Finite Group Databasebeta

← #7615092

Subgroups — #7615092

Order 512.

1684 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#45393C211yesmaximal, characteristic, complemented
2#45367C211yesmaximal, characteristic, complemented
3#32627C211yesmaximal, characteristic, complemented
4#32623C211yesmaximal, characteristic, complemented
5#31915C211yesmaximal, characteristic, complemented
6#31914C211yesmaximal, characteristic, complemented
7#28736C211yesmaximal, characteristic, complemented
8#28264C211yesmaximal, characteristic, complemented
9#28127C211yesmaximal, characteristic, complemented
10#28126C211yesmaximal, characteristic, complemented
11#28029C211yesmaximal, characteristic, complemented
12#28021C211yesmaximal, characteristic, complemented
13#27941C211yesmaximal, characteristic, complemented
14#27199C211yesmaximal, characteristic, complemented
15#27194C211yesmaximal, characteristic, complemented
16#27071C211yesmaximal, characteristic, complemented
17#27062C211yesmaximal, characteristic, complemented
18#26267C211yesmaximal, characteristic, complemented
19#26264C211yesmaximal, characteristic, complemented
20#25794C211yesmaximal, characteristic
21#24535C211yesmaximal, characteristic, complemented
22#24526C211yesmaximal, characteristic, complemented
23#24484C211yesmaximal, characteristic, complemented
24#24478C211yesmaximal, characteristic, complemented
25#23193C211yesmaximal, characteristic, complemented
26#22819C211yesmaximal, characteristic, complemented
27#22623C211yesmaximal, characteristic, complemented
28#22443C211yesmaximal, characteristic, complemented
29#21602C211yesmaximal, characteristic, complemented
30#21541C211yesmaximal, characteristic, complemented
31#21235C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#496C2211yescharacteristic
34C2×#493C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×C8×Q8C2211yescharacteristic, complemented
41C2×#442C2211yescharacteristic, complemented
42C2×#440C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#416C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C2×#405C2211yescharacteristic
48#2756—21no—
49#2749—21no—
50#2748—21no—
51#2741—21no—
52#2706—21no—
53#2705—21no—
54#2697—21no—
55#2685—21no—
56#2582C2211yescharacteristic, complemented
57#2557—21no—
58#2554—21no—
59#2554—21no—
60#2553—21no—
61#2548C2211yescharacteristic
62#2548C2211yescharacteristic, complemented
63#2538C2211yescharacteristic
64#2534—21no—
65#2521—21no—
66#2513C2211yescharacteristic
67#2512C2211yescharacteristic
68#2512C2211yescharacteristic, complemented
69#2512C2211yescharacteristic, complemented
70#2501C2211yescharacteristic
71#2500C2211yescharacteristic
72#2472—21no—
73#2461—21no—
74#2448C2211yescharacteristic, complemented
75#2445C2211yescharacteristic
76#2445C2211yescharacteristic
77#2445C2211yescharacteristic, complemented
78#2433C2211yescharacteristic
79#2431C2211yescharacteristic
80#2396C2211yescharacteristic
81#2367C2211yescharacteristic, complemented
82#2366C2211yescharacteristic
83#2357C2211yescharacteristic
84#2355C2211yescharacteristic, complemented
85#2347C2211yescharacteristic
86#2345C2211yescharacteristic
87#2341C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2324C2211yescharacteristic
90#2324C2211yescharacteristic
91#2311C2211yescharacteristic
92#2309C2211yescharacteristic
93#2094C2211yescharacteristic, complemented
94#2094C2211yescharacteristic, complemented
95#2093C2211yescharacteristic, complemented
96#2092C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2065C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic, complemented
115#2054C2211yescharacteristic, complemented
116#2054C2211yescharacteristic, complemented
117#2042C2211yescharacteristic, complemented
118#2041C2211yescharacteristic
119#2041C2211yescharacteristic
120#2041C2211yescharacteristic, complemented
121#2014C2211yescharacteristic
122#2012C2211yescharacteristic
123#2011C2211yescharacteristic
124#2011C2211yescharacteristic
125#1985C2211yescharacteristic, complemented
126#1983C2211yescharacteristic, complemented
127#1982C2211yescharacteristic
128#1982C2211yescharacteristic
129#1982C2211yescharacteristic, complemented
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1972C2211yescharacteristic
133#1972C2211yescharacteristic
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic, complemented
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1970C2211yescharacteristic
140#1970C2211yescharacteristic, complemented
141#1970C2211yescharacteristic, complemented
142#1968C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1944C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1940C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1936C2211yescharacteristic, complemented
151#1928C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1850C2211yescharacteristic
180#1850C2211yescharacteristic
181#1847C2211yescharacteristic, complemented
182#1844C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1823C2211yescharacteristic
185#1809C2211yescharacteristic
186#1805C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1798C2211yescharacteristic
191#1788C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#126—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250#496—24no—
251#493—42no—
252#482—42no—
253#481—42no—
254#469—24no—
255#449—42no—
256#447—42no—
257C8×Q8—42no—
258#442—42no—
259#440—24no—
260C4×SD16—42no—
261#428—24no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#416—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#102—42no—
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313#405—42no—
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400D411yescharacteristic
323#399—21no—
324#399—21no—
325#399—21no—
326#399D411yescharacteristic
327#398—21no—
328#398—21no—
329#398D411yescharacteristic
330#398D411yescharacteristic
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396D411yescharacteristic
343#396D411yescharacteristic
344#395D411yescharacteristic
345#394—21no—
346#394—21no—
347#394—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#393D411yescharacteristic
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
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#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
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#388—21no—
417#388—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#383—21no—
442#382—21no—
443#382C2311yescharacteristic
444#381—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
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—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2411yescharacteristic
533AGL(1,ℤ/8)—416no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16#4114yes—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16#4114yes—
564C22×C8—22no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575#127—22no—
576#127—41no—
577#127—41no—
578#127—41no—
579#127—41no—
580#127—41no—
581#126—82no—
582#126—82no—
583#126—82no—
584#124—22no—
585#124—41no—
586#124—82no—
587#124—82no—
588#123—82no—
589#123—82no—
590#123—82no—
591#123—82no—
592#123—82no—
593C22⋊Q8—82no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#120—82no—
599#120—82no—
600C4×Q8—22no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×D4—22no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—82no—
615#117—22no—
616#117—22no—
617#117—41no—
618#117—41no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
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—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—82no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
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
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—22no—
731#107—41no—
732#106—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#102—22no—
751#102—22no—
752#102—22no—
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—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777#97—22no—
778#97—22no—
779#97—22no—
780#97—41no—
781C4×C8—22no—
782C4×C8—22no—
783C4×C8—22no—
784C4×C8—41no—
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#95—21no—
806#95—21no—
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—81no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830#41—44no—
831#41—44no—
832#41—82no—
833#41—82no—
834C2×Q8—22no—
835C2×Q8—22no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—41no—
842C2×Q8C2×#4112yes—
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—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—42no—
875C2×D4—42no—
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—82no—
886C2×D4—82no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4C2×#4112yes—
907C22×C4—21no—
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—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C2×#4112yes—
954C22×C4H(5,𝔽2)12yes—
955C22×C4C2511yescharacteristic
956SD16—28no—
957SD16—44no—
958SD16—82no—
959D8—44no—
960D8—44no—
961D8—44no—
962D8—82no—
963D8—82no—
964D8—82no—
965M16—28no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
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—44no—
987C2×C8C2×#4112yes—
988C2×C8C2×#4112yes—
989C2×C8C2×#4112yes—
990C2×C8H(5,𝔽2)12yes—
991C4⋊C4—22no—
992C4⋊C4—22no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
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—
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⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—42no—
1105C42—42no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
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—41no—
1152C23—41no—
1153C23—41no—
1154C23—84no—
1155C23—84no—
1156C23—162no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23#55012yes—
1162C23C23×D411yescharacteristic
1163Q8—22no—
1164Q8—22no—
1165Q8—44no—
1166Q8—41no—
1167Q8—41no—
1168D4—22no—
1169D4—22no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—162no—
1192D4—162no—
1193D4—162no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
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—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
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—41no—
1270C2×C4—41no—
1271C2×C4—84no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4#55012yes—
1278C2×C4#57612yes—
1279C2×C4#57712yes—
1280C2×C4C22×#4111yescharacteristic
1281C2×C4C22×#4111yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—22no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8#55114yes—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—42no—
1303C22—42no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
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—168no—
1337C22C2×#55011yescharacteristic
1338C22D4×#4111yescharacteristic
1339C22#349611yescharacteristic
1340C22C2×#57611yescharacteristic
1341C22C2×#57711yescharacteristic
1342C22#358511yescharacteristic
1343C22#358511yescharacteristic
1344C4—22no—
1345C4—22no—
1346C4—22no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—42no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4C2×#55111yescharacteristic
1369C4#351011yescharacteristic
1370C4#351311yescharacteristic
1371C4#354211yescharacteristic
1372C2—42no—
1373C2—82no—
1374C2—161no—
1375C2—161no—
1376C2—161no—
1377C2—161no—
1378C2#5982011yescharacteristic
1379C2#6141911yescharacteristic
1380C2#6142111yescharacteristic
1381C2#6155411yescharacteristic
1382C2#6155511yescharacteristic
1383C2#6228011yescharacteristic
1384C2#6233411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25794C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45393C2semidirect
2. #45367C2semidirect
3. #32627C2semidirect
4. #32623C2semidirect
5. #31915C2semidirect
6. #31914C2semidirect
7. #28736C2semidirect
8. #28264C2semidirect
9. #28127C2semidirect
10. #28126C2semidirect
11. #28029C2semidirect
12. #28021C2semidirect
13. #27941C2semidirect
14. #27199C2semidirect
15. #27194C2semidirect
16. #27071C2semidirect
17. #27062C2semidirect
18. #26267C2semidirect
19. #26264C2semidirect
21. #24535C2semidirect
22. #24526C2semidirect
23. #24484C2semidirect
24. #24478C2semidirect
25. #23193C2semidirect
26. #22819C2semidirect
27. #22623C2semidirect
28. #22443C2semidirect
29. #21602C2semidirect
30. #21541C2semidirect
31. #21235C2semidirect
40. C2×C8×Q8C22semidirect
41. C2×#442C22semidirect
56. #2582C22semidirect
62. #2548C22semidirect
68. #2512C22semidirect
69. #2512C22semidirect
74. #2448C22semidirect
77. #2445C22semidirect
81. #2367C22semidirect
84. #2355C22semidirect
93. #2094C22semidirect
94. #2094C22semidirect
95. #2093C22semidirect
96. #2092C22semidirect
97. #2073C22semidirect
100. #2071C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
107. #2065C22semidirect
108. #2065C22semidirect
109. #2055C22semidirect
114. #2054C22semidirect
115. #2054C22semidirect
116. #2054C22semidirect
117. #2042C22semidirect
120. #2041C22semidirect
125. #1985C22semidirect
126. #1983C22semidirect
129. #1982C22semidirect
136. #1972C22semidirect
140. #1970C22semidirect
141. #1970C22semidirect
145. #1944C22semidirect
146. #1941C22semidirect
147. #1941C22semidirect
148. #1940C22semidirect
149. #1936C22semidirect
150. #1936C22semidirect
151. #1928C22semidirect
152. #1927C22semidirect
156. #1926C22semidirect
158. #1925C22semidirect
159. #1921C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1918C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
177. #1879C22semidirect
178. #1877C22semidirect
181. #1847C22semidirect
182. #1844C22semidirect
186. #1805C22semidirect
187. #1803C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. C4×#107C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. #1770C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#453932
#453672
#326272
#326232
#319152
#319142
#287362
#282642
#281272
#281262
#280292
#280212
#279412
#271992
#271942
#270712
#270622
#262672
#262642
#257942
#245352
#245262
#244842
#244782
#231932
#228192
#226232
#224432
#216022
#215412
#212352