Finite Group Databasebeta

← #7093575

Subgroups — #7093575

Order 512.

1591 conjugacy classes of subgroups.

The subgroup lattice has 1375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44985C211yesmaximal, characteristic, complemented
2#42566C211yesmaximal, characteristic, complemented
3#32675C211yesmaximal, characteristic, complemented
4#32597C211yesmaximal, characteristic, complemented
5#32306C211yesmaximal, characteristic, complemented
6#32060C211yesmaximal, characteristic, complemented
7#31834C211yesmaximal, characteristic, complemented
8#30711C211yesmaximal, characteristic, complemented
9#30539C211yesmaximal, characteristic, complemented
10#30501C211yesmaximal, characteristic, complemented
11#29529C211yesmaximal, characteristic, complemented
12#29510C211yesmaximal, characteristic, complemented
13#28932C211yesmaximal, characteristic, complemented
14#28332C211yesmaximal, characteristic, complemented
15#28067C211yesmaximal, characteristic, complemented
16#27934C211yesmaximal, characteristic, complemented
17#26961C211yesmaximal, characteristic, complemented
18#26644C211yesmaximal, characteristic, complemented
19#26563C211yesmaximal, characteristic, complemented
20#26547C211yesmaximal, characteristic, complemented
21#26318C211yesmaximal, characteristic, complemented
22#26130C211yesmaximal, characteristic, complemented
23#25068C211yesmaximal, characteristic, complemented
24#25040C211yesmaximal, characteristic, complemented
25#24901C211yesmaximal, characteristic, complemented
26#24861C211yesmaximal, characteristic, complemented
27#23808C211yesmaximal, characteristic, complemented
28#23274C211yesmaximal, characteristic, complemented
29#23022C211yesmaximal, characteristic, complemented
30#22858C211yesmaximal, characteristic, complemented
31#22232C211yesmaximal, characteristic, complemented
32C2×#490C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#481C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#466C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic, complemented
45C22×#106C2211yescharacteristic, complemented
46C22×#102C2211yescharacteristic
47#2826—21no—
48#2807—21no—
49#2796—21no—
50#2773—21no—
51#2749—21no—
52#2724—21no—
53#2688—21no—
54#2684—21no—
55#2668—21no—
56#2644C2211yescharacteristic
57#2631—21no—
58#2622—21no—
59#2602—21no—
60#2592C2211yescharacteristic, complemented
61#2580—21no—
62#2580C2211yescharacteristic
63#2548C2211yescharacteristic
64#2540C2211yescharacteristic
65#2504C2211yescharacteristic
66#2502C2211yescharacteristic
67#2501C2211yescharacteristic, complemented
68#2495C2211yescharacteristic
69#2490C2211yescharacteristic
70#2489C2211yescharacteristic, complemented
71#2458—21no—
72#2455—21no—
73#2433C2211yescharacteristic
74#2428C2211yescharacteristic
75#2428C2211yescharacteristic
76#2424—21no—
77#2423C2211yescharacteristic
78#2422C2211yescharacteristic, complemented
79#2420C2211yescharacteristic
80#2416C2211yescharacteristic
81#2408C2211yescharacteristic
82#2398C2211yescharacteristic
83#2361C2211yescharacteristic
84#2361C2211yescharacteristic
85#2360C2211yescharacteristic, complemented
86Q8×C4⋊C4C2211yescharacteristic, complemented
87D4×C4⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2330C2211yescharacteristic, complemented
90#2328C2211yescharacteristic
91#2326C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic, complemented
98#2093C2211yescharacteristic
99#2092C2211yescharacteristic, complemented
100#2092C2211yescharacteristic, complemented
101#2084C2211yescharacteristic, complemented
102#2083C2211yescharacteristic, complemented
103#2077C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic, complemented
112#2042C2211yescharacteristic, complemented
113#2036C2211yescharacteristic
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2025C2211yescharacteristic
120#2014C2211yescharacteristic
121#2014C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic, complemented
125#2011C2211yescharacteristic
126#2011C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic, complemented
129#1999C2211yescharacteristic
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic, complemented
132#1991C2211yescharacteristic, complemented
133#1985C2211yescharacteristic, complemented
134#1984C2211yescharacteristic, complemented
135#1982C2211yescharacteristic
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic
141#1957C2211yescharacteristic
142#1957C2211yescharacteristic
143#1949C2211yescharacteristic, complemented
144#1948C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic, complemented
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic, complemented
151#1934C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic, complemented
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic, complemented
165#1923C2211yescharacteristic
166#1923C2211yescharacteristic, complemented
167#1921C2211yescharacteristic, complemented
168#1920C2211yescharacteristic, complemented
169#1919C2211yescharacteristic, complemented
170#1893C2211yescharacteristic
171#1893C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1877C2211yescharacteristic
176#1874C2211yescharacteristic
177#1874C2211yescharacteristic, complemented
178#1872C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1853C2211yescharacteristic
188#1853C2211yescharacteristic, complemented
189#1852C2211yescharacteristic
190#1847C2211yescharacteristic, complemented
191#1847C2211yescharacteristic, complemented
192#1808C2211yescharacteristic
193#1802C2211yescharacteristic
194#1786C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201#1746C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C22⋊C4—21no—
249#490—24no—
250#481—42no—
251#481—42no—
252#480—42no—
253#466—42no—
254#465—24no—
255#465—42no—
256#450—42no—
257#447—24no—
258#442—42no—
259#440—42no—
260C4×SD16—42no—
261C4×D8—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#106—42no—
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102—42no—
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320#400—21no—
321#400—21no—
322#400D411yescharacteristic
323#400D411yescharacteristic
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—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#396—21no—
346#396—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394D411yescharacteristic
357#394D411yescharacteristic
358#393—21no—
359#393—21no—
360#393D411yescharacteristic
361#393D411yescharacteristic
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
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#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#383—21no—
444#382—21no—
445#382C2311yescharacteristic
446#382C2311yescharacteristic
447#381—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8C2×D411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559#127—22no—
560#127—41no—
561#127—41no—
562#127—41no—
563#125—22no—
564#125—41no—
565#124—41no—
566#124—41no—
567#124—82no—
568#123—82no—
569#123—82no—
570#123—82no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575#121—22no—
576#121—22no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—82no—
588#121—82no—
589#121—82no—
590#120—82no—
591#120—82no—
592#120—82no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—82no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—82no—
609C4×D4—82no—
610C4×D4—82no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
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—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
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—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—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—22no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102#4114yes—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766#97—22no—
767#97—22no—
768#97—41no—
769C4×C8—22no—
770C4×C8—41no—
771C4×C8—41no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
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#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—42no—
814C24—42no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822C2×Q8—22no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—41no—
830C2×Q8—41no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—41no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—44no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—82no—
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×D4C2×#4112yes—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
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—42no—
920C22×C4—81no—
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×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
953SD16—44no—
954SD16—44no—
955SD16—82no—
956D8—44no—
957D8—44no—
958D8—82no—
959C2×C8—21no—
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—44no—
981C2×C8—82no—
982C2×C8C2×#4112yes—
983C2×C8H(5,𝔽2)12yes—
984C2×C8H(5,𝔽2)12yes—
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—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
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⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4C2×#4112yes—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—22no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
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—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—42no—
1094C42—42no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—22no—
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—41no—
1137C23—41no—
1138C23—41no—
1139C23—84no—
1140C23—84no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23#57612yes—
1147C23#57712yes—
1148C23C23×D411yescharacteristic
1149Q8—44no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154D4—22no—
1155D4—22no—
1156D4—44no—
1157D4—41no—
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—84no—
1172D4—84no—
1173D4—84no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181D4—162no—
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—22no—
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—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—41no—
1219C2×C4—41no—
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—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—162no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4#57712yes—
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4#58511yescharacteristic
1273C2×C4#58511yescharacteristic
1274C2×C4#58511yescharacteristic
1275C8—22no—
1276C8—22no—
1277C8—22no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—168no—
1326C22D4×#4111yescharacteristic
1327C22#348511yescharacteristic
1328C22#349811yescharacteristic
1329C22C2×#57611yescharacteristic
1330C22C2×#57711yescharacteristic
1331C22C2×#57711yescharacteristic
1332C22#358511yescharacteristic
1333C4—22no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4#350611yescharacteristic
1358C4#351311yescharacteristic
1359C4#353311yescharacteristic
1360C4#354011yescharacteristic
1361C2—42no—
1362C2—42no—
1363C2—82no—
1364C2—161no—
1365C2—161no—
1366C2—161no—
1367C2#4427211yescharacteristic
1368C2#6149811yescharacteristic
1369C2#6152211yescharacteristic
1370C2#6174611yescharacteristic
1371C2#6176611yescharacteristic
1372C2#6243011yescharacteristic
1373C2#6245911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44985C2semidirect
2. #42566C2semidirect
3. #32675C2semidirect
4. #32597C2semidirect
5. #32306C2semidirect
6. #32060C2semidirect
7. #31834C2semidirect
8. #30711C2semidirect
9. #30539C2semidirect
10. #30501C2semidirect
11. #29529C2semidirect
12. #29510C2semidirect
13. #28932C2semidirect
14. #28332C2semidirect
15. #28067C2semidirect
16. #27934C2semidirect
17. #26961C2semidirect
18. #26644C2semidirect
19. #26563C2semidirect
20. #26547C2semidirect
21. #26318C2semidirect
22. #26130C2semidirect
23. #25068C2semidirect
24. #25040C2semidirect
25. #24901C2semidirect
26. #24861C2semidirect
27. #23808C2semidirect
28. #23274C2semidirect
29. #23022C2semidirect
30. #22858C2semidirect
31. #22232C2semidirect
34. C2×#481C22semidirect
42. C2×#440C22semidirect
44. C2×C4×D8C22semidirect
45. C22×#106C22semidirect
60. #2592C22semidirect
67. #2501C22semidirect
70. #2489C22semidirect
78. #2422C22semidirect
85. #2360C22semidirect
86. Q8×C4⋊C4C22semidirect
89. #2330C22semidirect
91. #2326C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
97. #2094C22semidirect
99. #2092C22semidirect
100. #2092C22semidirect
101. #2084C22semidirect
102. #2083C22semidirect
104. #2074C22semidirect
106. #2071C22semidirect
107. #2068C22semidirect
108. #2059C22semidirect
111. #2054C22semidirect
112. #2042C22semidirect
124. #2012C22semidirect
128. #2000C22semidirect
131. #1999C22semidirect
132. #1991C22semidirect
133. #1985C22semidirect
134. #1984C22semidirect
136. #1973C22semidirect
143. #1949C22semidirect
144. #1948C22semidirect
145. #1943C22semidirect
146. #1941C22semidirect
148. #1935C22semidirect
150. #1934C22semidirect
151. #1934C22semidirect
152. #1927C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
158. #1926C22semidirect
162. #1925C22semidirect
164. #1924C22semidirect
166. #1923C22semidirect
167. #1921C22semidirect
168. #1920C22semidirect
169. #1919C22semidirect
171. #1893C22semidirect
177. #1874C22semidirect
178. #1872C22semidirect
181. #1865C22semidirect
184. #1864C22semidirect
185. #1862C22semidirect
186. #1862C22semidirect
188. #1853C22semidirect
190. #1847C22semidirect
191. #1847C22semidirect
195. C4×#106C22semidirect
198. #1752C22semidirect
200. C8×C22⋊C4C22semidirect
201. #1746C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#449852
#425662
#326752
#325972
#323062
#320602
#318342
#307112
#305392
#305012
#295292
#295102
#289322
#283322
#280672
#279342
#269612
#266442
#265632
#265472
#263182
#261302
#250682
#250402
#249012
#248612
#238082
#232742
#230222
#228582
#222322