Finite Group Databasebeta

← #7204216

Subgroups — #7204216

Order 512.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52981C211yesmaximal, characteristic, complemented
2#35701C211yesmaximal, characteristic, complemented
3#33012C211yesmaximal, characteristic, complemented
4#32919C211yesmaximal, characteristic, complemented
5#32781C211yesmaximal, characteristic, complemented
6#32750C211yesmaximal, characteristic, complemented
7#32426C211yesmaximal, characteristic, complemented
8#31932C211yesmaximal, characteristic, complemented
9#31656C211yesmaximal, characteristic, complemented
10#31608C211yesmaximal, characteristic, complemented
11#31057C211yesmaximal, characteristic, complemented
12#31042C211yesmaximal, characteristic, complemented
13#31012C211yesmaximal, characteristic, complemented
14#30602C211yesmaximal, characteristic, complemented
15#30565C211yesmaximal, characteristic, complemented
16#30502C211yesmaximal, characteristic, complemented
17#30410C211yesmaximal, characteristic, complemented
18#30400C211yesmaximal, characteristic, complemented
19#27510C211yesmaximal, characteristic, complemented
20#27200C211yesmaximal, characteristic, complemented
21#27113C211yesmaximal, characteristic, complemented
22#26929C211yesmaximal, characteristic, complemented
23#26244C211yesmaximal, characteristic, complemented
24#26202C211yesmaximal, characteristic, complemented
25#25545C211yesmaximal, characteristic, complemented
26#25200C211yesmaximal, characteristic, complemented
27#25088C211yesmaximal, characteristic, complemented
28#24971C211yesmaximal, characteristic, complemented
29#24861C211yesmaximal, characteristic, complemented
30#23969C211yesmaximal, characteristic, complemented
31#23330C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#520C2211yescharacteristic, complemented
34C2×#484C2211yescharacteristic, complemented
35C2×#480C2211yescharacteristic
36C2×#480C2211yescharacteristic, complemented
37C2×#467C2211yescharacteristic, complemented
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#452C2211yescharacteristic, complemented
43C2×#449C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2842—21no—
49#2837—21no—
50#2829—21no—
51#2813—21no—
52#2705—21no—
53#2697—21no—
54#2685—21no—
55#2678—21no—
56#2633—21no—
57#2628C2211yescharacteristic, complemented
58#2624C2211yescharacteristic
59#2620C2211yescharacteristic
60#2611—21no—
61#2598—21no—
62#2542C2211yescharacteristic, complemented
63#2540C2211yescharacteristic
64#2538C2211yescharacteristic
65#2535C2211yescharacteristic
66#2512C2211yescharacteristic
67#2501C2211yescharacteristic
68#2497C2211yescharacteristic
69#2463—21no—
70#2463—21no—
71#2449—21no—
72#2449—21no—
73#2448C2211yescharacteristic
74#2435C2211yescharacteristic
75#2426C2211yescharacteristic
76#2423C2211yescharacteristic
77#2423C2211yescharacteristic, complemented
78#2417C2211yescharacteristic
79#2416C2211yescharacteristic
80#2408C2211yescharacteristic
81#2408C2211yescharacteristic
82#2407C2211yescharacteristic
83#2407C2211yescharacteristic, complemented
84#2397—21no—
85#2392C2211yescharacteristic
86#2361C2211yescharacteristic
87#2361C2211yescharacteristic, complemented
88#2356C2211yescharacteristic, complemented
89D4×C4⋊C4C2211yescharacteristic
90D4×C4⋊C4C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2093C2211yescharacteristic
95#2092C2211yescharacteristic
96#2087C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2065C2211yescharacteristic
111#2057C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#2023C2211yescharacteristic
131#2023C2211yescharacteristic
132#2015C2211yescharacteristic
133#2012C2211yescharacteristic
134#2001C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#1999C2211yescharacteristic
139#1983C2211yescharacteristic
140#1973C2211yescharacteristic
141#1970C2211yescharacteristic
142#1968C2211yescharacteristic
143#1959C2211yescharacteristic
144#1955C2211yescharacteristic, complemented
145#1954C2211yescharacteristic
146#1947C2211yescharacteristic, complemented
147#1947C2211yescharacteristic, complemented
148#1936C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1926C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic, complemented
156#1919C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
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#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1869C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1853C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic, complemented
189#1834C2211yescharacteristic, complemented
190#1824C2211yescharacteristic
191#1824C2211yescharacteristic, complemented
192#1818C2211yescharacteristic, complemented
193#1808C2211yescharacteristic
194#1803C2211yescharacteristic, complemented
195#1803C2211yescharacteristic, complemented
196#1802C2211yescharacteristic, complemented
197#1798C2211yescharacteristic, complemented
198#1788C2211yescharacteristic, complemented
199#1786C2211yescharacteristic
200#1776C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#554—42no—
214#554—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240#520—42no—
241#520—42no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C22×C4⋊C4—21no—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264#484—42no—
265#480—42no—
266#480—42no—
267#467—42no—
268#466—42no—
269#465—42no—
270#464—42no—
271#463—42no—
272#452—42no—
273#450—42no—
274#449—42no—
275#449—42no—
276#447—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#102—42no—
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#400—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#399—21no—
342#399—21no—
343#399—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398D411yescharacteristic
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397D411yescharacteristic
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396D411yescharacteristic
363#396D411yescharacteristic
364#395—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394D411yescharacteristic
378#394D411yescharacteristic
379#394D411yescharacteristic
380#393—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#392—21no—
385#392—21no—
386#392—21no—
387#392D411yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#390—21no—
392#390—21no—
393#390—21no—
394#390—21no—
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389—21no—
405#389—21no—
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
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#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#383—21no—
446#382C2311yescharacteristic
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457#379—21no—
458#379—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376—21no—
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×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570#126—82no—
571#125—44no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#123—82no—
577#123—82no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—44no—
583C22⋊Q8—44no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—82no—
591C22⋊Q8—82no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—82no—
605#120—82no—
606#120—82no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×D4—22no—
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—41no—
623C4×D4—44no—
624C4×D4—44no—
625C4×D4—44no—
626C4×D4—82no—
627C4×D4—82no—
628C4×D4—82no—
629C4×D4—82no—
630#117—41no—
631#117—41no—
632#117—44no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—44no—
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—22no—
749#107—41no—
750#107—41no—
751#107—41no—
752#107—41no—
753#107—41no—
754#107—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762#103—22no—
763#103—22no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800#97—41no—
801C4×C8—41no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24—21no—
833C24—21no—
834C24—42no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24C22×D411yescharacteristic
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844#41—44no—
845#41—44no—
846#41—44no—
847#41—44no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—42no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8H(5,𝔽2)12yes—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—22no—
866C2×D4—22no—
867C2×D4—22no—
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—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—41no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—44no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—82no—
903C2×D4—82no—
904C2×D4—82no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4H(5,𝔽2)12yes—
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—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C2511yescharacteristic
982Q16—82no—
983SD16—82no—
984SD16—82no—
985SD16—82no—
986D8—82no—
987D8—82no—
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—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—82no—
1013C2×C8—82no—
1014C4⋊C4—24no—
1015C4⋊C4—22no—
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—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4H(5,𝔽2)12yes—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C42—24no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—81no—
1134C42—81no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—84no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23#57712yes—
1183C23#57812yes—
1184C23C23×D411yescharacteristic
1185Q8—22no—
1186Q8—22no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—162no—
1194D4—22no—
1195D4—22no—
1196D4—44no—
1197D4—44no—
1198D4—44no—
1199D4—48no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—84no—
1211D4—84no—
1212D4—84no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—48no—
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—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4—162no—
1305C2×C4—162no—
1306C2×C4—162no—
1307C2×C4#57612yes—
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×H(5,𝔽2)11yescharacteristic
1310C2×C4C2×H(5,𝔽2)11yescharacteristic
1311C2×C4#58511yescharacteristic
1312C2×C4#58511yescharacteristic
1313C2×C4#58511yescharacteristic
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—42no—
1338C22—41no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—42no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—168no—
1365C22#348411yescharacteristic
1366C22#348511yescharacteristic
1367C22#348811yescharacteristic
1368C22C2×#57611yescharacteristic
1369C22C2×#57711yescharacteristic
1370C22C2×#57811yescharacteristic
1371C22#358511yescharacteristic
1372C4—22no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—41no—
1377C4—41no—
1378C4—41no—
1379C4—42no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—42no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4#352911yescharacteristic
1397C4#353311yescharacteristic
1398C4#353411yescharacteristic
1399C4#354211yescharacteristic
1400C2—42no—
1401C2—42no—
1402C2—81no—
1403C2—82no—
1404C2—161no—
1405C2—161no—
1406C2#4544811yescharacteristic
1407C2#6163211yescharacteristic
1408C2#6168811yescharacteristic
1409C2#6174611yescharacteristic
1410C2#6176411yescharacteristic
1411C2#6201711yescharacteristic
1412C2#6205311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52981C2semidirect
2. #35701C2semidirect
3. #33012C2semidirect
4. #32919C2semidirect
5. #32781C2semidirect
6. #32750C2semidirect
7. #32426C2semidirect
8. #31932C2semidirect
9. #31656C2semidirect
10. #31608C2semidirect
11. #31057C2semidirect
12. #31042C2semidirect
13. #31012C2semidirect
14. #30602C2semidirect
15. #30565C2semidirect
16. #30502C2semidirect
17. #30410C2semidirect
18. #30400C2semidirect
19. #27510C2semidirect
20. #27200C2semidirect
21. #27113C2semidirect
22. #26929C2semidirect
23. #26244C2semidirect
24. #26202C2semidirect
25. #25545C2semidirect
26. #25200C2semidirect
27. #25088C2semidirect
28. #24971C2semidirect
29. #24861C2semidirect
30. #23969C2semidirect
31. #23330C2semidirect
33. C2×#520C22semidirect
34. C2×#484C22semidirect
36. C2×#480C22semidirect
37. C2×#467C22semidirect
42. C2×#452C22semidirect
57. #2628C22semidirect
62. #2542C22semidirect
77. #2423C22semidirect
83. #2407C22semidirect
87. #2361C22semidirect
88. #2356C22semidirect
90. D4×C4⋊C4C22semidirect
91. #2100C22semidirect
92. #2097C22semidirect
93. #2096C22semidirect
96. #2087C22semidirect
97. #2086C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
101. #2077C22semidirect
103. #2076C22semidirect
107. #2071C22semidirect
108. #2068C22semidirect
111. #2057C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
121. #2035C22semidirect
129. #2024C22semidirect
137. #2000C22semidirect
144. #1955C22semidirect
146. #1947C22semidirect
147. #1947C22semidirect
148. #1936C22semidirect
149. #1928C22semidirect
153. #1925C22semidirect
155. #1923C22semidirect
156. #1919C22semidirect
157. #1917C22semidirect
158. #1916C22semidirect
164. #1880C22semidirect
168. #1878C22semidirect
169. #1878C22semidirect
170. #1877C22semidirect
175. #1872C22semidirect
176. #1872C22semidirect
180. #1869C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
185. #1853C22semidirect
188. #1850C22semidirect
189. #1834C22semidirect
191. #1824C22semidirect
192. #1818C22semidirect
194. #1803C22semidirect
195. #1803C22semidirect
196. #1802C22semidirect
197. #1798C22semidirect
198. #1788C22semidirect
200. #1776C22semidirect
201. C4×#103C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#529812
#357012
#330122
#329192
#327812
#327502
#324262
#319322
#316562
#316082
#310572
#310422
#310122
#306022
#305652
#305022
#304102
#304002
#275102
#272002
#271132
#269292
#262442
#262022
#255452
#252002
#250882
#249712
#248612
#239692
#233302