Subgroups — #14271399

Order 1856.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745292	C₂	1	2	yes	maximal, complemented
3	C₂×D₂₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745169	C₂	1	2	yes	maximal, complemented
5	#11745166	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₂₉	—	2	2	no	—
8	C₂×D₁₁₆	C₂²	1	2	yes	—
9	C₂×C₈×C₂₉	—	2	2	no	—
10	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	#90781	—	2	2	no	—
13	C₄⋊Dic₂₉	C₂²	1	2	yes	—
14	D₂₃₂	—	2	2	no	—
15	C₂³×C₂₉	D₄	1	1	yes	characteristic
16	C₂²×D₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	—	2	1	no	—
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂²⋊D₂₉	—	4	4	no	—
22	C₂×Dic₂₉	—	2	2	no	—
23	D₁₁₆	—	2	2	no	—
24	D₁₁₆	—	2	2	no	—
25	C₈×C₂₉	—	2	1	no	—
26	C₈×C₂₉	D₄	1	2	yes	complemented
27	C₂²×C₂₉	—	2	1	no	—
28	C₂²×C₂₉	—	2	1	no	—
29	C₂²×C₂₉	D₈	1	2	yes	complemented
30	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
31	C₂×D₂₉	—	4	2	no	—
32	C₂×D₂₉	—	4	2	no	—
33	C₂×D₂₉	—	4	2	no	—
34	C₄×C₂₉	—	2	1	no	—
35	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₂₉	#41	1	1	yes	characteristic
37	Dic₂₉	—	4	2	no	—
38	#466	—	29	1	no	maximal, Sylow
39	C₂×C₂₉	—	2	2	no	—
40	C₂×C₂₉	#121	1	1	yes	characteristic
41	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
42	C₂×C₂₉	#135	1	1	yes	characteristic
43	D₂₉	—	8	2	no	—
44	C₂×D₈	—	29	1	no	—
45	C₂²×C₈	D₂₉	1	1	yes	characteristic, complemented
46	#121	—	29	2	no	—
47	#107	—	29	1	no	—
48	#102	—	29	2	no	—
49	C₂₉	#466	1	1	yes	characteristic, complemented, Sylow
50	C₂×D₄	—	29	2	no	—
51	C₂×D₄	—	58	2	no	—
52	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
53	D₈	—	58	2	no	—
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
56	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
57	C₄⋊C₄	—	29	2	no	—
58	C₂²⋊C₄	—	58	2	no	—
59	C₂³	—	58	2	no	—
60	C₂³	D₁₁₆	1	1	yes	characteristic
61	D₄	—	58	2	no	—
62	D₄	—	58	2	no	—
63	D₄	—	116	4	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	58	2	no	—
67	C₂×C₄	D₁₁₆	1	1	yes	characteristic
68	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	C₂²⋊D₂₉	1	2	yes	complemented
71	C₂²	—	2	1	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	116	2	no	—
74	C₂²	—	116	2	no	—
75	C₂²	—	116	2	no	—
76	C₂²	D₂₃₂	1	2	yes	complemented
77	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	116	2	no	—
80	C₄	#90805	1	1	yes	characteristic
81	C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	—	232	2	no	—
84	C₂	C₂×D₂₃₂	1	1	yes	characteristic
85	C₂	#11745266	1	1	yes	characteristic
86	C₂	#11745292	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂²×C₈×C₂₉	C₂
socle	C₂²×C₂₉	C₂×D₄
hypercenter	C₂²×C₈	D₂₉
hypocenter	C₂₉	#466
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₈×C₂₉	C₂	semidirect
2. #11745292	C₂	semidirect
3. C₂×D₂₃₂	C₂	semidirect
4. #11745169	C₂	semidirect
5. #11745166	C₂	semidirect
26. C₈×C₂₉	D₄	semidirect
29. C₂²×C₂₉	D₈	semidirect
45. C₂²×C₈	D₂₉	semidirect
49. C₂₉	#466	semidirect
70. C₈	C₂²⋊D₂₉	semidirect
76. C₂²	D₂₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₂₉	2
#11745292	2
C₂×D₂₃₂	2
#11745169	2
#11745166	2
#466	29