Finite Group Databasebeta

← #6560179

Subgroups — #6560179

Order 512.

1718 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#38090C211yesmaximal, characteristic
2#37687C211yesmaximal, characteristic, complemented
3#30211C211yesmaximal, characteristic, complemented
4#30197C211yesmaximal, characteristic, complemented
5#30191C211yesmaximal, characteristic, complemented
6#29363C211yesmaximal, characteristic, complemented
7#29152C211yesmaximal, characteristic, complemented
8#29115C211yesmaximal, characteristic, complemented
9#29113C211yesmaximal, characteristic, complemented
10#27830C211yesmaximal, characteristic, complemented
11#27822C211yesmaximal, characteristic, complemented
12#27779C211yesmaximal, characteristic, complemented
13#27773C211yesmaximal, characteristic, complemented
14#27720C211yesmaximal, characteristic, complemented
15#27716C211yesmaximal, characteristic, complemented
16#27710C211yesmaximal, characteristic, complemented
17#27708C211yesmaximal, characteristic, complemented
18#27282C211yesmaximal, characteristic, complemented
19#27279C211yesmaximal, characteristic, complemented
20#27276C211yesmaximal, characteristic, complemented
21#27264C211yesmaximal, characteristic, complemented
22#25916C211yesmaximal, characteristic, complemented
23#25913C211yesmaximal, characteristic, complemented
24#23830C211yesmaximal, characteristic, complemented
25#23456C211yesmaximal, characteristic, complemented
26#23453C211yesmaximal, characteristic, complemented
27#22503C211yesmaximal, characteristic, complemented
28#22492C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22419C211yesmaximal, characteristic, complemented
31#20564C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C22×#125C2211yescharacteristic, complemented
36C2×#490C2211yescharacteristic
37C2×#490C2211yescharacteristic
38C2×#489C2211yescharacteristic, complemented
39C2×#488C2211yescharacteristic, complemented
40C2×#436C2211yescharacteristic
41C2×#435C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#418C2211yescharacteristic
45C22×#102C2211yescharacteristic
46#2857C2211yescharacteristic, complemented
47#2856C2211yescharacteristic
48#2726—21no—
49#2720—21no—
50#2713—21no—
51#2704—21no—
52#2676—21no—
53#2676—21no—
54#2668—21no—
55#2668—21no—
56#2660C2211yescharacteristic, complemented
57#2640C2211yescharacteristic
58#2629C2211yescharacteristic
59#2620C2211yescharacteristic
60#2552C2211yescharacteristic, complemented
61#2550C2211yescharacteristic, complemented
62#2544C2211yescharacteristic
63#2542C2211yescharacteristic
64#2500C2211yescharacteristic
65#2499C2211yescharacteristic
66#2473—21no—
67#2472—21no—
68#2472—21no—
69#2471—21no—
70#2471—21no—
71#2449—21no—
72#2442C2211yescharacteristic
73#2442C2211yescharacteristic, complemented
74#2441C2211yescharacteristic
75#2440—21no—
76#2440C2211yescharacteristic, complemented
77#2433C2211yescharacteristic
78#2431C2211yescharacteristic
79#2417—21no—
80#2352C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic
82#2330C2211yescharacteristic, complemented
83#2328C2211yescharacteristic
84#2309C2211yescharacteristic
85#2297C2211yescharacteristic
86#2290C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2074C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic, complemented
96#2072C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic, complemented
101#2042C2211yescharacteristic, complemented
102#2042C2211yescharacteristic, complemented
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2026C2211yescharacteristic, complemented
108#2026C2211yescharacteristic, complemented
109#2026C2211yescharacteristic, complemented
110#2026C2211yescharacteristic, complemented
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2025C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#2023C2211yescharacteristic, complemented
127#1993C2211yescharacteristic, complemented
128#1992C2211yescharacteristic, complemented
129#1992C2211yescharacteristic, complemented
130#1992C2211yescharacteristic, complemented
131#1990C2211yescharacteristic, complemented
132#1990C2211yescharacteristic, complemented
133#1988C2211yescharacteristic, complemented
134#1987C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1961C2211yescharacteristic
138#1959C2211yescharacteristic
139#1958C2211yescharacteristic
140#1957C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1933C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic, complemented
157#1895C2211yescharacteristic, complemented
158#1894C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1875C2211yescharacteristic
162#1874C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic, complemented
166#1874C2211yescharacteristic, complemented
167#1873C2211yescharacteristic
168#1872C2211yescharacteristic
169#1836C2211yescharacteristic, complemented
170#1835C2211yescharacteristic, complemented
171#1825C2211yescharacteristic
172#1825C2211yescharacteristic
173#1825C2211yescharacteristic, complemented
174#1825C2211yescharacteristic, complemented
175#1804C2211yescharacteristic
176#1804C2211yescharacteristic, complemented
177#1802C2211yescharacteristic
178#1802C2211yescharacteristic, complemented
179#1788C2211yescharacteristic
180#1788C2211yescharacteristic
181#1786C2211yescharacteristic
182#1786C2211yescharacteristic
183#1771C2211yescharacteristic, complemented
184#1770C2211yescharacteristic, complemented
185#1768C2211yescharacteristic, complemented
186#1762C2211yescharacteristic
187#1762C2211yescharacteristic, complemented
188C4×#102C2211yescharacteristic
189C4×#102C2211yescharacteristic, complemented
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194#1750C2211yescharacteristic
195#1749C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1736C2211yescharacteristic
198#1736C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1735C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#555—24no—
210#555—24no—
211#546—24no—
212#546—24no—
213#544—42no—
214#544—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#125—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125—42no—
225C2×#125—42no—
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×#124—21no—
232C2×#124—21no—
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×#121—21no—
244C2×#121—21no—
245C2×#121—21no—
246C2×#121—21no—
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#120—21no—
251C2×#120—21no—
252C2×#120—21no—
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4—21no—
263C22×C4⋊C4—21no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—21no—
268C22×C42C2311yescharacteristic
269#490—42no—
270#490—42no—
271#489—42no—
272#488—42no—
273#436—24no—
274#435—24no—
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277#418—42no—
278#417—42no—
279#417—42no—
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102—42no—
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#399—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
350#395—21no—
351#395—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#393—21no—
360#393—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#391—21no—
366#391—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388D411yescharacteristic
398#388D411yescharacteristic
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387D411yescharacteristic
406#387D411yescharacteristic
407#386—21no—
408#386—21no—
409#386—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#386D411yescharacteristic
419#386D411yescharacteristic
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#385D411yescharacteristic
427#384—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8C2411yescharacteristic
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C4⋊Q8—22no—
557C4⋊Q8—22no—
558C4⋊Q8—22no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—44no—
563#127—22no—
564#127—41no—
565#127—41no—
566#127—41no—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125—41no—
577#125—44no—
578#125—44no—
579#125—44no—
580#124—22no—
581#124—22no—
582#124—41no—
583#124—41no—
584#124—44no—
585#124—44no—
586#123—44no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—82no—
592C22⋊Q8—82no—
593C22⋊Q8—82no—
594C22⋊Q8—82no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—44no—
602#121—44no—
603#121—82no—
604#121—82no—
605#120—44no—
606#120—82no—
607#120—82no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—82no—
613C4×D4#4114yes—
614C4×D4#4114yes—
615#117—22no—
616#117—22no—
617#117—22no—
618#117—22no—
619#117—22no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—44no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
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—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—44no—
664C2×C4⋊C4—44no—
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
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—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
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×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C4⋊C8—22no—
737C4⋊C8—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#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774#97—22no—
775#97—41no—
776#97—41no—
777#97—41no—
778#97—41no—
779C4×C8—22no—
780C4×C8—41no—
781C4×C8—41no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816C24—21no—
817C24—21no—
818C24—21no—
819C24—42no—
820C24—42no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828#41—44no—
829#41—44no—
830#41—82no—
831#41—82no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—42no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—82no—
880C2×D4—82no—
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—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4#12414yes—
898C2×D42−1+412yes—
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—41no—
925C22×C4—41no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C2×#4112yes—
957C22×C4C2×#4112yes—
958C22×C4C2×#4112yes—
959C22×C4C2×#4112yes—
960C22×C4C2511yescharacteristic
961M16—82no—
962M16—82no—
963M16—82no—
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—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—82no—
989C4⋊C4—24no—
990C4⋊C4—24no—
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—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
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—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
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—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4#12414yes—
1049C4⋊C4H(5,𝔽2)12yes—
1050C4⋊C4H(5,𝔽2)12yes—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
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—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4#12414yes—
1089C22⋊C4#12414yes—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—41no—
1099C42—41no—
1100C42—42no—
1101C42—42no—
1102C42—42no—
1103C42—81no—
1104C42—81no—
1105C42C2×#4112yes—
1106C42C2×#4112yes—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—84no—
1141C23—84no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23C2×#12412yes—
1148C23C2×#12412yes—
1149C23C23×D411yescharacteristic
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—162no—
1155Q8—162no—
1156Q8—162no—
1157D4—22no—
1158D4—22no—
1159D4—44no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—84no—
1171D4—84no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
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—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
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—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
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—84no—
1259C2×C4—84no—
1260C2×C4—82no—
1261C2×C4—82no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4C2×#12412yes—
1267C2×C4C2×#12412yes—
1268C2×C4C2×#12412yes—
1269C2×C4C2×#12412yes—
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×2−1+411yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
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—42no—
1299C22—42no—
1300C22—42no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—168no—
1320C22C22×#12411yescharacteristic
1321C22#348411yescharacteristic
1322C22#348911yescharacteristic
1323C22#358511yescharacteristic
1324C22#358511yescharacteristic
1325C22#358511yescharacteristic
1326C22#358611yescharacteristic
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—42no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—42no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4#351411yescharacteristic
1353C4#351411yescharacteristic
1354C4#352011yescharacteristic
1355C4#352011yescharacteristic
1356C2—42no—
1357C2—42no—
1358C2—82no—
1359C2—161no—
1360C2—161no—
1361C2#3593911yescharacteristic
1362C2#6062111yescharacteristic
1363C2#6062611yescharacteristic
1364C2#6165311yescharacteristic
1365C2#6165611yescharacteristic
1366C2#6223511yescharacteristic
1367C2#6223611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38090C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37687C2semidirect
3. #30211C2semidirect
4. #30197C2semidirect
5. #30191C2semidirect
6. #29363C2semidirect
7. #29152C2semidirect
8. #29115C2semidirect
9. #29113C2semidirect
10. #27830C2semidirect
11. #27822C2semidirect
12. #27779C2semidirect
13. #27773C2semidirect
14. #27720C2semidirect
15. #27716C2semidirect
16. #27710C2semidirect
17. #27708C2semidirect
18. #27282C2semidirect
19. #27279C2semidirect
20. #27276C2semidirect
21. #27264C2semidirect
22. #25916C2semidirect
23. #25913C2semidirect
24. #23830C2semidirect
25. #23456C2semidirect
26. #23453C2semidirect
27. #22503C2semidirect
28. #22492C2semidirect
29. #22427C2semidirect
30. #22419C2semidirect
31. #20564C2semidirect
35. C22×#125C22semidirect
38. C2×#489C22semidirect
39. C2×#488C22semidirect
46. #2857C22semidirect
56. #2660C22semidirect
60. #2552C22semidirect
61. #2550C22semidirect
73. #2442C22semidirect
76. #2440C22semidirect
82. #2330C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2100C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
93. #2074C22semidirect
95. #2072C22semidirect
96. #2072C22semidirect
100. #2071C22semidirect
101. #2042C22semidirect
102. #2042C22semidirect
107. #2026C22semidirect
108. #2026C22semidirect
109. #2026C22semidirect
110. #2026C22semidirect
119. #2025C22semidirect
120. #2025C22semidirect
121. #2024C22semidirect
126. #2023C22semidirect
127. #1993C22semidirect
128. #1992C22semidirect
129. #1992C22semidirect
130. #1992C22semidirect
131. #1990C22semidirect
132. #1990C22semidirect
133. #1988C22semidirect
134. #1987C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
148. #1935C22semidirect
152. #1933C22semidirect
156. #1895C22semidirect
157. #1895C22semidirect
165. #1874C22semidirect
166. #1874C22semidirect
169. #1836C22semidirect
170. #1835C22semidirect
173. #1825C22semidirect
174. #1825C22semidirect
176. #1804C22semidirect
178. #1802C22semidirect
183. #1771C22semidirect
184. #1770C22semidirect
185. #1768C22semidirect
187. #1762C22semidirect
189. C4×#102C22semidirect
191. #1753C22semidirect
192. #1753C22semidirect
195. #1749C22semidirect
196. #1746C22semidirect
198. #1736C22semidirect
199. #1736C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#380902
#376872
#302112
#301972
#301912
#293632
#291522
#291152
#291132
#278302
#278222
#277792
#277732
#277202
#277162
#277102
#277082
#272822
#272792
#272762
#272642
#259162
#259132
#238302
#234562
#234532
#225032
#224922
#224272
#224192
#205642