Finite Group Databasebeta

← #7536051

Subgroups — #7536051

Order 512.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44961C211yesmaximal, characteristic, complemented
2#35846C211yesmaximal, characteristic, complemented
3#32654C211yesmaximal, characteristic, complemented
4#32626C211yesmaximal, characteristic, complemented
5#32182C211yesmaximal, characteristic, complemented
6#30757C211yesmaximal, characteristic, complemented
7#28893C211yesmaximal, characteristic, complemented
8#28588C211yesmaximal, characteristic, complemented
9#28350C211yesmaximal, characteristic, complemented
10#28320C211yesmaximal, characteristic, complemented
11#27513C211yesmaximal, characteristic, complemented
12#27215C211yesmaximal, characteristic, complemented
13#27202C211yesmaximal, characteristic, complemented
14#27083C211yesmaximal, characteristic, complemented
15#26613C211yesmaximal, characteristic, complemented
16#26591C211yesmaximal, characteristic, complemented
17#26261C211yesmaximal, characteristic, complemented
18#25796C211yesmaximal, characteristic
19#25636C211yesmaximal, characteristic, complemented
20#25220C211yesmaximal, characteristic, complemented
21#25084C211yesmaximal, characteristic, complemented
22#24487C211yesmaximal, characteristic, complemented
23#24367C211yesmaximal, characteristic
24#24205C211yesmaximal, characteristic, complemented
25#23246C211yesmaximal, characteristic, complemented
26#23194C211yesmaximal, characteristic, complemented
27#23112C211yesmaximal, characteristic, complemented
28#22928C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic, complemented
30#21465C211yesmaximal, characteristic, complemented
31#20932C211yesmaximal, characteristic
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#556C2211yescharacteristic, complemented
34C2×#520C2211yescharacteristic
35C2×#497C2211yescharacteristic
36C2×#495C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#470C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#461C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic, complemented
49C2×C4×Q16C2211yescharacteristic, complemented
50C2×#416C2211yescharacteristic
51C22×#102C2211yescharacteristic
52#2761—21no—
53#2735—21no—
54#2735—21no—
55#2723—21no—
56#2638—21no—
57#2621C2211yescharacteristic
58#2592C2211yescharacteristic
59#2583—21no—
60#2581C2211yescharacteristic, complemented
61#2561—21no—
62#2546C2211yescharacteristic, complemented
63#2538C2211yescharacteristic
64#2531—21no—
65#2526—21no—
66#2513C2211yescharacteristic
67#2512C2211yescharacteristic
68#2499C2211yescharacteristic
69#2484—21no—
70#2480—21no—
71#2478—21no—
72#2478—21no—
73#2466—21no—
74#2466—21no—
75#2448C2211yescharacteristic
76#2447C2211yescharacteristic
77#2447C2211yescharacteristic, complemented
78#2447C2211yescharacteristic, complemented
79#2435C2211yescharacteristic
80#2432C2211yescharacteristic
81#2432C2211yescharacteristic
82#2396C2211yescharacteristic
83#2395—21no—
84#2367C2211yescharacteristic
85#2365C2211yescharacteristic, complemented
86#2365C2211yescharacteristic, complemented
87#2360C2211yescharacteristic
88#2360C2211yescharacteristic
89#2357C2211yescharacteristic
90#2357C2211yescharacteristic, complemented
91#2346C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93#2323C2211yescharacteristic
94#2309C2211yescharacteristic
95#2095C2211yescharacteristic, complemented
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic, complemented
107#2056C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2054C2211yescharacteristic
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic, complemented
115#2016C2211yescharacteristic, complemented
116#2016C2211yescharacteristic, complemented
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2015C2211yescharacteristic, complemented
120#2013C2211yescharacteristic
121#2013C2211yescharacteristic
122#2013C2211yescharacteristic
123#2013C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#1985C2211yescharacteristic, complemented
128#1984C2211yescharacteristic, complemented
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic, complemented
131#1981C2211yescharacteristic, complemented
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic, complemented
136#1972C2211yescharacteristic
137#1971C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1960C2211yescharacteristic, complemented
142#1959C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1942C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1925C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1917C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1894C2211yescharacteristic
162#1892C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic, complemented
181#1872C2211yescharacteristic
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1851C2211yescharacteristic
188#1850C2211yescharacteristic
189#1803C2211yescharacteristic, complemented
190#1788C2211yescharacteristic
191#1776C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1750C2211yescharacteristic
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×M16C2311yescharacteristic
221C23×C8C2311yescharacteristic
222#556—42no—
223#556—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×#126—21no—
228C2×#126—21no—
229C2×#126—21no—
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239#520—42no—
240#520—42no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117—21no—
254C2×#117—21no—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4C2311yescharacteristic
259C22×C22⋊C4—21no—
260#497—24no—
261#495—42no—
262#485—24no—
263#485—42no—
264#470—42no—
265#467—42no—
266#464—42no—
267#463—42no—
268#461—24no—
269#452—24no—
270#450—24no—
271#450—42no—
272#440—42no—
273#440—42no—
274C4×Q16—42no—
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#416—42no—
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×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#102—42no—
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#400—21no—
330#400D411yescharacteristic
331#399—21no—
332#399D411yescharacteristic
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398D411yescharacteristic
338#398D411yescharacteristic
339#397—21no—
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#397—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396D411yescharacteristic
358#396D411yescharacteristic
359#395—21no—
360#395D411yescharacteristic
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#393—21no—
368#393D411yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
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#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
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#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#386—21no—
431#386—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#384C2311yescharacteristic
443#382—21no—
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#381—21no—
448#381—21no—
449#381—21no—
450#381—21no—
451#380—21no—
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456#379—21no—
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4—21no—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475#376—21no—
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8C2×D411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532AGL(1,ℤ/8)—416no—
533C2×Q16—22no—
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16#4114yes—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—41no—
568C2×D8—41no—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—41no—
572C22×C8—22no—
573C22×C8—41no—
574C22×C8—41no—
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589#126—44no—
590#126—44no—
591#126—82no—
592#124—22no—
593#124—22no—
594#124—22no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—41no—
599#124—41no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—44no—
607C22⋊Q8—82no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—44no—
629C4×D4—44no—
630#117—22no—
631#117—22no—
632#117—41no—
633#117—41no—
634#117—44no—
635#117—44no—
636C2×C4⋊C4—22no—
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—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—41no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
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—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#107—22no—
743#107—22no—
744#107—41no—
745#107—41no—
746#107—41no—
747#106—22no—
748#106—41no—
749#106—41no—
750C4⋊C8—22no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754#103—22no—
755#103—22no—
756#103—22no—
757#103—22no—
758#103—22no—
759#103—22no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786C22⋊C8—22no—
787C22⋊C8#4114yes—
788#97—22no—
789#97—41no—
790#97—41no—
791#97—41no—
792C4×C8—41no—
793C4×C8—41no—
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#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848#41—28no—
849#41—44no—
850#41—44no—
851#41—44no—
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—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—41no—
876C2×Q8—41no—
877C2×Q8—41no—
878C2×Q8C2×#4112yes—
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—21no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—81no—
905C2×D4C2×#4112yes—
906C2×D4H(5,𝔽2)12yes—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—24no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C2×#4112yes—
956C22×C4H(5,𝔽2)12yes—
957C22×C4C2511yescharacteristic
958Q16—44no—
959Q16—82no—
960Q16—82no—
961SD16—44no—
962SD16—44no—
963SD16—44no—
964SD16—44no—
965SD16—82no—
966SD16—82no—
967SD16—82no—
968D8—44no—
969D8—44no—
970M16—44no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—82no—
993C2×C8C2×#4112yes—
994C2×C8C2×#4112yes—
995C2×C8C2×#4112yes—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4H(5,𝔽2)12yes—
1047C22⋊C4—24no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
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—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—42no—
1103C42—42no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
1120C23—22no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—84no—
1141C23—84no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23#55012yes—
1148C23C23×D411yescharacteristic
1149Q8—22no—
1150Q8—22no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—82no—
1166D4—22no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—48no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—84no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
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—22no—
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—22no—
1224C2×C4—48no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
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—84no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4#55012yes—
1268C2×C4C22×#4111yescharacteristic
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4#58511yescharacteristic
1274C8—22no—
1275C8—22no—
1276C8—22no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—168no—
1311C22C2×#55011yescharacteristic
1312C22D4×#4111yescharacteristic
1313C22#348411yescharacteristic
1314C22#358411yescharacteristic
1315C22#358511yescharacteristic
1316C22#358611yescharacteristic
1317C22#358611yescharacteristic
1318C4—22no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—42no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4#348111yescharacteristic
1345C4#349011yescharacteristic
1346C4#351311yescharacteristic
1347C4#354211yescharacteristic
1348C2—42no—
1349C2—82no—
1350C2—82no—
1351C2—161no—
1352C2#5904511yescharacteristic
1353C2#6141511yescharacteristic
1354C2#6142311yescharacteristic
1355C2#6151311yescharacteristic
1356C2#6155011yescharacteristic
1357C2#6161411yescharacteristic
1358C2#6167611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44961C2semidirect
2. #35846C2semidirect
3. #32654C2semidirect
4. #32626C2semidirect
5. #32182C2semidirect
6. #30757C2semidirect
7. #28893C2semidirect
8. #28588C2semidirect
9. #28350C2semidirect
10. #28320C2semidirect
11. #27513C2semidirect
12. #27215C2semidirect
13. #27202C2semidirect
14. #27083C2semidirect
15. #26613C2semidirect
16. #26591C2semidirect
17. #26261C2semidirect
19. #25636C2semidirect
20. #25220C2semidirect
21. #25084C2semidirect
22. #24487C2semidirect
24. #24205C2semidirect
25. #23246C2semidirect
26. #23194C2semidirect
27. #23112C2semidirect
28. #22928C2semidirect
29. #22854C2semidirect
30. #21465C2semidirect
33. C2×#556C22semidirect
48. C2×#440C22semidirect
49. C2×C4×Q16C22semidirect
60. #2581C22semidirect
62. #2546C22semidirect
77. #2447C22semidirect
78. #2447C22semidirect
85. #2365C22semidirect
86. #2365C22semidirect
90. #2357C22semidirect
95. #2095C22semidirect
98. #2092C22semidirect
99. #2085C22semidirect
100. #2084C22semidirect
101. #2074C22semidirect
102. #2074C22semidirect
103. #2068C22semidirect
105. #2066C22semidirect
106. #2065C22semidirect
107. #2056C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
114. #2042C22semidirect
115. #2016C22semidirect
116. #2016C22semidirect
119. #2015C22semidirect
127. #1985C22semidirect
128. #1984C22semidirect
130. #1983C22semidirect
131. #1981C22semidirect
135. #1973C22semidirect
137. #1971C22semidirect
141. #1960C22semidirect
142. #1959C22semidirect
143. #1949C22semidirect
144. #1942C22semidirect
146. #1935C22semidirect
147. #1928C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
154. #1925C22semidirect
155. #1920C22semidirect
156. #1918C22semidirect
157. #1917C22semidirect
158. #1917C22semidirect
159. #1917C22semidirect
160. #1916C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
180. #1877C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
185. #1862C22semidirect
189. #1803C22semidirect
191. #1776C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1763C22semidirect
196. C4×#103C22semidirect
197. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#449612
#358462
#326542
#326262
#321822
#307572
#288932
#285882
#283502
#283202
#275132
#272152
#272022
#270832
#266132
#265912
#262612
#257962
#256362
#252202
#250842
#244872
#243672
#242052
#232462
#231942
#231122
#229282
#228542
#214652
#209322