Finite Group Databasebeta

← #6940688

Subgroups — #6940688

Order 512.

1302 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39077C211yesmaximal, characteristic
2#39067C211yesmaximal, characteristic
3#32863C211yesmaximal, characteristic, complemented
4#32828C211yesmaximal, characteristic, complemented
5#32542C211yesmaximal, characteristic, complemented
6#32476C211yesmaximal, characteristic, complemented
7#31984C211yesmaximal, characteristic, complemented
8#31968C211yesmaximal, characteristic, complemented
9#31907C211yesmaximal, characteristic, complemented
10#31892C211yesmaximal, characteristic, complemented
11#31242C211yesmaximal, characteristic, complemented
12#31173C211yesmaximal, characteristic, complemented
13#30148C211yesmaximal, characteristic, complemented
14#30131C211yesmaximal, characteristic, complemented
15#30004C211yesmaximal, characteristic, complemented
16#29837C211yesmaximal, characteristic, complemented
17#29786C211yesmaximal, characteristic
18#29549C211yesmaximal, characteristic, complemented
19#28283C211yesmaximal, characteristic, complemented
20#26349C211yesmaximal, characteristic
21#26337C211yesmaximal, characteristic
22#26014C211yesmaximal, characteristic
23#25971C211yesmaximal, characteristic
24#25219C211yesmaximal, characteristic
25#25095C211yesmaximal, characteristic
26#24616C211yesmaximal, characteristic
27#24532C211yesmaximal, characteristic
28#24514C211yesmaximal, characteristic
29#24480C211yesmaximal, characteristic
30#23613C211yesmaximal, characteristic
31#21980C211yesmaximal, characteristic
32C2×#483C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#462C2211yescharacteristic
38C2×#451C2211yescharacteristic
39C2×#433C2211yescharacteristic
40C2×#427C2211yescharacteristic
41C2×#424C2211yescharacteristic
42C2×#419C2211yescharacteristic
43C22×#103C2211yescharacteristic
44#2863C2211yescharacteristic
45#2863C2211yescharacteristic
46#2791—21no—
47#2765—21no—
48#2764—21no—
49#2762—21no—
50#2758—21no—
51#2755—21no—
52#2739—21no—
53#2738—21no—
54#2647C2211yescharacteristic
55#2642C2211yescharacteristic
56#2625C2211yescharacteristic
57#2625C2211yescharacteristic
58#2599—21no—
59#2588—21no—
60#2588—21no—
61#2575—21no—
62#2573—21no—
63#2565—21no—
64#2524—21no—
65#2514C2211yescharacteristic
66#2511C2211yescharacteristic
67#2507C2211yescharacteristic
68#2506C2211yescharacteristic
69#2502C2211yescharacteristic
70#2475—21no—
71#2453C2211yescharacteristic
72#2451C2211yescharacteristic
73#2446C2211yescharacteristic
74#2446C2211yescharacteristic
75#2441C2211yescharacteristic
76#2439C2211yescharacteristic
77#2434C2211yescharacteristic
78#2362C2211yescharacteristic
79#2362C2211yescharacteristic
80#2344C2211yescharacteristic
81Q8×C22⋊C4C2211yescharacteristic
82#2320C2211yescharacteristic
83#2320C2211yescharacteristic
84#2317C2211yescharacteristic
85#2310C2211yescharacteristic
86C4×C4⋊Q8C2211yescharacteristic
87C4×C4⋊Q8C2211yescharacteristic
88#2298C2211yescharacteristic
89#2100C2211yescharacteristic
90#2097C2211yescharacteristic
91#2097C2211yescharacteristic
92#2095C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2087C2211yescharacteristic
100#2086C2211yescharacteristic
101#2084C2211yescharacteristic
102#2072C2211yescharacteristic
103#2072C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2066C2211yescharacteristic
124#2066C2211yescharacteristic
125#2066C2211yescharacteristic
126#2066C2211yescharacteristic
127#2066C2211yescharacteristic
128#2066C2211yescharacteristic
129#2059C2211yescharacteristic
130#2059C2211yescharacteristic
131#2057C2211yescharacteristic
132#2056C2211yescharacteristic
133#2056C2211yescharacteristic
134#2056C2211yescharacteristic
135#2056C2211yescharacteristic
136#2056C2211yescharacteristic
137#2056C2211yescharacteristic
138#2056C2211yescharacteristic
139#2056C2211yescharacteristic
140#2043C2211yescharacteristic
141#2043C2211yescharacteristic
142#2043C2211yescharacteristic
143#2024C2211yescharacteristic
144#2016C2211yescharacteristic
145#1989C2211yescharacteristic
146#1981C2211yescharacteristic
147#1981C2211yescharacteristic
148#1981C2211yescharacteristic
149#1971C2211yescharacteristic
150#1969C2211yescharacteristic
151#1949C2211yescharacteristic
152#1948C2211yescharacteristic
153#1948C2211yescharacteristic
154#1948C2211yescharacteristic
155#1943C2211yescharacteristic
156#1941C2211yescharacteristic
157#1940C2211yescharacteristic
158#1940C2211yescharacteristic
159#1939C2211yescharacteristic
160#1939C2211yescharacteristic
161#1935C2211yescharacteristic
162#1935C2211yescharacteristic
163#1933C2211yescharacteristic
164#1933C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1927C2211yescharacteristic
168#1927C2211yescharacteristic
169#1921C2211yescharacteristic
170#1919C2211yescharacteristic
171#1918C2211yescharacteristic
172#1918C2211yescharacteristic
173#1892C2211yescharacteristic
174#1892C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1873C2211yescharacteristic
180#1873C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1843C2211yescharacteristic
192#1842C2211yescharacteristic
193#1832C2211yescharacteristic
194#1831C2211yescharacteristic
195#1824C2211yescharacteristic
196#1809C2211yescharacteristic
197#1805C2211yescharacteristic
198#1803C2211yescharacteristic
199#1803C2211yescharacteristic
200#1803C2211yescharacteristic
201#1787C2211yescharacteristic
202#1736C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226#483—42no—
227#479—42no—
228#475—42no—
229#475—42no—
230#470—42no—
231#462—42no—
232#451—42no—
233#433—42no—
234#427—42no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248#424—42no—
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×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263#419—42no—
264C2×#103—42no—
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#401—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#393—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388D411yescharacteristic
385#388D411yescharacteristic
386#388D411yescharacteristic
387#388D411yescharacteristic
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—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#387D411yescharacteristic
416#387D411yescharacteristic
417#387D411yescharacteristic
418#387D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#383—21no—
431#383—21no—
432#383—21no—
433#383—21no—
434#382—21no—
435#382—21no—
436#382—21no—
437#382C2311yescharacteristic
438#381—21no—
439#381—21no—
440#381—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376C2311yescharacteristic
459C43C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8—41no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2411yescharacteristic
505C2×Q16—22no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×Q16—41no—
509C2×Q16—41no—
510C2×Q16—41no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534#125—41no—
535#125—41no—
536#125—82no—
537C22⋊Q8—22no—
538C22⋊Q8—22no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×Q8—82no—
550#117—22no—
551#117—22no—
552#117—22no—
553#117—41no—
554#117—41no—
555#117—41no—
556#117—82no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
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⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2×D411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#107—22no—
646#107—41no—
647#107—41no—
648#107—41no—
649#107—41no—
650#106—22no—
651#106—22no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658C4⋊C8—41no—
659C4⋊C8—41no—
660C4⋊C8—41no—
661C4⋊C8—41no—
662C4⋊C8—41no—
663C4⋊C8—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—41no—
677#103—41no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698C22⋊C8—22no—
699C22⋊C8—22no—
700#97—41no—
701C4×C8—41no—
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#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
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#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770C24C22×D411yescharacteristic
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—82no—
803C2×Q8—82no—
804C2×Q82−1+412yes—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4H(5,𝔽2)12yes—
845C22×C42−1+412yes—
846C22×C4C2511yescharacteristic
847Q16—82no—
848Q16—82no—
849Q16—82no—
850M16—82no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—44no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4H(5,𝔽2)12yes—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C42—22no—
955C42—22no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—41no—
969C42—41no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23#53712yes—
987C23C23×D411yescharacteristic
988Q8—22no—
989Q8—22no—
990Q8—41no—
991Q8—41no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8—41no—
1002Q8—41no—
1003Q8—41no—
1004Q8—84no—
1005Q8—84no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
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—22no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
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—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—84no—
1095C2×C4—84no—
1096C2×C4#53712yes—
1097C2×C4#57712yes—
1098C2×C4#57812yes—
1099C2×C4C2×H(5,𝔽2)11yescharacteristic
1100C2×C4C2×H(5,𝔽2)11yescharacteristic
1101C2×C4C2×2−1+411yescharacteristic
1102C2×C4C2×2−1+411yescharacteristic
1103C2×C4#58511yescharacteristic
1104C2×C4#58511yescharacteristic
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C8—41no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—41no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22C2×#53711yescharacteristic
1121C22#348811yescharacteristic
1122C22#348911yescharacteristic
1123C22C2×#57711yescharacteristic
1124C22C2×#57811yescharacteristic
1125C22#358611yescharacteristic
1126C22#358611yescharacteristic
1127C4—22no—
1128C4—22no—
1129C4—22no—
1130C4—42no—
1131C4—41no—
1132C4—42no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—41no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4#353511yescharacteristic
1157C4#353811yescharacteristic
1158C4#354211yescharacteristic
1159C4#356411yescharacteristic
1160C2—42no—
1161C2#4198411yescharacteristic
1162C2#6092311yescharacteristic
1163C2#6092511yescharacteristic
1164C2#6205411yescharacteristic
1165C2#6208611yescharacteristic
1166C2#6215711yescharacteristic
1167C2#6219211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32863C2semidirect
4. #32828C2semidirect
5. #32542C2semidirect
6. #32476C2semidirect
7. #31984C2semidirect
8. #31968C2semidirect
9. #31907C2semidirect
10. #31892C2semidirect
11. #31242C2semidirect
12. #31173C2semidirect
13. #30148C2semidirect
14. #30131C2semidirect
15. #30004C2semidirect
16. #29837C2semidirect
18. #29549C2semidirect
19. #28283C2semidirect

Maximal subgroups

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

subgroupindex
#390772
#390672
#328632
#328282
#325422
#324762
#319842
#319682
#319072
#318922
#312422
#311732
#301482
#301312
#300042
#298372
#297862
#295492
#282832
#263492
#263372
#260142
#259712
#252192
#250952
#246162
#245322
#245142
#244802
#236132
#219802