Subgroups — #17994733

Order 4736.

188 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×C₄×#64436	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	C₄×#64436	C₄	1	2	yes	—
9	C₄×#64436	C₄	1	2	yes	—
10	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
11	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₃₇	—	2	2	no	—
13	C₂²×C₄×C₃₇	Q₈	1	2	yes	—
14	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	M₁₆×C₃₇	—	2	4	no	—
16	C₂×C₈×C₃₇	—	2	2	no	—
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₃₇	D₄	1	2	yes	—
20	#10596934	—	2	4	no	—
21	C₂×#64436	—	2	2	no	—
22	C₂×#64436	—	2	2	no	—
23	C₂×#64436	—	2	2	no	—
24	C₂×#64436	C₂×C₄	1	4	yes	—
25	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	—	2	4	no	—
27	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₃₇	#41	1	2	yes	—
32	C₂×C₄×C₃₇	#41	1	2	yes	—
33	C₈×C₃₇	—	4	2	no	—
34	#64436	—	2	4	no	—
35	#64436	—	4	2	no	—
36	C₂²×C₃₇	—	2	2	no	—
37	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₃₇	#125	1	2	yes	—
39	C₄×C₃₇	—	2	2	no	—
40	C₄×C₃₇	#108	1	4	yes	—
41	C₄×C₃₇	#117	1	2	yes	—
42	C₄×C₃₇	#124	1	1	yes	characteristic
43	C₄×C₃₇	#124	1	1	yes	characteristic
44	#1837	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	2	2	no	—
46	C₂×C₃₇	#382	1	1	yes	characteristic
47	C₂×C₃₇	C₂×#108	1	2	yes	—
48	#423	—	37	1	no	—
49	#423	D₃₇	1	1	yes	characteristic
50	C₂×C₄×C₈	—	37	1	no	—
51	#341	—	37	4	no	—
52	C₃₇	#1837	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	37	2	no	—
54	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
55	C₂²×C₈	—	37	2	no	—
56	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
57	C₄⋊C₈	—	2	2	no	—
58	C₄⋊C₈	—	74	2	no	—
59	C₄×C₈	—	37	2	no	—
60	C₄×C₈	—	37	2	no	—
61	C₂²×C₄	Dic₇₄	1	2	yes	—
62	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
63	M₁₆	—	2	4	no	—
64	M₁₆	—	74	4	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	—	37	4	no	—
67	C₂×C₈	—	74	2	no	—
68	C₂×C₈	—	74	2	no	—
69	C₂×C₈	—	74	2	no	—
70	C₄²	C₄×D₃₇	1	1	yes	characteristic
71	C₄²	C₄×D₃₇	1	1	yes	characteristic
72	C₄²	C₂²⋊D₃₇	1	2	yes	—
73	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	#10596936	1	2	yes	—
76	C₂×C₄	#10596936	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
78	C₂×C₄	#10596964	1	2	yes	—
79	C₂×C₄	#10596966	1	2	yes	—
80	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
81	C₈	—	4	2	no	—
82	C₈	—	74	4	no	—
83	C₈	—	148	2	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×#10596936	1	1	yes	characteristic
86	C₂²	#11924527	1	2	yes	—
87	C₄	—	2	2	no	—
88	C₄	#11924471	1	4	yes	—
89	C₄	#11924494	1	2	yes	—
90	C₄	#11924523	1	1	yes	characteristic
91	C₄	#11924525	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	#14557398	1	1	yes	characteristic
94	C₂	C₂×#11924471	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	#1837
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
52. C₃₇	#1837	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×C₄×#64436	2
#14557297	2
C₃₇×#423	2
#1837	37