Subgroups — #18009643

Order 4736.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924610	C₂	1	2	yes	maximal
2	C₂×#11924447	C₂	1	1	yes	maximal, characteristic
3	#11924610	—	2	2	no	—
4	#11924610	C₄	1	4	yes	complemented
5	C₂×#10596927	—	2	2	no	—
6	C₂²×#64436	C₄	1	1	yes	characteristic
7	C₂²×#64436	C₂²	1	1	yes	characteristic
8	#11924447	—	2	2	no	—
9	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₃₇	C₈	1	2	yes	—
11	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₄²×C₃₇	—	2	1	no	—
13	C₄²×C₃₇	—	2	1	no	—
14	C₂×#64436	—	2	1	no	—
15	C₂×#64436	—	2	1	no	—
16	C₂×#64436	C₈	1	2	yes	—
17	C₂×#64436	C₂×C₄	1	2	yes	—
18	C₂×#64436	D₄	1	1	yes	characteristic
19	C₂×#64436	D₄	1	2	yes	—
20	C₂×#64436	Q₈	1	1	yes	characteristic
21	#10596927	—	2	4	no	—
22	C₂³×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₃₇	—	2	2	no	—
24	C₂×C₄×C₃₇	—	4	2	no	—
25	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
31	#64436	—	2	2	no	—
32	#64436	C₂²⋊C₄	1	2	yes	—
33	#64436	C₄⋊C₄	1	2	yes	—
34	C₂²×C₃₇	—	2	2	no	—
35	C₂²×C₃₇	C₄×C₈	1	1	yes	characteristic
36	C₂²×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₃₇	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₃₇	—	4	2	no	—
39	C₄×C₃₇	#95	1	1	yes	characteristic
40	C₄×C₃₇	#97	1	1	yes	characteristic
41	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
43	#1377	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	1	no	—
45	C₂×C₃₇	—	2	1	no	—
46	C₂×C₃₇	#336	1	1	yes	characteristic
47	C₂×C₃₇	#349	1	2	yes	—
48	C₂×M₃₂	—	37	2	no	—
49	C₂×#97	—	37	1	no	—
50	C₃₇	#1377	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₈	—	37	1	no	—
52	C₂²×C₈	—	37	1	no	—
53	C₂×C₄²	#3866	1	1	yes	characteristic
54	M₃₂	—	37	4	no	—
55	M₃₂	—	74	2	no	—
56	C₂×C₁₆	—	74	2	no	—
57	#97	—	74	2	no	—
58	C₂²×C₄	#64438	1	2	yes	—
59	C₂²×C₄	C₂×#3866	1	1	yes	characteristic
60	C₂×C₈	—	37	2	no	—
61	C₂×C₈	—	37	1	no	—
62	C₂×C₈	—	37	1	no	—
63	C₂×C₈	—	37	2	no	—
64	C₂×C₈	—	37	2	no	—
65	C₂×C₈	—	74	1	no	—
66	C₂×C₈	—	74	1	no	—
67	C₄²	—	2	1	no	—
68	C₄²	—	2	1	no	—
69	C₁₆	—	74	4	no	—
70	C₂³	C₂×#64438	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
74	C₂×C₄	#10596953	1	1	yes	characteristic
75	C₂×C₄	C₄×#3866	1	1	yes	characteristic
76	C₂×C₄	C₄⋊#3866	1	1	yes	characteristic
77	C₂×C₄	#10596957	1	1	yes	characteristic
78	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
79	C₈	—	37	2	no	—
80	C₈	—	37	2	no	—
81	C₈	—	74	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄×#64438	1	1	yes	characteristic
84	C₂²	C₂²⋊#64438	1	1	yes	characteristic
85	C₂²	C₄⋊#64438	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	(C₂×#3866)⋊C₄	1	1	yes	characteristic
88	C₄	#11924591	1	1	yes	characteristic
89	C₄	#11924593	1	1	yes	characteristic
90	C₄	#11924603	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#14558399	1	1	yes	characteristic
94	C₂	#14558429	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#3866
commutator	C₂²×C₃₇	C₄×C₈
Frattini	C₂²×C₄	C₂×#3866
Fitting	C₂×C₄²×C₃₇	C₄
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂³×C₃₇	C₂×C₈
cosocle	C₂²×#64436	C₂²
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	#1377
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. #11924610	C₄	semidirect
50. C₃₇	#1377	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924610	2
C₂×#11924447	2
#1377	37