Finite Group Databasebeta

← #7013121

Subgroups — #7013121

Order 512.

1480 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45205C211yesmaximal, characteristic, complemented
2#42642C211yesmaximal, characteristic, complemented
3#32215C211yesmaximal, characteristic, complemented
4#32119C211yesmaximal, characteristic, complemented
5#32023C211yesmaximal, characteristic, complemented
6#31654C211yesmaximal, characteristic, complemented
7#31219C211yesmaximal, characteristic, complemented
8#30915C211yesmaximal, characteristic, complemented
9#30531C211yesmaximal, characteristic, complemented
10#30511C211yesmaximal, characteristic
11#28924C211yesmaximal, characteristic, complemented
12#28888C211yesmaximal, characteristic, complemented
13#28590C211yesmaximal, characteristic, complemented
14#28100C211yesmaximal, characteristic, complemented
15#27796C211yesmaximal, characteristic, complemented
16#27795C211yesmaximal, characteristic, complemented
17#27240C211yesmaximal, characteristic, complemented
18#27135C211yesmaximal, characteristic, complemented
19#27109C211yesmaximal, characteristic, complemented
20#26750C211yesmaximal, characteristic, complemented
21#26715C211yesmaximal, characteristic, complemented
22#26594C211yesmaximal, characteristic, complemented
23#25465C211yesmaximal, characteristic, complemented
24#25399C211yesmaximal, characteristic, complemented
25#25101C211yesmaximal, characteristic, complemented
26#24667C211yesmaximal, characteristic, complemented
27#23706C211yesmaximal, characteristic, complemented
28#23224C211yesmaximal, characteristic, complemented
29#22903C211yesmaximal, characteristic, complemented
30#22884C211yesmaximal, characteristic, complemented
31#22202C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#488C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#467C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic, complemented
40C2×#463C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#435C2211yescharacteristic
45C2×#433C2211yescharacteristic, complemented
46C2×#418C2211yescharacteristic
47#2826—21no—
48#2803—21no—
49#2796—21no—
50#2773—21no—
51#2752—21no—
52#2735—21no—
53#2730—21no—
54#2702—21no—
55#2685—21no—
56#2649—21no—
57#2626—21no—
58#2620C2211yescharacteristic
59#2595—21no—
60#2575—21no—
61#2542C2211yescharacteristic
62#2540C2211yescharacteristic
63#2538C2211yescharacteristic
64#2513—21no—
65#2513—21no—
66#2512C2211yescharacteristic
67#2497C2211yescharacteristic
68#2492C2211yescharacteristic
69#2491C2211yescharacteristic
70#2490C2211yescharacteristic
71#2490C2211yescharacteristic, complemented
72#2489C2211yescharacteristic
73#2489C2211yescharacteristic, complemented
74#2485C2211yescharacteristic
75#2472—21no—
76#2448C2211yescharacteristic
77#2448C2211yescharacteristic, complemented
78#2447C2211yescharacteristic, complemented
79#2435C2211yescharacteristic
80#2427C2211yescharacteristic
81#2408C2211yescharacteristic
82#2395C2211yescharacteristic
83#2370C2211yescharacteristic, complemented
84#2370C2211yescharacteristic, complemented
85#2367C2211yescharacteristic
86#2363C2211yescharacteristic
87#2362C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2324C2211yescharacteristic
90#2324C2211yescharacteristic, complemented
91#2323C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic, complemented
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2026C2211yescharacteristic, complemented
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2001C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic, complemented
131#1999C2211yescharacteristic
132#1989C2211yescharacteristic, complemented
133#1987C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic, complemented
138#1972C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic, complemented
141#1959C2211yescharacteristic, complemented
142#1948C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1940C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1921C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1920C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1894C2211yescharacteristic
169#1894C2211yescharacteristic, complemented
170#1893C2211yescharacteristic
171#1893C2211yescharacteristic
172#1893C2211yescharacteristic, complemented
173#1880C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1873C2211yescharacteristic
180#1870C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic, complemented
191#1802C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193C4×#107C2211yescharacteristic, complemented
194C4×#107C2211yescharacteristic, complemented
195#1770C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C22⋊C4—21no—
241#501—42no—
242#488—24no—
243#478—42no—
244#469—24no—
245#468—42no—
246#468—42no—
247#467—42no—
248#464—42no—
249#463—42no—
250#450—24no—
251#447—42no—
252C4×SD16—42no—
253#435—42no—
254#433—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#418—42no—
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400D411yescharacteristic
314#399—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#399D411yescharacteristic
320#398D411yescharacteristic
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397D411yescharacteristic
333#397D411yescharacteristic
334#397D411yescharacteristic
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394D411yescharacteristic
352#394D411yescharacteristic
353#393—21no—
354#393—21no—
355#392—21no—
356#392—21no—
357#391—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
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#388—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#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#382—21no—
433#382—21no—
434#381—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
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×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×D8—22no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#126—82no—
555#125—22no—
556#125—22no—
557#125—41no—
558#125—41no—
559#124—22no—
560#124—41no—
561#124—41no—
562#124—41no—
563#124—41no—
564#124—41no—
565#124—82no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—82no—
575C22⋊Q8—82no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#120—82no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
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⋊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⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
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⋊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×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—82no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—22no—
709#107—22no—
710#107—22no—
711#107—41no—
712#107—41no—
713#106—22no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—22no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723#103—22no—
724#103—22no—
725#103—22no—
726#103—22no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
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#4114yes—
751C22⋊C8—22no—
752C22⋊C8—22no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756#97—41no—
757#97—41no—
758#97—41no—
759C4×C8—22no—
760C4×C8—22no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#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#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—81no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—42no—
825C2×Q8—81no—
826C2×Q8—81no—
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—21no—
844C2×D4—41no—
845C2×D4—41no—
846C2×D4—41no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—44no—
851C2×D4—42no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—82no—
855C2×D4—82no—
856C2×D4—82no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4C2×#4112yes—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—42no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4—81no—
900C22×C4—81no—
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C2511yescharacteristic
914Q16—82no—
915SD16—44no—
916SD16—82no—
917SD16—82no—
918D8—82no—
919D8—82no—
920M16—82no—
921M16—82no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—82no—
945C2×C8C2×#4112yes—
946C2×C8H(5,𝔽2)12yes—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—41no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4C2×#4112yes—
996C4⋊C4H(5,𝔽2)12yes—
997C22⋊C4—41no—
998C22⋊C4—41no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—22no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
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—84no—
1105C23—84no—
1106C23—162no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23—162no—
1111C23C23×D411yescharacteristic
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—162no—
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—82no—
1134D4—84no—
1135D4—162no—
1136D4—162no—
1137D4—162no—
1138D4—162no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
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—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
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—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4C22×#4111yescharacteristic
1226C2×C4C2×H(5,𝔽2)11yescharacteristic
1227C2×C4C2×H(5,𝔽2)11yescharacteristic
1228C2×C4#58511yescharacteristic
1229C2×C4#58511yescharacteristic
1230C2×C4#58511yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—41no—
1234C8—41no—
1235C8—41no—
1236C8—41no—
1237C8—41no—
1238C8—41no—
1239C22—41no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
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—168no—
1275C22D4×#4111yescharacteristic
1276C22#348811yescharacteristic
1277C22#349611yescharacteristic
1278C22#358411yescharacteristic
1279C22#358511yescharacteristic
1280C22#358511yescharacteristic
1281C22#358611yescharacteristic
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—42no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—42no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4#350611yescharacteristic
1308C4#351411yescharacteristic
1309C4#355811yescharacteristic
1310C4#356611yescharacteristic
1311C2—81no—
1312C2—81no—
1313C2—82no—
1314C2—161no—
1315C2—161no—
1316C2#4303511yescharacteristic
1317C2#6151011yescharacteristic
1318C2#6152711yescharacteristic
1319C2#6205011yescharacteristic
1320C2#6207911yescharacteristic
1321C2#6228811yescharacteristic
1322C2#6234711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30511C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45205C2semidirect
2. #42642C2semidirect
3. #32215C2semidirect
4. #32119C2semidirect
5. #32023C2semidirect
6. #31654C2semidirect
7. #31219C2semidirect
8. #30915C2semidirect
9. #30531C2semidirect
11. #28924C2semidirect
12. #28888C2semidirect
13. #28590C2semidirect
14. #28100C2semidirect
15. #27796C2semidirect
16. #27795C2semidirect
17. #27240C2semidirect
18. #27135C2semidirect
19. #27109C2semidirect
20. #26750C2semidirect
21. #26715C2semidirect
22. #26594C2semidirect
23. #25465C2semidirect
24. #25399C2semidirect
25. #25101C2semidirect
26. #24667C2semidirect
27. #23706C2semidirect
28. #23224C2semidirect
29. #22903C2semidirect
30. #22884C2semidirect
31. #22202C2semidirect
32. C2×#501C22semidirect
38. C2×#467C22semidirect
39. C2×#464C22semidirect
45. C2×#433C22semidirect
71. #2490C22semidirect
73. #2489C22semidirect
77. #2448C22semidirect
78. #2447C22semidirect
83. #2370C22semidirect
84. #2370C22semidirect
90. #2324C22semidirect
91. #2323C22semidirect
92. #2100C22semidirect
93. #2088C22semidirect
94. #2084C22semidirect
95. #2083C22semidirect
97. #2077C22semidirect
98. #2072C22semidirect
99. #2068C22semidirect
102. #2066C22semidirect
104. #2059C22semidirect
105. #2056C22semidirect
110. #2036C22semidirect
113. #2035C22semidirect
118. #2026C22semidirect
121. #2024C22semidirect
122. #2023C22semidirect
130. #2000C22semidirect
132. #1989C22semidirect
133. #1987C22semidirect
137. #1973C22semidirect
140. #1968C22semidirect
141. #1959C22semidirect
142. #1948C22semidirect
143. #1947C22semidirect
144. #1940C22semidirect
147. #1935C22semidirect
149. #1934C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
152. #1927C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
163. #1921C22semidirect
164. #1920C22semidirect
165. #1920C22semidirect
166. #1917C22semidirect
167. #1916C22semidirect
169. #1894C22semidirect
172. #1893C22semidirect
177. #1878C22semidirect
181. #1865C22semidirect
182. #1863C22semidirect
184. #1862C22semidirect
187. #1850C22semidirect
190. #1809C22semidirect
191. #1802C22semidirect
193. C4×#107C22semidirect
194. C4×#107C22semidirect
195. #1770C22semidirect
196. #1763C22semidirect
197. #1763C22semidirect
201. #1753C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#452052
#426422
#322152
#321192
#320232
#316542
#312192
#309152
#305312
#305112
#289242
#288882
#285902
#281002
#277962
#277952
#272402
#271352
#271092
#267502
#267152
#265942
#254652
#253992
#251012
#246672
#237062
#232242
#229032
#228842
#222022