Subgroups — C₂×#11763917 #14546014

Order 2176.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763917	C₂	1	4	yes	maximal, direct product factor
2	C₂×#10587528	C₂	1	2	yes	maximal, complemented
3	C₂²×#63216	C₂	1	1	yes	maximal, characteristic
4	C₂²×#3622	C₄	1	1	yes	characteristic
5	C₂×#63216	C₄	1	2	yes	—
6	C₂×#63216	C₄	1	1	yes	characteristic
7	C₂×#63216	C₂²	1	1	yes	characteristic
8	C₂×#63216	C₂²	1	2	yes	—
9	#10587528	C₂²	1	4	yes	complemented
10	C₂²×C₄×C₁₇	C₈	1	1	yes	characteristic
11	C₂×#3622	C₈	1	2	yes	—
12	C₂×#3622	C₈	1	1	yes	characteristic
13	C₂×#3622	C₂×C₄	1	2	yes	—
14	C₂×#3622	C₂×C₄	1	1	yes	characteristic
15	#63216	C₂×C₄	1	1	yes	characteristic
16	#63216	C₂×C₄	1	2	yes	—
17	#63216	C₂³	1	1	yes	characteristic
18	C₂³×C₁₇	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₇	C₁₆	1	2	yes	—
20	C₂×C₄×C₁₇	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
22	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
23	#3622	C₂×C₈	1	2	yes	—
24	#3622	C₂×C₈	1	1	yes	characteristic
25	#3622	C₂²×C₄	1	1	yes	characteristic
26	C₂×M₆₄	—	17	1	no	maximal, Sylow
27	C₂²×C₁₇	—	2	2	no	—
28	C₂²×C₁₇	C₂×C₁₆	1	2	yes	—
29	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
30	C₄×C₁₇	C₂×C₁₆	1	2	yes	—
31	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
33	C₂²×C₁₆	—	17	1	no	—
34	M₆₄	—	17	4	no	—
35	C₂×C₃₂	—	17	2	no	—
36	C₂×C₁₇	—	2	2	no	—
37	C₂×C₁₇	M₆₄	1	2	yes	complemented
38	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
39	C₂²×C₈	—	17	1	no	—
40	C₂×C₁₆	—	17	1	no	—
41	C₂×C₁₆	—	17	2	no	—
42	C₂×C₁₆	—	17	2	no	—
43	C₂×C₁₆	—	17	1	no	—
44	C₃₂	—	17	4	no	—
45	C₁₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₄	#3633	1	1	yes	characteristic
47	C₂×C₈	—	17	2	no	—
48	C₂×C₈	—	17	2	no	—
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	17	1	no	—
51	C₁₆	—	17	1	no	—
52	C₁₆	—	17	1	no	—
53	C₁₆	—	17	2	no	—
54	C₂³	#63241	1	1	yes	characteristic
55	C₂×C₄	#63241	1	1	yes	characteristic
56	C₂×C₄	#63241	1	2	yes	—
57	C₂×C₄	C₂×#3633	1	2	yes	—
58	C₂×C₄	C₂×#3633	1	1	yes	characteristic
59	C₈	—	17	1	no	—
60	C₈	—	17	2	no	—
61	C₈	—	17	1	no	—
62	C₂²	—	2	2	no	—
63	C₂²	C₂×#63241	1	2	yes	—
64	C₂²	C₂×#63241	1	1	yes	characteristic
65	C₄	C₂×#63241	1	2	yes	—
66	C₄	C₂×#63241	1	1	yes	characteristic
67	C₄	C₂²×#3633	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	#11763917	1	2	yes	direct product factor
70	C₂	C₂²×#63241	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#3633
commutator	C₂×C₁₇	C₂²×C₁₆
Frattini	C₄	C₂²×#3633
Fitting	C₂²×C₄×C₁₇	C₈
socle	C₂²×C₁₇	C₂×C₁₆
prime radical	C₂³×C₁₇	C₁₆
cosocle	#63216	C₂³
hypercenter	C₂²×C₄	#3633
hypocenter	C₁₇	C₂×M₆₄
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #11763917	C₂	direct (N × H)
2. C₂×#10587528	C₂	semidirect
9. #10587528	C₂²	semidirect
37. C₂×C₁₇	M₆₄	semidirect
45. C₁₇	C₂×M₆₄	semidirect
69. C₂	#11763917	direct (N × H)

Maximal subgroups

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

subgroup	index
#11763917	2
C₂×#10587528	2
C₂²×#63216	2
C₂×M₆₄	17

Subgroups — C2×#11763917 #14546014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763917 #14546014