Subgroups — #16817458

Order 3712.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₂₃₂	C₂	1	1	yes	maximal, characteristic
2	#14270939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₃₂	C₄	1	1	yes	characteristic
5	C₄×D₁₁₆	—	2	1	no	—
6	C₂₉×C₄⋊C₈	—	2	1	no	—
7	C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
8	#11745169	—	2	1	no	—
9	#11745166	C₄	1	1	yes	characteristic
10	C₂×#90768	—	2	1	no	—
11	C₂×D₁₁₆	—	2	1	no	—
12	C₂×C₄×D₂₉	—	4	1	no	—
13	C₂×C₈×C₂₉	—	4	1	no	—
14	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
16	C₄²×C₂₉	D₄	1	1	yes	characteristic
17	#90781	—	4	1	no	—
18	C₄⋊Dic₂₉	—	2	1	no	—
19	D₂₃₂	—	2	1	no	—
20	D₂₃₂	C₈	1	2	yes	complemented
21	#90768	—	2	2	no	—
22	C₂²×D₂₉	—	4	1	no	—
23	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
25	C₂×C₄×C₂₉	SD₁₆	1	1	yes	characteristic
26	C₂×Dic₂₉	—	4	1	no	—
27	D₁₁₆	—	2	2	no	—
28	D₁₁₆	—	4	1	no	—
29	C₄×D₂₉	—	8	2	no	—
30	C₈×C₂₉	—	2	1	no	—
31	C₈×C₂₉	—	8	1	no	—
32	C₈×C₂₉	C₂×C₈	1	1	yes	characteristic
33	C₈×C₂₉	M₁₆	1	1	yes	characteristic
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	—	2	1	no	—
40	C₄×C₂₉	—	2	1	no	—
41	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₂₉	#104	1	1	yes	characteristic
43	Dic₂₉	—	8	1	no	—
44	C₄×D₈	—	29	1	no	—
45	#346	—	29	1	no	—
46	#334	D₂₉	1	1	yes	characteristic, complemented
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	—	29	1	no	—
55	C₄⋊C₈	—	2	1	no	—
56	#102	—	58	1	no	—
57	C₄×C₈	C₂×D₂₉	1	1	yes	characteristic
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	—	4	1	no	—
64	C₂×C₈	C₄×D₂₉	1	1	yes	characteristic
65	C₂×C₈	D₁₁₆	1	1	yes	characteristic
66	C₄⋊C₄	—	58	1	no	—
67	C₂²⋊C₄	—	116	1	no	—
68	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
69	C₁₆	—	58	2	no	—
70	C₂³	—	116	1	no	—
71	D₄	—	58	2	no	—
72	D₄	—	116	1	no	—
73	C₂×C₄	—	116	1	no	—
74	C₂×C₄	—	232	2	no	—
75	C₂×C₄	#90781	1	1	yes	characteristic
76	C₂×C₄	#90782	1	1	yes	characteristic
77	C₂×C₄	#90784	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	8	1	no	—
80	C₈	C₈×D₂₉	1	1	yes	characteristic
81	C₈	#90772	1	1	yes	characteristic
82	C₂²	—	116	2	no	—
83	C₂²	—	232	1	no	—
84	C₂²	—	232	1	no	—
85	C₂²	#11745157	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	232	1	no	—
89	C₄	#11745168	1	1	yes	characteristic
90	C₄	#11745173	1	1	yes	characteristic
91	C₂	—	232	2	no	—
92	C₂	#14270890	1	1	yes	characteristic
93	C₂	#14270972	1	1	yes	characteristic
94	C₂	#14270975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11745157
commutator	C₈×C₂₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₉
Fitting	C₂₉×#334	C₂
socle	C₂²×C₂₉	#102
prime radical	C₂×D₂₃₂	C₄
cosocle	C₄×C₈×C₂₉	C₂²
hypercenter	#334	D₂₉
hypocenter	C₂₉	#1333
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
2. #14270939	C₂	semidirect
3. C₂₉×#334	C₂	semidirect
20. D₂₃₂	C₈	semidirect
46. #334	D₂₉	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
C₄×D₂₃₂	2
#14270939	2
C₂₉×#334	2
#1333	29