Finite Group Databasebeta

← #6796309

Subgroups — #6796309

Order 512.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37859C211yesmaximal, characteristic, complemented
2#37671C211yesmaximal, characteristic
3#33054C211yesmaximal, characteristic, complemented
4#31952C211yesmaximal, characteristic, complemented
5#31844C211yesmaximal, characteristic, complemented
6#31745C211yesmaximal, characteristic, complemented
7#31705C211yesmaximal, characteristic, complemented
8#31353C211yesmaximal, characteristic, complemented
9#31301C211yesmaximal, characteristic, complemented
10#30660C211yesmaximal, characteristic, complemented
11#30537C211yesmaximal, characteristic, complemented
12#29780C211yesmaximal, characteristic, complemented
13#29743C211yesmaximal, characteristic, complemented
14#29171C211yesmaximal, characteristic, complemented
15#28589C211yesmaximal, characteristic, complemented
16#27869C211yesmaximal, characteristic, complemented
17#27529C211yesmaximal, characteristic, complemented
18#27405C211yesmaximal, characteristic, complemented
19#27357C211yesmaximal, characteristic, complemented
20#27120C211yesmaximal, characteristic, complemented
21#26734C211yesmaximal, characteristic, complemented
22#26666C211yesmaximal, characteristic, complemented
23#26639C211yesmaximal, characteristic, complemented
24#25512C211yesmaximal, characteristic, complemented
25#24920C211yesmaximal, characteristic, complemented
26#24554C211yesmaximal, characteristic, complemented
27#24383C211yesmaximal, characteristic
28#21898C211yesmaximal, characteristic, complemented
29#21766C211yesmaximal, characteristic
30#21530C211yesmaximal, characteristic, complemented
31#21050C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×#489C2211yescharacteristic, complemented
35C2×#485C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#441C2211yescharacteristic, complemented
41C2×#424C2211yescharacteristic
42C2×#407C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C2×#405C2211yescharacteristic
45#2848C2211yescharacteristic
46#2848C2211yescharacteristic
47#2745—21no—
48#2739—21no—
49#2736—21no—
50#2735—21no—
51#2707—21no—
52#2694—21no—
53#2685—21no—
54#2685—21no—
55#2628C2211yescharacteristic
56#2625C2211yescharacteristic
57#2624C2211yescharacteristic
58#2620C2211yescharacteristic
59#2575—21no—
60#2574—21no—
61#2530—21no—
62#2527—21no—
63#2499C2211yescharacteristic
64#2497C2211yescharacteristic
65#2494C2211yescharacteristic
66#2492C2211yescharacteristic
67#2490C2211yescharacteristic
68#2468—21no—
69#2466—21no—
70#2460—21no—
71#2454—21no—
72#2441C2211yescharacteristic
73#2439C2211yescharacteristic
74#2432C2211yescharacteristic
75#2429C2211yescharacteristic
76#2426C2211yescharacteristic
77#2423C2211yescharacteristic
78#2421C2211yescharacteristic
79#2362C2211yescharacteristic
80#2362C2211yescharacteristic
81#2346C2211yescharacteristic
82#2341C2211yescharacteristic
83#2323C2211yescharacteristic
84#2323C2211yescharacteristic
85#2314C2211yescharacteristic
86#2280C2211yescharacteristic
87#2280C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2092C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2075C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2059C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2042C2211yescharacteristic, complemented
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2016C2211yescharacteristic, complemented
123#2015C2211yescharacteristic, complemented
124#2001C2211yescharacteristic
125#2001C2211yescharacteristic
126#2001C2211yescharacteristic
127#2000C2211yescharacteristic
128#1990C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1989C2211yescharacteristic, complemented
131#1981C2211yescharacteristic, complemented
132#1981C2211yescharacteristic, complemented
133#1971C2211yescharacteristic, complemented
134#1958C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1926C2211yescharacteristic, complemented
144#1926C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1924C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1924C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic
154#1920C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic
162#1894C2211yescharacteristic
163#1894C2211yescharacteristic
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1880C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1873C2211yescharacteristic
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1873C2211yescharacteristic
178#1865C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1836C2211yescharacteristic, complemented
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1825C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#541—24no—
213#541—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#125—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#124C2311yescharacteristic
222#525—24no—
223#525—42no—
224C2×#123—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247#489—42no—
248#485—42no—
249#470—42no—
250#467—24no—
251#465—42no—
252#452—42no—
253#441—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263#424—42no—
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294#407—42no—
295C2×C22⋊C8—42no—
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304#405—42no—
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309#401—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#399—21no—
316#399—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#393—21no—
347#393—21no—
348#393—21no—
349#391—21no—
350#391—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
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#388—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#382—21no—
420#382C2311yescharacteristic
421#382C2311yescharacteristic
422#381—21no—
423#381D411yescharacteristic
424#381D411yescharacteristic
425#380—21no—
426#380D411yescharacteristic
427#380D411yescharacteristic
428#380D411yescharacteristic
429#380D411yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443#379D411yescharacteristic
444#379D411yescharacteristic
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376—21no—
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25C2×D411yescharacteristic
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4C2411yescharacteristic
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—21no—
511C23×C4—41no—
512C23×C4—41no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4C2×D411yescharacteristic
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×Q16—22no—
522C2×Q16—22no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—22no—
539C22×C8—41no—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—41no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554#126—44no—
555#126—44no—
556#125—22no—
557#125—41no—
558#125—44no—
559#125—44no—
560#124—41no—
561#124—41no—
562#123—44no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8#4114yes—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—41no—
583#120—44no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×D4—44no—
593C4×D4—44no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—41no—
601#117—41no—
602#117—41no—
603#117—41no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#107—22no—
708#107—41no—
709#107—41no—
710#107—41no—
711#106—22no—
712#106—41no—
713#106—41no—
714#106—41no—
715#106—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—22no—
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#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#102—22no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753C22⋊C8—41no—
754#97—22no—
755#97—22no—
756C4×C8—41no—
757C4×C8—41no—
758#95—21no—
759#95—21no—
760#95—21no—
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#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802C24—22no—
803C24—21no—
804C24—41no—
805C24—41no—
806C24—41no—
807C24—41no—
808C24—41no—
809C24—41no—
810C24C22×D411yescharacteristic
811C24C22×D411yescharacteristic
812C24C22×D411yescharacteristic
813#41—82no—
814#41—82no—
815#41—82no—
816#41—82no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
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—81no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8C2×#4112yes—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
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—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—42no—
894C22×C4—42no—
895C22×C4—82no—
896C22×C4—82no—
897C22×C4—82no—
898C22×C4—82no—
899C22×C4—81no—
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C2×#4112yes—
912C22×C4H(5,𝔽2)12yes—
913C22×C4C2511yescharacteristic
914Q16—44no—
915Q16—82no—
916SD16—82no—
917M16—44no—
918M16—82no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—44no—
943C2×C8—82no—
944C2×C8H(5,𝔽2)12yes—
945C4⋊C4—24no—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4C2×#4112yes—
1002C22⋊C4—24no—
1003C22⋊C4—22no—
1004C22⋊C4—22no—
1005C22⋊C4—41no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—41no—
1012C22⋊C4—41no—
1013C22⋊C4—41no—
1014C22⋊C4—41no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—42no—
1054C42—42no—
1055C42—42no—
1056C42—42no—
1057C42—81no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C42—81no—
1063C42—81no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—44no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—82no—
1093C23—82no—
1094C23—82no—
1095C23—82no—
1096C23—82no—
1097C23—82no—
1098C23#54612yes—
1099C23C23×D411yescharacteristic
1100Q8—22no—
1101Q8—22no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—162no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—84no—
1118D4—84no—
1119D4—84no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
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—82no—
1210C2×C4—82no—
1211C2×C4—82no—
1212C2×C4—84no—
1213C2×C4#54612yes—
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C2×H(5,𝔽2)11yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—41no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—22no—
1229C22—22no—
1230C22—22no—
1231C22—41no—
1232C22—41no—
1233C22—41no—
1234C22—41no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—88no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22#344911yescharacteristic
1258C22C2×#54611yescharacteristic
1259C22#349611yescharacteristic
1260C22#358411yescharacteristic
1261C22#358411yescharacteristic
1262C22#358611yescharacteristic
1263C22#358611yescharacteristic
1264C4—22no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—42no—
1270C4—41no—
1271C4—41no—
1272C4—42no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4#351311yescharacteristic
1291C4#352111yescharacteristic
1292C4#354211yescharacteristic
1293C4#354511yescharacteristic
1294C2—42no—
1295C2—81no—
1296C2—81no—
1297C2—161no—
1298C2#3894411yescharacteristic
1299C2#6098411yescharacteristic
1300C2#6098411yescharacteristic
1301C2#6119011yescharacteristic
1302C2#6119711yescharacteristic
1303C2#6228211yescharacteristic
1304C2#6229111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37859C2semidirect
3. #33054C2semidirect
4. #31952C2semidirect
5. #31844C2semidirect
6. #31745C2semidirect
7. #31705C2semidirect
8. #31353C2semidirect
9. #31301C2semidirect
10. #30660C2semidirect
11. #30537C2semidirect
12. #29780C2semidirect
13. #29743C2semidirect
14. #29171C2semidirect
15. #28589C2semidirect
16. #27869C2semidirect
17. #27529C2semidirect
18. #27405C2semidirect
19. #27357C2semidirect
20. #27120C2semidirect
21. #26734C2semidirect
22. #26666C2semidirect
23. #26639C2semidirect
24. #25512C2semidirect
25. #24920C2semidirect
26. #24554C2semidirect
28. #21898C2semidirect
30. #21530C2semidirect
31. #21050C2semidirect
34. C2×#489C22semidirect
40. C2×#441C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2097C22semidirect
91. #2092C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2084C22semidirect
95. #2084C22semidirect
100. #2072C22semidirect
101. #2071C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2059C22semidirect
107. #2057C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2043C22semidirect
111. #2042C22semidirect
120. #2026C22semidirect
121. #2024C22semidirect
122. #2016C22semidirect
123. #2015C22semidirect
128. #1990C22semidirect
129. #1989C22semidirect
130. #1989C22semidirect
131. #1981C22semidirect
132. #1981C22semidirect
133. #1971C22semidirect
134. #1958C22semidirect
135. #1943C22semidirect
136. #1936C22semidirect
137. #1935C22semidirect
138. #1934C22semidirect
139. #1933C22semidirect
140. #1933C22semidirect
141. #1933C22semidirect
142. #1927C22semidirect
143. #1926C22semidirect
144. #1926C22semidirect
145. #1926C22semidirect
154. #1920C22semidirect
155. #1919C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
168. #1880C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
178. #1865C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
184. #1836C22semidirect
191. #1805C22semidirect
192. #1805C22semidirect
193. #1803C22semidirect
194. #1803C22semidirect
198. #1776C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#378592
#376712
#330542
#319522
#318442
#317452
#317052
#313532
#313012
#306602
#305372
#297802
#297432
#291712
#285892
#278692
#275292
#274052
#273572
#271202
#267342
#266662
#266392
#255122
#249202
#245542
#243832
#218982
#217662
#215302
#210502