Finite Group Databasebeta

← #6612400

Subgroups — #6612400

Order 512.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36167C211yesmaximal, characteristic
2#36130C211yesmaximal, characteristic
3#33136C211yesmaximal, characteristic, complemented
4#33053C211yesmaximal, characteristic, complemented
5#32931C211yesmaximal, characteristic
6#29158C211yesmaximal, characteristic, complemented
7#29053C211yesmaximal, characteristic, complemented
8#29049C211yesmaximal, characteristic, complemented
9#28986C211yesmaximal, characteristic, complemented
10#28985C211yesmaximal, characteristic, complemented
11#28934C211yesmaximal, characteristic, complemented
12#28851C211yesmaximal, characteristic, complemented
13#28775C211yesmaximal, characteristic, complemented
14#28575C211yesmaximal, characteristic, complemented
15#28345C211yesmaximal, characteristic, complemented
16#28083C211yesmaximal, characteristic, complemented
17#27860C211yesmaximal, characteristic, complemented
18#27713C211yesmaximal, characteristic, complemented
19#27268C211yesmaximal, characteristic, complemented
20#26981C211yesmaximal, characteristic, complemented
21#25498C211yesmaximal, characteristic, complemented
22#24551C211yesmaximal, characteristic
23#24380C211yesmaximal, characteristic
24#23133C211yesmaximal, characteristic, complemented
25#22934C211yesmaximal, characteristic, complemented
26#22859C211yesmaximal, characteristic, complemented
27#22563C211yesmaximal, characteristic, complemented
28#21527C211yesmaximal, characteristic, complemented
29#21407C211yesmaximal, characteristic, complemented
30C2×#1892C211yesmaximal, characteristic
31C2×#1752C211yesmaximal, characteristic
32C24×C8C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×#491C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#451C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47C22×#97C2211yescharacteristic
48C22×#97C2211yescharacteristic
49#2857C2211yescharacteristic
50#2855C2211yescharacteristic
51#2855C2211yescharacteristic
52#2851C2211yescharacteristic
53#2848C2211yescharacteristic
54#2848C2211yescharacteristic
55#2577—21no—
56#2556—21no—
57#2549—21no—
58#2530—21no—
59#2505—21no—
60#2503C2211yescharacteristic
61#2495C2211yescharacteristic
62#2494C2211yescharacteristic
63#2493—21no—
64#2493—21no—
65#2492C2211yescharacteristic
66#2489C2211yescharacteristic
67#2483—21no—
68#2473—21no—
69#2465—21no—
70#2442C2211yescharacteristic
71#2440C2211yescharacteristic
72#2438—21no—
73#2437—21no—
74#2434C2211yescharacteristic
75#2429C2211yescharacteristic
76#2429C2211yescharacteristic
77#2423C2211yescharacteristic
78#2421C2211yescharacteristic
79#2360—21no—
80#2360C2211yescharacteristic
81#2360C2211yescharacteristic
82#2344C2211yescharacteristic
83#2343—21no—
84#2342—21no—
85#2342—21no—
86Q8×C22⋊C4C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C4×C22⋊Q8C2211yescharacteristic
89#2283C2211yescharacteristic
90C2×#380C2211yescharacteristic
91C2×C4×C22⋊C4C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2101C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2074C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2059C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2036C2211yescharacteristic
107#2036C2211yescharacteristic
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic
110#2026C2211yescharacteristic, complemented
111#2024C2211yescharacteristic, complemented
112#2016C2211yescharacteristic, complemented
113#2016C2211yescharacteristic, complemented
114#2001C2211yescharacteristic
115#2001C2211yescharacteristic
116#1993C2211yescharacteristic, complemented
117#1993C2211yescharacteristic, complemented
118#1992C2211yescharacteristic, complemented
119#1971C2211yescharacteristic, complemented
120#1971C2211yescharacteristic, complemented
121#1971C2211yescharacteristic, complemented
122#1960C2211yescharacteristic, complemented
123#1960C2211yescharacteristic, complemented
124#1960C2211yescharacteristic, complemented
125#1944C2211yescharacteristic, complemented
126#1944C2211yescharacteristic, complemented
127#1943C2211yescharacteristic, complemented
128#1935C2211yescharacteristic, complemented
129#1935C2211yescharacteristic, complemented
130#1935C2211yescharacteristic, complemented
131#1935C2211yescharacteristic, complemented
132#1935C2211yescharacteristic, complemented
133#1935C2211yescharacteristic, complemented
134#1935C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1928C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1927C2211yescharacteristic, complemented
142#1920C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1918C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1892C2211yescharacteristic
147#1892C2211yescharacteristic
148#1892C2211yescharacteristic
149#1892C2211yescharacteristic
150#1892C2211yescharacteristic
151#1892C2211yescharacteristic
152#1892C2211yescharacteristic
153#1892C2211yescharacteristic
154#1892C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1878C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1865C2211yescharacteristic, complemented
171#1863C2211yescharacteristic, complemented
172#1863C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1853C2211yescharacteristic
175#1852C2211yescharacteristic
176#1836C2211yescharacteristic, complemented
177#1823C2211yescharacteristic
178#1808C2211yescharacteristic
179#1808C2211yescharacteristic
180#1808C2211yescharacteristic
181#1807C2211yescharacteristic
182#1807C2211yescharacteristic
183#1787C2211yescharacteristic
184#1776C2211yescharacteristic, complemented
185#1763C2211yescharacteristic, complemented
186#1763C2211yescharacteristic, complemented
187#1763C2211yescharacteristic, complemented
188#1763C2211yescharacteristic, complemented
189#1763C2211yescharacteristic, complemented
190#1763C2211yescharacteristic, complemented
191#1752C2211yescharacteristic
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic
195#1752C2211yescharacteristic
196#1752C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201C2×#336C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C23×C8—24no—
209C23×C8—42no—
210C23×C8—42no—
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#533—24no—
220#533—42no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—24no—
231C2×C22⋊Q8—42no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×#117—21no—
248C2×#117—21no—
249C22×C4⋊C4—21no—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4D411yescharacteristic
256C22×C22⋊C4D411yescharacteristic
257C22×C42C2311yescharacteristic
258C22×C42C2311yescharacteristic
259#491—42no—
260#483—24no—
261#467—24no—
262#467—24no—
263#467—42no—
264#467—42no—
265#467—42no—
266#451—24no—
267#441—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#103—24no—
278C2×#103—42no—
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×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×C22⋊C8—24no—
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97—42no—
311C2×#97—42no—
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320#401—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#393—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#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#387—21no—
389#387—21no—
390#387—21no—
391#387—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#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#383—21no—
412#383—21no—
413#382—21no—
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#381—21no—
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
454C4×C22⋊C4D411yescharacteristic
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462C2×#95—21no—
463C2×#95D411yescharacteristic
464C2×#95D411yescharacteristic
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#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25C2×D411yescharacteristic
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C23×C4—22no—
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2×D411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—22no—
552C22×C8—22no—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8—416no—
565C22×C8#4114yes—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580#125—41no—
581#125—41no—
582#125—44no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—44no—
597C22⋊Q8—44no—
598C22⋊Q8—44no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—44no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8#4114yes—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—44no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616#117—44no—
617#117—44no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—44no—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—24no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—42no—
693C2×C22⋊C4—44no—
694C2×C22⋊C4—44no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—41no—
714C2×C42—41no—
715C2×C42C2×D411yescharacteristic
716C2×C42C2×D411yescharacteristic
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#107—22no—
724#107—22no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—22no—
730#106—41no—
731#106—41no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8#4114yes—
762#97—22no—
763#97—22no—
764#97—41no—
765#97—41no—
766#97—41no—
767#97—41no—
768#97—41no—
769#97—41no—
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#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—22no—
823C24—22no—
824C24—22no—
825C24—22no—
826C24—41no—
827C24—41no—
828C24#13714yes—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C24C22×D411yescharacteristic
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—44no—
859C2×Q8—44no—
860C2×Q8—42no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—82no—
864C2×Q8—82no—
865C2×Q8C2×#4112yes—
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—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C2×#4112yes—
945C22×C4C2×#4112yes—
946C22×C4C2×#4112yes—
947C22×C4H(5,𝔽2)12yes—
948C22×C4C2511yescharacteristic
949Q16—44no—
950Q16—82no—
951Q16—82no—
952C2×C8—28no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—44no—
973C2×C8—44no—
974C2×C8—44no—
975C2×C8—44no—
976C2×C8—44no—
977C2×C8—44no—
978C2×C8—44no—
979C2×C8C2×#4112yes—
980C2×C8C2×#4112yes—
981C2×C8C2×#4112yes—
982C2×C8C2×#4112yes—
983C2×C8H(5,𝔽2)12yes—
984C4⋊C4—24no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4C2×#4112yes—
1042C22⋊C4—24no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—22no—
1071C42—22no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—41no—
1081C42—41no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—28no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—28no—
1104C23—21no—
1105C23—21no—
1106C23—44no—
1107C23—44no—
1108C23—44no—
1109C23—44no—
1110C23—44no—
1111C23#53212yes—
1112C23#54612yes—
1113C23C2×#13712yes—
1114C23C2×#13712yes—
1115C23C2×#13712yes—
1116C23#57512yes—
1117C23#57812yes—
1118C23C23×D411yescharacteristic
1119Q8—22no—
1120Q8—22no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—84no—
1136Q8—84no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
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—22no—
1159C2×C4—22no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—44no—
1179C2×C4—44no—
1180C2×C4—44no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—44no—
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—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—82no—
1233C2×C4—82no—
1234C2×C4—82no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—84no—
1238C2×C4—162no—
1239C2×C4#53212yes—
1240C2×C4#54612yes—
1241C2×C4C22×#4111yescharacteristic
1242C2×C4C22×#4111yescharacteristic
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C8—22no—
1248C8—22no—
1249C8—22no—
1250C8—22no—
1251C8—22no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—22no—
1263C22—22no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—22no—
1269C22—22no—
1270C22—416no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22#318114yes—
1276C22#331214yes—
1277C22C2×#53211yescharacteristic
1278C22C2×#54611yescharacteristic
1279C22#349611yescharacteristic
1280C22C22×#13711yescharacteristic
1281C22C2×#57511yescharacteristic
1282C22C2×#57811yescharacteristic
1283C22#358411yescharacteristic
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—42no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4#347511yescharacteristic
1312C4#348111yescharacteristic
1313C4#349011yescharacteristic
1314C4#351311yescharacteristic
1315C2—24no—
1316C2—24no—
1317C2—42no—
1318C2#3631811yescharacteristic
1319C2C2×#318111yescharacteristic
1320C2#6070811yescharacteristic
1321C2C2×#331211yescharacteristic
1322C2#6114111yescharacteristic
1323C2#6225411yescharacteristic
1324C2#6225811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33136C2semidirect
4. #33053C2semidirect
6. #29158C2semidirect
7. #29053C2semidirect
8. #29049C2semidirect
9. #28986C2semidirect
10. #28985C2semidirect
11. #28934C2semidirect
12. #28851C2semidirect
13. #28775C2semidirect
14. #28575C2semidirect
15. #28345C2semidirect
16. #28083C2semidirect
17. #27860C2semidirect
18. #27713C2semidirect
19. #27268C2semidirect
20. #26981C2semidirect
21. #25498C2semidirect
24. #23133C2semidirect
25. #22934C2semidirect
26. #22859C2semidirect
27. #22563C2semidirect
28. #21527C2semidirect
29. #21407C2semidirect
35. C2×#491C22semidirect
43. C2×#441C22semidirect
92. #2101C22semidirect
93. #2101C22semidirect
94. #2097C22semidirect
95. #2097C22semidirect
96. #2085C22semidirect
97. #2083C22semidirect
100. #2074C22semidirect
101. #2072C22semidirect
102. #2059C22semidirect
103. #2057C22semidirect
104. #2043C22semidirect
105. #2043C22semidirect
110. #2026C22semidirect
111. #2024C22semidirect
112. #2016C22semidirect
113. #2016C22semidirect
116. #1993C22semidirect
117. #1993C22semidirect
118. #1992C22semidirect
119. #1971C22semidirect
120. #1971C22semidirect
121. #1971C22semidirect
122. #1960C22semidirect
123. #1960C22semidirect
124. #1960C22semidirect
125. #1944C22semidirect
126. #1944C22semidirect
127. #1943C22semidirect
128. #1935C22semidirect
129. #1935C22semidirect
130. #1935C22semidirect
131. #1935C22semidirect
132. #1935C22semidirect
133. #1935C22semidirect
134. #1935C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
137. #1935C22semidirect
138. #1928C22semidirect
139. #1928C22semidirect
140. #1928C22semidirect
141. #1927C22semidirect
142. #1920C22semidirect
143. #1919C22semidirect
144. #1918C22semidirect
145. #1918C22semidirect
164. #1878C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
170. #1865C22semidirect
171. #1863C22semidirect
172. #1863C22semidirect
173. #1863C22semidirect
176. #1836C22semidirect
184. #1776C22semidirect
185. #1763C22semidirect
186. #1763C22semidirect
187. #1763C22semidirect
188. #1763C22semidirect
189. #1763C22semidirect
190. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#361672
#361302
#331362
#330532
#329312
#291582
#290532
#290492
#289862
#289852
#289342
#288512
#287752
#285752
#283452
#280832
#278602
#277132
#272682
#269812
#254982
#245512
#243802
#231332
#229342
#228592
#225632
#215272
#214072
C2×#18922
C2×#17522