Finite Group Databasebeta

← #6546403

Subgroups — #6546403

Order 512.

1636 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36167C211yesmaximal, characteristic
2#36130C211yesmaximal, characteristic
3#30363C211yesmaximal, characteristic, complemented
4#30326C211yesmaximal, characteristic, complemented
5#29731C211yesmaximal, characteristic
6#29479C211yesmaximal, characteristic, complemented
7#29478C211yesmaximal, characteristic, complemented
8#29053C211yesmaximal, characteristic, complemented
9#29049C211yesmaximal, characteristic, complemented
10#28934C211yesmaximal, characteristic, complemented
11#28855C211yesmaximal, characteristic, complemented
12#28345C211yesmaximal, characteristic, complemented
13#28084C211yesmaximal, characteristic, complemented
14#27896C211yesmaximal, characteristic, complemented
15#27797C211yesmaximal, characteristic, complemented
16#27713C211yesmaximal, characteristic, complemented
17#27268C211yesmaximal, characteristic, complemented
18#26981C211yesmaximal, characteristic, complemented
19#26068C211yesmaximal, characteristic, complemented
20#25677C211yesmaximal, characteristic, complemented
21#25043C211yesmaximal, characteristic, complemented
22#24551C211yesmaximal, characteristic
23#24380C211yesmaximal, characteristic
24#23765C211yesmaximal, characteristic, complemented
25#23577C211yesmaximal, characteristic, complemented
26C2×#2035C211yesmaximal, characteristic
27#23028C211yesmaximal, characteristic, complemented
28#22934C211yesmaximal, characteristic, complemented
29#22859C211yesmaximal, characteristic, complemented
30#22563C211yesmaximal, characteristic, complemented
31#20526C211yesmaximal, characteristic
32C2×#533C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#491C2211yescharacteristic, complemented
36C2×#483C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#467C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#451C2211yescharacteristic
41C2×#441C2211yescharacteristic, complemented
42C2×#441C2211yescharacteristic, complemented
43C22×#106C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×C22⋊C8C2211yescharacteristic
47C22×C22⋊C8C2211yescharacteristic
48#2857C2211yescharacteristic
49#2855C2211yescharacteristic
50#2855C2211yescharacteristic
51#2851C2211yescharacteristic
52#2848C2211yescharacteristic
53#2848C2211yescharacteristic
54#2577—21no—
55#2556—21no—
56#2549—21no—
57#2530—21no—
58#2505—21no—
59#2503C2211yescharacteristic
60#2495C2211yescharacteristic
61#2494C2211yescharacteristic
62#2493—21no—
63#2493—21no—
64#2492C2211yescharacteristic
65#2489C2211yescharacteristic
66#2483—21no—
67#2473—21no—
68#2465—21no—
69#2442C2211yescharacteristic
70#2440C2211yescharacteristic
71#2438—21no—
72#2437—21no—
73#2434C2211yescharacteristic
74#2429C2211yescharacteristic
75#2429C2211yescharacteristic
76#2423C2211yescharacteristic
77#2421C2211yescharacteristic
78#2360—21no—
79#2360C2211yescharacteristic
80#2360C2211yescharacteristic
81#2344C2211yescharacteristic
82#2343—21no—
83#2342—21no—
84#2342—21no—
85Q8×C22⋊C4C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88#2283C2211yescharacteristic
89C2×#380C2211yescharacteristic
90C2×C4×C22⋊C4C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2074C2211yescharacteristic, complemented
102#2072C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2043C2211yescharacteristic, complemented
107#2036C2211yescharacteristic
108#2036C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2016C2211yescharacteristic, complemented
126#2016C2211yescharacteristic, complemented
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic
131#1993C2211yescharacteristic, complemented
132#1971C2211yescharacteristic, complemented
133#1971C2211yescharacteristic, complemented
134#1971C2211yescharacteristic, complemented
135#1971C2211yescharacteristic, complemented
136#1960C2211yescharacteristic, complemented
137#1960C2211yescharacteristic, complemented
138#1960C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1944C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1892C2211yescharacteristic
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1865C2211yescharacteristic, complemented
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1863C2211yescharacteristic, complemented
173#1863C2211yescharacteristic, complemented
174#1863C2211yescharacteristic, complemented
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1847C2211yescharacteristic, complemented
178#1836C2211yescharacteristic, complemented
179#1823C2211yescharacteristic
180#1808C2211yescharacteristic
181#1807C2211yescharacteristic
182#1807C2211yescharacteristic
183#1787C2211yescharacteristic
184#1776C2211yescharacteristic, complemented
185#1776C2211yescharacteristic, complemented
186#1763C2211yescharacteristic, complemented
187#1763C2211yescharacteristic, complemented
188#1763C2211yescharacteristic, complemented
189#1763C2211yescharacteristic, complemented
190#1752C2211yescharacteristic
191#1752C2211yescharacteristic
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic
195#1752C2211yescharacteristic
196#1752C2211yescharacteristic
197#1752C2211yescharacteristic
198#1749C2211yescharacteristic
199#1749C2211yescharacteristic
200#1749C2211yescharacteristic
201#1749C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#533—42no—
213#533—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—42no—
224C2×C22⋊Q8—42no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×#117—21no—
241C2×#117—21no—
242C22×C4⋊C4—21no—
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248C22×C22⋊C4D411yescharacteristic
249C22×C22⋊C4D411yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252#501—42no—
253#491—42no—
254#483—24no—
255#467—24no—
256#467—42no—
257#467—42no—
258#451—24no—
259#441—42no—
260#441—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106—42no—
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#103—24no—
276C2×#103—42no—
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×#103C2311yescharacteristic
303C2×C22⋊C8—24no—
304C2×C22⋊C8—24no—
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321#401—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#393—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—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#387—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#385—21no—
411#384C2311yescharacteristic
412#383—21no—
413#383—21no—
414#382—21no—
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#381—21no—
424#380—21no—
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4D411yescharacteristic
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4D411yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376—21no—
463C2×#95—21no—
464C2×#95D411yescharacteristic
465C2×#95D411yescharacteristic
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#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—41no—
516C23×C4—41no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8#4114yes—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#125—41no—
565#125—41no—
566#125—44no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—44no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—44no—
600#117—44no—
601#117—44no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
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—21no—
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—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—44no—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C22⋊C4—24no—
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—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—42no—
677C2×C22⋊C4—44no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—41no—
696C2×C42—41no—
697C2×C42—41no—
698C2×C42—41no—
699C2×C42C2×D411yescharacteristic
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#107—22no—
708#107—22no—
709#107—41no—
710#107—41no—
711#107—41no—
712#106—22no—
713#106—22no—
714#106—22no—
715#106—22no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—22no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—22no—
752C22⋊C8—22no—
753C22⋊C8#4114yes—
754#97—41no—
755#97—41no—
756#97—41no—
757#97—41no—
758#97—41no—
759#97—41no—
760#97—41no—
761#97—41no—
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#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#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—22no—
815C24—22no—
816C24—41no—
817C24—41no—
818C24—41no—
819C24—41no—
820C24#13714yes—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
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—42no—
848C2×Q8—42no—
849C2×Q8—42no—
850C2×Q8—44no—
851C2×Q8—44no—
852C2×Q8—42no—
853C2×Q8—81no—
854C2×Q8—81no—
855C2×Q8—82no—
856C2×Q8—82no—
857C2×Q8H(5,𝔽2)12yes—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—82no—
920C22×C4—82no—
921C22×C4—82no—
922C22×C4—82no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C2×#4112yes—
939C22×C4C2×#4112yes—
940C22×C4C2511yescharacteristic
941Q16—44no—
942Q16—44no—
943Q16—82no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
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—44no—
965C2×C8—82no—
966C2×C8—82no—
967C2×C8—82no—
968C2×C8C2×#4112yes—
969C2×C8C2×#4112yes—
970C2×C8C2×#4112yes—
971C2×C8C2×#4112yes—
972C4⋊C4—24no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
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—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4H(5,𝔽2)12yes—
1030C22⋊C4—24no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—41no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—28no—
1095C23—44no—
1096C23—44no—
1097C23—82no—
1098C23—82no—
1099C23—82no—
1100C23—82no—
1101C23#53212yes—
1102C23C2×#13712yes—
1103C23C2×#13712yes—
1104C23C2×#13712yes—
1105C23#57512yes—
1106C23C23×D411yescharacteristic
1107Q8—22no—
1108Q8—22no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—84no—
1124Q8—84no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—44no—
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—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—82no—
1219C2×C4—82no—
1220C2×C4—82no—
1221C2×C4—82no—
1222C2×C4—82no—
1223C2×C4—82no—
1224C2×C4—84no—
1225C2×C4—84no—
1226C2×C4—84no—
1227C2×C4—162no—
1228C2×C4#53212yes—
1229C2×C4C22×#4111yescharacteristic
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C2×H(5,𝔽2)11yescharacteristic
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C8—22no—
1236C8—22no—
1237C8—22no—
1238C8—22no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C22—22no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—22no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—88no—
1264C22#318114yes—
1265C22C2×#53211yescharacteristic
1266C22#348411yescharacteristic
1267C22#348511yescharacteristic
1268C22C22×#13711yescharacteristic
1269C22C2×#57511yescharacteristic
1270C22#358611yescharacteristic
1271C22#358611yescharacteristic
1272C4—22no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—42no—
1282C4—41no—
1283C4—41no—
1284C4—42no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4#349411yescharacteristic
1300C4#350511yescharacteristic
1301C4#351311yescharacteristic
1302C4#351411yescharacteristic
1303C2—24no—
1304C2—42no—
1305C2—42no—
1306C2#3576411yescharacteristic
1307C2C2×#318111yescharacteristic
1308C2#6071111yescharacteristic
1309C2#6157411yescharacteristic
1310C2#6158011yescharacteristic
1311C2#6170511yescharacteristic
1312C2#6171511yescharacteristic
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. #30363C2semidirect
4. #30326C2semidirect
6. #29479C2semidirect
7. #29478C2semidirect
8. #29053C2semidirect
9. #29049C2semidirect
10. #28934C2semidirect
11. #28855C2semidirect
12. #28345C2semidirect
13. #28084C2semidirect
14. #27896C2semidirect
15. #27797C2semidirect
16. #27713C2semidirect
17. #27268C2semidirect
18. #26981C2semidirect
19. #26068C2semidirect
20. #25677C2semidirect
21. #25043C2semidirect
24. #23765C2semidirect
25. #23577C2semidirect
27. #23028C2semidirect
28. #22934C2semidirect
29. #22859C2semidirect
30. #22563C2semidirect
34. C2×#501C22semidirect
35. C2×#491C22semidirect
41. C2×#441C22semidirect
42. C2×#441C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
101. #2074C22semidirect
102. #2072C22semidirect
103. #2059C22semidirect
104. #2058C22semidirect
105. #2043C22semidirect
106. #2043C22semidirect
123. #2026C22semidirect
124. #2024C22semidirect
125. #2016C22semidirect
126. #2016C22semidirect
131. #1993C22semidirect
132. #1971C22semidirect
133. #1971C22semidirect
134. #1971C22semidirect
135. #1971C22semidirect
136. #1960C22semidirect
137. #1960C22semidirect
138. #1960C22semidirect
139. #1944C22semidirect
140. #1944C22semidirect
141. #1943C22semidirect
142. #1943C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
151. #1928C22semidirect
152. #1928C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
156. #1927C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
169. #1865C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
172. #1863C22semidirect
173. #1863C22semidirect
174. #1863C22semidirect
177. #1847C22semidirect
178. #1836C22semidirect
184. #1776C22semidirect
185. #1776C22semidirect
186. #1763C22semidirect
187. #1763C22semidirect
188. #1763C22semidirect
189. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#361672
#361302
#303632
#303262
#297312
#294792
#294782
#290532
#290492
#289342
#288552
#283452
#280842
#278962
#277972
#277132
#272682
#269812
#260682
#256772
#250432
#245512
#243802
#237652
#235772
C2×#20352
#230282
#229342
#228592
#225632
#205262