Subgroups — C₂×#11924479 #14557956

Order 2368.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₉₆	C₂	1	1	yes	maximal, characteristic
2	#11924479	C₂	1	4	yes	maximal, direct product factor
3	C₂×#10596925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₃₇	—	2	1	no	—
6	C₂×D₁₄₈	—	2	1	no	—
7	Q₁₆×C₃₇	—	2	1	no	—
8	Q₁₆×C₃₇	C₂²	1	2	yes	complemented
9	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	D₂₉₆	—	2	1	no	—
11	D₂₉₆	C₂²	1	2	yes	—
12	#10596925	C₂²	1	2	yes	complemented
13	C₂²×D₃₇	—	4	1	no	—
14	Q₈×C₃₇	—	2	2	no	—
15	Q₈×C₃₇	—	4	1	no	—
16	C₂×C₄×C₃₇	—	4	1	no	—
17	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
18	D₁₄₈	—	2	2	no	—
19	D₁₄₈	—	4	1	no	—
20	C₈×C₃₇	D₄	1	1	yes	characteristic
21	C₈×C₃₇	C₂³	1	1	yes	characteristic
22	C₂²×C₃₇	D₈	1	1	yes	characteristic
23	C₂×D₃₇	—	4	2	no	—
24	C₂×D₃₇	—	8	2	no	—
25	C₄×C₃₇	—	4	2	no	—
26	C₄×C₃₇	D₈	1	1	yes	characteristic
27	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃₇	SD₃₂	1	2	yes	complemented
29	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
30	D₃₇	—	8	2	no	—
31	C₂×SD₃₂	—	37	1	no	maximal, Sylow
32	C₃₇	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
33	C₂×Q₁₆	D₃₇	1	1	yes	characteristic, complemented
34	C₂×D₈	—	37	1	no	—
35	SD₃₂	—	37	4	no	—
36	C₂×C₁₆	—	37	1	no	—
37	C₂×Q₈	—	2	1	no	—
38	C₂×D₄	—	74	1	no	—
39	Q₁₆	—	2	1	no	—
40	Q₁₆	C₂×D₃₇	1	2	yes	complemented
41	D₈	—	37	2	no	—
42	D₈	—	74	1	no	—
43	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
44	C₁₆	—	37	2	no	—
45	C₂³	—	148	1	no	—
46	Q₈	—	2	2	no	—
47	Q₈	—	4	1	no	—
48	D₄	—	74	2	no	—
49	D₄	—	148	1	no	—
50	C₂×C₄	—	4	1	no	—
51	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
52	C₈	C₂²⋊D₃₇	1	1	yes	characteristic
53	C₈	C₂²×D₃₇	1	1	yes	characteristic
54	C₂²	—	296	2	no	—
55	C₂²	—	148	2	no	—
56	C₂²	#10596939	1	1	yes	characteristic
57	C₄	—	4	2	no	—
58	C₄	#10596939	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
60	C₂	—	296	2	no	—
61	C₂	#11924479	1	2	yes	direct product factor
62	C₂	C₂×#10596939	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10596939
commutator, cosocle	C₈×C₃₇	C₂³
Frattini	C₈	C₂²×D₃₇
Fitting	C₂×Q₁₆×C₃₇	C₂
socle	C₂²×C₃₇	D₈
prime radical	C₂×D₂₉₆	C₂
hypercenter	C₂×Q₁₆	D₃₇
hypocenter	C₃₇	C₂×SD₃₂
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #11924479	C₂	direct (N × H)
3. C₂×#10596925	C₂	semidirect
4. C₂×Q₁₆×C₃₇	C₂	semidirect
8. Q₁₆×C₃₇	C₂²	semidirect
12. #10596925	C₂²	semidirect
28. C₂×C₃₇	SD₃₂	semidirect
32. C₃₇	C₂×SD₃₂	semidirect
33. C₂×Q₁₆	D₃₇	semidirect
40. Q₁₆	C₂×D₃₇	semidirect
61. C₂	#11924479	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×D₂₉₆	2
#11924479	2
C₂×#10596925	2
C₂×Q₁₆×C₃₇	2
C₂×SD₃₂	37

Subgroups — C2×#11924479 #14557956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924479 #14557956