Finite Group Databasebeta

← #14536775

Subgroups — #14536775

Order 2176.

344 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 125 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#11762749C212yesmaximal
2#11762748C212yesmaximal
3#11762747C212yesmaximal
4#11762707C211yesmaximal, characteristic
5#11762707C211yesmaximal, characteristic
6#11762696C212yesmaximal
7#11762695C212yesmaximal
8#11762690C212yesmaximal
9C17×#389C211yesmaximal, characteristic
10C2×C4⋊C4×C17C2212yes—
11C2×C4⋊C4×C17C2211yescharacteristic
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C42×C17C2211yescharacteristic
14C2×C4⋊Dic17C2211yescharacteristic
15C2×C4⋊Dic17C2211yescharacteristic
16C2×C4⋊Dic17C2211yescharacteristic
17C2×C4⋊Dic17C2211yescharacteristic
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×C4×Dic17C2212yes—
21C17×#95C2212yes—
22#10587502C2212yes—
23#10587502C2212yes—
24#10587502C2212yes—
25#10587502C2212yes—
26#10587502C2212yes—
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2212yes—
30#10587502C2212yes—
31C22×C4×C17C2312yes—
32C22×C4×C17C2312yes—
33C22×C4×C17C2311yescharacteristic
34C22×C4×C17C2311yescharacteristic
35C22×C4×C17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C4⋊C4×C17—22no—
41C4⋊C4×C17—24no—
42C4⋊C4×C17—41no—
43C42×C17—41no—
44C4⋊Dic17—22no—
45C4⋊Dic17—22no—
46C4⋊Dic17—41no—
47C4⋊Dic17—41no—
48#63225—24no—
49#63225—24no—
50C4×Dic17—42no—
51C23×C17C2411yescharacteristic
52C2×C4×C17—21no—
53C2×C4×C17—21no—
54C2×C4×C17—21no—
55C2×C4×C17—21no—
56C2×C4×C17—21no—
57C2×C4×C17—21no—
58C2×C4×C17—22no—
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×C4×C17#4112yes—
66C2×C4×C17#4112yes—
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×Dic17—22no—
78C2×Dic17—22no—
79#2810—171nomaximal, Sylow
80C22×C17C2×#4111yescharacteristic
81C22×C17C2×#4111yescharacteristic
82C22×C17C2×#4111yescharacteristic
83C22×C17H(5,𝔽2)11yescharacteristic
84C22×C172−1+411yescharacteristic
85C22×C172−1+411yescharacteristic
86C22×C172−1+411yescharacteristic
87C4×C17—22no—
88C4×C17—22no—
89C4×C17—22no—
90C4×C17—42no—
91C4×C17—42no—
92Dic17—42no—
93Dic17—42no—
94Dic17—42no—
95Dic17—42no—
96#400—172no—
97#400—172no—
98#400—172no—
99#389—171no—
100#389—171no—
101#389D1711yescharacteristic
102#387—172no—
103#387—172no—
104#387—172no—
105C2×C17#53911yescharacteristic
106C2×C17#53911yescharacteristic
107C2×C17#53911yescharacteristic
108C2×C17#55611yescharacteristic
109C2×C17#55611yescharacteristic
110C2×C17#55611yescharacteristic
111C2×C17#56411yescharacteristic
112C2×C4⋊C4—172no—
113C2×C4⋊C4—172no—
114C2×C4⋊C4—171no—
115C2×C4⋊C4—171no—
116C2×C4⋊C4—171no—
117C2×C4⋊C4—171no—
118C2×C4⋊C4C2×D1712yes—
119C2×C4⋊C4C2×D1711yescharacteristic
120C2×C4⋊C4C2×D1711yescharacteristic
121C2×C42—172no—
122C2×C42C2×D1711yescharacteristic
123#95—172no—
124#95—172no—
125#95—172no—
126#95—172no—
127#95—172no—
128#95—172no—
129#95—172no—
130#95—172no—
131#95—172no—
132#95C2×D1712yes—
133C17#281011yescharacteristic, complemented, Sylow
134C22×C4—172no—
135C22×C4—172no—
136C22×C4—172no—
137C22×C4—172no—
138C22×C4C22×D1712yes—
139C22×C4C22×D1712yes—
140C22×C4C22×D1711yescharacteristic
141C22×C4C22×D1711yescharacteristic
142C22×C4C22×D1711yescharacteristic
143C4⋊C4—22no—
144C4⋊C4—24no—
145C4⋊C4—41no—
146C4⋊C4—344no—
147C4⋊C4—342no—
148C4⋊C4—344no—
149C4⋊C4—342no—
150C4⋊C4—681no—
151C4⋊C4—681no—
152C42—41no—
153C42—682no—
154C23C23×D1711yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—342no—
168C2×C4—342no—
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×C4#6325212yes—
180C2×C4#6325412yes—
181C2×C4#6325612yes—
182C22C2×#6325211yescharacteristic
183C22C2×#6325411yescharacteristic
184C22#1058769111yescharacteristic
185C22C2×#6325611yescharacteristic
186C22#1058769411yescharacteristic
187C22#1058769711yescharacteristic
188C22#1058769711yescharacteristic
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—682no—
195C4—682no—
196C4—682no—
197C4—682no—
198C2#1176340411yescharacteristic
199C2#1176340611yescharacteristic
200C2#1176340811yescharacteristic
201C2#1176352911yescharacteristic
202C2#1176353211yescharacteristic
203C2#1176353311yescharacteristic
204C2C17⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#389C2
hypercenter#389D17
hypocenterC17#2810
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
133. C17#2810semidirect

Maximal subgroups

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

subgroupindex
#117627492
#117627482
#117627472
#117627072
#117626962
#117626952
#117626902
C17×#3892
#281017