Subgroups — #17992757

Order 4736.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557928	C₂	1	1	yes	maximal, characteristic
2	#14557328	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#355	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596942	—	2	1	no	—
5	C₂×#10596940	—	2	1	no	—
6	#11924536	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×Dic₇₄	—	2	1	no	—
14	M₁₆×C₃₇	—	4	1	no	—
15	C₂²⋊C₄×C₃₇	—	4	1	no	—
16	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊Dic₃₇	—	4	1	no	—
18	#10596942	—	4	2	no	—
19	#10596940	—	4	2	no	—
20	C₄⋊Dic₃₇	—	4	1	no	—
21	C₂×#64436	—	2	1	no	—
22	C₂³×C₃₇	—	2	1	no	—
23	Q₈×C₃₇	—	4	1	no	—
24	D₄×C₃₇	—	4	1	no	—
25	C₂×C₄×C₃₇	—	2	1	no	—
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	4	1	no	—
29	C₂×Dic₃₇	—	8	1	no	—
30	Dic₇₄	—	4	1	no	—
31	Dic₇₄	—	4	1	no	—
32	C₈×C₃₇	—	8	1	no	—
33	#64436	—	2	2	no	—
34	C₂²×C₃₇	—	4	1	no	—
35	C₂²×C₃₇	—	8	1	no	—
36	C₂²×C₃₇	#99	1	1	yes	characteristic
37	C₄×C₃₇	—	2	1	no	—
38	C₄×C₃₇	—	4	1	no	—
39	C₄×C₃₇	—	4	1	no	—
40	Dic₃₇	—	8	1	no	—
41	Dic₃₇	—	16	1	no	—
42	#1407	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	—	2	1	no	—
44	C₂×C₃₇	—	8	1	no	—
45	C₂×C₃₇	#353	1	1	yes	characteristic
46	#497	—	37	1	no	—
47	#355	D₃₇	1	1	yes	characteristic
48	#354	—	37	1	no	—
49	C₃₇	#1407	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	74	1	no	—
51	C₂×SD₁₆	—	74	1	no	—
52	C₄⋊Q₈	—	37	1	no	—
53	#124	C₂×D₃₇	1	1	yes	characteristic
54	#101	—	2	1	no	—
55	#99	—	74	1	no	—
56	#97	—	37	1	no	—
57	C₂×Q₈	—	74	1	no	—
58	C₂×Q₈	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₂×D₄	D₁₄₈	1	1	yes	characteristic
60	Q₁₆	—	148	2	no	—
61	SD₁₆	—	148	2	no	—
62	M₁₆	—	4	1	no	—
63	C₂×C₈	—	74	1	no	—
64	C₄⋊C₄	—	148	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	148	1	no	—
67	C₄²	C₄×D₃₇	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	148	1	no	—
71	Q₈	—	148	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	296	1	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	#10596938	1	1	yes	characteristic
78	C₈	—	8	1	no	—
79	C₈	—	74	2	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#11924450	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	296	1	no	—
87	C₄	—	592	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	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	C₂×D₄×C₃₇	D₄
cosocle	#124×C₃₇	C₂²
hypercenter	#355	D₃₇
hypocenter	C₃₇	#1407
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
6. #11924536	C₄	semidirect
8. #11924447	C₄	semidirect
49. C₃₇	#1407	semidirect

Maximal subgroups

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

subgroup	index
#14557928	2
#14557328	2
C₃₇×#355	2
#1407	37