Subgroups — C₄×#10596953 #14558495

Order 2368.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596953	C₂	1	2	yes	maximal
2	#11924591	C₂	1	2	yes	maximal, complemented
3	C₄×#64438	C₂	1	2	yes	maximal, complemented
4	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×D₃₇	C₄	1	1	yes	characteristic
6	C₂×C₄×D₃₇	C₄	1	1	yes	characteristic
7	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
8	C₂×#64438	C₂²	1	4	yes	—
9	#10596953	C₄	1	8	yes	direct product factor
10	C₄²×C₃₇	C₄	1	1	yes	characteristic
11	C₄×Dic₃₇	C₄	1	1	yes	characteristic
12	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
14	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
21	C₄×D₃₇	—	2	2	no	—
22	C₄×D₃₇	—	2	2	no	—
23	C₄×D₃₇	C₂×C₄	1	4	yes	—
24	#64438	C₂×C₄	1	8	yes	complemented
25	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₃₇	—	2	1	no	—
27	C₂×D₃₇	—	2	1	no	—
28	C₂×D₃₇	C₄²	1	2	yes	—
29	C₄×C₃₇	—	2	1	no	—
30	C₄×C₃₇	C₄²	1	2	yes	—
31	C₄×C₃₇	M₁₆	1	2	yes	complemented
32	Dic₃₇	—	2	1	no	—
33	Dic₃₇	M₁₆	1	2	yes	complemented
34	Dic₃₇	C₂²×C₄	1	2	yes	—
35	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₃₇	C₂×M₁₆	1	1	yes	characteristic
38	D₃₇	—	2	2	no	—
39	C₄×M₁₆	—	37	1	no	maximal, Sylow
40	C₃₇	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	37	2	no	—
42	C₂×C₄²	—	37	1	no	—
43	#97	—	37	2	no	—
44	C₄×C₈	—	37	2	no	—
45	C₂²×C₄	—	37	1	no	—
46	C₂²×C₄	—	37	1	no	—
47	C₂²×C₄	—	37	1	no	—
48	M₁₆	—	37	8	no	—
49	C₂×C₈	—	37	4	no	—
50	C₄²	—	37	1	no	—
51	C₄²	—	37	1	no	—
52	C₄²	—	37	1	no	—
53	C₄²	#3866	1	1	yes	characteristic
54	C₂³	—	37	1	no	—
55	C₂×C₄	—	37	1	no	—
56	C₂×C₄	—	37	1	no	—
57	C₂×C₄	—	37	4	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	74	2	no	—
60	C₂×C₄	—	74	2	no	—
61	C₂×C₄	C₂×#3866	1	1	yes	characteristic
62	C₂×C₄	C₂×#3866	1	1	yes	characteristic
63	C₂×C₄	C₂×#3866	1	1	yes	characteristic
64	C₈	—	37	8	no	—
65	C₂²	—	37	2	no	—
66	C₂²	—	74	1	no	—
67	C₂²	—	74	1	no	—
68	C₂²	C₂²×#3866	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	37	2	no	—
71	C₄	—	37	2	no	—
72	C₄	—	74	1	no	—
73	C₄	#10596953	1	2	yes	direct product factor
74	C₄	C₄×#3866	1	2	yes	—
75	C₂	—	74	2	no	—
76	C₂	C₂×C₄×#3866	1	1	yes	characteristic
77	C₂	D₃₇⋊M₁₆	1	1	yes	characteristic
78	C₂	C₂×#10596953	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#3866
commutator	C₂×C₃₇	C₂×C₄²
Frattini	C₂²	C₂²×#3866
Fitting	C₄²×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₄²	#3866
hypocenter	C₃₇	C₄×M₁₆
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #11924591	C₂	semidirect
3. C₄×#64438	C₂	semidirect
9. #10596953	C₄	direct (N × H)
24. #64438	C₂×C₄	semidirect
31. C₄×C₃₇	M₁₆	semidirect
33. Dic₃₇	M₁₆	semidirect
40. C₃₇	C₄×M₁₆	semidirect
73. C₄	#10596953	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10596953	2
#11924591	2
C₄×#64438	2
C₄²×D₃₇	2
C₄×M₁₆	37

Subgroups — C4×#10596953 #14558495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10596953 #14558495