Finite Group Databasebeta

← #6492088

Subgroups — #6492088

Order 512.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37546C211yesmaximal, characteristic
2#34244C211yesmaximal, characteristic, complemented
3#33121C211yesmaximal, characteristic, complemented
4#33120C211yesmaximal, characteristic, complemented
5#33115C211yesmaximal, characteristic, complemented
6#33115C211yesmaximal, characteristic, complemented
7#29935C211yesmaximal, characteristic, complemented
8#29935C211yesmaximal, characteristic, complemented
9#29932C211yesmaximal, characteristic, complemented
10#29931C211yesmaximal, characteristic, complemented
11#26327C211yesmaximal, characteristic, complemented
12#26326C211yesmaximal, characteristic, complemented
13#26325C211yesmaximal, characteristic, complemented
14#26324C211yesmaximal, characteristic, complemented
15#26241C211yesmaximal, characteristic, complemented
16#26240C211yesmaximal, characteristic, complemented
17#26239C211yesmaximal, characteristic, complemented
18#26238C211yesmaximal, characteristic, complemented
19#24892C211yesmaximal, characteristic, complemented
20#24890C211yesmaximal, characteristic, complemented
21#24888C211yesmaximal, characteristic, complemented
22#24886C211yesmaximal, characteristic, complemented
23#24884C211yesmaximal, characteristic, complemented
24#24882C211yesmaximal, characteristic, complemented
25#24880C211yesmaximal, characteristic, complemented
26#24878C211yesmaximal, characteristic, complemented
27#21963C211yesmaximal, characteristic, complemented
28#21850C211yesmaximal, characteristic, complemented
29#21806C211yesmaximal, characteristic, complemented
30#21362C211yesmaximal, characteristic, complemented
31#21261C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C22×#124C2211yescharacteristic
34C2×#484C2211yescharacteristic, complemented
35C2×#481C2211yescharacteristic
36C2×#485C2211yescharacteristic, complemented
37C2×#485C2211yescharacteristic, complemented
38C2×#482C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#483C2211yescharacteristic, complemented
41C2×#480C2211yescharacteristic
42C2×#431C2211yescharacteristic
43C2×#423C2211yescharacteristic
44C2×#419C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2820—21no—
49#2819—21no—
50#2662—21no—
51#2662—21no—
52#2626—21no—
53#2620C2211yescharacteristic
54#2620C2211yescharacteristic
55#2620C2211yescharacteristic
56#2620C2211yescharacteristic
57#2617—21no—
58#2592C2211yescharacteristic
59#2592C2211yescharacteristic
60#2540C2211yescharacteristic
61#2540C2211yescharacteristic
62#2411—21no—
63#2411—21no—
64#2409C2211yescharacteristic
65#2409C2211yescharacteristic
66#2408C2211yescharacteristic
67#2408C2211yescharacteristic
68#2374—21no—
69#2374—21no—
70#2372—21no—
71#2371—21no—
72#2355C2211yescharacteristic, complemented
73#2355C2211yescharacteristic, complemented
74#2354C2211yescharacteristic
75#2354C2211yescharacteristic
76#2352C2211yescharacteristic
77#2352C2211yescharacteristic
78#2352C2211yescharacteristic, complemented
79#2352C2211yescharacteristic, complemented
80#2333—21no—
81#2332—21no—
82#2314C2211yescharacteristic, complemented
83#2314C2211yescharacteristic, complemented
84C4×#126—21no—
85C4×#126—21no—
86#2285C2211yescharacteristic
87#2283C2211yescharacteristic
88#2274C2211yescharacteristic, complemented
89#2274C2211yescharacteristic, complemented
90C4×#117C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2094C2211yescharacteristic
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2074C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2072C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2036C2211yescharacteristic, complemented
108#2036C2211yescharacteristic, complemented
109#2036C2211yescharacteristic, complemented
110#2036C2211yescharacteristic, complemented
111#2035C2211yescharacteristic, complemented
112#2035C2211yescharacteristic, complemented
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#1984C2211yescharacteristic, complemented
124#1984C2211yescharacteristic, complemented
125#1983C2211yescharacteristic
126#1983C2211yescharacteristic
127#1983C2211yescharacteristic
128#1983C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1958C2211yescharacteristic
138#1958C2211yescharacteristic
139#1958C2211yescharacteristic
140#1958C2211yescharacteristic
141#1954C2211yescharacteristic, complemented
142#1954C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1949C2211yescharacteristic, complemented
145#1949C2211yescharacteristic, complemented
146#1949C2211yescharacteristic, complemented
147#1948C2211yescharacteristic, complemented
148#1948C2211yescharacteristic, complemented
149#1948C2211yescharacteristic, complemented
150#1948C2211yescharacteristic, complemented
151#1947C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1947C2211yescharacteristic, complemented
154#1947C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1928C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1927C2211yescharacteristic, complemented
163#1926C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1925C2211yescharacteristic
168#1925C2211yescharacteristic
169#1925C2211yescharacteristic
170#1925C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1873C2211yescharacteristic, complemented
176#1873C2211yescharacteristic, complemented
177#1872C2211yescharacteristic, complemented
178#1872C2211yescharacteristic, complemented
179#1870C2211yescharacteristic
180#1870C2211yescharacteristic
181#1870C2211yescharacteristic
182#1870C2211yescharacteristic
183#1854C2211yescharacteristic
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1798C2211yescharacteristic, complemented
192#1798C2211yescharacteristic, complemented
193#1798C2211yescharacteristic, complemented
194#1798C2211yescharacteristic, complemented
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199C4×#107C2211yescharacteristic, complemented
200C4×#107C2211yescharacteristic, complemented
201C4×#106C2211yescharacteristic, complemented
202C4×#106C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207#529—24no—
208#529—24no—
209C2×#126D411yescharacteristic
210C2×#126D411yescharacteristic
211C2×#125D411yescharacteristic
212C2×#124—21no—
213C2×#124—21no—
214C2×#124—24no—
215C2×#124—24no—
216C2×#124D411yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123D411yescharacteristic
222C2×#123D411yescharacteristic
223C2×C22⋊Q8D411yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121D411yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C42C2311yescharacteristic
251#485—42no—
252#485—42no—
253#484—42no—
254#483—42no—
255#482—42no—
256#482—42no—
257#481—42no—
258#480—42no—
259#431—24no—
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276#423—24no—
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#419—42no—
284#419—42no—
285#418—42no—
286#418—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#399—21no—
332#399—21no—
333#397—21no—
334#397—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#395—21no—
344#395—21no—
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#393—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#391—21no—
364#391—21no—
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
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#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#385—21no—
414#385—21no—
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#383—21no—
420#382—21no—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#379—21no—
436#379—21no—
437C4×C4⋊C4—21no—
438C4×C4⋊C4—21no—
439C4×C4⋊C4—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469#376—21no—
470#376—21no—
471C43—21no—
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—41no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
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×D4—41no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16—41no—
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545#126—24no—
546#126—24no—
547#125—24no—
548#124—24no—
549#124—22no—
550#124—22no—
551#124—22no—
552#124—22no—
553#124—22no—
554#124—22no—
555#124—22no—
556#124—22no—
557#124—44no—
558#124—44no—
559#123—24no—
560#123—24no—
561C22⋊Q8—24no—
562C22⋊Q8—41no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570#121—24no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#120—82no—
580#120—82no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—82no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—44no—
679C2×C22⋊C4—44no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42#4114yes—
709C2×C42#4114yes—
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#107—22no—
715#107—22no—
716#107—41no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#107—41no—
722#106—22no—
723#106—22no—
724#106—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
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—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C4×C8—22no—
779C4×C8—22no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
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—41no—
842C2×Q8—41no—
843C2×Q8—44no—
844C2×Q8—44no—
845C2×Q8—42no—
846C2×Q8—81no—
847C2×Q8—81no—
848C2×Q8—82no—
849C2×Q8—82no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—22no—
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—44no—
866C2×D4—44no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—42no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—81no—
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×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
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—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—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
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#12314yes—
934C22×C4#12314yes—
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2×#4112yes—
947C22×C4C2×#4112yes—
948C22×C4C2511yescharacteristic
949M16—82no—
950M16—82no—
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—21no—
965C2×C8—21no—
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—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
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—42no—
1008C4⋊C4—42no—
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⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4H(5,𝔽2)12yes—
1022C4⋊C4H(5,𝔽2)12yes—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
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—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—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42#12314yes—
1090C42#12314yes—
1091C42C2×#4112yes—
1092C42C2×#4112yes—
1093C42C2×#4112yes—
1094C42C2×#4112yes—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
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—41no—
1129C23—84no—
1130C23—84no—
1131C23—84no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23C2×#12312yes—
1137C23C23×D411yescharacteristic
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—82no—
1147Q8—84no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—82no—
1157D4—84no—
1158D4—82no—
1159D4—82no—
1160D4—162no—
1161D4—162no—
1162D4—162no—
1163D4—162no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
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—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—44no—
1199C2×C4—44no—
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—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—41no—
1247C2×C4—41no—
1248C2×C4—84no—
1249C2×C4—162no—
1250C2×C4—162no—
1251C2×C4C2×#12312yes—
1252C2×C4C2×#12312yes—
1253C2×C4C2×#12312yes—
1254C2×C4C2×#12312yes—
1255C2×C4C2×#12312yes—
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C22×#4111yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4C2×H(5,𝔽2)11yescharacteristic
1260C2×C4#58511yescharacteristic
1261C2×C4#58511yescharacteristic
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—168no—
1306C22C22×#12311yescharacteristic
1307C22#348811yescharacteristic
1308C22#348811yescharacteristic
1309C22#358411yescharacteristic
1310C22#358411yescharacteristic
1311C22#358511yescharacteristic
1312C22#358611yescharacteristic
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—22no—
1318C4—42no—
1319C4—42no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4#346011yescharacteristic
1339C4#346011yescharacteristic
1340C4#350811yescharacteristic
1341C4#351011yescharacteristic
1342C2—42no—
1343C2—81no—
1344C2—81no—
1345C2—161no—
1346C2—161no—
1347C2#3525411yescharacteristic
1348C2#6051611yescharacteristic
1349C2#6052011yescharacteristic
1350C2#6204711yescharacteristic
1351C2#6204811yescharacteristic
1352C2#6204911yescharacteristic
1353C2#6205011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34244C2semidirect
3. #33121C2semidirect
4. #33120C2semidirect
5. #33115C2semidirect
6. #33115C2semidirect
7. #29935C2semidirect
8. #29935C2semidirect
9. #29932C2semidirect
10. #29931C2semidirect
11. #26327C2semidirect
12. #26326C2semidirect
13. #26325C2semidirect
14. #26324C2semidirect
15. #26241C2semidirect
16. #26240C2semidirect
17. #26239C2semidirect
18. #26238C2semidirect
19. #24892C2semidirect
20. #24890C2semidirect
21. #24888C2semidirect
22. #24886C2semidirect
23. #24884C2semidirect
24. #24882C2semidirect
25. #24880C2semidirect
26. #24878C2semidirect
27. #21963C2semidirect
28. #21850C2semidirect
29. #21806C2semidirect
30. #21362C2semidirect
31. #21261C2semidirect
34. C2×#484C22semidirect
36. C2×#485C22semidirect
37. C2×#485C22semidirect
40. C2×#483C22semidirect
72. #2355C22semidirect
73. #2355C22semidirect
78. #2352C22semidirect
79. #2352C22semidirect
82. #2314C22semidirect
83. #2314C22semidirect
88. #2274C22semidirect
89. #2274C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
93. #2096C22semidirect
94. #2095C22semidirect
99. #2074C22semidirect
100. #2074C22semidirect
103. #2072C22semidirect
104. #2072C22semidirect
107. #2036C22semidirect
108. #2036C22semidirect
109. #2036C22semidirect
110. #2036C22semidirect
111. #2035C22semidirect
112. #2035C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
123. #1984C22semidirect
124. #1984C22semidirect
141. #1954C22semidirect
142. #1954C22semidirect
143. #1949C22semidirect
144. #1949C22semidirect
145. #1949C22semidirect
146. #1949C22semidirect
147. #1948C22semidirect
148. #1948C22semidirect
149. #1948C22semidirect
150. #1948C22semidirect
151. #1947C22semidirect
152. #1947C22semidirect
153. #1947C22semidirect
154. #1947C22semidirect
155. #1928C22semidirect
156. #1928C22semidirect
157. #1928C22semidirect
158. #1928C22semidirect
159. #1927C22semidirect
160. #1927C22semidirect
161. #1927C22semidirect
162. #1927C22semidirect
175. #1873C22semidirect
176. #1873C22semidirect
177. #1872C22semidirect
178. #1872C22semidirect
191. #1798C22semidirect
192. #1798C22semidirect
193. #1798C22semidirect
194. #1798C22semidirect
199. C4×#107C22semidirect
200. C4×#107C22semidirect
201. C4×#106C22semidirect
202. C4×#106C22semidirect

Maximal subgroups

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

subgroupindex
#375462
#342442
#331212
#331202
#331152
#299352
#299322
#299312
#263272
#263262
#263252
#263242
#262412
#262402
#262392
#262382
#248922
#248902
#248882
#248862
#248842
#248822
#248802
#248782
#219632
#218502
#218062
#213622
#212612