Subgroups — #14271552

Order 1856.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×#90773	C₂	1	2	yes	maximal, complemented
3	#11745237	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₁₆	—	2	2	no	—
7	C₂×D₁₁₆	C₂²	1	2	yes	—
8	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₈	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₉	C₂²	1	2	yes	—
11	C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	#90781	—	2	2	no	—
13	D₂₃₂	—	2	4	no	—
14	#90773	—	2	4	no	—
15	C₂²×D₂₉	—	2	1	no	—
16	C₂²×D₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	D₄	1	2	yes	—
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	—	2	1	no	—
20	D₁₁₆	—	2	2	no	—
21	D₁₁₆	—	2	2	no	—
22	D₁₁₆	—	2	2	no	—
23	D₁₁₆	—	4	4	no	—
24	Dic₅₈	—	2	2	no	—
25	C₈×C₂₉	D₄	1	4	yes	complemented
26	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₂₉	—	4	2	no	—
28	C₂×D₂₉	—	4	1	no	—
29	C₂×D₂₉	—	4	4	no	—
30	C₂×D₂₉	—	4	2	no	—
31	C₄×C₂₉	—	2	2	no	—
32	C₄×C₂₉	C₂×D₄	1	2	yes	—
33	Dic₂₉	—	4	1	no	—
34	#496	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	#127	1	1	yes	characteristic
36	C₂×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
37	D₂₉	—	8	2	no	—
38	D₂₉	—	8	1	no	—
39	C₂×SD₁₆	—	29	2	no	—
40	C₂×D₈	—	29	2	no	—
41	#127	—	29	1	no	—
42	#124	—	29	1	no	—
43	#97	D₂₉	1	1	yes	characteristic, complemented
44	C₂₉	#496	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₈	—	29	1	no	—
46	C₂×D₄	—	29	1	no	—
47	C₂×D₄	—	29	2	no	—
48	C₂×D₄	—	58	2	no	—
49	SD₁₆	—	58	4	no	—
50	D₈	—	58	4	no	—
51	C₂×C₈	C₂×D₂₉	1	2	yes	—
52	C₂²⋊C₄	—	58	2	no	—
53	C₄²	C₂×D₂₉	1	1	yes	characteristic
54	C₂³	—	58	1	no	—
55	C₂³	—	58	2	no	—
56	Q₈	—	58	2	no	—
57	D₄	—	58	2	no	—
58	D₄	—	58	2	no	—
59	D₄	—	58	2	no	—
60	D₄	—	116	4	no	—
61	C₂×C₄	—	58	1	no	—
62	C₂×C₄	D₁₁₆	1	2	yes	—
63	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
64	C₈	D₁₁₆	1	4	yes	complemented
65	C₂²	—	116	1	no	—
66	C₂²	—	116	2	no	—
67	C₂²	—	116	4	no	—
68	C₂²	—	116	2	no	—
69	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	116	1	no	—
72	C₄	C₂×D₁₁₆	1	2	yes	—
73	C₂	—	232	2	no	—
74	C₂	—	232	1	no	—
75	C₂	#11745236	1	1	yes	characteristic
76	C₂	#11745270	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#97	C₂
socle	C₂²×C₂₉	C₂×D₄
hypercenter	#97	D₂₉
hypocenter	C₂₉	#496
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₃₂	C₂	semidirect
2. C₂×#90773	C₂	semidirect
3. #11745237	C₂	semidirect
4. #11745236	C₂	semidirect
5. C₂₉×#97	C₂	semidirect
25. C₈×C₂₉	D₄	semidirect
43. #97	D₂₉	semidirect
44. C₂₉	#496	semidirect
64. C₈	D₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₂₃₂	2
C₂×#90773	2
#11745237	2
#11745236	2
C₂₉×#97	2
#496	29