Finite Group Databasebeta

← #7074199

Subgroups — #7074199

Order 512.

1461 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45367C211yesmaximal, characteristic, complemented
2#42621C211yesmaximal, characteristic, complemented
3#32640C211yesmaximal, characteristic, complemented
4#32612C211yesmaximal, characteristic, complemented
5#32532C211yesmaximal, characteristic, complemented
6#32077C211yesmaximal, characteristic, complemented
7#32063C211yesmaximal, characteristic, complemented
8#31286C211yesmaximal, characteristic, complemented
9#31148C211yesmaximal, characteristic, complemented
10#30460C211yesmaximal, characteristic
11#29468C211yesmaximal, characteristic, complemented
12#29087C211yesmaximal, characteristic, complemented
13#29086C211yesmaximal, characteristic, complemented
14#28898C211yesmaximal, characteristic, complemented
15#28746C211yesmaximal, characteristic, complemented
16#27486C211yesmaximal, characteristic, complemented
17#27482C211yesmaximal, characteristic, complemented
18#27402C211yesmaximal, characteristic, complemented
19#27245C211yesmaximal, characteristic, complemented
20#27240C211yesmaximal, characteristic, complemented
21#27217C211yesmaximal, characteristic, complemented
22#26896C211yesmaximal, characteristic, complemented
23#26709C211yesmaximal, characteristic, complemented
24#26257C211yesmaximal, characteristic, complemented
25#25482C211yesmaximal, characteristic, complemented
26#24512C211yesmaximal, characteristic, complemented
27#23706C211yesmaximal, characteristic, complemented
28#23099C211yesmaximal, characteristic, complemented
29#23079C211yesmaximal, characteristic, complemented
30#23059C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×#496C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×C4×SD16C2211yescharacteristic, complemented
40C2×#433C2211yescharacteristic
41#2832—21no—
42#2800—21no—
43#2798—21no—
44#2756—21no—
45#2749—21no—
46#2742—21no—
47#2702—21no—
48#2697—21no—
49#2685—21no—
50#2654—21no—
51#2625—21no—
52#2624C2211yescharacteristic
53#2592C2211yescharacteristic, complemented
54#2584C2211yescharacteristic, complemented
55#2554—21no—
56#2548C2211yescharacteristic
57#2538C2211yescharacteristic
58#2534—21no—
59#2513C2211yescharacteristic
60#2512C2211yescharacteristic
61#2511C2211yescharacteristic, complemented
62#2500C2211yescharacteristic
63#2496C2211yescharacteristic
64#2492C2211yescharacteristic
65#2490C2211yescharacteristic
66#2479—21no—
67#2472—21no—
68#2461—21no—
69#2453C2211yescharacteristic, complemented
70#2452C2211yescharacteristic, complemented
71#2448C2211yescharacteristic, complemented
72#2445C2211yescharacteristic
73#2445C2211yescharacteristic
74#2433C2211yescharacteristic
75#2427C2211yescharacteristic
76#2396C2211yescharacteristic
77#2369C2211yescharacteristic, complemented
78#2366C2211yescharacteristic
79#2357C2211yescharacteristic
80#2354C2211yescharacteristic, complemented
81#2347C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2323C2211yescharacteristic
85#2309C2211yescharacteristic
86#2097C2211yescharacteristic, complemented
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2076C2211yescharacteristic
95#2073C2211yescharacteristic, complemented
96#2072C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic, complemented
110#2042C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2014C2211yescharacteristic
123#2012C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1992C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1983C2211yescharacteristic, complemented
130#1982C2211yescharacteristic
131#1973C2211yescharacteristic
132#1973C2211yescharacteristic
133#1973C2211yescharacteristic, complemented
134#1972C2211yescharacteristic
135#1972C2211yescharacteristic
136#1972C2211yescharacteristic, complemented
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1957C2211yescharacteristic
141#1949C2211yescharacteristic, complemented
142#1948C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1943C2211yescharacteristic, complemented
145#1942C2211yescharacteristic, complemented
146#1939C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic, complemented
151#1936C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1923C2211yescharacteristic
169#1921C2211yescharacteristic, complemented
170#1921C2211yescharacteristic, complemented
171#1920C2211yescharacteristic, complemented
172#1919C2211yescharacteristic, complemented
173#1918C2211yescharacteristic, complemented
174#1917C2211yescharacteristic, complemented
175#1916C2211yescharacteristic, complemented
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic, complemented
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1875C2211yescharacteristic
185#1873C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193C4×#107C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#120—21no—
226C2×#120—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C22⋊C4—21no—
238#496—42no—
239#478—42no—
240#474—24no—
241#459—24no—
242#450—24no—
243#447—42no—
244#446—42no—
245C4×SD16—42no—
246#433—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400D411yescharacteristic
309#399—21no—
310#399—21no—
311#399D411yescharacteristic
312#398—21no—
313#398—21no—
314#398D411yescharacteristic
315#398D411yescharacteristic
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396D411yescharacteristic
330#396D411yescharacteristic
331#395—21no—
332#395D411yescharacteristic
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#393D411yescharacteristic
349#392—21no—
350#392—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
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#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—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#385—21no—
427#385—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#383—21no—
431#382C2311yescharacteristic
432#381—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440#379—21no—
441#379—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C4⋊Q8—22no—
540C4⋊Q8—41no—
541#127—22no—
542#127—41no—
543#127—41no—
544#127—41no—
545#126—82no—
546#126—82no—
547#125—41no—
548#125—41no—
549#124—41no—
550#124—41no—
551#124—82no—
552#123—82no—
553#123—82no—
554C22⋊Q8—22no—
555C22⋊Q8—41no—
556C22⋊Q8—82no—
557C22⋊Q8—82no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#120—82no—
563#120—82no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—82no—
577#117—41no—
578#117—41no—
579#117—41no—
580#117—41no—
581#117—82no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—22no—
695#106—41no—
696#106—41no—
697C4⋊C8—22no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102#4114yes—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735#97—22no—
736#97—41no—
737#97—41no—
738#97—41no—
739#97—41no—
740C4×C8—22no—
741C4×C8—41no—
742C4×C8—41no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—42no—
787C24—42no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24C22×D411yescharacteristic
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—41no—
801C2×Q8—41no—
802C2×Q8—41no—
803C2×Q8—42no—
804C2×Q8—81no—
805C2×Q8—81no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4C2×#4112yes—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2511yescharacteristic
899SD16—44no—
900SD16—82no—
901SD16—82no—
902D8—82no—
903D8—82no—
904D8—82no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8C2×#4112yes—
928C2×C8H(5,𝔽2)12yes—
929C4⋊C4—22no—
930C4⋊C4—22no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4C2×#4112yes—
980C22⋊C4—22no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—42no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—22no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—84no—
1086C23—84no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23C23×D411yescharacteristic
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—82no—
1098Q8—162no—
1099D4—22no—
1100D4—22no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—84no—
1116D4—84no—
1117D4—162no—
1118D4—162no—
1119D4—162no—
1120D4—162no—
1121D4—162no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—22no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—84no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4#57612yes—
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4#58511yescharacteristic
1208C2×C4#58511yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C8—22no—
1212C8—22no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C22—42no—
1220C22—41no—
1221C22—41no—
1222C22—42no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—42no—
1227C22—41no—
1228C22—41no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—168no—
1255C22D4×#4111yescharacteristic
1256C22#348711yescharacteristic
1257C22#349611yescharacteristic
1258C22C2×#57611yescharacteristic
1259C22#358511yescharacteristic
1260C22#358511yescharacteristic
1261C22#358611yescharacteristic
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—42no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4#351011yescharacteristic
1288C4#351411yescharacteristic
1289C4#353311yescharacteristic
1290C4#356611yescharacteristic
1291C2—81no—
1292C2—82no—
1293C2—161no—
1294C2—161no—
1295C2—161no—
1296C2#4392511yescharacteristic
1297C2#6151311yescharacteristic
1298C2#6151911yescharacteristic
1299C2#6192011yescharacteristic
1300C2#6193911yescharacteristic
1301C2#6228611yescharacteristic
1302C2#6235311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30460C2
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. #45367C2semidirect
2. #42621C2semidirect
3. #32640C2semidirect
4. #32612C2semidirect
5. #32532C2semidirect
6. #32077C2semidirect
7. #32063C2semidirect
8. #31286C2semidirect
9. #31148C2semidirect
11. #29468C2semidirect
12. #29087C2semidirect
13. #29086C2semidirect
14. #28898C2semidirect
15. #28746C2semidirect
16. #27486C2semidirect
17. #27482C2semidirect
18. #27402C2semidirect
19. #27245C2semidirect
20. #27240C2semidirect
21. #27217C2semidirect
22. #26896C2semidirect
23. #26709C2semidirect
24. #26257C2semidirect
25. #25482C2semidirect
26. #24512C2semidirect
27. #23706C2semidirect
28. #23099C2semidirect
29. #23079C2semidirect
30. #23059C2semidirect
31. #22052C2semidirect
38. C2×#446C22semidirect
39. C2×C4×SD16C22semidirect
53. #2592C22semidirect
54. #2584C22semidirect
61. #2511C22semidirect
69. #2453C22semidirect
70. #2452C22semidirect
71. #2448C22semidirect
77. #2369C22semidirect
80. #2354C22semidirect
86. #2097C22semidirect
88. #2093C22semidirect
89. #2088C22semidirect
90. #2087C22semidirect
91. #2086C22semidirect
92. #2083C22semidirect
95. #2073C22semidirect
96. #2072C22semidirect
97. #2068C22semidirect
100. #2067C22semidirect
104. #2055C22semidirect
105. #2055C22semidirect
109. #2054C22semidirect
110. #2042C22semidirect
119. #2025C22semidirect
121. #2023C22semidirect
126. #1993C22semidirect
127. #1992C22semidirect
128. #1985C22semidirect
129. #1983C22semidirect
133. #1973C22semidirect
136. #1972C22semidirect
138. #1970C22semidirect
141. #1949C22semidirect
142. #1948C22semidirect
143. #1947C22semidirect
144. #1943C22semidirect
145. #1942C22semidirect
146. #1939C22semidirect
150. #1936C22semidirect
151. #1936C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
158. #1926C22semidirect
163. #1925C22semidirect
164. #1925C22semidirect
169. #1921C22semidirect
170. #1921C22semidirect
171. #1920C22semidirect
172. #1919C22semidirect
173. #1918C22semidirect
174. #1917C22semidirect
175. #1916C22semidirect
181. #1879C22semidirect
186. #1862C22semidirect
187. #1862C22semidirect
192. #1776C22semidirect
193. C4×#107C22semidirect
194. #1771C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1763C22semidirect
200. #1762C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#453672
#426212
#326402
#326122
#325322
#320772
#320632
#312862
#311482
#304602
#294682
#290872
#290862
#288982
#287462
#274862
#274822
#274022
#272452
#272402
#272172
#268962
#267092
#262572
#254822
#245122
#237062
#230992
#230792
#230592
#220522