Finite Group Databasebeta

← #14534733

Subgroups — #14534733

Order 2176.

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

normal subgroups only

This group has 416 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
1C2×#10587630C211yesmaximal, characteristic
2C2×#10587576C211yesmaximal, characteristic
3#11762751C214yesmaximal
4#11762750C214yesmaximal
5#11762716C211yesmaximal, characteristic
6#11762715C211yesmaximal, characteristic
7#11762714C211yesmaximal, characteristic
8#11762655C211yesmaximal, characteristic
9C17×#391C211yesmaximal, characteristic
10C22×Q8×C17C2211yescharacteristic
11C22×Dic34C2211yescharacteristic
12C2×C4⋊C4×C17C2211yescharacteristic
13C2×C42×C17C2211yescharacteristic
14#10587630—24no—
15C2×C4⋊Dic17C2211yescharacteristic
16C2×C4⋊Dic17C2212yes—
17C2×#63225C2212yes—
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×C4×Dic17C2211yescharacteristic
21C2×C4×Dic17C2211yescharacteristic
22#10587576—24no—
23C17×#95C2214yes—
24#10587502C2214yes—
25#10587502C2214yes—
26#10587502C2214yes—
27#10587502C2212yes—
28#10587502C2212yes—
29C2×Q8×C17—22no—
30C2×Q8×C17—22no—
31C2×Q8×C17—22no—
32C22×C4×C17C2312yes—
33C22×C4×C17C2312yes—
34C22×C4×C17C2312yes—
35C22×C4×C17C2311yescharacteristic
36C22×Dic17C2312yes—
37C22×Dic17C2312yes—
38C22×Dic17C2312yes—
39C22×Dic17C2311yescharacteristic
40C22×Dic17C2311yescharacteristic
41C2×Dic34—22no—
42C2×Dic34—22no—
43C2×Dic34—22no—
44C4⋊C4×C17—22no—
45C42×C17—22no—
46C4⋊Dic17—22no—
47C4⋊Dic17—24no—
48#63225—24no—
49#63225—24no—
50#63225—24no—
51C4×Dic17—22no—
52C4×Dic17D414yes—
53C23×C17C2411yescharacteristic
54Q8×C17—44no—
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—24no—
62C2×C4×C17—22no—
63C2×C4×C17C2×D412yes—
64C2×C4×C17#4112yes—
65C2×C4×C17#4112yes—
66C2×Dic17—22no—
67C2×Dic17—22no—
68C2×Dic17—22no—
69C2×Dic17—22no—
70C2×Dic17—22no—
71C2×Dic17—22no—
72C2×Dic17—22no—
73C2×Dic17—24no—
74C2×Dic17—22no—
75C2×Dic17—22no—
76C2×Dic17C2×D412yes—
77C2×Dic17C2×D412yes—
78Dic34—44no—
79#2642—171nomaximal, Sylow
80C22×C17C22×D411yescharacteristic
81C22×C17C2×#4111yescharacteristic
82C22×C17C2×#4111yescharacteristic
83C22×C172−1+412yes—
84C22×C172−1+412yes—
85C4×C17—42no—
86C4×C17—42no—
87C4×C17—42no—
88C4×C17#12414yes—
89Dic17—22no—
90Dic17—22no—
91Dic17—42no—
92Dic17—42no—
93Dic17—42no—
94C2×C4⋊Q8—171no—
95C2×#125—171no—
96#400—174no—
97#400—174no—
98#391—171no—
99#391—171no—
100#391—171no—
101#391D1711yescharacteristic
102#376—171no—
103C2×C17C2×#12411yescharacteristic
104C2×C17#53611yescharacteristic
105C2×C17#53611yescharacteristic
106C2×C17#54112yes—
107C2×C17#54112yes—
108C22×Q8—171no—
109C22×Q8C2×D1711yescharacteristic
110C4⋊Q8—344no—
111#125—344no—
112C2×C4⋊C4—171no—
113C2×C4⋊C4—172no—
114C2×C4⋊C4—172no—
115C2×C4⋊C4—172no—
116C2×C4⋊C4—172no—
117C2×C4⋊C4C2×D1711yescharacteristic
118C2×C42—171no—
119C2×C42—171no—
120C2×C42C2×D1711yescharacteristic
121#95—172no—
122#95—172no—
123#95—174no—
124#95—174no—
125#95—174no—
126#95C2×D1714yes—
127C17#264211yescharacteristic, complemented, Sylow
128C2×Q8—22no—
129C2×Q8—22no—
130C2×Q8—22no—
131C2×Q8—342no—
132C2×Q8—342no—
133C2×Q8—342no—
134C22×C4—171no—
135C22×C4—171no—
136C22×C4—172no—
137C22×C4—172no—
138C22×C4—172no—
139C22×C4C22×D1712yes—
140C22×C4C22×D1712yes—
141C22×C4C22×D1712yes—
142C22×C4C22×D1711yescharacteristic
143C4⋊C4—22no—
144C4⋊C4—344no—
145C4⋊C4—344no—
146C4⋊C4—344no—
147C4⋊C4—344no—
148C4⋊C4—342no—
149C42—22no—
150C42—174no—
151C42—342no—
152C23C23×D1711yescharacteristic
153Q8—44no—
154Q8—684no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—172no—
164C2×C4—172no—
165C2×C4—342no—
166C2×C4—342no—
167C2×C4—342no—
168C2×C4—342no—
169C2×C4—342no—
170C2×C4—342no—
171C2×C4—342no—
172C2×C4—344no—
173C2×C4—342no—
174C2×C4—342no—
175C2×C4#6325212yes—
176C2×C4D4×D1712yes—
177C2×C4#6325412yes—
178C22C2×#6325211yescharacteristic
179C22C2×D4×D1711yescharacteristic
180C22C2×#6325411yescharacteristic
181C22#1058769412yes—
182C22#1058769712yes—
183C4—42no—
184C4—42no—
185C4—42no—
186C4—342no—
187C4—342no—
188C4—682no—
189C4—682no—
190C4—682no—
191C4#1058757114yes—
192C2C2×#1058757111yescharacteristic
193C2#1176337911yescharacteristic
194C2#1176338411yescharacteristic
195C2#1176341712yes—
196C2#1176341912yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#391C2
hypercenter#391D17
hypocenterC17#2642
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
127. C17#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#105876302
C2×#105875762
#117627512
#117627502
#117627162
#117627152
#117627142
#117626552
C17×#3912
#264217