Subgroups — #17994230

Order 4736.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557929	C₂	1	2	yes	maximal
2	#14557913	C₂	1	1	yes	maximal, characteristic
3	#14557883	C₂	1	2	yes	maximal
4	#14557254	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#498	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₄₈	—	2	2	no	—
7	#11924536	C₂²	1	1	yes	characteristic
8	#11924536	C₂²	1	1	yes	characteristic
9	#11924467	—	2	4	no	—
10	#11924460	—	2	4	no	—
11	C₄×#64436	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₃₇	C₂²	1	2	yes	—
13	#106×C₃₇	—	2	2	no	—
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₃₇	—	2	2	no	—
16	C₂×Dic₇₄	—	2	1	no	—
17	C₂×Dic₇₄	—	2	1	no	—
18	C₂×C₈×C₃₇	D₄	1	2	yes	—
19	C₄⋊C₄×C₃₇	—	2	2	no	—
20	C₄⋊C₄×C₃₇	—	2	2	no	—
21	C₄²×C₃₇	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₃₇	—	2	2	no	—
23	C₄⋊Dic₃₇	—	2	2	no	—
24	C₂×#64436	D₄	1	4	yes	—
25	Dic₁₄₈	—	4	4	no	—
26	Q₈×C₃₇	—	4	4	no	—
27	C₂×C₄×C₃₇	—	4	2	no	—
28	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₃₇	—	4	1	no	—
31	C₂×Dic₃₇	—	4	1	no	—
32	Dic₇₄	—	4	2	no	—
33	Dic₇₄	—	4	2	no	—
34	C₈×C₃₇	SD₁₆	1	4	yes	—
35	#64436	—	2	4	no	—
36	C₂²×C₃₇	#127	1	1	yes	characteristic
37	C₄×C₃₇	—	8	2	no	—
38	C₄×C₃₇	C₂×SD₁₆	1	2	yes	—
39	C₄×C₃₇	#137	1	4	yes	—
40	Dic₃₇	—	8	1	no	—
41	Dic₃₇	—	8	1	no	—
42	#1716	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	#492	1	1	yes	characteristic
44	C₂×C₃₇	#497	1	2	yes	—
45	#498	—	37	2	no	—
46	#498	D₃₇	1	1	yes	characteristic
47	#494	—	37	1	no	—
48	#487	—	37	2	no	—
49	#322	—	37	1	no	—
50	C₃₇	#1716	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₁₆	—	74	2	no	—
52	C₄⋊Q₈	—	37	1	no	—
53	C₄⋊Q₈	—	37	1	no	—
54	C₄⋊Q₈	C₂×D₃₇	1	2	yes	—
55	#106	—	2	2	no	—
56	#106	—	74	4	no	—
57	#103	—	74	4	no	—
58	C₄×C₈	—	37	2	no	—
59	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
60	C₂×Q₈	—	2	2	no	—
61	C₂×Q₈	—	74	1	no	—
62	C₂×Q₈	—	74	1	no	—
63	Q₁₆	—	148	4	no	—
64	C₂×C₈	—	37	4	no	—
65	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	2	no	—
68	C₄⋊C₄	—	74	2	no	—
69	C₄⋊C₄	—	74	2	no	—
70	C₄²	C₂²×D₃₇	1	1	yes	characteristic
71	Q₈	—	4	4	no	—
72	Q₈	—	148	2	no	—
73	Q₈	—	148	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	148	1	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	D₄×D₃₇	1	2	yes	—
78	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
79	C₈	—	74	4	no	—
80	C₈	#10596941	1	4	yes	—
81	C₂²	#11924532	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	296	1	no	—
84	C₄	—	296	1	no	—
85	C₄	C₂×#10596941	1	2	yes	—
86	C₄	#11924565	1	4	yes	—
87	C₂	#14557907	1	1	yes	characteristic
88	C₂	#14557924	1	2	yes	—

	subgroup	G/H
center	C₂²	#11924532
commutator, cosocle	C₄²×C₃₇	C₂³
Frattini	C₄²	C₂²×D₃₇
Fitting	C₃₇×#498	C₂
socle, prime radical	C₂²×C₃₇	#127
hypercenter	#498	D₃₇
hypocenter	C₃₇	#1716
LCS	G ▷ C₄²×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
50. C₃₇	#1716	semidirect

Maximal subgroups

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

subgroup	index
#14557929	2
#14557913	2
#14557883	2
#14557254	2
C₃₇×#498	2
#1716	37