Finite Group Databasebeta

← #7545405

Subgroups — #7545405

Order 512.

1751 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59872C211yesmaximal, characteristic, complemented
2#36128C211yesmaximal, characteristic
3#32096C211yesmaximal, characteristic, complemented
4#32094C211yesmaximal, characteristic, complemented
5#32080C211yesmaximal, characteristic, complemented
6#32078C211yesmaximal, characteristic, complemented
7#28756C211yesmaximal, characteristic, complemented
8#28756C211yesmaximal, characteristic, complemented
9#28650C211yesmaximal, characteristic, complemented
10#28650C211yesmaximal, characteristic, complemented
11#27760C211yesmaximal, characteristic, complemented
12#27760C211yesmaximal, characteristic, complemented
13#26770C211yesmaximal, characteristic, complemented
14#26768C211yesmaximal, characteristic, complemented
15#26754C211yesmaximal, characteristic, complemented
16#26752C211yesmaximal, characteristic, complemented
17#26541C211yesmaximal, characteristic, complemented
18#26538C211yesmaximal, characteristic, complemented
19#26334C211yesmaximal, characteristic, complemented
20#26332C211yesmaximal, characteristic, complemented
21#25655C211yesmaximal, characteristic, complemented
22#25655C211yesmaximal, characteristic, complemented
23#25288C211yesmaximal, characteristic, complemented
24#25288C211yesmaximal, characteristic, complemented
25#23231C211yesmaximal, characteristic, complemented
26#23229C211yesmaximal, characteristic, complemented
27#23152C211yesmaximal, characteristic, complemented
28#22545C211yesmaximal, characteristic, complemented
29#22545C211yesmaximal, characteristic, complemented
30#21617C211yesmaximal, characteristic, complemented
31#21617C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#532—21no—
35C2×#490C2211yescharacteristic
36C2×#490C2211yescharacteristic
37C2×#490C2211yescharacteristic
38C2×#490C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#478C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#446C2211yescharacteristic
43#2867C2211yescharacteristic
44#2856—21no—
45#2791—21no—
46#2713—21no—
47#2588—21no—
48#2585—21no—
49#2585—21no—
50#2584C2211yescharacteristic
51#2584C2211yescharacteristic
52#2570C2211yescharacteristic
53#2570C2211yescharacteristic
54#2548C2211yescharacteristic
55#2548C2211yescharacteristic
56#2541C2211yescharacteristic
57#2541C2211yescharacteristic
58#2541C2211yescharacteristic
59#2541C2211yescharacteristic
60#2520—21no—
61#2509—21no—
62#2509C2211yescharacteristic
63#2508C2211yescharacteristic
64#2507C2211yescharacteristic
65#2506C2211yescharacteristic
66#2431—21no—
67#2431—21no—
68#2428—21no—
69#2428—21no—
70#2428—21no—
71#2428—21no—
72#2370—21no—
73#2370C2211yescharacteristic
74#2370C2211yescharacteristic
75#2366C2211yescharacteristic
76#2366C2211yescharacteristic
77#2366C2211yescharacteristic
78#2366C2211yescharacteristic
79#2355C2211yescharacteristic
80#2355C2211yescharacteristic
81C4×C4⋊Q8C2211yescharacteristic
82C4×#125C2211yescharacteristic
83C4×#125C2211yescharacteristic
84C42×D4C2211yescharacteristic
85#2094C2211yescharacteristic
86#2093C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2073C2211yescharacteristic
90#2073C2211yescharacteristic
91#2071C2211yescharacteristic
92#2071C2211yescharacteristic
93#2067C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2065C2211yescharacteristic
101#2041C2211yescharacteristic
102#2041C2211yescharacteristic
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2041C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#1989C2211yescharacteristic
118#1989C2211yescharacteristic
119#1985C2211yescharacteristic
120#1985C2211yescharacteristic
121#1982C2211yescharacteristic
122#1982C2211yescharacteristic
123#1982C2211yescharacteristic
124#1982C2211yescharacteristic
125#1982C2211yescharacteristic
126#1982C2211yescharacteristic
127#1982C2211yescharacteristic
128#1982C2211yescharacteristic
129#1982C2211yescharacteristic
130#1982C2211yescharacteristic
131#1982C2211yescharacteristic
132#1982C2211yescharacteristic
133#1961C2211yescharacteristic
134#1961C2211yescharacteristic
135#1961C2211yescharacteristic
136#1961C2211yescharacteristic
137#1961C2211yescharacteristic
138#1961C2211yescharacteristic
139#1957C2211yescharacteristic
140#1957C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1940C2211yescharacteristic
144#1940C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1918C2211yescharacteristic
164#1918C2211yescharacteristic
165#1917C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1864C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1804C2211yescharacteristic
184#1804C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1771C2211yescharacteristic
192#1771C2211yescharacteristic
193#1767C2211yescharacteristic
194#1767C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×#41—21no—
204C22×#41—21no—
205#550—24no—
206#550—24no—
207#550—42no—
208#550—42no—
209#532—48no—
210C2×C4⋊Q8D411yescharacteristic
211C2×#127—21no—
212C2×#127—21no—
213C2×#127—21no—
214C2×#127—21no—
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124—21no—
229C2×#124—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C22×C42—21no—
258#490—24no—
259#490—24no—
260#490—42no—
261#490—42no—
262#478—24no—
263#478—24no—
264#446—42no—
265#446—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#395—21no—
345#395—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#392—21no—
351#392—21no—
352#392—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#391—21no—
359#391—21no—
360#391D411yescharacteristic
361#391D411yescharacteristic
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389D411yescharacteristic
385#389D411yescharacteristic
386#389D411yescharacteristic
387#389D411yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#384D411yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
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⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C43C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C2×#41—44no—
492C2×#41—44no—
493C2×#41—44no—
494C2×#41—44no—
495C2×#41—82no—
496C2×#41—82no—
497C22×Q8C2×D411yescharacteristic
498C22×Q8C2×D411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
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×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—24no—
540#127—22no—
541#127—22no—
542#127—22no—
543#127—22no—
544#127—22no—
545#127—22no—
546#127—22no—
547#127—22no—
548#127—22no—
549#127—22no—
550#127—22no—
551#127—22no—
552#127—41no—
553#127—41no—
554#127—41no—
555#127—41no—
556#127—41no—
557#127—41no—
558#127—41no—
559#127—41no—
560#127—44no—
561#127—82no—
562#127—82no—
563#127—82no—
564#125—22no—
565#125—22no—
566#125—22no—
567#125—44no—
568#125#4114yescomplemented
569#124—44no—
570#124—44no—
571#121—44no—
572#121—44no—
573#121—44no—
574#121—44no—
575#121—44no—
576#121—44no—
577#121—44no—
578#121—44no—
579#121—44no—
580#121—44no—
581#121—82no—
582#121—82no—
583#121—82no—
584#121—82no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—44no—
603C4×D4—44no—
604C4×D4—44no—
605C4×D4—44no—
606C4×D4#4114yes—
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⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—44no—
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2×D411yescharacteristic
690C2×C42C2×D411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#106—22no—
703#106—22no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709C4⋊C8—22no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#97—22no—
755#97—22no—
756#97—22no—
757#97—22no—
758#97—41no—
759#97—41no—
760C4×C8—41no—
761C4×C8—41no—
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#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806#41—816no—
807#41—816no—
808C2×Q8—22no—
809C2×Q8—22no—
810C2×Q8—22no—
811C2×Q8—22no—
812C2×Q8—41no—
813C2×Q8—41no—
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—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4C2×#4112yes—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—24no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C2511yescharacteristic
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—24no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4AGL(1,ℤ/8)14yes—
1028C4⋊C4C2×#4112yes—
1029C4⋊C4C2×#4112yes—
1030C4⋊C4C2×#4112yes—
1031C22⋊C4—24no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C42—22no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—41no—
1066C42—41no—
1067C42—41no—
1068C42—42no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42C2×#4112yes—
1080C42C2×#4112yes—
1081C42H(5,𝔽2)12yes—
1082C422−1+412yes—
1083C23—22no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23C23×D411yescharacteristic
1119Q8—44no—
1120Q8—44no—
1121D4—22no—
1122D4—22no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—84no—
1142D4—84no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—84no—
1149D4—84no—
1150D4—84no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159D4—162no—
1160D4—162no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—48no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—84no—
1231C2×C4—84no—
1232C2×C4—84no—
1233C2×C4—84no—
1234C2×C4—84no—
1235C2×C4—84no—
1236C2×C4#54612yes—
1237C2×C4#54612yes—
1238C2×C4#54812yes—
1239C2×C4#54812yes—
1240C2×C4C2×AGL(1,ℤ/8)12yes—
1241C2×C4C2×AGL(1,ℤ/8)12yes—
1242C2×C4C2×AGL(1,ℤ/8)12yes—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×2−1+411yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22C2×#54611yescharacteristic
1293C22C2×#54811yescharacteristic
1294C22#348711yescharacteristic
1295C22C22×AGL(1,ℤ/8)11yescharacteristic
1296C22#358511yescharacteristic
1297C22#358511yescharacteristic
1298C22#358511yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—42no—
1312C4—41no—
1313C4—41no—
1314C4—42no—
1315C4—41no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4#348011yescharacteristic
1325C4#350711yescharacteristic
1326C4#351711yescharacteristic
1327C4#355411yescharacteristic
1328C2—82no—
1329C2—161no—
1330C2—161no—
1331C2—161no—
1332C2—161no—
1333C2#5907811yescharacteristic
1334C2#6115511yescharacteristic
1335C2#6122311yescharacteristic
1336C2#6132111yescharacteristic
1337C2#6133711yescharacteristic
1338C2#6189011yescharacteristic
1339C2#6194511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36128C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59872C2semidirect
3. #32096C2semidirect
4. #32094C2semidirect
5. #32080C2semidirect
6. #32078C2semidirect
7. #28756C2semidirect
8. #28756C2semidirect
9. #28650C2semidirect
10. #28650C2semidirect
11. #27760C2semidirect
12. #27760C2semidirect
13. #26770C2semidirect
14. #26768C2semidirect
15. #26754C2semidirect
16. #26752C2semidirect
17. #26541C2semidirect
18. #26538C2semidirect
19. #26334C2semidirect
20. #26332C2semidirect
21. #25655C2semidirect
22. #25655C2semidirect
23. #25288C2semidirect
24. #25288C2semidirect
25. #23231C2semidirect
26. #23229C2semidirect
27. #23152C2semidirect
28. #22545C2semidirect
29. #22545C2semidirect
30. #21617C2semidirect
31. #21617C2semidirect
568. #125#41semidirect

Maximal subgroups

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

subgroupindex
#598722
#361282
#320962
#320942
#320802
#320782
#287562
#286502
#277602
#267702
#267682
#267542
#267522
#265412
#265382
#263342
#263322
#256552
#252882
#232312
#232292
#231522
#225452
#216172