Subgroups — #16834628

Order 3712.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272074	C₂	1	2	yes	maximal, complemented
2	#14271536	C₂	1	1	yes	maximal, characteristic
3	C₂×#90773	—	2	2	no	—
4	#11745236	C₄	1	1	yes	characteristic
5	#11745231	C₂²	1	1	yes	characteristic
6	#11745221	—	2	2	no	—
7	C₄×C₈×C₂₉	C₄	1	1	yes	characteristic
8	C₂×D₁₁₆	—	2	1	no	—
9	C₂×D₁₁₆	—	4	1	no	—
10	C₂×Dic₅₈	D₄	1	2	yes	—
11	#90800	—	4	2	no	—
12	C₂×C₈×C₂₉	—	2	1	no	—
13	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₂₉	—	4	1	no	—
15	#90773	—	4	4	no	—
16	C₂²×D₂₉	—	4	1	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×Dic₂₉	—	2	2	no	—
20	D₁₁₆	—	4	2	no	—
21	D₁₁₆	—	8	2	no	—
22	Dic₅₈	—	4	2	no	—
23	#6599	—	8	2	no	—
24	C₈×C₂₉	—	2	2	no	—
25	#1410	—	29	1	no	maximal, Sylow
26	C₂²×C₂₉	#99	1	1	yes	characteristic
27	C₂×D₂₉	—	8	2	no	—
28	C₂×D₂₉	—	8	1	no	—
29	C₄×C₂₉	—	2	2	no	—
30	C₄×C₂₉	—	2	1	no	—
31	Dic₂₉	—	4	2	no	—
32	#492	—	29	1	no	—
33	#356	—	29	2	no	—
34	C₂×C₂₉	—	2	1	no	—
35	C₂×C₂₉	#353	1	1	yes	characteristic
36	D₂₉	—	16	1	no	—
37	C₂×SD₁₆	—	58	2	no	—
38	C₄⋊Q₈	—	29	1	no	—
39	#127	—	29	1	no	—
40	#101	—	58	2	no	—
41	C₄×C₈	#1181	1	1	yes	characteristic
42	C₂₉	#1410	1	1	yes	characteristic, complemented, Sylow
43	C₂×Q₈	—	29	2	no	—
44	C₂×D₄	—	58	1	no	—
45	C₂×D₄	—	116	1	no	—
46	SD₁₆	—	116	4	no	—
47	M₁₆	—	116	2	no	—
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	116	1	no	—
50	C₄²	C₂×#1181	1	1	yes	characteristic
51	C₂³	—	116	1	no	—
52	Q₈	—	116	2	no	—
53	D₄	—	116	2	no	—
54	D₄	—	232	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	58	2	no	—
57	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	232	2	no	—
60	C₂²	—	232	2	no	—
61	C₂²	—	232	1	no	—
62	C₂²	#11745215	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	2	1	no	—
65	C₄	—	116	2	no	—
66	C₂	—	2	1	no	—
67	C₂	—	464	1	no	—
68	C₂	#14272068	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272068
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₄×C₈×C₂₉	C₄
socle	C₂×C₂₉	#353
prime radical	#11745236	C₄
cosocle	#11745231	C₂²
hypercenter	C₄×C₈	#1181
hypocenter	C₂₉	#1410
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #14272074	C₂	semidirect
42. C₂₉	#1410	semidirect

Maximal subgroups

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

subgroup	index
#14272074	2
#14271536	2
#1410	29