Subgroups — #17992590

Order 4736.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557315	C₂	1	1	yes	maximal, characteristic
2	#14557291	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#470	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	—	2	1	no	—
5	#11924476	—	2	1	no	—
6	C₂×Q₁₆×C₃₇	C₄	1	1	yes	characteristic
7	C₂×M₁₆×C₃₇	C₂²	1	1	yes	characteristic
8	C₂²⋊Q₈×C₃₇	—	2	1	no	—
9	#106×C₃₇	C₄	1	1	yes	characteristic
10	#103×C₃₇	—	2	1	no	—
11	C₂×Q₈×C₃₇	—	2	1	no	—
12	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
13	Q₁₆×C₃₇	—	4	1	no	—
14	M₁₆×C₃₇	—	4	1	no	—
15	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇	—	2	1	no	—
18	C₄⋊C₄×C₃₇	—	4	1	no	—
19	C₂²⋊C₄×C₃₇	—	4	1	no	—
20	#10596934	—	4	1	no	—
21	#10596934	—	4	1	no	—
22	C₂×#64436	—	2	2	no	—
23	#10596925	—	4	1	no	—
24	C₂³×C₃₇	SD₁₆	1	1	yes	characteristic
25	Q₈×C₃₇	—	4	1	no	—
26	Q₈×C₃₇	—	4	1	no	—
27	C₂×C₄×C₃₇	—	2	1	no	—
28	C₂×C₄×C₃₇	—	2	1	no	—
29	C₂×C₄×C₃₇	—	4	1	no	—
30	C₂×C₄×C₃₇	—	4	1	no	—
31	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
33	C₈×C₃₇	—	2	1	no	—
34	C₈×C₃₇	—	2	1	no	—
35	#64436	—	4	2	no	—
36	C₂²×C₃₇	—	2	1	no	—
37	C₂²×C₃₇	—	4	1	no	—
38	C₂²×C₃₇	#102	1	1	yes	characteristic
39	C₄×C₃₇	—	2	1	no	—
40	C₄×C₃₇	—	8	1	no	—
41	C₄×C₃₇	—	8	1	no	—
42	C₄×C₃₇	#99	1	1	yes	characteristic
43	C₄×C₃₇	#104	1	1	yes	characteristic
44	#1342	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	2	1	no	—
46	C₂×C₃₇	—	4	1	no	—
47	C₂×C₃₇	#327	1	1	yes	characteristic
48	#470	D₃₇	1	1	yes	characteristic
49	#349	—	37	1	no	—
50	#338	—	37	1	no	—
51	C₃₇	#1342	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	Dic₃₇	1	1	yes	characteristic
53	C₂×M₁₆	—	74	1	no	—
54	C₂×M₁₆	C₂×D₃₇	1	1	yes	characteristic
55	C₂²⋊Q₈	—	2	1	no	—
56	M₃₂	—	74	1	no	—
57	#106	Dic₃₇	1	1	yes	characteristic
58	#103	—	2	1	no	—
59	C₂×Q₈	—	2	1	no	—
60	C₂²×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
61	Q₁₆	—	4	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	148	1	no	—
64	M₁₆	—	148	1	no	—
65	C₂×C₈	—	74	2	no	—
66	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	4	1	no	—
71	C₁₆	—	148	1	no	—
72	C₂³	#10596940	1	1	yes	characteristic
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	4	1	no	—
79	C₂×C₄	#10596939	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊Dic₃₇	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	148	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#11924457	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	8	1	no	—
89	C₄	—	8	1	no	—
90	C₄	#11924451	1	1	yes	characteristic
91	C₄	#11924463	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#14557267	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557267
commutator	C₂×C₈×C₃₇	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₃₇
Fitting	C₃₇×#470	C₂
socle	C₂×C₃₇	#327
prime radical	C₂³×C₃₇	SD₁₆
cosocle	C₂×M₁₆×C₃₇	C₂²
hypercenter	#470	D₃₇
hypocenter	C₃₇	#1342
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #470

Complements

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

N	H ≅ G/N	type
51. C₃₇	#1342	semidirect

Maximal subgroups

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

subgroup	index
#14557315	2
#14557291	2
C₃₇×#470	2
#1342	37