Subgroups — #16834540

Order 3712.

140 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	C₂×#11745163	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
4	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
5	C₂²×#6597	C₂²	1	1	yes	characteristic
6	#11745214	—	2	2	no	—
7	#11745214	C₄	1	4	yes	complemented
8	C₂×#90770	—	2	2	no	—
9	#11745163	—	2	2	no	—
10	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×Dic₂₉	C₈	1	2	yes	—
12	C₂×C₈×C₂₉	—	2	1	no	—
13	C₂×C₈×C₂₉	—	2	1	no	—
14	C₂×C₈×C₂₉	C₈	1	2	yes	—
15	C₄×Dic₂₉	—	2	1	no	—
16	C₄×Dic₂₉	—	2	1	no	—
17	C₂×#6597	C₂×C₄	1	2	yes	—
18	C₂×#6597	D₄	1	1	yes	characteristic
19	C₂×#6597	D₄	1	2	yes	—
20	C₂×#6597	Q₈	1	1	yes	characteristic
21	#90770	—	2	4	no	—
22	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
29	C₂×Dic₂₉	—	2	2	no	—
30	C₂×Dic₂₉	—	4	2	no	—
31	C₈×C₂₉	—	2	2	no	—
32	#6597	C₂²⋊C₄	1	2	yes	—
33	#6597	C₄⋊C₄	1	2	yes	—
34	#1377	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	—	2	2	no	—
36	C₂²×C₂₉	C₄×C₈	1	1	yes	characteristic
37	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₂₉	C₄⋊C₈	1	1	yes	characteristic
39	C₄×C₂₉	#95	1	1	yes	characteristic
40	C₄×C₂₉	#97	1	1	yes	characteristic
41	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
43	Dic₂₉	—	4	2	no	—
44	C₂×M₃₂	—	29	2	no	—
45	C₂×#97	—	29	1	no	—
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	2	1	no	—
48	C₂×C₂₉	#336	1	1	yes	characteristic
49	C₂×C₂₉	#349	1	2	yes	—
50	C₂²×C₈	—	29	1	no	—
51	C₂²×C₈	#1181	1	1	yes	characteristic
52	C₂×C₄²	—	29	1	no	—
53	M₃₂	—	29	4	no	—
54	M₃₂	—	58	2	no	—
55	C₂×C₁₆	—	58	2	no	—
56	#97	—	58	2	no	—
57	C₂₉	#1377	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	29	2	no	—
59	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	29	2	no	—
63	C₂×C₈	—	29	1	no	—
64	C₂×C₈	—	29	1	no	—
65	C₂×C₈	—	29	2	no	—
66	C₂×C₈	#6599	1	2	yes	—
67	C₄²	—	58	1	no	—
68	C₄²	—	58	1	no	—
69	C₁₆	—	58	4	no	—
70	C₂³	D₂₉⋊C₈	1	1	yes	characteristic
71	C₂×C₄	—	58	2	no	—
72	C₂×C₄	—	116	2	no	—
73	C₂×C₄	#90796	1	1	yes	characteristic
74	C₂×C₄	C₄×#1181	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
76	C₂×C₄	C₂×#6599	1	1	yes	characteristic
77	C₂×C₄	#90800	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	29	2	no	—
81	C₈	—	29	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄×#6599	1	1	yes	characteristic
84	C₂²	#11745219	1	1	yes	characteristic
85	C₂²	#11745220	1	1	yes	characteristic
86	C₄	—	116	2	no	—
87	C₄	C₄⋊#6599	1	1	yes	characteristic
88	C₄	#11745218	1	1	yes	characteristic
89	C₄	(C₂×#1181)⋊C₄	1	1	yes	characteristic
90	C₄	C₂²⋊#6599	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#14272029	1	1	yes	characteristic
94	C₂	#14272060	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#1181
commutator	C₂²×C₂₉	C₄×C₈
Frattini	C₂²×C₄	C₂×#1181
Fitting	C₂²×C₈×C₂₉	C₄
socle	C₂²×C₂₉	C₂²⋊C₈
prime radical	C₂³×C₂₉	C₂×C₈
cosocle	C₂²×#6597	C₂²
hypercenter	C₂²×C₈	#1181
hypocenter	C₂₉	#1377
LCS	G ▷ C₂²×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
7. #11745214	C₄	semidirect
57. C₂₉	#1377	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
C₂×#11745163	2
#1377	29