Subgroups — #17994679

Order 4736.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557497	C₂	1	2	yes	maximal
2	#14557302	C₂	1	4	yes	maximal, complemented
3	C₂×#117×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	C₂²	1	4	yes	—
5	C₂²⋊#64436	—	2	4	no	—
6	C₂³×C₄×C₃₇	C₂²	1	1	yes	characteristic
7	#117×C₃₇	—	2	4	no	—
8	C₂×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
9	C₂×C₂²⋊C₄×C₃₇	C₄	1	2	yes	—
10	C₂×C₄²×C₃₇	C₄	1	2	yes	—
11	C₂⁴×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₃₇	—	2	4	no	—
13	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₃₇	C₂×C₄	1	4	yes	—
15	C₂²×C₄×C₃₇	D₄	1	4	yes	—
16	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇	—	2	4	no	—
18	C₂²⋊C₄×C₃₇	—	2	4	no	—
19	C₄²×C₃₇	—	2	4	no	—
20	#10596934	—	2	8	no	—
21	C₂×#64436	—	2	4	no	—
22	C₂³×C₃₇	—	2	2	no	—
23	C₂³×C₃₇	—	4	2	no	—
24	C₂³×C₃₇	C₂²⋊C₄	1	2	yes	—
25	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₇	—	2	2	no	—
27	C₂×C₄×C₃₇	—	2	8	no	—
28	C₂×C₄×C₃₇	—	2	4	no	—
29	C₂×C₄×C₃₇	—	4	4	no	—
30	C₂×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
31	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₇	#41	1	4	yes	—
33	#64436	—	4	4	no	—
34	C₂²×C₃₇	—	2	2	no	—
35	C₂²×C₃₇	—	2	2	no	—
36	C₂²×C₃₇	—	2	4	no	—
37	C₂²×C₃₇	—	4	4	no	—
38	C₂²×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₂²×C₃₇	#117	1	2	yes	—
40	C₄×C₃₇	—	2	2	no	—
41	C₄×C₃₇	—	4	4	no	—
42	C₄×C₃₇	#123	1	4	yes	—
43	#1822	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	2	no	—
45	C₂×C₃₇	—	4	2	no	—
46	C₂×C₃₇	#381	1	1	yes	characteristic
47	C₂×C₃₇	#413	1	2	yes	—
48	C₂×#117	D₃₇	1	1	yes	characteristic
49	#407	—	37	2	no	—
50	#343	—	37	4	no	—
51	C₃₇	#1822	1	1	yes	characteristic, complemented, Sylow
52	C₂³×C₄	C₂×D₃₇	1	1	yes	characteristic
53	C₂×M₁₆	—	37	4	no	—
54	#117	—	2	4	no	—
55	C₂×C₄⋊C₄	C₂×D₃₇	1	2	yes	—
56	C₂×C₂²⋊C₄	Dic₃₇	1	2	yes	—
57	C₂×C₄²	Dic₃₇	1	2	yes	—
58	C₂²⋊C₈	—	74	4	no	—
59	C₂⁴	C₂×Dic₃₇	1	1	yes	characteristic
60	C₂²×C₄	—	2	4	no	—
61	C₂²×C₄	C₂×Dic₃₇	1	1	yes	characteristic
62	C₂²×C₄	C₂×Dic₃₇	1	4	yes	—
63	C₂²×C₄	C₂²⋊D₃₇	1	4	yes	—
64	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
65	M₁₆	—	74	8	no	—
66	C₂×C₈	—	74	4	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₂²⋊C₄	—	2	4	no	—
69	C₄²	—	2	4	no	—
70	C₂³	—	2	2	no	—
71	C₂³	—	4	2	no	—
72	C₂³	C₂²⋊Dic₃₇	1	2	yes	—
73	C₂³	C₂²×Dic₃₇	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	8	no	—
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	—	4	4	no	—
78	C₂×C₄	C₂²⋊Dic₃₇	1	2	yes	—
79	C₂×C₄	#10596962	1	4	yes	—
80	C₂×C₄	C₂×C₂²⋊D₃₇	1	2	yes	—
81	C₈	—	148	4	no	—
82	C₂²	—	2	2	no	—
83	C₂²	—	2	4	no	—
84	C₂²	—	2	2	no	—
85	C₂²	—	4	4	no	—
86	C₂²	C₂×C₂²⋊Dic₃₇	1	1	yes	characteristic
87	C₂²	#11924495	1	2	yes	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₄	#11924519	1	4	yes	—
91	C₂	—	2	2	no	—
92	C₂	—	4	2	no	—
93	C₂	#14557396	1	1	yes	characteristic
94	C₂	#14557517	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊Dic₃₇
commutator	C₂³×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×#117×C₃₇	C₂
socle	C₂²×C₃₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₇	C₂×C₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×#117	D₃₇
hypocenter	C₃₇	#1822
LCS	G ▷ C₂³×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
2. #14557302	C₂	semidirect
51. C₃₇	#1822	semidirect

Maximal subgroups

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

subgroup	index
#14557497	2
#14557302	2
C₂×#117×C₃₇	2
#1822	37