Finite Group Databasebeta

← #6473996

Subgroups — #6473996

Order 512.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37285C211yesmaximal, characteristic, complemented
2#37282C211yesmaximal, characteristic, complemented
3#33219C211yesmaximal, characteristic, complemented
4#33181C211yesmaximal, characteristic, complemented
5#32937C211yesmaximal, characteristic, complemented
6#32936C211yesmaximal, characteristic
7#30195C211yesmaximal, characteristic, complemented
8#30191C211yesmaximal, characteristic, complemented
9#29735C211yesmaximal, characteristic, complemented
10#29734C211yesmaximal, characteristic, complemented
11#29061C211yesmaximal, characteristic, complemented
12#29057C211yesmaximal, characteristic, complemented
13#29052C211yesmaximal, characteristic, complemented
14#29048C211yesmaximal, characteristic, complemented
15#29004C211yesmaximal, characteristic, complemented
16#29003C211yesmaximal, characteristic, complemented
17#28982C211yesmaximal, characteristic, complemented
18#28981C211yesmaximal, characteristic, complemented
19#27853C211yesmaximal, characteristic, complemented
20#27835C211yesmaximal, characteristic, complemented
21#27798C211yesmaximal, characteristic, complemented
22#27793C211yesmaximal, characteristic, complemented
23#25424C211yesmaximal, characteristic, complemented
24#25413C211yesmaximal, characteristic, complemented
25#25043C211yesmaximal, characteristic, complemented
26#25038C211yesmaximal, characteristic, complemented
27#22195C211yesmaximal, characteristic, complemented
28#22194C211yesmaximal, characteristic, complemented
29#21542C211yesmaximal, characteristic, complemented
30#21536C211yesmaximal, characteristic, complemented
31#20389C211yesmaximal, characteristic, complemented
32C23×M16C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#495C2211yescharacteristic, complemented
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#469C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#466C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×C4×D8C2211yescharacteristic, complemented
45C22×C22⋊C8C2211yescharacteristic
46C2×#405C2211yescharacteristic
47C2×#405C2211yescharacteristic
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2847C2211yescharacteristic
51#2847C2211yescharacteristic
52#2786—21no—
53#2784—21no—
54#2781—21no—
55#2780—21no—
56#2779—21no—
57#2761—21no—
58#2751—21no—
59#2750—21no—
60#2750—21no—
61#2743—21no—
62#2715—21no—
63#2697—21no—
64#2695—21no—
65#2685—21no—
66#2685—21no—
67#2684—21no—
68#2629C2211yescharacteristic
69#2628C2211yescharacteristic
70#2620C2211yescharacteristic
71#2620C2211yescharacteristic
72#2497C2211yescharacteristic
73#2497C2211yescharacteristic
74#2496C2211yescharacteristic
75#2496C2211yescharacteristic
76#2492C2211yescharacteristic
77#2491C2211yescharacteristic
78#2490C2211yescharacteristic
79#2489C2211yescharacteristic
80#2427C2211yescharacteristic
81#2427C2211yescharacteristic
82#2426C2211yescharacteristic
83#2426C2211yescharacteristic
84#2423C2211yescharacteristic
85#2422C2211yescharacteristic
86#2421C2211yescharacteristic
87#2420C2211yescharacteristic
88#2324C2211yescharacteristic
89#2324C2211yescharacteristic
90#2323C2211yescharacteristic
91#2323C2211yescharacteristic
92#2280C2211yescharacteristic
93#2100C2211yescharacteristic, complemented
94#2100C2211yescharacteristic, complemented
95#2099C2211yescharacteristic, complemented
96#2099C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2074C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2042C2211yescharacteristic, complemented
106#2042C2211yescharacteristic, complemented
107#2042C2211yescharacteristic, complemented
108#2042C2211yescharacteristic, complemented
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic, complemented
119#2024C2211yescharacteristic, complemented
120#2023C2211yescharacteristic, complemented
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1991C2211yescharacteristic, complemented
126#1990C2211yescharacteristic, complemented
127#1972C2211yescharacteristic, complemented
128#1972C2211yescharacteristic, complemented
129#1971C2211yescharacteristic, complemented
130#1969C2211yescharacteristic, complemented
131#1968C2211yescharacteristic, complemented
132#1968C2211yescharacteristic, complemented
133#1959C2211yescharacteristic, complemented
134#1959C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1944C2211yescharacteristic, complemented
137#1943C2211yescharacteristic, complemented
138#1942C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1941C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1935C2211yescharacteristic, complemented
143#1934C2211yescharacteristic, complemented
144#1934C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1927C2211yescharacteristic, complemented
147#1926C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic
166#1892C2211yescharacteristic
167#1892C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1877C2211yescharacteristic, complemented
172#1877C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic, complemented
177#1847C2211yescharacteristic, complemented
178#1844C2211yescharacteristic, complemented
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1808C2211yescharacteristic
184#1807C2211yescharacteristic
185#1807C2211yescharacteristic
186#1807C2211yescharacteristic
187#1776C2211yescharacteristic, complemented
188C4×#106C2211yescharacteristic, complemented
189#1762C2211yescharacteristic, complemented
190#1762C2211yescharacteristic, complemented
191C4×#103C2211yescharacteristic, complemented
192C4×#103C2211yescharacteristic, complemented
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16—24no—
209C22×M16—42no—
210C22×M16—42no—
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247#501—42no—
248#495—42no—
249#470—24no—
250#470—42no—
251#469—24no—
252#469—42no—
253#467—42no—
254#466—42no—
255#465—24no—
256#465—24no—
257#441—42no—
258C4×D8—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
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×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8—24no—
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300#405—42no—
301#405—42no—
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#395—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#393—21no—
356#393—21no—
357#393—21no—
358#391—21no—
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—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#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#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#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382C2311yescharacteristic
431#381—21no—
432#381D411yescharacteristic
433#381D411yescharacteristic
434#380—21no—
435#380—21no—
436#380D411yescharacteristic
437#380D411yescharacteristic
438#380D411yescharacteristic
439#380D411yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454#379D411yescharacteristic
455#379D411yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—41no—
513C23×C4—41no—
514C23×C4—41no—
515C23×C4—41no—
516C23×C4C2×D411yescharacteristic
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×Q16—22no—
523C2×Q16—22no—
524C2×Q16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—416no—
546C2×M16#4114yes—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—22no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8#4114yes—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569#126—82no—
570#126—82no—
571#125—41no—
572#125—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—82no—
578#123—82no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#120—82no—
604#120—82no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
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⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—41no—
721#107—41no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—41no—
729#106—41no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
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—
754C22⋊C8—22no—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—22no—
758#97—22no—
759#97—22no—
760#97—41no—
761#97—41no—
762C4×C8—22no—
763C4×C8—22no—
764C4×C8—41no—
765C4×C8—41no—
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#95—21no—
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—22no—
809C24—22no—
810C24—21no—
811C24—21no—
812C24—41no—
813C24—41no—
814C24—41no—
815C24—41no—
816C24—41no—
817C24C22×D411yescharacteristic
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
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—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
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—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—21no—
873C22×C4—21no—
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—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—41no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2511yescharacteristic
928Q16—44no—
929SD16—82no—
930SD16—82no—
931D8—44no—
932M16—28no—
933M16—44no—
934M16—44no—
935M16—44no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
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—44no—
955C2×C8—44no—
956C2×C8—44no—
957C2×C8—44no—
958C2×C8C2×#4112yes—
959C2×C8C2×#4112yes—
960C2×C8C2×#4112yes—
961C2×C8C2×#4112yes—
962C2×C8H(5,𝔽2)12yes—
963C2×C8H(5,𝔽2)12yes—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
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—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
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—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
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—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C23—21no—
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—21no—
1099C23—21no—
1100C23—44no—
1101C23—44no—
1102C23—41no—
1103C23—41no—
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—82no—
1117C23—82no—
1118C23—82no—
1119C23—82no—
1120C23—82no—
1121C23#53212yes—
1122C23#57712yes—
1123C23C23×D411yescharacteristic
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—162no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144D4—162no—
1145D4—162no—
1146D4—162no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
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—44no—
1184C2×C4—44no—
1185C2×C4—44no—
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—41no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4#53212yes—
1239C2×C4C22×#4111yescharacteristic
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C8—22no—
1246C8—22no—
1247C8—22no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8#53814yes—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—88no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22C2×#53211yescharacteristic
1290C22#349611yescharacteristic
1291C22#349611yescharacteristic
1292C22C2×#57711yescharacteristic
1293C22#358411yescharacteristic
1294C22#358511yescharacteristic
1295C22#358611yescharacteristic
1296C4—22no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4C2×#53811yescharacteristic
1322C4#345511yescharacteristic
1323C4#350511yescharacteristic
1324C4#350611yescharacteristic
1325C2—42no—
1326C2—42no—
1327C2—81no—
1328C2—161no—
1329C2—161no—
1330C2#3500511yescharacteristic
1331C2#6070611yescharacteristic
1332C2#6070911yescharacteristic
1333C2#6231811yescharacteristic
1334C2#6231911yescharacteristic
1335C2#6232111yescharacteristic
1336C2#6232211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32936C2
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. #37285C2semidirect
2. #37282C2semidirect
3. #33219C2semidirect
4. #33181C2semidirect
5. #32937C2semidirect
7. #30195C2semidirect
8. #30191C2semidirect
9. #29735C2semidirect
10. #29734C2semidirect
11. #29061C2semidirect
12. #29057C2semidirect
13. #29052C2semidirect
14. #29048C2semidirect
15. #29004C2semidirect
16. #29003C2semidirect
17. #28982C2semidirect
18. #28981C2semidirect
19. #27853C2semidirect
20. #27835C2semidirect
21. #27798C2semidirect
22. #27793C2semidirect
23. #25424C2semidirect
24. #25413C2semidirect
25. #25043C2semidirect
26. #25038C2semidirect
27. #22195C2semidirect
28. #22194C2semidirect
29. #21542C2semidirect
30. #21536C2semidirect
31. #20389C2semidirect
33. C2×#501C22semidirect
34. C2×#495C22semidirect
43. C2×#441C22semidirect
44. C2×C4×D8C22semidirect
93. #2100C22semidirect
94. #2100C22semidirect
95. #2099C22semidirect
96. #2099C22semidirect
101. #2074C22semidirect
102. #2073C22semidirect
103. #2072C22semidirect
104. #2071C22semidirect
105. #2042C22semidirect
106. #2042C22semidirect
107. #2042C22semidirect
108. #2042C22semidirect
117. #2026C22semidirect
118. #2025C22semidirect
119. #2024C22semidirect
120. #2023C22semidirect
125. #1991C22semidirect
126. #1990C22semidirect
127. #1972C22semidirect
128. #1972C22semidirect
129. #1971C22semidirect
130. #1969C22semidirect
131. #1968C22semidirect
132. #1968C22semidirect
133. #1959C22semidirect
134. #1959C22semidirect
135. #1944C22semidirect
136. #1944C22semidirect
137. #1943C22semidirect
138. #1942C22semidirect
139. #1941C22semidirect
140. #1941C22semidirect
141. #1935C22semidirect
142. #1935C22semidirect
143. #1934C22semidirect
144. #1934C22semidirect
145. #1928C22semidirect
146. #1927C22semidirect
147. #1926C22semidirect
148. #1925C22semidirect
149. #1920C22semidirect
150. #1920C22semidirect
151. #1919C22semidirect
152. #1919C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
171. #1877C22semidirect
172. #1877C22semidirect
173. #1865C22semidirect
174. #1864C22semidirect
175. #1863C22semidirect
176. #1862C22semidirect
177. #1847C22semidirect
178. #1844C22semidirect
187. #1776C22semidirect
188. C4×#106C22semidirect
189. #1762C22semidirect
190. #1762C22semidirect
191. C4×#103C22semidirect
192. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#372852
#372822
#332192
#331812
#329372
#329362
#301952
#301912
#297352
#297342
#290612
#290572
#290522
#290482
#290042
#290032
#289822
#289812
#278532
#278352
#277982
#277932
#254242
#254132
#250432
#250382
#221952
#221942
#215422
#215362
#203892