Finite Group Databasebeta

← #6459252

Subgroups — #6459252

Order 512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35213C211yesmaximal, characteristic, complemented
2#35190C211yesmaximal, characteristic
3#27830C211yesmaximal, characteristic, complemented
4#27828C211yesmaximal, characteristic, complemented
5#27786C211yesmaximal, characteristic, complemented
6#27780C211yesmaximal, characteristic, complemented
7#27766C211yesmaximal, characteristic, complemented
8#27760C211yesmaximal, characteristic, complemented
9#27744C211yesmaximal, characteristic, complemented
10#27742C211yesmaximal, characteristic, complemented
11#27718C211yesmaximal, characteristic, complemented
12#27712C211yesmaximal, characteristic, complemented
13#27702C211yesmaximal, characteristic, complemented
14#27696C211yesmaximal, characteristic, complemented
15#27269C211yesmaximal, characteristic, complemented
16#27263C211yesmaximal, characteristic, complemented
17#27259C211yesmaximal, characteristic, complemented
18#27257C211yesmaximal, characteristic, complemented
19#23832C211yesmaximal, characteristic, complemented
20#23830C211yesmaximal, characteristic, complemented
21#23828C211yesmaximal, characteristic, complemented
22#23827C211yesmaximal, characteristic, complemented
23#21654C211yesmaximal, characteristic, complemented
24#21652C211yesmaximal, characteristic, complemented
25#21644C211yesmaximal, characteristic, complemented
26#21643C211yesmaximal, characteristic, complemented
27#21408C211yesmaximal, characteristic, complemented
28#21390C211yesmaximal, characteristic, complemented
29#20736C211yesmaximal, characteristic, complemented
30#20481C211yesmaximal, characteristic, complemented
31#20411C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#486C2211yescharacteristic
38C2×#431C2211yescharacteristic
39C2×#416C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C22×#97C2211yescharacteristic
42#2863—21no—
43#2863—21no—
44#2850—21no—
45#2850—21no—
46#2667—21no—
47#2665—21no—
48#2635—21no—
49#2635—21no—
50#2612—21no—
51#2612—21no—
52#2608—21no—
53#2607—21no—
54#2598—21no—
55#2598—21no—
56#2570C2211yescharacteristic
57#2570C2211yescharacteristic
58#2568C2211yescharacteristic
59#2550C2211yescharacteristic
60#2550C2211yescharacteristic
61#2548C2211yescharacteristic
62#2542C2211yescharacteristic
63#2541C2211yescharacteristic
64#2500C2211yescharacteristic
65#2500C2211yescharacteristic
66#2441C2211yescharacteristic
67#2441C2211yescharacteristic
68#2439C2211yescharacteristic
69#2439C2211yescharacteristic
70#2431C2211yescharacteristic
71#2431C2211yescharacteristic
72#2407—21no—
73#2407—21no—
74#2331C2211yescharacteristic
75#2331C2211yescharacteristic
76#2330C2211yescharacteristic
77#2330C2211yescharacteristic
78#2328C2211yescharacteristic
79#2328C2211yescharacteristic
80#2326C2211yescharacteristic
81#2326C2211yescharacteristic
82#2283C2211yescharacteristic
83#2283C2211yescharacteristic
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2074C2211yescharacteristic
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2042C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2026C2211yescharacteristic
110#2025C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2024C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#1993C2211yescharacteristic
118#1993C2211yescharacteristic
119#1993C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1990C2211yescharacteristic
123#1987C2211yescharacteristic
124#1987C2211yescharacteristic
125#1982C2211yescharacteristic
126#1982C2211yescharacteristic
127#1961C2211yescharacteristic
128#1961C2211yescharacteristic
129#1961C2211yescharacteristic
130#1959C2211yescharacteristic
131#1958C2211yescharacteristic
132#1957C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1893C2211yescharacteristic
150#1893C2211yescharacteristic
151#1893C2211yescharacteristic
152#1893C2211yescharacteristic
153#1875C2211yescharacteristic
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1875C2211yescharacteristic
157#1836C2211yescharacteristic
158#1836C2211yescharacteristic
159#1835C2211yescharacteristic
160#1834C2211yescharacteristic
161#1825C2211yescharacteristic
162#1825C2211yescharacteristic
163#1805C2211yescharacteristic
164#1805C2211yescharacteristic
165#1804C2211yescharacteristic
166#1804C2211yescharacteristic
167#1788C2211yescharacteristic
168#1788C2211yescharacteristic
169#1771C2211yescharacteristic
170#1771C2211yescharacteristic
171#1771C2211yescharacteristic
172#1771C2211yescharacteristic
173#1763C2211yescharacteristic
174#1763C2211yescharacteristic
175#1763C2211yescharacteristic
176#1763C2211yescharacteristic
177#1762C2211yescharacteristic
178#1762C2211yescharacteristic
179#1762C2211yescharacteristic
180#1762C2211yescharacteristic
181#1762C2211yescharacteristic
182#1762C2211yescharacteristic
183#1762C2211yescharacteristic
184#1762C2211yescharacteristic
185C4×#103C2211yescharacteristic
186C4×#103C2211yescharacteristic
187C4×#102C2211yescharacteristic
188C4×#102C2211yescharacteristic
189C4×#102C2211yescharacteristic
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1746C2211yescharacteristic
198#1746C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201#1726C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#532—24no—
208#532—24no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C4×#41—24no—
228C4×#41—24no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C42—21no—
243C22×C42C2311yescharacteristic
244#490—24no—
245#489—24no—
246#488—24no—
247#486—24no—
248#431—24no—
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251#416—24no—
252#416—24no—
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97—24no—
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#399—21no—
307#399—21no—
308#399—21no—
309#399—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#395—21no—
319#395—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#393—21no—
327#393—21no—
328#392—21no—
329#392—21no—
330#392—21no—
331#392—21no—
332#392—21no—
333#392—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
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#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
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#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—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#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#383D411yescharacteristic
416#383D411yescharacteristic
417#382D411yescharacteristic
418#382D411yescharacteristic
419#382C2311yescharacteristic
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#381D411yescharacteristic
427#381D411yescharacteristic
428#380D411yescharacteristic
429#380D411yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
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×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#376—21no—
446#376—21no—
447#376C2311yescharacteristic
448#376C2311yescharacteristic
449C43—21no—
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#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
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—44no—
497C2×#41—82no—
498C2×#41—82no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#127—22no—
544#127—22no—
545#127—22no—
546#127—22no—
547#127—41no—
548#127—41no—
549#125—22no—
550#125—22no—
551#125—41no—
552#125—41no—
553#124—22no—
554#124—22no—
555#124—41no—
556#124—41no—
557#124—44no—
558C22⋊Q8—82no—
559C22⋊Q8—82no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121—22no—
564#121—44no—
565#121—82no—
566#121—82no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—44no—
582#117—22no—
583#117—22no—
584#117—22no—
585#117—22no—
586#117—41no—
587#117—41no—
588#117—44no—
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⋊C4—21no—
613C2×C4⋊C4—21no—
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⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
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×C42—44no—
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42#4114yes—
676C2×C42#4114yes—
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C4⋊C8—22no—
684C4⋊C8—22no—
685#103—22no—
686#103—22no—
687#103—22no—
688#103—22no—
689#103—22no—
690#103—41no—
691#103—41no—
692#103#4114yescomplemented
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102#4114yescomplemented
717C22⋊C8—22no—
718C22⋊C8—22no—
719#97—22no—
720#97—22no—
721#97—22no—
722#97—22no—
723#97—22no—
724#97—22no—
725#97—41no—
726#97—41no—
727C4×C8—22no—
728C4×C8—22no—
729C4×C8—22no—
730C4×C8—22no—
731C4×C8—41no—
732C4×C8—41no—
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#95—21no—
764#95—21no—
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781C24—21no—
782C24—21no—
783C24—21no—
784C24C22×D411yescharacteristic
785#41—28no—
786#41—44no—
787#41—44no—
788#41—44no—
789#41—816no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8—42no—
799C2×Q8—42no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8—81no—
804C2×Q8C2×#4112yes—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4C2×#4112yes—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4#12414yes—
887C22×C4#12414yes—
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C2×#4112yes—
902C22×C4C2×#4112yes—
903C22×C4C2511yescharacteristic
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—44no—
927C2×C8—44no—
928C2×C8C2×#4112yes—
929C2×C8C2×#4112yes—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4C2×#4112yes—
982C4⋊C4C2×#4112yes—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—42no—
1023C42—42no—
1024C42—42no—
1025C42—42no—
1026C42—42no—
1027C42—81no—
1028C42—81no—
1029C42—81no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42#12414yes—
1034C42#12414yes—
1035C42C2×#4112yes—
1036C42C2×#4112yes—
1037C42C2×#4112yes—
1038C42C2×#4112yes—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—22no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23C2×#12412yes—
1067C23C23×D411yescharacteristic
1068Q8—22no—
1069Q8—22no—
1070Q8—41no—
1071Q8—41no—
1072Q8—84no—
1073Q8—162no—
1074Q8—162no—
1075D4—22no—
1076D4—22no—
1077D4—48no—
1078D4—41no—
1079D4—41no—
1080D4—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—84no—
1089D4—84no—
1090D4—84no—
1091D4—84no—
1092D4—162no—
1093D4—162no—
1094D4—162no—
1095D4—162no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—48no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—84no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4C2×#12412yes—
1181C2×C4C2×#12412yes—
1182C2×C4C2×#12412yes—
1183C2×C4C2×#12412yes—
1184C2×C4C2×#12412yes—
1185C2×C4C22×#4111yescharacteristic
1186C2×C4C22×#4111yescharacteristic
1187C2×C4C22×#4111yescharacteristic
1188C2×C4C22×#4111yescharacteristic
1189C2×C4#58511yescharacteristic
1190C2×C4#58511yescharacteristic
1191C8—22no—
1192C8—22no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22C22×#12411yescharacteristic
1228C22D4×#4111yescharacteristic
1229C22D4×#4111yescharacteristic
1230C22#358411yescharacteristic
1231C22#358411yescharacteristic
1232C22#358511yescharacteristic
1233C22#358511yescharacteristic
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—22no—
1238C4—22no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—42no—
1244C4—41no—
1245C4—41no—
1246C4—42no—
1247C4—41no—
1248C4—41no—
1249C4—42no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4#344411yescharacteristic
1261C4#345511yescharacteristic
1262C4#347511yescharacteristic
1263C4#347511yescharacteristic
1264C2—42no—
1265C2—82no—
1266C2—161no—
1267C2—161no—
1268C2#3481311yescharacteristic
1269C2#6061211yescharacteristic
1270C2#6061911yescharacteristic
1271C2#6152711yescharacteristic
1272C2#6152911yescharacteristic
1273C2#6153111yescharacteristic
1274C2#6153411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35190C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35213C2semidirect
3. #27830C2semidirect
4. #27828C2semidirect
5. #27786C2semidirect
6. #27780C2semidirect
7. #27766C2semidirect
8. #27760C2semidirect
9. #27744C2semidirect
10. #27742C2semidirect
11. #27718C2semidirect
12. #27712C2semidirect
13. #27702C2semidirect
14. #27696C2semidirect
15. #27269C2semidirect
16. #27263C2semidirect
17. #27259C2semidirect
18. #27257C2semidirect
19. #23832C2semidirect
20. #23830C2semidirect
21. #23828C2semidirect
22. #23827C2semidirect
23. #21654C2semidirect
24. #21652C2semidirect
25. #21644C2semidirect
26. #21643C2semidirect
27. #21408C2semidirect
28. #21390C2semidirect
29. #20736C2semidirect
30. #20481C2semidirect
31. #20411C2semidirect
692. #103#41semidirect
716. #102#41semidirect

Maximal subgroups

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

subgroupindex
#352132
#351902
#278302
#278282
#277862
#277802
#277662
#277602
#277442
#277422
#277182
#277122
#277022
#276962
#272692
#272632
#272592
#272572
#238322
#238302
#238282
#238272
#216542
#216522
#216442
#216432
#214082
#213902
#207362
#204812
#204112