Subgroups — #14543736

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	#11762887	C₂	1	1	yes	maximal, characteristic
4	C₄×D₄×C₁₇	C₄	1	1	yes	characteristic
5	C₂×#63223	—	2	1	no	—
6	C₂×#63216	—	2	1	no	—
7	C₂×#63216	—	2	1	no	—
8	C₂²⋊#3622	—	2	1	no	—
9	C₄⋊#3622	C₄	1	1	yes	characteristic
10	C₄×#3622	C₂²	1	1	yes	characteristic
11	C₂×D₄×C₁₇	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₁₇	—	2	1	no	—
13	C₄⋊C₄×C₁₇	C₈	1	1	yes	characteristic
14	C₂²⋊C₄×C₁₇	—	2	1	no	—
15	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
16	#63223	—	4	1	no	—
17	#63223	—	4	1	no	—
18	C₂×#3622	—	2	1	no	—
19	C₂×#3622	D₄	1	1	yes	characteristic
20	C₂×#3622	D₄	1	1	yes	characteristic
21	#63216	—	2	2	no	—
22	#63216	—	4	1	no	—
23	C₂³×C₁₇	—	2	1	no	—
24	D₄×C₁₇	—	4	1	no	—
25	C₂×C₄×C₁₇	—	2	1	no	—
26	C₂×C₄×C₁₇	—	4	1	no	—
27	C₂×C₄×C₁₇	—	4	1	no	—
28	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇	M₁₆	1	1	yes	characteristic
31	#3622	—	2	1	no	—
32	#3622	—	4	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	—	4	1	no	—
37	C₂²×C₁₇	—	4	1	no	—
38	C₂²×C₁₇	—	4	1	no	—
39	C₂²×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₁₇	—	2	1	no	—
41	C₄×C₁₇	—	2	1	no	—
42	C₄×C₁₇	—	4	1	no	—
43	C₄×C₁₇	#102	1	1	yes	characteristic
44	C₄×C₁₇	#104	1	1	yes	characteristic
45	#436	—	17	1	no	—
46	C₄⋊C₁₆	—	17	1	no	—
47	#346	—	17	1	no	—
48	C₂×C₁₇	—	8	1	no	—
49	C₂×C₁₇	D₄⋊C₈	1	1	yes	characteristic
50	C₂×C₁₇	#349	1	1	yes	characteristic
51	C₂×C₁₇	#350	1	1	yes	characteristic
52	C₂×M₁₆	—	34	1	no	—
53	C₄×D₄	#595	1	1	yes	characteristic
54	C₂×C₁₆	—	34	1	no	—
55	C₂×C₁₆	—	34	1	no	—
56	C₄⋊C₈	—	17	1	no	—
57	C₂²⋊C₈	—	34	1	no	—
58	C₄×C₈	—	17	1	no	—
59	C₁₇	#1330	1	1	yes	characteristic, complemented, Sylow
60	C₂×D₄	#3624	1	1	yes	characteristic
61	C₂²×C₄	—	2	1	no	—
62	M₁₆	—	68	1	no	—
63	M₁₆	—	68	1	no	—
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	34	1	no	—
67	C₄⋊C₄	#3624	1	1	yes	characteristic
68	C₂²⋊C₄	—	2	1	no	—
69	C₄²	C₂×#595	1	1	yes	characteristic
70	C₁₆	—	34	2	no	—
71	C₁₆	—	68	1	no	—
72	C₂³	—	2	1	no	—
73	D₄	—	4	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	4	1	no	—
77	C₂×C₄	C₂×#3624	1	1	yes	characteristic
78	C₂×C₄	#63247	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
80	C₈	—	17	1	no	—
81	C₈	—	17	1	no	—
82	C₈	—	34	1	no	—
83	C₈	—	68	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	C₂²⋊#3624	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	#10587547	1	1	yes	characteristic
92	C₄	#10587548	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	D₄⋊#3624	1	1	yes	characteristic
95	C₂	#11763705	1	1	yes	characteristic
96	C₂	#11763707	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₂×C₈
Frattini	C₄²	C₂×#595
Fitting	C₄×D₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₈
prime radical	C₂×D₄×C₁₇	C₈
cosocle	C₄×#3622	C₂²
hypercenter	C₄×D₄	#595
hypocenter	C₁₇	#1330
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

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
#11762887	2
#1330	17