Subgroups — #17994734

Order 4736.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557557	C₂	1	2	yes	maximal
2	#14557298	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	C₂²	1	4	yes	—
5	C₄⋊#64436	—	2	4	no	—
6	C₂²×C₈×C₃₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₃₇	C₄	1	2	yes	—
9	C₄×C₈×C₃₇	C₄	1	2	yes	—
10	C₂²×C₄×C₃₇	Q₈	1	2	yes	—
11	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
12	C₂×C₈×C₃₇	—	2	4	no	—
13	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
14	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₄²×C₃₇	D₄	1	2	yes	—
17	#10596934	—	2	8	no	—
18	C₂×#64436	—	2	4	no	—
19	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₃₇	—	2	4	no	—
21	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
22	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	#41	1	4	yes	—
26	C₈×C₃₇	—	2	4	no	—
27	#64436	—	4	4	no	—
28	C₂²×C₃₇	—	2	2	no	—
29	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₃₇	#125	1	2	yes	—
31	C₄×C₃₇	—	2	2	no	—
32	C₄×C₃₇	#108	1	4	yes	—
33	C₄×C₃₇	#117	1	2	yes	—
34	C₄×C₃₇	#124	1	2	yes	—
35	#1837	—	37	1	no	maximal, Sylow
36	C₂×C₃₇	—	2	2	no	—
37	C₂×C₃₇	#382	1	1	yes	characteristic
38	C₂×C₃₇	C₂×#108	1	2	yes	—
39	#423	—	37	2	no	—
40	C₂×C₄×C₈	D₃₇	1	1	yes	characteristic
41	#341	—	37	4	no	—
42	C₃₇	#1837	1	1	yes	characteristic, complemented, Sylow
43	C₂×M₁₆	—	37	4	no	—
44	C₂²×C₈	C₂×D₃₇	1	2	yes	—
45	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
46	C₄⋊C₈	—	74	4	no	—
47	C₄×C₈	Dic₃₇	1	2	yes	—
48	C₄×C₈	Dic₃₇	1	2	yes	—
49	C₂²×C₄	Dic₇₄	1	2	yes	—
50	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
51	M₁₆	—	74	8	no	—
52	C₂×C₈	—	2	4	no	—
53	C₂×C₈	—	74	4	no	—
54	C₂×C₈	C₂×Dic₃₇	1	4	yes	—
55	C₄²	D₁₄₈	1	2	yes	—
56	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
57	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
58	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
61	C₂×C₄	C₄⋊Dic₃₇	1	2	yes	—
62	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
63	C₂×C₄	#10596962	1	4	yes	—
64	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₈	—	148	4	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
69	C₂²	#11924528	1	2	yes	—
70	C₄	—	2	2	no	—
71	C₄	#11924472	1	4	yes	—
72	C₄	#11924495	1	2	yes	—
73	C₄	#11924524	1	2	yes	—
74	C₂	—	2	2	no	—
75	C₂	#14557399	1	1	yes	characteristic
76	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	#1837
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
42. 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
#14557298	2
C₂×C₄×C₈×C₃₇	2
#1837	37