Subgroups — C₂×#14557371 #17996897

Order 4736.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#14557371	C₂	1	4	yes	maximal, direct product factor
3	C₂×#11924442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₁₄₈	—	2	1	no	—
6	Dic₂₉₆	—	2	1	no	—
7	Dic₂₉₆	C₂²	1	2	yes	complemented
8	#11924442	C₂²	1	2	yes	complemented
9	C₂×D₈×C₃₇	—	2	1	no	—
10	D₁₆×C₃₇	—	2	1	no	—
11	D₁₆×C₃₇	C₂²	1	2	yes	—
12	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₃₇	—	4	1	no	—
14	C₂×Dic₇₄	—	4	1	no	—
15	D₈×C₃₇	—	2	2	no	—
16	D₈×C₃₇	—	4	1	no	—
17	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
18	Dic₁₄₈	—	2	2	no	—
19	Dic₁₄₈	—	4	1	no	—
20	C₁₆×C₃₇	D₄	1	1	yes	characteristic
21	C₁₆×C₃₇	C₂³	1	1	yes	characteristic
22	C₂³×C₃₇	—	8	1	no	—
23	D₄×C₃₇	—	4	2	no	—
24	D₄×C₃₇	—	8	1	no	—
25	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
26	C₂×Dic₃₇	—	8	1	no	—
27	Dic₇₄	—	4	2	no	—
28	Dic₇₄	—	8	1	no	—
29	C₈×C₃₇	D₈	1	1	yes	characteristic
30	C₈×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₃₇	—	8	2	no	—
32	C₂²×C₃₇	—	16	2	no	—
33	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
34	C₄×C₃₇	D₁₆	1	1	yes	characteristic
35	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
36	Dic₃₇	—	8	2	no	—
37	C₂×SD₆₄	—	37	1	no	maximal, Sylow
38	C₂×C₃₇	—	16	2	no	—
39	C₂×C₃₇	SD₆₄	1	2	yes	complemented
40	C₂×C₃₇	C₂×D₁₆	1	1	yes	characteristic
41	C₂×Q₃₂	—	37	1	no	—
42	C₂×D₁₆	D₃₇	1	1	yes	characteristic
43	SD₆₄	—	37	4	no	—
44	C₂×C₃₂	—	37	1	no	—
45	C₃₇	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	74	1	no	—
47	C₂×D₈	—	2	1	no	—
48	Q₃₂	—	37	2	no	—
49	Q₃₂	—	74	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	C₂×D₃₇	1	2	yes	—
52	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
53	C₃₂	—	37	2	no	—
54	C₂×Q₈	—	148	1	no	—
55	C₂×D₄	—	4	1	no	—
56	Q₁₆	—	74	2	no	—
57	Q₁₆	—	148	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
62	C₁₆	C₂²×D₃₇	1	1	yes	characteristic
63	C₂³	—	8	1	no	—
64	Q₈	—	296	1	no	—
65	Q₈	—	148	2	no	—
66	D₄	—	4	2	no	—
67	D₄	—	8	1	no	—
68	C₂×C₄	—	296	1	no	—
69	C₂×C₄	#10596939	1	1	yes	characteristic
70	C₈	#10596939	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
72	C₂²	—	8	2	no	—
73	C₂²	—	16	2	no	—
74	C₂²	#11924477	1	1	yes	characteristic
75	C₄	—	296	2	no	—
76	C₄	#11924477	1	1	yes	characteristic
77	C₄	C₂×#10596939	1	1	yes	characteristic
78	C₂	—	16	2	no	—
79	C₂	#14557371	1	2	yes	direct product factor
80	C₂	C₂×#11924477	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924477
commutator, cosocle	C₁₆×C₃₇	C₂³
Frattini	C₁₆	C₂²×D₃₇
Fitting, prime radical	C₂×D₁₆×C₃₇	C₂
socle	C₂²×C₃₇	D₁₆
hypercenter	C₂×D₁₆	D₃₇
hypocenter	C₃₇	C₂×SD₆₄
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₂₉₆	C₂	semidirect
2. #14557371	C₂	direct (N × H)
3. C₂×#11924442	C₂	semidirect
7. Dic₂₉₆	C₂²	semidirect
8. #11924442	C₂²	semidirect
39. C₂×C₃₇	SD₆₄	semidirect
45. C₃₇	C₂×SD₆₄	semidirect
79. C₂	#14557371	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×Dic₂₉₆	2
#14557371	2
C₂×#11924442	2
C₂×D₁₆×C₃₇	2
C₂×SD₆₄	37

Subgroups — C2×#14557371 #17996897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557371 #17996897