Subgroups — #14545829

Order 2176.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763912	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763903	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763843	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	—	2	1	no	—
5	C₂×#63241	—	2	1	no	—
6	C₂×#63241	—	2	1	no	—
7	#10587579	C₄	1	1	yes	characteristic
8	#10587543	—	2	1	no	—
9	C₄⋊#3624	C₄	1	1	yes	characteristic
10	C₄×#3624	C₂²	1	1	yes	characteristic
11	C₂×D₆₈	C₈	1	1	yes	characteristic
12	C₂×C₄×D₁₇	—	2	1	no	—
13	C₂×#3624	—	2	1	no	—
14	C₂×#3624	D₄	1	1	yes	characteristic
15	C₂×#3624	D₄	1	1	yes	characteristic
16	#63243	—	4	1	no	—
17	#63243	—	4	1	no	—
18	#63241	—	2	2	no	—
19	#63241	—	4	1	no	—
20	C₄⋊C₄×C₁₇	C₈	1	1	yes	characteristic
21	#63227	—	2	1	no	—
22	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×D₁₇	—	2	1	no	—
24	C₂×C₄×C₁₇	—	2	1	no	—
25	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₇	M₁₆	1	1	yes	characteristic
28	D₆₈	—	4	1	no	—
29	C₄×D₁₇	—	4	1	no	—
30	C₄×D₁₇	—	4	1	no	—
31	#3624	—	2	1	no	—
32	#3624	—	4	1	no	—
33	#3624	D₈	1	1	yes	characteristic
34	#3624	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	—	4	1	no	—
42	Dic₁₇	—	2	1	no	—
43	Dic₁₇	#102	1	1	yes	characteristic
44	Dic₁₇	#104	1	1	yes	characteristic
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	—	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	—	17	1	no	—
61	C₂²×C₄	—	34	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	#3633	1	1	yes	characteristic
68	C₂²⋊C₄	—	34	1	no	—
69	C₄²	—	17	1	no	—
70	C₁₆	—	34	2	no	—
71	C₁₆	—	68	1	no	—
72	C₂³	—	34	1	no	—
73	D₄	—	68	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	17	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	68	1	no	—
78	C₂×C₄	—	68	1	no	—
79	C₂×C₄	C₂×#3633	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	—	68	1	no	—
85	C₂²	—	68	1	no	—
86	C₂²	—	68	1	no	—
87	C₂²	C₂²⋊#3633	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	4	1	no	—
90	C₄	—	17	1	no	—
91	C₄	—	17	1	no	—
92	C₄	—	34	1	no	—
93	C₂	—	136	1	no	—
94	C₂	D₄⋊#3633	1	1	yes	characteristic
95	C₂	#11763908	1	1	yes	characteristic
96	C₂	#11763910	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#3633
commutator	C₂×C₄×C₁₇	C₂×C₈
Frattini	C₂×C₄	C₂×#3633
Fitting	C₄⋊C₄×C₁₇	C₈
socle	C₂²×C₁₇	C₂²⋊C₈
prime radical	C₂×D₆₈	C₈
cosocle	C₄×#3624	C₂²
hypercenter	C₄⋊C₄	#3633
hypocenter	C₁₇	#1330
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #11763912	C₂	semidirect
2. #11763903	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
#11763912	2
#11763903	2
#11763843	2
#1330	17