Finite Group Databasebeta

← #7594459

Subgroups — #7594459

Order 512.

1637 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45214C211yesmaximal, characteristic, complemented
2#45061C211yesmaximal, characteristic, complemented
3#31557C211yesmaximal, characteristic, complemented
4#31555C211yesmaximal, characteristic, complemented
5#31266C211yesmaximal, characteristic, complemented
6#31260C211yesmaximal, characteristic, complemented
7#29422C211yesmaximal, characteristic, complemented
8#29418C211yesmaximal, characteristic, complemented
9#28714C211yesmaximal, characteristic, complemented
10#27846C211yesmaximal, characteristic, complemented
11#27836C211yesmaximal, characteristic, complemented
12#27536C211yesmaximal, characteristic, complemented
13#27534C211yesmaximal, characteristic, complemented
14#27523C211yesmaximal, characteristic, complemented
15#27518C211yesmaximal, characteristic, complemented
16#27447C211yesmaximal, characteristic, complemented
17#27443C211yesmaximal, characteristic, complemented
18#27434C211yesmaximal, characteristic, complemented
19#27431C211yesmaximal, characteristic, complemented
20#26496C211yesmaximal, characteristic, complemented
21#26488C211yesmaximal, characteristic, complemented
22#25048C211yesmaximal, characteristic, complemented
23#25038C211yesmaximal, characteristic, complemented
24#24272C211yesmaximal, characteristic
25#22817C211yesmaximal, characteristic, complemented
26#22816C211yesmaximal, characteristic, complemented
27C22⋊C4×D8C211yesmaximal, characteristic, complemented
28#22436C211yesmaximal, characteristic, complemented
29#21568C211yesmaximal, characteristic, complemented
30#21541C211yesmaximal, characteristic, complemented
31#21536C211yesmaximal, characteristic, complemented
32C23×D8C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#469C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C2×#442C2211yescharacteristic
38C2×C4×D8C2211yescharacteristic
39C2×C4×D8C2211yescharacteristic
40C2×#435C2211yescharacteristic
41C2×#405C2211yescharacteristic, complemented
42#2778—21no—
43#2750—21no—
44#2749—21no—
45#2749—21no—
46#2746—21no—
47#2735—21no—
48#2728—21no—
49#2685—21no—
50#2572—21no—
51#2562C2211yescharacteristic
52#2547C2211yescharacteristic
53#2496C2211yescharacteristic
54#2495C2211yescharacteristic
55#2495C2211yescharacteristic
56#2494C2211yescharacteristic
57#2483—21no—
58#2482—21no—
59#2480—21no—
60#2472—21no—
61#2472—21no—
62#2471—21no—
63#2454C2211yescharacteristic, complemented
64#2454C2211yescharacteristic, complemented
65#2452C2211yescharacteristic, complemented
66#2452C2211yescharacteristic, complemented
67#2422C2211yescharacteristic, complemented
68#2420C2211yescharacteristic, complemented
69#2420C2211yescharacteristic, complemented
70#2420C2211yescharacteristic, complemented
71#2412—21no—
72#2408C2211yescharacteristic
73#2408C2211yescharacteristic
74#2395C2211yescharacteristic
75#2357C2211yescharacteristic, complemented
76#2357C2211yescharacteristic, complemented
77#2357C2211yescharacteristic, complemented
78#2354C2211yescharacteristic, complemented
79D4×C22⋊C4C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic, complemented
84#2324C2211yescharacteristic, complemented
85#2324C2211yescharacteristic, complemented
86#2324C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic, complemented
94#2076C2211yescharacteristic
95#2076C2211yescharacteristic, complemented
96#2075C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2073C2211yescharacteristic, complemented
100#2073C2211yescharacteristic, complemented
101#2073C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2034C2211yescharacteristic, complemented
110#2033C2211yescharacteristic, complemented
111#2033C2211yescharacteristic, complemented
112#2033C2211yescharacteristic, complemented
113#2025C2211yescharacteristic, complemented
114#2025C2211yescharacteristic, complemented
115#2023C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#1999C2211yescharacteristic
118#1999C2211yescharacteristic
119#1989C2211yescharacteristic, complemented
120#1987C2211yescharacteristic, complemented
121#1972C2211yescharacteristic
122#1972C2211yescharacteristic
123#1972C2211yescharacteristic
124#1972C2211yescharacteristic
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1944C2211yescharacteristic, complemented
128#1943C2211yescharacteristic, complemented
129#1941C2211yescharacteristic, complemented
130#1941C2211yescharacteristic, complemented
131#1936C2211yescharacteristic, complemented
132#1936C2211yescharacteristic, complemented
133#1934C2211yescharacteristic, complemented
134#1934C2211yescharacteristic, complemented
135#1926C2211yescharacteristic, complemented
136#1926C2211yescharacteristic, complemented
137#1925C2211yescharacteristic, complemented
138#1925C2211yescharacteristic, complemented
139#1925C2211yescharacteristic, complemented
140#1925C2211yescharacteristic, complemented
141#1925C2211yescharacteristic, complemented
142#1925C2211yescharacteristic, complemented
143#1924C2211yescharacteristic
144#1923C2211yescharacteristic
145#1921C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1893C2211yescharacteristic, complemented
152#1893C2211yescharacteristic, complemented
153#1893C2211yescharacteristic, complemented
154#1893C2211yescharacteristic, complemented
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1869C2211yescharacteristic
164#1864C2211yescharacteristic, complemented
165#1864C2211yescharacteristic, complemented
166#1864C2211yescharacteristic, complemented
167#1862C2211yescharacteristic, complemented
168#1862C2211yescharacteristic, complemented
169#1862C2211yescharacteristic, complemented
170#1862C2211yescharacteristic, complemented
171#1862C2211yescharacteristic, complemented
172#1850C2211yescharacteristic, complemented
173#1847C2211yescharacteristic, complemented
174#1846C2211yescharacteristic, complemented
175#1818C2211yescharacteristic, complemented
176#1809C2211yescharacteristic, complemented
177#1809C2211yescharacteristic, complemented
178#1808C2211yescharacteristic
179#1807C2211yescharacteristic
180#1807C2211yescharacteristic
181#1804C2211yescharacteristic, complemented
182#1804C2211yescharacteristic, complemented
183#1804C2211yescharacteristic, complemented
184#1802C2211yescharacteristic, complemented
185#1786C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1776C2211yescharacteristic, complemented
193C4×#106C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1770C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×D8—24no—
206C22×D8—24no—
207C22×D8—42no—
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#120—21no—
227C2×#120—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242C22×C22⋊C4—21no—
243#501—42no—
244#469—24no—
245#469—24no—
246#442—24no—
247#442—42no—
248C4×D8—24no—
249C4×D8—42no—
250#435—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295#405—42no—
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400D411yescharacteristic
309#399—21no—
310#399—21no—
311#399D411yescharacteristic
312#398D411yescharacteristic
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397D411yescharacteristic
324#397D411yescharacteristic
325#397D411yescharacteristic
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394D411yescharacteristic
338#394D411yescharacteristic
339#393—21no—
340#393—21no—
341#392—21no—
342#392—21no—
343#391—21no—
344#390—21no—
345#390—21no—
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#387—21no—
386#387—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#384C2311yescharacteristic
412#383—21no—
413#383—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#379—21no—
437#379—21no—
438#379—21no—
439#379—21no—
440#379—21no—
441#379—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C25—21no—
492C22×Q8—21no—
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—416no—
537C2×D8#4114yes—
538C2×D8#4114yes—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558#126—82no—
559#125—41no—
560#125—41no—
561#124—82no—
562#123—82no—
563C22⋊Q8—82no—
564C22⋊Q8—82no—
565#121—22no—
566#121—22no—
567#121—22no—
568#121—22no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—41no—
573#120—82no—
574#120—82no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593#117—41no—
594#117—41no—
595#117—82no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—82no—
675C2×C22⋊C4—82no—
676C2×C22⋊C4—82no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699#107—22no—
700#107—22no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—41no—
710#106—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743#97—22no—
744#97—22no—
745#97—22no—
746#97—41no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—41no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24C22×D411yescharacteristic
809C24C22×D411yescharacteristic
810C2×Q8—42no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×D4—22no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—44no—
841C2×D4—44no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4C2×#4112yes—
863C2×D4C2×#4112yes—
864C2×D4C2×#4112yes—
865C2×D4C2×#4112yes—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C2511yescharacteristic
927D8—28no—
928D8—28no—
929D8—44no—
930D8—44no—
931M16—44no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—44no—
954C2×C8—44no—
955C2×C8C2×#4112yes—
956C2×C8C2×#4112yes—
957C2×C8H(5,𝔽2)12yes—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—42no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C22⋊C4—22no—
1003C22⋊C4—22no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—81no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23#57612yes—
1130C23C23×D411yescharacteristic
1131Q8—162no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—22no—
1138D4—22no—
1139D4—22no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—82no—
1149D4—84no—
1150D4—84no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—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—21no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—84no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8#55114yes—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—41no—
1266C22—42no—
1267C22—42no—
1268C22—41no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—42no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
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—81no—
1298C22—81no—
1299C22—168no—
1300C22—168no—
1301C22D4×#4111yescharacteristic
1302C22D4×#4111yescharacteristic
1303C22#349611yescharacteristic
1304C22C2×#57611yescharacteristic
1305C22#358411yescharacteristic
1306C22#358511yescharacteristic
1307C22#358511yescharacteristic
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4C2×#55111yescharacteristic
1333C4#352111yescharacteristic
1334C4#352111yescharacteristic
1335C4#354011yescharacteristic
1336C2—42no—
1337C2—81no—
1338C2—82no—
1339C2—82no—
1340C2—82no—
1341C2—82no—
1342C2#5937511yescharacteristic
1343C2#6148911yescharacteristic
1344C2#6150511yescharacteristic
1345C2#6151911yescharacteristic
1346C2#6152911yescharacteristic
1347C2#6231511yescharacteristic
1348C2#6235111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24272C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45214C2semidirect
2. #45061C2semidirect
3. #31557C2semidirect
4. #31555C2semidirect
5. #31266C2semidirect
6. #31260C2semidirect
7. #29422C2semidirect
8. #29418C2semidirect
9. #28714C2semidirect
10. #27846C2semidirect
11. #27836C2semidirect
12. #27536C2semidirect
13. #27534C2semidirect
14. #27523C2semidirect
15. #27518C2semidirect
16. #27447C2semidirect
17. #27443C2semidirect
18. #27434C2semidirect
19. #27431C2semidirect
20. #26496C2semidirect
21. #26488C2semidirect
22. #25048C2semidirect
23. #25038C2semidirect
25. #22817C2semidirect
26. #22816C2semidirect
27. C22⋊C4×D8C2semidirect
28. #22436C2semidirect
29. #21568C2semidirect
30. #21541C2semidirect
31. #21536C2semidirect
33. C2×#501C22semidirect
41. C2×#405C22semidirect
63. #2454C22semidirect
64. #2454C22semidirect
65. #2452C22semidirect
66. #2452C22semidirect
67. #2422C22semidirect
68. #2420C22semidirect
69. #2420C22semidirect
70. #2420C22semidirect
75. #2357C22semidirect
76. #2357C22semidirect
77. #2357C22semidirect
78. #2354C22semidirect
83. #2324C22semidirect
84. #2324C22semidirect
85. #2324C22semidirect
86. #2324C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2100C22semidirect
93. #2077C22semidirect
95. #2076C22semidirect
99. #2073C22semidirect
100. #2073C22semidirect
101. #2073C22semidirect
102. #2071C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2065C22semidirect
106. #2065C22semidirect
109. #2034C22semidirect
110. #2033C22semidirect
111. #2033C22semidirect
112. #2033C22semidirect
113. #2025C22semidirect
114. #2025C22semidirect
115. #2023C22semidirect
116. #2023C22semidirect
119. #1989C22semidirect
120. #1987C22semidirect
127. #1944C22semidirect
128. #1943C22semidirect
129. #1941C22semidirect
130. #1941C22semidirect
131. #1936C22semidirect
132. #1936C22semidirect
133. #1934C22semidirect
134. #1934C22semidirect
135. #1926C22semidirect
136. #1926C22semidirect
137. #1925C22semidirect
138. #1925C22semidirect
139. #1925C22semidirect
140. #1925C22semidirect
141. #1925C22semidirect
142. #1925C22semidirect
145. #1921C22semidirect
146. #1921C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1917C22semidirect
150. #1916C22semidirect
151. #1893C22semidirect
152. #1893C22semidirect
153. #1893C22semidirect
154. #1893C22semidirect
164. #1864C22semidirect
165. #1864C22semidirect
166. #1864C22semidirect
167. #1862C22semidirect
168. #1862C22semidirect
169. #1862C22semidirect
170. #1862C22semidirect
171. #1862C22semidirect
172. #1850C22semidirect
173. #1847C22semidirect
174. #1846C22semidirect
175. #1818C22semidirect
176. #1809C22semidirect
177. #1809C22semidirect
181. #1804C22semidirect
182. #1804C22semidirect
183. #1804C22semidirect
184. #1802C22semidirect
191. #1776C22semidirect
192. #1776C22semidirect
193. C4×#106C22semidirect
194. #1771C22semidirect
195. #1770C22semidirect
196. #1762C22semidirect
197. #1762C22semidirect
198. C4×#102C22semidirect
199. C4×#102C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#452142
#450612
#315572
#315552
#312662
#312602
#294222
#294182
#287142
#278462
#278362
#275362
#275342
#275232
#275182
#274472
#274432
#274342
#274312
#264962
#264882
#250482
#250382
#242722
#228172
#228162
C22⋊C4×D82
#224362
#215682
#215412
#215362