Subgroups — #16835824

Order 3712.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745214	C₂	1	2	yes	maximal
2	C₄⋊#90770	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×#6597	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
5	C₂²×#6597	C₄	1	1	yes	characteristic
6	C₂²×#6597	C₂²	1	1	yes	characteristic
7	#11745214	—	2	4	no	—
8	C₂×#90770	C₂²	1	4	yes	—
9	C₄×#6597	C₄	1	2	yes	—
10	C₄×#6597	C₂²	1	2	yes	—
11	C₂²×C₄×C₂₉	C₈	1	2	yes	—
12	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₄²×C₂₉	C₈	1	1	yes	characteristic
14	C₄²×C₂₉	C₈	1	1	yes	characteristic
15	C₄²×C₂₉	C₂×C₄	1	2	yes	—
16	C₂×#6597	—	2	2	no	—
17	C₂×#6597	C₂×C₄	1	2	yes	—
18	C₂×#6597	C₂×C₄	1	1	yes	characteristic
19	C₂×#6597	D₄	1	2	yes	—
20	C₂×#6597	Q₈	1	2	yes	—
21	C₂×#6597	C₂³	1	1	yes	characteristic
22	#90770	—	2	4	no	—
23	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₂₉	—	2	4	no	—
25	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
30	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	#6597	—	2	2	no	—
32	#6597	C₄⋊C₄	1	2	yes	—
33	#6597	C₂×D₄	1	1	yes	characteristic
34	#6597	C₂×Q₈	1	1	yes	characteristic
35	#2150	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	—	2	2	no	—
37	C₂²×C₂₉	C₄⋊C₈	1	2	yes	—
38	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₂₉	—	2	2	no	—
40	C₄×C₂₉	C₄⋊C₈	1	2	yes	—
41	C₄×C₂₉	M₃₂	1	4	yes	complemented
42	C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
44	C₂×M₃₂	—	29	2	no	—
45	C₂×C₄×C₈	—	29	1	no	—
46	C₄⋊C₁₆	—	29	4	no	—
47	C₂×C₂₉	—	2	2	no	—
48	C₂×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
49	C₂×C₂₉	C₂×M₃₂	1	2	yes	—
50	C₂²×C₈	—	29	1	no	—
51	C₂²×C₈	—	29	1	no	—
52	C₂×C₄²	#1181	1	1	yes	characteristic
53	M₃₂	—	58	4	no	—
54	C₂×C₁₆	—	29	4	no	—
55	C₄×C₈	—	29	2	no	—
56	C₄×C₈	—	29	2	no	—
57	C₂₉	#2150	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	#6599	1	2	yes	—
59	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
60	C₂×C₈	—	29	2	no	—
61	C₂×C₈	—	29	2	no	—
62	C₂×C₈	—	29	1	no	—
63	C₂×C₈	—	29	1	no	—
64	C₂×C₈	—	29	2	no	—
65	C₂×C₈	—	58	2	no	—
66	C₄²	#6599	1	1	yes	characteristic
67	C₄²	#6599	1	1	yes	characteristic
68	C₄²	C₂×#1181	1	2	yes	—
69	C₁₆	—	58	4	no	—
70	C₂³	C₂×#6599	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	#90796	1	2	yes	—
73	C₂×C₄	C₄⋊#1181	1	2	yes	—
74	C₂×C₄	C₂×#6599	1	2	yes	—
75	C₂×C₄	C₂×#6599	1	2	yes	—
76	C₂×C₄	C₂×#6599	1	1	yes	characteristic
77	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
78	C₈	—	29	1	no	—
79	C₈	—	29	2	no	—
80	C₈	—	29	1	no	—
81	C₈	—	58	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄⋊#6599	1	2	yes	—
84	C₂²	C₂²×#6599	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	#11745214	1	4	yes	complemented
87	C₄	C₄⋊#6599	1	2	yes	—
88	C₄	C₂×#90796	1	1	yes	characteristic
89	C₄	C₂×C₄⋊#1181	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#6599	1	1	yes	characteristic
92	C₂	C₂×#11745214	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting	C₂×C₄²×C₂₉	C₄
prime radical	C₂³×C₂₉	C₂×C₈
cosocle	C₂×#6597	C₂³
hypercenter	C₂×C₄²	#1181
hypocenter	C₂₉	#2150
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#90770	C₂	semidirect
41. C₄×C₂₉	M₃₂	semidirect
57. C₂₉	#2150	semidirect
86. C₄	#11745214	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745214	2
C₄⋊#90770	2
C₂×C₄×#6597	2
#2150	29