Subgroups — #14271240

Order 1856.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90772	C₂	1	2	yes	maximal, complemented
2	C₄×D₁₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#11745168	C₂	1	2	yes	maximal, complemented
5	C₄×#6597	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₁₆	C₄	1	1	yes	characteristic
7	C₂×C₄×D₂₉	C₂²	1	2	yes	—
8	C₂×C₈×C₂₉	C₂²	1	2	yes	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	#90781	C₄	1	2	yes	—
11	C₄⋊Dic₂₉	C₄	1	1	yes	characteristic
12	C₂×#6597	C₂²	1	1	yes	characteristic
13	C₂×#6597	C₂²	1	1	yes	characteristic
14	#90772	—	2	4	no	—
15	C₂²×D₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
20	D₁₁₆	—	2	2	no	—
21	C₄×D₂₉	—	2	2	no	—
22	C₄×D₂₉	—	2	2	no	—
23	C₈×C₂₉	—	2	2	no	—
24	#6597	—	2	1	no	—
25	#6597	D₄	1	2	yes	complemented
26	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₂₉	—	2	2	no	—
28	C₂×D₂₉	—	2	2	no	—
29	C₂×D₂₉	—	2	2	no	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	M₁₆	1	2	yes	complemented
32	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₂₉	#41	1	1	yes	characteristic
34	Dic₂₉	—	2	2	no	—
35	#436	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	C₄×D₄	1	1	yes	characteristic
37	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
38	C₂×C₂₉	#131	1	1	yes	characteristic
39	D₂₉	—	4	2	no	—
40	C₂×M₁₆	—	29	2	no	—
41	C₄×D₄	—	29	1	no	—
42	C₄⋊C₈	D₂₉	1	1	yes	characteristic, complemented
43	C₂²⋊C₈	—	29	2	no	—
44	C₄×C₈	—	29	1	no	—
45	C₂₉	#436	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	—	29	1	no	—
47	C₂²×C₄	—	29	2	no	—
48	M₁₆	—	58	4	no	—
49	C₂×C₈	—	29	1	no	—
50	C₂×C₈	—	29	1	no	—
51	C₂×C₈	C₂×D₂₉	1	2	yes	—
52	C₄⋊C₄	—	29	1	no	—
53	C₂²⋊C₄	—	29	2	no	—
54	C₄²	C₂×D₂₉	1	1	yes	characteristic
55	C₂³	—	29	2	no	—
56	D₄	—	58	2	no	—
57	C₂×C₄	—	29	2	no	—
58	C₂×C₄	—	58	2	no	—
59	C₂×C₄	—	58	2	no	—
60	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
61	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	29	2	no	—
65	C₈	—	58	1	no	—
66	C₂²	—	58	2	no	—
67	C₂²	—	58	2	no	—
68	C₂²	—	58	2	no	—
69	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	58	2	no	—
72	C₄	#90772	1	2	yes	complemented
73	C₄	D₄×D₂₉	1	1	yes	characteristic
74	C₄	#90809	1	1	yes	characteristic
75	C₂	—	116	2	no	—
76	C₂	#11745255	1	1	yes	characteristic
77	C₂	C₂×#90772	1	1	yes	characteristic
78	C₂	#11745269	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator, socle	C₂²×C₂₉	C₂²×C₄
Fitting	C₂₉×C₄⋊C₈	C₂
prime radical	C₂×D₁₁₆	C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#436
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#90772	C₂	semidirect
3. C₂₉×C₄⋊C₈	C₂	semidirect
4. #11745168	C₂	semidirect
5. C₄×#6597	C₂	semidirect
25. #6597	D₄	semidirect
31. C₄×C₂₉	M₁₆	semidirect
42. C₄⋊C₈	D₂₉	semidirect
45. C₂₉	#436	semidirect
72. C₄	#90772	semidirect

Maximal subgroups

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

subgroup	index
C₂×#90772	2
C₄×D₁₁₆	2
C₂₉×C₄⋊C₈	2
#11745168	2
C₄×#6597	2
#436	29