Finite Group Databasebeta

← #6879833

Subgroups — #6879833

Order 512.

1549 conjugacy classes of subgroups.

The subgroup lattice has 1279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36480C211yesmaximal, characteristic, complemented
2#36264C211yesmaximal, characteristic
3#33268C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#32226C211yesmaximal, characteristic, complemented
6#31744C211yesmaximal, characteristic, complemented
7#31692C211yesmaximal, characteristic, complemented
8#31638C211yesmaximal, characteristic, complemented
9#31290C211yesmaximal, characteristic
10#30805C211yesmaximal, characteristic, complemented
11#30527C211yesmaximal, characteristic
12#30365C211yesmaximal, characteristic, complemented
13#30343C211yesmaximal, characteristic, complemented
14#29521C211yesmaximal, characteristic, complemented
15#29498C211yesmaximal, characteristic, complemented
16#29482C211yesmaximal, characteristic, complemented
17#29449C211yesmaximal, characteristic, complemented
18#29354C211yesmaximal, characteristic, complemented
19#29109C211yesmaximal, characteristic, complemented
20#27541C211yesmaximal, characteristic, complemented
21#27439C211yesmaximal, characteristic, complemented
22#27245C211yesmaximal, characteristic, complemented
23#27207C211yesmaximal, characteristic, complemented
24#27049C211yesmaximal, characteristic, complemented
25#27019C211yesmaximal, characteristic, complemented
26#26739C211yesmaximal, characteristic, complemented
27#26709C211yesmaximal, characteristic, complemented
28#22116C211yesmaximal, characteristic, complemented
29#22049C211yesmaximal, characteristic, complemented
30#21646C211yesmaximal, characteristic, complemented
31#21435C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#486C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#450C2211yescharacteristic
36#2863C2211yescharacteristic, complemented
37#2863C2211yescharacteristic, complemented
38#2860C2211yescharacteristic
39#2858C2211yescharacteristic
40#2857C2211yescharacteristic
41#2854C2211yescharacteristic
42#2610—21no—
43#2605—21no—
44#2605—21no—
45#2603—21no—
46#2567C2211yescharacteristic, complemented
47#2554—21no—
48#2551C2211yescharacteristic, complemented
49#2512C2211yescharacteristic
50#2509—21no—
51#2497C2211yescharacteristic
52#2497C2211yescharacteristic
53#2492C2211yescharacteristic
54#2492C2211yescharacteristic
55#2472—21no—
56#2465—21no—
57#2465—21no—
58#2461—21no—
59#2452C2211yescharacteristic
60#2445C2211yescharacteristic
61#2445C2211yescharacteristic
62#2440C2211yescharacteristic
63#2439—21no—
64#2433C2211yescharacteristic
65#2411—21no—
66#2369C2211yescharacteristic, complemented
67#2365—21no—
68#2361C2211yescharacteristic
69#2358—21no—
70#2355C2211yescharacteristic, complemented
71#2347—21no—
72D4×C22⋊C4C2211yescharacteristic
73C4×C4⋊Q8C2211yescharacteristic, complemented
74C4×C4⋊Q8C2211yescharacteristic, complemented
75C4×#127C2211yescharacteristic
76C4×C22⋊Q8C2211yescharacteristic
77#2293C2211yescharacteristic
78C2×#390C2211yescharacteristic
79C4×#117C2211yescharacteristic
80#2100C2211yescharacteristic, complemented
81#2099C2211yescharacteristic, complemented
82#2094C2211yescharacteristic
83#2093C2211yescharacteristic, complemented
84#2087C2211yescharacteristic, complemented
85#2083C2211yescharacteristic, complemented
86#2076C2211yescharacteristic
87#2076C2211yescharacteristic
88#2076C2211yescharacteristic
89#2072C2211yescharacteristic, complemented
90#2071C2211yescharacteristic
91#2071C2211yescharacteristic
92#2071C2211yescharacteristic
93#2071C2211yescharacteristic, complemented
94#2068C2211yescharacteristic, complemented
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic, complemented
97#2065C2211yescharacteristic
98#2058C2211yescharacteristic, complemented
99#2057C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic, complemented
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2036C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2024C2211yescharacteristic, complemented
111#2023C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#2014C2211yescharacteristic
118#2014C2211yescharacteristic
119#2000C2211yescharacteristic
120#1990C2211yescharacteristic, complemented
121#1988C2211yescharacteristic, complemented
122#1987C2211yescharacteristic, complemented
123#1987C2211yescharacteristic, complemented
124#1982C2211yescharacteristic
125#1982C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic
129#1973C2211yescharacteristic, complemented
130#1968C2211yescharacteristic
131#1957C2211yescharacteristic
132#1948C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1943C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic, complemented
152#1927C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic, complemented
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic, complemented
165#1921C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1852C2211yescharacteristic
186#1834C2211yescharacteristic, complemented
187#1824C2211yescharacteristic
188#1824C2211yescharacteristic
189#1802C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1767C2211yescharacteristic, complemented
194#1767C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199#1749C2211yescharacteristic
200#1749C2211yescharacteristic
201#1745C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207#551—48no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#124—21no—
218C2×#124—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#120—21no—
228C2×#120—21no—
229C2×C4×Q8—21no—
230C2×C4×Q8—21no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C2×#117D411yescharacteristic
240C2×#117D411yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C42C2311yescharacteristic
246#486—24no—
247#474—24no—
248#450—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×C4×C8C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#398—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#393—21no—
320#393—21no—
321#393—21no—
322#392—21no—
323#392—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#390—21no—
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390—21no—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
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#388—21no—
383#388—21no—
384#388—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#383—21no—
412#382—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#379—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4D411yescharacteristic
437C4×C22⋊C4D411yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440#376D411yescharacteristic
441#376D411yescharacteristic
442C43C2311yescharacteristic
443C43C2311yescharacteristic
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#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C25—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8C2411yescharacteristic
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2411yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—44no—
536#127—22no—
537#127—41no—
538#127—41no—
539#127—41no—
540#126—44no—
541#126—44no—
542#124—44no—
543#124—82no—
544#123—44no—
545#123—44no—
546#123—44no—
547C22⋊Q8—22no—
548C22⋊Q8—44no—
549C22⋊Q8—41no—
550C22⋊Q8—44no—
551C22⋊Q8—82no—
552#121—41no—
553#121—41no—
554#120—44no—
555#120—44no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—82no—
559C4×Q8—82no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—44no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—44no—
568C4×D4—82no—
569#117—24no—
570#117—24no—
571#117—44no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
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—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
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—44no—
649C2×C22⋊C4—44no—
650C2×C22⋊C4—82no—
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—41no—
663C2×C42—41no—
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680#107—22no—
681#107—22no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689C4⋊C8—22no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692C4⋊C8—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#103—41no—
697#103—41no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—22no—
702#102—22no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102#4114yes—
719C22⋊C8—22no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723#97—41no—
724#97—41no—
725#97—41no—
726#97—41no—
727#97—41no—
728#97—41no—
729C4×C8—22no—
730C4×C8—41no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
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#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771C24—21no—
772C24—21no—
773C24—21no—
774C24—42no—
775C24—42no—
776C24—42no—
777C24—42no—
778C24—81no—
779C24—81no—
780C24—81no—
781C24C22×D411yescharacteristic
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—42no—
818C2×D4—42no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—82no—
836C2×D4—82no—
837C2×D4—82no—
838C2×D4—82no—
839C2×D4C2×#4112yes—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C2511yescharacteristic
891SD16—82no—
892SD16—82no—
893SD16—82no—
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—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8C2×#4112yes—
918C4⋊C4—22no—
919C4⋊C4—22no—
920C4⋊C4—22no—
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—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
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⋊C4AGL(1,ℤ/8)14yes—
972C4⋊C4C2×#4112yes—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—22no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
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—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
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#13714yes—
1008C42—22no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—41no—
1028C42—41no—
1029C42—41no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
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—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—84no—
1065C23—84no—
1066C23—84no—
1067C23—84no—
1068C23—162no—
1069C23—162no—
1070C23—162no—
1071C23C2×#13712yes—
1072C23C23×D411yescharacteristic
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—84no—
1078Q8—84no—
1079Q8—162no—
1080Q8—162no—
1081D4—22no—
1082D4—22no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—84no—
1094D4—84no—
1095D4—84no—
1096D4—84no—
1097D4—162no—
1098D4—162no—
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—21no—
1113C2×C4—21no—
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—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—44no—
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—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—84no—
1178C2×C4—82no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4—162no—
1182C2×C4C2×AGL(1,ℤ/8)12yes—
1183C2×C4C2×AGL(1,ℤ/8)12yes—
1184C2×C4C2×AGL(1,ℤ/8)12yes—
1185C2×C4C2×#13712yes—
1186C2×C4C2×#13712yes—
1187C2×C4C22×#4111yescharacteristic
1188C2×C4#58511yescharacteristic
1189C2×C4#58511yescharacteristic
1190C2×C4#58511yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—22no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—168no—
1230C22#344911yescharacteristic
1231C22D4×#4111yescharacteristic
1232C22#350011yescharacteristic
1233C22C22×AGL(1,ℤ/8)11yescharacteristic
1234C22C22×#13711yescharacteristic
1235C22#358511yescharacteristic
1236C22#358511yescharacteristic
1237C4—22no—
1238C4—22no—
1239C4—22no—
1240C4—22no—
1241C4—22no—
1242C4—41no—
1243C4—42no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4—81no—
1258C4—81no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4#351011yescharacteristic
1264C4#352111yescharacteristic
1265C4#356611yescharacteristic
1266C4#356811yescharacteristic
1267C2—42no—
1268C2—82no—
1269C2—161no—
1270C2—161no—
1271C2#3994711yescharacteristic
1272C2#6096911yescharacteristic
1273C2#6100311yescharacteristic
1274C2#6145111yescharacteristic
1275C2#6145311yescharacteristic
1276C2#6258211yescharacteristic
1277C2#6258811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36480C2semidirect
3. #33268C2semidirect
4. #32430C2semidirect
5. #32226C2semidirect
6. #31744C2semidirect
7. #31692C2semidirect
8. #31638C2semidirect
10. #30805C2semidirect
12. #30365C2semidirect
13. #30343C2semidirect
14. #29521C2semidirect
15. #29498C2semidirect
16. #29482C2semidirect
17. #29449C2semidirect
18. #29354C2semidirect
19. #29109C2semidirect
20. #27541C2semidirect
21. #27439C2semidirect
22. #27245C2semidirect
23. #27207C2semidirect
24. #27049C2semidirect
25. #27019C2semidirect
26. #26739C2semidirect
27. #26709C2semidirect
28. #22116C2semidirect
29. #22049C2semidirect
30. #21646C2semidirect
31. #21435C2semidirect
36. #2863C22semidirect
37. #2863C22semidirect
46. #2567C22semidirect
48. #2551C22semidirect
66. #2369C22semidirect
70. #2355C22semidirect
73. C4×C4⋊Q8C22semidirect
74. C4×C4⋊Q8C22semidirect
80. #2100C22semidirect
81. #2099C22semidirect
83. #2093C22semidirect
84. #2087C22semidirect
85. #2083C22semidirect
89. #2072C22semidirect
93. #2071C22semidirect
94. #2068C22semidirect
96. #2067C22semidirect
98. #2058C22semidirect
99. #2057C22semidirect
100. #2057C22semidirect
103. #2055C22semidirect
110. #2024C22semidirect
115. #2023C22semidirect
116. #2023C22semidirect
120. #1990C22semidirect
121. #1988C22semidirect
122. #1987C22semidirect
123. #1987C22semidirect
129. #1973C22semidirect
132. #1948C22semidirect
133. #1944C22semidirect
134. #1943C22semidirect
135. #1943C22semidirect
136. #1943C22semidirect
137. #1942C22semidirect
145. #1936C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
151. #1933C22semidirect
152. #1927C22semidirect
159. #1925C22semidirect
164. #1921C22semidirect
165. #1921C22semidirect
166. #1920C22semidirect
167. #1920C22semidirect
168. #1918C22semidirect
169. #1918C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
172. #1916C22semidirect
173. #1916C22semidirect
176. #1880C22semidirect
179. #1877C22semidirect
181. #1865C22semidirect
184. #1862C22semidirect
186. #1834C22semidirect
193. #1767C22semidirect
194. #1767C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
201. #1745C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#364802
#362642
#332682
#324302
#322262
#317442
#316922
#316382
#312902
#308052
#305272
#303652
#303432
#295212
#294982
#294822
#294492
#293542
#291092
#275412
#274392
#272452
#272072
#270492
#270192
#267392
#267092
#221162
#220492
#216462
#214352