Finite Group Databasebeta

← #6593705

Subgroups — #6593705

Order 512.

1781 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37962C211yesmaximal, characteristic, complemented
2#34288C211yesmaximal, characteristic
3#33203C211yesmaximal, characteristic, complemented
4#32963C211yesmaximal, characteristic, complemented
5#32953C211yesmaximal, characteristic, complemented
6#28730C211yesmaximal, characteristic, complemented
7#28288C211yesmaximal, characteristic, complemented
8#27636C211yesmaximal, characteristic, complemented
9#27635C211yesmaximal, characteristic, complemented
10#27541C211yesmaximal, characteristic, complemented
11#27531C211yesmaximal, characteristic, complemented
12#27528C211yesmaximal, characteristic, complemented
13#27525C211yesmaximal, characteristic, complemented
14#27052C211yesmaximal, characteristic, complemented
15#27036C211yesmaximal, characteristic, complemented
16#27033C211yesmaximal, characteristic, complemented
17#27030C211yesmaximal, characteristic, complemented
18#26308C211yesmaximal, characteristic, complemented
19#26302C211yesmaximal, characteristic, complemented
20#25897C211yesmaximal, characteristic
21#25890C211yesmaximal, characteristic
22#24712C211yesmaximal, characteristic, complemented
23#24702C211yesmaximal, characteristic, complemented
24#23226C211yesmaximal, characteristic, complemented
25#23218C211yesmaximal, characteristic, complemented
26#22974C211yesmaximal, characteristic, complemented
27#22962C211yesmaximal, characteristic, complemented
28#22800C211yesmaximal, characteristic, complemented
29#21624C211yesmaximal, characteristic, complemented
30#20746C211yesmaximal, characteristic, complemented
31#20733C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#477C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#474C2211yescharacteristic
42C2×#433C2211yescharacteristic, complemented
43C2×#431C2211yescharacteristic
44#2857C2211yescharacteristic
45#2762—21no—
46#2759—21no—
47#2745—21no—
48#2740—21no—
49#2660C2211yescharacteristic, complemented
50#2628C2211yescharacteristic, complemented
51#2604—21no—
52#2563C2211yescharacteristic
53#2562C2211yescharacteristic
54#2560—21no—
55#2528—21no—
56#2497C2211yescharacteristic
57#2496C2211yescharacteristic, complemented
58#2494C2211yescharacteristic
59#2494C2211yescharacteristic, complemented
60#2465—21no—
61#2370C2211yescharacteristic, complemented
62#2367C2211yescharacteristic
63#2365C2211yescharacteristic, complemented
64#2361—21no—
65#2361C2211yescharacteristic
66#2360C2211yescharacteristic
67#2359—21no—
68#2358—21no—
69D4×C4⋊C4C2211yescharacteristic
70D4×C4⋊C4C2211yescharacteristic
71#2342—21no—
72#2339C2211yescharacteristic
73D4×C22⋊C4C2211yescharacteristic
74#2331C2211yescharacteristic, complemented
75#2326C2211yescharacteristic
76#2325—21no—
77#2324C2211yescharacteristic
78#2322—21no—
79#2314C2211yescharacteristic, complemented
80C4×C22⋊Q8C2211yescharacteristic
81C4×#120—21no—
82#2290C2211yescharacteristic
83C2×#385—21no—
84#2283C2211yescharacteristic
85#2275C2211yescharacteristic
86#2077C2211yescharacteristic
87#2077C2211yescharacteristic, complemented
88#2076C2211yescharacteristic
89#2076C2211yescharacteristic
90#2076C2211yescharacteristic
91#2076C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2075C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2068C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2036C2211yescharacteristic
103#2036C2211yescharacteristic
104#2036C2211yescharacteristic
105#2035C2211yescharacteristic
106#2034C2211yescharacteristic
107#2033C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#1992C2211yescharacteristic, complemented
111#1990C2211yescharacteristic, complemented
112#1989C2211yescharacteristic, complemented
113#1987C2211yescharacteristic, complemented
114#1987C2211yescharacteristic, complemented
115#1983C2211yescharacteristic
116#1983C2211yescharacteristic
117#1955C2211yescharacteristic
118#1954C2211yescharacteristic
119#1949C2211yescharacteristic, complemented
120#1949C2211yescharacteristic, complemented
121#1949C2211yescharacteristic, complemented
122#1947C2211yescharacteristic, complemented
123#1947C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1947C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1942C2211yescharacteristic, complemented
128#1942C2211yescharacteristic, complemented
129#1942C2211yescharacteristic, complemented
130#1936C2211yescharacteristic
131#1934C2211yescharacteristic
132#1933C2211yescharacteristic, complemented
133#1933C2211yescharacteristic, complemented
134#1928C2211yescharacteristic, complemented
135#1927C2211yescharacteristic, complemented
136#1926C2211yescharacteristic
137#1925C2211yescharacteristic
138#1924C2211yescharacteristic
139#1923C2211yescharacteristic
140#1923C2211yescharacteristic, complemented
141#1923C2211yescharacteristic, complemented
142#1921C2211yescharacteristic, complemented
143#1921C2211yescharacteristic, complemented
144#1919C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1918C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1864C2211yescharacteristic
149#1863C2211yescharacteristic, complemented
150#1863C2211yescharacteristic, complemented
151#1862C2211yescharacteristic
152#1862C2211yescharacteristic
153#1862C2211yescharacteristic
154#1862C2211yescharacteristic
155#1862C2211yescharacteristic
156#1862C2211yescharacteristic
157#1862C2211yescharacteristic
158#1852C2211yescharacteristic
159#1852C2211yescharacteristic
160#1852C2211yescharacteristic, complemented
161#1852C2211yescharacteristic, complemented
162#1843C2211yescharacteristic, complemented
163#1824C2211yescharacteristic
164#1824C2211yescharacteristic
165#1824C2211yescharacteristic, complemented
166#1823C2211yescharacteristic, complemented
167#1805C2211yescharacteristic, complemented
168#1805C2211yescharacteristic, complemented
169#1804C2211yescharacteristic
170#1804C2211yescharacteristic
171#1804C2211yescharacteristic
172#1804C2211yescharacteristic
173#1804C2211yescharacteristic
174#1803C2211yescharacteristic, complemented
175#1802C2211yescharacteristic
176#1802C2211yescharacteristic
177#1802C2211yescharacteristic
178#1798C2211yescharacteristic, complemented
179#1797C2211yescharacteristic
180#1788C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1788C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189C4×#107C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191C8×C4⋊C4C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206#546—24no—
207#546—24no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#126—21no—
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121—21no—
217C2×#121C2311yescharacteristic
218C2×#120—21no—
219#520—24no—
220#520—42no—
221C2×C4×Q8—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—24no—
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—42no—
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—
241C2×#117C2311yescharacteristic
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250#489—24no—
251#488—24no—
252#478—24no—
253#477—42no—
254#474—24no—
255#474—24no—
256#474—42no—
257#433—42no—
258#431—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#401—21no—
318#401—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#394—21no—
334#393—21no—
335#393—21no—
336#393—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390—21no—
344#390—21no—
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388D411yescharacteristic
373#388D411yescharacteristic
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387D411yescharacteristic
389#387D411yescharacteristic
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386D411yescharacteristic
397#386D411yescharacteristic
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385D411yescharacteristic
410#385D411yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#380—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
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
455#376—21no—
456#376C2311yescharacteristic
457C2×#95—21no—
458C2×#95—21no—
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#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—44no—
526C23×C4—82no—
527C23×C4—82no—
528C23×C4C2×D411yescharacteristic
529C23×C4C2×D411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—22no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544#126—82no—
545#125—22no—
546#125—22no—
547#124—22no—
548#124#4114yes—
549#123—28no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—82no—
553#121—28no—
554#121—22no—
555#121—22no—
556#120—28no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—41no—
561C4×Q8—82no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—44no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—44no—
578C4×D4—44no—
579C4×D4—44no—
580C4×D4—82no—
581C4×D4—82no—
582C4×D4#4114yes—
583C4×D4#4114yes—
584#117—22no—
585#117—22no—
586#117—44no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
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—41no—
614C2×C4⋊C4—44no—
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⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—28no—
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—44no—
661C2×C22⋊C4—82no—
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
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×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—22no—
692#107—22no—
693#107—22no—
694#107—22no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#106—22no—
701#106—41no—
702C4⋊C8—22no—
703C4⋊C8—22no—
704C4⋊C8—22no—
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—22no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
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—22no—
728#102—22no—
729#102—22no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742#97—22no—
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#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795C24—21no—
796C24—24no—
797C24—21no—
798C24—42no—
799C24—42no—
800C24—42no—
801C24—42no—
802C24—81no—
803C24—81no—
804C24C22×D411yescharacteristic
805C24C22×D411yescharacteristic
806#41—44no—
807#41—44no—
808#41—44no—
809#41—44no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8C2×#4112yes—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—22no—
825C2×D4—24no—
826C2×D4—22no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—41no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—44no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4C2×#4112yes—
847C2×D4C2×#4112yes—
848C2×D4C2×#4112yes—
849C2×D42−1+412yes—
850C22×C4—24no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
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—24no—
871C22×C4—24no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—816no—
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2511yescharacteristic
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×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—22no—
954C4⋊C4—22no—
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—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—41no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4C2×#4112yes—
1003C4⋊C4C2×#4112yes—
1004C22⋊C4—24no—
1005C22⋊C4—24no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—24no—
1009C22⋊C4—24no—
1010C22⋊C4—24no—
1011C22⋊C4—22no—
1012C22⋊C4—24no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
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—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C42—22no—
1038C42—22no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—42no—
1046C42—42no—
1047C42—42no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42C2×#4112yes—
1057C42C2×#4112yes—
1058C42C2×#4112yes—
1059C42H(5,𝔽2)12yes—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—22no—
1065C23—21no—
1066C23—22no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—22no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—48no—
1078C23—48no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—84no—
1090C23—84no—
1091C23—84no—
1092C23—84no—
1093C23—84no—
1094C23#57812yes—
1095C23C23×D411yescharacteristic
1096Q8—22no—
1097Q8—22no—
1098Q8—41no—
1099Q8—41no—
1100Q8—84no—
1101Q8—162no—
1102D4—22no—
1103D4—22no—
1104D4—22no—
1105D4—22no—
1106D4—22no—
1107D4—44no—
1108D4—48no—
1109D4—48no—
1110D4—41no—
1111D4—41no—
1112D4—84no—
1113D4#55614yes—
1114C2×C4—21no—
1115C2×C4—21no—
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—22no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—22no—
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—44no—
1149C2×C4—44no—
1150C2×C4—48no—
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—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—84no—
1199C2×C4—84no—
1200C2×C4—84no—
1201C2×C4—84no—
1202C2×C4—84no—
1203C2×C4—84no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4#52512yes—
1208C2×C4#52512yes—
1209C2×C4#54612yes—
1210C2×C4#54612yes—
1211C2×C4#57612yes—
1212C2×C4C22×#4111yescharacteristic
1213C2×C4C22×#4111yescharacteristic
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×2−1+411yescharacteristic
1217C2×C4#58511yescharacteristic
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C22—24no—
1227C22—22no—
1228C22—22no—
1229C22—22no—
1230C22—41no—
1231C22—42no—
1232C22—41no—
1233C22—42no—
1234C22—42no—
1235C22—41no—
1236C22—42no—
1237C22—42no—
1238C22—41no—
1239C22—42no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—42no—
1244C22—41no—
1245C22—42no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—816no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22C2×#52511yescharacteristic
1256C22C2×#54611yescharacteristic
1257C22#348911yescharacteristic
1258C22C2×#57611yescharacteristic
1259C22C2×#57811yescharacteristic
1260C22#358411yescharacteristic
1261C22#358511yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—41no—
1268C4—41no—
1269C4—42no—
1270C4—42no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4C2×#55611yescharacteristic
1289C4#347511yescharacteristic
1290C4#350611yescharacteristic
1291C4#352011yescharacteristic
1292C2—42no—
1293C2—44no—
1294C2—81no—
1295C2—82no—
1296C2#3616111yescharacteristic
1297C2#6057011yescharacteristic
1298C2#6058911yescharacteristic
1299C2#6117311yescharacteristic
1300C2#6118311yescharacteristic
1301C2#6217511yescharacteristic
1302C2#6220111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37962C2semidirect
3. #33203C2semidirect
4. #32963C2semidirect
5. #32953C2semidirect
6. #28730C2semidirect
7. #28288C2semidirect
8. #27636C2semidirect
9. #27635C2semidirect
10. #27541C2semidirect
11. #27531C2semidirect
12. #27528C2semidirect
13. #27525C2semidirect
14. #27052C2semidirect
15. #27036C2semidirect
16. #27033C2semidirect
17. #27030C2semidirect
18. #26308C2semidirect
19. #26302C2semidirect
22. #24712C2semidirect
23. #24702C2semidirect
24. #23226C2semidirect
25. #23218C2semidirect
26. #22974C2semidirect
27. #22962C2semidirect
28. #22800C2semidirect
29. #21624C2semidirect
30. #20746C2semidirect
31. #20733C2semidirect
37. C2×#477C22semidirect
42. C2×#433C22semidirect
49. #2660C22semidirect
50. #2628C22semidirect
57. #2496C22semidirect
59. #2494C22semidirect
61. #2370C22semidirect
63. #2365C22semidirect
74. #2331C22semidirect
79. #2314C22semidirect
87. #2077C22semidirect
91. #2076C22semidirect
92. #2076C22semidirect
93. #2075C22semidirect
94. #2074C22semidirect
96. #2072C22semidirect
98. #2068C22semidirect
99. #2068C22semidirect
110. #1992C22semidirect
111. #1990C22semidirect
112. #1989C22semidirect
113. #1987C22semidirect
114. #1987C22semidirect
119. #1949C22semidirect
120. #1949C22semidirect
121. #1949C22semidirect
122. #1947C22semidirect
123. #1947C22semidirect
124. #1947C22semidirect
125. #1947C22semidirect
126. #1944C22semidirect
127. #1942C22semidirect
128. #1942C22semidirect
129. #1942C22semidirect
132. #1933C22semidirect
133. #1933C22semidirect
134. #1928C22semidirect
135. #1927C22semidirect
140. #1923C22semidirect
141. #1923C22semidirect
142. #1921C22semidirect
143. #1921C22semidirect
144. #1919C22semidirect
145. #1918C22semidirect
146. #1918C22semidirect
147. #1918C22semidirect
149. #1863C22semidirect
150. #1863C22semidirect
160. #1852C22semidirect
161. #1852C22semidirect
162. #1843C22semidirect
165. #1824C22semidirect
166. #1823C22semidirect
167. #1805C22semidirect
168. #1805C22semidirect
174. #1803C22semidirect
178. #1798C22semidirect
188. #1776C22semidirect
189. C4×#107C22semidirect
190. #1771C22semidirect
191. C8×C4⋊C4C22semidirect
192. #1768C22semidirect
193. #1763C22semidirect
196. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#379622
#342882
#332032
#329632
#329532
#287302
#282882
#276362
#276352
#275412
#275312
#275282
#275252
#270522
#270362
#270332
#270302
#263082
#263022
#258972
#258902
#247122
#247022
#232262
#232182
#229742
#229622
#228002
#216242
#207462
#207332