Finite Group Databasebeta

← #7549361

Subgroups — #7549361

Order 512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45187C211yesmaximal, characteristic, complemented
2#36000C211yesmaximal, characteristic, complemented
3#32209C211yesmaximal, characteristic, complemented
4#32192C211yesmaximal, characteristic, complemented
5#31830C211yesmaximal, characteristic, complemented
6#31305C211yesmaximal, characteristic, complemented
7#29029C211yesmaximal, characteristic, complemented
8#28933C211yesmaximal, characteristic, complemented
9#27404C211yesmaximal, characteristic, complemented
10#27262C211yesmaximal, characteristic, complemented
11#27231C211yesmaximal, characteristic, complemented
12#27208C211yesmaximal, characteristic, complemented
13#27014C211yesmaximal, characteristic, complemented
14#26782C211yesmaximal, characteristic, complemented
15#26747C211yesmaximal, characteristic, complemented
16#26355C211yesmaximal, characteristic, complemented
17#26207C211yesmaximal, characteristic, complemented
18#25511C211yesmaximal, characteristic, complemented
19#25286C211yesmaximal, characteristic, complemented
20#25101C211yesmaximal, characteristic, complemented
21#25085C211yesmaximal, characteristic, complemented
22#24789C211yesmaximal, characteristic, complemented
23#24512C211yesmaximal, characteristic, complemented
24#24434C211yesmaximal, characteristic
25#23135C211yesmaximal, characteristic, complemented
26#23105C211yesmaximal, characteristic, complemented
27#22913C211yesmaximal, characteristic, complemented
28#22569C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic, complemented
30#21398C211yesmaximal, characteristic, complemented
31#21063C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#477C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic, complemented
39C2×#463C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#433C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2711—21no—
49#2694—21no—
50#2685—21no—
51#2685—21no—
52#2651—21no—
53#2624C2211yescharacteristic
54#2578—21no—
55#2560—21no—
56#2558—21no—
57#2545C2211yescharacteristic
58#2525—21no—
59#2521—21no—
60#2512C2211yescharacteristic, complemented
61#2507C2211yescharacteristic, complemented
62#2497C2211yescharacteristic, complemented
63#2491C2211yescharacteristic, complemented
64#2490—21no—
65#2490C2211yescharacteristic
66#2480—21no—
67#2480—21no—
68#2476—21no—
69#2454C2211yescharacteristic
70#2448C2211yescharacteristic
71#2440C2211yescharacteristic
72#2435C2211yescharacteristic
73#2432C2211yescharacteristic
74#2426—21no—
75#2426C2211yescharacteristic
76#2416C2211yescharacteristic
77#2415C2211yescharacteristic
78#2396—21no—
79#2395C2211yescharacteristic
80#2367C2211yescharacteristic
81#2365C2211yescharacteristic, complemented
82#2363C2211yescharacteristic
83#2363C2211yescharacteristic, complemented
84#2362C2211yescharacteristic
85#2354C2211yescharacteristic
86#2354C2211yescharacteristic, complemented
87#2347C2211yescharacteristic, complemented
88#2341C2211yescharacteristic
89#2309C2211yescharacteristic
90#2274C2211yescharacteristic
91#2099C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2076C2211yescharacteristic, complemented
95#2072C2211yescharacteristic, complemented
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2043C2211yescharacteristic, complemented
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic, complemented
117#2025C2211yescharacteristic, complemented
118#2023C2211yescharacteristic
119#2013C2211yescharacteristic, complemented
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#1999C2211yescharacteristic
123#1989C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1981C2211yescharacteristic, complemented
128#1981C2211yescharacteristic, complemented
129#1973C2211yescharacteristic, complemented
130#1972C2211yescharacteristic
131#1970C2211yescharacteristic
132#1959C2211yescharacteristic
133#1959C2211yescharacteristic
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1940C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1934C2211yescharacteristic
143#1928C2211yescharacteristic, complemented
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1894C2211yescharacteristic
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1880C2211yescharacteristic, complemented
166#1880C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1877C2211yescharacteristic, complemented
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1873C2211yescharacteristic
173#1873C2211yescharacteristic
174#1873C2211yescharacteristic, complemented
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1869C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1808C2211yescharacteristic, complemented
187#1802C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1786C2211yescharacteristic
191#1771C2211yescharacteristic, complemented
192#1763C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#541—24no—
215#541—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×C4×Q8—21no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117—21no—
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253#489—42no—
254#477—42no—
255#468—42no—
256#465—24no—
257#465—42no—
258#463—24no—
259#449—42no—
260#447—42no—
261#435—42no—
262#433—42no—
263#428—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277#418—24no—
278#416—24no—
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400D411yescharacteristic
324#399—21no—
325#399—21no—
326#399—21no—
327#399D411yescharacteristic
328#398—21no—
329#398—21no—
330#398—21no—
331#398D411yescharacteristic
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397D411yescharacteristic
338#397D411yescharacteristic
339#397D411yescharacteristic
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#395—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394D411yescharacteristic
360#394D411yescharacteristic
361#393—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
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#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#383—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
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×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—22no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×D8—22no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560#126—44no—
561#126—44no—
562#126—82no—
563#125—22no—
564#125—41no—
565#125—44no—
566#125—44no—
567#124—22no—
568#124—22no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—41no—
573#124—82no—
574#123—44no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—82no—
581C22⋊Q8#4114yes—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—44no—
587#121—41no—
588#121—41no—
589#121—82no—
590#120—44no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—82no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—41no—
603C4×D4—41no—
604#117—22no—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—41no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—82no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—22no—
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⋊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—41no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
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—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—44no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—22no—
728#107—41no—
729#107—41no—
730#107—41no—
731#106—22no—
732#106—22no—
733#106—41no—
734#106—41no—
735C4⋊C8—22no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
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—
770#102—41no—
771#102#4114yes—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—41no—
778#97—41no—
779#97—41no—
780#97—41no—
781C4×C8—41no—
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#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827#41—44no—
828#41—82no—
829#41—82no—
830#41—82no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—42no—
843C2×Q8—42no—
844C2×Q8—81no—
845C2×Q8C2×#4112yes—
846C2×D4—22no—
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—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4C2×#4112yes—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C2×#4112yes—
934C22×C4H(5,𝔽2)12yes—
935C22×C4C2511yescharacteristic
936SD16—82no—
937SD16—82no—
938D8—82no—
939D8—82no—
940M16—44no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
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—82no—
965C2×C8—82no—
966C2×C8C2×#4112yes—
967C4⋊C4—24no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4C2×#4112yes—
1018C4⋊C4C2×#4112yes—
1019C4⋊C4H(5,𝔽2)12yes—
1020C22⋊C4—24no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—42no—
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—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—22no—
1107C23—21no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—84no—
1129C23—84no—
1130C23—162no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23#54612yes—
1136C23C23×D411yescharacteristic
1137Q8—22no—
1138Q8—22no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—84no—
1146D4—22no—
1147D4—22no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—84no—
1159D4—82no—
1160D4—84no—
1161D4—162no—
1162D4—162no—
1163D4—162no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
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—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
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—41no—
1231C2×C4—41no—
1232C2×C4—41no—
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—84no—
1247C2×C4—84no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4#54612yes—
1251C2×C4C22×#4111yescharacteristic
1252C2×C4C22×#4111yescharacteristic
1253C2×C4C2×H(5,𝔽2)11yescharacteristic
1254C2×C4C2×H(5,𝔽2)11yescharacteristic
1255C2×C4#58511yescharacteristic
1256C2×C4#58511yescharacteristic
1257C8—22no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C22—22no—
1266C22—22no—
1267C22—22no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—41no—
1278C22—42no—
1279C22—41no—
1280C22—41no—
1281C22—42no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—168no—
1301C22C2×#54611yescharacteristic
1302C22D4×#4111yescharacteristic
1303C22#348811yescharacteristic
1304C22#358411yescharacteristic
1305C22#358511yescharacteristic
1306C22#358511yescharacteristic
1307C22#358611yescharacteristic
1308C4—22no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—41no—
1317C4—41no—
1318C4—42no—
1319C4—41no—
1320C4—41no—
1321C4—42no—
1322C4—41no—
1323C4—42no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4#347511yescharacteristic
1334C4#351411yescharacteristic
1335C4#351911yescharacteristic
1336C4#356011yescharacteristic
1337C2—42no—
1338C2—81no—
1339C2—82no—
1340C2—161no—
1341C2—161no—
1342C2#5909111yescharacteristic
1343C2#6118911yescharacteristic
1344C2#6122211yescharacteristic
1345C2#6151011yescharacteristic
1346C2#6153111yescharacteristic
1347C2#6201311yescharacteristic
1348C2#6207511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24434C2
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. #45187C2semidirect
2. #36000C2semidirect
3. #32209C2semidirect
4. #32192C2semidirect
5. #31830C2semidirect
6. #31305C2semidirect
7. #29029C2semidirect
8. #28933C2semidirect
9. #27404C2semidirect
10. #27262C2semidirect
11. #27231C2semidirect
12. #27208C2semidirect
13. #27014C2semidirect
14. #26782C2semidirect
15. #26747C2semidirect
16. #26355C2semidirect
17. #26207C2semidirect
18. #25511C2semidirect
19. #25286C2semidirect
20. #25101C2semidirect
21. #25085C2semidirect
22. #24789C2semidirect
23. #24512C2semidirect
25. #23135C2semidirect
26. #23105C2semidirect
27. #22913C2semidirect
28. #22569C2semidirect
29. #22424C2semidirect
30. #21398C2semidirect
31. #21063C2semidirect
35. C2×#477C22semidirect
38. C2×#465C22semidirect
60. #2512C22semidirect
61. #2507C22semidirect
62. #2497C22semidirect
63. #2491C22semidirect
81. #2365C22semidirect
83. #2363C22semidirect
86. #2354C22semidirect
87. #2347C22semidirect
91. #2099C22semidirect
92. #2096C22semidirect
93. #2088C22semidirect
94. #2076C22semidirect
95. #2072C22semidirect
97. #2068C22semidirect
100. #2066C22semidirect
102. #2065C22semidirect
103. #2059C22semidirect
104. #2058C22semidirect
108. #2043C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
116. #2033C22semidirect
117. #2025C22semidirect
119. #2013C22semidirect
123. #1989C22semidirect
124. #1989C22semidirect
127. #1981C22semidirect
128. #1981C22semidirect
129. #1973C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1940C22semidirect
140. #1936C22semidirect
141. #1935C22semidirect
143. #1928C22semidirect
153. #1924C22semidirect
154. #1923C22semidirect
155. #1920C22semidirect
156. #1919C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1917C22semidirect
160. #1917C22semidirect
164. #1880C22semidirect
165. #1880C22semidirect
166. #1880C22semidirect
169. #1877C22semidirect
174. #1873C22semidirect
178. #1865C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
184. #1850C22semidirect
185. #1825C22semidirect
186. #1808C22semidirect
191. #1771C22semidirect
192. #1763C22semidirect
193. #1763C22semidirect
194. #1763C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
200. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#451872
#360002
#322092
#321922
#318302
#313052
#290292
#289332
#274042
#272622
#272312
#272082
#270142
#267822
#267472
#263552
#262072
#255112
#252862
#251012
#250852
#247892
#245122
#244342
#231352
#231052
#229132
#225692
#224242
#213982
#210632