Subgroups — #16834451

Order 3712.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272052	C₂	1	1	yes	maximal, characteristic, complemented
2	#14272024	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271245	C₂	1	1	yes	maximal, characteristic
4	C₂×D₂₃₂	C₄	1	1	yes	characteristic
5	#11745255	—	2	1	no	—
6	C₄⋊#6599	—	2	1	no	—
7	C₂×#90770	—	2	1	no	—
8	C₂₉×#107	C₄	1	1	yes	characteristic
9	C₈×Dic₂₉	C₂²	1	1	yes	characteristic
10	#11745157	—	2	1	no	—
11	C₂×D₁₁₆	—	2	1	no	—
12	C₂×C₄×D₂₉	—	4	1	no	—
13	C₂×#6599	—	4	1	no	—
14	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₄⋊C₄×C₂₉	—	2	1	no	—
16	#90781	—	4	1	no	—
17	C₄×Dic₂₉	D₄	1	1	yes	characteristic
18	C₂×#6597	D₄	1	1	yes	characteristic
19	D₂₃₂	—	2	1	no	—
20	D₂₃₂	C₈	1	2	yes	complemented
21	#90770	—	2	2	no	—
22	C₂²×D₂₉	—	4	1	no	—
23	C₂×C₄×C₂₉	—	4	1	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₂₉	D₈	1	1	yes	characteristic
26	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
27	D₁₁₆	—	2	2	no	—
28	D₁₁₆	—	4	1	no	—
29	C₄×D₂₉	—	8	2	no	—
30	#6599	—	8	1	no	—
31	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
32	C₈×C₂₉	M₁₆	1	1	yes	characteristic
33	#6597	—	2	1	no	—
34	#1333	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	#102	1	1	yes	characteristic
36	C₂×D₂₉	—	4	2	no	—
37	C₂×D₂₉	—	8	1	no	—
38	C₂×D₂₉	—	8	1	no	—
39	C₄×C₂₉	—	8	1	no	—
40	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₂₉	#104	1	1	yes	characteristic
42	Dic₂₉	—	2	1	no	—
43	Dic₂₉	—	2	1	no	—
44	C₄×D₈	—	29	1	no	—
45	#346	—	29	1	no	—
46	#334	—	29	1	no	—
47	C₂×C₂₉	D₄⋊C₈	1	1	yes	characteristic
48	C₂×C₂₉	#360	1	1	yes	characteristic
49	C₂×C₂₉	#361	1	1	yes	characteristic
50	D₂₉	—	8	2	no	—
51	C₂×D₈	—	29	1	no	—
52	C₄×D₄	—	58	1	no	—
53	C₂×C₁₆	—	58	1	no	—
54	#107	#1181	1	1	yes	characteristic
55	C₄⋊C₈	—	58	1	no	—
56	#102	—	58	1	no	—
57	C₄×C₈	—	29	1	no	—
58	C₂₉	#1333	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₄	—	58	1	no	—
60	C₂²×C₄	—	116	1	no	—
61	D₈	—	29	2	no	—
62	D₈	—	58	1	no	—
63	C₂×C₈	—	29	1	no	—
64	C₂×C₈	—	116	1	no	—
65	C₂×C₈	C₂×#1181	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₂²⋊C₄	—	116	1	no	—
68	C₄²	—	29	1	no	—
69	C₁₆	—	58	2	no	—
70	C₂³	—	116	1	no	—
71	D₄	—	58	2	no	—
72	D₄	—	116	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	29	1	no	—
75	C₂×C₄	—	29	1	no	—
76	C₂×C₄	—	232	2	no	—
77	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
78	C₈	—	58	1	no	—
79	C₈	—	232	1	no	—
80	C₈	D₂₉⋊C₈	1	1	yes	characteristic
81	C₈	#90796	1	1	yes	characteristic
82	C₂²	—	116	2	no	—
83	C₂²	—	232	1	no	—
84	C₂²	—	232	1	no	—
85	C₂²	#11745223	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	—	58	1	no	—
88	C₄	—	58	1	no	—
89	C₄	#11745219	1	1	yes	characteristic
90	C₄	#11745226	1	1	yes	characteristic
91	C₂	—	232	2	no	—
92	C₂	#14272011	1	1	yes	characteristic
93	C₂	#14272080	1	1	yes	characteristic
94	C₂	#14272081	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745223
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂₉×#107	C₄
socle	C₂²×C₂₉	#102
prime radical	C₂×D₂₃₂	C₄
cosocle	C₈×Dic₂₉	C₂²
hypercenter	#107	#1181
hypocenter	C₂₉	#1333
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
1. #14272052	C₂	semidirect
2. #14272024	C₂	semidirect
20. D₂₃₂	C₈	semidirect
58. C₂₉	#1333	semidirect

Maximal subgroups

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

subgroup	index
#14272052	2
#14272024	2
#14271245	2
#1333	29