104. #2071C22semidirect
105. #2068C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2065C22semidirect
109. #2065C22semidirect
110. #2065C22semidirect
111. #2065C22semidirect
112. #2055C22semidirect
113. #2055C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
122. #2034C22semidirect
123. #2034C22semidirect
126. #2000C22semidirect
127. #2000C22semidirect
130. #1985C22semidirect
131. #1983C22semidirect
132. #1973C22semidirect
137. #1959C22semidirect
139. #1949C22semidirect
140. #1947C22semidirect
141. #1944C22semidirect
142. #1941C22semidirect
143. #1936C22semidirect
144. #1936C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1935C22semidirect
149. #1934C22semidirect
150. #1934C22semidirect
151. #1933C22semidirect
152. #1926C22semidirect
153. #1926C22semidirect
154. #1925C22semidirect
157. #1923C22semidirect
158. #1923C22semidirect
159. #1921C22semidirect
160. #1920C22semidirect
161. #1920C22semidirect
162. #1894C22semidirect
164. #1880C22semidirect
171. #1877C22semidirect
172. #1875C22semidirect
173. #1874C22semidirect
174. #1874C22semidirect
175. #1865C22semidirect
176. #1864C22semidirect
177. #1864C22semidirect
178. #1862C22semidirect
179. #1862C22semidirect
180. #1862C22semidirect
181. #1854C22semidirect
182. #1851C22semidirect
184. #1834C22semidirect
187. #1804C22semidirect
188. #1802C22semidirect
189. #1802C22semidirect
195. #1767C22semidirect
196. C4×C4⋊C8C22semidirect
197. #1762C22semidirect
198. C4×#103C22semidirect
199. C4×#102C22semidirect
200. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#598432
#390242
#326662
#326142
#324122
#319332
#316812
#313062
#310442
#306072
#294452
#294292
#288472
#281942
#275342
#275182
#269662
#269292
#266172
#265492
#253052
#252422
#252182
#249012
#243552
#242722
#236802
#232062
#231432
C22⋊C4×D82
#221552