Finite Group Databasebeta

← #6843892

Subgroups — #6843892

Order 512.

1571 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42839C211yesmaximal, characteristic, complemented
2#42606C211yesmaximal, characteristic, complemented
3#33140C211yesmaximal, characteristic, complemented
4#32533C211yesmaximal, characteristic, complemented
5#32459C211yesmaximal, characteristic, complemented
6#31322C211yesmaximal, characteristic, complemented
7#31322C211yesmaximal, characteristic, complemented
8#31240C211yesmaximal, characteristic, complemented
9#31057C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#30401C211yesmaximal, characteristic, complemented
12#30035C211yesmaximal, characteristic, complemented
13#30023C211yesmaximal, characteristic, complemented
14#29101C211yesmaximal, characteristic, complemented
15#29087C211yesmaximal, characteristic, complemented
16#28107C211yesmaximal, characteristic, complemented
17#28103C211yesmaximal, characteristic, complemented
18#28074C211yesmaximal, characteristic, complemented
19#28062C211yesmaximal, characteristic, complemented
20#27250C211yesmaximal, characteristic, complemented
21#27243C211yesmaximal, characteristic, complemented
22#27053C211yesmaximal, characteristic, complemented
23#27048C211yesmaximal, characteristic, complemented
24#25356C211yesmaximal, characteristic, complemented
25#25346C211yesmaximal, characteristic, complemented
26#25133C211yesmaximal, characteristic, complemented
27#25124C211yesmaximal, characteristic, complemented
28#22883C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic, complemented
30#21523C211yesmaximal, characteristic, complemented
31#21496C211yesmaximal, characteristic, complemented
32C2×#475C2211yescharacteristic, complemented
33C2×#476C2211yescharacteristic
34C2×#469C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×#436C2211yescharacteristic, complemented
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic
44C2×#417C2211yescharacteristic, complemented
45C22×#102C2211yescharacteristic
46C2×#405C2211yescharacteristic, complemented
47#2830—21no—
48#2824—21no—
49#2803—21no—
50#2781—21no—
51#2768—21no—
52#2710—21no—
53#2686—21no—
54#2685—21no—
55#2684—21no—
56#2676—21no—
57#2661—21no—
58#2653—21no—
59#2636—21no—
60#2626—21no—
61#2624C2211yescharacteristic
62#2624C2211yescharacteristic, complemented
63#2576—21no—
64#2563C2211yescharacteristic
65#2563C2211yescharacteristic, complemented
66#2537C2211yescharacteristic
67#2536C2211yescharacteristic
68#2513C2211yescharacteristic, complemented
69#2512C2211yescharacteristic
70#2497C2211yescharacteristic
71#2494C2211yescharacteristic, complemented
72#2491C2211yescharacteristic
73#2491C2211yescharacteristic
74#2487C2211yescharacteristic
75#2486C2211yescharacteristic
76#2452C2211yescharacteristic
77#2451C2211yescharacteristic, complemented
78#2424—21no—
79#2416C2211yescharacteristic
80#2416C2211yescharacteristic
81#2408C2211yescharacteristic
82#2408C2211yescharacteristic
83#2407C2211yescharacteristic
84#2407C2211yescharacteristic, complemented
85#2392C2211yescharacteristic
86#2361C2211yescharacteristic
87#2360C2211yescharacteristic
88#2341C2211yescharacteristic, complemented
89D4×C22⋊C4C2211yescharacteristic
90#2324C2211yescharacteristic
91#2323C2211yescharacteristic, complemented
92#2094C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2073C2211yescharacteristic
103#2072C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2058C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic, complemented
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic, complemented
130#2000C2211yescharacteristic
131#1999C2211yescharacteristic
132#1993C2211yescharacteristic, complemented
133#1990C2211yescharacteristic, complemented
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1970C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1954C2211yescharacteristic
140#1949C2211yescharacteristic, complemented
141#1947C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1934C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1895C2211yescharacteristic
165#1895C2211yescharacteristic
166#1895C2211yescharacteristic
167#1894C2211yescharacteristic, complemented
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1893C2211yescharacteristic, complemented
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1853C2211yescharacteristic, complemented
185#1853C2211yescharacteristic, complemented
186#1823C2211yescharacteristic
187#1823C2211yescharacteristic, complemented
188#1809C2211yescharacteristic, complemented
189#1809C2211yescharacteristic, complemented
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic, complemented
192#1798C2211yescharacteristic, complemented
193#1788C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202C8×C22⋊C4C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#124—21no—
217C2×#124—21no—
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245#476—42no—
246#475—42no—
247#469—42no—
248#465—24no—
249#450—24no—
250#449—24no—
251#449—42no—
252#447—42no—
253C4×SD16—42no—
254#436—42no—
255#435—42no—
256#435—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#417—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102—42no—
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307#405—42no—
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398D411yescharacteristic
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397D411yescharacteristic
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396D411yescharacteristic
338#396D411yescharacteristic
339#395—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394D411yescharacteristic
356#394D411yescharacteristic
357#394D411yescharacteristic
358#393—21no—
359#393—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392D411yescharacteristic
370#391—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
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#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#384C2311yescharacteristic
433#382—21no—
434#382—21no—
435#382C2311yescharacteristic
436#381—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
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—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16#4114yes—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×M16—22no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C2×M16—41no—
548C2×M16—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567#126—82no—
568#124—82no—
569#124—82no—
570#123—82no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—82no—
576#121—22no—
577#121—22no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—82no—
589#121—82no—
590#121—82no—
591#120—82no—
592#120—82no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—82no—
608#117—41no—
609#117—41no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
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—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—82no—
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—41no—
717#107—41no—
718#106—22no—
719#106—22no—
720#106—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—41no—
737#103—41no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758C22⋊C8—22no—
759C22⋊C8—22no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764#97—22no—
765#97—41no—
766#97—41no—
767C4×C8—22no—
768C4×C8—41no—
769C4×C8—41no—
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#95—21no—
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806C24—21no—
807C24—21no—
808C24—21no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24C22×D411yescharacteristic
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819#41—44no—
820#41—82no—
821#41—82no—
822#41—82no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8C2×#4112yes—
835C2×D4—22no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—21no—
839C2×D4—21no—
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—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—44no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4C2×#4112yes—
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—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C2511yescharacteristic
948SD16—44no—
949SD16—82no—
950D8—82no—
951D8—82no—
952M16—44no—
953M16—82no—
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—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—44no—
976C2×C8—82no—
977C2×C8C2×#4112yes—
978C2×C8H(5,𝔽2)12yes—
979C2×C8H(5,𝔽2)12yes—
980C4⋊C4—22no—
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—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
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—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
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—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—42no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—22no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—84no—
1139C23—84no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23#57712yes—
1146C23C23×D411yescharacteristic
1147Q8—22no—
1148Q8—22no—
1149Q8—41no—
1150Q8—41no—
1151Q8—162no—
1152Q8—162no—
1153D4—22no—
1154D4—22no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—82no—
1166D4—82no—
1167D4—82no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
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—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
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—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—84no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4#57712yes—
1265C2×C4C22×#4111yescharacteristic
1266C2×C4C2×H(5,𝔽2)11yescharacteristic
1267C2×C4C2×H(5,𝔽2)11yescharacteristic
1268C2×C4#58511yescharacteristic
1269C2×C4#58511yescharacteristic
1270C2×C4#58511yescharacteristic
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—41no—
1290C22—41no—
1291C22—42no—
1292C22—41no—
1293C22—42no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22D4×#4111yescharacteristic
1323C22#349611yescharacteristic
1324C22#349611yescharacteristic
1325C22C2×#57711yescharacteristic
1326C22C2×#57711yescharacteristic
1327C22#358511yescharacteristic
1328C22#358511yescharacteristic
1329C4—22no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4#345911yescharacteristic
1354C4#351411yescharacteristic
1355C4#353411yescharacteristic
1356C4#356811yescharacteristic
1357C2—42no—
1358C2—81no—
1359C2—81no—
1360C2—82no—
1361C2—161no—
1362C2—161no—
1363C2#3945211yescharacteristic
1364C2#6148311yescharacteristic
1365C2#6150411yescharacteristic
1366C2#6230811yescharacteristic
1367C2#6231911yescharacteristic
1368C2#6231911yescharacteristic
1369C2#6234611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
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. #42839C2semidirect
2. #42606C2semidirect
3. #33140C2semidirect
4. #32533C2semidirect
5. #32459C2semidirect
6. #31322C2semidirect
7. #31322C2semidirect
8. #31240C2semidirect
9. #31057C2semidirect
10. #30408C2semidirect
11. #30401C2semidirect
12. #30035C2semidirect
13. #30023C2semidirect
14. #29101C2semidirect
15. #29087C2semidirect
16. #28107C2semidirect
17. #28103C2semidirect
18. #28074C2semidirect
19. #28062C2semidirect
20. #27250C2semidirect
21. #27243C2semidirect
22. #27053C2semidirect
23. #27048C2semidirect
24. #25356C2semidirect
25. #25346C2semidirect
26. #25133C2semidirect
27. #25124C2semidirect
28. #22883C2semidirect
29. #22874C2semidirect
30. #21523C2semidirect
31. #21496C2semidirect
32. C2×#475C22semidirect
41. C2×#436C22semidirect
44. C2×#417C22semidirect
46. C2×#405C22semidirect
62. #2624C22semidirect
65. #2563C22semidirect
68. #2513C22semidirect
71. #2494C22semidirect
77. #2451C22semidirect
84. #2407C22semidirect
88. #2341C22semidirect
91. #2323C22semidirect
92. #2094C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
103. #2072C22semidirect
104. #2067C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
110. #2058C22semidirect
111. #2058C22semidirect
118. #2035C22semidirect
125. #2034C22semidirect
129. #2023C22semidirect
132. #1993C22semidirect
133. #1990C22semidirect
140. #1949C22semidirect
141. #1947C22semidirect
142. #1943C22semidirect
143. #1941C22semidirect
144. #1941C22semidirect
145. #1939C22semidirect
149. #1936C22semidirect
150. #1935C22semidirect
152. #1934C22semidirect
153. #1934C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
159. #1924C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
167. #1894C22semidirect
170. #1893C22semidirect
179. #1869C22semidirect
180. #1865C22semidirect
184. #1853C22semidirect
185. #1853C22semidirect
187. #1823C22semidirect
188. #1809C22semidirect
189. #1809C22semidirect
191. #1807C22semidirect
192. #1798C22semidirect
193. #1788C22semidirect
195. C4×#106C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#428392
#426062
#331402
#325332
#324592
#313222
#312402
#310572
#304082
#304012
#300352
#300232
#291012
#290872
#281072
#281032
#280742
#280622
#272502
#272432
#270532
#270482
#253562
#253462
#251332
#251242
#228832
#228742
#215232
#214962