Subgroups — #14272144

Order 1856.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90809	C₂	1	1	yes	maximal, characteristic
2	#11745345	C₂	1	2	yes	maximal, complemented
3	#11745215	C₂	1	4	yes	maximal, complemented
4	C₂×Q₈×C₂₉	C₄	1	1	yes	characteristic, complemented
5	#90809	—	2	2	no	—
6	#90809	—	2	2	no	—
7	C₂×D₁₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂×D₁₁₆	C₂²	1	2	yes	—
9	C₂×C₄×D₂₉	C₄	1	2	yes	complemented
10	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
11	C₂²⋊#1181	C₂²	1	4	yes	—
12	C₄⋊#1181	—	2	2	no	—
13	C₄×#1181	—	2	2	no	—
14	C₂²×D₂₉	C₂×C₄	1	2	yes	—
15	C₂²×D₂₉	C₂³	1	1	yes	characteristic
16	C₂×#1181	—	2	4	no	—
17	Q₈×C₂₉	—	2	2	no	—
18	C₂×C₄×C₂₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	D₁₁₆	—	2	4	no	—
22	D₁₁₆	—	2	2	no	—
23	C₄×D₂₉	—	2	2	no	—
24	C₄×D₂₉	—	2	2	no	—
25	C₄×D₂₉	D₄	1	2	yes	—
26	C₄×D₂₉	D₄	1	2	yes	—
27	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₂₉	—	2	2	no	—
29	C₂×D₂₉	—	4	1	no	—
30	C₂×D₂₉	—	4	2	no	—
31	C₂×D₂₉	C₂×D₄	1	2	yes	—
32	#1181	—	4	4	no	—
33	C₄×C₂₉	—	2	2	no	—
34	C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
35	Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
37	#410	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	—	2	1	no	—
39	C₂×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	D₂₉	—	2	2	no	—
41	D₂₉	—	4	2	no	—
42	C₂×#41	—	29	1	no	—
43	#117	—	29	2	no	—
44	#99	—	29	4	no	—
45	C₂₉	#410	1	1	yes	characteristic, complemented, Sylow
46	#41	—	58	2	no	—
47	#41	—	58	2	no	—
48	C₂×Q₈	#1181	1	1	yes	characteristic, complemented
49	C₂×D₄	—	29	2	no	—
50	C₂×D₄	—	29	1	no	—
51	C₂²×C₄	—	29	1	no	—
52	C₂²×C₄	—	29	2	no	—
53	C₄⋊C₄	—	58	2	no	—
54	C₂²⋊C₄	—	29	4	no	—
55	C₄²	—	58	2	no	—
56	C₂³	—	29	1	no	—
57	C₂³	—	29	2	no	—
58	Q₈	—	2	2	no	—
59	D₄	—	58	4	no	—
60	D₄	—	58	2	no	—
61	C₂×C₄	—	29	1	no	—
62	C₂×C₄	—	29	2	no	—
63	C₂×C₄	—	29	2	no	—
64	C₂×C₄	—	58	2	no	—
65	C₂×C₄	—	58	2	no	—
66	C₂×C₄	—	58	4	no	—
67	C₂×C₄	C₂×#1181	1	2	yes	—
68	C₂×C₄	C₂×#1181	1	1	yes	characteristic
69	C₂²	—	29	2	no	—
70	C₂²	—	58	2	no	—
71	C₂²	—	116	1	no	—
72	C₂²	—	116	2	no	—
73	C₂²	C₂²×#1181	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	29	1	no	—
76	C₄	—	29	1	no	—
77	C₄	—	116	4	no	—
78	C₄	C₂²⋊#1181	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	58	2	no	—
81	C₂	—	116	2	no	—
82	C₂	C₂×C₂²⋊#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#1181
commutator	C₂²×C₂₉	C₂²×C₄
Frattini	C₂²	C₂²×#1181
Fitting	C₂×Q₈×C₂₉	C₄
socle	C₂×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂×#90809	C₂
cosocle	C₂²×D₂₉	C₂³
hypercenter	C₂×Q₈	#1181
hypocenter	C₂₉	#410
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #11745345	C₂	semidirect
3. #11745215	C₂	semidirect
4. C₂×Q₈×C₂₉	C₄	semidirect
7. C₂×D₁₁₆	C₄	semidirect
9. C₂×C₄×D₂₉	C₄	semidirect
45. C₂₉	#410	semidirect
48. C₂×Q₈	#1181	semidirect

Maximal subgroups

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

subgroup	index
C₂×#90809	2
#11745345	2
#11745215	2
#410	29