Finite Group Databasebeta

← #6848688

Subgroups — #6848688

Order 512.

1378 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39510C211yesmaximal, characteristic
2#35209C211yesmaximal, characteristic
3#33200C211yesmaximal, characteristic, complemented
4#32221C211yesmaximal, characteristic, complemented
5#32219C211yesmaximal, characteristic, complemented
6#32201C211yesmaximal, characteristic, complemented
7#32199C211yesmaximal, characteristic, complemented
8#31509C211yesmaximal, characteristic, complemented
9#31505C211yesmaximal, characteristic, complemented
10#31501C211yesmaximal, characteristic, complemented
11#31497C211yesmaximal, characteristic, complemented
12#29701C211yesmaximal, characteristic, complemented
13#29701C211yesmaximal, characteristic, complemented
14#28725C211yesmaximal, characteristic, complemented
15#28611C211yesmaximal, characteristic
16#28611C211yesmaximal, characteristic
17#28287C211yesmaximal, characteristic, complemented
18#27643C211yesmaximal, characteristic, complemented
19#27642C211yesmaximal, characteristic, complemented
20#26459C211yesmaximal, characteristic, complemented
21#26457C211yesmaximal, characteristic, complemented
22#25357C211yesmaximal, characteristic
23#25353C211yesmaximal, characteristic
24#25290C211yesmaximal, characteristic, complemented
25#25290C211yesmaximal, characteristic, complemented
26#24854C211yesmaximal, characteristic, complemented
27#24850C211yesmaximal, characteristic, complemented
28#22652C211yesmaximal, characteristic
29#21898C211yesmaximal, characteristic, complemented
30#21898C211yesmaximal, characteristic, complemented
31#21618C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#491C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#479C2211yescharacteristic
38C2×#479C2211yescharacteristic
39C2×#479C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#424C2211yescharacteristic
44C2×#424C2211yescharacteristic
45#2860—21no—
46#2859—21no—
47#2859C2211yescharacteristic
48#2800—21no—
49#2800—21no—
50#2776—21no—
51#2776—21no—
52#2664—21no—
53#2664—21no—
54#2629C2211yescharacteristic
55#2629C2211yescharacteristic
56#2594—21no—
57#2594—21no—
58#2562C2211yescharacteristic
59#2562C2211yescharacteristic
60#2552C2211yescharacteristic
61#2546C2211yescharacteristic
62#2542C2211yescharacteristic
63#2538C2211yescharacteristic
64#2525—21no—
65#2525—21no—
66#2519—21no—
67#2519—21no—
68#2512—21no—
69#2506—21no—
70#2495C2211yescharacteristic
71#2495C2211yescharacteristic
72#2494C2211yescharacteristic
73#2494C2211yescharacteristic
74#2489C2211yescharacteristic
75#2489C2211yescharacteristic
76#2429C2211yescharacteristic
77#2429C2211yescharacteristic
78#2370C2211yescharacteristic
79#2370C2211yescharacteristic
80#2323C2211yescharacteristic
81#2323C2211yescharacteristic
82#2314C2211yescharacteristic
83#2314C2211yescharacteristic
84C4×C4⋊Q8C2211yescharacteristic
85C4×#125C2211yescharacteristic
86#2293C2211yescharacteristic
87C42×Q8C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2075C2211yescharacteristic
96#2074C2211yescharacteristic
97#2074C2211yescharacteristic
98#2074C2211yescharacteristic
99#2074C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2066C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2043C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2043C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2035C2211yescharacteristic
127#2035C2211yescharacteristic
128#1992C2211yescharacteristic
129#1992C2211yescharacteristic
130#1989C2211yescharacteristic
131#1989C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1989C2211yescharacteristic
135#1989C2211yescharacteristic
136#1989C2211yescharacteristic
137#1981C2211yescharacteristic
138#1981C2211yescharacteristic
139#1981C2211yescharacteristic
140#1981C2211yescharacteristic
141#1981C2211yescharacteristic
142#1981C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1948C2211yescharacteristic
147#1948C2211yescharacteristic
148#1947C2211yescharacteristic
149#1947C2211yescharacteristic
150#1940C2211yescharacteristic
151#1940C2211yescharacteristic
152#1928C2211yescharacteristic
153#1928C2211yescharacteristic
154#1927C2211yescharacteristic
155#1927C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1918C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic
166#1894C2211yescharacteristic
167#1894C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1892C2211yescharacteristic
173#1892C2211yescharacteristic
174#1865C2211yescharacteristic
175#1863C2211yescharacteristic
176#1851C2211yescharacteristic
177#1851C2211yescharacteristic
178#1850C2211yescharacteristic
179#1850C2211yescharacteristic
180#1842C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1808C2211yescharacteristic
184#1807C2211yescharacteristic
185#1805C2211yescharacteristic
186#1805C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1803C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1803C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1776C2211yescharacteristic
199#1776C2211yescharacteristic
200#1767C2211yescharacteristic
201#1763C2211yescharacteristic
202#1763C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#541—24no—
208#541—24no—
209#541—42no—
210#541—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#125—21no—
221C2×#125—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241#491—42no—
242#491—42no—
243#479—24no—
244#479—42no—
245#479—42no—
246#479—42no—
247#479—42no—
248#435—42no—
249#435—42no—
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262#424—42no—
263#424—42no—
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306#401—21no—
307#401—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#399—21no—
315#399—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#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#394—21no—
341#394—21no—
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390D411yescharacteristic
349#390D411yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389D411yescharacteristic
367#389D411yescharacteristic
368#389C2311yescharacteristic
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#388D411yescharacteristic
397#388D411yescharacteristic
398#388D411yescharacteristic
399#388D411yescharacteristic
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#384—21no—
415#384—21no—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#383—21no—
421#382—21no—
422#382—21no—
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C43—21no—
458C43C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4C2×D411yescharacteristic
497C23×C4C2411yescharacteristic
498C23×C4C2411yescharacteristic
499C2×M16—41no—
500C2×M16—41no—
501C2×M16—41no—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16—41no—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525#126—44no—
526#126—44no—
527#126—44no—
528#126—44no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—22no—
533#125—22no—
534#125—22no—
535#125—22no—
536#125—22no—
537#125—41no—
538#125—41no—
539#125—44no—
540#125—44no—
541#125—44no—
542#125—44no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—41no—
555C4×Q8—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—41no—
564C4×Q8#4114yes—
565C4×D4—22no—
566C4×D4—22no—
567#117—22no—
568#117—22no—
569#117—22no—
570#117—22no—
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⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681#107—22no—
682#107—22no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#106—22no—
688#106—22no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696C4⋊C8—22no—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—41no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705#103—22no—
706#103—22no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733#97—22no—
734#97—22no—
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#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
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#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24C22×D411yescharacteristic
783C24C22×D411yescharacteristic
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—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8C2×#4112yes—
802C2×D4—22no—
803C2×D4—41no—
804C2×D4—41no—
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—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
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×C4C22×D411yescharacteristic
845C22×C4C2511yescharacteristic
846M16—82no—
847M16—82no—
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—
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—82no—
873C2×C8—82no—
874C4⋊C4—22no—
875C4⋊C4—24no—
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—21no—
904C4⋊C4—41no—
905C4⋊C4—41no—
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—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
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⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4C2×#4112yes—
947C4⋊C42−1+412yes—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—41no—
957C22⋊C4—41no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C42—24no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—41no—
982C42—41no—
983C42—41no—
984C42—41no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42C2×#4112yes—
999C42H(5,𝔽2)12yes—
1000C42H(5,𝔽2)12yes—
1001C422−1+412yes—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23C23×D411yescharacteristic
1017Q8—22no—
1018Q8—22no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026Q8—41no—
1027Q8—41no—
1028Q8—41no—
1029D4—82no—
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—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—22no—
1063C2×C4—21no—
1064C2×C4—21no—
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—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4#53712yes—
1119C2×C4#53712yes—
1120C2×C4#54612yes—
1121C2×C4#54612yes—
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C2×H(5,𝔽2)11yescharacteristic
1124C2×C4C2×H(5,𝔽2)11yescharacteristic
1125C2×C4C2×2−1+411yescharacteristic
1126C2×C4C2×2−1+411yescharacteristic
1127C2×C4#58511yescharacteristic
1128C8—41no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—41no—
1146C22—41no—
1147C22—41no—
1148C22—41no—
1149C22—41no—
1150C22C2×#53711yescharacteristic
1151C22C2×#54611yescharacteristic
1152C22#348911yescharacteristic
1153C22#358411yescharacteristic
1154C22#358611yescharacteristic
1155C22#358611yescharacteristic
1156C22#358611yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—41no—
1171C4—42no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4#350711yescharacteristic
1186C4#351111yescharacteristic
1187C4#354611yescharacteristic
1188C4#355011yescharacteristic
1189C2—81no—
1190C2—81no—
1191C2#3946811yescharacteristic
1192C2#6092111yescharacteristic
1193C2#6093211yescharacteristic
1194C2#6120411yescharacteristic
1195C2#6122411yescharacteristic
1196C2#6216011yescharacteristic
1197C2#6222511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33200C2semidirect
4. #32221C2semidirect
5. #32219C2semidirect
6. #32201C2semidirect
7. #32199C2semidirect
8. #31509C2semidirect
9. #31505C2semidirect
10. #31501C2semidirect
11. #31497C2semidirect
12. #29701C2semidirect
13. #29701C2semidirect
14. #28725C2semidirect
17. #28287C2semidirect
18. #27643C2semidirect
19. #27642C2semidirect
20. #26459C2semidirect
21. #26457C2semidirect
24. #25290C2semidirect
25. #25290C2semidirect
26. #24854C2semidirect
27. #24850C2semidirect
29. #21898C2semidirect
30. #21898C2semidirect
31. #21618C2semidirect

Maximal subgroups

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

subgroupindex
#395102
#352092
#332002
#322212
#322192
#322012
#321992
#315092
#315052
#315012
#314972
#297012
#287252
#286112
#282872
#276432
#276422
#264592
#264572
#253572
#253532
#252902
#248542
#248502
#226522
#218982
#216182