Subgroups — #18009809

Order 4736.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558549	C₂	1	2	yes	maximal
2	#64438⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#64438	C₄	1	4	yes	—
5	C₂²⋊#64438	C₄	1	4	yes	—
6	C₄×#64438	C₂²	1	4	yes	—
7	C₂²×#64436	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₃₇	C₂²	1	1	yes	characteristic
9	C₈×Dic₃₇	C₄	1	2	yes	—
10	C₈×Dic₃₇	C₂²	1	2	yes	—
11	C₂²×C₈×C₃₇	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₃₇	C₂×C₄	1	2	yes	—
14	C₂×#64438	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₃₇	—	2	2	no	—
16	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
17	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
19	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
20	C₂×#64436	—	2	2	no	—
21	C₂×#64436	C₂×C₄	1	2	yes	—
22	C₂³×C₃₇	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
25	C₂×C₄×C₃₇	M₁₆	1	2	yes	—
26	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×Dic₃₇	—	2	4	no	—
28	C₂×Dic₃₇	C₄²	1	2	yes	—
29	C₂×Dic₃₇	C₂²×C₄	1	2	yes	—
30	#64438	—	2	8	no	—
31	C₈×C₃₇	—	2	2	no	—
32	#64436	—	2	2	no	—
33	C₂²×C₃₇	—	2	2	no	—
34	C₂²×C₃₇	#97	1	2	yes	—
35	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₃₇	#97	1	2	yes	—
37	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
38	C₄×C₃₇	C₂×M₁₆	1	1	yes	characteristic
39	Dic₃₇	—	2	2	no	—
40	Dic₃₇	#131	1	4	yes	—
41	#1452	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	—	2	2	no	—
43	C₂×C₃₇	C₂×#97	1	1	yes	characteristic
44	C₂×C₃₇	#405	1	2	yes	—
45	#431	—	37	2	no	—
46	C₂×C₄×C₈	—	37	1	no	—
47	#322	—	37	4	no	—
48	C₃₇	#1452	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₈	—	37	1	no	—
50	C₂²×C₈	#3866	1	1	yes	characteristic
51	C₂×C₄²	—	37	1	no	—
52	C₄⋊C₈	—	37	4	no	—
53	C₂²⋊C₈	—	37	4	no	—
54	C₄×C₈	—	37	4	no	—
55	C₄×C₈	—	37	2	no	—
56	C₄×C₈	—	37	2	no	—
57	C₂²×C₄	—	37	2	no	—
58	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	—	37	8	no	—
61	C₂×C₈	—	37	2	no	—
62	C₂×C₈	—	74	2	no	—
63	C₂×C₈	C₂×#3866	1	2	yes	—
64	C₄²	—	37	2	no	—
65	C₄²	—	37	1	no	—
66	C₄²	—	37	1	no	—
67	C₂³	C₄×#3866	1	1	yes	characteristic
68	C₂×C₄	—	37	2	no	—
69	C₂×C₄	—	37	2	no	—
70	C₂×C₄	—	74	4	no	—
71	C₂×C₄	#10596953	1	2	yes	—
72	C₂×C₄	C₄×#3866	1	1	yes	characteristic
73	C₂×C₄	#10596957	1	2	yes	—
74	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	74	8	no	—
77	C₈	—	74	2	no	—
78	C₂²	—	2	2	no	—
79	C₂²	#11924591	1	2	yes	—
80	C₂²	C₂×C₄×#3866	1	1	yes	characteristic
81	C₄	—	37	4	no	—
82	C₄	—	74	2	no	—
83	C₄	#11924591	1	2	yes	—
84	C₄	C₂×#10596957	1	1	yes	characteristic
85	C₄	C₂×#10596953	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₂×#11924591	1	1	yes	characteristic
88	C₂	#14558496	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#3866
commutator, socle	C₂²×C₃₇	C₂×C₄²
Fitting	C₂²×C₈×C₃₇	C₄
prime radical	C₂³×C₃₇	C₄²
cosocle	C₄×Dic₃₇	C₂³
hypercenter	C₂²×C₈	#3866
hypocenter	C₃₇	#1452
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #64438⋊C₈	C₂	semidirect
48. C₃₇	#1452	semidirect

Maximal subgroups

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

subgroup	index
#14558549	2
#64438⋊C₈	2
C₂×C₈×Dic₃₇	2
#1452	37