Finite Group Databasebeta

← #7188535

Subgroups — #7188535

Order 512.

1332 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44911C211yesmaximal, characteristic, complemented
2#42459C211yesmaximal, characteristic, complemented
3#32536C211yesmaximal, characteristic, complemented
4#32525C211yesmaximal, characteristic, complemented
5#32431C211yesmaximal, characteristic, complemented
6#32427C211yesmaximal, characteristic, complemented
7#32215C211yesmaximal, characteristic, complemented
8#32207C211yesmaximal, characteristic, complemented
9#30679C211yesmaximal, characteristic
10#30664C211yesmaximal, characteristic, complemented
11#28867C211yesmaximal, characteristic, complemented
12#28845C211yesmaximal, characteristic, complemented
13#28822C211yesmaximal, characteristic, complemented
14#27904C211yesmaximal, characteristic, complemented
15#27794C211yesmaximal, characteristic
16#27788C211yesmaximal, characteristic, complemented
17#27137C211yesmaximal, characteristic, complemented
18#27130C211yesmaximal, characteristic, complemented
19#26470C211yesmaximal, characteristic, complemented
20#26328C211yesmaximal, characteristic, complemented
21#26021C211yesmaximal, characteristic, complemented
22#25464C211yesmaximal, characteristic, complemented
23#25458C211yesmaximal, characteristic, complemented
24#25296C211yesmaximal, characteristic, complemented
25#25068C211yesmaximal, characteristic, complemented
26#24767C211yesmaximal, characteristic
27#23766C211yesmaximal, characteristic, complemented
28#23109C211yesmaximal, characteristic, complemented
29#22958C211yesmaximal, characteristic, complemented
30#22738C211yesmaximal, characteristic, complemented
31#21967C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#499C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×C8×Q8C2211yescharacteristic
40C2×#424C2211yescharacteristic
41#2837—21no—
42#2800—21no—
43#2798—21no—
44#2790—21no—
45#2788—21no—
46#2772—21no—
47#2727—21no—
48#2718—21no—
49#2715—21no—
50#2652—21no—
51#2637—21no—
52#2620C2211yescharacteristic
53#2601—21no—
54#2592—21no—
55#2592C2211yescharacteristic
56#2580C2211yescharacteristic
57#2566C2211yescharacteristic
58#2565C2211yescharacteristic
59#2552C2211yescharacteristic
60#2550C2211yescharacteristic
61#2512C2211yescharacteristic
62#2512C2211yescharacteristic
63#2512C2211yescharacteristic
64#2511C2211yescharacteristic
65#2497C2211yescharacteristic
66#2496C2211yescharacteristic
67#2491C2211yescharacteristic
68#2490C2211yescharacteristic
69#2490C2211yescharacteristic
70#2489C2211yescharacteristic
71#2478—21no—
72#2469—21no—
73#2458—21no—
74#2423C2211yescharacteristic
75#2422C2211yescharacteristic
76#2396C2211yescharacteristic
77#2370C2211yescharacteristic
78#2369C2211yescharacteristic
79#2367C2211yescharacteristic
80#2354C2211yescharacteristic
81Q8×C4⋊C4C2211yescharacteristic
82Q8×C4⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2314C2211yescharacteristic
85#2314C2211yescharacteristic
86#2099C2211yescharacteristic
87#2096C2211yescharacteristic
88#2094C2211yescharacteristic
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2085C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic
101#2066C2211yescharacteristic
102#2066C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2058C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2026C2211yescharacteristic
123#2025C2211yescharacteristic
124#2025C2211yescharacteristic
125#2023C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1985C2211yescharacteristic
129#1983C2211yescharacteristic
130#1972C2211yescharacteristic
131#1970C2211yescharacteristic
132#1968C2211yescharacteristic
133#1968C2211yescharacteristic
134#1959C2211yescharacteristic
135#1958C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1948C2211yescharacteristic
146#1948C2211yescharacteristic
147#1948C2211yescharacteristic
148#1948C2211yescharacteristic
149#1944C2211yescharacteristic
150#1941C2211yescharacteristic
151#1940C2211yescharacteristic
152#1939C2211yescharacteristic
153#1939C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic
156#1928C2211yescharacteristic
157#1928C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1921C2211yescharacteristic
169#1920C2211yescharacteristic
170#1919C2211yescharacteristic
171#1919C2211yescharacteristic
172#1916C2211yescharacteristic
173#1916C2211yescharacteristic
174#1894C2211yescharacteristic
175#1893C2211yescharacteristic
176#1880C2211yescharacteristic
177#1879C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic
180#1851C2211yescharacteristic
181#1850C2211yescharacteristic
182#1847C2211yescharacteristic
183#1834C2211yescharacteristic
184#1834C2211yescharacteristic
185#1834C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic
190#1802C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#106C2211yescharacteristic
193C4×#106C2211yescharacteristic
194C4×#106C2211yescharacteristic
195#1771C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#126—21no—
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×C4×Q8—21no—
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229#501—42no—
230#499—42no—
231#478—42no—
232#475—42no—
233#469—42no—
234#465—42no—
235#463—24no—
236C8×Q8—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255#424—24no—
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400D411yescharacteristic
298#399—21no—
299#399—21no—
300#399D411yescharacteristic
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398D411yescharacteristic
308#398D411yescharacteristic
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396D411yescharacteristic
327#396D411yescharacteristic
328#395—21no—
329#395D411yescharacteristic
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#394—21no—
335#394—21no—
336#393—21no—
337#393—21no—
338#393—21no—
339#393D411yescharacteristic
340#391—21no—
341#391—21no—
342#391—21no—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390—21no—
349#390—21no—
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384—21no—
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382—21no—
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8C2×D411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2411yescharacteristic
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×D8—22no—
501C2×D8—41no—
502C2×D8—41no—
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—41no—
506C22×C8—22no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519#126—82no—
520#126—82no—
521#126—82no—
522#126—82no—
523#125—22no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#125—41no—
529#124—22no—
530#124—22no—
531#124—82no—
532#123—82no—
533C22⋊Q8—41no—
534C22⋊Q8—41no—
535#121—22no—
536#121—41no—
537#121—41no—
538#121—41no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—82no—
544C4×Q8—82no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—41no—
548C4×D4—41no—
549#117—22no—
550#117—22no—
551#117—82no—
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⋊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⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
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⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—22no—
667#106—22no—
668#106—22no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8#4114yes—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706C22⋊C8—22no—
707C22⋊C8—41no—
708#97—22no—
709#97—41no—
710C4×C8—22no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—41no—
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#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759C24—21no—
760C24—21no—
761C24C22×D411yescharacteristic
762C2×Q8—22no—
763C2×Q8—22no—
764C2×Q8—22no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—42no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—81no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—42no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
832SD16—82no—
833D8—82no—
834M16—82no—
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—82no—
857C2×C8C2×#4112yes—
858C2×C8C2×#4112yes—
859C2×C82−1+412yes—
860C4⋊C4—22no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
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—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
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⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
927C22⋊C4—22no—
928C22⋊C4—22no—
929C22⋊C4—22no—
930C22⋊C4—22no—
931C22⋊C4—41no—
932C22⋊C4—41no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—42no—
938C22⋊C4—42no—
939C22⋊C4—42no—
940C22⋊C4—42no—
941C22⋊C4—42no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—42no—
974C42—42no—
975C42—42no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42C2×#4112yes—
986C422−1+412yes—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23C23×D411yescharacteristic
1009Q8—28no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—162no—
1015D4—41no—
1016D4—41no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—162no—
1024D4—162no—
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—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
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—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
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—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—84no—
1107C2×C4—162no—
1108C2×C4#54712yes—
1109C2×C4#54712yes—
1110C2×C4#57712yes—
1111C2×C4#57712yes—
1112C2×C4C22×#4111yescharacteristic
1113C2×C4C2×H(5,𝔽2)11yescharacteristic
1114C2×C4C2×2−1+411yescharacteristic
1115C2×C4C2×2−1+411yescharacteristic
1116C2×C4#58511yescharacteristic
1117C2×C4#58511yescharacteristic
1118C8—22no—
1119C8—22no—
1120C8—22no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22C2×#54711yescharacteristic
1148C22#348811yescharacteristic
1149C22#349711yescharacteristic
1150C22C2×#57711yescharacteristic
1151C22C2×#57711yescharacteristic
1152C22#358411yescharacteristic
1153C22#358511yescharacteristic
1154C4—22no—
1155C4—22no—
1156C4—22no—
1157C4—22no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4#351411yescharacteristic
1182C4#351811yescharacteristic
1183C4#355211yescharacteristic
1184C4#356511yescharacteristic
1185C2—81no—
1186C2—161no—
1187C2—161no—
1188C2#4528711yescharacteristic
1189C2#6125911yescharacteristic
1190C2#6128311yescharacteristic
1191C2#6204511yescharacteristic
1192C2#6206811yescharacteristic
1193C2#6238611yescharacteristic
1194C2#6240111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#469C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44911C2semidirect
2. #42459C2semidirect
3. #32536C2semidirect
4. #32525C2semidirect
5. #32431C2semidirect
6. #32427C2semidirect
7. #32215C2semidirect
8. #32207C2semidirect
10. #30664C2semidirect
11. #28867C2semidirect
12. #28845C2semidirect
13. #28822C2semidirect
14. #27904C2semidirect
16. #27788C2semidirect
17. #27137C2semidirect
18. #27130C2semidirect
19. #26470C2semidirect
20. #26328C2semidirect
21. #26021C2semidirect
22. #25464C2semidirect
23. #25458C2semidirect
24. #25296C2semidirect
25. #25068C2semidirect
27. #23766C2semidirect
28. #23109C2semidirect
29. #22958C2semidirect
30. #22738C2semidirect
31. #21967C2semidirect

Maximal subgroups

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

subgroupindex
#449112
#424592
#325362
#325252
#324312
#324272
#322152
#322072
#306792
#306642
#288672
#288452
#288222
#279042
#277942
#277882
#271372
#271302
#264702
#263282
#260212
#254642
#254582
#252962
#250682
#247672
#237662
#231092
#229582
#227382
#219672