Finite Group Databasebeta

← #6475806

Subgroups — #6475806

Order 512.

1672 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35302C211yesmaximal, characteristic, complemented
2#35260C211yesmaximal, characteristic, complemented
3#33219C211yesmaximal, characteristic, complemented
4#33181C211yesmaximal, characteristic, complemented
5#33054C211yesmaximal, characteristic, complemented
6#33047C211yesmaximal, characteristic, complemented
7#29743C211yesmaximal, characteristic, complemented
8#29742C211yesmaximal, characteristic
9#29735C211yesmaximal, characteristic, complemented
10#29734C211yesmaximal, characteristic, complemented
11#29486C211yesmaximal, characteristic, complemented
12#29485C211yesmaximal, characteristic, complemented
13#29479C211yesmaximal, characteristic, complemented
14#29476C211yesmaximal, characteristic, complemented
15#29475C211yesmaximal, characteristic, complemented
16#29472C211yesmaximal, characteristic, complemented
17#29467C211yesmaximal, characteristic, complemented
18#29464C211yesmaximal, characteristic, complemented
19#27904C211yesmaximal, characteristic, complemented
20#27895C211yesmaximal, characteristic, complemented
21#27884C211yesmaximal, characteristic, complemented
22#27876C211yesmaximal, characteristic, complemented
23#25684C211yesmaximal, characteristic, complemented
24#25679C211yesmaximal, characteristic, complemented
25#25610C211yesmaximal, characteristic, complemented
26#25601C211yesmaximal, characteristic, complemented
27#22203C211yesmaximal, characteristic, complemented
28#22199C211yesmaximal, characteristic, complemented
29#22195C211yesmaximal, characteristic, complemented
30#22194C211yesmaximal, characteristic, complemented
31#20379C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C2×#501C2211yescharacteristic, complemented
36C2×#495C2211yescharacteristic, complemented
37C2×#489C2211yescharacteristic, complemented
38C2×#488C2211yescharacteristic, complemented
39C2×#470C2211yescharacteristic
40C2×#469C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#407C2211yescharacteristic
44C22×C22⋊C8C2211yescharacteristic
45C2×#405C2211yescharacteristic
46C2×#405C2211yescharacteristic
47#2857C2211yescharacteristic
48#2855C2211yescharacteristic
49#2854C2211yescharacteristic
50#2850C2211yescharacteristic
51#2848C2211yescharacteristic
52#2848C2211yescharacteristic
53#2847C2211yescharacteristic
54#2847C2211yescharacteristic
55#2629C2211yescharacteristic
56#2629C2211yescharacteristic
57#2628C2211yescharacteristic
58#2625C2211yescharacteristic
59#2624C2211yescharacteristic
60#2620C2211yescharacteristic
61#2620C2211yescharacteristic
62#2620C2211yescharacteristic
63#2609—21no—
64#2609—21no—
65#2601—21no—
66#2601—21no—
67#2579—21no—
68#2534—21no—
69#2481—21no—
70#2479—21no—
71#2477—21no—
72#2474—21no—
73#2472—21no—
74#2470—21no—
75#2449—21no—
76#2418—21no—
77#2413—21no—
78#2411—21no—
79#2324C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic
82#2323C2211yescharacteristic
83#2323C2211yescharacteristic
84#2323C2211yescharacteristic
85#2314C2211yescharacteristic
86C4×C22⋊Q8C2211yescharacteristic
87C4×#121C2211yescharacteristic
88#2285C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2036C2211yescharacteristic
98#2036C2211yescharacteristic
99#2036C2211yescharacteristic
100#2036C2211yescharacteristic
101#2035C2211yescharacteristic
102#2035C2211yescharacteristic
103#2035C2211yescharacteristic
104#2035C2211yescharacteristic
105#2034C2211yescharacteristic
106#2034C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2001C2211yescharacteristic
114#2001C2211yescharacteristic
115#2000C2211yescharacteristic
116#2000C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#1999C2211yescharacteristic
120#1999C2211yescharacteristic
121#1992C2211yescharacteristic, complemented
122#1991C2211yescharacteristic, complemented
123#1990C2211yescharacteristic, complemented
124#1990C2211yescharacteristic, complemented
125#1972C2211yescharacteristic, complemented
126#1971C2211yescharacteristic, complemented
127#1968C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1959C2211yescharacteristic, complemented
130#1959C2211yescharacteristic, complemented
131#1959C2211yescharacteristic, complemented
132#1958C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1941C2211yescharacteristic, complemented
137#1936C2211yescharacteristic, complemented
138#1936C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1935C2211yescharacteristic, complemented
141#1934C2211yescharacteristic, complemented
142#1934C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1925C2211yescharacteristic, complemented
152#1925C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic, complemented
172#1879C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic, complemented
176#1877C2211yescharacteristic, complemented
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1847C2211yescharacteristic, complemented
186#1844C2211yescharacteristic, complemented
187#1836C2211yescharacteristic, complemented
188#1834C2211yescharacteristic, complemented
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1808C2211yescharacteristic
192#1807C2211yescharacteristic
193#1750C2211yescharacteristic
194#1750C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1749C2211yescharacteristic
199C4×C22⋊C8C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#542—42no—
213#542—42no—
214C2×C4⋊Q8C2311yescharacteristic
215#529—42no—
216#529—42no—
217C2×#126—21no—
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117—21no—
249C2×#117—21no—
250C2×#117—42no—
251C2×#117—42no—
252C2×#117D411yescharacteristic
253C2×#117D411yescharacteristic
254C2×#117D411yescharacteristic
255C2×#117D411yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4D411yescharacteristic
261C22×C4⋊C4D411yescharacteristic
262C22×C22⋊C4D411yescharacteristic
263C22×C22⋊C4D411yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266#501—42no—
267#495—42no—
268#489—42no—
269#488—42no—
270#470—24no—
271#469—24no—
272#465—24no—
273#465—24no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310#407—24no—
311C2×C22⋊C8—24no—
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320#405—42no—
321#405—42no—
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#393—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#390—21no—
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
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#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#382—21no—
438#382C2311yescharacteristic
439#381—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
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#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
496C25C2×D411yescharacteristic
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—41no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2×D411yescharacteristic
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×Q16—22no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16#4114yes—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8#4114yes—
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C4⋊Q8—22no—
559C4⋊Q8—22no—
560#126—44no—
561#126—44no—
562#125—22no—
563#125—22no—
564#124—22no—
565#124—22no—
566#124—22no—
567#124—22no—
568#124—44no—
569#123—44no—
570#123—44no—
571#123—82no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—44no—
585C22⋊Q8—82no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#120—82no—
599#120—82no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4—82no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—42no—
619#117—42no—
620#117—42no—
621#117—42no—
622#117—44no—
623#117—82no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—42no—
650C2×C4⋊C4—42no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
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—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—42no—
710C2×C22⋊C4—42no—
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—22no—
720C2×C42—22no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42C2×D411yescharacteristic
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#106—22no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747#106—41no—
748#106—41no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—22no—
781#97—22no—
782#97—22no—
783#97—41no—
784#97—41no—
785C4×C8—22no—
786C4×C8—22no—
787C4×C8—41no—
788C4×C8—41no—
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—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823C24—22no—
824C24—22no—
825C24—21no—
826C24—21no—
827C24—41no—
828C24—41no—
829C24—41no—
830C24—41no—
831C24—41no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—42no—
848C2×Q8—81no—
849C2×Q8—81no—
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—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
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—22no—
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—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
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×C4C2×#4112yes—
953C22×C4C2×#4112yes—
954C22×C4C2511yescharacteristic
955Q16—82no—
956SD16—82no—
957SD16—82no—
958D8—82no—
959M16—44no—
960M16—44no—
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—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—44no—
982C2×C8—44no—
983C2×C8C2×#4112yes—
984C2×C8C2×#4112yes—
985C2×C8C2×#4112yes—
986C2×C8C2×#4112yes—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
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—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—22no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
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—
1090C42—22no—
1091C42—22no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—41no—
1099C42—41no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42H(5,𝔽2)12yes—
1107C42H(5,𝔽2)12yes—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—44no—
1128C23—44no—
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—82no—
1144C23—82no—
1145C23—82no—
1146C23—82no—
1147C23—82no—
1148C23#53212yes—
1149C23#57712yes—
1150C23C23×D411yescharacteristic
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—162no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—84no—
1169D4—84no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—44no—
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—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—82no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—162no—
1267C2×C4#53212yes—
1268C2×C4#53412yes—
1269C2×C4#53412yes—
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—22no—
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—88no—
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—
1320C22C2×#53211yescharacteristic
1321C22C2×#53411yescharacteristic
1322C22#344911yescharacteristic
1323C22C2×#57711yescharacteristic
1324C22#358411yescharacteristic
1325C22#358511yescharacteristic
1326C22#358611yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4#350511yescharacteristic
1353C4#350511yescharacteristic
1354C4#350611yescharacteristic
1355C4#350611yescharacteristic
1356C2—42no—
1357C2—42no—
1358C2—81no—
1359C2—161no—
1360C2—161no—
1361C2#3503211yescharacteristic
1362C2#6070611yescharacteristic
1363C2#6070911yescharacteristic
1364C2#6076511yescharacteristic
1365C2#6076611yescharacteristic
1366C2#6097711yescharacteristic
1367C2#6098511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#29742C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35302C2semidirect
2. #35260C2semidirect
3. #33219C2semidirect
4. #33181C2semidirect
5. #33054C2semidirect
6. #33047C2semidirect
7. #29743C2semidirect
9. #29735C2semidirect
10. #29734C2semidirect
11. #29486C2semidirect
12. #29485C2semidirect
13. #29479C2semidirect
14. #29476C2semidirect
15. #29475C2semidirect
16. #29472C2semidirect
17. #29467C2semidirect
18. #29464C2semidirect
19. #27904C2semidirect
20. #27895C2semidirect
21. #27884C2semidirect
22. #27876C2semidirect
23. #25684C2semidirect
24. #25679C2semidirect
25. #25610C2semidirect
26. #25601C2semidirect
27. #22203C2semidirect
28. #22199C2semidirect
29. #22195C2semidirect
30. #22194C2semidirect
31. #20379C2semidirect
35. C2×#501C22semidirect
36. C2×#495C22semidirect
37. C2×#489C22semidirect
38. C2×#488C22semidirect
121. #1992C22semidirect
122. #1991C22semidirect
123. #1990C22semidirect
124. #1990C22semidirect
125. #1972C22semidirect
126. #1971C22semidirect
127. #1968C22semidirect
128. #1968C22semidirect
129. #1959C22semidirect
130. #1959C22semidirect
131. #1959C22semidirect
132. #1958C22semidirect
133. #1944C22semidirect
134. #1943C22semidirect
135. #1942C22semidirect
136. #1941C22semidirect
137. #1936C22semidirect
138. #1936C22semidirect
139. #1935C22semidirect
140. #1935C22semidirect
141. #1934C22semidirect
142. #1934C22semidirect
143. #1933C22semidirect
144. #1933C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
147. #1927C22semidirect
148. #1927C22semidirect
149. #1926C22semidirect
150. #1925C22semidirect
151. #1925C22semidirect
152. #1925C22semidirect
153. #1920C22semidirect
154. #1920C22semidirect
155. #1919C22semidirect
156. #1919C22semidirect
157. #1919C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
171. #1879C22semidirect
172. #1879C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
175. #1877C22semidirect
176. #1877C22semidirect
177. #1865C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
184. #1862C22semidirect
185. #1847C22semidirect
186. #1844C22semidirect
187. #1836C22semidirect
188. #1834C22semidirect

Maximal subgroups

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

subgroupindex
#353022
#352602
#332192
#331812
#330542
#330472
#297432
#297422
#297352
#297342
#294862
#294852
#294792
#294762
#294752
#294722
#294672
#294642
#279042
#278952
#278842
#278762
#256842
#256792
#256102
#256012
#222032
#221992
#221952
#221942
#203792