Subgroups — #26041533

Order 11584.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₄₄₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668432	C₂	1	1	yes	maximal, characteristic, complemented
3	#19153791	C₂	1	2	yes	maximal, complemented
4	#19153736	C₂	1	2	yes	maximal, complemented
5	#106×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₇₂₄	—	2	2	no	—
7	C₂×D₇₂₄	C₂²	1	2	yes	—
8	C₂×C₄×D₁₈₁	C₂²	1	1	yes	characteristic
9	D₁₄₄₈	—	2	2	no	—
10	#15668432	—	2	2	no	—
11	C₂×#13089678	C₂²	1	1	yes	characteristic
12	#15668426	—	2	2	no	—
13	C₂×C₈×C₁₈₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₈₁	C₂²	1	2	yes	—
15	C₂²×D₁₈₁	—	2	2	no	—
16	C₂²×D₁₈₁	D₄	1	1	yes	characteristic
17	D₇₂₄	—	2	2	no	—
18	D₇₂₄	—	2	2	no	—
19	D₇₂₄	—	4	4	no	—
20	C₂×Dic₁₈₁	D₄	1	1	yes	characteristic
21	C₄×D₁₈₁	—	2	1	no	—
22	C₄×D₁₈₁	—	2	1	no	—
23	#13089678	—	2	1	no	—
24	C₂×C₄×C₁₈₁	—	2	2	no	—
25	C₂×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
26	C₈×C₁₈₁	D₄	1	2	yes	complemented
27	C₂²×C₁₈₁	C₂×D₄	1	1	yes	characteristic
28	C₂×D₁₈₁	—	2	1	no	—
29	C₂×D₁₈₁	—	2	2	no	—
30	C₂×D₁₈₁	—	4	2	no	—
31	C₂×D₁₈₁	—	4	2	no	—
32	C₂×D₁₈₁	—	4	2	no	—
33	C₄×C₁₈₁	—	4	2	no	—
34	C₄×C₁₈₁	C₂×D₄	1	1	yes	characteristic
35	C₄×C₁₈₁	#41	1	1	yes	characteristic
36	Dic₁₈₁	—	2	1	no	—
37	C₂×C₁₈₁	#121	1	1	yes	characteristic
38	C₂×C₁₈₁	AGL(1,ℤ/8)	1	2	yes	—
39	D₁₈₁	—	4	1	no	—
40	D₁₈₁	—	8	2	no	—
41	C₁₈₁	#469	1	1	yes	characteristic, complemented, Sylow
42	#469	—	181	1	no	maximal, Sylow
43	C₂×D₈	—	181	1	no	—
44	C₂×M₁₆	—	181	1	no	—
45	#121	—	181	2	no	—
46	#106	D₁₈₁	1	1	yes	characteristic, complemented
47	#102	—	181	2	no	—
48	C₂×D₄	—	362	2	no	—
49	C₂×D₄	—	181	2	no	—
50	C₂²×C₄	—	181	1	no	—
51	D₈	—	362	2	no	—
52	M₁₆	—	362	2	no	—
53	C₂×C₈	—	181	1	no	—
54	C₂×C₈	C₂×D₁₈₁	1	1	yes	characteristic
55	C₄⋊C₄	C₂×D₁₈₁	1	2	yes	—
56	C₂²⋊C₄	—	362	2	no	—
57	C₂³	—	362	2	no	—
58	C₂³	—	181	1	no	—
59	D₄	—	362	2	no	—
60	D₄	—	362	2	no	—
61	D₄	—	724	4	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	362	1	no	—
64	C₂×C₄	—	362	1	no	—
65	C₂×C₄	—	181	1	no	—
66	C₂×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
67	C₈	—	362	1	no	—
68	C₈	D₇₂₄	1	2	yes	complemented
69	C₂²	—	362	1	no	—
70	C₂²	—	362	2	no	—
71	C₂²	—	724	2	no	—
72	C₂²	—	724	2	no	—
73	C₂²	—	724	2	no	—
74	C₂²	D₄×D₁₈₁	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	362	1	no	—
77	C₄	C₂×D₇₂₄	1	1	yes	characteristic
78	C₄	#15668450	1	1	yes	characteristic
79	C₂	—	1448	2	no	—
80	C₂	—	724	1	no	—
81	C₂	#19153791	1	1	yes	characteristic
82	C₂	#19153843	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₈₁
commutator, cosocle	C₂×C₄×C₁₈₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₈₁
Fitting	#106×C₁₈₁	C₂
socle	C₂²×C₁₈₁	C₂×D₄
hypercenter	#106	D₁₈₁
hypocenter	C₁₈₁	#469
LCS	G ▷ C₂×C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₄₄₈	C₂	semidirect
2. C₂×#15668432	C₂	semidirect
3. #19153791	C₂	semidirect
4. #19153736	C₂	semidirect
5. #106×C₁₈₁	C₂	semidirect
26. C₈×C₁₈₁	D₄	semidirect
41. C₁₈₁	#469	semidirect
46. #106	D₁₈₁	semidirect
68. C₈	D₇₂₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₄₄₈	2
C₂×#15668432	2
#19153791	2
#19153736	2
#106×C₁₈₁	2
#469	181