Finite Group Databasebeta

← #7025468

Subgroups — #7025468

Order 512.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45315C211yesmaximal, characteristic, complemented
2#45187C211yesmaximal, characteristic, complemented
3#32129C211yesmaximal, characteristic, complemented
4#31793C211yesmaximal, characteristic, complemented
5#31150C211yesmaximal, characteristic, complemented
6#30761C211yesmaximal, characteristic, complemented
7#30730C211yesmaximal, characteristic, complemented
8#30533C211yesmaximal, characteristic, complemented
9#30523C211yesmaximal, characteristic, complemented
10#30523C211yesmaximal, characteristic, complemented
11#28926C211yesmaximal, characteristic, complemented
12#28126C211yesmaximal, characteristic, complemented
13#27236C211yesmaximal, characteristic, complemented
14#27027C211yesmaximal, characteristic, complemented
15#26794C211yesmaximal, characteristic, complemented
16#26787C211yesmaximal, characteristic, complemented
17#26734C211yesmaximal, characteristic, complemented
18#26698C211yesmaximal, characteristic, complemented
19#26625C211yesmaximal, characteristic, complemented
20#26597C211yesmaximal, characteristic, complemented
21#26267C211yesmaximal, characteristic, complemented
22#25770C211yesmaximal, characteristic
23#25283C211yesmaximal, characteristic, complemented
24#25094C211yesmaximal, characteristic, complemented
25#24163C211yesmaximal, characteristic, complemented
26#24048C211yesmaximal, characteristic, complemented
27#23584C211yesmaximal, characteristic, complemented
28#23225C211yesmaximal, characteristic, complemented
29#22863C211yesmaximal, characteristic, complemented
30#22364C211yesmaximal, characteristic, complemented
31#22056C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#481C2211yescharacteristic
38C2×#482C2211yescharacteristic
39C2×#479C2211yescharacteristic, complemented
40C2×#478C2211yescharacteristic, complemented
41C2×#468C2211yescharacteristic, complemented
42C2×#461C2211yescharacteristic, complemented
43C2×#459C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#447C2211yescharacteristic
48C2×#440C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic, complemented
50C2×#417C2211yescharacteristic
51#2797—21no—
52#2797—21no—
53#2752—21no—
54#2724—21no—
55#2711—21no—
56#2694—21no—
57#2685—21no—
58#2685—21no—
59#2600—21no—
60#2593—21no—
61#2558—21no—
62#2545C2211yescharacteristic
63#2541C2211yescharacteristic
64#2490—21no—
65#2490C2211yescharacteristic
66#2490C2211yescharacteristic
67#2490C2211yescharacteristic
68#2490C2211yescharacteristic, complemented
69#2490C2211yescharacteristic, complemented
70#2486C2211yescharacteristic
71#2480—21no—
72#2480—21no—
73#2454C2211yescharacteristic
74#2448C2211yescharacteristic
75#2445—21no—
76#2445—21no—
77#2445C2211yescharacteristic, complemented
78#2445C2211yescharacteristic, complemented
79#2435C2211yescharacteristic
80#2432C2211yescharacteristic
81#2426C2211yescharacteristic
82#2415C2211yescharacteristic
83#2395C2211yescharacteristic
84#2370C2211yescharacteristic, complemented
85#2370C2211yescharacteristic, complemented
86#2367C2211yescharacteristic
87#2362C2211yescharacteristic
88#2361C2211yescharacteristic, complemented
89#2361C2211yescharacteristic, complemented
90#2341C2211yescharacteristic
91#2324C2211yescharacteristic
92#2324C2211yescharacteristic
93#2309C2211yescharacteristic
94#2087C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2068C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic, complemented
100#2059C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2054C2211yescharacteristic
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2043C2211yescharacteristic, complemented
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2041C2211yescharacteristic, complemented
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic, complemented
117#2026C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic, complemented
121#2014C2211yescharacteristic, complemented
122#2013C2211yescharacteristic, complemented
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2000C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic, complemented
132#1999C2211yescharacteristic
133#1999C2211yescharacteristic
134#1989C2211yescharacteristic, complemented
135#1989C2211yescharacteristic, complemented
136#1983C2211yescharacteristic
137#1983C2211yescharacteristic
138#1983C2211yescharacteristic
139#1981C2211yescharacteristic, complemented
140#1972C2211yescharacteristic
141#1970C2211yescharacteristic
142#1970C2211yescharacteristic
143#1970C2211yescharacteristic
144#1968C2211yescharacteristic, complemented
145#1955C2211yescharacteristic
146#1944C2211yescharacteristic, complemented
147#1939C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic, complemented
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1923C2211yescharacteristic, complemented
165#1923C2211yescharacteristic, complemented
166#1919C2211yescharacteristic, complemented
167#1918C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1895C2211yescharacteristic
171#1895C2211yescharacteristic, complemented
172#1880C2211yescharacteristic, complemented
173#1880C2211yescharacteristic, complemented
174#1880C2211yescharacteristic, complemented
175#1880C2211yescharacteristic, complemented
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1875C2211yescharacteristic
181#1872C2211yescharacteristic, complemented
182#1870C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1863C2211yescharacteristic, complemented
187#1854C2211yescharacteristic
188#1852C2211yescharacteristic, complemented
189#1851C2211yescharacteristic, complemented
190#1825C2211yescharacteristic
191#1798C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195C4×#106C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, 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×#127—21no—
220C2×#127C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#125—21no—
224C2×#125—21no—
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#125C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#496—42no—
259#488—24no—
260#488—42no—
261#482—42no—
262#481—42no—
263#479—42no—
264#478—42no—
265#468—42no—
266#461—42no—
267#459—42no—
268#449—24no—
269#449—42no—
270#447—24no—
271#447—42no—
272#440—42no—
273C4×SD16—42no—
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#417—42no—
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#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×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400D411yescharacteristic
333#399—21no—
334#399—21no—
335#399D411yescharacteristic
336#398—21no—
337#398D411yescharacteristic
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397D411yescharacteristic
347#397D411yescharacteristic
348#397D411yescharacteristic
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#394—21no—
354#394—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#394D411yescharacteristic
369#394D411yescharacteristic
370#392—21no—
371#392—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390—21no—
386#390—21no—
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#389—21no—
400#389—21no—
401#389—21no—
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#388—21no—
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#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#381—21no—
447#380—21no—
448#380—21no—
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C4⋊Q8—22no—
571C4⋊Q8—41no—
572#127—41no—
573#127—41no—
574#127—82no—
575#126—44no—
576#126—44no—
577#125—22no—
578#125—22no—
579#125—22no—
580#125—41no—
581#125—41no—
582#125—41no—
583#125—44no—
584#125—44no—
585#124—22no—
586#124—22no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#123—44no—
592#123—82no—
593#123—82no—
594#123—82no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—44no—
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—
627C4×D4—82no—
628C4×D4—82no—
629#117—41no—
630#117—41no—
631#117—41no—
632#117—41no—
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—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
719C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#107—22no—
746#107—41no—
747#107—41no—
748#107—41no—
749#106—22no—
750#106—22no—
751#106—22no—
752#106—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758#103—22no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—22no—
775#102—22no—
776#102—41no—
777#102—41no—
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#4114yes—
790C22⋊C8—22no—
791C22⋊C8—22no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797#97—41no—
798#97—41no—
799C4×C8—22no—
800C4×C8—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#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845#41—44no—
846#41—82no—
847#41—82no—
848#41—82no—
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—21no—
860C2×Q8H(5,𝔽2)12yes—
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—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
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—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—82no—
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×D4—81no—
918C2×D4C2×#4112yes—
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—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
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×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2511yescharacteristic
971SD16—44no—
972SD16—44no—
973SD16—82no—
974SD16—82no—
975D8—82no—
976D8—82no—
977D8—82no—
978D8—82no—
979M16—82no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8C2×#4112yes—
1004C4⋊C4—24no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4C2×#4112yes—
1050C4⋊C4H(5,𝔽2)12yes—
1051C4⋊C4H(5,𝔽2)12yes—
1052C22⋊C4—24no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—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—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—42no—
1119C42—42no—
1120C42—81no—
1121C42—81no—
1122C42—81no—
1123C42—81no—
1124C42—81no—
1125C42—81no—
1126C42—81no—
1127C42—81no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—22no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
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—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—84no—
1171C23—84no—
1172C23—162no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23C23×D411yescharacteristic
1178Q8—22no—
1179Q8—22no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186D4—22no—
1187D4—22no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—82no—
1203D4—84no—
1204D4—84no—
1205D4—84no—
1206D4—84no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
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—21no—
1233C2×C4—21no—
1234C2×C4—22no—
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—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—22no—
1251C2×C4—21no—
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—84no—
1293C2×C4—162no—
1294C2×C4—162no—
1295C2×C4—162no—
1296C2×C4—162no—
1297C2×C4C22×#4111yescharacteristic
1298C2×C4C2×H(5,𝔽2)11yescharacteristic
1299C2×C4C2×H(5,𝔽2)11yescharacteristic
1300C2×C4C2×H(5,𝔽2)11yescharacteristic
1301C2×C4#58511yescharacteristic
1302C2×C4#58511yescharacteristic
1303C8—22no—
1304C8—41no—
1305C8—41no—
1306C8—41no—
1307C8—41no—
1308C8—41no—
1309C8—41no—
1310C8—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
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—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—168no—
1354C22D4×#4111yescharacteristic
1355C22#348411yescharacteristic
1356C22#348811yescharacteristic
1357C22#358411yescharacteristic
1358C22#358411yescharacteristic
1359C22#358511yescharacteristic
1360C22#358511yescharacteristic
1361C4—41no—
1362C4—41no—
1363C4—42no—
1364C4—41no—
1365C4—41no—
1366C4—42no—
1367C4—41no—
1368C4—41no—
1369C4—42no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4—81no—
1381C4—81no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4#350811yescharacteristic
1386C4#351311yescharacteristic
1387C4#354011yescharacteristic
1388C4#355811yescharacteristic
1389C2—81no—
1390C2—81no—
1391C2—82no—
1392C2—161no—
1393C2—161no—
1394C2—161no—
1395C2#4310511yescharacteristic
1396C2#6153111yescharacteristic
1397C2#6153611yescharacteristic
1398C2#6165111yescharacteristic
1399C2#6166311yescharacteristic
1400C2#6201411yescharacteristic
1401C2#6202811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25770C2
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. #45315C2semidirect
2. #45187C2semidirect
3. #32129C2semidirect
4. #31793C2semidirect
5. #31150C2semidirect
6. #30761C2semidirect
7. #30730C2semidirect
8. #30533C2semidirect
9. #30523C2semidirect
10. #30523C2semidirect
11. #28926C2semidirect
12. #28126C2semidirect
13. #27236C2semidirect
14. #27027C2semidirect
15. #26794C2semidirect
16. #26787C2semidirect
17. #26734C2semidirect
18. #26698C2semidirect
19. #26625C2semidirect
20. #26597C2semidirect
21. #26267C2semidirect
23. #25283C2semidirect
24. #25094C2semidirect
25. #24163C2semidirect
26. #24048C2semidirect
27. #23584C2semidirect
28. #23225C2semidirect
29. #22863C2semidirect
30. #22364C2semidirect
31. #22056C2semidirect
39. C2×#479C22semidirect
40. C2×#478C22semidirect
41. C2×#468C22semidirect
42. C2×#461C22semidirect
48. C2×#440C22semidirect
49. C2×C4×SD16C22semidirect
68. #2490C22semidirect
69. #2490C22semidirect
77. #2445C22semidirect
78. #2445C22semidirect
84. #2370C22semidirect
85. #2370C22semidirect
88. #2361C22semidirect
89. #2361C22semidirect
94. #2087C22semidirect
95. #2075C22semidirect
96. #2068C22semidirect
99. #2065C22semidirect
100. #2059C22semidirect
101. #2059C22semidirect
102. #2055C22semidirect
107. #2043C22semidirect
110. #2041C22semidirect
115. #2035C22semidirect
116. #2034C22semidirect
117. #2026C22semidirect
120. #2025C22semidirect
121. #2014C22semidirect
122. #2013C22semidirect
131. #2000C22semidirect
134. #1989C22semidirect
135. #1989C22semidirect
139. #1981C22semidirect
144. #1968C22semidirect
146. #1944C22semidirect
147. #1939C22semidirect
149. #1935C22semidirect
151. #1934C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
156. #1926C22semidirect
161. #1925C22semidirect
164. #1923C22semidirect
165. #1923C22semidirect
166. #1919C22semidirect
167. #1918C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
171. #1895C22semidirect
172. #1880C22semidirect
173. #1880C22semidirect
174. #1880C22semidirect
175. #1880C22semidirect
181. #1872C22semidirect
183. #1865C22semidirect
186. #1863C22semidirect
188. #1852C22semidirect
189. #1851C22semidirect
195. C4×#106C22semidirect
196. #1770C22semidirect
197. #1763C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect
201. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#453152
#451872
#321292
#317932
#311502
#307612
#307302
#305332
#305232
#289262
#281262
#272362
#270272
#267942
#267872
#267342
#266982
#266252
#265972
#262672
#257702
#252832
#250942
#241632
#240482
#235842
#232252
#228632
#223642
#220562