Subgroups — #14272033

Order 1856.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#1181	C₂	1	1	yes	maximal, characteristic
2	C₂×#90796	C₂	1	1	yes	maximal, characteristic
3	#11745254	C₂	1	1	yes	maximal, characteristic
4	C₂²×#1181	—	2	1	no	—
5	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
6	C₂×#6599	—	2	1	no	—
7	C₄×#1181	—	2	1	no	—
8	C₄×#1181	C₄	1	2	yes	complemented
9	#90796	—	2	1	no	—
10	#90796	C₄	1	2	yes	complemented
11	C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic, complemented
12	#90781	—	2	1	no	—
13	C₄⋊Dic₂₉	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₂₉	—	2	1	no	—
15	C₂²×D₂₉	D₄	1	1	yes	characteristic
16	C₂×#1181	—	2	2	no	—
17	C₂×#1181	—	2	2	no	—
18	C₂×#1181	—	2	2	no	—
19	C₂×C₄×C₂₉	—	2	1	no	—
20	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₉	—	2	1	no	—
22	C₂×Dic₂₉	D₄	1	1	yes	characteristic
23	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄×D₂₉	D₄	1	1	yes	characteristic
26	C₄×D₂₉	Q₈	1	1	yes	characteristic
27	#6599	—	2	2	no	—
28	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×D₂₉	—	2	1	no	—
30	C₂×D₂₉	—	2	1	no	—
31	C₂×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×D₂₉	C₄⋊C₄	1	1	yes	characteristic
33	#1181	—	2	4	no	—
34	C₄×C₂₉	—	4	1	no	—
35	C₄×C₂₉	C₄²	1	1	yes	characteristic
36	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
37	Dic₂₉	—	4	1	no	—
38	Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
39	Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
40	#339	—	29	1	no	maximal, Sylow
41	C₂×C₂₉	#95	1	1	yes	characteristic
42	C₂×C₂₉	#104	1	1	yes	characteristic
43	C₂×C₂₉	#104	1	1	yes	characteristic
44	D₂₉	—	2	1	no	—
45	D₂₉	—	2	1	no	—
46	C₂×M₁₆	—	29	1	no	—
47	#117	—	29	1	no	—
48	C₂×C₄²	—	29	1	no	—
49	C₂₉	#339	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	29	1	no	—
51	C₂²×C₄	—	58	1	no	—
52	M₁₆	—	29	2	no	—
53	M₁₆	—	58	1	no	—
54	C₂×C₈	—	58	1	no	—
55	C₄⋊C₄	—	29	1	no	—
56	C₄⋊C₄	#1181	1	1	yes	characteristic, complemented
57	C₂²⋊C₄	—	58	1	no	—
58	C₄²	—	29	2	no	—
59	C₄²	—	58	1	no	—
60	C₄²	—	58	1	no	—
61	C₂³	—	29	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	29	1	no	—
64	C₂×C₄	—	29	1	no	—
65	C₂×C₄	—	29	1	no	—
66	C₂×C₄	—	29	1	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	58	2	no	—
69	C₂×C₄	—	58	2	no	—
70	C₂×C₄	—	58	2	no	—
71	C₂×C₄	—	58	1	no	—
72	C₂×C₄	C₂×#1181	1	1	yes	characteristic
73	C₈	—	58	2	no	—
74	C₂²	—	29	1	no	—
75	C₂²	—	29	1	no	—
76	C₂²	—	58	1	no	—
77	C₂²	—	58	1	no	—
78	C₂²	C₂²⋊#1181	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	—	29	1	no	—
81	C₄	—	29	1	no	—
82	C₄	—	58	4	no	—
83	C₄	—	116	1	no	—
84	C₄	C₄×#1181	1	1	yes	characteristic
85	C₄	C₄⋊#1181	1	1	yes	characteristic
86	C₂	—	58	1	no	—
87	C₂	—	58	1	no	—
88	C₂	(C₂×#1181)⋊C₄	1	1	yes	characteristic
89	C₂	#11745224	1	1	yes	characteristic
90	C₂	#11745226	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#1181
commutator	C₄×C₂₉	C₄²
Frattini	C₂×C₄	C₂×#1181
Fitting	C₄⋊C₄×C₂₉	C₄
socle	C₂²×C₂₉	C₂²⋊C₄
prime radical	C₂²×D₂₉	D₄
cosocle	C₂×C₄×D₂₉	C₂²
hypercenter	C₄⋊C₄	#1181
hypocenter	C₂₉	#339
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. C₄×#1181	C₄	semidirect
10. #90796	C₄	semidirect
11. C₄⋊C₄×C₂₉	C₄	semidirect
13. C₄⋊Dic₂₉	C₄	semidirect
49. C₂₉	#339	semidirect
56. C₄⋊C₄	#1181	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#1181	2
C₂×#90796	2
#11745254	2
#339	29