Subgroups — #17994736

Order 4736.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557557	C₂	1	1	yes	maximal, characteristic
2	C₂×#11924447	C₂	1	1	yes	maximal, characteristic
3	#14557297	C₂	1	4	yes	maximal
4	C₃₇×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#10596934	C₂²	1	2	yes	—
6	C₂²×#64436	C₂²	1	2	yes	—
7	C₄⋊#64436	—	2	2	no	—
8	#11924447	C₄	1	4	yes	—
9	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
10	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₃₇	—	2	2	no	—
12	C₂²×C₄×C₃₇	Q₈	1	2	yes	—
13	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
14	M₁₆×C₃₇	—	2	4	no	—
15	C₂×C₈×C₃₇	—	2	2	no	—
16	C₄²×C₃₇	C₂×C₄	1	2	yes	—
17	C₄²×C₃₇	D₄	1	2	yes	—
18	#10596934	—	2	4	no	—
19	C₂×#64436	—	2	2	no	—
20	C₂×#64436	—	2	2	no	—
21	C₂×#64436	—	2	2	no	—
22	C₂×#64436	C₂×C₄	1	4	yes	—
23	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₃₇	—	4	2	no	—
25	C₂×C₄×C₃₇	C₄⋊C₄	1	4	yes	—
26	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	#41	1	2	yes	—
29	C₂×C₄×C₃₇	#41	1	2	yes	—
30	C₈×C₃₇	—	4	2	no	—
31	#64436	—	2	4	no	—
32	#64436	—	4	2	no	—
33	C₂²×C₃₇	—	2	2	no	—
34	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂²×C₃₇	#125	1	2	yes	—
36	C₄×C₃₇	—	2	4	no	—
37	C₄×C₃₇	#117	1	2	yes	—
38	C₄×C₃₇	#124	1	1	yes	characteristic
39	C₄×C₃₇	#124	1	1	yes	characteristic
40	#1838	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	—	2	2	no	—
42	C₂×C₃₇	#382	1	1	yes	characteristic
43	C₂×C₃₇	#430	1	2	yes	—
44	#423	—	37	1	no	—
45	#423	D₃₇	1	1	yes	characteristic
46	C₂×#97	—	37	1	no	—
47	#341	—	37	4	no	—
48	C₃₇	#1838	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₁₆	—	37	2	no	—
50	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
51	C₂²×C₈	—	37	2	no	—
52	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
53	C₄⋊C₈	—	2	2	no	—
54	C₄⋊C₈	—	74	2	no	—
55	#97	—	37	4	no	—
56	C₂²×C₄	Dic₇₄	1	2	yes	—
57	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
58	M₁₆	—	2	4	no	—
59	M₁₆	—	74	4	no	—
60	C₂×C₈	—	2	2	no	—
61	C₂×C₈	—	37	4	no	—
62	C₂×C₈	—	74	2	no	—
63	C₂×C₈	—	74	2	no	—
64	C₂×C₈	—	74	2	no	—
65	C₄²	C₄×D₃₇	1	2	yes	—
66	C₄²	C₂²⋊D₃₇	1	2	yes	—
67	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	#10596936	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
71	C₂×C₄	#10596964	1	2	yes	—
72	C₂×C₄	#10596966	1	2	yes	—
73	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	74	4	no	—
76	C₈	—	148	2	no	—
77	C₂²	—	2	2	no	—
78	C₂²	C₂×#10596936	1	1	yes	characteristic
79	C₂²	#11924527	1	2	yes	—
80	C₄	—	2	4	no	—
81	C₄	#11924494	1	2	yes	—
82	C₄	#11924523	1	1	yes	characteristic
83	C₄	#11924525	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#14557398	1	1	yes	characteristic
86	C₂	#14557581	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₃₇
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#423	C₂
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂³×C₃₇	C₂×Q₈
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#423	D₃₇
hypocenter	C₃₇	#1838
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

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

Maximal subgroups

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

subgroup	index
#14557557	2
C₂×#11924447	2
#14557297	2
C₃₇×#423	2
#1838	37