Finite Group Databasebeta

← #7205090

Subgroups — #7205090

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45499C211yesmaximal, characteristic
2#36545C211yesmaximal, characteristic
3#33010C211yesmaximal, characteristic
4#32957C211yesmaximal, characteristic
5#32774C211yesmaximal, characteristic
6#32724C211yesmaximal, characteristic
7#32650C211yesmaximal, characteristic, complemented
8#32570C211yesmaximal, characteristic, complemented
9#32168C211yesmaximal, characteristic, complemented
10#32084C211yesmaximal, characteristic, complemented
11#31904C211yesmaximal, characteristic, complemented
12#31576C211yesmaximal, characteristic, complemented
13#31292C211yesmaximal, characteristic
14#31292C211yesmaximal, characteristic
15#31151C211yesmaximal, characteristic, complemented
16#30990C211yesmaximal, characteristic
17#30816C211yesmaximal, characteristic, complemented
18#30530C211yesmaximal, characteristic
19#27492C211yesmaximal, characteristic, complemented
20#27364C211yesmaximal, characteristic, complemented
21#27100C211yesmaximal, characteristic
22#27068C211yesmaximal, characteristic, complemented
23#27036C211yesmaximal, characteristic
24#26894C211yesmaximal, characteristic, complemented
25#26790C211yesmaximal, characteristic
26#26559C211yesmaximal, characteristic
27#26532C211yesmaximal, characteristic, complemented
28#26466C211yesmaximal, characteristic, complemented
29#25651C211yesmaximal, characteristic, complemented
30#24191C211yesmaximal, characteristic, complemented
31#23336C211yesmaximal, characteristic
32C2×#557C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#484C2211yescharacteristic
36C2×#477C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#477C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#451C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42#2857C2211yescharacteristic
43#2857C2211yescharacteristic
44#2855C2211yescharacteristic
45#2851—21no—
46#2841—21no—
47#2805—21no—
48#2799—21no—
49#2791—21no—
50#2729—21no—
51#2720—21no—
52#2713—21no—
53#2584—21no—
54#2582C2211yescharacteristic
55#2582C2211yescharacteristic
56#2581—21no—
57#2567C2211yescharacteristic
58#2552C2211yescharacteristic
59#2551C2211yescharacteristic
60#2546C2211yescharacteristic
61#2511C2211yescharacteristic
62#2511C2211yescharacteristic
63#2507C2211yescharacteristic
64#2497C2211yescharacteristic
65#2497C2211yescharacteristic
66#2492C2211yescharacteristic
67#2473—21no—
68#2473—21no—
69#2462—21no—
70#2462—21no—
71#2451C2211yescharacteristic
72#2446C2211yescharacteristic
73#2446C2211yescharacteristic
74#2434C2211yescharacteristic
75#2434C2211yescharacteristic
76#2423C2211yescharacteristic
77#2378—21no—
78#2365C2211yescharacteristic
79#2365C2211yescharacteristic
80#2360C2211yescharacteristic
81#2360C2211yescharacteristic
82#2355C2211yescharacteristic
83C4×C22⋊Q8—21no—
84C4×C22⋊Q8C2211yescharacteristic
85#2100C2211yescharacteristic
86#2095C2211yescharacteristic
87#2095C2211yescharacteristic
88#2095C2211yescharacteristic
89#2095C2211yescharacteristic
90#2095C2211yescharacteristic
91#2095C2211yescharacteristic
92#2087C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2072C2211yescharacteristic
97#2072C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2057C2211yescharacteristic
106#2056C2211yescharacteristic
107#2056C2211yescharacteristic
108#2056C2211yescharacteristic
109#2056C2211yescharacteristic
110#2043C2211yescharacteristic
111#2043C2211yescharacteristic
112#2043C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2043C2211yescharacteristic
116#2043C2211yescharacteristic
117#2043C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2024C2211yescharacteristic
125#2024C2211yescharacteristic
126#2024C2211yescharacteristic
127#2016C2211yescharacteristic
128#2016C2211yescharacteristic
129#2016C2211yescharacteristic
130#2016C2211yescharacteristic
131#2001C2211yescharacteristic
132#2001C2211yescharacteristic
133#1984C2211yescharacteristic
134#1984C2211yescharacteristic
135#1981C2211yescharacteristic
136#1981C2211yescharacteristic
137#1981C2211yescharacteristic
138#1969C2211yescharacteristic
139#1969C2211yescharacteristic
140#1969C2211yescharacteristic
141#1956C2211yescharacteristic
142#1956C2211yescharacteristic
143#1956C2211yescharacteristic
144#1947C2211yescharacteristic
145#1947C2211yescharacteristic
146#1942C2211yescharacteristic
147#1942C2211yescharacteristic
148#1939C2211yescharacteristic
149#1939C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1928C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1928C2211yescharacteristic
159#1928C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic
165#1921C2211yescharacteristic
166#1921C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1916C2211yescharacteristic
171#1878C2211yescharacteristic
172#1878C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1863C2211yescharacteristic
178#1863C2211yescharacteristic
179#1863C2211yescharacteristic
180#1863C2211yescharacteristic
181#1863C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1852C2211yescharacteristic
190#1852C2211yescharacteristic
191#1824C2211yescharacteristic
192#1817C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1797C2211yescharacteristic
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1787C2211yescharacteristic
200C4×#107C2211yescharacteristic
201C4×#107C2211yescharacteristic
202C4×#103C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208#557—42no—
209#557—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125—21no—
219C2×#125—21no—
220C2×#125—21no—
221C2×#125—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8D411yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—42no—
231C2×C4×Q8—42no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C42—21no—
243C22×C42C2311yescharacteristic
244#487—42no—
245#484—42no—
246#477—42no—
247#477—42no—
248#477—42no—
249#462—42no—
250#451—42no—
251C4×Q16—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#393—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391—21no—
352#391D411yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389D411yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—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#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387D411yescharacteristic
420#387D411yescharacteristic
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385D411yescharacteristic
429#385D411yescharacteristic
430#384—21no—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382—21no—
437#381—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380D411yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8C2×D411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2411yescharacteristic
510C2×Q16—22no—
511C2×Q16—22no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×Q16—41no—
515C2×Q16—41no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×Q16—41no—
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C4⋊Q8—22no—
531C4⋊Q8—22no—
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544C4⋊Q8—82no—
545#125—44no—
546#125—44no—
547#125—44no—
548#125—82no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C22⋊Q8—82no—
556C22⋊Q8Q1618yescomplemented
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—44no—
572C4×Q8—44no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—44no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
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—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—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—44no—
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—41no—
666C2×C42—41no—
667C2×C42—44no—
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#107—22no—
677#107—22no—
678#107—22no—
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688C4⋊C8—41no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693C4⋊C8—41no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C4×C8—41no—
731C4×C8—41no—
732C4×C8—41no—
733C4×C8—41no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
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#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#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789C24C22×D411yescharacteristic
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—41no—
819C2×Q8—41no—
820C2×Q8—42no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—42no—
824C2×Q8—44no—
825C2×Q8—44no—
826C2×Q8—44no—
827C2×Q8—44no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8C2×Q1614yes—
834C2×Q8H(5,𝔽2)12yes—
835C2×Q82−1+412yes—
836C22×C4—21no—
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—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—81no—
869C22×C4C2×Q1614yes—
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C2511yescharacteristic
884Q16—44no—
885Q16—82no—
886Q16—82no—
887Q16—82no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
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—
912C4⋊C4—24no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4C2×Q1614yes—
984C4⋊C4C2×Q1614yes—
985C4⋊C4C2×Q1614yes—
986C4⋊C4H(5,𝔽2)12yes—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4C2×Q1614yes—
996C22⋊C4C2×Q1614yes—
997C42—24no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—41no—
1011C42—41no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—42no—
1016C42—42no—
1017C42—81no—
1018C42—81no—
1019C42—81no—
1020C42—81no—
1021C42—81no—
1022C42—81no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23C22×Q1612yes—
1030C23C23×D411yescharacteristic
1031Q8—22no—
1032Q8—22no—
1033Q8—22no—
1034Q8—22no—
1035Q8—44no—
1036Q8—48no—
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—41no—
1053Q8—162no—
1054Q8—162no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—44no—
1092C2×C4—48no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
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—82no—
1143C2×C4—84no—
1144C2×C4C22×Q1612yes—
1145C2×C4C22×Q1612yes—
1146C2×C4C22×Q1612yes—
1147C2×C4C22×Q1612yes—
1148C2×C4C22×Q1612yes—
1149C2×C4C22×Q1612yes—
1150C2×C4C2×H(5,𝔽2)11yescharacteristic
1151C2×C4C2×H(5,𝔽2)11yescharacteristic
1152C2×C4C2×2−1+411yescharacteristic
1153C2×C4#58511yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C8—41no—
1157C8—41no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22#348411yescharacteristic
1172C22#348711yescharacteristic
1173C22#348911yescharacteristic
1174C22C23×Q1611yescharacteristic
1175C22#358511yescharacteristic
1176C22#358611yescharacteristic
1177C22#358611yescharacteristic
1178C4—22no—
1179C4—22no—
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—42no—
1188C4—42no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—42no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4#352911yescharacteristic
1208C4#353311yescharacteristic
1209C4#353511yescharacteristic
1210C4#354111yescharacteristic
1211C2—42no—
1212C2#4545011yescharacteristic
1213C2#6156311yescharacteristic
1214C2#6165611yescharacteristic
1215C2#6188411yescharacteristic
1216C2#6194011yescharacteristic
1217C2#6210011yescharacteristic
1218C2#6222511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
7. #32650C2semidirect
8. #32570C2semidirect
9. #32168C2semidirect
10. #32084C2semidirect
11. #31904C2semidirect
12. #31576C2semidirect
15. #31151C2semidirect
17. #30816C2semidirect
19. #27492C2semidirect
20. #27364C2semidirect
22. #27068C2semidirect
24. #26894C2semidirect
27. #26532C2semidirect
28. #26466C2semidirect
29. #25651C2semidirect
30. #24191C2semidirect
556. C22⋊Q8Q16semidirect

Maximal subgroups

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

subgroupindex
#454992
#365452
#330102
#329572
#327742
#327242
#326502
#325702
#321682
#320842
#319042
#315762
#312922
#311512
#309902
#308162
#305302
#274922
#273642
#271002
#270682
#270362
#268942
#267902
#265592
#265322
#264662
#256512
#241912
#233362