Subgroups — C₂×#11924597 #14558517

Order 2368.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596957	C₂	1	2	yes	maximal
2	#11924597	C₂	1	4	yes	maximal, direct product factor
3	C₂²×Dic₇₄	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₇	C₄	1	1	yes	characteristic
5	C₂²×Dic₃₇	C₄	1	1	yes	characteristic
6	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₄	—	2	2	no	—
8	C₂×Dic₇₄	—	2	2	no	—
9	C₂×Dic₇₄	C₄	1	2	yes	—
10	C₂×Dic₇₄	C₂²	1	2	yes	—
11	#10596957	—	2	2	no	—
12	#10596957	C₂²	1	4	yes	—
13	C₂×#64438	—	2	2	no	—
14	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	—	2	1	no	—
16	C₂×C₄×C₃₇	—	2	1	no	—
17	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
18	C₂×Dic₃₇	—	2	1	no	—
19	C₂×Dic₃₇	—	2	1	no	—
20	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
21	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₃₇	D₄	1	2	yes	—
23	C₂×Dic₃₇	D₄	1	2	yes	—
24	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
25	Dic₇₄	—	2	4	no	—
26	Dic₇₄	—	2	4	no	—
27	#64438	—	2	4	no	—
28	C₂²×C₃₇	—	2	2	no	—
29	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₃₇	—	2	2	no	—
33	Dic₃₇	—	2	2	no	—
34	Dic₃₇	C₂²⋊C₄	1	2	yes	—
35	Dic₃₇	C₂×D₄	1	2	yes	—
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	—	2	1	no	—
38	C₂×C₃₇	#101	1	2	yes	complemented
39	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×#101	—	37	1	no	maximal, Sylow
41	C₃₇	C₂×#101	1	1	yes	characteristic, complemented, Sylow
42	C₂²×Q₈	—	37	1	no	—
43	C₂×M₁₆	—	37	2	no	—
44	#101	—	37	4	no	—
45	C₂×Q₈	—	37	2	no	—
46	C₂×Q₈	—	37	2	no	—
47	C₂×Q₈	—	74	2	no	—
48	C₂×Q₈	—	74	2	no	—
49	C₂²×C₄	—	37	1	no	—
50	C₂²×C₄	—	37	1	no	—
51	C₂²×C₄	#3866	1	1	yes	characteristic
52	M₁₆	—	37	4	no	—
53	M₁₆	—	74	2	no	—
54	C₂×C₈	—	74	2	no	—
55	C₂³	C₂×#3866	1	1	yes	characteristic
56	Q₈	—	74	4	no	—
57	Q₈	—	74	4	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	37	2	no	—
61	C₂×C₄	—	37	2	no	—
62	C₂×C₄	—	37	1	no	—
63	C₂×C₄	—	37	1	no	—
64	C₂×C₄	—	37	2	no	—
65	C₂×C₄	—	74	1	no	—
66	C₂×C₄	—	74	1	no	—
67	C₂×C₄	C₂×#3866	1	2	yes	—
68	C₈	—	74	4	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊#3866	1	1	yes	characteristic
71	C₂²	C₂²⋊#3866	1	1	yes	characteristic
72	C₂²	C₂²×#3866	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	37	2	no	—
75	C₄	—	37	2	no	—
76	C₄	—	74	2	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#11924597	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#3866
commutator	C₂²×C₃₇	C₂²×C₄
Frattini	C₂²	C₂²×#3866
Fitting	C₂²×C₄×C₃₇	C₄
socle	C₂²×C₃₇	C₂²⋊C₄
prime radical	C₂³×C₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₂²×C₄	#3866
hypocenter	C₃₇	C₂×#101
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #11924597	C₂	direct (N × H)
38. C₂×C₃₇	#101	semidirect
41. C₃₇	C₂×#101	semidirect
79. C₂	#11924597	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×#10596957	2
#11924597	2
C₂²×Dic₇₄	2
C₂×#101	37

Subgroups — C2×#11924597 #14558517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924597 #14558517