Finite Group Databasebeta

← #7090747

Subgroups — #7090747

Order 512.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45420C211yesmaximal, characteristic, complemented
2#45057C211yesmaximal, characteristic
3#32654C211yesmaximal, characteristic, complemented
4#32556C211yesmaximal, characteristic, complemented
5#31996C211yesmaximal, characteristic, complemented
6#31603C211yesmaximal, characteristic, complemented
7#31567C211yesmaximal, characteristic, complemented
8#31314C211yesmaximal, characteristic, complemented
9#30999C211yesmaximal, characteristic, complemented
10#30415C211yesmaximal, characteristic, complemented
11#29382C211yesmaximal, characteristic, complemented
12#29377C211yesmaximal, characteristic, complemented
13#29042C211yesmaximal, characteristic, complemented
14#27534C211yesmaximal, characteristic, complemented
15#26971C211yesmaximal, characteristic, complemented
16#26947C211yesmaximal, characteristic, complemented
17#26550C211yesmaximal, characteristic, complemented
18#25169C211yesmaximal, characteristic, complemented
19#25102C211yesmaximal, characteristic, complemented
20#24922C211yesmaximal, characteristic, complemented
21#24920C211yesmaximal, characteristic, complemented
22#24356C211yesmaximal, characteristic, complemented
23#24202C211yesmaximal, characteristic, complemented
24#24194C211yesmaximal, characteristic, complemented
25#24049C211yesmaximal, characteristic, complemented
26#23852C211yesmaximal, characteristic, complemented
27#23694C211yesmaximal, characteristic, complemented
28#22867C211yesmaximal, characteristic, complemented
29C22⋊C4×SD16C211yesmaximal, characteristic, complemented
30#22390C211yesmaximal, characteristic, complemented
31#22160C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#559C2211yescharacteristic
34C2×#546C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#468C2211yescharacteristic, complemented
37C2×#464C2211yescharacteristic, complemented
38C2×#460C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#451C2211yescharacteristic
43C2×#448C2211yescharacteristic
44C2×#441C2211yescharacteristic, complemented
45C2×#441C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic
47C2×C4×SD16C2211yescharacteristic
48C2×#417C2211yescharacteristic
49#2763—21no—
50#2758—21no—
51#2758—21no—
52#2742—21no—
53#2703—21no—
54#2693—21no—
55#2678—21no—
56#2676—21no—
57#2581C2211yescharacteristic, complemented
58#2581C2211yescharacteristic, complemented
59#2578—21no—
60#2578—21no—
61#2538C2211yescharacteristic
62#2537C2211yescharacteristic
63#2523—21no—
64#2517—21no—
65#2495C2211yescharacteristic
66#2495C2211yescharacteristic
67#2487C2211yescharacteristic
68#2472—21no—
69#2457—21no—
70#2433C2211yescharacteristic
71#2431C2211yescharacteristic
72#2428C2211yescharacteristic
73#2426C2211yescharacteristic
74#2424—21no—
75#2421C2211yescharacteristic
76#2421C2211yescharacteristic, complemented
77#2421C2211yescharacteristic, complemented
78#2420C2211yescharacteristic
79#2412—21no—
80#2409C2211yescharacteristic
81#2398C2211yescharacteristic
82#2360C2211yescharacteristic, complemented
83#2360C2211yescharacteristic, complemented
84#2341C2211yescharacteristic
85Q8×C22⋊C4C2211yescharacteristic
86Q8×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88#2328C2211yescharacteristic
89#2326C2211yescharacteristic
90#2320C2211yescharacteristic, complemented
91#2320C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2101C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2095C2211yescharacteristic, complemented
97#2092C2211yescharacteristic
98#2087C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic, complemented
103#2075C2211yescharacteristic
104#2073C2211yescharacteristic
105#2072C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2056C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic, complemented
123#2033C2211yescharacteristic
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2015C2211yescharacteristic, complemented
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic, complemented
132#1985C2211yescharacteristic, complemented
133#1984C2211yescharacteristic, complemented
134#1982C2211yescharacteristic
135#1973C2211yescharacteristic, complemented
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1961C2211yescharacteristic
139#1958C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic, complemented
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1894C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic, complemented
163#1878C2211yescharacteristic, complemented
164#1878C2211yescharacteristic, complemented
165#1878C2211yescharacteristic, complemented
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic, complemented
171#1877C2211yescharacteristic, complemented
172#1874C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1853C2211yescharacteristic, complemented
186#1851C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1840C2211yescharacteristic, complemented
189#1807C2211yescharacteristic
190#1805C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1788C2211yescharacteristic
194#1787C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1768C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202C8×C22⋊C4C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16—24no—
209C22×SD16—42no—
210C22×SD16—42no—
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#559—42no—
220#559—42no—
221#546—42no—
222#546—42no—
223C2×#127C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#124—21no—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×#120—21no—
243C2×#120—21no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260#480—42no—
261#468—42no—
262#464—42no—
263#460—24no—
264#460—42no—
265#452—24no—
266#452—42no—
267#451—42no—
268#448—42no—
269#441—42no—
270#441—42no—
271C4×SD16—42no—
272C4×SD16—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#417—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400D411yescharacteristic
337#400D411yescharacteristic
338#399—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397D411yescharacteristic
346#397D411yescharacteristic
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394D411yescharacteristic
359#394D411yescharacteristic
360#393—21no—
361#393D411yescharacteristic
362#393D411yescharacteristic
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#390—21no—
380#390—21no—
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#389—21no—
388#389—21no—
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—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#384C2311yescharacteristic
437#383—21no—
438#383—21no—
439#383—21no—
440#383—21no—
441#382—21no—
442#382—21no—
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
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×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8C2×D411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×D411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—416no—
569C2×SD16#4114yes—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C22×C8—22no—
574C22×C8—41no—
575C22×C8—41no—
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584#127—22no—
585#127—22no—
586#127—41no—
587#127—41no—
588#124—22no—
589#124—22no—
590#124—22no—
591#124—41no—
592#124—44no—
593#123—44no—
594#123—44no—
595#123—44no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—82no—
603#121—22no—
604#121—44no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—82no—
611#121—82no—
612#120—44no—
613#120—82no—
614#120—82no—
615C4×Q8—22no—
616C4×Q8—22no—
617C4×Q8—22no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×D4—22no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—44no—
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—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
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—44no—
707C2×C22⋊C4—82no—
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—41no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—22no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743#103—22no—
744#103—22no—
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#103—41no—
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—
773#102—41no—
774#102—41no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781#97—41no—
782#97—41no—
783C4×C8—41no—
784C4×C8—41no—
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#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#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—44no—
846#41—82no—
847#41—82no—
848#41—82no—
849C2×Q8—21no—
850C2×Q8—21no—
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×Q8—21no—
864C2×Q8—41no—
865C2×Q8—41no—
866C2×Q8—41no—
867C2×Q8—42no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—81no—
871C2×Q8—82no—
872C2×Q8—82no—
873C2×Q8—82no—
874C2×Q8C2×#4112yes—
875C2×Q8H(5,𝔽2)12yes—
876C2×Q8H(5,𝔽2)12yes—
877C2×D4—22no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—44no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—82no—
917C2×D4—82no—
918C2×D4—82no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4C2×#4112yes—
928C2×D4H(5,𝔽2)12yes—
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—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
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×C4—81no—
974C22×C4—81no—
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×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C2511yescharacteristic
988Q16—44no—
989Q16—44no—
990SD16—28no—
991SD16—44no—
992SD16—44no—
993SD16—44no—
994SD16—82no—
995SD16—82no—
996M16—82no—
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—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—44no—
1021C2×C8C2×#4112yes—
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—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—41no—
1045C4⋊C4—41no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
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⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
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—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—81no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—22no—
1135C23—22no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
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—84no—
1159C23—84no—
1160C23—84no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23—162no—
1165C23#57712yes—
1166C23C23×D411yescharacteristic
1167Q8—22no—
1168Q8—22no—
1169Q8—22no—
1170Q8—22no—
1171Q8—22no—
1172Q8—22no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—82no—
1180Q8—84no—
1181D4—22no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—82no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
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—22no—
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—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
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—84no—
1287C2×C4—84no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4C22×#4111yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4C2×H(5,𝔽2)11yescharacteristic
1297C2×C4#58511yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—22no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—42no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—42no—
1326C22—42no—
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—168no—
1343C22D4×#4111yescharacteristic
1344C22#348411yescharacteristic
1345C22#348811yescharacteristic
1346C22C2×#57711yescharacteristic
1347C22#358411yescharacteristic
1348C22#358511yescharacteristic
1349C22#358611yescharacteristic
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4#349011yescharacteristic
1376C4#351311yescharacteristic
1377C4#353411yescharacteristic
1378C4#356011yescharacteristic
1379C2—42no—
1380C2—81no—
1381C2—82no—
1382C2—82no—
1383C2—161no—
1384C2#4423111yescharacteristic
1385C2#6147211yescharacteristic
1386C2#6151311yescharacteristic
1387C2#6161811yescharacteristic
1388C2#6162511yescharacteristic
1389C2#6200911yescharacteristic
1390C2#6203011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45057C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45420C2semidirect
3. #32654C2semidirect
4. #32556C2semidirect
5. #31996C2semidirect
6. #31603C2semidirect
7. #31567C2semidirect
8. #31314C2semidirect
9. #30999C2semidirect
10. #30415C2semidirect
11. #29382C2semidirect
12. #29377C2semidirect
13. #29042C2semidirect
14. #27534C2semidirect
15. #26971C2semidirect
16. #26947C2semidirect
17. #26550C2semidirect
18. #25169C2semidirect
19. #25102C2semidirect
20. #24922C2semidirect
21. #24920C2semidirect
22. #24356C2semidirect
23. #24202C2semidirect
24. #24194C2semidirect
25. #24049C2semidirect
26. #23852C2semidirect
27. #23694C2semidirect
28. #22867C2semidirect
29. C22⋊C4×SD16C2semidirect
30. #22390C2semidirect
31. #22160C2semidirect
36. C2×#468C22semidirect
37. C2×#464C22semidirect
44. C2×#441C22semidirect
45. C2×#441C22semidirect
57. #2581C22semidirect
58. #2581C22semidirect
76. #2421C22semidirect
77. #2421C22semidirect
82. #2360C22semidirect
83. #2360C22semidirect
90. #2320C22semidirect
91. #2320C22semidirect
92. #2101C22semidirect
93. #2101C22semidirect
94. #2099C22semidirect
95. #2097C22semidirect
96. #2095C22semidirect
98. #2087C22semidirect
99. #2085C22semidirect
100. #2084C22semidirect
102. #2077C22semidirect
105. #2072C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
110. #2056C22semidirect
115. #2042C22semidirect
120. #2036C22semidirect
122. #2034C22semidirect
126. #2015C22semidirect
131. #2000C22semidirect
132. #1985C22semidirect
133. #1984C22semidirect
135. #1973C22semidirect
139. #1958C22semidirect
140. #1949C22semidirect
141. #1942C22semidirect
144. #1935C22semidirect
145. #1934C22semidirect
146. #1928C22semidirect
149. #1925C22semidirect
152. #1924C22semidirect
153. #1923C22semidirect
155. #1894C22semidirect
162. #1880C22semidirect
163. #1878C22semidirect
164. #1878C22semidirect
165. #1878C22semidirect
170. #1877C22semidirect
171. #1877C22semidirect
172. #1874C22semidirect
175. #1865C22semidirect
177. #1864C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
185. #1853C22semidirect
186. #1851C22semidirect
188. #1840C22semidirect
190. #1805C22semidirect
191. #1805C22semidirect
198. #1768C22semidirect
200. C4×#103C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#454202
#450572
#326542
#325562
#319962
#316032
#315672
#313142
#309992
#304152
#293822
#293772
#290422
#275342
#269712
#269472
#265502
#251692
#251022
#249222
#249202
#243562
#242022
#241942
#240492
#238522
#236942
#228672
C22⋊C4×SD162
#223902
#221602