Subgroups — #14546018

Order 2176.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763918	C₂	1	2	yes	maximal, complemented
2	#11763917	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763916	C₂	1	2	yes	maximal, complemented
4	C₂×#10587528	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763868	C₂	1	1	yes	maximal, characteristic
6	#10587593	C₄	1	1	yes	characteristic
7	#10587538	C₄	1	1	yes	characteristic
8	C₂×#63216	C₂²	1	1	yes	characteristic
9	#10587530	C₄	1	2	yes	—
10	#10587529	C₂²	1	2	yes	—
11	#10587528	C₂²	1	1	yes	characteristic
12	#10587528	C₂²	1	1	yes	characteristic
13	#10587528	C₂²	1	2	yes	—
14	#63252	C₈	1	1	yes	characteristic
15	M₁₆×C₁₇	C₈	1	1	yes	characteristic
16	C₂×#3622	C₂×C₄	1	1	yes	characteristic
17	#63218	C₈	1	2	yes	—
18	C₈×D₁₇	C₂×C₄	1	2	yes	—
19	#63216	C₂×C₄	1	2	yes	—
20	#63216	C₂×C₄	1	1	yes	characteristic
21	#63216	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₁₇	C₁₆	1	2	yes	—
24	D₆₈	C₁₆	1	1	yes	characteristic
25	C₄×D₁₇	C₂×C₈	1	2	yes	—
26	Dic₃₄	C₁₆	1	1	yes	characteristic
27	C₈×C₁₇	C₂×C₈	1	2	yes	—
28	#3622	C₂×C₈	1	1	yes	characteristic
29	#3622	C₂²×C₄	1	1	yes	characteristic
30	#2258	—	17	1	no	maximal, Sylow
31	C₂²×C₁₇	C₂×C₁₆	1	1	yes	characteristic
32	C₂×D₁₇	C₂×C₁₆	1	2	yes	—
33	C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
34	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
35	Dic₁₇	C₂×C₁₆	1	2	yes	—
36	#504	—	17	1	no	—
37	M₆₄	—	17	1	no	—
38	M₆₄	—	17	2	no	—
39	C₂×C₃₂	—	17	1	no	—
40	C₂×C₃₂	—	17	2	no	—
41	C₂×C₁₇	—	2	1	no	—
42	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
43	D₁₇	—	2	2	no	—
44	#131	—	17	1	no	—
45	M₃₂	—	17	2	no	—
46	M₃₂	—	17	1	no	—
47	C₂×C₁₆	—	17	2	no	—
48	C₂×C₁₆	—	17	1	no	—
49	C₃₂	—	17	1	no	—
50	C₃₂	—	17	1	no	—
51	C₃₂	—	17	2	no	—
52	C₁₇	#2258	1	1	yes	characteristic, complemented, Sylow
53	#41	—	17	1	no	—
54	M₁₆	—	17	2	no	—
55	M₁₆	#3633	1	1	yes	characteristic
56	C₂×C₈	—	17	1	no	—
57	C₂×C₈	—	17	2	no	—
58	C₁₆	—	17	1	no	—
59	C₁₆	—	17	2	no	—
60	C₁₆	—	17	1	no	—
61	Q₈	—	17	1	no	—
62	D₄	—	17	2	no	—
63	D₄	—	17	1	no	—
64	C₂×C₄	—	17	2	no	—
65	C₂×C₄	C₂×#3633	1	1	yes	characteristic
66	C₈	—	17	1	no	—
67	C₈	—	17	1	no	—
68	C₈	C₂×#3633	1	2	yes	—
69	C₂²	—	17	2	no	—
70	C₂²	#10587665	1	1	yes	characteristic
71	C₄	—	17	2	no	—
72	C₄	#10587665	1	1	yes	characteristic
73	C₄	C₂²×#3633	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	34	2	no	—
76	C₂	C₂×#10587665	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×#3633
commutator, socle	C₂×C₁₇	C₂²×C₁₆
Fitting	M₁₆×C₁₇	C₈
prime radical	#63252	C₈
cosocle	#63216	C₂³
hypercenter	M₁₆	#3633
hypocenter	C₁₇	#2258
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #11763918	C₂	semidirect
2. #11763917	C₂	semidirect
3. #11763916	C₂	semidirect
4. C₂×#10587528	C₂	semidirect
52. C₁₇	#2258	semidirect

Maximal subgroups

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

subgroup	index
#11763918	2
#11763917	2
#11763916	2
C₂×#10587528	2
#11763868	2
#2258	17