Finite Group Databasebeta

← #14536767

Subgroups — #14536767

Order 2176.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#11762748C211yesmaximal, characteristic
2#11762743C212yesmaximal
3#11762742C212yesmaximal
4#11762714C211yesmaximal, characteristic
5#11762713C212yesmaximal
6#11762706C212yesmaximal
7#11762694C212yesmaximal
8#11762691C212yesmaximal
9C17×#400C211yesmaximal, characteristic
10C22×Dic34C2211yescharacteristic
11C2×C4⋊C4×C17C2211yescharacteristic
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C4⋊Dic17C2212yes—
14C2×C4⋊Dic17C2211yescharacteristic
15C2×#63225C2212yes—
16C2×#63225C2212yes—
17C2×#63225C2212yes—
18C2×#63225C2212yes—
19C2×C4×Dic17C2212yes—
20C2×C4×Dic17C2211yescharacteristic
21C17×#95C2211yescharacteristic
22C17×#95C2212yes—
23C17×#95C2212yes—
24#10587502C2212yes—
25#10587502C2212yes—
26#10587502C2212yes—
27#10587502C2211yescharacteristic
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2212yes—
31C22×C4×C17C2311yescharacteristic
32C22×C4×C17C2311yescharacteristic
33C22×C4×C17C2312yes—
34C22×C4×C17C2312yes—
35C22×C4×C17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C2×Dic34—41no—
41C2×Dic34—41no—
42C2×Dic34Q814yes—
43C4⋊C4×C17—41no—
44C4⋊C4×C17—41no—
45C4⋊Dic17—24no—
46C4⋊Dic17—41no—
47#63225—24no—
48#63225—24no—
49#63225—42no—
50#63225—42no—
51C4×Dic17—42no—
52C4×Dic17—41no—
53C23×C17C2411yescharacteristic
54C2×C4×C17—21no—
55C2×C4×C17—21no—
56C2×C4×C17—22no—
57C2×C4×C17—22no—
58C2×C4×C17—22no—
59C2×C4×C17—21no—
60C2×C4×C17—22no—
61C2×C4×C17—21no—
62C2×C4×C17—22no—
63C2×C4×C17—22no—
64C2×C4×C17—22no—
65C2×C4×C17—22no—
66C2×C4×C17C2×Q812yes—
67C2×Dic17—22no—
68C2×Dic17—22no—
69C2×Dic17—22no—
70C2×Dic17—22no—
71C2×Dic17—22no—
72C2×Dic17—22no—
73C2×Dic17—22no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76C2×Dic17—22no—
77C2×Dic17C2×Q814yes—
78C2×Dic17#4114yes—
79Dic34—44no—
80#2809—171nomaximal, Sylow
81C22×C17C22×Q811yescharacteristic
82C22×C17C2×#4112yes—
83C22×C17H(5,𝔽2)11yescharacteristic
84C22×C17H(5,𝔽2)11yescharacteristic
85C22×C172−1+412yes—
86C4×C17—22no—
87C4×C17—42no—
88C4×C17—42no—
89C4×C17—41no—
90C4×C17—41no—
91Dic17—24no—
92Dic17—24no—
93Dic17—42no—
94Dic17—42no—
95#400—171no—
96#400D1711yescharacteristic
97#398—172no—
98#398—172no—
99#391—171no—
100#391—172no—
101#389—172no—
102#387—172no—
103#387—172no—
104C2×C17#53912yes—
105C2×C17#54311yescharacteristic
106C2×C17#55511yescharacteristic
107C2×C17#55712yes—
108C2×C17#56311yescharacteristic
109C22×Q8—171no—
110C2×C4⋊C4—172no—
111C2×C4⋊C4—172no—
112C2×C4⋊C4—172no—
113C2×C4⋊C4—172no—
114C2×C4⋊C4—172no—
115C2×C4⋊C4—171no—
116C2×C4⋊C4C2×D1711yescharacteristic
117C2×C4⋊C4C2×D1711yescharacteristic
118C2×C42—172no—
119C2×C42—171no—
120#95—171no—
121#95—172no—
122#95—172no—
123#95—172no—
124#95—172no—
125#95—172no—
126#95—172no—
127#95C2×D1711yescharacteristic
128#95C2×D1712yes—
129#95C2×D1712yes—
130C17#280911yescharacteristic, complemented, Sylow
131C2×Q8—174no—
132C2×Q8—681no—
133C2×Q8—681no—
134C22×C4—172no—
135C22×C4—172no—
136C22×C4—172no—
137C22×C4—172no—
138C22×C4C22×D1711yescharacteristic
139C22×C4C22×D1711yescharacteristic
140C22×C4C22×D1712yes—
141C22×C4C22×D1712yes—
142C22×C4C22×D1711yescharacteristic
143C4⋊C4—41no—
144C4⋊C4—41no—
145C4⋊C4—344no—
146C4⋊C4—344no—
147C4⋊C4—344no—
148C4⋊C4—682no—
149C4⋊C4—682no—
150C4⋊C4—681no—
151C42—681no—
152C42—682no—
153C23C23×D1711yescharacteristic
154Q8—684no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—174no—
168C2×C4—174no—
169C2×C4—342no—
170C2×C4—342no—
171C2×C4—342no—
172C2×C4—342no—
173C2×C4—342no—
174C2×C4—342no—
175C2×C4—342no—
176C2×C4—342no—
177C2×C4—342no—
178C2×C4—342no—
179C2×C4Q8×D1712yes—
180C22#1058769111yescharacteristic
181C22C2×Q8×D1711yescharacteristic
182C22#41×D1712yes—
183C22#1058769611yescharacteristic
184C22#1058769712yes—
185C4—22no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—42no—
190C4—344no—
191C4—344no—
192C4—682no—
193C4—682no—
194C2#1176340012yes—
195C2#1176343411yescharacteristic
196C2#1176352111yescharacteristic
197C2#1176353612yes—
198C2#1176356211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#400C2
hypercenter#400D17
hypocenterC17#2809
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
130. C17#2809semidirect

Maximal subgroups

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

subgroupindex
#117627482
#117627432
#117627422
#117627142
#117627132
#117627062
#117626942
#117626912
C17×#4002
#280917