Subgroups — #17996176

Order 4736.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557582	C₂	1	1	yes	maximal, characteristic
2	#14557303	C₂	1	2	yes	maximal
3	#14557298	C₂	1	2	yes	maximal
4	#14557291	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	C₂²	1	2	yes	—
7	C₂×#10596934	C₂²	1	2	yes	—
8	#11924472	—	2	2	no	—
9	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	#117×C₃₇	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₃₇	—	2	2	no	—
13	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
14	M₁₆×C₃₇	—	2	2	no	—
15	C₂×C₈×C₃₇	—	2	1	no	—
16	C₂×C₈×C₃₇	—	2	2	no	—
17	C₂×C₈×C₃₇	D₄	1	2	yes	—
18	C₄⋊C₄×C₃₇	—	2	1	no	—
19	C₂²⋊C₄×C₃₇	Q₈	1	2	yes	—
20	C₄²×C₃₇	—	2	1	no	—
21	#10596934	—	2	2	no	—
22	#10596934	—	2	2	no	—
23	#10596934	—	2	2	no	—
24	#10596934	—	2	2	no	—
25	C₂×#64436	—	2	2	no	—
26	C₂×#64436	—	2	2	no	—
27	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₃₇	—	2	2	no	—
29	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₃₇	#41	1	1	yes	characteristic
31	C₂×C₄×C₃₇	#41	1	2	yes	—
32	C₂×C₄×C₃₇	#41	1	2	yes	—
33	C₈×C₃₇	—	2	2	no	—
34	C₈×C₃₇	—	4	1	no	—
35	#64436	—	4	2	no	—
36	#64436	—	4	2	no	—
37	C₂²×C₃₇	—	4	1	no	—
38	C₂²×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₃₇	#125	1	2	yes	—
40	C₄×C₃₇	—	4	2	no	—
41	C₄×C₃₇	#123	1	1	yes	characteristic
42	C₄×C₃₇	#124	1	1	yes	characteristic
43	C₄×C₃₇	#126	1	2	yes	—
44	#2103	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	2	1	no	—
46	C₂×C₃₇	—	2	2	no	—
47	C₂×C₃₇	#400	1	1	yes	characteristic
48	#430	—	37	1	no	—
49	#424	D₃₇	1	1	yes	characteristic
50	#344	—	37	2	no	—
51	#341	—	37	2	no	—
52	#338	—	37	1	no	—
53	C₃₇	#2103	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	37	2	no	—
55	C₂×M₁₆	—	37	2	no	—
56	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
57	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
58	#117	C₂×D₃₇	1	1	yes	characteristic
59	#108	—	74	2	no	—
60	C₄⋊C₈	—	2	2	no	—
61	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	74	2	no	—
64	M₁₆	—	74	2	no	—
65	M₁₆	—	74	2	no	—
66	M₁₆	—	74	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	74	2	no	—
70	C₂×C₈	—	74	2	no	—
71	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Dic₇₄	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	#10596962	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	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	148	2	no	—
84	C₈	—	148	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#11924515	1	1	yes	characteristic
87	C₂²	#11924527	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	#11924517	1	1	yes	characteristic
90	C₄	#11924525	1	1	yes	characteristic
91	C₄	#11924531	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#14557472	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924525
commutator, cosocle	C₂²×C₄×C₃₇	C₂³
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#424	C₂
socle	C₂×C₃₇	#400
prime radical	C₂³×C₃₇	C₂×Q₈
hypercenter	#424	D₃₇
hypocenter	C₃₇	#2103
LCS	G ▷ C₂²×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
53. C₃₇	#2103	semidirect

Maximal subgroups

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

subgroup	index
#14557582	2
#14557303	2
#14557298	2
#14557291	2
C₃₇×#424	2
#2103	37