Subgroups — #16834427

Order 3712.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272059	C₂	1	2	yes	maximal, complemented
2	#14271129	C₂	1	1	yes	maximal, characteristic
3	C₂×#90805	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
5	C₂×#90777	C₂²	1	1	yes	characteristic
6	#11745214	—	2	2	no	—
7	#11745168	—	2	2	no	—
8	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₂₉	—	2	1	no	—
10	#90805	—	4	1	no	—
11	#90805	—	4	1	no	—
12	C₂×D₁₁₆	C₈	1	1	yes	characteristic
13	C₂×C₄×D₂₉	—	2	1	no	—
14	C₂×Dic₅₈	C₈	1	1	yes	characteristic
15	C₂×C₈×C₂₉	—	2	1	no	—
16	C₂×C₈×C₂₉	—	4	1	no	—
17	#90777	—	4	1	no	—
18	C₂×#6597	D₄	1	2	yes	—
19	#90770	—	4	2	no	—
20	C₂³×C₂₉	M₁₆	1	1	yes	characteristic
21	C₂²×D₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	—	2	1	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
26	C₂²⋊D₂₉	—	4	2	no	—
27	C₂×Dic₂₉	—	2	1	no	—
28	D₁₁₆	—	4	1	no	—
29	C₄×D₂₉	—	4	1	no	—
30	C₄×D₂₉	—	4	1	no	—
31	Dic₅₈	—	4	1	no	—
32	C₈×C₂₉	—	4	1	no	—
33	#6597	—	2	2	no	—
34	#1321	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	—	2	1	no	—
36	C₂²×C₂₉	—	4	1	no	—
37	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×D₂₉	—	4	2	no	—
39	C₂×D₂₉	—	4	1	no	—
40	C₄×C₂₉	—	2	1	no	—
41	C₄×C₂₉	#99	1	1	yes	characteristic
42	C₄×C₂₉	#100	1	1	yes	characteristic
43	Dic₂₉	—	4	1	no	—
44	#408	—	29	1	no	—
45	#349	—	29	2	no	—
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	4	1	no	—
48	C₂×C₂₉	#323	1	1	yes	characteristic
49	D₂₉	—	8	1	no	—
50	C₂×#41	—	29	1	no	—
51	C₂×M₁₆	—	29	1	no	—
52	C₂²×C₈	#1181	1	1	yes	characteristic
53	M₃₂	—	58	2	no	—
54	C₂²⋊C₈	—	58	2	no	—
55	C₂₉	#1321	1	1	yes	characteristic, complemented, Sylow
56	#41	—	116	1	no	—
57	#41	—	116	1	no	—
58	C₂×Q₈	—	29	1	no	—
59	C₂×D₄	—	29	1	no	—
60	C₂×D₄	—	58	1	no	—
61	C₂²×C₄	—	58	1	no	—
62	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
63	M₁₆	—	116	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	4	1	no	—
66	C₂×C₈	—	29	2	no	—
67	C₁₆	—	116	2	no	—
68	C₂³	—	58	1	no	—
69	C₂³	#90796	1	1	yes	characteristic
70	Q₈	—	116	1	no	—
71	D₄	—	116	1	no	—
72	D₄	—	116	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	58	1	no	—
76	C₂×C₄	—	116	1	no	—
77	C₂×C₄	—	116	1	no	—
78	C₂×C₄	D₂₉⋊C₈	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	58	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	116	2	no	—
85	C₂²	—	116	1	no	—
86	C₂²	#11745219	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	116	1	no	—
89	C₄	#11745215	1	1	yes	characteristic
90	C₄	#11745229	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	4	1	no	—
93	C₂	—	232	1	no	—
94	C₂	#14272007	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745215
commutator	C₂×C₄×C₂₉	C₂×C₈
Frattini	C₂²×C₄	C₂×#1181
Fitting	C₂²×C₈×C₂₉	C₄
socle	C₂×C₂₉	#323
prime radical	C₂×#90805	C₄
cosocle	C₂×#90777	C₂²
hypercenter	C₂²×C₈	#1181
hypocenter	C₂₉	#1321
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #14272059	C₂	semidirect
55. C₂₉	#1321	semidirect

Maximal subgroups

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

subgroup	index
#14272059	2
#14271129	2
#1321	29