Finite Group Databasebeta

← #6741453

Subgroups — #6741453

Order 512.

1610 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42836C211yesmaximal, characteristic, complemented
2#36004C211yesmaximal, characteristic
3#32962C211yesmaximal, characteristic, complemented
4#31681C211yesmaximal, characteristic, complemented
5#31483C211yesmaximal, characteristic, complemented
6#31290C211yesmaximal, characteristic, complemented
7#31240C211yesmaximal, characteristic, complemented
8#31118C211yesmaximal, characteristic, complemented
9#30988C211yesmaximal, characteristic, complemented
10#30608C211yesmaximal, characteristic, complemented
11#30424C211yesmaximal, characteristic, complemented
12#30372C211yesmaximal, characteristic, complemented
13#30035C211yesmaximal, characteristic, complemented
14#29068C211yesmaximal, characteristic, complemented
15#28958C211yesmaximal, characteristic, complemented
16#27465C211yesmaximal, characteristic, complemented
17#27169C211yesmaximal, characteristic, complemented
18#27039C211yesmaximal, characteristic, complemented
19#26912C211yesmaximal, characteristic, complemented
20#26755C211yesmaximal, characteristic, complemented
21#26670C211yesmaximal, characteristic, complemented
22#26629C211yesmaximal, characteristic, complemented
23#26533C211yesmaximal, characteristic, complemented
24#26373C211yesmaximal, characteristic, complemented
25#26357C211yesmaximal, characteristic, complemented
26#24133C211yesmaximal, characteristic, complemented
27#24104C211yesmaximal, characteristic, complemented
28#23041C211yesmaximal, characteristic, complemented
29#23003C211yesmaximal, characteristic, complemented
30#22364C211yesmaximal, characteristic, complemented
31#21459C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#481C2211yescharacteristic, complemented
35C2×#475C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic
44C2×#428C2211yescharacteristic, complemented
45#2839—21no—
46#2792—21no—
47#2773—21no—
48#2718—21no—
49#2689—21no—
50#2663—21no—
51#2650—21no—
52#2631—21no—
53#2628C2211yescharacteristic
54#2624C2211yescharacteristic
55#2598—21no—
56#2575—21no—
57#2571C2211yescharacteristic, complemented
58#2540—21no—
59#2536C2211yescharacteristic
60#2509C2211yescharacteristic, complemented
61#2497C2211yescharacteristic
62#2496C2211yescharacteristic, complemented
63#2486C2211yescharacteristic
64#2472—21no—
65#2472—21no—
66#2452C2211yescharacteristic
67#2452C2211yescharacteristic
68#2451C2211yescharacteristic, complemented
69#2440C2211yescharacteristic, complemented
70#2433C2211yescharacteristic
71#2428C2211yescharacteristic
72#2428C2211yescharacteristic
73#2424—21no—
74#2424—21no—
75#2423C2211yescharacteristic
76#2421C2211yescharacteristic, complemented
77#2408C2211yescharacteristic
78#2395C2211yescharacteristic
79#2392—21no—
80#2366C2211yescharacteristic
81#2366C2211yescharacteristic
82#2363C2211yescharacteristic
83#2363C2211yescharacteristic
84#2360C2211yescharacteristic, complemented
85Q8×C4⋊C4C2211yescharacteristic, complemented
86#2347C2211yescharacteristic
87#2323C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2075C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2058C2211yescharacteristic, complemented
109#2058C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2035C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic, complemented
123#2023C2211yescharacteristic, complemented
124#2014C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic, complemented
128#1993C2211yescharacteristic, complemented
129#1982C2211yescharacteristic
130#1968C2211yescharacteristic
131#1957C2211yescharacteristic
132#1957C2211yescharacteristic
133#1955C2211yescharacteristic
134#1948C2211yescharacteristic, complemented
135#1947C2211yescharacteristic, complemented
136#1943C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1939C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic, complemented
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic, complemented
152#1923C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1917C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic
170#1873C2211yescharacteristic
171#1873C2211yescharacteristic, complemented
172#1870C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1851C2211yescharacteristic, complemented
188#1825C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic, complemented
192#1798C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196C4×#107C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208#555—42no—
209#555—42no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#124—21no—
216C2×#124—21no—
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×#120—21no—
233#518—42no—
234#518—42no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255#481—42no—
256#476—42no—
257#475—42no—
258#474—42no—
259#468—24no—
260#460—24no—
261#450—24no—
262#440—42no—
263#440—42no—
264C4×SD16—42no—
265#428—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400D411yescharacteristic
331#399—21no—
332#399—21no—
333#399—21no—
334#399D411yescharacteristic
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398D411yescharacteristic
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397D411yescharacteristic
346#397D411yescharacteristic
347#397D411yescharacteristic
348#396—21no—
349#396—21no—
350#396—21no—
351#395—21no—
352#395—21no—
353#395—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394D411yescharacteristic
361#394D411yescharacteristic
362#393—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
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#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384—21no—
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#383—21no—
436#382—21no—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—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×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#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×Q8—21no—
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16#4114yes—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#127—22no—
549#127—22no—
550#127—41no—
551#127—41no—
552#126—82no—
553#124—44no—
554#124—44no—
555#123—82no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—82no—
561C22⋊Q8—82no—
562C22⋊Q8—82no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121—44no—
567#121—41no—
568#121—41no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—82no—
573#121—82no—
574#120—82no—
575#120—82no—
576#120—82no—
577C4×Q8—22no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—44no—
596C4×D4—44no—
597C4×D4—82no—
598C4×D4—82no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—41no—
603#117—41no—
604#117—44no—
605#117—41no—
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⋊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—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×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—44no—
683C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
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—22no—
712#106—22no—
713#106—22no—
714#106—22no—
715#106—41no—
716#106—41no—
717#106—41no—
718#106—41no—
719#106—41no—
720#106—41no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726#103—22no—
727#103—22no—
728#103—22no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752C22⋊C8—22no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759#97—41no—
760#97—41no—
761C4×C8—41no—
762C4×C8—41no—
763C4×C8—41no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—42no—
822C2×Q8—81no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8C2×#4112yes—
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—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—41no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4C2×#4112yes—
879C2×D42−1+412yes—
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—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—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
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×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C2511yescharacteristic
936SD16—44no—
937SD16—44no—
938SD16—44no—
939M16—44no—
940C2×C8—21no—
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×C8C2×#4112yes—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
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—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1018C4⋊C4H(5,𝔽2)12yes—
1019C22⋊C4—24no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—42no—
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—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
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—
1060C42—24no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—42no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—48no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—162no—
1116C23—162no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23C23×D411yescharacteristic
1122Q8—22no—
1123Q8—22no—
1124Q8—41no—
1125Q8—41no—
1126Q8—162no—
1127Q8—162no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—48no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—84no—
1142D4—84no—
1143D4—82no—
1144D4—162no—
1145D4—162no—
1146D4—162no—
1147D4—162no—
1148D4—162no—
1149D4—162no—
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—21no—
1163C2×C4—22no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—22no—
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—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—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—84no—
1232C2×C4—162no—
1233C2×C4—162no—
1234C2×C4—162no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4#57712yes—
1238C2×C4#57712yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×2−1+411yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—22no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C22—42no—
1254C22—41no—
1255C22—41no—
1256C22—42no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—42no—
1271C22—41no—
1272C22—41no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—168no—
1289C22D4×#4111yescharacteristic
1290C22#348411yescharacteristic
1291C22#348911yescharacteristic
1292C22C2×#57711yescharacteristic
1293C22C2×#57711yescharacteristic
1294C22#358511yescharacteristic
1295C22#358511yescharacteristic
1296C4—22no—
1297C4—22no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—42no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—42no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4#345911yescharacteristic
1322C4#352011yescharacteristic
1323C4#353911yescharacteristic
1324C4#354111yescharacteristic
1325C2—81no—
1326C2—81no—
1327C2—82no—
1328C2—82no—
1329C2—161no—
1330C2#3782411yescharacteristic
1331C2#6152111yescharacteristic
1332C2#6155411yescharacteristic
1333C2#6165311yescharacteristic
1334C2#6166211yescharacteristic
1335C2#6216411yescharacteristic
1336C2#6217911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36004C2
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. #42836C2semidirect
3. #32962C2semidirect
4. #31681C2semidirect
5. #31483C2semidirect
6. #31290C2semidirect
7. #31240C2semidirect
8. #31118C2semidirect
9. #30988C2semidirect
10. #30608C2semidirect
11. #30424C2semidirect
12. #30372C2semidirect
13. #30035C2semidirect
14. #29068C2semidirect
15. #28958C2semidirect
16. #27465C2semidirect
17. #27169C2semidirect
18. #27039C2semidirect
19. #26912C2semidirect
20. #26755C2semidirect
21. #26670C2semidirect
22. #26629C2semidirect
23. #26533C2semidirect
24. #26373C2semidirect
25. #26357C2semidirect
26. #24133C2semidirect
27. #24104C2semidirect
28. #23041C2semidirect
29. #23003C2semidirect
30. #22364C2semidirect
31. #21459C2semidirect
34. C2×#481C22semidirect
35. C2×#475C22semidirect
42. C2×#440C22semidirect
44. C2×#428C22semidirect
57. #2571C22semidirect
60. #2509C22semidirect
62. #2496C22semidirect
68. #2451C22semidirect
69. #2440C22semidirect
76. #2421C22semidirect
84. #2360C22semidirect
85. Q8×C4⋊C4C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
92. #2092C22semidirect
93. #2088C22semidirect
94. #2086C22semidirect
95. #2084C22semidirect
101. #2066C22semidirect
102. #2066C22semidirect
107. #2065C22semidirect
108. #2058C22semidirect
109. #2058C22semidirect
110. #2058C22semidirect
111. #2055C22semidirect
122. #2034C22semidirect
123. #2023C22semidirect
127. #2000C22semidirect
128. #1993C22semidirect
134. #1948C22semidirect
135. #1947C22semidirect
136. #1943C22semidirect
137. #1941C22semidirect
138. #1941C22semidirect
139. #1941C22semidirect
140. #1939C22semidirect
143. #1936C22semidirect
145. #1934C22semidirect
146. #1928C22semidirect
148. #1926C22semidirect
151. #1923C22semidirect
152. #1923C22semidirect
153. #1921C22semidirect
154. #1921C22semidirect
155. #1920C22semidirect
156. #1919C22semidirect
157. #1919C22semidirect
158. #1917C22semidirect
159. #1916C22semidirect
161. #1895C22semidirect
165. #1880C22semidirect
171. #1873C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
181. #1862C22semidirect
182. #1862C22semidirect
186. #1854C22semidirect
187. #1851C22semidirect
188. #1825C22semidirect
191. #1804C22semidirect
196. C4×#107C22semidirect
197. #1770C22semidirect
199. C4×#103C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#428362
#360042
#329622
#316812
#314832
#312902
#312402
#311182
#309882
#306082
#304242
#303722
#300352
#290682
#289582
#274652
#271692
#270392
#269122
#267552
#266702
#266292
#265332
#263732
#263572
#241332
#241042
#230412
#230032
#223642
#214592