Finite Group Databasebeta

← #7577328

Subgroups — #7577328

Order 512.

1566 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59484C211yesmaximal, characteristic, complemented
2#36251C211yesmaximal, characteristic, complemented
3#31665C211yesmaximal, characteristic, complemented
4#31625C211yesmaximal, characteristic, complemented
5#31222C211yesmaximal, characteristic, complemented
6#31008C211yesmaximal, characteristic, complemented
7#29497C211yesmaximal, characteristic, complemented
8#29429C211yesmaximal, characteristic, complemented
9#29023C211yesmaximal, characteristic, complemented
10#27795C211yesmaximal, characteristic, complemented
11#27422C211yesmaximal, characteristic, complemented
12#27369C211yesmaximal, characteristic, complemented
13#27229C211yesmaximal, characteristic, complemented
14#27168C211yesmaximal, characteristic, complemented
15#27055C211yesmaximal, characteristic, complemented
16#26971C211yesmaximal, characteristic, complemented
17#26900C211yesmaximal, characteristic, complemented
18#26731C211yesmaximal, characteristic, complemented
19#26713C211yesmaximal, characteristic, complemented
20#26585C211yesmaximal, characteristic, complemented
21#26488C211yesmaximal, characteristic, complemented
22#25466C211yesmaximal, characteristic, complemented
23#25148C211yesmaximal, characteristic
24#25101C211yesmaximal, characteristic, complemented
25#23280C211yesmaximal, characteristic, complemented
26#23108C211yesmaximal, characteristic, complemented
27#23105C211yesmaximal, characteristic, complemented
28#22880C211yesmaximal, characteristic, complemented
29#22584C211yesmaximal, characteristic, complemented
30C4×#463C211yesmaximal, characteristic, complemented
31#21113C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#478C2211yescharacteristic
34C2×#468C2211yescharacteristic
35C2×#463C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic, complemented
41C2×C4×D8C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43C2×#418C2211yescharacteristic
44#2860C2211yescharacteristic, complemented
45#2854—21no—
46#2750—21no—
47#2736—21no—
48#2578—21no—
49#2572—21no—
50#2563C2211yescharacteristic
51#2561—21no—
52#2554—21no—
53#2553—21no—
54#2531—21no—
55#2518—21no—
56#2507C2211yescharacteristic, complemented
57#2495C2211yescharacteristic
58#2492C2211yescharacteristic
59#2490C2211yescharacteristic
60#2480—21no—
61#2477—21no—
62#2476—21no—
63#2467—21no—
64#2454C2211yescharacteristic, complemented
65#2452C2211yescharacteristic
66#2447C2211yescharacteristic
67#2447C2211yescharacteristic
68#2445C2211yescharacteristic, complemented
69#2435C2211yescharacteristic
70#2428C2211yescharacteristic
71#2422C2211yescharacteristic
72#2421C2211yescharacteristic
73#2370C2211yescharacteristic, complemented
74#2367C2211yescharacteristic
75#2366C2211yescharacteristic, complemented
76#2363C2211yescharacteristic
77#2363C2211yescharacteristic
78#2357C2211yescharacteristic
79#2354C2211yescharacteristic, complemented
80#2346C2211yescharacteristic
81#2342—21no—
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×#126C2211yescharacteristic
85C4×#124C2211yescharacteristic
86#2293C2211yescharacteristic
87#2290—21no—
88C42×D4C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2076C2211yescharacteristic
95#2073C2211yescharacteristic, complemented
96#2071C2211yescharacteristic
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2066C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic, complemented
102#2065C2211yescharacteristic, complemented
103#2055C2211yescharacteristic, complemented
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2026C2211yescharacteristic, complemented
113#2025C2211yescharacteristic
114#2023C2211yescharacteristic, complemented
115#2023C2211yescharacteristic, complemented
116#2014C2211yescharacteristic, complemented
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2011C2211yescharacteristic
120#2000C2211yescharacteristic
121#1988C2211yescharacteristic, complemented
122#1983C2211yescharacteristic
123#1973C2211yescharacteristic, complemented
124#1972C2211yescharacteristic
125#1972C2211yescharacteristic
126#1970C2211yescharacteristic
127#1970C2211yescharacteristic
128#1968C2211yescharacteristic, complemented
129#1961C2211yescharacteristic, complemented
130#1959C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1949C2211yescharacteristic, complemented
133#1947C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1940C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1935C2211yescharacteristic, complemented
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1895C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic, complemented
174#1873C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic
184#1851C2211yescharacteristic
185#1825C2211yescharacteristic
186#1809C2211yescharacteristic
187#1804C2211yescharacteristic, complemented
188#1786C2211yescharacteristic
189C4×#107C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192C4×C4⋊C8C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1744C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126D411yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117—21no—
236C2×#117—21no—
237C2×#117C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C42—21no—
241#501—42no—
242#478—42no—
243#468—42no—
244#463—24no—
245#463—24no—
246#459—24no—
247#447—24no—
248#447—42no—
249C4×SD16—42no—
250C4×D8—24no—
251C4×D8—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267#418—24no—
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#400—21no—
307#400—21no—
308#400—21no—
309#399—21no—
310#398—21no—
311#398—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#393—21no—
330#393—21no—
331#393—21no—
332#393—21no—
333#392—21no—
334#391—21no—
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#388—21no—
366#388—21no—
367#388—21no—
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#388—21no—
386#388D411yescharacteristic
387#388D411yescharacteristic
388#388D411yescharacteristic
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387D411yescharacteristic
394#387D411yescharacteristic
395#387D411yescharacteristic
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#383—21no—
414#383D411yescharacteristic
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#381—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#379—21no—
429#379—21no—
430#379—21no—
431#379—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
457C43C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8#4114yes—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#127—22no—
549#127—41no—
550#126—42no—
551#126—82no—
552#125—22no—
553#125—41no—
554#124—22no—
555#124—22no—
556#124—41no—
557#124—41no—
558#123—82no—
559#123—82no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—82no—
563#121—22no—
564#121—22no—
565#121—41no—
566#121—41no—
567#121—82no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—44no—
587#117—22no—
588#117—41no—
589#117—82no—
590#117—82no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
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—44no—
668C2×C22⋊C4—82no—
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—82no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—22no—
696#107—22no—
697#107—22no—
698#107—41no—
699#107—41no—
700#107—41no—
701#106—22no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—41no—
714#103—41no—
715#103—41no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
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#4114yes—
738C22⋊C8—22no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741#97—41no—
742#97—41no—
743#97—41no—
744C4×C8—22no—
745C4×C8—41no—
746C4×C8—41no—
747C4×C8—41no—
748#95—21no—
749#95—21no—
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#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
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
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
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—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—82no—
844C2×D4—82no—
845C2×D4—82no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4C2×#4112yes—
851C2×D4C2×#4112yes—
852C2×D4C2×#4112yes—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C2511yescharacteristic
909SD16—44no—
910SD16—82no—
911D8—44no—
912D8—44no—
913D8—82no—
914D8—82no—
915M16—82no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8C2×#4112yes—
939C2×C8C2×#4112yes—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4C2×#4112yes—
983C4⋊C4H(5,𝔽2)12yes—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C42—22no—
1034C42—22no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—41no—
1048C42—41no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—21no—
1063C23—22no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23C23×D411yescharacteristic
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—162no—
1106D4—22no—
1107D4—22no—
1108D4—22no—
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—84no—
1123D4—84no—
1124D4—162no—
1125D4—162no—
1126D4—162no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
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—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
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—84no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4#57512yes—
1213C2×C4#57612yes—
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—22no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—42no—
1229C22—41no—
1230C22—42no—
1231C22—42no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—41no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—168no—
1264C22D4×#4111yescharacteristic
1265C22D4×#4111yescharacteristic
1266C22#348811yescharacteristic
1267C22C2×#57511yescharacteristic
1268C22C2×#57611yescharacteristic
1269C22#358411yescharacteristic
1270C22#358511yescharacteristic
1271C4—22no—
1272C4—22no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—42no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—42no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4#347511yescharacteristic
1297C4#350511yescharacteristic
1298C4#351411yescharacteristic
1299C4#356611yescharacteristic
1300C2—81no—
1301C2—82no—
1302C2—82no—
1303C2—82no—
1304C2—161no—
1305C2#5916411yescharacteristic
1306C2#6144211yescharacteristic
1307C2#6144411yescharacteristic
1308C2#6153111yescharacteristic
1309C2#6153911yescharacteristic
1310C2#6197511yescharacteristic
1311C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25148C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59484C2semidirect
2. #36251C2semidirect
3. #31665C2semidirect
4. #31625C2semidirect
5. #31222C2semidirect
6. #31008C2semidirect
7. #29497C2semidirect
8. #29429C2semidirect
9. #29023C2semidirect
10. #27795C2semidirect
11. #27422C2semidirect
12. #27369C2semidirect
13. #27229C2semidirect
14. #27168C2semidirect
15. #27055C2semidirect
16. #26971C2semidirect
17. #26900C2semidirect
18. #26731C2semidirect
19. #26713C2semidirect
20. #26585C2semidirect
21. #26488C2semidirect
22. #25466C2semidirect
24. #25101C2semidirect
25. #23280C2semidirect
26. #23108C2semidirect
27. #23105C2semidirect
28. #22880C2semidirect
29. #22584C2semidirect
30. C4×#463C2semidirect
31. #21113C2semidirect
32. C2×#501C22semidirect
40. C2×C4×SD16C22semidirect
44. #2860C22semidirect
56. #2507C22semidirect
64. #2454C22semidirect
68. #2445C22semidirect
73. #2370C22semidirect
75. #2366C22semidirect
79. #2354C22semidirect
88. C42×D4C22semidirect
89. #2101C22semidirect
90. #2099C22semidirect
91. #2087C22semidirect
92. #2085C22semidirect
93. #2085C22semidirect
95. #2073C22semidirect
99. #2066C22semidirect
101. #2065C22semidirect
102. #2065C22semidirect
103. #2055C22semidirect
112. #2026C22semidirect
114. #2023C22semidirect
115. #2023C22semidirect
116. #2014C22semidirect
121. #1988C22semidirect
123. #1973C22semidirect
128. #1968C22semidirect
129. #1961C22semidirect
131. #1949C22semidirect
132. #1949C22semidirect
133. #1947C22semidirect
134. #1943C22semidirect
135. #1941C22semidirect
136. #1940C22semidirect
138. #1935C22semidirect
141. #1934C22semidirect
142. #1933C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
148. #1926C22semidirect
152. #1925C22semidirect
156. #1921C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1916C22semidirect
162. #1916C22semidirect
164. #1880C22semidirect
173. #1877C22semidirect
177. #1863C22semidirect
180. #1862C22semidirect
181. #1862C22semidirect
182. #1862C22semidirect
187. #1804C22semidirect
189. C4×#107C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
192. C4×C4⋊C8C22semidirect
195. #1762C22semidirect
196. C4×#103C22semidirect
199. C4×#102C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#594842
#362512
#316652
#316252
#312222
#310082
#294972
#294292
#290232
#277952
#274222
#273692
#272292
#271682
#270552
#269712
#269002
#267312
#267132
#265852
#264882
#254662
#251482
#251012
#232802
#231082
#231052
#228802
#225842
C4×#4632
#211132