Subgroups — #14531077

Order 2176.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763225	C₂	1	1	yes	maximal, characteristic
2	#11762643	C₂	1	1	yes	maximal, characteristic, complemented
3	#11762642	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	#10587587	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	#10587483	C₄	1	1	yes	characteristic
9	#10587469	C₄	1	2	yes	—
10	C₁₆×D₁₇	C₂²	1	2	yes	—
11	C₁₇×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₇×C₃₂	C₂²	1	1	yes	characteristic
13	#10587465	C₂²	1	2	yes	—
14	#63252	C₈	1	1	yes	characteristic
15	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
16	#63223	C₈	1	1	yes	characteristic
17	#63218	C₈	1	2	yes	—
18	C₈×D₁₇	C₂×C₄	1	2	yes	—
19	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₁₇	C₂³	1	1	yes	characteristic
21	#63214	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
28	C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	#3622	C₂×C₈	1	2	yes	—
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	2	no	—
40	C₂×C₃₂	D₁₇	1	1	yes	characteristic, complemented
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	1	no	—
46	M₃₂	—	17	2	no	—
47	C₂×C₁₆	—	17	2	no	—
48	C₂×C₁₆	C₂×D₁₇	1	1	yes	characteristic
49	C₃₂	—	17	2	no	—
50	C₃₂	C₂×D₁₇	1	1	yes	characteristic
51	C₃₂	C₂×D₁₇	1	1	yes	characteristic
52	C₁₇	#2258	1	1	yes	characteristic, complemented, Sylow
53	#41	—	17	1	no	—
54	M₁₆	—	17	1	no	—
55	M₁₆	—	17	2	no	—
56	C₂×C₈	—	17	2	no	—
57	C₂×C₈	C₄×D₁₇	1	1	yes	characteristic
58	C₁₆	—	17	2	no	—
59	C₁₆	C₄×D₁₇	1	1	yes	characteristic
60	C₁₆	C₂²×D₁₇	1	1	yes	characteristic
61	Q₈	—	17	1	no	—
62	D₄	—	17	2	no	—
63	D₄	—	17	1	no	—
64	C₂×C₄	—	17	2	no	—
65	C₂×C₄	C₈×D₁₇	1	1	yes	characteristic
66	C₈	—	17	2	no	—
67	C₈	C₈×D₁₇	1	1	yes	characteristic
68	C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
69	C₂²	—	17	2	no	—
70	C₂²	C₁₆×D₁₇	1	1	yes	characteristic
71	C₄	—	17	2	no	—
72	C₄	C₁₆×D₁₇	1	1	yes	characteristic
73	C₄	C₂×C₈×D₁₇	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	34	2	no	—
76	C₂	C₂×C₁₆×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₁₇
commutator, socle	C₂×C₁₇	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₂×C₁₇×C₃₂	C₂
prime radical	#63252	C₈
cosocle	C₁₆×C₁₇	C₂³
hypercenter	C₂×C₃₂	D₁₇
hypocenter	C₁₇	#2258
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #11762643	C₂	semidirect
3. #11762642	C₂	semidirect
4. C₃₂×D₁₇	C₂	semidirect
5. C₂×C₁₇×C₃₂	C₂	semidirect
40. C₂×C₃₂	D₁₇	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
#11763225	2
#11762643	2
#11762642	2
C₃₂×D₁₇	2
C₂×C₁₇×C₃₂	2
#2258	17