Finite Group Databasebeta

← #14534022

Subgroups — #14534022

Order 2176.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#11762751C212yesmaximal
2#11762748C211yesmaximal, characteristic
3#11762706C212yesmaximal
4#11762704C212yesmaximal
5#11762678C211yesmaximal, characteristic
6#11762673C212yesmaximal
7#11762673C212yesmaximal
8#11762660C212yesmaximal
9C17×#400C211yesmaximal, characteristic
10C2×C4⋊C4×C17C2211yescharacteristic
11C2×C4⋊C4×C17C2211yescharacteristic
12C2×C4⋊Dic17C2211yescharacteristic
13C2×C4⋊Dic17C2211yescharacteristic
14C2×#63225C2212yes—
15C2×#63225C2212yes—
16C2×#63225C2212yes—
17C2×#63225C2212yes—
18C2×#63225C2212yes—
19C2×C4×Dic17C2212yes—
20C2×C4×Dic17C2212yes—
21C2×C4×Dic17C2211yescharacteristic
22C17×#95C2212yes—
23C17×#95C2212yes—
24C17×#95C2211yescharacteristic
25#10587502C2212yes—
26#10587502C2212yes—
27#10587502C2212yes—
28#10587502C2212yes—
29#10587502C2211yescharacteristic
30#10587502C2212yes—
31C22×C4×C17C2312yes—
32C22×C4×C17C2311yescharacteristic
33C22×C4×C17C2312yes—
34C22×C4×C17C2311yescharacteristic
35C22×C4×C17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2312yes—
40C4⋊C4×C17—41no—
41C4⋊C4×C17—41no—
42C4⋊Dic17—41no—
43C4⋊Dic17—41no—
44#63225—24no—
45#63225—24no—
46#63225—24no—
47#63225—24no—
48#63225—42no—
49C4×Dic17—24no—
50C4×Dic17—24no—
51C4×Dic17Q814yes—
52C23×C17C2411yescharacteristic
53C2×C4×C17—21no—
54C2×C4×C17—21no—
55C2×C4×C17—22no—
56C2×C4×C17—22no—
57C2×C4×C17—22no—
58C2×C4×C17—22no—
59C2×C4×C17—22no—
60C2×C4×C17—22no—
61C2×C4×C17—21no—
62C2×C4×C17—22no—
63C2×C4×C17—21no—
64C2×C4×C17—22no—
65C2×C4×C17C2×Q812yes—
66C2×Dic17—22no—
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×Dic17C2×Q814yes—
76C2×Dic17#4114yes—
77C2×Dic17#4114yes—
78#2571—171nomaximal, Sylow
79C22×C17C22×Q811yescharacteristic
80C22×C17C2×#4112yes—
81C22×C17C2×#4112yes—
82C22×C17H(5,𝔽2)11yescharacteristic
83C22×C172−1+411yescharacteristic
84C4×C17—22no—
85C4×C17—42no—
86C4×C17—42no—
87C4×C17—41no—
88C4×C17—41no—
89Dic17—42no—
90Dic17—42no—
91Dic17—42no—
92Dic17#12518yes—
93#400—171no—
94#400—172no—
95#400D1711yescharacteristic
96#389—172no—
97#389—172no—
98#384—171no—
99#382—172no—
100#382—172no—
101C4×C4⋊C4—172no—
102C2×C17C2×#12512yes—
103C2×C17#54411yescharacteristic
104C2×C17#55511yescharacteristic
105C2×C17#55612yes—
106C2×C17#55911yescharacteristic
107C2×C4⋊C4—172no—
108C2×C4⋊C4—172no—
109C2×C4⋊C4—172no—
110C2×C4⋊C4—172no—
111C2×C4⋊C4—171no—
112C2×C4⋊C4—172no—
113C2×C4⋊C4—171no—
114C2×C4⋊C4C2×D1711yescharacteristic
115C2×C4⋊C4C2×D1711yescharacteristic
116C2×C42—171no—
117C2×C42—172no—
118C2×C42—172no—
119#95—172no—
120#95—171no—
121#95—172no—
122#95—172no—
123#95—172no—
124#95—172no—
125#95C2×D1712yes—
126#95C2×D1711yescharacteristic
127#95C2×D1712yes—
128C17#257111yescharacteristic, complemented, Sylow
129C22×C4—172no—
130C22×C4—172no—
131C22×C4—172no—
132C22×C4—172no—
133C22×C4C22×D1712yes—
134C22×C4C22×D1711yescharacteristic
135C22×C4C22×D1712yes—
136C22×C4C22×D1711yescharacteristic
137C22×C4C22×D1711yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—344no—
141C4⋊C4—344no—
142C4⋊C4—344no—
143C4⋊C4—344no—
144C4⋊C4—682no—
145C4⋊C4—681no—
146C4⋊C4—681no—
147C42—174no—
148C42—344no—
149C42—344no—
150C23C23×D1711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—174no—
164C2×C4—174no—
165C2×C4—174no—
166C2×C4—342no—
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×C4Q8×D1712yes—
176C22#1058769111yescharacteristic
177C22C2×Q8×D1711yescharacteristic
178C22#41×D1712yes—
179C22#41×D1712yes—
180C22#1058769711yescharacteristic
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—178no—
187C4—682no—
188C4—682no—
189C4—682no—
190C2#125×D1712yes—
191C2#1176343811yescharacteristic
192C2#1176352111yescharacteristic
193C2#1176352612yes—
194C2#1176354311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#400C2
hypercenter#400D17
hypocenterC17#2571
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
128. C17#2571semidirect

Maximal subgroups

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

subgroupindex
#117627512
#117627482
#117627062
#117627042
#117626782
#117626732
#117626602
C17×#4002
#257117