Finite Group Databasebeta

← #7338491

Subgroups — #7338491

Order 512.

1587 conjugacy classes of subgroups.

The subgroup lattice has 1397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52970C211yesmaximal, characteristic, complemented
2#45187C211yesmaximal, characteristic, complemented
3#31849C211yesmaximal, characteristic, complemented
4#31750C211yesmaximal, characteristic, complemented
5#31729C211yesmaximal, characteristic, complemented
6#31651C211yesmaximal, characteristic, complemented
7#31462C211yesmaximal, characteristic, complemented
8#31411C211yesmaximal, characteristic, complemented
9#31155C211yesmaximal, characteristic, complemented
10#30992C211yesmaximal, characteristic, complemented
11#30925C211yesmaximal, characteristic, complemented
12#30743C211yesmaximal, characteristic, complemented
13#30523C211yesmaximal, characteristic, complemented
14#30454C211yesmaximal, characteristic, complemented
15#29721C211yesmaximal, characteristic, complemented
16#29699C211yesmaximal, characteristic, complemented
17#29116C211yesmaximal, characteristic, complemented
18#28916C211yesmaximal, characteristic, complemented
19#27754C211yesmaximal, characteristic, complemented
20#27272C211yesmaximal, characteristic, complemented
21#27231C211yesmaximal, characteristic, complemented
22#26907C211yesmaximal, characteristic, complemented
23#26843C211yesmaximal, characteristic, complemented
24#26734C211yesmaximal, characteristic, complemented
25#26664C211yesmaximal, characteristic, complemented
26#25607C211yesmaximal, characteristic, complemented
27#25327C211yesmaximal, characteristic, complemented
28#24547C211yesmaximal, characteristic, complemented
29#24444C211yesmaximal, characteristic, complemented
30#24257C211yesmaximal, characteristic, complemented
31#22364C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#492C2211yescharacteristic, complemented
35C2×#490C2211yescharacteristic, complemented
36C2×#488C2211yescharacteristic
37C2×#477C2211yescharacteristic, complemented
38C2×#475C2211yescharacteristic, complemented
39C2×#469C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#449C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×#442C2211yescharacteristic
47C2×#417C2211yescharacteristic
48#2829—21no—
49#2826—21no—
50#2824—21no—
51#2814—21no—
52#2750—21no—
53#2711—21no—
54#2694—21no—
55#2686—21no—
56#2685—21no—
57#2685—21no—
58#2676—21no—
59#2671—21no—
60#2628C2211yescharacteristic
61#2619C2211yescharacteristic
62#2570C2211yescharacteristic, complemented
63#2566C2211yescharacteristic, complemented
64#2558—21no—
65#2545C2211yescharacteristic
66#2537C2211yescharacteristic
67#2504C2211yescharacteristic, complemented
68#2491C2211yescharacteristic, complemented
69#2490—21no—
70#2490C2211yescharacteristic
71#2490C2211yescharacteristic
72#2480—21no—
73#2480—21no—
74#2454C2211yescharacteristic
75#2452C2211yescharacteristic, complemented
76#2448C2211yescharacteristic
77#2445C2211yescharacteristic, complemented
78#2442C2211yescharacteristic, complemented
79#2435C2211yescharacteristic
80#2432C2211yescharacteristic
81#2428C2211yescharacteristic, complemented
82#2426C2211yescharacteristic
83#2420C2211yescharacteristic
84#2416C2211yescharacteristic
85#2415C2211yescharacteristic
86#2395C2211yescharacteristic
87#2367C2211yescharacteristic
88#2362C2211yescharacteristic
89#2341C2211yescharacteristic
90#2309C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2076C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2059C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2025C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2011C2211yescharacteristic
131#2011C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic, complemented
137#2000C2211yescharacteristic, complemented
138#1999C2211yescharacteristic
139#1991C2211yescharacteristic, complemented
140#1989C2211yescharacteristic, complemented
141#1983C2211yescharacteristic
142#1970C2211yescharacteristic
143#1970C2211yescharacteristic
144#1960C2211yescharacteristic, complemented
145#1959C2211yescharacteristic
146#1958C2211yescharacteristic
147#1955C2211yescharacteristic
148#1939C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic, complemented
162#1923C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1895C2211yescharacteristic, complemented
168#1894C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1880C2211yescharacteristic, complemented
172#1880C2211yescharacteristic, complemented
173#1880C2211yescharacteristic, complemented
174#1880C2211yescharacteristic, complemented
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1875C2211yescharacteristic
180#1875C2211yescharacteristic
181#1874C2211yescharacteristic
182#1872C2211yescharacteristic, complemented
183#1870C2211yescharacteristic
184#1864C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1851C2211yescharacteristic, complemented
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1823C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1770C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×M16C2311yescharacteristic
214#546—42no—
215#546—42no—
216#541—42no—
217#541—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#492—42no—
259#490—42no—
260#488—42no—
261#477—42no—
262#475—42no—
263#469—42no—
264#463—42no—
265#463—42no—
266#449—42no—
267#449—42no—
268#447—42no—
269#447—42no—
270#442—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#417—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#400D411yescharacteristic
329#399—21no—
330#399—21no—
331#399—21no—
332#399D411yescharacteristic
333#398—21no—
334#398—21no—
335#398D411yescharacteristic
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397D411yescharacteristic
344#397D411yescharacteristic
345#397D411yescharacteristic
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#395—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394D411yescharacteristic
374#394D411yescharacteristic
375#393—21no—
376#393—21no—
377#393—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#389—21no—
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#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#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#384C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#381—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454#379—21no—
455#379—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⋊C4C2311yescharacteristic
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×Q8—21no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#127—41no—
573#127—41no—
574#126—44no—
575#126—44no—
576#125—22no—
577#125—41no—
578#125—41no—
579#125—41no—
580#125—44no—
581#125—44no—
582#124—22no—
583#124—22no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—82no—
589#123—44no—
590#123—82no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—82no—
598#121—22no—
599#121—41no—
600#121—44no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—82no—
610#121—82no—
611#121—82no—
612#120—44no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×D4—22no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627#117—41no—
628#117—41no—
629#117—41no—
630#117—41no—
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—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
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⋊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—44no—
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#107—41no—
741#107—41no—
742#106—22no—
743#106—22no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749#103—22no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
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—22no—
765#102—22no—
766#102—22no—
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—
778#102—41no—
779#102—41no—
780#102—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—
789#97—41no—
790C4×C8—41no—
791C4×C8—41no—
792C4×C8—41no—
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#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
837C24C22×D411yescharacteristic
838#41—44no—
839#41—82no—
840#41—82no—
841#41—82no—
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×Q8—81no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8H(5,𝔽2)12yes—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
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×D4H(5,𝔽2)12yes—
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—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C2511yescharacteristic
967SD16—82no—
968SD16—82no—
969SD16—82no—
970SD16—82no—
971D8—44no—
972D8—82no—
973D8—82no—
974D8—82no—
975M16—82no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
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—
1000C4⋊C4—24no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
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—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1049C22⋊C4—24no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
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—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
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—22no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
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—41no—
1163C23—84no—
1164C23—84no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23—162no—
1169C23—162no—
1170C23C23×D411yescharacteristic
1171Q8—22no—
1172Q8—22no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—162no—
1180D4—22no—
1181D4—22no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—82no—
1197D4—84no—
1198D4—84no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203D4—162no—
1204D4—162no—
1205D4—162no—
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—21no—
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—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
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—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—84no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4#58511yescharacteristic
1295C2×C4#58511yescharacteristic
1296C2×C4#58511yescharacteristic
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C22—41no—
1306C22—41no—
1307C22—42no—
1308C22—41no—
1309C22—41no—
1310C22—42no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—41no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
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—168no—
1348C22#348411yescharacteristic
1349C22#348811yescharacteristic
1350C22#350011yescharacteristic
1351C22#358411yescharacteristic
1352C22#358411yescharacteristic
1353C22#358511yescharacteristic
1354C22#358511yescharacteristic
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—42no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—42no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4#353411yescharacteristic
1380C4#354211yescharacteristic
1381C4#354511yescharacteristic
1382C4#356211yescharacteristic
1383C2—81no—
1384C2—81no—
1385C2—82no—
1386C2—161no—
1387C2—161no—
1388C2—161no—
1389C2#4795511yescharacteristic
1390C2#6165111yescharacteristic
1391C2#6166611yescharacteristic
1392C2#6202411yescharacteristic
1393C2#6204711yescharacteristic
1394C2#6260111yescharacteristic
1395C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52970C2semidirect
2. #45187C2semidirect
3. #31849C2semidirect
4. #31750C2semidirect
5. #31729C2semidirect
6. #31651C2semidirect
7. #31462C2semidirect
8. #31411C2semidirect
9. #31155C2semidirect
10. #30992C2semidirect
11. #30925C2semidirect
12. #30743C2semidirect
13. #30523C2semidirect
14. #30454C2semidirect
15. #29721C2semidirect
16. #29699C2semidirect
17. #29116C2semidirect
18. #28916C2semidirect
19. #27754C2semidirect
20. #27272C2semidirect
21. #27231C2semidirect
22. #26907C2semidirect
23. #26843C2semidirect
24. #26734C2semidirect
25. #26664C2semidirect
26. #25607C2semidirect
27. #25327C2semidirect
28. #24547C2semidirect
29. #24444C2semidirect
30. #24257C2semidirect
31. #22364C2semidirect
34. C2×#492C22semidirect
35. C2×#490C22semidirect
37. C2×#477C22semidirect
38. C2×#475C22semidirect
62. #2570C22semidirect
63. #2566C22semidirect
67. #2504C22semidirect
68. #2491C22semidirect
75. #2452C22semidirect
77. #2445C22semidirect
78. #2442C22semidirect
81. #2428C22semidirect
91. #2101C22semidirect
92. #2099C22semidirect
93. #2087C22semidirect
94. #2076C22semidirect
100. #2072C22semidirect
102. #2065C22semidirect
103. #2059C22semidirect
104. #2059C22semidirect
105. #2055C22semidirect
106. #2055C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
121. #2033C22semidirect
122. #2026C22semidirect
136. #2000C22semidirect
137. #2000C22semidirect
139. #1991C22semidirect
140. #1989C22semidirect
144. #1960C22semidirect
148. #1939C22semidirect
151. #1936C22semidirect
152. #1935C22semidirect
155. #1934C22semidirect
156. #1933C22semidirect
157. #1926C22semidirect
161. #1923C22semidirect
162. #1923C22semidirect
163. #1920C22semidirect
164. #1919C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
167. #1895C22semidirect
168. #1894C22semidirect
169. #1880C22semidirect
170. #1880C22semidirect
171. #1880C22semidirect
172. #1880C22semidirect
173. #1880C22semidirect
174. #1880C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
182. #1872C22semidirect
185. #1862C22semidirect
186. #1851C22semidirect
189. #1823C22semidirect
190. #1805C22semidirect
191. #1805C22semidirect
192. #1805C22semidirect
198. #1770C22semidirect
199. C4×#103C22semidirect
200. C4×#102C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#529702
#451872
#318492
#317502
#317292
#316512
#314622
#314112
#311552
#309922
#309252
#307432
#305232
#304542
#297212
#296992
#291162
#289162
#277542
#272722
#272312
#269072
#268432
#267342
#266642
#256072
#253272
#245472
#244442
#242572
#223642