Subgroups — #44470427

Order 29888.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21418730	C₂	1	2	yes	maximal, complemented
2	C₂×#21418728	C₂	1	2	yes	maximal, complemented
3	#28417950	C₂	1	1	yes	maximal, characteristic, complemented
4	#28417864	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₄₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₈₆₈	—	2	2	no	—
7	C₂×D₁₈₆₈	C₂²	1	2	yes	—
8	#21418730	—	2	4	no	—
9	#21418728	—	2	4	no	—
10	C₂×C₄₆₇⋊C₈	C₂²	1	2	yes	—
11	C₂×Q₈×C₄₆₇	C₂²	1	1	yes	characteristic
12	C₂×D₄×C₄₆₇	C₂²	1	1	yes	characteristic
13	C₂²⋊C₄×C₄₆₇	—	2	2	no	—
14	C₄²×C₄₆₇	C₂²	1	1	yes	characteristic
15	C₂²×D₄₆₇	—	2	2	no	—
16	D₁₈₆₈	—	2	2	no	—
17	D₁₈₆₈	—	2	2	no	—
18	D₁₈₆₈	—	4	4	no	—
19	C₄₆₇⋊C₈	D₄	1	4	yes	complemented
20	C₂³×C₄₆₇	—	2	1	no	—
21	Q₈×C₄₆₇	—	2	2	no	—
22	D₄×C₄₆₇	—	2	2	no	—
23	C₂×C₄×C₄₆₇	—	2	1	no	—
24	C₂×C₄×C₄₆₇	D₄	1	2	yes	—
25	C₂×C₄×C₄₆₇	C₂³	1	1	yes	characteristic
26	C₂²×C₄₆₇	—	4	1	no	—
27	C₂²×C₄₆₇	—	4	2	no	—
28	C₂²×C₄₆₇	C₂×D₄	1	1	yes	characteristic
29	C₂×D₄₆₇	—	4	2	no	—
30	C₂×D₄₆₇	—	4	4	no	—
31	C₄×C₄₆₇	—	2	2	no	—
32	C₄×C₄₆₇	—	4	1	no	—
33	C₄×C₄₆₇	C₂×D₄	1	2	yes	—
34	C₂×C₄₆₇	—	8	1	no	—
35	C₂×C₄₆₇	#127	1	1	yes	characteristic
36	C₂×C₄₆₇	AGL(1,ℤ/8)	1	2	yes	—
37	D₄₆₇	—	8	2	no	—
38	C₄₆₇	#496	1	1	yes	characteristic, complemented, Sylow
39	#496	—	467	1	no	maximal, Sylow
40	C₂×SD₁₆	—	467	2	no	—
41	C₂×D₈	—	467	2	no	—
42	#127	—	467	1	no	—
43	#124	D₄₆₇	1	1	yes	characteristic, complemented
44	#97	—	467	1	no	—
45	C₂×Q₈	C₂×D₄₆₇	1	1	yes	characteristic
46	C₂×D₄	—	934	2	no	—
47	C₂×D₄	—	467	2	no	—
48	C₂×D₄	C₂×D₄₆₇	1	1	yes	characteristic
49	SD₁₆	—	934	4	no	—
50	D₈	—	934	4	no	—
51	C₂×C₈	—	467	2	no	—
52	C₂²⋊C₄	—	2	2	no	—
53	C₄²	C₂×D₄₆₇	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	C₂³	—	934	2	no	—
56	Q₈	—	2	2	no	—
57	D₄	—	2	2	no	—
58	D₄	—	1868	4	no	—
59	D₄	—	934	2	no	—
60	D₄	—	934	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	C₂²⋊D₄₆₇	1	2	yes	—
63	C₂×C₄	C₂²×D₄₆₇	1	1	yes	characteristic
64	C₈	—	467	4	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	4	2	no	—
67	C₂²	—	1868	2	no	—
68	C₂²	—	1868	4	no	—
69	C₂²	C₂×C₂²⋊D₄₆₇	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	4	1	no	—
72	C₄	D₄×D₄₆₇	1	2	yes	—
73	C₂	—	8	1	no	—
74	C₂	—	3736	2	no	—
75	C₂	#28417949	1	1	yes	characteristic
76	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	#124×C₄₆₇	C₂
socle	C₂²×C₄₆₇	C₂×D₄
hypercenter	#124	D₄₆₇
hypocenter	C₄₆₇	#496
LCS	G ▷ C₂×C₄×C₄₆₇ ▷ C₂×C₄₆₇ ▷ C₄₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. C₂×#21418730	C₂	semidirect
2. C₂×#21418728	C₂	semidirect
3. #28417950	C₂	semidirect
4. #28417864	C₂	semidirect
5. #124×C₄₆₇	C₂	semidirect
19. C₄₆₇⋊C₈	D₄	semidirect
38. C₄₆₇	#496	semidirect
43. #124	D₄₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21418730	2
C₂×#21418728	2
#28417950	2
#28417864	2
#124×C₄₆₇	2
#496	467