Subgroups — #18009519

Order 4736.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#10596927	C₂	1	2	yes	maximal, complemented
2	#14557501	C₂	1	1	yes	maximal, characteristic
3	C₂×#10596927	—	2	2	no	—
4	C₂×#10596962	C₄	1	1	yes	characteristic
5	C₂²×#64436	C₂²	1	1	yes	characteristic
6	#11924448	—	2	2	no	—
7	C₂×M₁₆×C₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₃₇	—	2	1	no	—
10	#10596962	—	4	1	no	—
11	#10596962	—	4	1	no	—
12	C₂×D₁₄₈	C₈	1	1	yes	characteristic
13	C₂×C₄×D₃₇	—	2	1	no	—
14	C₂×Dic₇₄	C₈	1	1	yes	characteristic
15	M₁₆×C₃₇	—	4	1	no	—
16	C₂×C₈×C₃₇	—	2	1	no	—
17	C₂×#64436	—	4	1	no	—
18	C₂×#64436	D₄	1	2	yes	—
19	#10596927	—	4	2	no	—
20	C₂³×C₃₇	M₁₆	1	1	yes	characteristic
21	C₂²×D₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	—	2	1	no	—
23	C₂×C₄×C₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂²⋊D₃₇	—	4	2	no	—
27	C₂×Dic₃₇	—	2	1	no	—
28	D₁₄₈	—	4	1	no	—
29	C₄×D₃₇	—	4	1	no	—
30	C₄×D₃₇	—	4	1	no	—
31	Dic₇₄	—	4	1	no	—
32	C₈×C₃₇	—	4	1	no	—
33	#64436	—	2	2	no	—
34	C₂²×C₃₇	—	2	1	no	—
35	C₂²×C₃₇	—	2	2	no	—
36	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₃₇	—	4	1	no	—
38	C₂×D₃₇	—	4	2	no	—
39	C₄×C₃₇	—	2	1	no	—
40	C₄×C₃₇	#99	1	1	yes	characteristic
41	C₄×C₃₇	#100	1	1	yes	characteristic
42	Dic₃₇	—	4	1	no	—
43	#1315	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	4	1	no	—
45	C₂×C₃₇	#323	1	1	yes	characteristic
46	C₂×C₃₇	#350	1	2	yes	—
47	D₃₇	—	8	1	no	—
48	#408	—	37	1	no	—
49	C₂²⋊C₁₆	—	37	2	no	—
50	C₃₇	#1315	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	—	37	1	no	—
52	C₂×M₁₆	#3866	1	1	yes	characteristic
53	C₂²×C₈	—	37	1	no	—
54	C₂×C₁₆	—	74	2	no	—
55	C₂²⋊C₈	—	74	2	no	—
56	#41	—	148	1	no	—
57	#41	—	148	1	no	—
58	C₂×Q₈	—	37	1	no	—
59	C₂×D₄	—	37	1	no	—
60	C₂×D₄	—	74	1	no	—
61	C₂²×C₄	—	74	1	no	—
62	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	37	2	no	—
66	C₂×C₈	—	148	1	no	—
67	C₁₆	—	148	2	no	—
68	C₂³	—	74	1	no	—
69	C₂³	#10596953	1	1	yes	characteristic
70	Q₈	—	148	1	no	—
71	D₄	—	148	1	no	—
72	D₄	—	148	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	74	1	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	—	148	1	no	—
78	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	74	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	148	1	no	—
85	C₂²	—	148	2	no	—
86	C₂²	#11924593	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	148	1	no	—
89	C₄	#11924595	1	1	yes	characteristic
90	C₄	#11924596	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	296	1	no	—
93	C₂	#14558377	1	1	yes	characteristic
94	C₂	#14558432	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₂²×C₄	C₂×#3866
Fitting	C₂×M₁₆×C₃₇	C₄
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂×#10596962	C₄
cosocle	C₂²×#64436	C₂²
hypercenter	C₂×M₁₆	#3866
hypocenter	C₃₇	#1315
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#10596927	C₂	semidirect
50. C₃₇	#1315	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#10596927	2
#14557501	2
#1315	37