Finite Group Databasebeta

← #7327518

Subgroups — #7327518

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59038C211yesmaximal, characteristic, complemented
2#45663C211yesmaximal, characteristic, complemented
3#32433C211yesmaximal, characteristic, complemented
4#31937C211yesmaximal, characteristic, complemented
5#31646C211yesmaximal, characteristic, complemented
6#31603C211yesmaximal, characteristic, complemented
7#31387C211yesmaximal, characteristic, complemented
8#31325C211yesmaximal, characteristic, complemented
9#31267C211yesmaximal, characteristic, complemented
10#30998C211yesmaximal, characteristic, complemented
11#30595C211yesmaximal, characteristic, complemented
12#30502C211yesmaximal, characteristic, complemented
13#30407C211yesmaximal, characteristic, complemented
14#30396C211yesmaximal, characteristic, complemented
15#30009C211yesmaximal, characteristic, complemented
16#29666C211yesmaximal, characteristic, complemented
17#28573C211yesmaximal, characteristic, complemented
18#28141C211yesmaximal, characteristic, complemented
19#27523C211yesmaximal, characteristic, complemented
20#27073C211yesmaximal, characteristic, complemented
21#26596C211yesmaximal, characteristic, complemented
22#25499C211yesmaximal, characteristic, complemented
23#25388C211yesmaximal, characteristic, complemented
24#25155C211yesmaximal, characteristic, complemented
25#25113C211yesmaximal, characteristic, complemented
26#24534C211yesmaximal, characteristic, complemented
27#24428C211yesmaximal, characteristic, complemented
28#24359C211yesmaximal, characteristic, complemented
29#24264C211yesmaximal, characteristic, complemented
30#23852C211yesmaximal, characteristic, complemented
31#22168C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C2×#467C2211yescharacteristic, complemented
36C2×#466C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#464C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#451C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic, complemented
49C2×C8×D4C2211yescharacteristic
50C2×C8×D4C2211yescharacteristic, complemented
51C2×#416C2211yescharacteristic
52#2855C2211yescharacteristic, complemented
53#2850C2211yescharacteristic, complemented
54#2824—21no—
55#2797—21no—
56#2796—21no—
57#2742—21no—
58#2737—21no—
59#2737—21no—
60#2693—21no—
61#2688—21no—
62#2678—21no—
63#2566C2211yescharacteristic
64#2562C2211yescharacteristic
65#2559—21no—
66#2540C2211yescharacteristic, complemented
67#2538C2211yescharacteristic
68#2537C2211yescharacteristic
69#2535C2211yescharacteristic
70#2511C2211yescharacteristic, complemented
71#2499C2211yescharacteristic, complemented
72#2495C2211yescharacteristic
73#2480—21no—
74#2470—21no—
75#2456—21no—
76#2447C2211yescharacteristic, complemented
77#2436C2211yescharacteristic
78#2427C2211yescharacteristic, complemented
79#2422C2211yescharacteristic
80#2421C2211yescharacteristic
81#2415C2211yescharacteristic, complemented
82#2414C2211yescharacteristic
83#2411—21no—
84#2409C2211yescharacteristic
85#2409C2211yescharacteristic
86#2408C2211yescharacteristic
87#2407C2211yescharacteristic
88#2377—21no—
89#2367C2211yescharacteristic
90#2358—21no—
91#2341C2211yescharacteristic
92D4×C22⋊C4C2211yescharacteristic
93C4×#121C2211yescharacteristic
94C4×#121C2211yescharacteristic
95#2101C2211yescharacteristic, complemented
96#2095C2211yescharacteristic, complemented
97#2093C2211yescharacteristic
98#2087C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2072C2211yescharacteristic, complemented
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2036C2211yescharacteristic, complemented
121#2035C2211yescharacteristic, complemented
122#2034C2211yescharacteristic, complemented
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2026C2211yescharacteristic, complemented
128#2025C2211yescharacteristic, complemented
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic, complemented
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2012C2211yescharacteristic
135#2001C2211yescharacteristic, complemented
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic
138#2000C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic, complemented
142#1999C2211yescharacteristic
143#1969C2211yescharacteristic, complemented
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1958C2211yescharacteristic, complemented
147#1949C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1928C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1926C2211yescharacteristic, complemented
153#1925C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic, complemented
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic, complemented
164#1892C2211yescharacteristic, complemented
165#1892C2211yescharacteristic, complemented
166#1892C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1875C2211yescharacteristic
178#1869C2211yescharacteristic
179#1869C2211yescharacteristic
180#1869C2211yescharacteristic
181#1869C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1854C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1850C2211yescharacteristic, complemented
189#1834C2211yescharacteristic, complemented
190#1825C2211yescharacteristic, complemented
191#1807C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1804C2211yescharacteristic
194#1803C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199#1786C2211yescharacteristic
200#1786C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C2×#336C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16—42no—
209C22×SD16—42no—
210C22×SD16—42no—
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C23×C8C2311yescharacteristic
220C23×C8C2311yescharacteristic
221C23×C8C2311yescharacteristic
222#546—42no—
223#546—42no—
224#529—42no—
225#529—42no—
226C2×#126—21no—
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121—21no—
242C2×#121D411yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266C22×C42C2311yescharacteristic
267#467—42no—
268#466—42no—
269#466—42no—
270#465—42no—
271#465—42no—
272#464—42no—
273#463—42no—
274#463—42no—
275#452—42no—
276#452—42no—
277#451—42no—
278#449—42no—
279#447—42no—
280C4×SD16—42no—
281C8×D4—42no—
282C8×D4—42no—
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294#416—42no—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#395—21no—
356#395—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#393—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390D411yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389D411yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388D411yescharacteristic
413#388D411yescharacteristic
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—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#386—21no—
434#386D411yescharacteristic
435#386D411yescharacteristic
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#383—21no—
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#381—21no—
451#381—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380D411yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#379—21no—
465#379—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C22⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C2×D411yescharacteristic
534C22×D4C2×D411yescharacteristic
535C22×D4C2×D411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C2×D411yescharacteristic
546C23×C4C2×D411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—416no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8—41no—
589C22×C8—41no—
590C22×C8C2411yescharacteristic
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598#126—44no—
599#125—41no—
600#125—41no—
601#124—22no—
602#124—22no—
603#124—41no—
604#124—41no—
605#124—41no—
606#124—41no—
607#123—44no—
608#123—44no—
609#123—82no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—41no—
616C22⋊Q8—41no—
617C22⋊Q8—41no—
618C22⋊Q8—41no—
619C22⋊Q8—41no—
620C22⋊Q8—41no—
621C22⋊Q8—41no—
622#121—24no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—44no—
627#121—41no—
628#121—41no—
629#121—41no—
630#121—44no—
631#121—41no—
632#121—41no—
633#121—41no—
634#121—41no—
635#121—41no—
636#121—41no—
637#120—44no—
638#120—44no—
639C4×Q8—22no—
640C4×Q8—41no—
641C4×Q8—41no—
642C4×Q8—41no—
643C4×D4—22no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—41no—
647C4×D4—41no—
648C4×D4—41no—
649C4×D4—41no—
650C4×D4—41no—
651C4×D4—41no—
652C4×D4—41no—
653C4×D4—41no—
654C4×D4—41no—
655C4×D4—41no—
656C4×D4—41no—
657C4×D4—44no—
658C4×D4—82no—
659#117—44no—
660#117—41no—
661#117—41no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2×D411yescharacteristic
684C2×C4⋊C4C2×D411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—44no—
737C2×C22⋊C4—82no—
738C2×C22⋊C4C2×D411yescharacteristic
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—41no—
754C2×C42—41no—
755C2×C42C2×D411yescharacteristic
756C2×C42C2×D411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761#107—41no—
762#107—41no—
763#107—41no—
764#107—41no—
765#106—41no—
766#106—41no—
767#106—41no—
768C4⋊C8—22no—
769C4⋊C8—41no—
770C4⋊C8—41no—
771C4⋊C8—41no—
772#103—22no—
773#103—22no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#102—22no—
788#102—22no—
789#102—22no—
790#102—22no—
791#102—22no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798#102—41no—
799#102—41no—
800#102—41no—
801#102—41no—
802C22⋊C8—22no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805C22⋊C8—41no—
806C22⋊C8—41no—
807C22⋊C8—41no—
808C22⋊C8—41no—
809C22⋊C8—41no—
810C4×C8—22no—
811C4×C8—41no—
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#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95—21no—
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—42no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24C22×D411yescharacteristic
861C24C22×D411yescharacteristic
862C24C22×D411yescharacteristic
863#41—44no—
864#41—82no—
865#41—82no—
866#41—82no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—44no—
885C2×Q8—81no—
886C2×Q8—81no—
887C2×Q8—81no—
888C2×Q8—82no—
889C2×Q8—82no—
890C2×Q8—82no—
891C2×Q8H(5,𝔽2)12yes—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—41no—
911C2×D4—41no—
912C2×D4—41no—
913C2×D4—41no—
914C2×D4—41no—
915C2×D4—41no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—42no—
919C2×D4—44no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—81no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—82no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4#13514yes—
945C2×D4H(5,𝔽2)12yes—
946C2×D4H(5,𝔽2)12yes—
947C22×C4—21no—
948C22×C4—22no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—81no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—81no—
1001C22×C4—81no—
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D411yescharacteristic
1013C22×C4C2511yescharacteristic
1014Q16—82no—
1015Q16—82no—
1016SD16—44no—
1017SD16—44no—
1018SD16—44no—
1019SD16—44no—
1020SD16—44no—
1021D8—82no—
1022D8—82no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—44no—
1047C2×C8—82no—
1048C2×C8—82no—
1049C2×C8—82no—
1050C2×C8H(5,𝔽2)12yes—
1051C4⋊C4—22no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—41no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C4⋊C4—81no—
1090C4⋊C4—81no—
1091C4⋊C4—81no—
1092C4⋊C4—81no—
1093C4⋊C4—81no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—41no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C22⋊C4—81no—
1145C42—21no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—41no—
1154C42—41no—
1155C42—42no—
1156C42—81no—
1157C42—81no—
1158C42—81no—
1159C42—81no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—22no—
1176C23—21no—
1177C23—22no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—84no—
1201C23—84no—
1202C23—84no—
1203C23—162no—
1204C23—162no—
1205C23—162no—
1206C23—162no—
1207C23C2×#13512yes—
1208C23C2×#13512yes—
1209C23C23×D411yescharacteristic
1210Q8—22no—
1211Q8—22no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—84no—
1223D4—22no—
1224D4—22no—
1225D4—22no—
1226D4—22no—
1227D4—44no—
1228D4—44no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—82no—
1238D4—84no—
1239D4—84no—
1240D4—84no—
1241D4—84no—
1242D4—162no—
1243D4—162no—
1244D4—162no—
1245D4—162no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
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—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—82no—
1330C2×C4—82no—
1331C2×C4—84no—
1332C2×C4—84no—
1333C2×C4—84no—
1334C2×C4—162no—
1335C2×C4—162no—
1336C2×C4—162no—
1337C2×C4C2×#13512yes—
1338C2×C4C2×H(5,𝔽2)11yescharacteristic
1339C2×C4C2×H(5,𝔽2)11yescharacteristic
1340C2×C4C2×H(5,𝔽2)11yescharacteristic
1341C2×C4C2×H(5,𝔽2)11yescharacteristic
1342C2×C4#58511yescharacteristic
1343C2×C4#58511yescharacteristic
1344C8—22no—
1345C8—41no—
1346C8—41no—
1347C8—41no—
1348C8—41no—
1349C8—41no—
1350C8—41no—
1351C8—41no—
1352C22—22no—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—22no—
1357C22—22no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—42no—
1367C22—41no—
1368C22—41no—
1369C22—41no—
1370C22—42no—
1371C22—42no—
1372C22—41no—
1373C22—42no—
1374C22—41no—
1375C22—41no—
1376C22—42no—
1377C22—42no—
1378C22—41no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—168no—
1395C22#348411yescharacteristic
1396C22#348811yescharacteristic
1397C22#349611yescharacteristic
1398C22C22×#13511yescharacteristic
1399C22#358411yescharacteristic
1400C22#358511yescharacteristic
1401C22#358611yescharacteristic
1402C4—22no—
1403C4—41no—
1404C4—41no—
1405C4—41no—
1406C4—41no—
1407C4—42no—
1408C4—41no—
1409C4—41no—
1410C4—41no—
1411C4—41no—
1412C4—41no—
1413C4—41no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4—81no—
1421C4—81no—
1422C4—81no—
1423C4—81no—
1424C4—81no—
1425C4—81no—
1426C4#353211yescharacteristic
1427C4#353411yescharacteristic
1428C4#354211yescharacteristic
1429C4#356011yescharacteristic
1430C2—42no—
1431C2—42no—
1432C2—81no—
1433C2—82no—
1434C2—82no—
1435C2—161no—
1436C2#4793411yescharacteristic
1437C2#6156811yescharacteristic
1438C2#6162511yescharacteristic
1439C2#6195511yescharacteristic
1440C2#6202311yescharacteristic
1441C2#6224411yescharacteristic
1442C2#6233311yescharacteristic
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. #59038C2semidirect
2. #45663C2semidirect
3. #32433C2semidirect
4. #31937C2semidirect
5. #31646C2semidirect
6. #31603C2semidirect
7. #31387C2semidirect
8. #31325C2semidirect
9. #31267C2semidirect
10. #30998C2semidirect
11. #30595C2semidirect
12. #30502C2semidirect
13. #30407C2semidirect
14. #30396C2semidirect
15. #30009C2semidirect
16. #29666C2semidirect
17. #28573C2semidirect
18. #28141C2semidirect
19. #27523C2semidirect
20. #27073C2semidirect
21. #26596C2semidirect
22. #25499C2semidirect
23. #25388C2semidirect
24. #25155C2semidirect
25. #25113C2semidirect
26. #24534C2semidirect
27. #24428C2semidirect
28. #24359C2semidirect
29. #24264C2semidirect
30. #23852C2semidirect
31. #22168C2semidirect
35. C2×#467C22semidirect
40. C2×#464C22semidirect
48. C2×C4×SD16C22semidirect
50. C2×C8×D4C22semidirect
52. #2855C22semidirect
53. #2850C22semidirect
66. #2540C22semidirect
70. #2511C22semidirect
71. #2499C22semidirect
76. #2447C22semidirect
78. #2427C22semidirect
81. #2415C22semidirect
95. #2101C22semidirect
96. #2095C22semidirect
98. #2087C22semidirect
99. #2085C22semidirect
101. #2077C22semidirect
104. #2074C22semidirect
106. #2072C22semidirect
108. #2068C22semidirect
109. #2066C22semidirect
111. #2059C22semidirect
117. #2042C22semidirect
119. #2036C22semidirect
120. #2036C22semidirect
121. #2035C22semidirect
122. #2034C22semidirect
125. #2033C22semidirect
126. #2026C22semidirect
127. #2026C22semidirect
128. #2025C22semidirect
131. #2015C22semidirect
135. #2001C22semidirect
141. #2000C22semidirect
143. #1969C22semidirect
146. #1958C22semidirect
147. #1949C22semidirect
149. #1928C22semidirect
150. #1928C22semidirect
151. #1927C22semidirect
152. #1926C22semidirect
155. #1923C22semidirect
156. #1918C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
161. #1893C22semidirect
163. #1892C22semidirect
164. #1892C22semidirect
165. #1892C22semidirect
166. #1892C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
181. #1869C22semidirect
182. #1865C22semidirect
186. #1854C22semidirect
188. #1850C22semidirect
189. #1834C22semidirect
190. #1825C22semidirect
192. #1805C22semidirect
194. #1803C22semidirect
195. #1802C22semidirect
196. #1797C22semidirect
202. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
#590382
#456632
#324332
#319372
#316462
#316032
#313872
#313252
#312672
#309982
#305952
#305022
#304072
#303962
#300092
#296662
#285732
#281412
#275232
#270732
#265962
#254992
#253882
#251552
#251132
#245342
#244282
#243592
#242642
#238522
#221682