Finite Group Databasebeta

← #7531138

Subgroups — #7531138

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59219C211yesmaximal, characteristic, complemented
2#36215C211yesmaximal, characteristic, complemented
3#31706C211yesmaximal, characteristic, complemented
4#31694C211yesmaximal, characteristic, complemented
5#31370C211yesmaximal, characteristic, complemented
6#31350C211yesmaximal, characteristic, complemented
7#28960C211yesmaximal, characteristic, complemented
8#28949C211yesmaximal, characteristic, complemented
9#28197C211yesmaximal, characteristic, complemented
10#27880C211yesmaximal, characteristic, complemented
11#27743C211yesmaximal, characteristic, complemented
12#27536C211yesmaximal, characteristic, complemented
13#27525C211yesmaximal, characteristic, complemented
14#27434C211yesmaximal, characteristic, complemented
15#27431C211yesmaximal, characteristic, complemented
16#27309C211yesmaximal, characteristic, complemented
17#27296C211yesmaximal, characteristic, complemented
18#26125C211yesmaximal, characteristic, complemented
19#25068C211yesmaximal, characteristic, complemented
20#24913C211yesmaximal, characteristic
21#24893C211yesmaximal, characteristic
22#24823C211yesmaximal, characteristic, complemented
23#24704C211yesmaximal, characteristic, complemented
24#24347C211yesmaximal, characteristic, complemented
25#23052C211yesmaximal, characteristic, complemented
26#22774C211yesmaximal, characteristic, complemented
27#22772C211yesmaximal, characteristic, complemented
28#22676C211yesmaximal, characteristic, complemented
29#22522C211yesmaximal, characteristic, complemented
30#21452C211yesmaximal, characteristic
31#20732C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C2×#478C2211yescharacteristic, complemented
35C2×#447C2211yescharacteristic
36C2×#446C2211yescharacteristic, complemented
37C2×#442C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×#431C2211yescharacteristic
42#2851C2211yescharacteristic
43#2848—21no—
44#2765—21no—
45#2765—21no—
46#2580C2211yescharacteristic
47#2579—21no—
48#2571C2211yescharacteristic, complemented
49#2566C2211yescharacteristic
50#2564—21no—
51#2538C2211yescharacteristic, complemented
52#2536—21no—
53#2507C2211yescharacteristic, complemented
54#2507C2211yescharacteristic, complemented
55#2494—21no—
56#2494C2211yescharacteristic
57#2494C2211yescharacteristic
58#2486—21no—
59#2470—21no—
60#2470—21no—
61#2454C2211yescharacteristic
62#2452C2211yescharacteristic
63#2450—21no—
64#2449—21no—
65#2442C2211yescharacteristic
66#2440C2211yescharacteristic
67#2437—21no—
68#2437—21no—
69#2422C2211yescharacteristic
70#2422C2211yescharacteristic
71#2360—21no—
72#2357C2211yescharacteristic, complemented
73#2357C2211yescharacteristic, complemented
74Q8×C4⋊C4C2211yescharacteristic, complemented
75#2349C2211yescharacteristic
76#2349C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic, complemented
79D4×C22⋊C4C2211yescharacteristic
80D4×C22⋊C4C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×#121C2211yescharacteristic
83C2×#385—21no—
84#2285C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2067C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2025C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#1992C2211yescharacteristic, complemented
118#1992C2211yescharacteristic, complemented
119#1992C2211yescharacteristic, complemented
120#1990C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1989C2211yescharacteristic, complemented
123#1987C2211yescharacteristic, complemented
124#1985C2211yescharacteristic, complemented
125#1949C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1942C2211yescharacteristic, complemented
128#1941C2211yescharacteristic, complemented
129#1941C2211yescharacteristic, complemented
130#1940C2211yescharacteristic, complemented
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic, complemented
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1926C2211yescharacteristic
140#1925C2211yescharacteristic
141#1924C2211yescharacteristic
142#1924C2211yescharacteristic
143#1923C2211yescharacteristic
144#1923C2211yescharacteristic
145#1921C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1916C2211yescharacteristic, complemented
153#1879C2211yescharacteristic
154#1879C2211yescharacteristic
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1874C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic, complemented
166#1862C2211yescharacteristic
167#1862C2211yescharacteristic
168#1862C2211yescharacteristic
169#1862C2211yescharacteristic, complemented
170#1853C2211yescharacteristic
171#1847C2211yescharacteristic, complemented
172#1836C2211yescharacteristic, complemented
173#1836C2211yescharacteristic, complemented
174#1835C2211yescharacteristic, complemented
175#1823C2211yescharacteristic
176#1823C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1804C2211yescharacteristic, complemented
180#1804C2211yescharacteristic, complemented
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1771C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1749C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C24×C4—21no—
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207#554—24no—
208#554—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#123—21no—
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8D411yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—24no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—42no—
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×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C22×C4⋊C4—21no—
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C42C2311yescharacteristic
249#478—42no—
250#447—24no—
251#446—42no—
252#442—24no—
253#442—24no—
254#442—42no—
255C4×D8—24no—
256#431—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#401—21no—
306#401—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#393—21no—
333#391D411yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389D411yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387D411yescharacteristic
375#387D411yescharacteristic
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#385—21no—
382#385—21no—
383#385—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385D411yescharacteristic
402#385D411yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380D411yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
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×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446C2×#95—21no—
447C2×#95—21no—
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
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—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
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×C4—44no—
517C23×C4—82no—
518C23×C4—82no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—41no—
527C2×D8#4114yes—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C4⋊Q8—22no—
537C4⋊Q8—41no—
538#125—22no—
539#125—22no—
540#125—22no—
541#125—41no—
542#123—82no—
543#123—82no—
544C22⋊Q8—42no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—44no—
549C22⋊Q8—82no—
550C22⋊Q8—82no—
551#121—22no—
552#121—41no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×Q8—82no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—44no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—44no—
579C4×D4—82no—
580C4×D4#4114yes—
581#117—82no—
582C2×C4⋊C4—22no—
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—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⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—82no—
615C2×C4⋊C4—82no—
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
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—44no—
670C2×C22⋊C4—44no—
671C2×C22⋊C4—82no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—22no—
677C2×C42—22no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—41no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—22no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—22no—
702C4⋊C8—22no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727C22⋊C8—22no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731#97—22no—
732#97—22no—
733#97—22no—
734#97—41no—
735C4×C8—22no—
736C4×C8—41no—
737C4×C8—41no—
738C4×C8—41no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
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#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780C24—21no—
781C24—24no—
782C24—21no—
783C24—21no—
784C24—42no—
785C24—42no—
786C24—42no—
787C24—42no—
788C24—81no—
789C24—81no—
790C24C22×D411yescharacteristic
791C2×Q8—22no—
792C2×Q8—22no—
793C2×Q8—41no—
794C2×Q8—42no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×D4—24no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—81no—
820C2×D4C2×#4112yes—
821C2×D4C2×#4112yes—
822C2×D4C2×#4112yes—
823C2×D42−1+412yes—
824C2×D42−1+412yes—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—24no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—41no—
850C22×C4—41no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—816no—
886C22×C4—81no—
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C2511yescharacteristic
901D8—28no—
902D8—44no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
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×C8C2×#4112yes—
927C4⋊C4—22no—
928C4⋊C4—22no—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
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—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
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⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4C2×#4112yes—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—24no—
994C22⋊C4—22no—
995C22⋊C4—41no—
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—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
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—
1026C42—22no—
1027C42—22no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—42no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42C2×#4112yes—
1044C42H(5,𝔽2)12yes—
1045C23—21no—
1046C23—22no—
1047C23—21no—
1048C23—22no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—21no—
1053C23—21no—
1054C23—22no—
1055C23—22no—
1056C23—48no—
1057C23—48no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—84no—
1075C23—84no—
1076C23—84no—
1077C23—84no—
1078C23—84no—
1079C23#57612yes—
1080C23C23×D411yescharacteristic
1081Q8—44no—
1082Q8—162no—
1083D4—22no—
1084D4—22no—
1085D4—22no—
1086D4—22no—
1087D4—22no—
1088D4—22no—
1089D4—22no—
1090D4—48no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—84no—
1096D4#55214yes—
1097C2×C4—28no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
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—82no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—84no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4#54612yes—
1190C2×C4#54612yes—
1191C2×C4#57512yes—
1192C2×C4#57712yes—
1193C2×C4C22×#4111yescharacteristic
1194C2×C4C22×#4111yescharacteristic
1195C2×C4C2×H(5,𝔽2)11yescharacteristic
1196C2×C4C2×2−1+411yescharacteristic
1197C2×C4C2×2−1+411yescharacteristic
1198C2×C4#58511yescharacteristic
1199C8—22no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C22—22no—
1208C22—22no—
1209C22—24no—
1210C22—22no—
1211C22—42no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—41no—
1216C22—41no—
1217C22—42no—
1218C22—41no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—816no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×#54611yescharacteristic
1237C22D4×#4111yescharacteristic
1238C22#348611yescharacteristic
1239C22C2×#57511yescharacteristic
1240C22C2×#57611yescharacteristic
1241C22C2×#57711yescharacteristic
1242C22#358511yescharacteristic
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4C2×#55211yescharacteristic
1270C4#349511yescharacteristic
1271C4#352011yescharacteristic
1272C4#354111yescharacteristic
1273C2—42no—
1274C2—44no—
1275C2—82no—
1276C2—82no—
1277C2#5902711yescharacteristic
1278C2#6116411yescharacteristic
1279C2#6116711yescharacteristic
1280C2#6144811yescharacteristic
1281C2#6151911yescharacteristic
1282C2#6183511yescharacteristic
1283C2#6185011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
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. #59219C2semidirect
2. #36215C2semidirect
3. #31706C2semidirect
4. #31694C2semidirect
5. #31370C2semidirect
6. #31350C2semidirect
7. #28960C2semidirect
8. #28949C2semidirect
9. #28197C2semidirect
10. #27880C2semidirect
11. #27743C2semidirect
12. #27536C2semidirect
13. #27525C2semidirect
14. #27434C2semidirect
15. #27431C2semidirect
16. #27309C2semidirect
17. #27296C2semidirect
18. #26125C2semidirect
19. #25068C2semidirect
22. #24823C2semidirect
23. #24704C2semidirect
24. #24347C2semidirect
25. #23052C2semidirect
26. #22774C2semidirect
27. #22772C2semidirect
28. #22676C2semidirect
29. #22522C2semidirect
31. #20732C2semidirect
34. C2×#478C22semidirect
36. C2×#446C22semidirect
48. #2571C22semidirect
51. #2538C22semidirect
53. #2507C22semidirect
54. #2507C22semidirect
72. #2357C22semidirect
73. #2357C22semidirect
74. Q8×C4⋊C4C22semidirect
78. D4×C4⋊C4C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2099C22semidirect
91. #2088C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2086C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
97. #2084C22semidirect
98. #2083C22semidirect
109. #2059C22semidirect
110. #2058C22semidirect
115. #2025C22semidirect
116. #2023C22semidirect
117. #1992C22semidirect
118. #1992C22semidirect
119. #1992C22semidirect
120. #1990C22semidirect
121. #1989C22semidirect
122. #1989C22semidirect
123. #1987C22semidirect
124. #1985C22semidirect
125. #1949C22semidirect
126. #1944C22semidirect
127. #1942C22semidirect
128. #1941C22semidirect
129. #1941C22semidirect
130. #1940C22semidirect
133. #1936C22semidirect
136. #1934C22semidirect
137. #1934C22semidirect
138. #1934C22semidirect
145. #1921C22semidirect
146. #1921C22semidirect
147. #1921C22semidirect
148. #1920C22semidirect
149. #1919C22semidirect
150. #1919C22semidirect
151. #1916C22semidirect
152. #1916C22semidirect
165. #1864C22semidirect
169. #1862C22semidirect
171. #1847C22semidirect
172. #1836C22semidirect
173. #1836C22semidirect
174. #1835C22semidirect
179. #1804C22semidirect
180. #1804C22semidirect
187. #1802C22semidirect
191. #1771C22semidirect
192. #1771C22semidirect
193. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#592192
#362152
#317062
#316942
#313702
#313502
#289602
#289492
#281972
#278802
#277432
#275362
#275252
#274342
#274312
#273092
#272962
#261252
#250682
#249132
#248932
#248232
#247042
#243472
#230522
#227742
#227722
#226762
#225222
#214522
#207322