Finite Group Databasebeta

← #6830346

Subgroups — #6830346

Order 512.

1573 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42956C211yesmaximal, characteristic, complemented
2#42673C211yesmaximal, characteristic
3#33056C211yesmaximal, characteristic, complemented
4#31985C211yesmaximal, characteristic, complemented
5#31981C211yesmaximal, characteristic, complemented
6#31679C211yesmaximal, characteristic, complemented
7#31678C211yesmaximal, characteristic, complemented
8#31364C211yesmaximal, characteristic, complemented
9#31362C211yesmaximal, characteristic, complemented
10#31291C211yesmaximal, characteristic, complemented
11#31287C211yesmaximal, characteristic, complemented
12#29962C211yesmaximal, characteristic, complemented
13#29764C211yesmaximal, characteristic, complemented
14#29012C211yesmaximal, characteristic, complemented
15#29008C211yesmaximal, characteristic, complemented
16#28862C211yesmaximal, characteristic, complemented
17#28858C211yesmaximal, characteristic, complemented
18#28113C211yesmaximal, characteristic, complemented
19#28111C211yesmaximal, characteristic, complemented
20#27284C211yesmaximal, characteristic, complemented
21#27284C211yesmaximal, characteristic, complemented
22#26205C211yesmaximal, characteristic, complemented
23#26201C211yesmaximal, characteristic, complemented
24#25262C211yesmaximal, characteristic, complemented
25#25256C211yesmaximal, characteristic, complemented
26#24039C211yesmaximal, characteristic, complemented
27#24038C211yesmaximal, characteristic, complemented
28#22427C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#21494C211yesmaximal, characteristic, complemented
31#21089C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#491C2211yescharacteristic, complemented
35C2×#484C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#436C2211yescharacteristic
39C2×#436C2211yescharacteristic, complemented
40C2×#417C2211yescharacteristic
41C2×#417C2211yescharacteristic
42C2×#418C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C2×#405C2211yescharacteristic
45#2839—21no—
46#2812—21no—
47#2744—21no—
48#2743—21no—
49#2724—21no—
50#2701—21no—
51#2701—21no—
52#2699—21no—
53#2695—21no—
54#2693—21no—
55#2667—21no—
56#2652—21no—
57#2629C2211yescharacteristic
58#2622—21no—
59#2622—21no—
60#2621C2211yescharacteristic
61#2553—21no—
62#2509C2211yescharacteristic, complemented
63#2508C2211yescharacteristic, complemented
64#2497C2211yescharacteristic, complemented
65#2496C2211yescharacteristic, complemented
66#2487C2211yescharacteristic
67#2487C2211yescharacteristic, complemented
68#2486C2211yescharacteristic
69#2486C2211yescharacteristic, complemented
70#2483—21no—
71#2447C2211yescharacteristic
72#2447C2211yescharacteristic
73#2442C2211yescharacteristic, complemented
74#2442C2211yescharacteristic, complemented
75#2432C2211yescharacteristic
76#2432C2211yescharacteristic
77#2420C2211yescharacteristic
78#2420C2211yescharacteristic
79#2415C2211yescharacteristic
80#2415C2211yescharacteristic
81#2407C2211yescharacteristic
82#2407C2211yescharacteristic
83#2392C2211yescharacteristic
84#2352C2211yescharacteristic
85#2352C2211yescharacteristic
86#2316C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2093C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2075C2211yescharacteristic, complemented
100#2074C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#1991C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1958C2211yescharacteristic
132#1958C2211yescharacteristic
133#1956C2211yescharacteristic, complemented
134#1955C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1941C2211yescharacteristic, complemented
137#1940C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1923C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1894C2211yescharacteristic, complemented
163#1894C2211yescharacteristic, complemented
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1873C2211yescharacteristic
169#1873C2211yescharacteristic
170#1872C2211yescharacteristic, complemented
171#1872C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1836C2211yescharacteristic, complemented
181#1824C2211yescharacteristic, complemented
182#1823C2211yescharacteristic, complemented
183#1809C2211yescharacteristic, complemented
184#1809C2211yescharacteristic, complemented
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1798C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196C8×C4⋊C4C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#546—24no—
211#546—24no—
212#546—42no—
213#546—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246#491—42no—
247#484—42no—
248#483—42no—
249#436—42no—
250#436—42no—
251#436—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264#418—42no—
265#417—42no—
266#417—42no—
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#102—24no—
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308#405—42no—
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#398D411yescharacteristic
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397D411yescharacteristic
350#396—21no—
351#396—21no—
352#396—21no—
353#396D411yescharacteristic
354#396D411yescharacteristic
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394D411yescharacteristic
366#394D411yescharacteristic
367#394D411yescharacteristic
368#392—21no—
369#392—21no—
370#392D411yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—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#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#384C2311yescharacteristic
430#382—21no—
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#381—21no—
437#381—21no—
438#381—21no—
439#381—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4#4114yes—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556#126—82no—
557#125—41no—
558#125—41no—
559#124—22no—
560#124—22no—
561#124—41no—
562#124—41no—
563#123—44no—
564#123—44no—
565#123—82no—
566#123—82no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575#121—22no—
576#121—22no—
577#121—44no—
578#121—44no—
579#121—41no—
580#121—41no—
581#120—44no—
582#120—44no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593#117—41no—
594#117—41no—
595#117—41no—
596#117—41no—
597#117—41no—
598#117—41no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—44no—
682C2×C22⋊C4—44no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715#103—22no—
716#103—22no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747C22⋊C8—22no—
748C22⋊C8—22no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754C22⋊C8—41no—
755#97—22no—
756#97—41no—
757C4×C8—22no—
758C4×C8—41no—
759C4×C8—41no—
760C4×C8—41no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—24no—
808C24—81no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817#41—44no—
818#41—44no—
819#41—82no—
820#41—82no—
821#41—82no—
822#41—82no—
823#41—82no—
824#41—82no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—24no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—44no—
851C2×D4—44no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4C2×#4112yes—
876C2×D4C2×#4112yes—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C2×#4112yes—
940C22×C4H(5,𝔽2)12yes—
941C22×C4C2511yescharacteristic
942M16—44no—
943M16—82no—
944M16—82no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—44no—
969C2×C8H(5,𝔽2)12yes—
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—22no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—22no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23#54612yes—
1124C23C23×D411yescharacteristic
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—22no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—84no—
1142D4—82no—
1143D4—82no—
1144D4—82no—
1145D4—84no—
1146D4—84no—
1147D4—162no—
1148D4—162no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4#54612yes—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—22no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—168no—
1293C22C2×#54611yescharacteristic
1294C22#349611yescharacteristic
1295C22#350011yescharacteristic
1296C22#358411yescharacteristic
1297C22#358411yescharacteristic
1298C22#358511yescharacteristic
1299C22#358611yescharacteristic
1300C4—22no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4#345911yescharacteristic
1326C4#349111yescharacteristic
1327C4#353411yescharacteristic
1328C4#356011yescharacteristic
1329C2—42no—
1330C2—81no—
1331C2—81no—
1332C2—82no—
1333C2—82no—
1334C2#3941411yescharacteristic
1335C2#6118711yescharacteristic
1336C2#6118811yescharacteristic
1337C2#6229411yescharacteristic
1338C2#6234411yescharacteristic
1339C2#6261211yescharacteristic
1340C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42673C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42956C2semidirect
3. #33056C2semidirect
4. #31985C2semidirect
5. #31981C2semidirect
6. #31679C2semidirect
7. #31678C2semidirect
8. #31364C2semidirect
9. #31362C2semidirect
10. #31291C2semidirect
11. #31287C2semidirect
12. #29962C2semidirect
13. #29764C2semidirect
14. #29012C2semidirect
15. #29008C2semidirect
16. #28862C2semidirect
17. #28858C2semidirect
18. #28113C2semidirect
19. #28111C2semidirect
20. #27284C2semidirect
21. #27284C2semidirect
22. #26205C2semidirect
23. #26201C2semidirect
24. #25262C2semidirect
25. #25256C2semidirect
26. #24039C2semidirect
27. #24038C2semidirect
28. #22427C2semidirect
29. #22427C2semidirect
30. #21494C2semidirect
31. #21089C2semidirect
34. C2×#491C22semidirect
39. C2×#436C22semidirect
62. #2509C22semidirect
63. #2508C22semidirect
64. #2497C22semidirect
65. #2496C22semidirect
67. #2487C22semidirect
69. #2486C22semidirect
73. #2442C22semidirect
74. #2442C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
98. #2076C22semidirect
99. #2075C22semidirect
100. #2074C22semidirect
101. #2074C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
118. #2036C22semidirect
119. #2036C22semidirect
120. #2035C22semidirect
121. #2035C22semidirect
128. #1991C22semidirect
133. #1956C22semidirect
134. #1955C22semidirect
135. #1942C22semidirect
136. #1941C22semidirect
137. #1940C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
148. #1933C22semidirect
149. #1933C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
154. #1923C22semidirect
155. #1923C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
162. #1894C22semidirect
163. #1894C22semidirect
170. #1872C22semidirect
171. #1872C22semidirect
180. #1836C22semidirect
181. #1824C22semidirect
182. #1823C22semidirect
183. #1809C22semidirect
184. #1809C22semidirect
196. C8×C4⋊C4C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#429562
#426732
#330562
#319852
#319812
#316792
#316782
#313642
#313622
#312912
#312872
#299622
#297642
#290122
#290082
#288622
#288582
#281132
#281112
#272842
#262052
#262012
#252622
#252562
#240392
#240382
#224272
#214942
#210892