Subgroups — #18010525

Order 4736.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558399	C₂	1	6	yes	maximal
2	#14557378	C₂	1	1	yes	maximal, characteristic
3	C₂²×#64438	C₂²	1	4	yes	—
4	C₂×C₄×Dic₃₇	C₂²	1	3	yes	—
5	#11924443	C₄	1	3	yes	—
6	#95×C₃₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₃₇	C₂×C₄	1	3	yes	—
8	C₂²×Dic₃₇	C₂×C₄	1	3	yes	—
9	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
10	C₂×#64438	—	2	12	no	—
11	C₄×Dic₃₇	—	2	6	no	—
12	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₃₇	—	2	3	no	—
14	C₂×C₄×C₃₇	—	2	6	no	—
15	C₂×Dic₃₇	—	2	3	no	—
16	C₂×Dic₃₇	—	2	3	no	—
17	C₂×Dic₃₇	—	2	3	no	—
18	C₂×Dic₃₇	#41	1	6	yes	—
19	#64438	—	4	4	no	—
20	C₂²×C₃₇	#117	1	3	yes	—
21	C₂²×C₃₇	#131	1	3	yes	—
22	C₂²×C₃₇	#131	1	1	yes	characteristic
23	C₄×C₃₇	—	4	3	no	—
24	Dic₃₇	—	4	3	no	—
25	Dic₃₇	#126	1	4	yes	—
26	#1840	—	37	1	no	maximal, Sylow
27	C₂×C₃₇	#383	1	1	yes	characteristic
28	C₂×C₃₇	#433	1	3	yes	—
29	C₂×C₃₇	#433	1	3	yes	—
30	#376	—	37	1	no	—
31	#336	—	37	6	no	—
32	C₃₇	#1840	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₈	—	37	4	no	—
34	C₂×C₄²	—	37	3	no	—
35	#95	—	37	3	no	—
36	#95	#3866	1	1	yes	characteristic
37	C₂²×C₄	—	37	1	no	—
38	C₂²×C₄	—	37	3	no	—
39	C₂²×C₄	C₂×#3866	1	3	yes	—
40	C₂×C₈	—	74	12	no	—
41	C₄²	—	74	6	no	—
42	C₂³	C₂²×#3866	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	37	6	no	—
46	C₂×C₄	—	74	3	no	—
47	C₂×C₄	—	74	3	no	—
48	C₂×C₄	—	74	3	no	—
49	C₈	—	148	4	no	—
50	C₂²	#11924615	1	3	yes	—
51	C₂²	#11924623	1	3	yes	—
52	C₂²	#11924624	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	37	4	no	—
55	C₄	—	148	3	no	—
56	C₂	#14558478	1	1	yes	characteristic
57	C₂	#14558557	1	3	yes	—
58	C₂	#14558558	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#3866
commutator, socle, prime radical	C₂³×C₃₇	C₂²×C₄
Fitting	#95×C₃₇	C₄
cosocle	C₂²×Dic₃₇	C₂³
hypercenter	#95	#3866
hypocenter	C₃₇	#1840
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
32. C₃₇	#1840	semidirect

Maximal subgroups

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

subgroup	index
#14558399	2
#14557378	2
#1840	37