Subgroups — #16834503

Order 3712.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272086	C₂	1	2	yes	maximal, complemented
2	#14271537	C₂	1	1	yes	maximal, characteristic
3	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
4	C₂×#90784	—	2	2	no	—
5	#11745236	C₄	1	1	yes	characteristic
6	#11745214	—	2	2	no	—
7	C₄×#6597	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₂₉	—	2	1	no	—
9	C₂×D₁₁₆	—	2	1	no	—
10	C₂×D₁₁₆	—	4	1	no	—
11	C₄⋊C₄×C₂₉	—	4	1	no	—
12	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
13	#90784	—	4	2	no	—
14	#90784	—	4	2	no	—
15	C₂×#6597	D₄	1	2	yes	—
16	#90770	—	4	2	no	—
17	C₂²×D₂₉	—	4	1	no	—
18	Q₈×C₂₉	—	4	2	no	—
19	C₂×C₄×C₂₉	—	2	1	no	—
20	C₂×C₄×C₂₉	—	4	1	no	—
21	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
22	D₁₁₆	—	4	2	no	—
23	D₁₁₆	—	8	2	no	—
24	#6597	D₈	1	2	yes	—
25	#6597	SD₁₆	1	2	yes	—
26	#1359	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	#100	1	1	yes	characteristic
28	C₂×D₂₉	—	8	2	no	—
29	C₂×D₂₉	—	8	1	no	—
30	C₄×C₂₉	—	2	2	no	—
31	C₄×C₂₉	—	8	1	no	—
32	C₄×C₂₉	#102	1	2	yes	—
33	#492	—	29	1	no	—
34	#364	—	29	2	no	—
35	C₂×C₂₉	—	2	1	no	—
36	C₂×C₂₉	#331	1	1	yes	characteristic
37	D₂₉	—	16	1	no	—
38	C₂×SD₁₆	—	58	2	no	—
39	C₄⋊Q₈	#1181	1	1	yes	characteristic
40	#127	—	29	1	no	—
41	M₃₂	—	58	2	no	—
42	C₄×C₈	—	29	1	no	—
43	C₂₉	#1359	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	58	1	no	—
46	C₂×D₄	—	116	1	no	—
47	SD₁₆	—	116	2	no	—
48	SD₁₆	—	116	2	no	—
49	C₂×C₈	—	29	2	no	—
50	C₄⋊C₄	—	4	1	no	—
51	C₄²	C₂×#1181	1	1	yes	characteristic
52	C₁₆	—	116	2	no	—
53	C₂³	—	116	1	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	116	2	no	—
56	D₄	—	232	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
60	C₈	—	29	2	no	—
61	C₈	—	29	2	no	—
62	C₂²	—	232	2	no	—
63	C₂²	—	232	1	no	—
64	C₂²	#11745229	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	8	1	no	—
67	C₄	#11745223	1	2	yes	—
68	C₂	—	2	1	no	—
69	C₂	—	464	1	no	—
70	C₂	#14272021	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272021
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×C₄⋊Q₈	C₄
socle	C₂×C₂₉	#331
prime radical	#11745236	C₄
cosocle	C₄×#6597	C₂²
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	#1359
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #14272086	C₂	semidirect
43. C₂₉	#1359	semidirect

Maximal subgroups

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

subgroup	index
#14272086	2
#14271537	2
#1359	29