Subgroups — C₂×#11924525 #14558051

Order 2368.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₄₈	C₂	1	1	yes	maximal, characteristic
2	#11924525	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10596938	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×Dic₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₃₇	C₂²	1	2	yes	—
7	C₂×Q₈×C₃₇	—	2	4	no	—
8	C₂×Q₈×C₃₇	C₂²	1	4	yes	complemented
9	C₂²×C₄×C₃₇	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₇	C₂²	1	2	yes	—
12	C₂×D₁₄₈	—	2	4	no	—
13	C₂×D₁₄₈	C₂²	1	4	yes	—
14	#10596938	C₂²	1	16	yes	complemented
15	C₄×Dic₃₇	C₂²	1	4	yes	complemented
16	C₂³×C₃₇	C₂³	1	1	yes	characteristic
17	C₂²×D₃₇	—	2	4	no	—
18	C₂²×D₃₇	—	2	8	no	—
19	C₂²×D₃₇	C₂³	1	4	yes	—
20	Q₈×C₃₇	—	2	8	no	—
21	C₂×C₄×C₃₇	—	2	4	no	—
22	C₂×C₄×C₃₇	D₄	1	4	yes	—
23	C₂×C₄×C₃₇	C₂³	1	4	yes	—
24	C₂×C₄×C₃₇	C₂³	1	2	yes	—
25	C₂×Dic₃₇	—	2	4	no	—
26	C₂×Dic₃₇	C₂³	1	4	yes	—
27	D₁₄₈	—	2	8	no	—
28	C₂²×C₃₇	C₂×D₄	1	2	yes	—
29	C₂²×C₃₇	#41	1	4	yes	—
30	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
31	C₂×D₃₇	—	2	4	no	—
32	C₂×D₃₇	—	2	8	no	—
33	C₂×D₃₇	—	4	8	no	—
34	C₄×C₃₇	—	2	4	no	—
35	C₄×C₃₇	C₂×D₄	1	4	yes	—
36	Dic₃₇	—	2	4	no	—
37	C₂×C₃₇	#124	1	4	yes	complemented
38	C₂×C₃₇	C₂²×D₄	1	1	yes	characteristic
39	C₂×C₃₇	C₂×#41	1	2	yes	—
40	D₃₇	—	4	4	no	—
41	C₂×#124	—	37	1	no	maximal, Sylow
42	C₃₇	C₂×#124	1	1	yes	characteristic, complemented, Sylow
43	C₂²×Q₈	D₃₇	1	1	yes	characteristic, complemented
44	C₂²×D₄	—	37	1	no	—
45	#124	—	37	8	no	—
46	C₂×C₂²⋊C₄	—	37	4	no	—
47	C₂×C₄²	—	37	1	no	—
48	C₂⁴	—	37	2	no	—
49	C₂×Q₈	—	2	4	no	—
50	C₂×Q₈	C₂×D₃₇	1	4	yes	complemented
51	C₂×D₄	—	37	4	no	—
52	C₂×D₄	—	74	4	no	—
53	C₂²×C₄	—	37	2	no	—
54	C₂²×C₄	C₂×D₃₇	1	2	yes	—
55	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
56	C₂²⋊C₄	—	37	16	no	—
57	C₄²	—	37	4	no	—
58	C₂³	—	37	4	no	—
59	C₂³	—	74	8	no	—
60	C₂³	—	74	4	no	—
61	C₂³	C₂²×D₃₇	1	1	yes	characteristic
62	Q₈	—	2	8	no	—
63	D₄	—	74	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	37	4	no	—
66	C₂×C₄	—	74	4	no	—
67	C₂×C₄	C₂²⋊D₃₇	1	4	yes	—
68	C₂×C₄	C₂²×D₃₇	1	4	yes	—
69	C₂×C₄	C₂²×D₃₇	1	2	yes	—
70	C₂²	—	74	4	no	—
71	C₂²	—	74	8	no	—
72	C₂²	—	148	8	no	—
73	C₂²	#10596966	1	4	yes	—
74	C₂²	C₂×C₂²⋊D₃₇	1	2	yes	—
75	C₂²	C₂³×D₃₇	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	74	4	no	—
78	C₄	C₂×C₂²⋊D₃₇	1	4	yes	—
79	C₂	—	148	4	no	—
80	C₂	#11924525	1	4	yes	direct product factor
81	C₂	C₂²×C₂²⋊D₃₇	1	1	yes	characteristic
82	C₂	C₂×#10596966	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₃₇
commutator, cosocle	C₂²×C₃₇	C₂⁴
Frattini	C₂²	C₂³×D₃₇
Fitting	C₂²×Q₈×C₃₇	C₂
socle	C₂³×C₃₇	C₂³
prime radical	C₂²×D₁₄₈	C₂
hypercenter	C₂²×Q₈	D₃₇
hypocenter	C₃₇	C₂×#124
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
2. #11924525	C₂	direct (N × H)
3. C₂×#10596938	C₂	semidirect
4. C₂×C₄×Dic₃₇	C₂	semidirect
5. C₂²×Q₈×C₃₇	C₂	semidirect
8. C₂×Q₈×C₃₇	C₂²	semidirect
14. #10596938	C₂²	semidirect
15. C₄×Dic₃₇	C₂²	semidirect
37. C₂×C₃₇	#124	semidirect
42. C₃₇	C₂×#124	semidirect
43. C₂²×Q₈	D₃₇	semidirect
50. C₂×Q₈	C₂×D₃₇	semidirect
80. C₂	#11924525	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₄₈	2
#11924525	2
C₂×#10596938	2
C₂×C₄×Dic₃₇	2
C₂²×Q₈×C₃₇	2
C₂×#124	37

Subgroups — C2×#11924525 #14558051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924525 #14558051