Subgroups — #17994193

Order 4736.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557938	C₂	1	1	yes	maximal, characteristic
2	#14557931	C₂	1	2	yes	maximal
3	#14557913	C₂	1	1	yes	maximal, characteristic
4	#14557884	C₂	1	2	yes	maximal
5	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₄₈	—	2	2	no	—
7	#11924536	C₂²	1	2	yes	—
8	#11924536	C₂²	1	2	yes	—
9	#11924470	—	2	2	no	—
10	#11924468	—	2	4	no	—
11	#11924461	—	2	4	no	—
12	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₇₄	—	2	2	no	—
16	C₂×Dic₇₄	—	2	2	no	—
17	C₂×C₈×C₃₇	D₄	1	2	yes	—
18	C₂×C₈×C₃₇	D₄	1	2	yes	—
19	C₂×C₈×C₃₇	D₄	1	2	yes	—
20	C₄²×C₃₇	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₃₇	—	2	2	no	—
22	C₄⋊Dic₃₇	—	2	2	no	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₄⋊Dic₃₇	—	2	2	no	—
25	Dic₁₄₈	—	4	4	no	—
26	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₃₇	—	4	2	no	—
30	C₂×Dic₃₇	—	4	2	no	—
31	Dic₇₄	—	4	4	no	—
32	Dic₇₄	—	4	4	no	—
33	C₈×C₃₇	—	2	2	no	—
34	C₈×C₃₇	SD₁₆	1	4	yes	—
35	C₈×C₃₇	Q₁₆	1	4	yes	complemented
36	C₂²×C₃₇	#127	1	1	yes	characteristic
37	C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
38	C₄×C₃₇	C₂×Q₁₆	1	2	yes	—
39	C₄×C₃₇	#135	1	2	yes	—
40	Dic₃₇	—	8	2	no	—
41	Dic₃₇	—	8	2	no	—
42	#1707	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	#492	1	1	yes	characteristic
44	C₂×C₃₇	#494	1	1	yes	characteristic
45	C₂×C₃₇	#495	1	1	yes	characteristic
46	#500	—	37	1	no	—
47	#498	—	37	2	no	—
48	#494	—	37	1	no	—
49	#487	—	37	2	no	—
50	C₈²	D₃₇	1	1	yes	characteristic
51	C₃₇	#1707	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	74	2	no	—
53	C₄⋊Q₈	—	37	2	no	—
54	C₄⋊Q₈	—	37	2	no	—
55	#107	—	74	2	no	—
56	#106	—	74	4	no	—
57	#103	—	74	4	no	—
58	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
59	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
60	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
61	C₂×Q₈	—	74	2	no	—
62	C₂×Q₈	—	74	2	no	—
63	Q₁₆	—	148	4	no	—
64	C₂×C₈	D₁₄₈	1	2	yes	—
65	C₂×C₈	D₁₄₈	1	2	yes	—
66	C₂×C₈	D₁₄₈	1	2	yes	—
67	C₄⋊C₄	—	74	2	no	—
68	C₄⋊C₄	—	74	2	no	—
69	C₄⋊C₄	—	74	2	no	—
70	C₄⋊C₄	—	74	2	no	—
71	C₄²	C₂²×D₃₇	1	1	yes	characteristic
72	Q₈	—	148	4	no	—
73	Q₈	—	148	4	no	—
74	C₂×C₄	—	148	2	no	—
75	C₂×C₄	—	148	2	no	—
76	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
77	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
78	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	#10596930	1	4	yes	—
81	C₈	Dic₁₄₈	1	4	yes	complemented
82	C₂²	#11924533	1	1	yes	characteristic
83	C₄	—	296	2	no	—
84	C₄	—	296	2	no	—
85	C₄	C₂×#10596930	1	2	yes	—
86	C₄	C₂×Dic₁₄₈	1	2	yes	—
87	C₄	#11924558	1	2	yes	—
88	C₂	#14557906	1	1	yes	characteristic
89	C₂	#14557913	1	1	yes	characteristic
90	C₂	#14557917	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924533
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₈²×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	#127
hypercenter	C₈²	D₃₇
hypocenter	C₃₇	#1707
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
35. C₈×C₃₇	Q₁₆	semidirect
51. C₃₇	#1707	semidirect
81. C₈	Dic₁₄₈	semidirect

Maximal subgroups

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

subgroup	index
#14557938	2
#14557931	2
#14557913	2
#14557884	2
C₈²×C₃₇	2
#1707	37