Finite Group Databasebeta

← #7204447

Subgroups — #7204447

Order 512.

1631 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45701C211yesmaximal, characteristic, complemented
2#36436C211yesmaximal, characteristic, complemented
3#33006C211yesmaximal, characteristic, complemented
4#32910C211yesmaximal, characteristic, complemented
5#32778C211yesmaximal, characteristic, complemented
6#32746C211yesmaximal, characteristic, complemented
7#32436C211yesmaximal, characteristic, complemented
8#31945C211yesmaximal, characteristic, complemented
9#31655C211yesmaximal, characteristic, complemented
10#31613C211yesmaximal, characteristic, complemented
11#31057C211yesmaximal, characteristic, complemented
12#31033C211yesmaximal, characteristic, complemented
13#31008C211yesmaximal, characteristic, complemented
14#30619C211yesmaximal, characteristic, complemented
15#30569C211yesmaximal, characteristic, complemented
16#30513C211yesmaximal, characteristic, complemented
17#30424C211yesmaximal, characteristic, complemented
18#30405C211yesmaximal, characteristic, complemented
19#27513C211yesmaximal, characteristic, complemented
20#27204C211yesmaximal, characteristic, complemented
21#27114C211yesmaximal, characteristic, complemented
22#26936C211yesmaximal, characteristic, complemented
23#26245C211yesmaximal, characteristic, complemented
24#26225C211yesmaximal, characteristic, complemented
25#25548C211yesmaximal, characteristic, complemented
26#25231C211yesmaximal, characteristic, complemented
27#25084C211yesmaximal, characteristic, complemented
28#24975C211yesmaximal, characteristic, complemented
29#24873C211yesmaximal, characteristic, complemented
30#23963C211yesmaximal, characteristic, complemented
31#23331C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic, complemented
34C2×#485C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#483C2211yescharacteristic, complemented
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic, complemented
39C2×#467C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#452C2211yescharacteristic, complemented
43C2×#449C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2854C2211yescharacteristic
49#2853—21no—
50#2851C2211yescharacteristic, complemented
51#2850C2211yescharacteristic
52#2837—21no—
53#2756—21no—
54#2756—21no—
55#2735—21no—
56#2703—21no—
57#2697—21no—
58#2668—21no—
59#2602—21no—
60#2600—21no—
61#2565C2211yescharacteristic, complemented
62#2540C2211yescharacteristic
63#2536C2211yescharacteristic
64#2536C2211yescharacteristic
65#2513C2211yescharacteristic
66#2504C2211yescharacteristic
67#2495C2211yescharacteristic
68#2478—21no—
69#2476—21no—
70#2468—21no—
71#2464—21no—
72#2448C2211yescharacteristic
73#2435C2211yescharacteristic
74#2426C2211yescharacteristic
75#2422C2211yescharacteristic
76#2420C2211yescharacteristic, complemented
77#2417C2211yescharacteristic
78#2416C2211yescharacteristic
79#2408C2211yescharacteristic
80#2408C2211yescharacteristic
81#2407C2211yescharacteristic
82#2407C2211yescharacteristic, complemented
83#2375—21no—
84#2362C2211yescharacteristic, complemented
85#2360C2211yescharacteristic
86#2357C2211yescharacteristic, complemented
87#2354C2211yescharacteristic, complemented
88#2352C2211yescharacteristic
89C4×#123—21no—
90C4×#121C2211yescharacteristic
91#2100C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2085C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2054C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic, complemented
122#2035C2211yescharacteristic, complemented
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2026C2211yescharacteristic, complemented
130#2025C2211yescharacteristic
131#2025C2211yescharacteristic
132#2015C2211yescharacteristic
133#2012C2211yescharacteristic
134#2001C2211yescharacteristic, complemented
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic
139#1983C2211yescharacteristic
140#1972C2211yescharacteristic
141#1970C2211yescharacteristic
142#1968C2211yescharacteristic
143#1959C2211yescharacteristic
144#1955C2211yescharacteristic, complemented
145#1954C2211yescharacteristic
146#1949C2211yescharacteristic, complemented
147#1948C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1893C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1878C2211yescharacteristic, complemented
169#1878C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1875C2211yescharacteristic
174#1874C2211yescharacteristic, complemented
175#1873C2211yescharacteristic, complemented
176#1872C2211yescharacteristic
177#1870C2211yescharacteristic
178#1870C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1852C2211yescharacteristic
186#1852C2211yescharacteristic, complemented
187#1851C2211yescharacteristic, complemented
188#1850C2211yescharacteristic
189#1835C2211yescharacteristic, complemented
190#1825C2211yescharacteristic, complemented
191#1824C2211yescharacteristic
192#1817C2211yescharacteristic, complemented
193#1807C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1805C2211yescharacteristic, complemented
196#1804C2211yescharacteristic, complemented
197#1797C2211yescharacteristic, complemented
198#1788C2211yescharacteristic, complemented
199#1786C2211yescharacteristic
200#1776C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#553—42no—
214#553—42no—
215C2×#126—21no—
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121—21no—
229C2×#121D411yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C4×#41—42no—
239C4×#41—42no—
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C42—21no—
257C22×C42C2311yescharacteristic
258#485—42no—
259#483—42no—
260#482—42no—
261#468—42no—
262#468—42no—
263#467—42no—
264#464—42no—
265#463—42no—
266#452—42no—
267#450—42no—
268#449—42no—
269#449—42no—
270#447—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102—42no—
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×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—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#396—21no—
343#396—21no—
344#396—21no—
345#394—21no—
346#394—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#394—21no—
357#392—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390D411yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#389—21no—
379#389D411yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
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#388D411yescharacteristic
407#388D411yescharacteristic
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—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#386D411yescharacteristic
427#386D411yescharacteristic
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#384C2311yescharacteristic
435#383—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#381—21no—
441#381—21no—
442#380—21no—
443#380D411yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379—21no—
453#379—21no—
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2×D411yescharacteristic
531C23×C4C2×D411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567#126—44no—
568#125—41no—
569#125—41no—
570#124—41no—
571#124—41no—
572#124—41no—
573#124—41no—
574#123—44no—
575#123—44no—
576#123—82no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587#121—22no—
588#121—22no—
589#121—42no—
590#121—44no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—82no—
602#120—44no—
603#120—82no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—44no—
621C4×D4—44no—
622C4×D4—44no—
623#117—22no—
624#117—22no—
625#117—44no—
626#117—41no—
627#117—41no—
628C2×C4⋊C4—22no—
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⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
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—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—41no—
728C2×C42—41no—
729C2×C42—44no—
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—41no—
738#107—41no—
739#107—41no—
740#107—41no—
741#106—41no—
742#106—41no—
743#106—41no—
744#106—41no—
745#106—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—41no—
789C4×C8—41no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838#41—44no—
839#41—44no—
840#41—44no—
841#41—44no—
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—22no—
855C2×D4—22no—
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—42no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—41no—
878C2×D4—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4H(5,𝔽2)12yes—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—24no—
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—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—42no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—41no—
947C22×C4—41no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C2511yescharacteristic
973Q16—82no—
974SD16—82no—
975SD16—82no—
976SD16—82no—
977D8—82no—
978D8—82no—
979M16—82no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—82no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4H(5,𝔽2)12yes—
1051C22⋊C4—24no—
1052C22⋊C4—22no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—41no—
1112C42—41no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—84no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23—162no—
1169C23#57512yes—
1170C23C23×D411yescharacteristic
1171Q8—22no—
1172Q8—22no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179D4—22no—
1180D4—22no—
1181D4—48no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—82no—
1193D4—82no—
1194D4—82no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
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—21no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—48no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—84no—
1288C2×C4—82no—
1289C2×C4—82no—
1290C2×C4—84no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×H(5,𝔽2)11yescharacteristic
1296C2×C4#58511yescharacteristic
1297C2×C4#58511yescharacteristic
1298C2×C4#58511yescharacteristic
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—42no—
1323C22—41no—
1324C22—41no—
1325C22—42no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—42no—
1330C22—41no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—168no—
1350C22#348411yescharacteristic
1351C22#348511yescharacteristic
1352C22#348811yescharacteristic
1353C22C2×#57511yescharacteristic
1354C22#358411yescharacteristic
1355C22#358411yescharacteristic
1356C22#358511yescharacteristic
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4#352911yescharacteristic
1382C4#353311yescharacteristic
1383C4#353411yescharacteristic
1384C4#354211yescharacteristic
1385C2—42no—
1386C2—81no—
1387C2—81no—
1388C2—82no—
1389C2—161no—
1390C2—161no—
1391C2#4544811yescharacteristic
1392C2#6159711yescharacteristic
1393C2#6161411yescharacteristic
1394C2#6171411yescharacteristic
1395C2#6179011yescharacteristic
1396C2#6199211yescharacteristic
1397C2#6204911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45701C2semidirect
2. #36436C2semidirect
3. #33006C2semidirect
4. #32910C2semidirect
5. #32778C2semidirect
6. #32746C2semidirect
7. #32436C2semidirect
8. #31945C2semidirect
9. #31655C2semidirect
10. #31613C2semidirect
11. #31057C2semidirect
12. #31033C2semidirect
13. #31008C2semidirect
14. #30619C2semidirect
15. #30569C2semidirect
16. #30513C2semidirect
17. #30424C2semidirect
18. #30405C2semidirect
19. #27513C2semidirect
20. #27204C2semidirect
21. #27114C2semidirect
22. #26936C2semidirect
23. #26245C2semidirect
24. #26225C2semidirect
25. #25548C2semidirect
26. #25231C2semidirect
27. #25084C2semidirect
28. #24975C2semidirect
29. #24873C2semidirect
30. #23963C2semidirect
31. #23331C2semidirect
33. C2×C4×#41C22semidirect
34. C2×#485C22semidirect
36. C2×#483C22semidirect
38. C2×#468C22semidirect
42. C2×#452C22semidirect
50. #2851C22semidirect
61. #2565C22semidirect
76. #2420C22semidirect
82. #2407C22semidirect
84. #2362C22semidirect
86. #2357C22semidirect
87. #2354C22semidirect
91. #2100C22semidirect
92. #2097C22semidirect
95. #2092C22semidirect
96. #2088C22semidirect
97. #2086C22semidirect
98. #2085C22semidirect
99. #2085C22semidirect
100. #2085C22semidirect
101. #2077C22semidirect
102. #2076C22semidirect
104. #2074C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
118. #2036C22semidirect
121. #2035C22semidirect
122. #2035C22semidirect
129. #2026C22semidirect
134. #2001C22semidirect
144. #1955C22semidirect
146. #1949C22semidirect
147. #1948C22semidirect
148. #1935C22semidirect
149. #1928C22semidirect
153. #1925C22semidirect
155. #1923C22semidirect
156. #1918C22semidirect
157. #1917C22semidirect
158. #1916C22semidirect
164. #1880C22semidirect
168. #1878C22semidirect
169. #1878C22semidirect
170. #1877C22semidirect
174. #1874C22semidirect
175. #1873C22semidirect
178. #1870C22semidirect
181. #1865C22semidirect
182. #1864C22semidirect
183. #1863C22semidirect
184. #1862C22semidirect
186. #1852C22semidirect
187. #1851C22semidirect
189. #1835C22semidirect
190. #1825C22semidirect
192. #1817C22semidirect
194. #1805C22semidirect
195. #1805C22semidirect
196. #1804C22semidirect
197. #1797C22semidirect
198. #1788C22semidirect
200. #1776C22semidirect
201. C4×#103C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#457012
#364362
#330062
#329102
#327782
#327462
#324362
#319452
#316552
#316132
#310572
#310332
#310082
#306192
#305692
#305132
#304242
#304052
#275132
#272042
#271142
#269362
#262452
#262252
#255482
#252312
#250842
#249752
#248732
#239632
#233312