Finite Group Databasebeta

← #6764956

Subgroups — #6764956

Order 512.

1370 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#37986C211yesmaximal, characteristic, complemented
2#37795C211yesmaximal, characteristic
3#33134C211yesmaximal, characteristic
4#32248C211yesmaximal, characteristic, complemented
5#32185C211yesmaximal, characteristic, complemented
6#32148C211yesmaximal, characteristic, complemented
7#32099C211yesmaximal, characteristic, complemented
8#31664C211yesmaximal, characteristic, complemented
9#31595C211yesmaximal, characteristic, complemented
10#31546C211yesmaximal, characteristic, complemented
11#31483C211yesmaximal, characteristic, complemented
12#30191C211yesmaximal, characteristic
13#29786C211yesmaximal, characteristic, complemented
14#29173C211yesmaximal, characteristic, complemented
15#28589C211yesmaximal, characteristic
16#27870C211yesmaximal, characteristic, complemented
17#27865C211yesmaximal, characteristic
18#27570C211yesmaximal, characteristic, complemented
19#27441C211yesmaximal, characteristic, complemented
20#27313C211yesmaximal, characteristic, complemented
21#27212C211yesmaximal, characteristic, complemented
22#27091C211yesmaximal, characteristic, complemented
23#27024C211yesmaximal, characteristic, complemented
24#26782C211yesmaximal, characteristic, complemented
25#26715C211yesmaximal, characteristic, complemented
26#25509C211yesmaximal, characteristic
27#25504C211yesmaximal, characteristic, complemented
28#22203C211yesmaximal, characteristic, complemented
29#21896C211yesmaximal, characteristic
30#21407C211yesmaximal, characteristic, complemented
31#21021C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#470C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#424C2211yescharacteristic
38C22×#97C2211yescharacteristic
39#2855C2211yescharacteristic
40#2854C2211yescharacteristic
41#2769—21no—
42#2766—21no—
43#2765—21no—
44#2765—21no—
45#2725—21no—
46#2720—21no—
47#2680—21no—
48#2674—21no—
49#2629C2211yescharacteristic
50#2625C2211yescharacteristic
51#2625C2211yescharacteristic
52#2620C2211yescharacteristic
53#2606—21no—
54#2573—21no—
55#2571C2211yescharacteristic
56#2565C2211yescharacteristic
57#2551C2211yescharacteristic
58#2545C2211yescharacteristic
59#2528—21no—
60#2515—21no—
61#2514C2211yescharacteristic
62#2514C2211yescharacteristic
63#2508C2211yescharacteristic
64#2507C2211yescharacteristic
65#2474—21no—
66#2470—21no—
67#2469—21no—
68#2452C2211yescharacteristic
69#2451C2211yescharacteristic
70#2448C2211yescharacteristic
71#2446C2211yescharacteristic
72#2429—21no—
73#2370C2211yescharacteristic
74#2367C2211yescharacteristic
75#2355C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77#2323C2211yescharacteristic
78#2323C2211yescharacteristic
79#2314C2211yescharacteristic
80#2296C2211yescharacteristic
81#2283C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2095C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2085C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic
97#2072C2211yescharacteristic
98#2072C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic
101#2068C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2056C2211yescharacteristic
108#2056C2211yescharacteristic
109#2043C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic
118#2024C2211yescharacteristic
119#2016C2211yescharacteristic
120#2015C2211yescharacteristic
121#2015C2211yescharacteristic
122#1993C2211yescharacteristic
123#1993C2211yescharacteristic
124#1988C2211yescharacteristic
125#1987C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic
130#1960C2211yescharacteristic
131#1960C2211yescharacteristic
132#1943C2211yescharacteristic
133#1943C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1921C2211yescharacteristic
147#1920C2211yescharacteristic
148#1919C2211yescharacteristic
149#1919C2211yescharacteristic
150#1919C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1917C2211yescharacteristic
155#1917C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1917C2211yescharacteristic
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1877C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1808C2211yescharacteristic
191#1805C2211yescharacteristic
192#1804C2211yescharacteristic
193#1803C2211yescharacteristic
194#1802C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198#1763C2211yescharacteristic
199#1729C2211yescharacteristic
200#1729C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#542—24no—
211#542—42no—
212#533—24no—
213#533—42no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×C4×Q8—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C42C2311yescharacteristic
244#470—24no—
245#470—42no—
246#465—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256#424—42no—
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#97—42no—
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292#401—21no—
293#401—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#399—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#395—21no—
327#395—21no—
328#395—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#391—21no—
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389D411yescharacteristic
354#389D411yescharacteristic
355#389D411yescharacteristic
356#389D411yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#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#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385D411yescharacteristic
407#385D411yescharacteristic
408#385D411yescharacteristic
409#385D411yescharacteristic
410#384—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383—21no—
416#383—21no—
417#382—21no—
418#382—21no—
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#381—21no—
424#381—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444#376—21no—
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4C2×D411yescharacteristic
496C23×C4C2×D411yescharacteristic
497C23×C4C2411yescharacteristic
498C2×Q16—22no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×Q16—41no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C2×M16—41no—
513C22×C8—22no—
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—41no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—22no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—82no—
534#126—44no—
535#125—41no—
536#125—41no—
537#125—44no—
538#124—22no—
539#124—41no—
540#124—41no—
541#124—41no—
542#124—44no—
543#123—44no—
544#123—82no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—44no—
551C22⋊Q8—44no—
552C22⋊Q8—82no—
553C22⋊Q8#4114yes—
554#121—22no—
555#121—22no—
556C4×Q8—22no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—44no—
567C4×D4—22no—
568C4×D4—41no—
569#117—22no—
570#117—22no—
571#117—41no—
572#117—41no—
573#117—44no—
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⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
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×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⋊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⋊C4—21no—
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
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×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674#107—22no—
675#107—41no—
676#107—41no—
677#107—41no—
678#106—22no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—22no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#103—41no—
699#103—41no—
700#103—41no—
701#103—41no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#97—41no—
714#97—41no—
715#97—41no—
716#97—41no—
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#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771C24—21no—
772C24C22×D411yescharacteristic
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—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—81no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8C2×#4112yes—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
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—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—81no—
833C22×C4—81no—
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×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C2×#4112yes—
848C22×C4H(5,𝔽2)12yes—
849C22×C4C2511yescharacteristic
850Q16—82no—
851Q16—82no—
852SD16—82no—
853M16—82no—
854M16—82no—
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—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—44no—
879C2×C8—44no—
880C2×C82−1+412yes—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—22no—
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—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
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—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⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4C2×#4112yes—
949C22⋊C4—24no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C42—22no—
973C42—22no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23#54612yes—
1011C23C23×D411yescharacteristic
1012Q8—22no—
1013Q8—22no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—84no—
1025Q8—162no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—162no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
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—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—44no—
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—41no—
1119C2×C4—82no—
1120C2×C4—162no—
1121C2×C4#54612yes—
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C2×H(5,𝔽2)11yescharacteristic
1124C2×C4C2×2−1+411yescharacteristic
1125C2×C4#58511yescharacteristic
1126C2×C4#58511yescharacteristic
1127C2×C4#58511yescharacteristic
1128C8—22no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22#344911yescharacteristic
1151C22C2×#54611yescharacteristic
1152C22#349711yescharacteristic
1153C22#358511yescharacteristic
1154C22#358611yescharacteristic
1155C22#358611yescharacteristic
1156C22#358611yescharacteristic
1157C4—22no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—42no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
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#351511yescharacteristic
1186C4#352111yescharacteristic
1187C4#353311yescharacteristic
1188C4#353511yescharacteristic
1189C2—42no—
1190C2—161no—
1191C2#3808711yescharacteristic
1192C2#6097511yescharacteristic
1193C2#6102111yescharacteristic
1194C2#6117611yescharacteristic
1195C2#6118011yescharacteristic
1196C2#6238911yescharacteristic
1197C2#6239111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37986C2semidirect
4. #32248C2semidirect
5. #32185C2semidirect
6. #32148C2semidirect
7. #32099C2semidirect
8. #31664C2semidirect
9. #31595C2semidirect
10. #31546C2semidirect
11. #31483C2semidirect
13. #29786C2semidirect
14. #29173C2semidirect
16. #27870C2semidirect
18. #27570C2semidirect
19. #27441C2semidirect
20. #27313C2semidirect
21. #27212C2semidirect
22. #27091C2semidirect
23. #27024C2semidirect
24. #26782C2semidirect
25. #26715C2semidirect
27. #25504C2semidirect
28. #22203C2semidirect
30. #21407C2semidirect
31. #21021C2semidirect

Maximal subgroups

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

subgroupindex
#379862
#377952
#331342
#322482
#321852
#321482
#320992
#316642
#315952
#315462
#314832
#301912
#297862
#291732
#285892
#278702
#278652
#275702
#274412
#273132
#272122
#270912
#270242
#267822
#267152
#255092
#255042
#222032
#218962
#214072
#210212