Finite Group Databasebeta

← #7087147

Subgroups — #7087147

Order 512.

1551 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45294C211yesmaximal, characteristic, complemented
2#42544C211yesmaximal, characteristic, complemented
3#32541C211yesmaximal, characteristic, complemented
4#32179C211yesmaximal, characteristic, complemented
5#32079C211yesmaximal, characteristic, complemented
6#32071C211yesmaximal, characteristic, complemented
7#30886C211yesmaximal, characteristic, complemented
8#30615C211yesmaximal, characteristic, complemented
9#30472C211yesmaximal, characteristic
10#30448C211yesmaximal, characteristic, complemented
11#29569C211yesmaximal, characteristic, complemented
12#28957C211yesmaximal, characteristic, complemented
13#28928C211yesmaximal, characteristic, complemented
14#28630C211yesmaximal, characteristic, complemented
15#28468C211yesmaximal, characteristic, complemented
16#28365C211yesmaximal, characteristic, complemented
17#27083C211yesmaximal, characteristic, complemented
18#26643C211yesmaximal, characteristic, complemented
19#26585C211yesmaximal, characteristic, complemented
20#26552C211yesmaximal, characteristic, complemented
21#26261C211yesmaximal, characteristic, complemented
22#26173C211yesmaximal, characteristic, complemented
23#25418C211yesmaximal, characteristic, complemented
24#25377C211yesmaximal, characteristic, complemented
25#25176C211yesmaximal, characteristic, complemented
26#25105C211yesmaximal, characteristic, complemented
27#23812C211yesmaximal, characteristic, complemented
28#23285C211yesmaximal, characteristic, complemented
29#23010C211yesmaximal, characteristic, complemented
30#22880C211yesmaximal, characteristic, complemented
31#22159C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic, complemented
33C2×#496C2211yescharacteristic
34C2×#495C2211yescharacteristic
35C2×#488C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#463C2211yescharacteristic, complemented
43C2×#461C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic, complemented
49C2×C4×Q16C2211yescharacteristic, complemented
50C2×C4×SD16C2211yescharacteristic, complemented
51C2×C4×D8C2211yescharacteristic
52C2×#418C2211yescharacteristic
53#2826—21no—
54#2800—21no—
55#2783—21no—
56#2778—21no—
57#2761—21no—
58#2757—21no—
59#2753—21no—
60#2697—21no—
61#2685—21no—
62#2641C2211yescharacteristic
63#2636—21no—
64#2622—21no—
65#2594—21no—
66#2587—21no—
67#2545C2211yescharacteristic, complemented
68#2544C2211yescharacteristic
69#2544C2211yescharacteristic
70#2515—21no—
71#2513—21no—
72#2513C2211yescharacteristic, complemented
73#2512C2211yescharacteristic
74#2507C2211yescharacteristic, complemented
75#2499C2211yescharacteristic
76#2489C2211yescharacteristic
77#2454C2211yescharacteristic
78#2448C2211yescharacteristic
79#2447C2211yescharacteristic, complemented
80#2435C2211yescharacteristic
81#2433C2211yescharacteristic
82#2429C2211yescharacteristic
83#2426C2211yescharacteristic
84#2426C2211yescharacteristic
85#2426C2211yescharacteristic
86#2422C2211yescharacteristic
87#2418—21no—
88#2401C2211yescharacteristic
89#2366C2211yescharacteristic
90#2365C2211yescharacteristic, complemented
91#2363C2211yescharacteristic
92#2362C2211yescharacteristic
93#2351C2211yescharacteristic, complemented
94D4×C22⋊C4C2211yescharacteristic
95#2326C2211yescharacteristic
96#2326C2211yescharacteristic, complemented
97#2320C2211yescharacteristic, complemented
98#2095C2211yescharacteristic, complemented
99#2095C2211yescharacteristic, complemented
100#2093C2211yescharacteristic
101#2093C2211yescharacteristic, complemented
102#2092C2211yescharacteristic
103#2087C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic, complemented
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2013C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic, complemented
133#2011C2211yescharacteristic
134#2001C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1992C2211yescharacteristic, complemented
139#1983C2211yescharacteristic
140#1983C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic, complemented
144#1972C2211yescharacteristic
145#1971C2211yescharacteristic, complemented
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic, complemented
148#1961C2211yescharacteristic
149#1957C2211yescharacteristic
150#1949C2211yescharacteristic, complemented
151#1948C2211yescharacteristic, complemented
152#1943C2211yescharacteristic, complemented
153#1942C2211yescharacteristic, complemented
154#1940C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic, complemented
157#1934C2211yescharacteristic
158#1934C2211yescharacteristic
159#1933C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1926C2211yescharacteristic, complemented
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1923C2211yescharacteristic
168#1918C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1916C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1895C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic, complemented
178#1880C2211yescharacteristic, complemented
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic
181#1879C2211yescharacteristic, complemented
182#1878C2211yescharacteristic, complemented
183#1878C2211yescharacteristic, complemented
184#1877C2211yescharacteristic
185#1873C2211yescharacteristic
186#1865C2211yescharacteristic, complemented
187#1865C2211yescharacteristic, complemented
188#1864C2211yescharacteristic
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic, complemented
191#1862C2211yescharacteristic, complemented
192#1854C2211yescharacteristic
193#1851C2211yescharacteristic
194#1803C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1768C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#125C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×#120—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C22⋊C4—21no—
247#497—42no—
248#496—42no—
249#495—42no—
250#488—42no—
251#482—42no—
252#470—42no—
253#468—42no—
254#464—24no—
255#464—42no—
256#463—42no—
257#461—42no—
258#460—24no—
259#450—42no—
260#450—42no—
261#447—24no—
262#440—42no—
263#440—42no—
264C4×Q16—42no—
265C4×SD16—42no—
266C4×D8—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#418—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#401D411yescharacteristic
324#400—21no—
325#400D411yescharacteristic
326#400D411yescharacteristic
327#400D411yescharacteristic
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397D411yescharacteristic
344#397D411yescharacteristic
345#397D411yescharacteristic
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396D411yescharacteristic
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#392—21no—
370#392—21no—
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
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#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#383—21no—
451#382—21no—
452#382—21no—
453#382—21no—
454#382C2311yescharacteristic
455#381—21no—
456#380—21no—
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460#379—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474#376C2311yescharacteristic
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—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C2×Q16—22no—
526C2×Q16—22no—
527C2×Q16—22no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×Q16—41no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×M16—22no—
562C2×M16—41no—
563C2×M16—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—41no—
574#127—22no—
575#127—41no—
576#127—41no—
577#127—41no—
578#126—82no—
579#125—41no—
580#125—41no—
581#124—22no—
582#124—22no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#123—82no—
592C22⋊Q8—22no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—41no—
602#120—82no—
603#120—82no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—82no—
623#117—41no—
624#117—41no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—82no—
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—41no—
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#4114yes—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—41no—
776#97—22no—
777#97—41no—
778#97—41no—
779#97—41no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—41no—
783#95—21no—
784#95—21no—
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#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8H(5,𝔽2)12yes—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4C2×#4112yes—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C2511yescharacteristic
947Q16—44no—
948Q16—82no—
949SD16—44no—
950SD16—44no—
951SD16—44no—
952SD16—82no—
953SD16—82no—
954SD16—82no—
955SD16—82no—
956D8—44no—
957D8—82no—
958D8—82no—
959M16—82no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
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×C8C2×#4112yes—
982C2×C8H(5,𝔽2)12yes—
983C2×C8H(5,𝔽2)12yes—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—41no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4C2×#4112yes—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
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—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—22no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
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—84no—
1137C23—84no—
1138C23—162no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23C23×D411yescharacteristic
1144Q8—22no—
1145Q8—22no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156D4—22no—
1157D4—22no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—84no—
1173D4—84no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
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—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
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—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4—162no—
1262C2×C4C22×#4111yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4C2×H(5,𝔽2)11yescharacteristic
1265C2×C4C2×H(5,𝔽2)11yescharacteristic
1266C2×C4#58511yescharacteristic
1267C2×C4#58511yescharacteristic
1268C8—22no—
1269C8—22no—
1270C8—22no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C22—42no—
1277C22—41no—
1278C22—42no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—42no—
1284C22—41no—
1285C22—41no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
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—81no—
1311C22—168no—
1312C22D4×#4111yescharacteristic
1313C22#348811yescharacteristic
1314C22#349811yescharacteristic
1315C22#358411yescharacteristic
1316C22#358511yescharacteristic
1317C22#358511yescharacteristic
1318C22#358611yescharacteristic
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4#350611yescharacteristic
1345C4#351911yescharacteristic
1346C4#353311yescharacteristic
1347C4#353411yescharacteristic
1348C2—81no—
1349C2—82no—
1350C2—161no—
1351C2—161no—
1352C2—161no—
1353C2#4418411yescharacteristic
1354C2#6150311yescharacteristic
1355C2#6153611yescharacteristic
1356C2#6204911yescharacteristic
1357C2#6208511yescharacteristic
1358C2#6244111yescharacteristic
1359C2#6246211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30472C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45294C2semidirect
2. #42544C2semidirect
3. #32541C2semidirect
4. #32179C2semidirect
5. #32079C2semidirect
6. #32071C2semidirect
7. #30886C2semidirect
8. #30615C2semidirect
10. #30448C2semidirect
11. #29569C2semidirect
12. #28957C2semidirect
13. #28928C2semidirect
14. #28630C2semidirect
15. #28468C2semidirect
16. #28365C2semidirect
17. #27083C2semidirect
18. #26643C2semidirect
19. #26585C2semidirect
20. #26552C2semidirect
21. #26261C2semidirect
22. #26173C2semidirect
23. #25418C2semidirect
24. #25377C2semidirect
25. #25176C2semidirect
26. #25105C2semidirect
27. #23812C2semidirect
28. #23285C2semidirect
29. #23010C2semidirect
30. #22880C2semidirect
31. #22159C2semidirect
32. C2×#497C22semidirect
35. C2×#488C22semidirect
42. C2×#463C22semidirect
48. C2×#440C22semidirect
49. C2×C4×Q16C22semidirect
50. C2×C4×SD16C22semidirect
67. #2545C22semidirect
72. #2513C22semidirect
74. #2507C22semidirect
79. #2447C22semidirect
90. #2365C22semidirect
93. #2351C22semidirect
96. #2326C22semidirect
97. #2320C22semidirect
98. #2095C22semidirect
99. #2095C22semidirect
101. #2093C22semidirect
103. #2087C22semidirect
104. #2074C22semidirect
107. #2065C22semidirect
108. #2059C22semidirect
109. #2056C22semidirect
111. #2055C22semidirect
114. #2054C22semidirect
115. #2043C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
123. #2026C22semidirect
125. #2015C22semidirect
132. #2012C22semidirect
138. #1992C22semidirect
140. #1983C22semidirect
143. #1973C22semidirect
145. #1971C22semidirect
147. #1968C22semidirect
150. #1949C22semidirect
151. #1948C22semidirect
152. #1943C22semidirect
153. #1942C22semidirect
154. #1940C22semidirect
156. #1936C22semidirect
159. #1933C22semidirect
160. #1928C22semidirect
162. #1926C22semidirect
164. #1925C22semidirect
168. #1918C22semidirect
169. #1917C22semidirect
170. #1916C22semidirect
171. #1916C22semidirect
177. #1880C22semidirect
178. #1880C22semidirect
181. #1879C22semidirect
182. #1878C22semidirect
183. #1878C22semidirect
186. #1865C22semidirect
187. #1865C22semidirect
190. #1862C22semidirect
191. #1862C22semidirect
194. #1803C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1768C22semidirect
198. #1763C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#452942
#425442
#325412
#321792
#320792
#320712
#308862
#306152
#304722
#304482
#295692
#289572
#289282
#286302
#284682
#283652
#270832
#266432
#265852
#265522
#262612
#261732
#254182
#253772
#251762
#251052
#238122
#232852
#230102
#228802
#221592