Subgroups — #17994197

Order 4736.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557931	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557906	C₂	1	1	yes	maximal, characteristic
3	#14557884	C₂	1	2	yes	maximal, complemented
4	#14557880	C₂	1	2	yes	maximal
5	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10596930	—	2	2	no	—
7	#11924536	C₂²	1	2	yes	—
8	#11924536	C₂²	1	1	yes	characteristic
9	#11924533	C₂²	1	1	yes	characteristic
10	#11924468	—	2	2	no	—
11	#11924461	—	2	4	no	—
12	#11924458	—	2	4	no	—
13	C₄×C₈×C₃₇	C₂²	1	2	yes	—
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×D₁₄₈	—	2	1	no	—
16	C₂×D₁₄₈	—	2	2	no	—
17	C₂×Dic₇₄	—	2	1	no	—
18	C₂×Dic₇₄	—	2	2	no	—
19	C₂×C₈×C₃₇	D₄	1	4	yes	—
20	C₂×C₈×C₃₇	D₄	1	2	yes	—
21	C₄²×C₃₇	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₃₇	—	2	2	no	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₄⋊Dic₃₇	—	2	2	no	—
25	#10596930	—	4	4	no	—
26	C₂²×D₃₇	—	4	1	no	—
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
29	C₂×Dic₃₇	—	4	1	no	—
30	C₂×Dic₃₇	—	4	2	no	—
31	D₁₄₈	—	4	2	no	—
32	D₁₄₈	—	4	4	no	—
33	Dic₇₄	—	4	2	no	—
34	Dic₇₄	—	4	4	no	—
35	C₈×C₃₇	—	2	4	no	—
36	C₈×C₃₇	SD₁₆	1	4	yes	—
37	C₂²×C₃₇	#127	1	1	yes	characteristic
38	C₂×D₃₇	—	8	1	no	—
39	C₂×D₃₇	—	8	2	no	—
40	C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
41	C₄×C₃₇	#135	1	4	yes	—
42	Dic₃₇	—	8	1	no	—
43	Dic₃₇	—	8	2	no	—
44	#1708	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	#492	1	1	yes	characteristic
46	C₂×C₃₇	#495	1	2	yes	—
47	D₃₇	—	16	1	no	—
48	#498	—	37	1	no	—
49	#492	—	37	1	no	—
50	#487	—	37	2	no	—
51	#486	—	37	2	no	—
52	C₈²	D₃₇	1	1	yes	characteristic, complemented
53	C₃₇	#1708	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	74	2	no	—
55	C₄⋊Q₈	—	37	2	no	—
56	C₄⋊Q₈	—	37	1	no	—
57	#127	—	37	1	no	—
58	#106	—	74	2	no	—
59	#103	—	74	4	no	—
60	#102	—	74	4	no	—
61	C₄×C₈	C₂×D₃₇	1	2	yes	—
62	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
63	C₂×Q₈	—	74	2	no	—
64	C₂×Q₈	—	74	1	no	—
65	C₂×D₄	—	74	2	no	—
66	C₂×D₄	—	74	1	no	—
67	SD₁₆	—	148	4	no	—
68	C₂×C₈	D₁₄₈	1	4	yes	—
69	C₂×C₈	D₁₄₈	1	2	yes	—
70	C₄⋊C₄	—	74	2	no	—
71	C₄⋊C₄	—	74	2	no	—
72	C₄⋊C₄	—	74	2	no	—
73	C₄²	C₂²×D₃₇	1	1	yes	characteristic
74	C₂³	—	148	1	no	—
75	Q₈	—	148	2	no	—
76	Q₈	—	148	4	no	—
77	D₄	—	148	2	no	—
78	D₄	—	148	4	no	—
79	C₂×C₄	—	148	1	no	—
80	C₂×C₄	—	148	2	no	—
81	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
82	C₂×C₄	C₂×D₁₄₈	1	2	yes	—
83	C₈	—	2	4	no	—
84	C₈	#10596930	1	4	yes	—
85	C₂²	—	296	1	no	—
86	C₂²	—	296	2	no	—
87	C₂²	#11924533	1	1	yes	characteristic
88	C₄	—	296	1	no	—
89	C₄	—	296	2	no	—
90	C₄	C₂×#10596930	1	2	yes	—
91	C₄	#11924558	1	4	yes	—
92	C₂	—	592	1	no	—
93	C₂	#14557906	1	1	yes	characteristic
94	C₂	#14557917	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924533
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₈²×C₃₇	C₂
socle	C₂²×C₃₇	#127
prime radical	#11924533	C₂²
hypercenter	C₈²	D₃₇
hypocenter	C₃₇	#1708
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #14557931	C₂	semidirect
3. #14557884	C₂	semidirect
5. C₈²×C₃₇	C₂	semidirect
52. C₈²	D₃₇	semidirect
53. C₃₇	#1708	semidirect

Maximal subgroups

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

subgroup	index
#14557931	2
#14557906	2
#14557884	2
#14557880	2
C₈²×C₃₇	2
#1708	37