Subgroups — #16817660

Order 3712.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271542	C₂	1	1	yes	maximal, characteristic
2	#14270962	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#356	C₂	1	1	yes	maximal, characteristic
4	C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
5	C₂×#90785	—	2	1	no	—
6	C₂×#90785	—	2	1	no	—
7	#11745231	C₄	1	1	yes	characteristic
8	C₂₉×#101	—	2	1	no	—
9	#11745184	—	2	1	no	—
10	C₄×#6597	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₂₉	D₄	1	1	yes	characteristic
13	C₂×Dic₅₈	—	2	1	no	—
14	M₁₆×C₂₉	—	4	1	no	—
15	C₄⋊C₄×C₂₉	—	4	1	no	—
16	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
17	#90785	—	4	2	no	—
18	#90785	—	4	2	no	—
19	C₄⋊Dic₂₉	—	4	1	no	—
20	#90777	—	4	1	no	—
21	C₂×#6597	—	2	1	no	—
22	Q₈×C₂₉	—	4	1	no	—
23	Q₈×C₂₉	—	4	1	no	—
24	C₂×C₄×C₂₉	—	2	1	no	—
25	C₂×C₄×C₂₉	—	2	1	no	—
26	C₂×C₄×C₂₉	—	2	1	no	—
27	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	1	no	—
29	Dic₅₈	—	4	1	no	—
30	Dic₅₈	—	4	1	no	—
31	C₈×C₂₉	—	8	1	no	—
32	#6597	—	2	2	no	—
33	#6597	—	8	1	no	—
34	#1411	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	#99	1	1	yes	characteristic
36	C₄×C₂₉	—	2	2	no	—
37	C₄×C₂₉	—	2	1	no	—
38	C₄×C₂₉	—	4	1	no	—
39	C₄×C₂₉	—	4	1	no	—
40	Dic₂₉	—	8	1	no	—
41	#494	—	29	1	no	—
42	#356	—	29	1	no	—
43	#356	D₂₉	1	1	yes	characteristic
44	C₂×C₂₉	—	2	1	no	—
45	C₂×C₂₉	#353	1	1	yes	characteristic
46	C₂×Q₁₆	—	58	1	no	—
47	C₂×Q₁₆	—	58	1	no	—
48	C₄⋊Q₈	—	29	1	no	—
49	C₄⋊Q₈	C₂×D₂₉	1	1	yes	characteristic
50	#101	—	2	1	no	—
51	#101	—	58	1	no	—
52	C₄×C₈	—	29	1	no	—
53	C₂₉	#1411	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₈	—	58	1	no	—
55	C₂×Q₈	D₁₁₆	1	1	yes	characteristic
56	C₂×Q₈	C₂²⋊D₂₉	1	1	yes	characteristic
57	Q₁₆	—	116	2	no	—
58	Q₁₆	—	116	2	no	—
59	M₁₆	—	4	1	no	—
60	M₁₆	—	116	1	no	—
61	C₂×C₈	—	58	1	no	—
62	C₄⋊C₄	—	4	1	no	—
63	C₄⋊C₄	—	116	1	no	—
64	C₄²	C₄×D₂₉	1	1	yes	characteristic
65	Q₈	—	4	1	no	—
66	Q₈	—	4	1	no	—
67	Q₈	—	116	1	no	—
68	Q₈	—	116	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	116	1	no	—
73	C₂×C₄	#90781	1	1	yes	characteristic
74	C₈	—	8	1	no	—
75	C₈	—	58	2	no	—
76	C₈	—	232	1	no	—
77	C₂²	#11745154	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	1	no	—
80	C₄	—	4	1	no	—
81	C₄	—	4	1	no	—
82	C₄	—	232	1	no	—
83	C₂	—	2	1	no	—
84	C₂	#14270955	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270955
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₂₉
Fitting	C₂₉×#356	C₂
socle	C₂×C₂₉	#353
prime radical	C₂²×C₂₉	#99
cosocle	C₂₉×C₄⋊Q₈	C₂²
hypercenter	#356	D₂₉
hypocenter	C₂₉	#1411
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
53. C₂₉	#1411	semidirect

Maximal subgroups

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

subgroup	index
#14271542	2
#14270962	2
C₂₉×#356	2
#1411	29