Subgroups — #16834623

Order 3712.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272068	C₂	1	2	yes	maximal, complemented
2	#14271539	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#127	C₄	1	1	yes	characteristic, complemented
4	C₂×#90782	—	2	2	no	—
5	#11745236	C₂²	1	1	yes	characteristic
6	#11745215	—	2	2	no	—
7	C₄×#6597	C₄	1	1	yes	characteristic, complemented
8	C₂×D₄×C₂₉	—	2	1	no	—
9	C₂×D₄×C₂₉	—	4	1	no	—
10	C₂×D₁₁₆	—	4	1	no	—
11	C₂×D₁₁₆	D₄	1	2	yes	—
12	C₂²⋊#1181	—	4	2	no	—
13	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
14	#90782	—	4	4	no	—
15	C₂×#6597	—	2	1	no	—
16	C₂³×C₂₉	—	4	1	no	—
17	C₂²×D₂₉	—	2	2	no	—
18	C₂×#1181	—	8	2	no	—
19	D₄×C₂₉	—	4	2	no	—
20	D₄×C₂₉	—	8	2	no	—
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
23	D₁₁₆	—	4	2	no	—
24	D₁₁₆	—	8	2	no	—
25	#6597	—	2	2	no	—
26	#1408	—	29	1	no	maximal, Sylow
27	C₂²×C₂₉	—	8	2	no	—
28	C₂²×C₂₉	—	8	1	no	—
29	C₂²×C₂₉	#99	1	1	yes	characteristic
30	C₂×D₂₉	—	4	2	no	—
31	C₂×D₂₉	—	8	2	no	—
32	#1181	—	16	2	no	—
33	C₄×C₂₉	—	2	2	no	—
34	C₄×C₂₉	—	2	1	no	—
35	#493	—	29	1	no	—
36	#353	—	29	2	no	—
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	—	16	1	no	—
39	C₂×C₂₉	#353	1	1	yes	characteristic
40	D₂₉	—	8	2	no	—
41	C₂×D₈	—	58	2	no	—
42	#127	—	29	1	no	—
43	#127	#1181	1	1	yes	characteristic, complemented
44	#99	—	58	2	no	—
45	C₄×C₈	—	29	1	no	—
46	C₂₉	#1408	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₄	—	2	1	no	—
48	C₂×D₄	—	4	1	no	—
49	C₂×D₄	—	29	2	no	—
50	C₂×D₄	—	116	1	no	—
51	D₈	—	116	4	no	—
52	C₂×C₈	—	58	1	no	—
53	C₂²⋊C₄	—	116	2	no	—
54	C₄²	C₂×#1181	1	1	yes	characteristic
55	C₂³	—	4	1	no	—
56	C₂³	—	58	2	no	—
57	D₄	—	4	2	no	—
58	D₄	—	8	2	no	—
59	D₄	—	116	2	no	—
60	D₄	—	232	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	232	2	no	—
63	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
64	C₈	—	58	2	no	—
65	C₂²	—	8	2	no	—
66	C₂²	—	8	1	no	—
67	C₂²	—	116	2	no	—
68	C₂²	—	232	2	no	—
69	C₂²	#11745227	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	—	464	2	no	—
73	C₂	—	2	1	no	—
74	C₂	—	16	1	no	—
75	C₂	—	232	2	no	—
76	C₂	#14272067	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14272067
commutator	C₄²×C₂₉	C₂×C₄
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×#127	C₄
socle	C₂×C₂₉	#353
prime radical	#14271539	C₂
cosocle	#11745236	C₂²
hypercenter	#127	#1181
hypocenter	C₂₉	#1408
LCS	G ▷ C₄²×C₂₉ ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #14272068	C₂	semidirect
3. C₂₉×#127	C₄	semidirect
7. C₄×#6597	C₄	semidirect
43. #127	#1181	semidirect
46. C₂₉	#1408	semidirect

Maximal subgroups

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

subgroup	index
#14272068	2
#14271539	2
#1408	29