Finite Group Databasebeta

← #6911683

Subgroups — #6911683

Order 512.

1480 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39046C211yesmaximal, characteristic
2#37687C211yesmaximal, characteristic, complemented
3#32845C211yesmaximal, characteristic, complemented
4#32742C211yesmaximal, characteristic, complemented
5#32253C211yesmaximal, characteristic, complemented
6#32231C211yesmaximal, characteristic, complemented
7#31370C211yesmaximal, characteristic, complemented
8#31352C211yesmaximal, characteristic, complemented
9#30971C211yesmaximal, characteristic, complemented
10#30951C211yesmaximal, characteristic, complemented
11#30799C211yesmaximal, characteristic, complemented
12#30781C211yesmaximal, characteristic, complemented
13#30303C211yesmaximal, characteristic, complemented
14#30172C211yesmaximal, characteristic, complemented
15#30163C211yesmaximal, characteristic, complemented
16#29990C211yesmaximal, characteristic, complemented
17#29640C211yesmaximal, characteristic, complemented
18#29406C211yesmaximal, characteristic, complemented
19#29115C211yesmaximal, characteristic, complemented
20#26019C211yesmaximal, characteristic, complemented
21#26001C211yesmaximal, characteristic, complemented
22#25968C211yesmaximal, characteristic, complemented
23#25960C211yesmaximal, characteristic, complemented
24#25822C211yesmaximal, characteristic, complemented
25#24953C211yesmaximal, characteristic, complemented
26#24938C211yesmaximal, characteristic, complemented
27#24882C211yesmaximal, characteristic
28#24865C211yesmaximal, characteristic
29#24305C211yesmaximal, characteristic, complemented
30#23456C211yesmaximal, characteristic, complemented
31#22006C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C22×#125C2211yescharacteristic, complemented
34C2×#501C2211yescharacteristic, complemented
35C2×#499C2211yescharacteristic, complemented
36C2×#481C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic
40C2×#418C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2857C2211yescharacteristic, complemented
43#2854C2211yescharacteristic
44#2761—21no—
45#2735—21no—
46#2726—21no—
47#2720—21no—
48#2713—21no—
49#2706—21no—
50#2704—21no—
51#2697—21no—
52#2660C2211yescharacteristic, complemented
53#2644C2211yescharacteristic
54#2629C2211yescharacteristic
55#2629C2211yescharacteristic
56#2603—21no—
57#2552C2211yescharacteristic, complemented
58#2550C2211yescharacteristic, complemented
59#2534—21no—
60#2531—21no—
61#2512C2211yescharacteristic
62#2490C2211yescharacteristic
63#2485C2211yescharacteristic
64#2480—21no—
65#2473—21no—
66#2454C2211yescharacteristic
67#2449—21no—
68#2442C2211yescharacteristic
69#2442C2211yescharacteristic, complemented
70#2441C2211yescharacteristic
71#2440—21no—
72#2440C2211yescharacteristic, complemented
73#2422C2211yescharacteristic
74#2417—21no—
75#2408C2211yescharacteristic
76#2352C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78#2346C2211yescharacteristic
79D4×C22⋊C4C2211yescharacteristic
80#2330C2211yescharacteristic, complemented
81#2319C2211yescharacteristic
82#2309C2211yescharacteristic
83C4×#121C2211yescharacteristic
84#2290C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2094C2211yescharacteristic
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2084C2211yescharacteristic, complemented
102#2083C2211yescharacteristic, complemented
103#2077C2211yescharacteristic, complemented
104#2077C2211yescharacteristic, complemented
105#2076C2211yescharacteristic, complemented
106#2076C2211yescharacteristic, complemented
107#2073C2211yescharacteristic
108#2071C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic
111#2067C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2059C2211yescharacteristic, complemented
116#2059C2211yescharacteristic, complemented
117#2059C2211yescharacteristic, complemented
118#2059C2211yescharacteristic, complemented
119#2059C2211yescharacteristic, complemented
120#2059C2211yescharacteristic, complemented
121#2059C2211yescharacteristic, complemented
122#2059C2211yescharacteristic, complemented
123#2058C2211yescharacteristic, complemented
124#2057C2211yescharacteristic, complemented
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2025C2211yescharacteristic
130#2025C2211yescharacteristic
131#2025C2211yescharacteristic
132#2025C2211yescharacteristic
133#2025C2211yescharacteristic
134#2025C2211yescharacteristic
135#2025C2211yescharacteristic
136#2025C2211yescharacteristic
137#2023C2211yescharacteristic
138#2023C2211yescharacteristic
139#2023C2211yescharacteristic
140#2023C2211yescharacteristic
141#1992C2211yescharacteristic, complemented
142#1990C2211yescharacteristic, complemented
143#1989C2211yescharacteristic, complemented
144#1989C2211yescharacteristic, complemented
145#1949C2211yescharacteristic, complemented
146#1948C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1925C2211yescharacteristic
155#1924C2211yescharacteristic, complemented
156#1923C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1870C2211yescharacteristic
170#1869C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic, complemented
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic, complemented
181#1851C2211yescharacteristic
182#1850C2211yescharacteristic
183#1840C2211yescharacteristic, complemented
184#1832C2211yescharacteristic, complemented
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1824C2211yescharacteristic, complemented
188#1823C2211yescharacteristic, complemented
189#1817C2211yescharacteristic, complemented
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1804C2211yescharacteristic
195#1802C2211yescharacteristic
196#1797C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1750C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#544—42no—
207#544—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#125—21no—
213C2×#125—21no—
214C2×#125—21no—
215C2×#125—42no—
216C2×#125—42no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#120—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C4⋊C4—21no—
241C22×C4⋊C4—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#501—42no—
248#499—42no—
249#481—42no—
250#480—42no—
251#478—42no—
252#478—42no—
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—42no—
274C2×#102—42no—
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299#400—21no—
300#400—21no—
301#399—21no—
302#399—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#392—21no—
339#391—21no—
340#391—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388D411yescharacteristic
383#388D411yescharacteristic
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387D411yescharacteristic
390#387D411yescharacteristic
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386D411yescharacteristic
397#386D411yescharacteristic
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385D411yescharacteristic
406#385D411yescharacteristic
407#384—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#379—21no—
430#379—21no—
431#379—21no—
432#379—21no—
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4C2×D411yescharacteristic
511C23×C4C2×D411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×M16—22no—
515C2×M16—41no—
516C2×M16—41no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—44no—
533#126—82no—
534#125—22no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—22no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—41no—
544#125—41no—
545#125—41no—
546#125—44no—
547#125—44no—
548#125—44no—
549#123—82no—
550#123—82no—
551C22⋊Q8—44no—
552C22⋊Q8—44no—
553C22⋊Q8—82no—
554C22⋊Q8—82no—
555#121—22no—
556#121—41no—
557#121—41no—
558#121—41no—
559#120—82no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—82no—
567C4×D4—82no—
568#117—22no—
569#117—22no—
570#117—22no—
571#117—41no—
572#117—41no—
573#117—41no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—82no—
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#107—22no—
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#106—22no—
699#106—22no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734#97—41no—
735C4×C8—41no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774C24—21no—
775C24—21no—
776C24—42no—
777C24—42no—
778C24—81no—
779C24—81no—
780C24—81no—
781C24—81no—
782C24—81no—
783C24C22×D411yescharacteristic
784C24C22×D411yescharacteristic
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—41no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—82no—
813C2×D4—82no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—81no—
818C2×D42−1+412yes—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C42−1+412yes—
877C22×C42−1+412yes—
878C22×C4C2511yescharacteristic
879M16—82no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—82no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4H(5,𝔽2)12yes—
974C4⋊C4H(5,𝔽2)12yes—
975C22⋊C4—22no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
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⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—41no—
1024C42—41no—
1025C42—42no—
1026C42—42no—
1027C42—42no—
1028C42—81no—
1029C42—81no—
1030C42—81no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—22no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—84no—
1058C23—84no—
1059C23—162no—
1060C23—162no—
1061C23—162no—
1062C23—162no—
1063C23—162no—
1064C23#53612yes—
1065C23#57712yes—
1066C23C23×D411yescharacteristic
1067Q8—162no—
1068Q8—162no—
1069D4—22no—
1070D4—22no—
1071D4—44no—
1072D4—41no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—41no—
1078D4—84no—
1079D4—84no—
1080D4—162no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—82no—
1167C2×C4—82no—
1168C2×C4—84no—
1169C2×C4—84no—
1170C2×C4—162no—
1171C2×C4—162no—
1172C2×C4—162no—
1173C2×C4#53612yes—
1174C2×C4C2×H(5,𝔽2)11yescharacteristic
1175C2×C4C2×H(5,𝔽2)11yescharacteristic
1176C2×C4C2×2−1+411yescharacteristic
1177C2×C4C2×2−1+411yescharacteristic
1178C2×C4C2×2−1+411yescharacteristic
1179C2×C4#58511yescharacteristic
1180C8—41no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C8—41no—
1186C8—41no—
1187C8—41no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—22no—
1193C22—22no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—168no—
1217C22C2×#53611yescharacteristic
1218C22#348411yescharacteristic
1219C22#348911yescharacteristic
1220C22C2×#57711yescharacteristic
1221C22#358411yescharacteristic
1222C22#358511yescharacteristic
1223C22#358511yescharacteristic
1224C4—22no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—42no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—42no—
1236C4—41no—
1237C4—41no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4#353811yescharacteristic
1251C4#353811yescharacteristic
1252C4#356111yescharacteristic
1253C4#356111yescharacteristic
1254C2—42no—
1255C2—42no—
1256C2—82no—
1257C2—161no—
1258C2#4059511yescharacteristic
1259C2#6087311yescharacteristic
1260C2#6089011yescharacteristic
1261C2#6164111yescharacteristic
1262C2#6165311yescharacteristic
1263C2#6216411yescharacteristic
1264C2#6219511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #37687C2semidirect
3. #32845C2semidirect
4. #32742C2semidirect
5. #32253C2semidirect
6. #32231C2semidirect
7. #31370C2semidirect
8. #31352C2semidirect
9. #30971C2semidirect
10. #30951C2semidirect
11. #30799C2semidirect
12. #30781C2semidirect
13. #30303C2semidirect
14. #30172C2semidirect
15. #30163C2semidirect
16. #29990C2semidirect
17. #29640C2semidirect
18. #29406C2semidirect
19. #29115C2semidirect
20. #26019C2semidirect
21. #26001C2semidirect
22. #25968C2semidirect
23. #25960C2semidirect
24. #25822C2semidirect
25. #24953C2semidirect
26. #24938C2semidirect
29. #24305C2semidirect
30. #23456C2semidirect
31. #22006C2semidirect
33. C22×#125C22semidirect
34. C2×#501C22semidirect
35. C2×#499C22semidirect
42. #2857C22semidirect
52. #2660C22semidirect
57. #2552C22semidirect
58. #2550C22semidirect
69. #2442C22semidirect
72. #2440C22semidirect
80. #2330C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2084C22semidirect
100. #2084C22semidirect
101. #2084C22semidirect
102. #2083C22semidirect
103. #2077C22semidirect
104. #2077C22semidirect
105. #2076C22semidirect
106. #2076C22semidirect
115. #2059C22semidirect
116. #2059C22semidirect
117. #2059C22semidirect
118. #2059C22semidirect
119. #2059C22semidirect
120. #2059C22semidirect
121. #2059C22semidirect
122. #2059C22semidirect
123. #2058C22semidirect
124. #2057C22semidirect
141. #1992C22semidirect
142. #1990C22semidirect
143. #1989C22semidirect
144. #1989C22semidirect
145. #1949C22semidirect
146. #1948C22semidirect
155. #1924C22semidirect
156. #1923C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1919C22semidirect
161. #1919C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
178. #1853C22semidirect
180. #1852C22semidirect
183. #1840C22semidirect
184. #1832C22semidirect
187. #1824C22semidirect
188. #1823C22semidirect
189. #1817C22semidirect
196. #1797C22semidirect

Maximal subgroups

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

subgroupindex
#390462
#376872
#328452
#327422
#322532
#322312
#313702
#313522
#309712
#309512
#307992
#307812
#303032
#301722
#301632
#299902
#296402
#294062
#291152
#260192
#260012
#259682
#259602
#258222
#249532
#249382
#248822
#248652
#243052
#234562
#220062