Finite Group Databasebeta

← #7205462

Subgroups — #7205462

Order 512.

1787 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45640C211yesmaximal, characteristic, complemented
2#36101C211yesmaximal, characteristic, complemented
3#33002C211yesmaximal, characteristic, complemented
4#32959C211yesmaximal, characteristic, complemented
5#32776C211yesmaximal, characteristic, complemented
6#32719C211yesmaximal, characteristic, complemented
7#32666C211yesmaximal, characteristic, complemented
8#32576C211yesmaximal, characteristic, complemented
9#32178C211yesmaximal, characteristic, complemented
10#32078C211yesmaximal, characteristic, complemented
11#31913C211yesmaximal, characteristic, complemented
12#31573C211yesmaximal, characteristic, complemented
13#31314C211yesmaximal, characteristic, complemented
14#31290C211yesmaximal, characteristic, complemented
15#31172C211yesmaximal, characteristic, complemented
16#30984C211yesmaximal, characteristic, complemented
17#30827C211yesmaximal, characteristic, complemented
18#30539C211yesmaximal, characteristic, complemented
19#27493C211yesmaximal, characteristic, complemented
20#27379C211yesmaximal, characteristic, complemented
21#27096C211yesmaximal, characteristic, complemented
22#27080C211yesmaximal, characteristic, complemented
23#27046C211yesmaximal, characteristic, complemented
24#26888C211yesmaximal, characteristic, complemented
25#26802C211yesmaximal, characteristic, complemented
26#26546C211yesmaximal, characteristic, complemented
27#26538C211yesmaximal, characteristic, complemented
28#26463C211yesmaximal, characteristic, complemented
29#25655C211yesmaximal, characteristic, complemented
30#24184C211yesmaximal, characteristic, complemented
31#23341C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#525—21no—
34C22×C4×D4C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#480C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic, complemented
40C2×#459C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic, complemented
43#2856C2211yescharacteristic
44#2854C2211yescharacteristic
45#2851C2211yescharacteristic
46#2847—21no—
47#2827—21no—
48#2793—21no—
49#2777—21no—
50#2770—21no—
51#2707—21no—
52#2690—21no—
53#2680—21no—
54#2584C2211yescharacteristic, complemented
55#2570C2211yescharacteristic, complemented
56#2552C2211yescharacteristic, complemented
57#2541C2211yescharacteristic
58#2538C2211yescharacteristic
59#2538C2211yescharacteristic, complemented
60#2513C2211yescharacteristic, complemented
61#2513C2211yescharacteristic, complemented
62#2506C2211yescharacteristic, complemented
63#2497C2211yescharacteristic
64#2495C2211yescharacteristic
65#2490C2211yescharacteristic
66#2456—21no—
67#2456—21no—
68#2454C2211yescharacteristic, complemented
69#2445C2211yescharacteristic
70#2445C2211yescharacteristic
71#2433C2211yescharacteristic
72#2433C2211yescharacteristic
73#2424—21no—
74#2424—21no—
75#2422C2211yescharacteristic
76#2414—21no—
77#2407—21no—
78#2376—21no—
79#2366C2211yescharacteristic
80#2366C2211yescharacteristic
81#2361C2211yescharacteristic
82#2361C2211yescharacteristic
83#2354C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85#2100C2211yescharacteristic, complemented
86#2094C2211yescharacteristic
87#2094C2211yescharacteristic, complemented
88#2093C2211yescharacteristic, complemented
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic, complemented
91#2092C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2065C2211yescharacteristic, complemented
104#2065C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic, complemented
108#2054C2211yescharacteristic, complemented
109#2054C2211yescharacteristic, complemented
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic, complemented
116#2041C2211yescharacteristic, complemented
117#2041C2211yescharacteristic, complemented
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2025C2211yescharacteristic
125#2025C2211yescharacteristic, complemented
126#2025C2211yescharacteristic, complemented
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#2011C2211yescharacteristic
130#2011C2211yescharacteristic, complemented
131#1999C2211yescharacteristic
132#1999C2211yescharacteristic
133#1985C2211yescharacteristic, complemented
134#1984C2211yescharacteristic, complemented
135#1982C2211yescharacteristic
136#1982C2211yescharacteristic
137#1982C2211yescharacteristic
138#1972C2211yescharacteristic
139#1972C2211yescharacteristic, complemented
140#1970C2211yescharacteristic
141#1961C2211yescharacteristic
142#1957C2211yescharacteristic
143#1957C2211yescharacteristic
144#1949C2211yescharacteristic, complemented
145#1947C2211yescharacteristic, complemented
146#1944C2211yescharacteristic, complemented
147#1942C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1936C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic, complemented
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic, complemented
159#1925C2211yescharacteristic, complemented
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic, complemented
165#1921C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1862C2211yescharacteristic, complemented
189#1853C2211yescharacteristic
190#1852C2211yescharacteristic
191#1823C2211yescharacteristic
192#1817C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic
195#1802C2211yescharacteristic, complemented
196#1797C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200#1776C2211yescharacteristic, complemented
201C4×#106C2211yescharacteristic, complemented
202#1762C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210#550—42no—
211#550—42no—
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220#525—48no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8D411yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—42no—
250C2×C4×D4—42no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C42C2311yescharacteristic
262#490—42no—
263#480—42no—
264#478—42no—
265#478—42no—
266#478—42no—
267#459—42no—
268#447—42no—
269C4×D8—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#399—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#391D411yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389D411yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387D411yescharacteristic
418#387D411yescharacteristic
419#386—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#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385D411yescharacteristic
435#385D411yescharacteristic
436#384—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#383—21no—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380D411yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
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⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C2×#41—44no—
493C2×#41—44no—
494C2×#41—82no—
495C22×Q8C2×D411yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
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—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—44no—
530C23×C4—44no—
531C23×C4—82no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#127—22no—
556#127—22no—
557#127—22no—
558#127—22no—
559#127—41no—
560#127—41no—
561#127—41no—
562#127—41no—
563#127—41no—
564#127—41no—
565#125—41no—
566#125—41no—
567#125—41no—
568#125—41no—
569#125—82no—
570#123—44no—
571#123—44no—
572#123—44no—
573#123—82no—
574C22⋊Q8—24no—
575C22⋊Q8—44no—
576C22⋊Q8—82no—
577#121—44no—
578#121—44no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—44no—
584#121—44no—
585#121—44no—
586#121—41no—
587#121—41no—
588#121—82no—
589#121—82no—
590#120—44no—
591#120—44no—
592#120—82no—
593#120—82no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—44no—
611C4×D4—44no—
612C4×D4—44no—
613C4×D4—44no—
614C4×D4—44no—
615C4×D4—44no—
616#117—44no—
617C2×C4⋊C4—22no—
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⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—44no—
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—41no—
711C2×C42—41no—
712C2×C42C2×D411yescharacteristic
713C2×C42C2×D411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—22no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—22no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
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#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774#97—41no—
775#97—41no—
776C4×C8—41no—
777C4×C8—41no—
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#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—42no—
817C24—42no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24C22×D411yescharacteristic
824#41—816no—
825C2×Q8—22no—
826C2×Q8—22no—
827C2×Q8—41no—
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—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
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—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
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×D4H(5,𝔽2)12yes—
903C2×D42−1+412yes—
904C22×C4—24no—
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—22no—
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—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—816no—
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C2511yescharacteristic
966D8—44no—
967D8—82no—
968D8—82no—
969D8—82no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4H(5,𝔽2)12yes—
1047C22⋊C4—24no—
1048C22⋊C4—22no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4AGL(1,ℤ/8)14yes—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—41no—
1103C42—41no—
1104C42—42no—
1105C42—42no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—22no—
1116C23—22no—
1117C23—48no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—84no—
1152C23—84no—
1153C23—84no—
1154C23—84no—
1155C23—84no—
1156C23—84no—
1157C23C2×AGL(1,ℤ/8)12yes—
1158C23C23×D411yescharacteristic
1159Q8—44no—
1160D4—22no—
1161D4—22no—
1162D4—22no—
1163D4—22no—
1164D4—48no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—84no—
1182D4—84no—
1183D4—84no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193D4—162no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—44no—
1232C2×C4—48no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—82no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—162no—
1277C2×C4C2×AGL(1,ℤ/8)12yes—
1278C2×C4C2×AGL(1,ℤ/8)12yes—
1279C2×C4#57612yes—
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×2−1+411yescharacteristic
1283C2×C4#58511yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—42no—
1307C22—816no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22#348411yescharacteristic
1338C22#348711yescharacteristic
1339C22#348911yescharacteristic
1340C22C22×AGL(1,ℤ/8)11yescharacteristic
1341C22C2×#57611yescharacteristic
1342C22#358411yescharacteristic
1343C22#358511yescharacteristic
1344C4—22no—
1345C4—22no—
1346C4—22no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—42no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4#352911yescharacteristic
1369C4#353311yescharacteristic
1370C4#353511yescharacteristic
1371C4#354111yescharacteristic
1372C2—42no—
1373C2—82no—
1374C2—82no—
1375C2—161no—
1376C2—161no—
1377C2—161no—
1378C2#4545011yescharacteristic
1379C2#6159111yescharacteristic
1380C2#6162811yescharacteristic
1381C2#6189011yescharacteristic
1382C2#6192611yescharacteristic
1383C2#6213711yescharacteristic
1384C2#6218711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45640C2semidirect
2. #36101C2semidirect
3. #33002C2semidirect
4. #32959C2semidirect
5. #32776C2semidirect
6. #32719C2semidirect
7. #32666C2semidirect
8. #32576C2semidirect
9. #32178C2semidirect
10. #32078C2semidirect
11. #31913C2semidirect
12. #31573C2semidirect
13. #31314C2semidirect
14. #31290C2semidirect
15. #31172C2semidirect
16. #30984C2semidirect
17. #30827C2semidirect
18. #30539C2semidirect
19. #27493C2semidirect
20. #27379C2semidirect
21. #27096C2semidirect
22. #27080C2semidirect
23. #27046C2semidirect
24. #26888C2semidirect
25. #26802C2semidirect
26. #26546C2semidirect
27. #26538C2semidirect
28. #26463C2semidirect
29. #25655C2semidirect
30. #24184C2semidirect
31. #23341C2semidirect
39. C2×#478C22semidirect
42. C2×C4×D8C22semidirect
54. #2584C22semidirect
55. #2570C22semidirect
56. #2552C22semidirect
59. #2538C22semidirect
60. #2513C22semidirect
61. #2513C22semidirect
62. #2506C22semidirect
68. #2454C22semidirect
85. #2100C22semidirect
87. #2094C22semidirect
88. #2093C22semidirect
90. #2092C22semidirect
91. #2092C22semidirect
92. #2088C22semidirect
93. #2084C22semidirect
94. #2084C22semidirect
95. #2083C22semidirect
96. #2073C22semidirect
99. #2067C22semidirect
102. #2065C22semidirect
103. #2065C22semidirect
104. #2065C22semidirect
105. #2059C22semidirect
107. #2054C22semidirect
108. #2054C22semidirect
109. #2054C22semidirect
115. #2041C22semidirect
116. #2041C22semidirect
117. #2041C22semidirect
125. #2025C22semidirect
126. #2025C22semidirect
130. #2011C22semidirect
133. #1985C22semidirect
134. #1984C22semidirect
139. #1972C22semidirect
144. #1949C22semidirect
145. #1947C22semidirect
146. #1944C22semidirect
147. #1942C22semidirect
148. #1940C22semidirect
149. #1939C22semidirect
152. #1934C22semidirect
155. #1926C22semidirect
156. #1926C22semidirect
158. #1925C22semidirect
159. #1925C22semidirect
164. #1921C22semidirect
165. #1921C22semidirect
166. #1920C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
170. #1916C22semidirect
176. #1879C22semidirect
179. #1864C22semidirect
186. #1862C22semidirect
187. #1862C22semidirect
188. #1862C22semidirect
195. #1802C22semidirect
200. #1776C22semidirect
201. C4×#106C22semidirect
202. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#456402
#361012
#330022
#329592
#327762
#327192
#326662
#325762
#321782
#320782
#319132
#315732
#313142
#312902
#311722
#309842
#308272
#305392
#274932
#273792
#270962
#270802
#270462
#268882
#268022
#265462
#265382
#264632
#256552
#241842
#233412