Subgroups — #14558612

Order 2368.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924624	C₂	1	2	yes	maximal, complemented
2	#11924623	C₂	1	6	yes	maximal, complemented
3	C₂×#10596953	C₂	1	3	yes	maximal, complemented
4	D₃₇⋊M₁₆	C₂	1	3	yes	maximal, complemented
5	#41×D₃₇	C₂	1	1	yes	maximal, characteristic
6	#41×C₃₇	C₄	1	1	yes	characteristic
7	#10596966	C₂²	1	1	yes	characteristic
8	Q₈×D₃₇	C₄	1	1	yes	characteristic
9	#10596964	C₂²	1	3	yes	—
10	D₄×D₃₇	C₄	1	3	yes	—
11	#10596962	C₄	1	3	yes	—
12	C₂×C₄×D₃₇	C₂²	1	3	yes	—
13	#10596957	C₂²	1	6	yes	complemented
14	C₂×#64438	C₂²	1	6	yes	complemented
15	#10596953	C₂²	1	1	yes	characteristic
16	#10596953	C₂²	1	3	yes	—
17	#10596953	C₂²	1	6	yes	complemented
18	D₃₇⋊C₈	C₂²	1	6	yes	complemented
19	C₂²×D₃₇	C₂×C₄	1	3	yes	—
20	Q₈×C₃₇	C₂×C₄	1	1	yes	characteristic
21	D₄×C₃₇	C₂×C₄	1	3	yes	—
22	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
23	C₂²⋊D₃₇	C₂×C₄	1	6	yes	—
24	C₂×Dic₃₇	C₂³	1	3	yes	—
25	D₁₄₈	C₂×C₄	1	3	yes	—
26	C₄×D₃₇	C₂×C₄	1	3	yes	—
27	C₄×D₃₇	C₂×C₄	1	3	yes	—
28	C₄×D₃₇	C₂³	1	3	yes	—
29	C₄×D₃₇	C₂³	1	1	yes	characteristic
30	Dic₇₄	C₂×C₄	1	3	yes	—
31	#64438	C₂³	1	2	yes	—
32	#64438	C₂³	1	6	yes	—
33	C₂²×C₃₇	C₂²×C₄	1	3	yes	—
34	C₂×D₃₇	—	4	3	no	—
35	C₂×D₃₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₃₇	C₂²×C₄	1	3	yes	—
37	C₄×C₃₇	C₂²×C₄	1	3	yes	—
38	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
39	Dic₃₇	C₂²×C₄	1	3	yes	—
40	Dic₃₇	C₂⁴	1	1	yes	characteristic
41	C₂×C₃₇	—	2	3	no	—
42	C₂×C₃₇	C₂³×C₄	1	1	yes	characteristic
43	D₃₇	—	2	1	no	—
44	D₃₇	—	2	3	no	—
45	#568	—	37	1	no	maximal, Sylow
46	C₃₇	#568	1	1	yes	characteristic, complemented, Sylow
47	C₂×#41	—	37	1	no	—
48	#131	—	37	6	no	—
49	#131	—	37	2	no	—
50	C₂×M₁₆	—	37	3	no	—
51	C₂×M₁₆	—	37	3	no	—
52	#41	—	37	1	no	—
53	#41	—	37	3	no	—
54	#41	—	37	3	no	—
55	#41	#3866	1	1	yes	characteristic
56	C₂×Q₈	—	37	1	no	—
57	C₂×D₄	—	37	3	no	—
58	C₂²×C₄	—	37	3	no	—
59	M₁₆	—	37	1	no	—
60	M₁₆	—	37	3	no	—
61	M₁₆	—	37	6	no	—
62	M₁₆	—	37	6	no	—
63	C₂×C₈	—	37	6	no	—
64	C₂×C₈	—	37	6	no	—
65	C₂³	—	37	3	no	—
66	Q₈	—	37	3	no	—
67	Q₈	C₂×#3866	1	1	yes	characteristic
68	D₄	—	37	6	no	—
69	D₄	—	37	3	no	—
70	D₄	C₂×#3866	1	3	yes	—
71	C₂×C₄	—	37	3	no	—
72	C₂×C₄	—	37	3	no	—
73	C₂×C₄	—	37	1	no	—
74	C₂×C₄	—	37	3	no	—
75	C₂×C₄	—	37	3	no	—
76	C₂×C₄	C₂×#3866	1	3	yes	—
77	C₈	—	37	2	no	—
78	C₈	—	37	6	no	—
79	C₂²	—	37	1	no	—
80	C₂²	—	37	3	no	—
81	C₂²	—	148	3	no	—
82	C₂²	C₂²×#3866	1	3	yes	—
83	C₄	—	37	1	no	—
84	C₄	—	37	3	no	—
85	C₄	C₂²×#3866	1	1	yes	characteristic
86	C₄	C₂²×#3866	1	3	yes	—
87	C₂	—	2	3	no	—
88	C₂	—	74	1	no	—
89	C₂	—	74	3	no	—
90	C₂	C₂³×#3866	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#3866
commutator, socle	C₂×C₃₇	C₂³×C₄
Fitting	#41×C₃₇	C₄
prime radical	#41×D₃₇	C₂
cosocle	Dic₃₇	C₂⁴
hypercenter	#41	#3866
hypocenter	C₃₇	#568
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #11924624	C₂	semidirect
2. #11924623	C₂	semidirect
3. C₂×#10596953	C₂	semidirect
4. D₃₇⋊M₁₆	C₂	semidirect
13. #10596957	C₂²	semidirect
14. C₂×#64438	C₂²	semidirect
17. #10596953	C₂²	semidirect
18. D₃₇⋊C₈	C₂²	semidirect
46. C₃₇	#568	semidirect

Maximal subgroups

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

subgroup	index
#11924624	2
#11924623	2
C₂×#10596953	2
D₃₇⋊M₁₆	2
#41×D₃₇	2
#568	37