Finite Group Databasebeta

← #7074373

Subgroups — #7074373

Order 512.

1514 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59637C211yesmaximal, characteristic, complemented
2#40093C211yesmaximal, characteristic, complemented
3#32640C211yesmaximal, characteristic, complemented
4#32620C211yesmaximal, characteristic, complemented
5#32541C211yesmaximal, characteristic, complemented
6#32062C211yesmaximal, characteristic, complemented
7#32060C211yesmaximal, characteristic, complemented
8#31286C211yesmaximal, characteristic, complemented
9#31166C211yesmaximal, characteristic, complemented
10#30472C211yesmaximal, characteristic
11#29480C211yesmaximal, characteristic, complemented
12#29093C211yesmaximal, characteristic, complemented
13#29072C211yesmaximal, characteristic, complemented
14#28902C211yesmaximal, characteristic, complemented
15#28746C211yesmaximal, characteristic, complemented
16#27489C211yesmaximal, characteristic, complemented
17#27471C211yesmaximal, characteristic, complemented
18#27393C211yesmaximal, characteristic, complemented
19#27238C211yesmaximal, characteristic, complemented
20#27222C211yesmaximal, characteristic, complemented
21#27202C211yesmaximal, characteristic, complemented
22#26888C211yesmaximal, characteristic, complemented
23#26692C211yesmaximal, characteristic, complemented
24#26258C211yesmaximal, characteristic, complemented
25#25475C211yesmaximal, characteristic, complemented
26#24501C211yesmaximal, characteristic, complemented
27#23696C211yesmaximal, characteristic, complemented
28#23095C211yesmaximal, characteristic, complemented
29#23079C211yesmaximal, characteristic, complemented
30#23052C211yesmaximal, characteristic, complemented
31#22046C211yesmaximal, characteristic, complemented
32C2×#496C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×C4×D8C2211yescharacteristic, complemented
40C2×#431C2211yescharacteristic
41#2855C2211yescharacteristic
42#2797—21no—
43#2772—21no—
44#2754—21no—
45#2752—21no—
46#2723—21no—
47#2715—21no—
48#2665—21no—
49#2602—21no—
50#2592C2211yescharacteristic, complemented
51#2584C2211yescharacteristic, complemented
52#2580C2211yescharacteristic
53#2557—21no—
54#2548C2211yescharacteristic
55#2513C2211yescharacteristic
56#2513C2211yescharacteristic
57#2512C2211yescharacteristic, complemented
58#2504C2211yescharacteristic
59#2496C2211yescharacteristic
60#2491C2211yescharacteristic
61#2489C2211yescharacteristic
62#2472—21no—
63#2468—21no—
64#2454C2211yescharacteristic, complemented
65#2451C2211yescharacteristic, complemented
66#2447—21no—
67#2447C2211yescharacteristic, complemented
68#2445C2211yescharacteristic
69#2445C2211yescharacteristic
70#2433C2211yescharacteristic
71#2426C2211yescharacteristic
72#2418—21no—
73#2412—21no—
74#2369C2211yescharacteristic, complemented
75#2366C2211yescharacteristic
76#2358—21no—
77#2357C2211yescharacteristic
78#2355C2211yescharacteristic, complemented
79#2345C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81#2334—21no—
82C4×C22⋊Q8C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×#390C2211yescharacteristic
86#2097C2211yescharacteristic, complemented
87#2093C2211yescharacteristic
88#2092C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2075C2211yescharacteristic
94#2075C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic, complemented
99#2067C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic, complemented
109#2054C2211yescharacteristic, complemented
110#2042C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2035C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2012C2211yescharacteristic
123#2011C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1991C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1983C2211yescharacteristic, complemented
130#1982C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic, complemented
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic, complemented
136#1970C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1957C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1948C2211yescharacteristic, complemented
144#1944C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1940C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic, complemented
161#1926C2211yescharacteristic, complemented
162#1926C2211yescharacteristic, complemented
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1923C2211yescharacteristic
168#1923C2211yescharacteristic
169#1921C2211yescharacteristic, complemented
170#1921C2211yescharacteristic, complemented
171#1920C2211yescharacteristic, complemented
172#1919C2211yescharacteristic, complemented
173#1918C2211yescharacteristic, complemented
174#1916C2211yescharacteristic, complemented
175#1916C2211yescharacteristic, complemented
176#1880C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1877C2211yescharacteristic
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic, complemented
184#1874C2211yescharacteristic
185#1872C2211yescharacteristic
186#1864C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1853C2211yescharacteristic
189#1853C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193C4×#107C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196C8×C4⋊C4C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8D411yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×#120—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C42C2311yescharacteristic
241#496—42no—
242#478—42no—
243#474—24no—
244#460—24no—
245#450—42no—
246#447—24no—
247#446—42no—
248C4×D8—42no—
249#431—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×#97C2311yescharacteristic
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#399—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#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#393—21no—
338#393—21no—
339#393—21no—
340#392—21no—
341#392—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391D411yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#389—21no—
371#389—21no—
372#389—21no—
373#389D411yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
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#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387D411yescharacteristic
406#387D411yescharacteristic
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385D411yescharacteristic
423#385D411yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#381—21no—
432#380—21no—
433#380—21no—
434#380D411yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#379—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
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×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C4⋊Q8—22no—
543C4⋊Q8—41no—
544#127—22no—
545#127—41no—
546#127—41no—
547#127—41no—
548#126—44no—
549#126—82no—
550#125—41no—
551#125—41no—
552#124—41no—
553#124—41no—
554#124—82no—
555#124—82no—
556#123—82no—
557#123—82no—
558C22⋊Q8—42no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561#121—22no—
562#121—41no—
563#121—41no—
564#121—41no—
565#120—44no—
566#120—82no—
567C4×Q8—22no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×D4—22no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—82no—
580C4×D4—82no—
581C4×D4—82no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
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—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
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—82no—
664C2×C22⋊C4—82no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—41no—
679C2×C42—41no—
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688#107—22no—
689#107—22no—
690#107—22no—
691#107—41no—
692#107—41no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—22no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
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#4114yes—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736#97—22no—
737#97—41no—
738#97—41no—
739#97—41no—
740C4×C8—22no—
741C4×C8—41no—
742C4×C8—41no—
743C4×C8—41no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
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#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—42no—
790C24—42no—
791C24—42no—
792C24—42no—
793C24—81no—
794C24—81no—
795C24—81no—
796C24C22×D411yescharacteristic
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—41no—
804C2×Q8—41no—
805C2×Q8—41no—
806C2×Q8—42no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×D4—21no—
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—21no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—81no—
857C2×D4C2×#4112yes—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—22no—
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—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—41no—
879C22×C4—41no—
880C22×C4—41no—
881C22×C4—41no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
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×C4—81no—
896C22×C4—81no—
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×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C2511yescharacteristic
911SD16—82no—
912SD16—82no—
913SD16—82no—
914D8—44no—
915D8—82no—
916D8—82no—
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×C8—21no—
939C2×C8C2×#4112yes—
940C2×C8H(5,𝔽2)12yes—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
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—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—41no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4C2×#4112yes—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—41no—
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—81no—
1010C22⋊C4—81no—
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—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
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—81no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
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—84no—
1092C23—84no—
1093C23—84no—
1094C23—84no—
1095C23—162no—
1096C23—162no—
1097C23—162no—
1098C23#57612yes—
1099C23C23×D411yescharacteristic
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—82no—
1105Q8—162no—
1106D4—22no—
1107D4—22no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
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—84no—
1125D4—84no—
1126D4—162no—
1127D4—162no—
1128D4—162no—
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—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
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—44no—
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—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—82no—
1208C2×C4—162no—
1209C2×C4—162no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4#57512yes—
1214C2×C4#57712yes—
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C2×C4#58511yescharacteristic
1221C8—22no—
1222C8—22no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C22—22no—
1230C22—22no—
1231C22—22no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
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—81no—
1264C22—168no—
1265C22D4×#4111yescharacteristic
1266C22#348711yescharacteristic
1267C22#349611yescharacteristic
1268C22C2×#57511yescharacteristic
1269C22C2×#57611yescharacteristic
1270C22C2×#57711yescharacteristic
1271C22#358511yescharacteristic
1272C4—22no—
1273C4—22no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—42no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4#351011yescharacteristic
1298C4#351411yescharacteristic
1299C4#353311yescharacteristic
1300C4#356611yescharacteristic
1301C2—42no—
1302C2—82no—
1303C2—161no—
1304C2—161no—
1305C2—161no—
1306C2#4392511yescharacteristic
1307C2#6144511yescharacteristic
1308C2#6151911yescharacteristic
1309C2#6189811yescharacteristic
1310C2#6192111yescharacteristic
1311C2#6228011yescharacteristic
1312C2#6230511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30472C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59637C2semidirect
2. #40093C2semidirect
3. #32640C2semidirect
4. #32620C2semidirect
5. #32541C2semidirect
6. #32062C2semidirect
7. #32060C2semidirect
8. #31286C2semidirect
9. #31166C2semidirect
11. #29480C2semidirect
12. #29093C2semidirect
13. #29072C2semidirect
14. #28902C2semidirect
15. #28746C2semidirect
16. #27489C2semidirect
17. #27471C2semidirect
18. #27393C2semidirect
19. #27238C2semidirect
20. #27222C2semidirect
21. #27202C2semidirect
22. #26888C2semidirect
23. #26692C2semidirect
24. #26258C2semidirect
25. #25475C2semidirect
26. #24501C2semidirect
27. #23696C2semidirect
28. #23095C2semidirect
29. #23079C2semidirect
30. #23052C2semidirect
31. #22046C2semidirect
38. C2×#446C22semidirect
39. C2×C4×D8C22semidirect
50. #2592C22semidirect
51. #2584C22semidirect
57. #2512C22semidirect
64. #2454C22semidirect
65. #2451C22semidirect
67. #2447C22semidirect
74. #2369C22semidirect
78. #2355C22semidirect
86. #2097C22semidirect
88. #2092C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2086C22semidirect
92. #2084C22semidirect
95. #2074C22semidirect
96. #2073C22semidirect
98. #2067C22semidirect
99. #2067C22semidirect
105. #2055C22semidirect
108. #2054C22semidirect
109. #2054C22semidirect
110. #2042C22semidirect
119. #2025C22semidirect
121. #2023C22semidirect
126. #1993C22semidirect
127. #1991C22semidirect
128. #1985C22semidirect
129. #1983C22semidirect
132. #1973C22semidirect
135. #1972C22semidirect
139. #1968C22semidirect
141. #1949C22semidirect
142. #1949C22semidirect
143. #1948C22semidirect
144. #1944C22semidirect
145. #1943C22semidirect
146. #1940C22semidirect
150. #1936C22semidirect
151. #1935C22semidirect
155. #1934C22semidirect
156. #1928C22semidirect
160. #1926C22semidirect
161. #1926C22semidirect
162. #1926C22semidirect
169. #1921C22semidirect
170. #1921C22semidirect
171. #1920C22semidirect
172. #1919C22semidirect
173. #1918C22semidirect
174. #1916C22semidirect
175. #1916C22semidirect
183. #1877C22semidirect
186. #1864C22semidirect
187. #1863C22semidirect
192. #1776C22semidirect
193. C4×#107C22semidirect
194. #1771C22semidirect
195. #1771C22semidirect
196. C8×C4⋊C4C22semidirect
198. C4×#103C22semidirect
200. C4×#102C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#596372
#400932
#326402
#326202
#325412
#320622
#320602
#312862
#311662
#304722
#294802
#290932
#290722
#289022
#287462
#274892
#274712
#273932
#272382
#272222
#272022
#268882
#266922
#262582
#254752
#245012
#236962
#230952
#230792
#230522
#220462