Subgroups — #17994735

Order 4736.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557556	C₂	1	2	yes	maximal
2	C₂×#11924446	C₂	1	1	yes	maximal, characteristic
3	#14557298	C₂	1	1	yes	maximal, characteristic
4	#14557297	C₂	1	2	yes	maximal
5	C₃₇×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	C₂²	1	2	yes	—
7	C₂²×#64436	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
9	#11924465	—	2	4	no	—
10	#11924446	C₄	1	4	yes	—
11	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
12	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
14	C₂²×Dic₃₇	Q₈	1	2	yes	—
15	M₁₆×C₃₇	—	2	2	no	—
16	M₁₆×C₃₇	—	2	2	no	—
17	C₂×C₈×C₃₇	—	2	2	no	—
18	C₂×C₈×C₃₇	—	2	2	no	—
19	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
20	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
21	C₄×Dic₃₇	D₄	1	2	yes	—
22	#10596934	—	2	2	no	—
23	#10596934	—	2	2	no	—
24	C₂×#64436	—	2	2	no	—
25	C₂×#64436	—	2	2	no	—
26	C₂×#64436	C₂×C₄	1	2	yes	—
27	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	#41	1	2	yes	—
31	C₂×C₄×C₃₇	#41	1	2	yes	—
32	C₂×Dic₃₇	—	4	2	no	—
33	C₂×Dic₃₇	C₄⋊C₄	1	4	yes	—
34	C₈×C₃₇	—	2	2	no	—
35	C₈×C₃₇	—	4	2	no	—
36	#64436	—	2	2	no	—
37	#64436	—	4	2	no	—
38	C₂²×C₃₇	—	2	2	no	—
39	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₃₇	#125	1	2	yes	—
41	C₄×C₃₇	#117	1	1	yes	characteristic
42	C₄×C₃₇	#117	1	1	yes	characteristic
43	C₄×C₃₇	#124	1	2	yes	—
44	Dic₃₇	—	2	4	no	—
45	#1838	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	2	no	—
47	C₂×C₃₇	#382	1	1	yes	characteristic
48	C₂×C₃₇	#430	1	2	yes	—
49	#423	—	37	2	no	—
50	C₂×#97	—	37	1	no	—
51	#341	—	37	2	no	—
52	#341	—	37	1	no	—
53	#341	D₃₇	1	1	yes	characteristic
54	C₃₇	#1838	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₁₆	—	37	2	no	—
56	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
57	C₂²×C₈	—	37	1	no	—
58	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
59	C₂×C₄²	—	37	1	no	—
60	C₄⋊C₈	—	74	4	no	—
61	#97	—	37	4	no	—
62	C₂²×C₄	—	37	2	no	—
63	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	74	2	no	—
67	M₁₆	—	74	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	37	2	no	—
71	C₂×C₈	—	74	2	no	—
72	C₂×C₈	—	74	2	no	—
73	C₂×C₈	C₄×D₃₇	1	2	yes	—
74	C₄²	—	37	2	no	—
75	C₄²	—	37	2	no	—
76	C₂³	Q₈×D₃₇	1	1	yes	characteristic
77	C₂×C₄	—	37	4	no	—
78	C₂×C₄	—	148	2	no	—
79	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
80	C₂×C₄	#10596962	1	2	yes	—
81	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
82	C₂×C₄	#10596964	1	2	yes	—
83	C₈	—	2	2	no	—
84	C₈	—	4	2	no	—
85	C₈	—	74	2	no	—
86	C₈	—	148	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	C₄⋊C₄×D₃₇	1	1	yes	characteristic
89	C₂²	#11924526	1	2	yes	—
90	C₄	—	74	4	no	—
91	C₄	#11924492	1	1	yes	characteristic
92	C₄	#11924493	1	1	yes	characteristic
93	C₄	#11924522	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	#14557397	1	1	yes	characteristic
96	C₂	#14557580	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₃₇
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#341	C₂
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂³×C₃₇	C₂×Q₈
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#341	D₃₇
hypocenter	C₃₇	#1838
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

Complements

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

N	H ≅ G/N	type
54. C₃₇	#1838	semidirect

Maximal subgroups

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

subgroup	index
#14557556	2
C₂×#11924446	2
#14557298	2
#14557297	2
C₃₇×#341	2
#1838	37