Finite Group Databasebeta

← #14536964

Subgroups — #14536964

Order 2176.

332 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17⋊#401C212yesmaximal
2#11762751C212yesmaximal
3#11762749C212yesmaximal
4#11762748C211yesmaximal, characteristic
5#11762742C212yesmaximal
6#11762729C212yesmaximal
7#11762714C211yesmaximal, characteristic
8#11762695C212yesmaximal
9C17×#398C211yesmaximal, characteristic
10C22×Dic34C2211yescharacteristic
11C2×C4⋊C4×C17C2212yes—
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C4⋊C4×C17C2211yescharacteristic
14C2×C4⋊Dic17C2212yes—
15C2×C4⋊Dic17C2211yescharacteristic
16C2×#63225C2212yes—
17C2×#63225C2212yes—
18C2×C4×Dic17C2211yescharacteristic
19C17×#95C2212yes—
20C17×#95C2211yescharacteristic
21#10587502C2212yes—
22#10587502C2212yes—
23#10587502C2212yes—
24#10587502C2212yes—
25#10587502C2212yes—
26#10587502C2212yes—
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2211yescharacteristic
31C22×C4×C17C2312yes—
32C22×C4×C17C2311yescharacteristic
33C22×C4×C17C2311yescharacteristic
34C22×C4×C17C2312yes—
35C22×C4×C17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C2×Dic34—22no—
41C2×Dic34—41no—
42C2×Dic34—41no—
43C4⋊C4×C17—24no—
44C4⋊C4×C17—41no—
45C4⋊C4×C17—41no—
46C4⋊Dic17—42no—
47C4⋊Dic17—41no—
48#63225—42no—
49#63225—42no—
50C4×Dic17—41no—
51C23×C17C2411yescharacteristic
52C2×C4×C17—21no—
53C2×C4×C17—21no—
54C2×C4×C17—22no—
55C2×C4×C17—22no—
56C2×C4×C17—21no—
57C2×C4×C17—22no—
58C2×C4×C17—21no—
59C2×C4×C17—22no—
60C2×C4×C17—22no—
61C2×C4×C17—22no—
62C2×C4×C17—22no—
63C2×C4×C17—22no—
64C2×C4×C17#4112yes—
65C2×Dic17—22no—
66C2×Dic17—22no—
67C2×Dic17—22no—
68C2×Dic17—22no—
69C2×Dic17—22no—
70C2×Dic17—22no—
71C2×Dic17—22no—
72C2×Dic17—24no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76Dic34—44no—
77#2833—171nomaximal, Sylow
78C22×C17C2×#4111yescharacteristic
79C22×C17H(5,𝔽2)11yescharacteristic
80C22×C17H(5,𝔽2)11yescharacteristic
81C22×C172−1+412yes—
82C22×C172−1+412yes—
83C4×C17—22no—
84C4×C17—42no—
85C4×C17—42no—
86C4×C17—41no—
87C4×C17—41no—
88Dic17—42no—
89Dic17—42no—
90Dic17—42no—
91Dic17—42no—
92#401—172no—
93#400—171no—
94#400—172no—
95#400—172no—
96#398—172no—
97#398D1711yescharacteristic
98#395—172no—
99#391—171no—
100#387—172no—
101C2×C17#53811yescharacteristic
102C2×C17#54112yes—
103C2×C17#56311yescharacteristic
104C2×C17#56311yescharacteristic
105C2×C17#56312yes—
106C22×Q8—171no—
107C2×C4⋊C4—172no—
108C2×C4⋊C4—172no—
109C2×C4⋊C4—172no—
110C2×C4⋊C4—171no—
111C2×C4⋊C4C2×D1712yes—
112C2×C4⋊C4C2×D1711yescharacteristic
113C2×C4⋊C4C2×D1711yescharacteristic
114C2×C42—171no—
115#95—172no—
116#95—172no—
117#95—172no—
118#95—172no—
119#95—172no—
120#95—172no—
121#95—172no—
122#95—172no—
123#95—172no—
124#95—171no—
125#95C2×D1712yes—
126#95C2×D1711yescharacteristic
127C17#283311yescharacteristic, complemented, Sylow
128C2×Q8—342no—
129C2×Q8—681no—
130C2×Q8—681no—
131C22×C4—172no—
132C22×C4—172no—
133C22×C4—172no—
134C22×C4—172no—
135C22×C4C22×D1712yes—
136C22×C4C22×D1711yescharacteristic
137C22×C4C22×D1711yescharacteristic
138C22×C4C22×D1712yes—
139C22×C4C22×D1711yescharacteristic
140C4⋊C4—24no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—682no—
144C4⋊C4—682no—
145C4⋊C4—681no—
146C4⋊C4—682no—
147C42—681no—
148C23C23×D1711yescharacteristic
149Q8—684no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—342no—
163C2×C4—342no—
164C2×C4—342no—
165C2×C4—344no—
166C2×C4—342no—
167C2×C4—342no—
168C2×C4—342no—
169C2×C4—342no—
170C2×C4—342no—
171C2×C4—342no—
172C2×C4—342no—
173C2×C4#6325412yes—
174C22C2×#6325411yescharacteristic
175C22#1058769111yescharacteristic
176C22#1058769412yes—
177C22#1058769611yescharacteristic
178C22#1058769712yes—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—42no—
183C4—42no—
184C4—682no—
185C4—682no—
186C4—682no—
187C4—682no—
188C2#1176339611yescharacteristic
189C2#1176341912yes—
190C2#1176355811yescharacteristic
191C2#1176356211yescharacteristic
192C2#1176356312yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#398C2
hypercenter#398D17
hypocenterC17#2833
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
127. C17#2833semidirect

Maximal subgroups

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

subgroupindex
C17⋊#4012
#117627512
#117627492
#117627482
#117627422
#117627292
#117627142
#117626952
C17×#3982
#283317