Subgroups — #17992553

Order 4736.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557612	C₂	1	1	yes	maximal, characteristic
2	#14557309	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10596929	—	2	1	no	—
5	C₄×D₁₄₈	C₄	1	1	yes	characteristic
6	C₂×#10596925	—	2	1	no	—
7	C₄⋊#64436	C₄	1	1	yes	characteristic
8	#11924448	—	2	1	no	—
9	C₂×C₁₆×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₄₈	C₈	1	1	yes	characteristic
12	C₂×C₄×D₃₇	—	2	1	no	—
13	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
16	#10596938	—	2	1	no	—
17	C₄⋊Dic₃₇	C₈	1	1	yes	characteristic
18	C₂×#64436	—	2	1	no	—
19	#10596929	—	4	1	no	—
20	#10596929	—	4	1	no	—
21	C₁₆×C₃₇	—	4	1	no	—
22	#10596925	—	2	2	no	—
23	C₂²×D₃₇	—	2	1	no	—
24	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
27	C₂×Dic₃₇	—	2	1	no	—
28	D₁₄₈	—	4	1	no	—
29	C₄×D₃₇	—	4	1	no	—
30	C₄×D₃₇	—	4	1	no	—
31	C₈×C₃₇	—	2	1	no	—
32	C₈×C₃₇	D₈	1	1	yes	characteristic
33	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
34	#64436	—	4	1	no	—
35	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₃₇	—	4	1	no	—
37	C₂×D₃₇	—	4	1	no	—
38	C₂×D₃₇	—	4	1	no	—
39	C₄×C₃₇	—	2	1	no	—
40	C₄×C₃₇	—	2	1	no	—
41	C₄×C₃₇	#102	1	1	yes	characteristic
42	C₄×C₃₇	#104	1	1	yes	characteristic
43	Dic₃₇	—	4	1	no	—
44	#1330	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃₇	#349	1	1	yes	characteristic
47	C₂×C₃₇	#350	1	1	yes	characteristic
48	D₃₇	—	8	1	no	—
49	#436	—	37	1	no	—
50	C₄⋊C₁₆	D₃₇	1	1	yes	characteristic, complemented
51	#346	—	37	1	no	—
52	C₃₇	#1330	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	74	1	no	—
54	C₄×D₄	—	37	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₂×C₁₆	—	74	1	no	—
57	C₄⋊C₈	—	37	1	no	—
58	C₂²⋊C₈	—	74	1	no	—
59	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
60	C₂×D₄	—	37	1	no	—
61	C₂²×C₄	—	74	1	no	—
62	M₁₆	—	148	1	no	—
63	M₁₆	—	148	1	no	—
64	C₂×C₈	—	74	1	no	—
65	C₂×C₈	D₁₄₈	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
67	C₄⋊C₄	—	37	1	no	—
68	C₂²⋊C₄	—	74	1	no	—
69	C₄²	C₄×D₃₇	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	74	2	no	—
72	C₂³	—	74	1	no	—
73	D₄	—	148	1	no	—
74	C₂×C₄	—	74	1	no	—
75	C₂×C₄	—	148	1	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
78	C₂×C₄	#10596929	1	1	yes	characteristic
79	C₂×C₄	#10596938	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	148	1	no	—
82	C₈	#10596939	1	1	yes	characteristic
83	C₈	#10596941	1	1	yes	characteristic
84	C₂²	—	148	1	no	—
85	C₂²	—	148	1	no	—
86	C₂²	—	148	1	no	—
87	C₂²	#11924448	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	148	1	no	—
91	C₄	#11924456	1	1	yes	characteristic
92	C₄	#11924462	1	1	yes	characteristic
93	C₂	—	296	1	no	—
94	C₂	#14557260	1	1	yes	characteristic
95	C₂	#14557314	1	1	yes	characteristic
96	C₂	#14557316	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10596938
commutator	C₂×C₄×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×C₄⋊C₁₆	C₂
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂×D₁₄₈	C₈
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	C₄⋊C₁₆	D₃₇
hypocenter	C₃₇	#1330
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #14557309	C₂	semidirect
3. C₃₇×C₄⋊C₁₆	C₂	semidirect
50. C₄⋊C₁₆	D₃₇	semidirect
52. C₃₇	#1330	semidirect

Maximal subgroups

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

subgroup	index
#14557612	2
#14557309	2
C₃₇×C₄⋊C₁₆	2
#1330	37