Finite Group Databasebeta

← #6832185

Subgroups — #6832185

Order 512.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40030C211yesmaximal, characteristic, complemented
2#39495C211yesmaximal, characteristic, complemented
3#33048C211yesmaximal, characteristic, complemented
4#32622C211yesmaximal, characteristic, complemented
5#32613C211yesmaximal, characteristic, complemented
6#32433C211yesmaximal, characteristic, complemented
7#32431C211yesmaximal, characteristic, complemented
8#31172C211yesmaximal, characteristic, complemented
9#31168C211yesmaximal, characteristic, complemented
10#30875C211yesmaximal, characteristic, complemented
11#30874C211yesmaximal, characteristic, complemented
12#29954C211yesmaximal, characteristic, complemented
13#29712C211yesmaximal, characteristic, complemented
14#29099C211yesmaximal, characteristic, complemented
15#29071C211yesmaximal, characteristic, complemented
16#28421C211yesmaximal, characteristic, complemented
17#28405C211yesmaximal, characteristic, complemented
18#27280C211yesmaximal, characteristic, complemented
19#27276C211yesmaximal, characteristic, complemented
20#26835C211yesmaximal, characteristic, complemented
21#26827C211yesmaximal, characteristic, complemented
22#26363C211yesmaximal, characteristic, complemented
23#26361C211yesmaximal, characteristic, complemented
24#25304C211yesmaximal, characteristic, complemented
25#25298C211yesmaximal, characteristic, complemented
26#24366C211yesmaximal, characteristic, complemented
27#24366C211yesmaximal, characteristic, complemented
28#22880C211yesmaximal, characteristic, complemented
29#22868C211yesmaximal, characteristic, complemented
30#21600C211yesmaximal, characteristic, complemented
31#21236C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#490C2211yescharacteristic, complemented
34C2×#488C2211yescharacteristic, complemented
35C2×#486C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic, complemented
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#459C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×#446C2211yescharacteristic, complemented
45C2×#442C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#417C2211yescharacteristic
49C2×#418C2211yescharacteristic
50C2×C4×M16C2211yescharacteristic
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic
53#2804—21no—
54#2780—21no—
55#2780—21no—
56#2732—21no—
57#2714—21no—
58#2703—21no—
59#2688—21no—
60#2676—21no—
61#2648—21no—
62#2626—21no—
63#2592C2211yescharacteristic, complemented
64#2580C2211yescharacteristic
65#2580C2211yescharacteristic
66#2566C2211yescharacteristic
67#2566C2211yescharacteristic
68#2559—21no—
69#2557—21no—
70#2548C2211yescharacteristic, complemented
71#2544C2211yescharacteristic, complemented
72#2541C2211yescharacteristic, complemented
73#2512C2211yescharacteristic, complemented
74#2511C2211yescharacteristic, complemented
75#2454C2211yescharacteristic
76#2454C2211yescharacteristic
77#2452C2211yescharacteristic
78#2452C2211yescharacteristic
79#2447C2211yescharacteristic, complemented
80#2445C2211yescharacteristic, complemented
81#2442C2211yescharacteristic
82#2442C2211yescharacteristic
83#2437—21no—
84#2437—21no—
85#2431C2211yescharacteristic
86#2431C2211yescharacteristic
87#2363C2211yescharacteristic
88#2363C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90D4×C22⋊C4C2211yescharacteristic
91#2333—21no—
92#2315—21no—
93C4×C22⋊Q8C2211yescharacteristic
94#2297C2211yescharacteristic
95C2×#390C2211yescharacteristic
96#2095C2211yescharacteristic, complemented
97#2094C2211yescharacteristic, complemented
98#2092C2211yescharacteristic, complemented
99#2092C2211yescharacteristic, complemented
100#2088C2211yescharacteristic, complemented
101#2086C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2073C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2042C2211yescharacteristic, complemented
123#2042C2211yescharacteristic, complemented
124#2041C2211yescharacteristic, complemented
125#2041C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2025C2211yescharacteristic, complemented
128#2024C2211yescharacteristic, complemented
129#2023C2211yescharacteristic, complemented
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2011C2211yescharacteristic
133#2011C2211yescharacteristic
134#2011C2211yescharacteristic
135#2011C2211yescharacteristic
136#1990C2211yescharacteristic, complemented
137#1985C2211yescharacteristic, complemented
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1972C2211yescharacteristic
141#1972C2211yescharacteristic
142#1972C2211yescharacteristic
143#1970C2211yescharacteristic
144#1970C2211yescharacteristic
145#1970C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic
148#1961C2211yescharacteristic, complemented
149#1958C2211yescharacteristic, complemented
150#1957C2211yescharacteristic, complemented
151#1949C2211yescharacteristic, complemented
152#1949C2211yescharacteristic, complemented
153#1940C2211yescharacteristic, complemented
154#1936C2211yescharacteristic
155#1936C2211yescharacteristic, complemented
156#1936C2211yescharacteristic, complemented
157#1936C2211yescharacteristic, complemented
158#1936C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1935C2211yescharacteristic, complemented
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic, complemented
163#1934C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1925C2211yescharacteristic
166#1920C2211yescharacteristic, complemented
167#1918C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1895C2211yescharacteristic
171#1895C2211yescharacteristic
172#1895C2211yescharacteristic
173#1895C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1877C2211yescharacteristic
181#1877C2211yescharacteristic
182#1874C2211yescharacteristic
183#1874C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic, complemented
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1851C2211yescharacteristic
191#1851C2211yescharacteristic
192#1834C2211yescharacteristic, complemented
193#1797C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1771C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic
202#1753C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#126—21no—
223C2×#125C2311yescharacteristic
224C2×#125C2311yescharacteristic
225C2×#124—21no—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8D411yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C42C2311yescharacteristic
253#490—42no—
254#488—42no—
255#486—42no—
256#478—42no—
257#478—42no—
258#463—42no—
259#463—42no—
260#459—42no—
261#459—42no—
262#447—24no—
263#447—24no—
264#446—42no—
265#442—42no—
266C4×D8—42no—
267#428—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282#418—42no—
283#417—42no—
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C4×M16—42no—
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#399—21no—
335#398—21no—
336#398—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#393—21no—
360#393—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#391—21no—
368#391D411yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#389—21no—
397#389D411yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387D411yescharacteristic
414#387D411yescharacteristic
415#386—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#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385D411yescharacteristic
446#385D411yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#381—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380—21no—
456#380—21no—
457#380D411yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#379—21no—
461#379—21no—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4#4114yes—
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541AGL(1,ℤ/8)—416no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—41no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582#127—41no—
583#127—41no—
584#127—41no—
585#127—41no—
586#127—41no—
587#127—41no—
588#126—82no—
589#125—41no—
590#125—41no—
591#125—41no—
592#125—41no—
593#124—41no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—82no—
598#123—82no—
599C22⋊Q8—42no—
600C22⋊Q8—82no—
601C22⋊Q8—82no—
602C22⋊Q8—82no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—44no—
608#121—82no—
609#121—82no—
610#121—82no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625#117—41no—
626#117—41no—
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⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×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⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4—82no—
715C2×C22⋊C4—82no—
716C2×C22⋊C4—82no—
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—41no—
725C2×C42—41no—
726C2×C42C2×D411yescharacteristic
727C2×C42C2×D411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#107—22no—
735#107—41no—
736#107—41no—
737#107—41no—
738#106—22no—
739#106—41no—
740#106—41no—
741#106—41no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748#103—22no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780C22⋊C8—22no—
781C22⋊C8—22no—
782#97—22no—
783#97—22no—
784#97—41no—
785#97—41no—
786C4×C8—22no—
787C4×C8—22no—
788C4×C8—41no—
789C4×C8—41no—
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#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24—24no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—42no—
831C24—42no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
837#41—44no—
838#41—44no—
839#41—82no—
840#41—82no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—41no—
848C2×Q8—41no—
849C2×Q8—41no—
850C2×Q8—42no—
851C2×Q8—81no—
852C2×Q8—81no—
853C2×D4—24no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4C2×#4112yes—
916C2×D4C2×#4112yes—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C2×#4112yes—
976C22×C42−1+412yes—
977C22×C4C2511yescharacteristic
978SD16—44no—
979SD16—44no—
980D8—44no—
981D8—44no—
982D8—44no—
983D8—44no—
984D8—82no—
985D8—82no—
986M16—28no—
987M16—44no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8H(5,𝔽2)12yes—
1010C2×C8H(5,𝔽2)12yes—
1011C2×C8H(5,𝔽2)12yes—
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—22no—
1015C4⋊C4—22no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—42no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—41no—
1123C42—41no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—22no—
1135C23—48no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—84no—
1170C23—84no—
1171C23—162no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23#54812yes—
1176C23C23×D411yescharacteristic
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—82no—
1182Q8—162no—
1183D4—22no—
1184D4—22no—
1185D4—22no—
1186D4—22no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—84no—
1204D4—84no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—82no—
1287C2×C4—82no—
1288C2×C4—84no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4#54812yes—
1297C2×C4#57512yes—
1298C2×C4#57612yes—
1299C2×C4C22×#4111yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4C2×2−1+411yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—22no—
1307C8—22no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22—42no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—168no—
1356C22C2×#54811yescharacteristic
1357C22#349611yescharacteristic
1358C22#349811yescharacteristic
1359C22C2×#57511yescharacteristic
1360C22C2×#57611yescharacteristic
1361C22#358511yescharacteristic
1362C22#358511yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—22no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4#345911yescharacteristic
1388C4#349011yescharacteristic
1389C4#353611yescharacteristic
1390C4#356111yescharacteristic
1391C2—42no—
1392C2—82no—
1393C2—82no—
1394C2—161no—
1395C2—161no—
1396C2—161no—
1397C2#3942011yescharacteristic
1398C2#6131811yescharacteristic
1399C2#6133911yescharacteristic
1400C2#6229811yescharacteristic
1401C2#6231511yescharacteristic
1402C2#6242611yescharacteristic
1403C2#6244311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40030C2semidirect
2. #39495C2semidirect
3. #33048C2semidirect
4. #32622C2semidirect
5. #32613C2semidirect
6. #32433C2semidirect
7. #32431C2semidirect
8. #31172C2semidirect
9. #31168C2semidirect
10. #30875C2semidirect
11. #30874C2semidirect
12. #29954C2semidirect
13. #29712C2semidirect
14. #29099C2semidirect
15. #29071C2semidirect
16. #28421C2semidirect
17. #28405C2semidirect
18. #27280C2semidirect
19. #27276C2semidirect
20. #26835C2semidirect
21. #26827C2semidirect
22. #26363C2semidirect
23. #26361C2semidirect
24. #25304C2semidirect
25. #25298C2semidirect
26. #24366C2semidirect
27. #24366C2semidirect
28. #22880C2semidirect
29. #22868C2semidirect
30. #21600C2semidirect
31. #21236C2semidirect
33. C2×#490C22semidirect
34. C2×#488C22semidirect
35. C2×#486C22semidirect
36. C2×#478C22semidirect
37. C2×#478C22semidirect
44. C2×#446C22semidirect
63. #2592C22semidirect
70. #2548C22semidirect
71. #2544C22semidirect
72. #2541C22semidirect
73. #2512C22semidirect
74. #2511C22semidirect
79. #2447C22semidirect
80. #2445C22semidirect
96. #2095C22semidirect
97. #2094C22semidirect
98. #2092C22semidirect
99. #2092C22semidirect
100. #2088C22semidirect
101. #2086C22semidirect
102. #2074C22semidirect
103. #2073C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
111. #2065C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
122. #2042C22semidirect
123. #2042C22semidirect
124. #2041C22semidirect
125. #2041C22semidirect
126. #2026C22semidirect
127. #2025C22semidirect
128. #2024C22semidirect
129. #2023C22semidirect
136. #1990C22semidirect
137. #1985C22semidirect
148. #1961C22semidirect
149. #1958C22semidirect
150. #1957C22semidirect
151. #1949C22semidirect
152. #1949C22semidirect
153. #1940C22semidirect
155. #1936C22semidirect
156. #1936C22semidirect
157. #1936C22semidirect
158. #1936C22semidirect
159. #1935C22semidirect
160. #1935C22semidirect
162. #1934C22semidirect
163. #1934C22semidirect
166. #1920C22semidirect
167. #1918C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
185. #1864C22semidirect
187. #1862C22semidirect
192. #1834C22semidirect
196. #1771C22semidirect
197. #1771C22semidirect
198. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#400302
#394952
#330482
#326222
#326132
#324332
#324312
#311722
#311682
#308752
#308742
#299542
#297122
#290992
#290712
#284212
#284052
#272802
#272762
#268352
#268272
#263632
#263612
#253042
#252982
#243662
#228802
#228682
#216002
#212362