Finite Group Databasebeta

← #7291229

Subgroups — #7291229

Order 512.

1533 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42814C211yesmaximal, characteristic, complemented
2#42581C211yesmaximal, characteristic
3#32845C211yesmaximal, characteristic, complemented
4#32646C211yesmaximal, characteristic, complemented
5#32564C211yesmaximal, characteristic, complemented
6#31948C211yesmaximal, characteristic, complemented
7#31708C211yesmaximal, characteristic, complemented
8#31552C211yesmaximal, characteristic, complemented
9#31372C211yesmaximal, characteristic, complemented
10#31325C211yesmaximal, characteristic, complemented
11#31276C211yesmaximal, characteristic, complemented
12#31140C211yesmaximal, characteristic, complemented
13#31004C211yesmaximal, characteristic, complemented
14#30629C211yesmaximal, characteristic, complemented
15#30608C211yesmaximal, characteristic, complemented
16#29459C211yesmaximal, characteristic, complemented
17#29377C211yesmaximal, characteristic, complemented
18#29152C211yesmaximal, characteristic, complemented
19#28844C211yesmaximal, characteristic, complemented
20#27710C211yesmaximal, characteristic, complemented
21#27254C211yesmaximal, characteristic, complemented
22#26987C211yesmaximal, characteristic, complemented
23#26670C211yesmaximal, characteristic, complemented
24#26425C211yesmaximal, characteristic, complemented
25#25960C211yesmaximal, characteristic, complemented
26#25935C211yesmaximal, characteristic, complemented
27#25559C211yesmaximal, characteristic, complemented
28#24921C211yesmaximal, characteristic, complemented
29#24346C211yesmaximal, characteristic, complemented
30#23969C211yesmaximal, characteristic, complemented
31#22390C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#554C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#480C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#468C2211yescharacteristic, complemented
38C2×#460C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2825—21no—
43#2822—21no—
44#2778—21no—
45#2697—21no—
46#2690—21no—
47#2690—21no—
48#2678—21no—
49#2677—21no—
50#2677—21no—
51#2676—21no—
52#2660C2211yescharacteristic, complemented
53#2648—21no—
54#2644C2211yescharacteristic
55#2634—21no—
56#2633—21no—
57#2617—21no—
58#2562C2211yescharacteristic
59#2548C2211yescharacteristic
60#2546C2211yescharacteristic, complemented
61#2538C2211yescharacteristic
62#2536—21no—
63#2500C2211yescharacteristic
64#2494C2211yescharacteristic
65#2472—21no—
66#2442C2211yescharacteristic
67#2442C2211yescharacteristic, complemented
68#2440C2211yescharacteristic
69#2440C2211yescharacteristic, complemented
70#2433C2211yescharacteristic
71#2428C2211yescharacteristic
72#2428C2211yescharacteristic
73#2423C2211yescharacteristic
74#2423C2211yescharacteristic, complemented
75#2422C2211yescharacteristic
76#2421C2211yescharacteristic
77#2421C2211yescharacteristic, complemented
78#2414C2211yescharacteristic
79#2408C2211yescharacteristic
80#2398C2211yescharacteristic
81#2363C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2328C2211yescharacteristic
84#2320C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2097C2211yescharacteristic, complemented
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic
92#2087C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic
98#2076C2211yescharacteristic
99#2075C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2057C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2036C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic, complemented
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic, complemented
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic, complemented
124#2025C2211yescharacteristic, complemented
125#2023C2211yescharacteristic
126#2023C2211yescharacteristic
127#2023C2211yescharacteristic
128#2023C2211yescharacteristic, complemented
129#2014C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#1992C2211yescharacteristic, complemented
134#1988C2211yescharacteristic, complemented
135#1985C2211yescharacteristic, complemented
136#1984C2211yescharacteristic, complemented
137#1973C2211yescharacteristic
138#1961C2211yescharacteristic
139#1957C2211yescharacteristic
140#1943C2211yescharacteristic, complemented
141#1942C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1933C2211yescharacteristic, complemented
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1892C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic, complemented
166#1880C2211yescharacteristic, complemented
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1874C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1852C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1850C2211yescharacteristic
185#1840C2211yescharacteristic, complemented
186#1836C2211yescharacteristic, complemented
187#1835C2211yescharacteristic, complemented
188#1825C2211yescharacteristic, complemented
189#1824C2211yescharacteristic
190#1807C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1768C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#557—42no—
210#557—42no—
211#554—42no—
212#554—42no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8—21no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#125—21no—
220C2×#125—21no—
221C2×#125—21no—
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×#124—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256#486—42no—
257#480—42no—
258#478—42no—
259#468—42no—
260#460—42no—
261#450—42no—
262#440—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102—42no—
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#401—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400D411yescharacteristic
320#400D411yescharacteristic
321#399—21no—
322#399—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397D411yescharacteristic
341#397D411yescharacteristic
342#396—21no—
343#396—21no—
344#396—21no—
345#395—21no—
346#395—21no—
347#395—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394D411yescharacteristic
360#394D411yescharacteristic
361#393D411yescharacteristic
362#393D411yescharacteristic
363#392—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390—21no—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#380—21no—
434#380—21no—
435#380—21no—
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376C2311yescharacteristic
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#340C2311yescharacteristic
477#340C2311yescharacteristic
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×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2×D411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C22×C8—41no—
534C22×C8—41no—
535C22×C8—41no—
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C4⋊Q8—22no—
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548C4⋊Q8—44no—
549C4⋊Q8—82no—
550#127—22no—
551#127—41no—
552#127—41no—
553#127—41no—
554#125—22no—
555#125—41no—
556#125—41no—
557#125—41no—
558#125—44no—
559#125—44no—
560#125—44no—
561#124—82no—
562#123—82no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571C22⋊Q8—82no—
572#121—22no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—82no—
581#121—82no—
582#120—82no—
583#120—82no—
584#120—82no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—44no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—44no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603#117—41no—
604#117—41no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
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—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
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—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
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—82no—
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708#107—22no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#103—22no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753#97—41no—
754#97—41no—
755C4×C8—41no—
756C4×C8—41no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—81no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C2×Q8—22no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—41no—
816C2×Q8—41no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8H(5,𝔽2)12yes—
824C2×D4—22no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—44no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—82no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D42−1+412yes—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C2511yescharacteristic
929SD16—44no—
930SD16—82no—
931SD16—82no—
932M16—82no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—82no—
958C4⋊C4—24no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4H(5,𝔽2)12yes—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C42—24no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—42no—
1069C42—42no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—84no—
1108C23—84no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23—162no—
1114C23#57712yes—
1115C23C23×D411yescharacteristic
1116Q8—22no—
1117Q8—22no—
1118Q8—41no—
1119Q8—41no—
1120Q8—82no—
1121Q8—84no—
1122Q8—162no—
1123D4—22no—
1124D4—22no—
1125D4—44no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—84no—
1137D4—162no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144D4—162no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4—162no—
1230C2×C4—162no—
1231C2×C4—162no—
1232C2×C4#57612yes—
1233C2×C4C2×H(5,𝔽2)11yescharacteristic
1234C2×C4C2×H(5,𝔽2)11yescharacteristic
1235C2×C4C2×2−1+411yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C2×C4#58511yescharacteristic
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—42no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—42no—
1262C22—42no—
1263C22—41no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—168no—
1283C22#348411yescharacteristic
1284C22#348911yescharacteristic
1285C22#350011yescharacteristic
1286C22C2×#57611yescharacteristic
1287C22C2×#57711yescharacteristic
1288C22#358511yescharacteristic
1289C22#358611yescharacteristic
1290C4—22no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—42no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—42no—
1302C4—41no—
1303C4—41no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4#353511yescharacteristic
1316C4#354111yescharacteristic
1317C4#354511yescharacteristic
1318C4#355111yescharacteristic
1319C2—42no—
1320C2—81no—
1321C2—82no—
1322C2—161no—
1323C2—161no—
1324C2#4776011yescharacteristic
1325C2#6161111yescharacteristic
1326C2#6161711yescharacteristic
1327C2#6216411yescharacteristic
1328C2#6218011yescharacteristic
1329C2#6255011yescharacteristic
1330C2#6257511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42581C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42814C2semidirect
3. #32845C2semidirect
4. #32646C2semidirect
5. #32564C2semidirect
6. #31948C2semidirect
7. #31708C2semidirect
8. #31552C2semidirect
9. #31372C2semidirect
10. #31325C2semidirect
11. #31276C2semidirect
12. #31140C2semidirect
13. #31004C2semidirect
14. #30629C2semidirect
15. #30608C2semidirect
16. #29459C2semidirect
17. #29377C2semidirect
18. #29152C2semidirect
19. #28844C2semidirect
20. #27710C2semidirect
21. #27254C2semidirect
22. #26987C2semidirect
23. #26670C2semidirect
24. #26425C2semidirect
25. #25960C2semidirect
26. #25935C2semidirect
27. #25559C2semidirect
28. #24921C2semidirect
29. #24346C2semidirect
30. #23969C2semidirect
31. #22390C2semidirect
32. C2×#557C22semidirect
35. C2×#480C22semidirect
37. C2×#468C22semidirect
52. #2660C22semidirect
60. #2546C22semidirect
67. #2442C22semidirect
69. #2440C22semidirect
74. #2423C22semidirect
77. #2421C22semidirect
84. #2320C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2097C22semidirect
92. #2087C22semidirect
93. #2086C22semidirect
94. #2085C22semidirect
95. #2083C22semidirect
96. #2083C22semidirect
104. #2066C22semidirect
106. #2065C22semidirect
107. #2059C22semidirect
108. #2057C22semidirect
109. #2057C22semidirect
116. #2034C22semidirect
119. #2033C22semidirect
123. #2025C22semidirect
124. #2025C22semidirect
128. #2023C22semidirect
133. #1992C22semidirect
134. #1988C22semidirect
135. #1985C22semidirect
136. #1984C22semidirect
140. #1943C22semidirect
141. #1942C22semidirect
143. #1936C22semidirect
146. #1933C22semidirect
148. #1926C22semidirect
152. #1924C22semidirect
153. #1923C22semidirect
154. #1919C22semidirect
155. #1919C22semidirect
156. #1918C22semidirect
165. #1880C22semidirect
166. #1880C22semidirect
168. #1877C22semidirect
172. #1873C22semidirect
175. #1865C22semidirect
177. #1863C22semidirect
180. #1862C22semidirect
181. #1854C22semidirect
183. #1851C22semidirect
185. #1840C22semidirect
186. #1836C22semidirect
187. #1835C22semidirect
188. #1825C22semidirect
192. #1804C22semidirect
193. #1803C22semidirect
195. #1802C22semidirect
198. #1768C22semidirect
199. C4×#103C22semidirect
200. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#428142
#425812
#328452
#326462
#325642
#319482
#317082
#315522
#313722
#313252
#312762
#311402
#310042
#306292
#306082
#294592
#293772
#291522
#288442
#277102
#272542
#269872
#266702
#264252
#259602
#259352
#255592
#249212
#243462
#239692
#223902