Subgroups — #17992754

Order 4736.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557923	C₂	1	1	yes	maximal, characteristic
2	#14557328	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10596941	—	2	1	no	—
5	C₂×#10596939	—	2	1	no	—
6	#11924533	C₄	1	1	yes	characteristic, complemented
7	#11924451	—	2	1	no	—
8	#11924447	C₄	1	1	yes	characteristic, complemented
9	#124×C₃₇	C₂²	1	1	yes	characteristic
10	#101×C₃₇	—	2	1	no	—
11	C₂×Q₈×C₃₇	D₄	1	1	yes	characteristic
12	C₂×D₄×C₃₇	D₄	1	1	yes	characteristic
13	C₂×D₁₄₈	—	2	1	no	—
14	C₂×D₁₄₈	—	4	1	no	—
15	M₁₆×C₃₇	—	4	1	no	—
16	C₂²⋊C₄×C₃₇	—	4	1	no	—
17	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂²⋊Dic₃₇	—	4	1	no	—
19	#10596941	—	4	2	no	—
20	#10596939	—	4	2	no	—
21	C₂×#64436	—	2	1	no	—
22	C₂³×C₃₇	—	2	1	no	—
23	C₂²×D₃₇	—	4	1	no	—
24	Q₈×C₃₇	—	4	1	no	—
25	D₄×C₃₇	—	4	1	no	—
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	—	2	1	no	—
28	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₃₇	—	8	1	no	—
30	D₁₄₈	—	4	1	no	—
31	D₁₄₈	—	4	1	no	—
32	D₁₄₈	—	8	2	no	—
33	C₈×C₃₇	—	8	1	no	—
34	#64436	—	2	2	no	—
35	C₂²×C₃₇	—	4	1	no	—
36	C₂²×C₃₇	—	8	1	no	—
37	C₂²×C₃₇	#99	1	1	yes	characteristic
38	C₂×D₃₇	—	8	2	no	—
39	C₂×D₃₇	—	8	1	no	—
40	C₄×C₃₇	—	2	1	no	—
41	C₄×C₃₇	—	4	1	no	—
42	C₄×C₃₇	—	4	1	no	—
43	Dic₃₇	—	16	1	no	—
44	#1406	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	2	1	no	—
46	C₂×C₃₇	—	8	1	no	—
47	C₂×C₃₇	#353	1	1	yes	characteristic
48	D₃₇	—	16	1	no	—
49	#496	—	37	1	no	—
50	#355	D₃₇	1	1	yes	characteristic, complemented
51	#354	—	37	1	no	—
52	C₃₇	#1406	1	1	yes	characteristic, complemented, Sylow
53	C₂×SD₁₆	—	74	1	no	—
54	C₂×D₈	—	74	1	no	—
55	#127	—	37	1	no	—
56	#124	C₂×D₃₇	1	1	yes	characteristic
57	#101	—	2	1	no	—
58	#99	—	74	1	no	—
59	#97	—	37	1	no	—
60	C₂×Q₈	C₂²⋊D₃₇	1	1	yes	characteristic
61	C₂×D₄	—	74	1	no	—
62	C₂×D₄	—	148	1	no	—
63	C₂×D₄	D₁₄₈	1	1	yes	characteristic
64	SD₁₆	—	148	2	no	—
65	D₈	—	148	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	74	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	148	1	no	—
70	C₄²	C₄×D₃₇	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	148	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	296	2	no	—
76	D₄	—	148	1	no	—
77	D₄	—	148	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	296	1	no	—
81	C₂×C₄	#10596938	1	1	yes	characteristic
82	C₈	—	8	1	no	—
83	C₈	—	74	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	296	2	no	—
87	C₂²	—	296	1	no	—
88	C₂²	#11924450	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	592	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	592	1	no	—
96	C₂	#14557325	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557325
commutator	C₄²×C₃₇	C₂×C₄
Frattini	#124	C₂×D₃₇
Fitting	C₃₇×#355	C₂
socle	C₂×C₃₇	#353
prime radical	#14557923	C₂
cosocle	#124×C₃₇	C₂²
hypercenter	#355	D₃₇
hypocenter	C₃₇	#1406
LCS	G ▷ C₄²×C₃₇ ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
2. #14557328	C₂	semidirect
3. C₃₇×#355	C₂	semidirect
6. #11924533	C₄	semidirect
8. #11924447	C₄	semidirect
50. #355	D₃₇	semidirect
52. C₃₇	#1406	semidirect

Maximal subgroups

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

subgroup	index
#14557923	2
#14557328	2
C₃₇×#355	2
#1406	37