Subgroups — #44470403

Order 29888.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28417950	C₂	1	1	yes	maximal, characteristic
2	#28417873	C₂	1	4	yes	maximal, complemented
3	#28417864	C₂	1	1	yes	maximal, characteristic, complemented
4	#125×C₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₈₆₈	—	2	2	no	—
6	C₂×D₁₈₆₈	C₂²	1	2	yes	—
7	C₂×C₄₆₇⋊C₈	C₂²	1	2	yes	—
8	C₄⋊C₄×C₄₆₇	—	2	2	no	—
9	C₄⋊C₄×C₄₆₇	C₂²	1	2	yes	—
10	C₄²×C₄₆₇	C₂²	1	1	yes	characteristic
11	C₂²×D₄₆₇	—	2	2	no	—
12	D₁₈₆₈	—	2	4	no	—
13	D₁₈₆₈	—	4	4	no	—
14	C₄₆₇⋊C₈	—	2	2	no	—
15	C₂×C₄×C₄₆₇	—	2	2	no	—
16	C₂×C₄×C₄₆₇	D₄	1	2	yes	—
17	C₂×C₄×C₄₆₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄₆₇	C₂×D₄	1	1	yes	characteristic
19	C₂×D₄₆₇	—	4	2	no	—
20	C₂×D₄₆₇	—	4	4	no	—
21	C₄×C₄₆₇	—	2	2	no	—
22	C₄×C₄₆₇	—	4	2	no	—
23	C₄×C₄₆₇	#41	1	2	yes	—
24	C₂×C₄₆₇	#124	1	1	yes	characteristic
25	C₂×C₄₆₇	AGL(1,ℤ/8)	1	2	yes	—
26	D₄₆₇	—	8	2	no	—
27	C₄₆₇	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	467	1	no	maximal, Sylow
29	#127	—	467	1	no	—
30	#125	D₄₆₇	1	1	yes	characteristic, complemented
31	#102	—	467	4	no	—
32	#97	—	467	1	no	—
33	C₂×D₄	—	934	2	no	—
34	C₂×D₄	—	467	2	no	—
35	C₂×C₈	—	467	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	C₂×D₄₆₇	1	2	yes	—
38	C₄²	C₂×D₄₆₇	1	1	yes	characteristic
39	C₂³	—	934	2	no	—
40	D₄	—	1868	4	no	—
41	D₄	—	934	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₂²⋊D₄₆₇	1	2	yes	—
44	C₂×C₄	C₂²×D₄₆₇	1	1	yes	characteristic
45	C₈	—	934	2	no	—
46	C₂²	—	1868	2	no	—
47	C₂²	—	1868	4	no	—
48	C₂²	C₂×C₂²⋊D₄₆₇	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₄	#21418744	1	2	yes	—
52	C₂	—	3736	2	no	—
53	C₂	#28417942	1	1	yes	characteristic
54	C₂	#28417978	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₆₇
commutator, cosocle	C₂×C₄×C₄₆₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₆₇
Fitting	#125×C₄₆₇	C₂
socle	C₂²×C₄₆₇	C₂×D₄
prime radical	#28417950	C₂
hypercenter	#125	D₄₆₇
hypocenter	C₄₆₇	#490
LCS	G ▷ C₂×C₄×C₄₆₇ ▷ C₂×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #28417873	C₂	semidirect
3. #28417864	C₂	semidirect
4. #125×C₄₆₇	C₂	semidirect
27. C₄₆₇	#490	semidirect
30. #125	D₄₆₇	semidirect

Maximal subgroups

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

subgroup	index
#28417950	2
#28417873	2
#28417864	2
#125×C₄₆₇	2
#490	467