Finite Group Databasebeta

← #6477975

Subgroups — #6477975

Order 512.

1915 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35005C211yesmaximal, characteristic, complemented
2#34136C211yesmaximal, characteristic, complemented
3#32981C211yesmaximal, characteristic, complemented
4#32980C211yesmaximal, characteristic, complemented
5#32958C211yesmaximal, characteristic, complemented
6#32904C211yesmaximal, characteristic, complemented
7#29970C211yesmaximal, characteristic, complemented
8#29758C211yesmaximal, characteristic, complemented
9#29600C211yesmaximal, characteristic, complemented
10#29600C211yesmaximal, characteristic, complemented
11#27122C211yesmaximal, characteristic, complemented
12#27118C211yesmaximal, characteristic, complemented
13#27098C211yesmaximal, characteristic, complemented
14#27094C211yesmaximal, characteristic, complemented
15#26954C211yesmaximal, characteristic, complemented
16#26950C211yesmaximal, characteristic, complemented
17#26930C211yesmaximal, characteristic, complemented
18#26926C211yesmaximal, characteristic, complemented
19#26805C211yesmaximal, characteristic, complemented
20#26801C211yesmaximal, characteristic, complemented
21#26797C211yesmaximal, characteristic, complemented
22#26793C211yesmaximal, characteristic, complemented
23#26677C211yesmaximal, characteristic, complemented
24#26673C211yesmaximal, characteristic, complemented
25#26669C211yesmaximal, characteristic, complemented
26#26665C211yesmaximal, characteristic, complemented
27#22051C211yesmaximal, characteristic, complemented
28#22045C211yesmaximal, characteristic, complemented
29#21904C211yesmaximal, characteristic, complemented
30#21582C211yesmaximal, characteristic, complemented
31C4×#482C211yesmaximal, characteristic, complemented
32C2×#538—21no—
33C2×#525C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#481C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#482C2211yescharacteristic
41C2×#480C2211yescharacteristic
42C2×#477C2211yescharacteristic, complemented
43C2×#476C2211yescharacteristic, complemented
44C2×#460C2211yescharacteristic, complemented
45C2×#459C2211yescharacteristic, complemented
46C2×#449C2211yescharacteristic
47C2×#449C2211yescharacteristic
48#2857C2211yescharacteristic
49#2856C2211yescharacteristic
50#2847C2211yescharacteristic
51#2847C2211yescharacteristic
52#2639—21no—
53#2617—21no—
54#2559—21no—
55#2559—21no—
56#2557—21no—
57#2557—21no—
58#2496C2211yescharacteristic
59#2496C2211yescharacteristic
60#2491C2211yescharacteristic
61#2491C2211yescharacteristic
62#2428C2211yescharacteristic
63#2428C2211yescharacteristic
64#2422C2211yescharacteristic
65#2422C2211yescharacteristic
66#2363C2211yescharacteristic
67#2363C2211yescharacteristic
68#2362C2211yescharacteristic
69#2362C2211yescharacteristic
70#2361C2211yescharacteristic
71#2361C2211yescharacteristic
72#2360C2211yescharacteristic
73#2360C2211yescharacteristic
74#2359—21no—
75#2359—21no—
76#2358—21no—
77#2358—21no—
78#2325—21no—
79C4×#121C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2297C2211yescharacteristic
82#2296C2211yescharacteristic
83#2293—21no—
84#2290—21no—
85#2290—21no—
86C42×D4—21no—
87C4×#117C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic
89#2100C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2086C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2067C2211yescharacteristic, complemented
98#2067C2211yescharacteristic, complemented
99#2065C2211yescharacteristic, complemented
100#2065C2211yescharacteristic, complemented
101#2058C2211yescharacteristic, complemented
102#2057C2211yescharacteristic, complemented
103#2041C2211yescharacteristic, complemented
104#2041C2211yescharacteristic, complemented
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2000C2211yescharacteristic
114#2000C2211yescharacteristic
115#2000C2211yescharacteristic
116#2000C2211yescharacteristic
117#1999C2211yescharacteristic
118#1999C2211yescharacteristic
119#1999C2211yescharacteristic
120#1999C2211yescharacteristic
121#1973C2211yescharacteristic, complemented
122#1972C2211yescharacteristic, complemented
123#1970C2211yescharacteristic, complemented
124#1968C2211yescharacteristic, complemented
125#1936C2211yescharacteristic, complemented
126#1935C2211yescharacteristic, complemented
127#1934C2211yescharacteristic, complemented
128#1933C2211yescharacteristic, complemented
129#1928C2211yescharacteristic, complemented
130#1927C2211yescharacteristic, complemented
131#1926C2211yescharacteristic, complemented
132#1926C2211yescharacteristic, complemented
133#1926C2211yescharacteristic, complemented
134#1925C2211yescharacteristic, complemented
135#1925C2211yescharacteristic, complemented
136#1925C2211yescharacteristic, complemented
137#1924C2211yescharacteristic
138#1924C2211yescharacteristic
139#1924C2211yescharacteristic
140#1924C2211yescharacteristic
141#1923C2211yescharacteristic
142#1923C2211yescharacteristic
143#1923C2211yescharacteristic
144#1923C2211yescharacteristic
145#1921C2211yescharacteristic, complemented
146#1920C2211yescharacteristic, complemented
147#1919C2211yescharacteristic, complemented
148#1918C2211yescharacteristic, complemented
149#1880C2211yescharacteristic, complemented
150#1880C2211yescharacteristic, complemented
151#1879C2211yescharacteristic, complemented
152#1879C2211yescharacteristic, complemented
153#1879C2211yescharacteristic, complemented
154#1879C2211yescharacteristic, complemented
155#1877C2211yescharacteristic, complemented
156#1877C2211yescharacteristic, complemented
157#1875C2211yescharacteristic
158#1875C2211yescharacteristic
159#1875C2211yescharacteristic
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1865C2211yescharacteristic, complemented
166#1865C2211yescharacteristic, complemented
167#1862C2211yescharacteristic, complemented
168#1862C2211yescharacteristic, complemented
169#1854C2211yescharacteristic
170#1854C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1824C2211yescharacteristic
182#1823C2211yescharacteristic
183#1803C2211yescharacteristic, complemented
184#1803C2211yescharacteristic, complemented
185#1802C2211yescharacteristic, complemented
186#1802C2211yescharacteristic, complemented
187#1797C2211yescharacteristic
188#1797C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1779C2211yescharacteristic
192#1779C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196C4×#106C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#538—48no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#124—21no—
215C2×#124—21no—
216#525—24no—
217#525—24no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121—21no—
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C4×#41—42no—
240C4×#41—42no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×#117—21no—
256C2×#117—21no—
257C2×#117—21no—
258C2×#117—42no—
259C2×#117—42no—
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—21no—
268C22×C22⋊C4D411yescharacteristic
269C22×C22⋊C4D411yescharacteristic
270C22×C42—21no—
271C22×C42—21no—
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274#482—24no—
275#482—24no—
276#482—42no—
277#482—42no—
278#481—42no—
279#480—42no—
280#477—42no—
281#476—42no—
282#460—42no—
283#459—42no—
284#449—24no—
285#449—24no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×#106C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299C2×C4⋊C8C2311yescharacteristic
300C2×C4⋊C8C2311yescharacteristic
301C2×C4⋊C8C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×C22⋊C8C2311yescharacteristic
337C2×C22⋊C8C2311yescharacteristic
338C2×#97C2311yescharacteristic
339C2×#97C2311yescharacteristic
340C2×C4×C8C2311yescharacteristic
341C2×C4×C8C2311yescharacteristic
342#400—21no—
343#400—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#392—21no—
357#392—21no—
358#391—21no—
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
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#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#380—21no—
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4D411yescharacteristic
454C4×C22⋊C4D411yescharacteristic
455C4×C22⋊C4D411yescharacteristic
456C4×C22⋊C4D411yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462C2×#95D411yescharacteristic
463C2×#95D411yescharacteristic
464C43—21no—
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#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497C25C2×D411yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41#4114yes—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
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×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—22no—
522C23×C4—22no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4—41no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565#127—41no—
566#127—41no—
567#126—44no—
568#126—44no—
569#124—44no—
570#124—44no—
571#123—28no—
572#123—44no—
573#123—44no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—44no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—44no—
588#121—44no—
589#121—44no—
590#121—44no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#120—28no—
600#120—44no—
601#120—44no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×D4—28no—
607C4×D4—28no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4—44no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—22no—
627#117—44no—
628#117—44no—
629#117—44no—
630#117—41no—
631#117—41no—
632#117—41no—
633#117—41no—
634#117#4114yes—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
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—41no—
657C2×C4⋊C4—41no—
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×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
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—24no—
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—42no—
709C2×C22⋊C4—44no—
710C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—41no—
732C2×C42—41no—
733C2×C42—41no—
734C2×C42—41no—
735C2×C42—44no—
736C2×C42—44no—
737C2×C42C2×D411yescharacteristic
738C2×C42C2×D411yescharacteristic
739C2×C42C2×D411yescharacteristic
740C2×C42C2×D411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#107—22no—
746#107—22no—
747#107—22no—
748#107—22no—
749#107—41no—
750#107—41no—
751#106—22no—
752#106—22no—
753#106—22no—
754#106—22no—
755#106—41no—
756#106—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—22no—
788C22⋊C8—22no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797#97—41no—
798#97—41no—
799C4×C8—41no—
800C4×C8—41no—
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—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—22no—
835C24—22no—
836C24—21no—
837C24—21no—
838C24—41no—
839C24—41no—
840C24—41no—
841C24—41no—
842C24—41no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846#41—44no—
847#41—44no—
848#41—44no—
849#41—44no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—42no—
856C2×Q8—81no—
857C2×Q8—81no—
858C2×Q8C2×#4112yes—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—24no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
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—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4C2×#4112yes—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—22no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—24no—
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—22no—
936C22×C4—22no—
937C22×C4—22no—
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—41no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—41no—
955C22×C4—41no—
956C22×C4—41no—
957C22×C4—41no—
958C22×C4—41no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C2×#4112yes—
997C22×C4C2×#4112yes—
998C22×C4C2511yescharacteristic
999SD16—82no—
1000SD16—82no—
1001D8—82no—
1002D8—82no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4C2×#4112yes—
1067C4⋊C4C2×#4112yes—
1068C4⋊C4H(5,𝔽2)12yes—
1069C4⋊C4H(5,𝔽2)12yes—
1070C22⋊C4—24no—
1071C22⋊C4—24no—
1072C22⋊C4—24no—
1073C22⋊C4—24no—
1074C22⋊C4—24no—
1075C22⋊C4—24no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4AGL(1,ℤ/8)14yes—
1115C42—24no—
1116C42—24no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—41no—
1126C42—41no—
1127C42—41no—
1128C42—41no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—81no—
1139C42—81no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—22no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—44no—
1161C23—44no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—82no—
1183C23—82no—
1184C23—82no—
1185C23—82no—
1186C23—82no—
1187C23#52512yes—
1188C23C2×AGL(1,ℤ/8)12yes—
1189C23C23×D411yescharacteristic
1190Q8—22no—
1191Q8—22no—
1192Q8—41no—
1193Q8—41no—
1194Q8—162no—
1195D4—22no—
1196D4—22no—
1197D4—48no—
1198D4—48no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—84no—
1210D4—84no—
1211D4—84no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
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—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—44no—
1257C2×C4—44no—
1258C2×C4—48no—
1259C2×C4—44no—
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—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—82no—
1303C2×C4—82no—
1304C2×C4—82no—
1305C2×C4—84no—
1306C2×C4—84no—
1307C2×C4—82no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4#52512yes—
1313C2×C4C2×AGL(1,ℤ/8)12yes—
1314C2×C4C2×AGL(1,ℤ/8)12yes—
1315C2×C4#57512yes—
1316C2×C4C22×#4111yescharacteristic
1317C2×C4C22×#4111yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4#58511yescharacteristic
1321C2×C4#58511yescharacteristic
1322C8—41no—
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—42no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—42no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—88no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22C2×#52511yescharacteristic
1374C22#348411yescharacteristic
1375C22#348511yescharacteristic
1376C22C22×AGL(1,ℤ/8)11yescharacteristic
1377C22C2×#57511yescharacteristic
1378C22#358411yescharacteristic
1379C22#358411yescharacteristic
1380C4—22no—
1381C4—22no—
1382C4—22no—
1383C4—22no—
1384C4—41no—
1385C4—41no—
1386C4—42no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—42no—
1391C4—42no—
1392C4—41no—
1393C4—42no—
1394C4—41no—
1395C4—42no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4#346011yescharacteristic
1405C4#346011yescharacteristic
1406C4#350511yescharacteristic
1407C4#350511yescharacteristic
1408C2—42no—
1409C2—42no—
1410C2—81no—
1411C2—82no—
1412C2—161no—
1413C2—161no—
1414C2#3509111yescharacteristic
1415C2#6055711yescharacteristic
1416C2#6056111yescharacteristic
1417C2#6159811yescharacteristic
1418C2#6160611yescharacteristic
1419C2#6173311yescharacteristic
1420C2#6173411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35005C2semidirect
2. #34136C2semidirect
3. #32981C2semidirect
4. #32980C2semidirect
5. #32958C2semidirect
6. #32904C2semidirect
7. #29970C2semidirect
8. #29758C2semidirect
9. #29600C2semidirect
10. #29600C2semidirect
11. #27122C2semidirect
12. #27118C2semidirect
13. #27098C2semidirect
14. #27094C2semidirect
15. #26954C2semidirect
16. #26950C2semidirect
17. #26930C2semidirect
18. #26926C2semidirect
19. #26805C2semidirect
20. #26801C2semidirect
21. #26797C2semidirect
22. #26793C2semidirect
23. #26677C2semidirect
24. #26673C2semidirect
25. #26669C2semidirect
26. #26665C2semidirect
27. #22051C2semidirect
28. #22045C2semidirect
29. #21904C2semidirect
30. #21582C2semidirect
31. C4×#482C2semidirect
42. C2×#477C22semidirect
43. C2×#476C22semidirect
44. C2×#460C22semidirect
45. C2×#459C22semidirect
89. #2100C22semidirect
90. #2100C22semidirect
91. #2088C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2086C22semidirect
95. #2084C22semidirect
96. #2083C22semidirect
97. #2067C22semidirect
98. #2067C22semidirect
99. #2065C22semidirect
100. #2065C22semidirect
101. #2058C22semidirect
102. #2057C22semidirect
103. #2041C22semidirect
104. #2041C22semidirect
121. #1973C22semidirect
122. #1972C22semidirect
123. #1970C22semidirect
124. #1968C22semidirect
125. #1936C22semidirect
126. #1935C22semidirect
127. #1934C22semidirect
128. #1933C22semidirect
129. #1928C22semidirect
130. #1927C22semidirect
131. #1926C22semidirect
132. #1926C22semidirect
133. #1926C22semidirect
134. #1925C22semidirect
135. #1925C22semidirect
136. #1925C22semidirect
145. #1921C22semidirect
146. #1920C22semidirect
147. #1919C22semidirect
148. #1918C22semidirect
149. #1880C22semidirect
150. #1880C22semidirect
151. #1879C22semidirect
152. #1879C22semidirect
153. #1879C22semidirect
154. #1879C22semidirect
155. #1877C22semidirect
156. #1877C22semidirect
165. #1865C22semidirect
166. #1865C22semidirect
167. #1862C22semidirect
168. #1862C22semidirect
183. #1803C22semidirect
184. #1803C22semidirect
185. #1802C22semidirect
186. #1802C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. C4×#107C22semidirect
196. C4×#106C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#350052
#341362
#329812
#329802
#329582
#329042
#299702
#297582
#296002
#271222
#271182
#270982
#270942
#269542
#269502
#269302
#269262
#268052
#268012
#267972
#267932
#266772
#266732
#266692
#266652
#220512
#220452
#219042
#215822
C4×#4822