Finite Group Databasebeta

← #7576561

Subgroups — #7576561

Order 512.

1785 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59562C211yesmaximal, characteristic, complemented
2#36457C211yesmaximal, characteristic, complemented
3#32623C211yesmaximal, characteristic, complemented
4#32606C211yesmaximal, characteristic, complemented
5#32277C211yesmaximal, characteristic, complemented
6#31261C211yesmaximal, characteristic, complemented
7#29558C211yesmaximal, characteristic, complemented
8#29552C211yesmaximal, characteristic, complemented
9#28984C211yesmaximal, characteristic, complemented
10#28975C211yesmaximal, characteristic, complemented
11#28091C211yesmaximal, characteristic, complemented
12#28074C211yesmaximal, characteristic, complemented
13#27548C211yesmaximal, characteristic, complemented
14#27532C211yesmaximal, characteristic, complemented
15#27243C211yesmaximal, characteristic, complemented
16#27222C211yesmaximal, characteristic, complemented
17#26812C211yesmaximal, characteristic, complemented
18#26797C211yesmaximal, characteristic, complemented
19#24912C211yesmaximal, characteristic, complemented
20#24896C211yesmaximal, characteristic, complemented
21#24341C211yesmaximal, characteristic, complemented
22#24329C211yesmaximal, characteristic, complemented
23#24034C211yesmaximal, characteristic, complemented
24#23869C211yesmaximal, characteristic
25#23270C211yesmaximal, characteristic, complemented
26#22877C211yesmaximal, characteristic, complemented
27#22857C211yesmaximal, characteristic, complemented
28#22443C211yesmaximal, characteristic, complemented
29#22443C211yesmaximal, characteristic, complemented
30#21124C211yesmaximal, characteristic, complemented
31#21115C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×Q82C2211yescharacteristic, complemented
34C2×#550C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44C2×C4×SD16C2211yescharacteristic
45C2×#416C2211yescharacteristic, complemented
46#2858—21no—
47#2858C2211yescharacteristic, complemented
48#2778—21no—
49#2735—21no—
50#2580C2211yescharacteristic
51#2576—21no—
52#2563—21no—
53#2563C2211yescharacteristic
54#2548—21no—
55#2548C2211yescharacteristic, complemented
56#2538C2211yescharacteristic
57#2497C2211yescharacteristic
58#2494C2211yescharacteristic
59#2491—21no—
60#2491—21no—
61#2491—21no—
62#2491—21no—
63#2491C2211yescharacteristic
64#2491C2211yescharacteristic
65#2491C2211yescharacteristic, complemented
66#2491C2211yescharacteristic, complemented
67#2485C2211yescharacteristic
68#2477—21no—
69#2472—21no—
70#2471—21no—
71#2422C2211yescharacteristic
72#2420C2211yescharacteristic
73#2411—21no—
74#2408C2211yescharacteristic
75#2363C2211yescharacteristic
76#2363C2211yescharacteristic
77#2342—21no—
78#2341C2211yescharacteristic
79#2341C2211yescharacteristic
80#2341C2211yescharacteristic, complemented
81#2341C2211yescharacteristic, complemented
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×#124—21no—
85C4×#124C2211yescharacteristic
86#2293C2211yescharacteristic
87#2293C2211yescharacteristic
88C42×Q8C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2092C2211yescharacteristic, complemented
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic, complemented
95#2075C2211yescharacteristic
96#2075C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic, complemented
99#2065C2211yescharacteristic, complemented
100#2065C2211yescharacteristic, complemented
101#2058C2211yescharacteristic, complemented
102#2058C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2041C2211yescharacteristic, complemented
108#2041C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2011C2211yescharacteristic
118#2011C2211yescharacteristic
119#1999C2211yescharacteristic
120#1999C2211yescharacteristic
121#1993C2211yescharacteristic, complemented
122#1990C2211yescharacteristic, complemented
123#1985C2211yescharacteristic, complemented
124#1984C2211yescharacteristic, complemented
125#1972C2211yescharacteristic
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1970C2211yescharacteristic
129#1970C2211yescharacteristic
130#1970C2211yescharacteristic
131#1936C2211yescharacteristic, complemented
132#1936C2211yescharacteristic, complemented
133#1936C2211yescharacteristic, complemented
134#1934C2211yescharacteristic, complemented
135#1934C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic, complemented
141#1926C2211yescharacteristic, complemented
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1924C2211yescharacteristic
146#1924C2211yescharacteristic, complemented
147#1923C2211yescharacteristic
148#1923C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic, complemented
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1870C2211yescharacteristic
172#1869C2211yescharacteristic
173#1865C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1854C2211yescharacteristic, complemented
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1805C2211yescharacteristic, complemented
184#1803C2211yescharacteristic, complemented
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic, complemented
189#1786C2211yescharacteristic
190#1786C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195C4×#103C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1745C2211yescharacteristic, complemented
202#1744C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—24no—
208C2×AGL(1,ℤ/8)—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217Q82—42no—
218Q82—42no—
219#550—42no—
220#550—42no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#127—21no—
228C2×#127C2311yescharacteristic
229C2×#124—21no—
230C2×#124—21no—
231C2×#124—21no—
232C2×#124—21no—
233C2×#124—21no—
234C2×#124—21no—
235C2×#124—21no—
236C2×#124D411yescharacteristic
237C2×#123—21no—
238C2×C22⋊Q8—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#120—21no—
246C2×C4×Q8—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117—21no—
261C2×#117C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264#482—42no—
265#476—42no—
266#474—42no—
267#449—24no—
268#449—24no—
269#447—42no—
270#440—24no—
271#440—42no—
272C4×SD16—24no—
273C4×SD16—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286#416—42no—
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#400—21no—
329#399—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#392—21no—
355#391D411yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390D411yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
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#388—21no—
403#388—21no—
404#388D411yescharacteristic
405#388D411yescharacteristic
406#388D411yescharacteristic
407#388D411yescharacteristic
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384C2311yescharacteristic
422#382—21no—
423#382D411yescharacteristic
424#382C2311yescharacteristic
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C43—21no—
463C43C2311yescharacteristic
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#336C2311yescharacteristic
485#336C2311yescharacteristic
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—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—21no—
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C2×D411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542AGL(1,ℤ/8)—416no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16#4114yes—
548C2×SD16#4114yes—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—22no—
562C2×M16—22no—
563C2×M16—41no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—22no—
576C4⋊Q8—22no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580C4⋊Q8—41no—
581C4⋊Q8—44no—
582C4⋊Q8—44no—
583C4⋊Q8—44no—
584#127—41no—
585#127—41no—
586#127—44no—
587#124—42no—
588#124—44no—
589#124—82no—
590#124—82no—
591#124—82no—
592#124—82no—
593#124—82no—
594#124—82no—
595#123—82no—
596C22⋊Q8—82no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—44no—
606#121—44no—
607#120—82no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—44no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—44no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632#117—41no—
633#117—41no—
634#117—82no—
635#117—82no—
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⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—44no—
713C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—41no—
747#107—41no—
748#106—22no—
749#106—22no—
750#106—41no—
751#106—41no—
752#106—41no—
753#106—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790#97—22no—
791#97—41no—
792#97—41no—
793C4×C8—22no—
794C4×C8—41no—
795C4×C8—41no—
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#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—42no—
830C24—42no—
831C24—42no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838#41—44no—
839#41—44no—
840#41—82no—
841#41—82no—
842#41—82no—
843#41—82no—
844#41—82no—
845#41—82no—
846C2×Q8—22no—
847C2×Q8—22no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—41no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—42no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8C2×#4112yes—
862C2×Q8C2×#4112yes—
863C2×Q8H(5,𝔽2)12yes—
864C2×D4—22no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—44no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4C2×#4112yes—
921C2×D4C2×#4112yes—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C2511yescharacteristic
977SD16—28no—
978SD16—28no—
979D8—44no—
980D8—44no—
981D8—82no—
982D8—82no—
983M16—44no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—82no—
1007C2×C8C2×#4112yes—
1008C2×C8C2×#4112yes—
1009C4⋊C4—24no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4H(5,𝔽2)12yes—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
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—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C42—24no—
1107C42—22no—
1108C42—22no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—41no—
1120C42—41no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—81no—
1129C42—81no—
1130C42—81no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—84no—
1174C23—84no—
1175C23—84no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23C23×D411yescharacteristic
1181Q8—22no—
1182Q8—22no—
1183Q8—22no—
1184Q8—44no—
1185Q8—162no—
1186Q8—162no—
1187Q8—162no—
1188Q8#55114yes—
1189D4—22no—
1190D4—22no—
1191D4—22no—
1192D4—22no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—82no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209D4—84no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—84no—
1295C2×C4—84no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4#57512yes—
1299C2×C4#57612yes—
1300C2×C4#57712yes—
1301C2×C4C22×#4111yescharacteristic
1302C2×C4C22×#4111yescharacteristic
1303C2×C4C2×H(5,𝔽2)11yescharacteristic
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4#58511yescharacteristic
1306C2×C4#58511yescharacteristic
1307C8—22no—
1308C8—22no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C22—42no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—42no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—168no—
1358C22D4×#4111yescharacteristic
1359C22D4×#4111yescharacteristic
1360C22#348411yescharacteristic
1361C22C2×#57511yescharacteristic
1362C22C2×#57611yescharacteristic
1363C22C2×#57711yescharacteristic
1364C22#358511yescharacteristic
1365C4—24no—
1366C4—22no—
1367C4—22no—
1368C4—22no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—42no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4C2×#55111yescharacteristic
1390C4#351411yescharacteristic
1391C4#351411yescharacteristic
1392C4#354511yescharacteristic
1393C2—81no—
1394C2—81no—
1395C2—82no—
1396C2—82no—
1397C2—161no—
1398C2—161no—
1399C2#5916211yescharacteristic
1400C2#6144911yescharacteristic
1401C2#6145911yescharacteristic
1402C2#6149811yescharacteristic
1403C2#6155411yescharacteristic
1404C2#6159411yescharacteristic
1405C2#6168811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23869C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59562C2semidirect
2. #36457C2semidirect
3. #32623C2semidirect
4. #32606C2semidirect
5. #32277C2semidirect
6. #31261C2semidirect
7. #29558C2semidirect
8. #29552C2semidirect
9. #28984C2semidirect
10. #28975C2semidirect
11. #28091C2semidirect
12. #28074C2semidirect
13. #27548C2semidirect
14. #27532C2semidirect
15. #27243C2semidirect
16. #27222C2semidirect
17. #26812C2semidirect
18. #26797C2semidirect
19. #24912C2semidirect
20. #24896C2semidirect
21. #24341C2semidirect
22. #24329C2semidirect
23. #24034C2semidirect
25. #23270C2semidirect
26. #22877C2semidirect
27. #22857C2semidirect
28. #22443C2semidirect
29. #22443C2semidirect
30. #21124C2semidirect
31. #21115C2semidirect
33. C2×Q82C22semidirect
35. C2×#482C22semidirect
45. C2×#416C22semidirect
47. #2858C22semidirect
55. #2548C22semidirect
65. #2491C22semidirect
66. #2491C22semidirect
80. #2341C22semidirect
81. #2341C22semidirect
88. C42×Q8C22semidirect
89. #2094C22semidirect
90. #2092C22semidirect
94. #2077C22semidirect
96. #2075C22semidirect
97. #2073C22semidirect
98. #2071C22semidirect
99. #2065C22semidirect
100. #2065C22semidirect
101. #2058C22semidirect
102. #2058C22semidirect
103. #2057C22semidirect
104. #2057C22semidirect
107. #2041C22semidirect
108. #2041C22semidirect
121. #1993C22semidirect
122. #1990C22semidirect
123. #1985C22semidirect
124. #1984C22semidirect
131. #1936C22semidirect
132. #1936C22semidirect
133. #1936C22semidirect
134. #1934C22semidirect
135. #1934C22semidirect
136. #1934C22semidirect
140. #1926C22semidirect
141. #1926C22semidirect
143. #1925C22semidirect
144. #1925C22semidirect
146. #1924C22semidirect
148. #1923C22semidirect
149. #1921C22semidirect
150. #1919C22semidirect
151. #1919C22semidirect
152. #1918C22semidirect
156. #1893C22semidirect
173. #1865C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
179. #1854C22semidirect
180. #1854C22semidirect
183. #1805C22semidirect
184. #1803C22semidirect
188. #1788C22semidirect
191. #1776C22semidirect
192. C4×#106C22semidirect
193. #1763C22semidirect
195. C4×#103C22semidirect
199. #1752C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1745C22semidirect
202. #1744C22semidirect

Maximal subgroups

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

subgroupindex
#595622
#364572
#326232
#326062
#322772
#312612
#295582
#295522
#289842
#289752
#280912
#280742
#275482
#275322
#272432
#272222
#268122
#267972
#249122
#248962
#243412
#243292
#240342
#238692
#232702
#228772
#228572
#224432
#211242
#211152