Subgroups — #16834438

Order 3712.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14272059	C₂	1	2	yes	maximal
2	#14271187	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
4	C₂×#90777	C₄	1	1	yes	characteristic
5	C₂×#90777	C₂²	1	1	yes	characteristic
6	#11745214	—	2	2	no	—
7	C₄⋊#6597	—	2	2	no	—
8	C₂²×C₄×C₂₉	—	2	1	no	—
9	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
10	C₄²×C₂₉	—	2	1	no	—
11	C₄²×C₂₉	C₈	1	1	yes	characteristic
12	C₄²×C₂₉	C₈	1	1	yes	characteristic
13	#90777	—	4	1	no	—
14	#90777	—	4	1	no	—
15	C₂×#6597	—	2	1	no	—
16	C₂×#6597	D₄	1	2	yes	—
17	#90770	—	4	2	no	—
18	C₂³×C₂₉	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₉	—	2	1	no	—
20	C₂×C₄×C₂₉	—	2	1	no	—
21	C₂×C₄×C₂₉	—	2	1	no	—
22	C₂×C₄×C₂₉	—	2	1	no	—
23	C₂×C₄×C₂₉	—	4	2	no	—
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
26	#6597	—	2	2	no	—
27	#6597	—	4	1	no	—
28	#1327	—	29	1	no	maximal, Sylow
29	C₂²×C₂₉	—	2	1	no	—
30	C₂²×C₂₉	—	4	1	no	—
31	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₂₉	—	2	2	no	—
33	C₄×C₂₉	—	2	1	no	—
34	C₄×C₂₉	—	4	1	no	—
35	C₄×C₂₉	#99	1	1	yes	characteristic
36	C₄×C₂₉	#101	1	1	yes	characteristic
37	#423	—	29	1	no	—
38	#349	—	29	2	no	—
39	C₂×C₂₉	—	2	1	no	—
40	C₂×C₂₉	—	4	1	no	—
41	C₂×C₂₉	#324	1	1	yes	characteristic
42	C₂×M₁₆	—	29	1	no	—
43	C₂×M₁₆	—	29	1	no	—
44	C₂×C₄²	#1181	1	1	yes	characteristic
45	M₃₂	—	58	2	no	—
46	C₄⋊C₈	—	58	2	no	—
47	C₂₉	#1327	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	2	1	no	—
49	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
50	M₁₆	—	116	1	no	—
51	M₁₆	—	116	1	no	—
52	C₂×C₈	—	29	2	no	—
53	C₂×C₈	—	58	1	no	—
54	C₄²	—	2	1	no	—
55	C₄²	#6599	1	1	yes	characteristic
56	C₄²	#6599	1	1	yes	characteristic
57	C₁₆	—	116	2	no	—
58	C₂³	#90800	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	C₂×#6599	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
66	C₈	—	58	2	no	—
67	C₈	—	116	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂²⋊#6599	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	2	1	no	—
73	C₄	—	4	1	no	—
74	C₄	#11745215	1	1	yes	characteristic
75	C₄	#11745221	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#14272008	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11745215
commutator	C₂×C₄×C₂₉	C₂×C₈
Frattini	C₂²×C₄	C₂×#1181
Fitting	C₂×C₄²×C₂₉	C₄
socle	C₂×C₂₉	#324
prime radical	C₂³×C₂₉	M₁₆
cosocle	C₂×#90777	C₂²
hypercenter	C₂×C₄²	#1181
hypocenter	C₂₉	#1327
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
47. C₂₉	#1327	semidirect

Maximal subgroups

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

subgroup	index
#14272059	2
#14271187	2
#1327	29