Subgroups — #44470773

Order 29888.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28417940	C₂	1	4	yes	maximal, complemented
2	#28417934	C₂	1	4	yes	maximal, complemented
3	C₄×Dic₉₃₄	C₂	1	2	yes	maximal, complemented
4	D₄×Dic₄₆₇	C₂	1	4	yes	maximal, complemented
5	#127×C₄₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₃₄	C₂²	1	2	yes	—
7	C₂²×Dic₄₆₇	C₂²	1	4	yes	—
8	C₄⋊Dic₄₆₇	C₂²	1	2	yes	—
9	Dic₄₆₇⋊C₄	C₂²	1	4	yes	—
10	C₂²⋊Dic₄₆₇	C₂²	1	8	yes	—
11	C₂²⋊Dic₄₆₇	C₂²	1	4	yes	—
12	C₄×Dic₄₆₇	C₂²	1	4	yes	—
13	C₂×D₄×C₄₆₇	C₂²	1	4	yes	—
14	C₂×D₄×C₄₆₇	C₂²	1	2	yes	—
15	C₄²×C₄₆₇	C₂²	1	1	yes	characteristic
16	Dic₉₃₄	—	2	4	no	—
17	C₂×Dic₄₆₇	—	4	4	no	—
18	C₂×Dic₄₆₇	C₂³	1	4	yes	—
19	C₂×Dic₄₆₇	C₂³	1	4	yes	—
20	C₂³×C₄₆₇	C₂³	1	4	yes	—
21	D₄×C₄₆₇	—	2	8	no	—
22	D₄×C₄₆₇	—	4	2	no	—
23	C₂×C₄×C₄₆₇	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₄₆₇	C₂³	1	2	yes	—
25	C₂²×C₄₆₇	—	2	8	no	—
26	C₂²×C₄₆₇	—	2	4	no	—
27	C₂²×C₄₆₇	C₂⁴	1	1	yes	characteristic
28	C₄×C₄₆₇	—	2	1	no	—
29	C₄×C₄₆₇	#41	1	4	yes	—
30	Dic₄₆₇	—	2	4	no	—
31	Dic₄₆₇	—	2	4	no	—
32	C₂×C₄₆₇	—	4	4	no	—
33	C₂×C₄₆₇	C₂×#41	1	2	yes	—
34	C₂×C₄₆₇	H(5,𝔽₂)	1	1	yes	characteristic
35	C₄₆₇	#559	1	1	yes	characteristic, complemented, Sylow
36	#559	—	467	1	no	maximal, Sylow
37	#127	D₄₆₇	1	1	yes	characteristic
38	#124	—	467	4	no	—
39	#123	—	467	4	no	—
40	C₄×Q₈	—	467	2	no	—
41	C₄×D₄	—	467	4	no	—
42	C₂×Q₈	—	467	2	no	—
43	C₂×D₄	C₂×D₄₆₇	1	4	yes	—
44	C₂×D₄	C₂×D₄₆₇	1	2	yes	—
45	C₂²×C₄	—	467	4	no	—
46	C₄⋊C₄	—	467	2	no	—
47	C₄⋊C₄	—	467	4	no	—
48	C₂²⋊C₄	—	467	8	no	—
49	C₂²⋊C₄	—	467	4	no	—
50	C₄²	—	467	4	no	—
51	C₄²	C₂×D₄₆₇	1	1	yes	characteristic
52	C₂³	C₂²×D₄₆₇	1	4	yes	—
53	Q₈	—	934	4	no	—
54	D₄	—	2	8	no	—
55	D₄	—	4	2	no	—
56	C₂×C₄	—	1868	4	no	—
57	C₂×C₄	—	467	4	no	—
58	C₂×C₄	—	467	4	no	—
59	C₂×C₄	C₂²×D₄₆₇	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₄₆₇	1	2	yes	—
61	C₂²	—	2	8	no	—
62	C₂²	—	2	4	no	—
63	C₂²	C₂³×D₄₆₇	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	934	4	no	—
66	C₄	—	934	4	no	—
67	C₄	#21418742	1	4	yes	—
68	C₂	—	4	4	no	—
69	C₂	C₂×#21418742	1	2	yes	—
70	C₂	#28417998	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₆₇
commutator, socle, cosocle	C₂²×C₄₆₇	C₂⁴
Fitting, prime radical	#127×C₄₆₇	C₂
hypercenter	#127	D₄₆₇
hypocenter	C₄₆₇	#559
LCS	G ▷ C₂²×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #28417940	C₂	semidirect
2. #28417934	C₂	semidirect
3. C₄×Dic₉₃₄	C₂	semidirect
4. D₄×Dic₄₆₇	C₂	semidirect
35. C₄₆₇	#559	semidirect

Maximal subgroups

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

subgroup	index
#28417940	2
#28417934	2
C₄×Dic₉₃₄	2
D₄×Dic₄₆₇	2
#127×C₄₆₇	2
#559	467