Group #16949067 — subgroups

Subgroups — #16949067

Order 4352.

262 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531066	C₂	1	1	yes	maximal, characteristic
2	#14531064	C₂	1	2	yes	maximal
3	#14528401	C₂	1	2	yes	maximal
4	C₁₆×#3622	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#2254	C₂	1	1	yes	maximal, characteristic
6	#11763214	C₂²	1	2	yes	—
7	#11763212	—	2	2	no	—
8	#11763188	—	2	2	no	—
9	#11762637	—	2	2	no	—
10	#11762636	—	2	4	no	—
11	C₄×#63214	C₂²	1	1	yes	characteristic
12	C₈×#3622	C₂²	1	1	yes	characteristic
13	C₁₇×#500	C₂²	1	2	yes	—
14	C₁₇×#367	—	2	2	no	—
15	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×C₄⋊Q₈	—	2	2	no	—
17	C₂×#63231	—	4	4	no	—
18	#10587555	—	2	2	no	—
19	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
20	C₁₇×#107	—	2	2	no	—
21	C₁₇×#107	—	2	2	no	—
22	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
23	#10587489	—	2	2	no	—
24	#10587489	—	2	2	no	—
25	C₂×#63214	D₄	1	2	yes	—
26	#10587478	—	4	4	no	—
27	C₄×#3622	D₄	1	2	yes	—
28	C₂×Q₈×C₁₇	—	4	2	no	—
29	C₂×Dic₃₄	—	4	2	no	—
30	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
32	C₄⋊C₄×C₁₇	—	4	2	no	—
33	C₄⋊C₄×C₁₇	—	4	2	no	—
34	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
35	#63231	—	8	8	no	—
36	C₄⋊Dic₁₇	—	4	2	no	—
37	C₄⋊Dic₁₇	—	4	2	no	—
38	C₂×#3622	D₈	1	4	yes	—
39	C₁₆×C₁₇	Q₁₆	1	4	yes	complemented
40	#63214	Q₁₆	1	4	yes	complemented
41	#12523	—	17	1	no	maximal, Sylow
42	Q₈×C₁₇	—	8	4	no	—
43	C₂×C₄×C₁₇	—	8	2	no	—
44	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
45	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
46	C₂×Dic₁₇	—	8	2	no	—
47	Dic₃₄	—	8	4	no	—
48	C₈×C₁₇	C₂×Q₁₆	1	2	yes	—
49	C₈×C₁₇	C₂×Q₁₆	1	2	yes	—
50	#3622	SD₃₂	1	8	yes	—
51	#2254	—	17	2	no	—
52	#2254	—	17	1	no	—
53	#2254	D₁₇	1	1	yes	characteristic
54	#1713	—	17	2	no	—
55	C₈×C₁₆	—	17	1	no	—
56	C₂²×C₁₇	#493	1	1	yes	characteristic
57	C₄×C₁₇	—	16	2	no	—
58	C₄×C₁₇	#494	1	1	yes	characteristic
59	C₄×C₁₇	#494	1	1	yes	characteristic
60	C₄×C₁₇	C₂×SD₃₂	1	4	yes	—
61	Dic₁₇	—	16	2	no	—
62	#500	—	17	2	no	—
63	#500	—	34	2	no	—
64	#500	C₂×D₁₇	1	2	yes	—
65	#494	—	34	2	no	—
66	#367	—	2	2	no	—
67	#367	—	34	4	no	—
68	#367	—	34	2	no	—
69	C₄×C₁₆	—	17	1	no	—
70	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
71	C₈²	—	17	1	no	—
72	C₂×C₁₇	#1713	1	1	yes	characteristic
73	C₂×C₁₇	#2248	1	2	yes	—
74	C₂×Q₁₆	—	68	4	no	—
75	C₄⋊Q₈	—	2	2	no	—
76	C₄⋊Q₈	—	34	2	no	—
77	C₂×C₁₆	—	17	2	no	—
78	C₂×C₁₆	C₂²⋊D₁₇	1	2	yes	—
79	#107	—	2	2	no	—
80	#107	—	2	2	no	—
81	#107	—	34	2	no	—
82	#107	—	34	2	no	—
83	#107	—	68	4	no	—
84	C₄×C₈	—	17	2	no	—
85	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
86	C₁₇	#12523	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	4	2	no	—
88	C₂×Q₈	—	68	2	no	—
89	Q₁₆	—	136	8	no	—
90	C₂×C₈	—	17	4	no	—
91	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
92	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
93	C₄⋊C₄	—	4	2	no	—
94	C₄⋊C₄	—	4	2	no	—
95	C₄⋊C₄	—	68	2	no	—
96	C₄⋊C₄	—	68	2	no	—
97	C₄²	D₄×D₁₇	1	1	yes	characteristic
98	C₁₆	—	17	4	no	—
99	C₁₆	#63231	1	4	yes	complemented
100	Q₈	—	8	4	no	—
101	Q₈	—	136	4	no	—
102	C₂×C₄	—	8	2	no	—
103	C₂×C₄	—	136	2	no	—
104	C₂×C₄	D₈×D₁₇	1	2	yes	—
105	C₂×C₄	#10587626	1	1	yes	characteristic
106	C₈	—	17	8	no	—
107	C₈	Q₁₆×D₁₇	1	2	yes	—
108	C₈	C₂×#63231	1	2	yes	—
109	C₂²	#11763184	1	1	yes	characteristic
110	C₄	—	16	2	no	—
111	C₄	—	272	2	no	—
112	C₄	#11763187	1	1	yes	characteristic
113	C₄	#11763188	1	1	yes	characteristic
114	C₄	SD₃₂×D₁₇	1	4	yes	—
115	C₂	#14528401	1	1	yes	characteristic
116	C₂	#14531038	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14531066

C₂

yes

maximal, characteristic

#14531064

C₂

yes

maximal

#14528401

C₂

yes

maximal

C₁₆×#3622

C₂

yes

maximal, characteristic

C₁₇×#2254

C₂

yes

maximal, characteristic

#11763214

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₈×#3622

C₂²

yes

characteristic

C₁₇×#500

C₂²

yes

—

C₁₇×#367

—

C₄×C₁₆×C₁₇

C₂²

yes

characteristic

C₁₇×C₄⋊Q₈

—

C₂×#63231

—

#10587555

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₁₇×#107

—

C₁₇×#107

—

C₄×C₈×C₁₇

C₂³

yes

—

—

D₄

yes

—

#10587478

—

C₄×#3622

D₄

yes

—

C₂×Q₈×C₁₇

—

C₂×Dic₃₄

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

#63231

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₂×#3622

D₈

yes

—

C₁₆×C₁₇

Q₁₆

yes

complemented

#63214

Q₁₆

yes

complemented

#12523

—

maximal, Sylow

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×Dic₁₇

—

Dic₃₄

—

C₈×C₁₇

C₂×Q₁₆

yes

—

C₈×C₁₇

C₂×Q₁₆

yes

—

#3622

SD₃₂

yes

—

#2254

—

#2254

—

#2254

D₁₇

yes

characteristic

#1713

—

C₈×C₁₆

—

C₂²×C₁₇

#493

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

C₂×SD₃₂

yes

—

Dic₁₇

—

#500

—

#500

—

#500

C₂×D₁₇

yes

—

—

—

—

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₇

yes

characteristic

C₈²

—

C₂×C₁₇

#1713

yes

characteristic

C₂×C₁₇

#2248

yes

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₇

yes

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12523

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

136

—

C₂×C₈

—

C₂×C₈

D₄×D₁₇

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₄×D₁₇

yes

characteristic

C₁₆

—

C₁₆

#63231

yes

complemented

100

Q₈

—

101

Q₈

—

136

—

102

C₂×C₄

—

103

C₂×C₄

—

136

—

104

C₂×C₄

D₈×D₁₇

yes

—

105

C₂×C₄

#10587626

yes

characteristic

106

C₈

—

107

C₈

Q₁₆×D₁₇

yes

—

108

C₈

C₂×#63231

yes

—

109

C₂²

#11763184

yes

characteristic

110

C₄

—

111

C₄

—

272

—

112

C₄

#11763187

yes

characteristic

113

C₄

#11763188

yes

characteristic

114

C₄

SD₃₂×D₁₇

yes

—

115

C₂

#14528401

yes

characteristic

116

C₂

#14531038

yes

—

	subgroup	G/H
center	C₂²	#11763184
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#2254	C₂
socle, prime radical	C₂²×C₁₇	#493
hypercenter	#2254	D₁₇
hypocenter	C₁₇	#12523
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2254

subgroup

G/H

center

C₂²

#11763184

commutator, cosocle

C₄×C₈×C₁₇

C₂³

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#2254

C₂

C₂²×C₁₇

D₁₇

C₁₇

G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2254

N	H ≅ G/N	type
39. C₁₆×C₁₇	Q₁₆	semidirect
40. #63214	Q₁₆	semidirect
86. C₁₇	#12523	semidirect
99. C₁₆	#63231	semidirect

H ≅ G/N

type

39. C₁₆×C₁₇

Q₁₆

semidirect

40. #63214

Q₁₆

semidirect

86. C₁₇

#12523

semidirect

99. C₁₆

#63231

semidirect

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

subgroup	index
#14531066	2
#14531064	2
#14528401	2
C₁₆×#3622	2
C₁₇×#2254	2
#12523	17

subgroup

index

#14531066

#14531064

#14528401

C₁₆×#3622

C₁₇×#2254

#12523

Subgroups — #16949067

Conjugacy classes of subgroups

Complements

Maximal subgroups