Subgroups — #14543737

Order 2176.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#63216	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763697	C₂	1	1	yes	maximal, characteristic, complemented
3	#11762886	C₂	1	1	yes	maximal, characteristic
4	C₂×#63218	—	2	1	no	—
5	C₄×D₆₈	C₄	1	1	yes	characteristic
6	C₂×#63216	—	2	1	no	—
7	C₂×#63216	—	2	1	no	—
8	C₁₇×C₄⋊C₈	C₄	1	1	yes	characteristic
9	#10587491	—	2	1	no	—
10	C₄×#3622	C₂²	1	1	yes	characteristic
11	C₂×D₆₈	C₈	1	1	yes	characteristic
12	C₂×C₄×D₁₇	—	2	1	no	—
13	C₂×C₈×C₁₇	—	2	1	no	—
14	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
15	#63227	—	2	1	no	—
16	C₄⋊Dic₁₇	C₈	1	1	yes	characteristic
17	C₂×#3622	D₄	1	1	yes	characteristic
18	C₂×#3622	D₄	1	1	yes	characteristic
19	#63218	—	4	1	no	—
20	#63218	—	4	1	no	—
21	#63216	—	2	2	no	—
22	#63216	—	4	1	no	—
23	C₂²×D₁₇	—	2	1	no	—
24	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
27	C₂×Dic₁₇	—	2	1	no	—
28	D₆₈	—	4	1	no	—
29	C₄×D₁₇	—	4	1	no	—
30	C₄×D₁₇	—	4	1	no	—
31	C₈×C₁₇	—	4	1	no	—
32	#3622	—	2	1	no	—
33	#3622	D₈	1	1	yes	characteristic
34	#3622	SD₁₆	1	1	yes	characteristic
35	#1330	—	17	1	no	maximal, Sylow
36	C₂²×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₁₇	—	4	1	no	—
38	C₂×D₁₇	—	4	1	no	—
39	C₂×D₁₇	—	4	1	no	—
40	C₄×C₁₇	—	2	1	no	—
41	C₄×C₁₇	—	2	1	no	—
42	C₄×C₁₇	#102	1	1	yes	characteristic
43	C₄×C₁₇	#104	1	1	yes	characteristic
44	Dic₁₇	—	4	1	no	—
45	#436	—	17	1	no	—
46	C₄⋊C₁₆	—	17	1	no	—
47	#346	—	17	1	no	—
48	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
49	C₂×C₁₇	#349	1	1	yes	characteristic
50	C₂×C₁₇	#350	1	1	yes	characteristic
51	D₁₇	—	8	1	no	—
52	C₂×M₁₆	—	34	1	no	—
53	C₄×D₄	—	17	1	no	—
54	C₂×C₁₆	—	34	1	no	—
55	C₂×C₁₆	—	34	1	no	—
56	C₄⋊C₈	#595	1	1	yes	characteristic
57	C₂²⋊C₈	—	34	1	no	—
58	C₄×C₈	—	17	1	no	—
59	C₁₇	#1330	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₄	—	17	1	no	—
61	C₂²×C₄	—	34	1	no	—
62	M₁₆	—	68	1	no	—
63	M₁₆	—	68	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	17	1	no	—
67	C₄⋊C₄	—	17	1	no	—
68	C₂²⋊C₄	—	34	1	no	—
69	C₄²	C₂×#595	1	1	yes	characteristic
70	C₁₆	—	34	2	no	—
71	C₁₆	—	68	1	no	—
72	C₂³	—	34	1	no	—
73	D₄	—	68	1	no	—
74	C₂×C₄	—	34	1	no	—
75	C₂×C₄	—	68	1	no	—
76	C₂×C₄	—	68	1	no	—
77	C₂×C₄	#63242	1	1	yes	characteristic
78	C₂×C₄	#63243	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	17	1	no	—
82	C₈	—	17	1	no	—
83	C₈	—	34	1	no	—
84	C₂²	—	68	1	no	—
85	C₂²	—	68	1	no	—
86	C₂²	—	68	1	no	—
87	C₂²	#10587543	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	68	1	no	—
91	C₄	#10587547	1	1	yes	characteristic
92	C₄	#10587550	1	1	yes	characteristic
93	C₂	—	136	1	no	—
94	C₂	#11763657	1	1	yes	characteristic
95	C₂	#11763706	1	1	yes	characteristic
96	C₂	#11763708	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂×C₈
Frattini	C₄²	C₂×#595
Fitting	C₁₇×C₄⋊C₈	C₄
socle	C₂²×C₁₇	C₂²⋊C₈
prime radical	C₂×D₆₈	C₈
cosocle	C₄×#3622	C₂²
hypercenter	C₄⋊C₈	#595
hypocenter	C₁₇	#1330
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₄⋊#63216	C₂	semidirect
2. #11763697	C₂	semidirect
59. C₁₇	#1330	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#63216	2
#11763697	2
#11762886	2
#1330	17