Finite Group Databasebeta

← #7017425

Subgroups — #7017425

Order 512.

1683 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#45010C211yesmaximal, characteristic, complemented
2#42760C211yesmaximal, characteristic, complemented
3#32275C211yesmaximal, characteristic, complemented
4#31921C211yesmaximal, characteristic, complemented
5#31674C211yesmaximal, characteristic, complemented
6#31672C211yesmaximal, characteristic, complemented
7#31245C211yesmaximal, characteristic, complemented
8#31029C211yesmaximal, characteristic, complemented
9#31029C211yesmaximal, characteristic, complemented
10#30398C211yesmaximal, characteristic, complemented
11#29489C211yesmaximal, characteristic, complemented
12#29076C211yesmaximal, characteristic, complemented
13#28908C211yesmaximal, characteristic, complemented
14#28090C211yesmaximal, characteristic, complemented
15#27525C211yesmaximal, characteristic, complemented
16#27230C211yesmaximal, characteristic, complemented
17#26819C211yesmaximal, characteristic, complemented
18#26813C211yesmaximal, characteristic, complemented
19#26635C211yesmaximal, characteristic, complemented
20#25890C211yesmaximal, characteristic, complemented
21#25532C211yesmaximal, characteristic, complemented
22#25253C211yesmaximal, characteristic, complemented
23#24515C211yesmaximal, characteristic, complemented
24#24275C211yesmaximal, characteristic, complemented
25#24124C211yesmaximal, characteristic, complemented
26#23863C211yesmaximal, characteristic, complemented
27#23712C211yesmaximal, characteristic, complemented
28#23130C211yesmaximal, characteristic, complemented
29#23090C211yesmaximal, characteristic, complemented
30#22442C211yesmaximal, characteristic, complemented
31#22053C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#485C2211yescharacteristic, complemented
37C2×#485C2211yescharacteristic, complemented
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic, complemented
40C2×#466C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#442C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47C2×#435C2211yescharacteristic
48C2×#433C2211yescharacteristic, complemented
49#2825—21no—
50#2765—21no—
51#2756—21no—
52#2753—21no—
53#2752—21no—
54#2706—21no—
55#2695—21no—
56#2688—21no—
57#2678—21no—
58#2649—21no—
59#2643—21no—
60#2625C2211yescharacteristic, complemented
61#2562C2211yescharacteristic
62#2535C2211yescharacteristic, complemented
63#2514C2211yescharacteristic, complemented
64#2510—21no—
65#2494C2211yescharacteristic
66#2489C2211yescharacteristic
67#2489C2211yescharacteristic, complemented
68#2486C2211yescharacteristic
69#2485C2211yescharacteristic
70#2480—21no—
71#2454C2211yescharacteristic
72#2454C2211yescharacteristic, complemented
73#2447C2211yescharacteristic
74#2427C2211yescharacteristic
75#2420—21no—
76#2418—21no—
77#2415C2211yescharacteristic
78#2415C2211yescharacteristic, complemented
79#2412—21no—
80#2408C2211yescharacteristic
81#2407C2211yescharacteristic
82#2407C2211yescharacteristic
83#2407C2211yescharacteristic
84#2392C2211yescharacteristic
85#2363C2211yescharacteristic
86#2363C2211yescharacteristic, complemented
87#2339C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2324C2211yescharacteristic
90#2324C2211yescharacteristic, complemented
91#2311C2211yescharacteristic
92#2097C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2076C2211yescharacteristic
98#2076C2211yescharacteristic
99#2075C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2056C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2054C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic, complemented
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic, complemented
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2012C2211yescharacteristic
126#2001C2211yescharacteristic, complemented
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic, complemented
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1991C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1972C2211yescharacteristic
137#1969C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1954C2211yescharacteristic
141#1954C2211yescharacteristic
142#1954C2211yescharacteristic, complemented
143#1944C2211yescharacteristic, complemented
144#1940C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic
157#1924C2211yescharacteristic, complemented
158#1923C2211yescharacteristic
159#1921C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1894C2211yescharacteristic
163#1892C2211yescharacteristic, complemented
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic, complemented
171#1877C2211yescharacteristic, complemented
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1875C2211yescharacteristic, complemented
175#1874C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1869C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1862C2211yescharacteristic
181#1854C2211yescharacteristic, complemented
182#1853C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1804C2211yescharacteristic
187#1788C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195C8×C4⋊C4C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1750C2211yescharacteristic, complemented
202#1735C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217#553—42no—
218#553—42no—
219#546—42no—
220#546—42no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256#488—42no—
257#485—42no—
258#485—42no—
259#478—42no—
260#478—42no—
261#466—24no—
262#465—42no—
263#452—42no—
264#452—42no—
265#449—24no—
266#442—42no—
267C4×D8—42no—
268#435—42no—
269#433—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#401—21no—
329#401—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#398—21no—
339#398D411yescharacteristic
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397D411yescharacteristic
354#396—21no—
355#396—21no—
356#396D411yescharacteristic
357#396D411yescharacteristic
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394D411yescharacteristic
368#394D411yescharacteristic
369#394D411yescharacteristic
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392D411yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#387—21no—
415#387—21no—
416#387—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#386—21no—
431#386—21no—
432#386—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#383—21no—
442#382—21no—
443#382—21no—
444#382C2311yescharacteristic
445#381—21no—
446#381—21no—
447#381—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#379—21no—
463#379—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C2×#95—21no—
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#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
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—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545AGL(1,ℤ/8)—416no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8#4114yes—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8—22no—
568C22×C8—41no—
569C22×C8—41no—
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578#126—44no—
579#125—22no—
580#125—41no—
581#125—41no—
582#125—41no—
583#124—22no—
584#124—41no—
585#123—44no—
586#123—44no—
587#123—82no—
588C22⋊Q8—22no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—44no—
607#121—44no—
608#120—44no—
609#120—82no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—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—
625C4×D4—41no—
626C4×D4—44no—
627#117—22no—
628#117—41no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
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—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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—44no—
709C2×C22⋊C4—82no—
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—41no—
734#107—41no—
735#107—41no—
736#106—22no—
737#106—22no—
738#106—41no—
739#106—41no—
740#106—41no—
741C4⋊C8—22no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783#97—22no—
784#97—41no—
785C4×C8—41no—
786C4×C8—41no—
787C4×C8—41no—
788C4×C8—41no—
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#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#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—21no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842C24C22×D411yescharacteristic
843#41—44no—
844#41—82no—
845#41—82no—
846#41—82no—
847#41—82no—
848#41—82no—
849#41—82no—
850#41—82no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×D4—24no—
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—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—81no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
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—
917C2×D4H(5,𝔽2)12yes—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
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—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C2511yescharacteristic
985Q16—82no—
986SD16—44no—
987SD16—44no—
988SD16—82no—
989D8—28no—
990D8—44no—
991M16—44no—
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×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—82no—
1015C2×C8C2×#4112yes—
1016C2×C8H(5,𝔽2)12yes—
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—21no—
1037C4⋊C4—21no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
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—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4H(5,𝔽2)12yes—
1062C22⋊C4—24no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
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—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—42no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—22no—
1139C23—22no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
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—84no—
1169C23—84no—
1170C23—84no—
1171C23—162no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23C23×D411yescharacteristic
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184D4—22no—
1185D4—22no—
1186D4—22no—
1187D4—22no—
1188D4—22no—
1189D4—22no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—84no—
1197D4—82no—
1198D4—82no—
1199D4—82no—
1200D4—84no—
1201D4—84no—
1202D4—84no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
1206D4—162no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
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—22no—
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—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—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—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4C22×#4111yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—22no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—42no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—42no—
1342C22—41no—
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—
1356C22D4×#4111yescharacteristic
1357C22#348411yescharacteristic
1358C22#349611yescharacteristic
1359C22#358411yescharacteristic
1360C22#358411yescharacteristic
1361C22#358411yescharacteristic
1362C22#358511yescharacteristic
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4#349011yescharacteristic
1388C4#351411yescharacteristic
1389C4#354611yescharacteristic
1390C4#356011yescharacteristic
1391C2—81no—
1392C2—81no—
1393C2—81no—
1394C2—82no—
1395C2—82no—
1396C2—82no—
1397C2#4304311yescharacteristic
1398C2#6150111yescharacteristic
1399C2#6153611yescharacteristic
1400C2#6162511yescharacteristic
1401C2#6163511yescharacteristic
1402C2#6231311yescharacteristic
1403C2#6234411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45010C2semidirect
2. #42760C2semidirect
3. #32275C2semidirect
4. #31921C2semidirect
5. #31674C2semidirect
6. #31672C2semidirect
7. #31245C2semidirect
8. #31029C2semidirect
9. #31029C2semidirect
10. #30398C2semidirect
11. #29489C2semidirect
12. #29076C2semidirect
13. #28908C2semidirect
14. #28090C2semidirect
15. #27525C2semidirect
16. #27230C2semidirect
17. #26819C2semidirect
18. #26813C2semidirect
19. #26635C2semidirect
20. #25890C2semidirect
21. #25532C2semidirect
22. #25253C2semidirect
23. #24515C2semidirect
24. #24275C2semidirect
25. #24124C2semidirect
26. #23863C2semidirect
27. #23712C2semidirect
28. #23130C2semidirect
29. #23090C2semidirect
30. #22442C2semidirect
31. #22053C2semidirect
36. C2×#485C22semidirect
37. C2×#485C22semidirect
39. C2×#478C22semidirect
48. C2×#433C22semidirect
60. #2625C22semidirect
62. #2535C22semidirect
63. #2514C22semidirect
67. #2489C22semidirect
72. #2454C22semidirect
78. #2415C22semidirect
86. #2363C22semidirect
90. #2324C22semidirect
92. #2097C22semidirect
93. #2088C22semidirect
96. #2077C22semidirect
99. #2075C22semidirect
101. #2068C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2066C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
110. #2059C22semidirect
111. #2056C22semidirect
112. #2056C22semidirect
116. #2036C22semidirect
120. #2034C22semidirect
123. #2026C22semidirect
126. #2001C22semidirect
129. #2000C22semidirect
132. #1991C22semidirect
137. #1969C22semidirect
139. #1968C22semidirect
142. #1954C22semidirect
143. #1944C22semidirect
144. #1940C22semidirect
145. #1935C22semidirect
146. #1935C22semidirect
150. #1934C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1927C22semidirect
155. #1927C22semidirect
157. #1924C22semidirect
159. #1921C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
163. #1892C22semidirect
170. #1877C22semidirect
171. #1877C22semidirect
174. #1875C22semidirect
175. #1874C22semidirect
176. #1872C22semidirect
178. #1869C22semidirect
181. #1854C22semidirect
182. #1853C22semidirect
183. #1852C22semidirect
194. #1776C22semidirect
195. C8×C4⋊C4C22semidirect
198. C4×#102C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1750C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#450102
#427602
#322752
#319212
#316742
#316722
#312452
#310292
#303982
#294892
#290762
#289082
#280902
#275252
#272302
#268192
#268132
#266352
#258902
#255322
#252532
#245152
#242752
#241242
#238632
#237122
#231302
#230902
#224422
#220532