Subgroups — #16834465

Order 3712.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272060	C₂	1	1	yes	maximal, characteristic
2	#14272031	C₂	1	1	yes	maximal, characteristic
3	#14271422	C₂	1	1	yes	maximal, characteristic
4	#11745345	—	2	1	no	—
5	C₂×Dic₁₁₆	C₄	1	1	yes	characteristic, complemented
6	C₂×#90772	C₂²	1	1	yes	characteristic
7	#11745259	—	2	1	no	—
8	#11745214	—	2	1	no	—
9	C₂₉×#106	C₄	1	1	yes	characteristic, complemented
10	#11745158	—	2	1	no	—
11	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
12	C₂×Dic₅₈	—	2	1	no	—
13	C₂²⋊#1181	—	4	1	no	—
14	C₄⋊#1181	—	4	1	no	—
15	C₄×#1181	—	2	2	no	—
16	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₄⋊C₄×C₂₉	—	2	1	no	—
18	#90781	—	4	1	no	—
19	C₄⋊Dic₂₉	—	4	1	no	—
20	C₂×#6597	D₄	1	1	yes	characteristic
21	Dic₁₁₆	—	4	1	no	—
22	#90772	—	4	1	no	—
23	#90770	—	4	1	no	—
24	C₂²×D₂₉	D₈	1	1	yes	characteristic
25	C₂×#1181	—	4	2	no	—
26	C₂×C₄×C₂₉	—	4	1	no	—
27	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	1	no	—
29	C₂×Dic₂₉	SD₁₆	1	1	yes	characteristic
30	C₄×D₂₉	—	2	1	no	—
31	C₄×D₂₉	—	2	1	no	—
32	Dic₅₈	—	4	1	no	—
33	Dic₅₈	—	4	1	no	—
34	C₈×C₂₉	—	2	1	no	—
35	#6597	—	2	1	no	—
36	#1340	—	29	1	no	maximal, Sylow
37	C₂²×C₂₉	#102	1	1	yes	characteristic
38	C₂×D₂₉	—	2	1	no	—
39	C₂×D₂₉	—	4	1	no	—
40	#1181	—	8	2	no	—
41	C₄×C₂₉	—	8	1	no	—
42	C₄×C₂₉	#99	1	1	yes	characteristic
43	C₄×C₂₉	#104	1	1	yes	characteristic
44	Dic₂₉	—	2	1	no	—
45	Dic₂₉	—	8	1	no	—
46	#470	—	29	1	no	—
47	#349	—	29	1	no	—
48	H(3,ℤ/4)	—	29	1	no	—
49	C₂×C₂₉	—	2	1	no	—
50	C₂×C₂₉	#327	1	1	yes	characteristic
51	D₂₉	—	4	1	no	—
52	C₂×Q₁₆	—	29	1	no	—
53	C₂×M₁₆	—	29	1	no	—
54	C₂²⋊Q₈	—	58	1	no	—
55	#117	—	58	1	no	—
56	M₃₂	—	58	1	no	—
57	#106	#1181	1	1	yes	characteristic, complemented
58	#103	—	58	1	no	—
59	C₂₉	#1340	1	1	yes	characteristic, complemented, Sylow
60	C₂×Q₈	—	58	1	no	—
61	C₂²×C₄	—	29	1	no	—
62	Q₁₆	—	116	1	no	—
63	M₁₆	—	116	1	no	—
64	C₂×C₈	—	29	1	no	—
65	C₂×C₈	C₂×#1181	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₄⋊C₄	—	116	1	no	—
68	C₄⋊C₄	—	116	1	no	—
69	C₂²⋊C₄	—	116	1	no	—
70	C₂²⋊C₄	—	116	1	no	—
71	C₄²	—	58	2	no	—
72	C₁₆	—	116	1	no	—
73	C₂³	—	29	1	no	—
74	Q₈	—	116	1	no	—
75	Q₈	—	116	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	—	29	1	no	—
78	C₂×C₄	—	58	1	no	—
79	C₂×C₄	—	58	1	no	—
80	C₂×C₄	—	116	2	no	—
81	C₂×C₄	—	116	1	no	—
82	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	58	1	no	—
85	C₂²	—	58	1	no	—
86	C₂²	—	116	1	no	—
87	C₂²	#11745223	1	1	yes	characteristic
88	C₄	—	8	1	no	—
89	C₄	—	58	1	no	—
90	C₄	—	232	2	no	—
91	C₄	—	232	1	no	—
92	C₄	#11745215	1	1	yes	characteristic
93	C₄	#11745226	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	116	1	no	—
96	C₂	#14272015	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272015
commutator	C₂×C₈×C₂₉	C₂×C₄
Frattini	C₂×C₈	C₂×#1181
Fitting	C₂₉×#106	C₄
socle	C₂×C₂₉	#327
prime radical	C₂²×D₂₉	D₈
cosocle	C₂×#90772	C₂²
hypercenter	#106	#1181
hypocenter	C₂₉	#1340
LCS	G ▷ C₂×C₈×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
5. C₂×Dic₁₁₆	C₄	semidirect
9. C₂₉×#106	C₄	semidirect
57. #106	#1181	semidirect
59. C₂₉	#1340	semidirect

Maximal subgroups

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

subgroup	index
#14272060	2
#14272031	2
#14271422	2
#1340	29