Subgroups — #17994768

Order 4736.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924472	C₂	1	4	yes	maximal
2	#14557557	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	C₂²	1	4	yes	—
5	#11924472	—	2	8	no	—
6	C₄⋊#64436	—	2	4	no	—
7	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
8	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₃₇	C₄	1	2	yes	—
10	C₄×C₈×C₃₇	C₄	1	2	yes	—
11	C₂²×C₄×C₃₇	Q₈	1	2	yes	—
12	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₃₇	D₄	1	4	yes	—
15	C₂×C₈×C₃₇	Q₈	1	4	yes	—
16	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₃₇	D₄	1	2	yes	—
19	#10596934	—	2	8	no	—
20	C₂×#64436	—	2	4	no	—
21	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₃₇	—	2	4	no	—
23	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
29	C₈×C₃₇	C₄⋊C₄	1	8	yes	—
30	#64436	—	4	4	no	—
31	C₂²×C₃₇	—	2	2	no	—
32	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₃₇	C₄⋊Q₈	1	2	yes	—
34	C₄×C₃₇	—	2	2	no	—
35	C₄×C₃₇	#108	1	4	yes	complemented
36	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₃₇	#127	1	1	yes	characteristic
38	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
39	#1848	—	37	1	no	maximal, Sylow
40	C₂×C₃₇	—	2	2	no	—
41	C₂×C₃₇	#384	1	1	yes	characteristic
42	C₂×C₃₇	C₂×#108	1	2	yes	—
43	C₂×#108	—	37	4	no	—
44	#423	—	37	2	no	—
45	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic
46	C₃₇	#1848	1	1	yes	characteristic, complemented, Sylow
47	C₂×M₁₆	—	37	4	no	—
48	C₂²×C₈	C₂×D₃₇	1	2	yes	—
49	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
50	#108	—	74	8	no	—
51	C₄⋊C₈	—	74	4	no	—
52	C₄×C₈	Dic₃₇	1	2	yes	—
53	C₄×C₈	Dic₃₇	1	2	yes	—
54	C₂²×C₄	Dic₇₄	1	2	yes	—
55	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
56	M₁₆	—	74	8	no	—
57	C₂×C₈	—	74	4	no	—
58	C₂×C₈	Dic₇₄	1	4	yes	—
59	C₂×C₈	D₁₄₈	1	4	yes	—
60	C₂×C₈	C₂×Dic₃₇	1	4	yes	—
61	C₄²	D₁₄₈	1	2	yes	—
62	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
63	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
64	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
68	C₂×C₄	C₂×Dic₇₄	1	2	yes	—
69	C₂×C₄	C₂×D₁₄₈	1	2	yes	—
70	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
72	C₈	—	148	4	no	—
73	C₈	C₄⋊Dic₃₇	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
76	C₂²	#11924536	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	#11924472	1	4	yes	complemented
79	C₄	C₂×C₄⋊Dic₃₇	1	2	yes	—
80	C₄	#11924533	1	1	yes	characteristic
81	C₄	#11924536	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	#14557403	1	1	yes	characteristic
84	C₂	C₂×#11924472	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₄₈
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₂×C₄×C₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂³×C₃₇	C₂×Q₈
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₂×C₄×C₈	D₃₇
hypocenter	C₃₇	#1848
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
35. C₄×C₃₇	#108	semidirect
46. C₃₇	#1848	semidirect
78. C₄	#11924472	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924472	2
#14557557	2
C₂×C₄×C₈×C₃₇	2
#1848	37