Subgroups — #16817662

Order 3712.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14271527	C₂	1	1	yes	maximal, characteristic
2	#14270956	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#353	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#127	C₂²	1	1	yes	characteristic
5	#11745232	C₄	1	1	yes	characteristic, complemented
6	C₂₉×#99	—	2	1	no	—
7	#11745182	—	2	1	no	—
8	#11745180	—	2	1	no	—
9	#11745180	—	2	1	no	—
10	#11745151	C₄	1	1	yes	characteristic, complemented
11	C₂×D₄×C₂₉	—	4	1	no	—
12	C₂×D₄×C₂₉	D₄	1	1	yes	characteristic
13	C₂×D₄×C₂₉	D₄	1	1	yes	characteristic
14	C₂²⋊C₄×C₂₉	—	4	1	no	—
15	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²⋊Dic₂₉	—	4	1	no	—
17	C₄⋊Dic₂₉	—	2	1	no	—
18	#90779	—	4	1	no	—
19	C₂×#6597	—	2	1	no	—
20	C₂³×C₂₉	—	2	1	no	—
21	C₂³×C₂₉	—	2	1	no	—
22	D₄×C₂₉	—	4	1	no	—
23	D₄×C₂₉	—	4	1	no	—
24	D₄×C₂₉	—	8	2	no	—
25	C₂×C₄×C₂₉	—	2	1	no	—
26	C₂×C₄×C₂₉	—	8	1	no	—
27	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₂₉	—	4	1	no	—
29	C₂×Dic₂₉	—	8	1	no	—
30	#6597	—	4	1	no	—
31	#1412	—	29	1	no	maximal, Sylow
32	C₂²×C₂₉	—	4	1	no	—
33	C₂²×C₂₉	—	4	1	no	—
34	C₂²×C₂₉	—	8	1	no	—
35	C₂²×C₂₉	—	8	1	no	—
36	C₂²×C₂₉	#99	1	1	yes	characteristic
37	C₄×C₂₉	—	2	1	no	—
38	C₄×C₂₉	—	4	1	no	—
39	C₄×C₂₉	—	16	1	no	—
40	Dic₂₉	—	8	1	no	—
41	Dic₂₉	—	16	1	no	—
42	#490	—	29	1	no	—
43	#353	—	29	1	no	—
44	#353	D₂₉	1	1	yes	characteristic
45	C₂×C₂₉	—	2	1	no	—
46	C₂×C₂₉	—	8	1	no	—
47	C₂×C₂₉	—	8	1	no	—
48	C₂×C₂₉	#354	1	1	yes	characteristic
49	#127	C₂×D₂₉	1	1	yes	characteristic
50	#125	—	29	1	no	—
51	#102	—	58	1	no	—
52	#102	—	58	1	no	—
53	#99	—	2	1	no	—
54	#99	—	58	1	no	—
55	#97	—	29	1	no	—
56	C₂₉	#1412	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	4	1	no	—
58	C₂×D₄	D₁₁₆	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₂₉	1	1	yes	characteristic
60	C₂×C₈	—	58	1	no	—
61	C₄⋊C₄	—	58	1	no	—
62	C₄⋊C₄	—	116	1	no	—
63	C₂²⋊C₄	—	4	1	no	—
64	C₂²⋊C₄	—	116	1	no	—
65	C₄²	C₄×D₂₉	1	1	yes	characteristic
66	C₂³	—	2	1	no	—
67	C₂³	—	2	1	no	—
68	D₄	—	4	1	no	—
69	D₄	—	4	1	no	—
70	D₄	—	8	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	8	1	no	—
73	C₂×C₄	—	116	1	no	—
74	C₂×C₄	—	232	1	no	—
75	C₂×C₄	#90781	1	1	yes	characteristic
76	C₈	—	116	1	no	—
77	C₂²	—	4	1	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	8	1	no	—
80	C₂²	—	8	1	no	—
81	C₂²	#11745154	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	4	1	no	—
84	C₄	—	16	1	no	—
85	C₄	—	464	1	no	—
86	C₄	—	232	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	8	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#14270957	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14270957
commutator	C₄²×C₂₉	C₂×C₄
Frattini	#127	C₂×D₂₉
Fitting	C₂₉×#353	C₂
socle	C₂×C₂₉	#354
prime radical, cosocle	C₂₉×#127	C₂²
hypercenter	#353	D₂₉
hypocenter	C₂₉	#1412
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #353

Complements

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

N	H ≅ G/N	type
5. #11745232	C₄	semidirect
10. #11745151	C₄	semidirect
56. C₂₉	#1412	semidirect

Maximal subgroups

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

subgroup	index
#14271527	2
#14270956	2
C₂₉×#353	2
#1412	29