Subgroups — #17994344

Order 4736.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924447	C₂	1	1	yes	maximal, characteristic
2	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	#14557287	C₂	1	4	yes	maximal
4	C₂×#97×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64436	C₂²	1	2	yes	—
6	C₂×C₄×Dic₃₇	C₄	1	4	yes	—
7	C₂×C₄×Dic₃₇	C₂²	1	2	yes	—
8	#11924447	C₄	1	4	yes	complemented
9	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
10	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
11	#97×C₃₇	C₄	1	4	yes	complemented
12	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
14	C₂²×Dic₃₇	C₂×C₄	1	4	yes	—
15	C₂×C₈×C₃₇	—	2	4	no	—
16	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
17	C₄²×C₃₇	C₂×C₄	1	2	yes	—
18	C₄²×C₃₇	C₂×C₄	1	2	yes	—
19	C₄×Dic₃₇	—	2	4	no	—
20	C₄×Dic₃₇	—	2	8	no	—
21	C₂×#64436	—	2	4	no	—
22	C₂×#64436	C₂×C₄	1	4	yes	—
23	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₃₇	—	2	4	no	—
25	C₂×C₄×C₃₇	C₄²	1	4	yes	—
26	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	#41	1	4	yes	—
29	C₂×Dic₃₇	—	2	4	no	—
30	C₂×Dic₃₇	—	2	4	no	—
31	C₂×Dic₃₇	M₁₆	1	8	yes	—
32	C₈×C₃₇	—	2	4	no	—
33	#64436	—	2	4	no	—
34	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
35	C₂²×C₃₇	#117	1	2	yes	—
36	C₂²×C₃₇	C₂×M₁₆	1	4	yes	—
37	C₄×C₃₇	—	2	4	no	—
38	C₄×C₃₇	#117	1	2	yes	—
39	C₄×C₃₇	#117	1	2	yes	—
40	Dic₃₇	—	2	8	no	—
41	#1745	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	#376	1	1	yes	characteristic
43	C₂×C₃₇	C₄×M₁₆	1	2	yes	—
44	C₂×C₃₇	#432	1	4	yes	—
45	C₂×#97	—	37	1	no	—
46	C₂×#97	D₃₇	1	1	yes	characteristic
47	C₄³	—	37	1	no	—
48	#336	—	37	4	no	—
49	C₃₇	#1745	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₈	—	37	2	no	—
51	C₂²×C₈	C₂×D₃₇	1	2	yes	—
52	C₂×C₄²	—	37	4	no	—
53	C₂×C₄²	—	37	2	no	—
54	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
55	#97	—	37	4	no	—
56	#97	Dic₃₇	1	4	yes	complemented
57	C₂²×C₄	—	37	4	no	—
58	C₂²×C₄	C₄×D₃₇	1	2	yes	—
59	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
60	C₂×C₈	—	2	4	no	—
61	C₂×C₈	—	37	4	no	—
62	C₂×C₈	—	74	4	no	—
63	C₂×C₈	C₂×Dic₃₇	1	4	yes	—
64	C₄²	—	74	8	no	—
65	C₄²	—	74	4	no	—
66	C₄²	C₄×D₃₇	1	2	yes	—
67	C₄²	C₂×Dic₃₇	1	2	yes	—
68	C₂³	C₂×C₄×D₃₇	1	1	yes	characteristic
69	C₂×C₄	—	2	4	no	—
70	C₂×C₄	—	37	8	no	—
71	C₂×C₄	—	74	4	no	—
72	C₂×C₄	—	74	4	no	—
73	C₂×C₄	C₄×Dic₃₇	1	4	yes	—
74	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
75	C₂×C₄	#10596962	1	4	yes	—
76	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
77	C₈	—	2	4	no	—
78	C₈	—	74	4	no	—
79	C₂²	C₂×C₄×Dic₃₇	1	1	yes	characteristic
80	C₂²	#11924493	1	2	yes	—
81	C₂²	M₁₆×D₃₇	1	4	yes	—
82	C₄	—	2	4	no	—
83	C₄	—	74	8	no	—
84	C₄	#11924493	1	2	yes	—
85	C₄	#11924495	1	2	yes	—
86	C₂	#14557379	1	1	yes	characteristic
87	C₂	M₁₆×Dic₃₇	1	2	yes	—
88	C₂	#14557588	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator	C₂²×C₃₇	C₂×C₄²
Fitting	C₂×#97×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×#97	D₃₇
hypocenter	C₃₇	#1745
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
8. #11924447	C₄	semidirect
11. #97×C₃₇	C₄	semidirect
49. C₃₇	#1745	semidirect
56. #97	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924447	2
C₄²×Dic₃₇	2
#14557287	2
C₂×#97×C₃₇	2
#1745	37