Finite Group Databasebeta

← #6436866

Subgroups — #6436866

Order 512.

1412 conjugacy classes of subgroups.

The subgroup lattice has 1167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35304C211yesmaximal, characteristic, complemented
2#34056C211yesmaximal, characteristic
3#30005C211yesmaximal, characteristic, complemented
4#30004C211yesmaximal, characteristic, complemented
5#30003C211yesmaximal, characteristic, complemented
6#30002C211yesmaximal, characteristic, complemented
7#29993C211yesmaximal, characteristic, complemented
8#29992C211yesmaximal, characteristic, complemented
9#29991C211yesmaximal, characteristic, complemented
10#29990C211yesmaximal, characteristic, complemented
11#29974C211yesmaximal, characteristic, complemented
12#29974C211yesmaximal, characteristic, complemented
13#29971C211yesmaximal, characteristic, complemented
14#29970C211yesmaximal, characteristic, complemented
15#29958C211yesmaximal, characteristic
16#29958C211yesmaximal, characteristic
17#29955C211yesmaximal, characteristic
18#29954C211yesmaximal, characteristic
19#23793C211yesmaximal, characteristic, complemented
20#23792C211yesmaximal, characteristic, complemented
21#23791C211yesmaximal, characteristic, complemented
22#23790C211yesmaximal, characteristic, complemented
23#23789C211yesmaximal, characteristic, complemented
24#23788C211yesmaximal, characteristic, complemented
25#23787C211yesmaximal, characteristic, complemented
26#23786C211yesmaximal, characteristic, complemented
27#21366C211yesmaximal, characteristic, complemented
28#21362C211yesmaximal, characteristic, complemented
29#20814C211yesmaximal, characteristic, complemented
30#20743C211yesmaximal, characteristic
31#20736C211yesmaximal, characteristic
32C2×C4×#41C2211yescharacteristic
33C2×#432C2211yescharacteristic
34C2×#431C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2851C2211yescharacteristic
38#2851C2211yescharacteristic
39#2660C2211yescharacteristic
40#2660C2211yescharacteristic
41#2647C2211yescharacteristic
42#2647C2211yescharacteristic
43#2612—21no—
44#2612—21no—
45#2606—21no—
46#2605—21no—
47#2569—21no—
48#2549—21no—
49#2438—21no—
50#2438—21no—
51#2331C2211yescharacteristic
52#2331C2211yescharacteristic
53#2330C2211yescharacteristic
54#2330C2211yescharacteristic
55#2320C2211yescharacteristic
56#2320C2211yescharacteristic
57#2320C2211yescharacteristic
58#2320C2211yescharacteristic
59#2319C2211yescharacteristic
60#2319C2211yescharacteristic
61#2319C2211yescharacteristic
62#2319C2211yescharacteristic
63#2318—21no—
64#2318—21no—
65#2318—21no—
66#2318—21no—
67#2298—21no—
68#2298—21no—
69#2297C2211yescharacteristic
70#2297C2211yescharacteristic
71#2296C2211yescharacteristic
72#2296C2211yescharacteristic
73#2285C2211yescharacteristic
74#2283—21no—
75#2283—21no—
76#2283C2211yescharacteristic
77C4×#117C2211yescharacteristic
78C2×#376C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2097C2211yescharacteristic
89#2096C2211yescharacteristic
90#2095C2211yescharacteristic
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2088C2211yescharacteristic
102#2088C2211yescharacteristic
103#2087C2211yescharacteristic
104#2087C2211yescharacteristic
105#2087C2211yescharacteristic
106#2087C2211yescharacteristic
107#2086C2211yescharacteristic
108#2086C2211yescharacteristic
109#2086C2211yescharacteristic
110#2086C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2067C2211yescharacteristic
116#2067C2211yescharacteristic
117#2067C2211yescharacteristic
118#2067C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2065C2211yescharacteristic
124#2065C2211yescharacteristic
125#2065C2211yescharacteristic
126#2065C2211yescharacteristic
127#2059C2211yescharacteristic
128#2059C2211yescharacteristic
129#2059C2211yescharacteristic
130#2059C2211yescharacteristic
131#2058C2211yescharacteristic
132#2058C2211yescharacteristic
133#2057C2211yescharacteristic
134#2057C2211yescharacteristic
135#2026C2211yescharacteristic
136#2026C2211yescharacteristic
137#2025C2211yescharacteristic
138#2025C2211yescharacteristic
139#2024C2211yescharacteristic
140#2024C2211yescharacteristic
141#2023C2211yescharacteristic
142#2023C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1948C2211yescharacteristic
148#1948C2211yescharacteristic
149#1947C2211yescharacteristic
150#1947C2211yescharacteristic
151#1854C2211yescharacteristic
152#1854C2211yescharacteristic
153#1854C2211yescharacteristic
154#1854C2211yescharacteristic
155#1854C2211yescharacteristic
156#1854C2211yescharacteristic
157#1854C2211yescharacteristic
158#1854C2211yescharacteristic
159#1843C2211yescharacteristic
160#1843C2211yescharacteristic
161#1832C2211yescharacteristic
162#1832C2211yescharacteristic
163#1825C2211yescharacteristic
164#1825C2211yescharacteristic
165#1825C2211yescharacteristic
166#1825C2211yescharacteristic
167#1805C2211yescharacteristic
168#1805C2211yescharacteristic
169#1804C2211yescharacteristic
170#1804C2211yescharacteristic
171#1803C2211yescharacteristic
172#1803C2211yescharacteristic
173#1802C2211yescharacteristic
174#1802C2211yescharacteristic
175#1797C2211yescharacteristic
176#1797C2211yescharacteristic
177#1797C2211yescharacteristic
178#1797C2211yescharacteristic
179#1788C2211yescharacteristic
180#1788C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187C4×#107C2211yescharacteristic
188C4×#107C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1768C2211yescharacteristic
192#1768C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic
200C4×#103C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×C22⋊Q8—21no—
209C2×C22⋊Q8—21no—
210C4×#41—24no—
211C4×#41Q818yescomplemented
212C2×C4×Q8C2311yescharacteristic
213C2×C4×Q8C2311yescharacteristic
214C2×C4×D4—21no—
215C2×C4×D4—21no—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×#117—21no—
219C2×#117—21no—
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C22×C42—21no—
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227#432—24no—
228#431—24no—
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#395—21no—
294#395—21no—
295#395—21no—
296#395—21no—
297#391—21no—
298#391—21no—
299#391—21no—
300#391—21no—
301#391—21no—
302#391—21no—
303#391C2311yescharacteristic
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#390C2311yescharacteristic
308#390C2311yescharacteristic
309#390C2311yescharacteristic
310#390C2311yescharacteristic
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389—21no—
316#389—21no—
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#388—21no—
334#388—21no—
335#388—21no—
336#388—21no—
337#388—21no—
338#388—21no—
339#388—21no—
340#388—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#386—21no—
362#386—21no—
363#386—21no—
364#386—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385—21no—
373#384C2311yescharacteristic
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#384C2311yescharacteristic
377#383—21no—
378#383—21no—
379#383—21no—
380#383—21no—
381#383—21no—
382#382—21no—
383#382—21no—
384#382—21no—
385#382—21no—
386#382—21no—
387#382C2311yescharacteristic
388#382C2311yescharacteristic
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#381—21no—
392#381—21no—
393#381—21no—
394#381—21no—
395#381—21no—
396#380—21no—
397#380—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380—21no—
402#380—21no—
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4—21no—
411C4×C4⋊C4—21no—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427#376—21no—
428#376—21no—
429#376D411yescharacteristic
430#376D411yescharacteristic
431#376D411yescharacteristic
432#376D411yescharacteristic
433#376C2311yescharacteristic
434#376C2311yescharacteristic
435#376C2311yescharacteristic
436#376C2311yescharacteristic
437C2×#95D411yescharacteristic
438C2×#95D411yescharacteristic
439C2×#95D411yescharacteristic
440C2×#95D411yescharacteristic
441C43—21no—
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C2×#41—22no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41C2×Q814yes—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2×D411yescharacteristic
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2×D411yescharacteristic
500C23×C4C2×D411yescharacteristic
501C23×C4C2×D411yescharacteristic
502C23×C4C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—41no—
512C4⋊Q8—41no—
513C4⋊Q8—41no—
514C4⋊Q8—41no—
515#125—41no—
516#125—41no—
517#125—41no—
518#125—41no—
519C22⋊Q8—82no—
520C22⋊Q8—82no—
521C4×Q8—22no—
522C4×Q8—22no—
523C4×Q8C2×Q814yes—
524C4×Q8C2×Q814yes—
525C4×D4—28no—
526C4×D4—28no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4C2×Q814yes—
530C4×D4C2×Q814yes—
531#117—22no—
532#117—28no—
533#117—41no—
534#117—41no—
535#117—41no—
536#117—41no—
537#117—82no—
538#117C2×Q814yes—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—21no—
605C2×C42—28no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×Q814yes—
627C2×C42#4114yes—
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634#107—41no—
635#107—41no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650C4⋊C8—22no—
651C4⋊C8—22no—
652C4⋊C8—22no—
653C4⋊C8—22no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657C4⋊C8—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#103—41no—
670#102—41no—
671#102—41no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681C22⋊C8—22no—
682#97—22no—
683#97—22no—
684C4×C8—22no—
685C4×C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95C2×D411yescharacteristic
731#95C2×D411yescharacteristic
732#95C2×D411yescharacteristic
733#95C2×D411yescharacteristic
734#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24C22×D411yescharacteristic
748#41—44no—
749#41—44no—
750#41—44no—
751#41—44no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—81no—
760C2×Q8—81no—
761C2×Q8—81no—
762C2×Q8—81no—
763C2×Q8C22×Q812yes—
764C2×D4—24no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—42no—
771C2×D4—42no—
772C2×D4C22×Q812yes—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—41no—
796C22×C4—41no—
797C22×C4—41no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4—41no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4C22⋊Q814yes—
818C22×C4C22⋊Q814yes—
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×Q812yes—
833C22×C4C2×#4112yes—
834C22×C4C2511yescharacteristic
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4C22×Q812yes—
918C4⋊C4C22×Q812yes—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C42—24no—
937C42—24no—
938C42—24no—
939C42—21no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—41no—
948C42—41no—
949C42—41no—
950C42—41no—
951C42—42no—
952C42—42no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42C22⋊Q814yes—
962C42C22⋊Q814yes—
963C42C22×Q812yes—
964C42C22×Q812yes—
965C42C2×#4112yes—
966C42C2×#4112yes—
967C23—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—21no—
972C23—21no—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊Q812yes—
981C23C23×D411yescharacteristic
982Q8—22no—
983Q8—22no—
984Q8—41no—
985Q8—41no—
986Q8—162no—
987Q8—162no—
988D4—22no—
989D4—22no—
990D4—48no—
991D4—41no—
992D4—41no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—48no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—84no—
1080C2×C4—84no—
1081C2×C4—82no—
1082C2×C4—82no—
1083C2×C4—82no—
1084C2×C4—82no—
1085C2×C4C2×C22⋊Q812yes—
1086C2×C4C2×C22⋊Q812yes—
1087C2×C4C2×C22⋊Q812yes—
1088C2×C4C2×C22⋊Q812yes—
1089C2×C4C2×C22⋊Q812yes—
1090C2×C4C23×Q811yescharacteristic
1091C2×C4C22×#4111yescharacteristic
1092C2×C4#58511yescharacteristic
1093C2×C4#58511yescharacteristic
1094C2×C4#58511yescharacteristic
1095C2×C4#58511yescharacteristic
1096C8—41no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22C22×C22⋊Q811yescharacteristic
1119C22#344911yescharacteristic
1120C22#344911yescharacteristic
1121C22#358411yescharacteristic
1122C22#358411yescharacteristic
1123C22#358511yescharacteristic
1124C22#358611yescharacteristic
1125C4—22no—
1126C4—22no—
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4#345511yescharacteristic
1154C4#345511yescharacteristic
1155C4#345811yescharacteristic
1156C4#345811yescharacteristic
1157C2—42no—
1158C2—82no—
1159C2#3463411yescharacteristic
1160C2#6048911yescharacteristic
1161C2#6049311yescharacteristic
1162C2#6098411yescharacteristic
1163C2#6098511yescharacteristic
1164C2#6098611yescharacteristic
1165C2#6098711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#41C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35304C2semidirect
3. #30005C2semidirect
4. #30004C2semidirect
5. #30003C2semidirect
6. #30002C2semidirect
7. #29993C2semidirect
8. #29992C2semidirect
9. #29991C2semidirect
10. #29990C2semidirect
11. #29974C2semidirect
12. #29974C2semidirect
13. #29971C2semidirect
14. #29970C2semidirect
19. #23793C2semidirect
20. #23792C2semidirect
21. #23791C2semidirect
22. #23790C2semidirect
23. #23789C2semidirect
24. #23788C2semidirect
25. #23787C2semidirect
26. #23786C2semidirect
27. #21366C2semidirect
28. #21362C2semidirect
29. #20814C2semidirect
211. C4×#41Q8semidirect

Maximal subgroups

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

subgroupindex
#353042
#340562
#300052
#300042
#300032
#300022
#299932
#299922
#299912
#299902
#299742
#299712
#299702
#299582
#299552
#299542
#237932
#237922
#237912
#237902
#237892
#237882
#237872
#237862
#213662
#213622
#208142
#207432
#207362