Finite Group Databasebeta

← #14534665

Subgroups — #14534665

Order 2176.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10587576C211yesmaximal, characteristic
2C2×#10587573C211yesmaximal, characteristic
3#11762750C212yesmaximal
4#11762749C211yesmaximal, characteristic
5#11762748C211yesmaximal, characteristic
6#11762740C211yesmaximal, characteristic
7#11762729C212yesmaximal
8#11762696C212yesmaximal
9#11762695C212yesmaximal
10#11762676C211yesmaximal, characteristic
11C17×#398C211yesmaximal, characteristic
12C22×Dic34C2211yescharacteristic
13C2×C4⋊C4×C17C2212yes—
14C2×C4⋊C4×C17C2211yescharacteristic
15C2×C4⋊C4×C17C2211yescharacteristic
16C2×C4⋊Dic17C2212yes—
17C2×C4⋊Dic17C2211yescharacteristic
18C2×#63225C2212yes—
19C2×#63225C2212yes—
20C2×#63225C2211yescharacteristic
21C2×#63225C2211yescharacteristic
22C2×C4×Dic17C2211yescharacteristic
23C2×C4×Dic17C2211yescharacteristic
24C2×C4×Dic17C2211yescharacteristic
25#10587576—24no—
26#10587573—24no—
27C17×#95C2212yes—
28C17×#95C2211yescharacteristic
29#10587502C2212yes—
30#10587502C2212yes—
31#10587502C2212yes—
32#10587502C2212yes—
33#10587502C2212yes—
34#10587502C2212yes—
35#10587502C2212yes—
36#10587502C2211yescharacteristic
37C22×C4×C17C2312yes—
38C22×C4×C17C2311yescharacteristic
39C22×C4×C17C2312yes—
40C22×C4×C17C2311yescharacteristic
41C22×C4×C17C2311yescharacteristic
42C22×Dic17C2312yes—
43C22×Dic17C2311yescharacteristic
44C22×Dic17C2312yes—
45C22×Dic17C2311yescharacteristic
46C22×Dic17C2311yescharacteristic
47C22×Dic17C2311yescharacteristic
48C2×Dic34—22no—
49C2×Dic34—22no—
50C2×Dic34—22no—
51C4⋊C4×C17—22no—
52C4⋊C4×C17—22no—
53C4⋊C4×C17—24no—
54C4⋊Dic17—22no—
55C4⋊Dic17—24no—
56#63225—22no—
57#63225—22no—
58#63225—24no—
59#63225—24no—
60C4×Dic17—22no—
61C4×Dic17—22no—
62C4×Dic17D414yes—
63C23×C17C2411yescharacteristic
64C2×C4×C17—21no—
65C2×C4×C17—21no—
66C2×C4×C17—22no—
67C2×C4×C17—21no—
68C2×C4×C17—22no—
69C2×C4×C17—22no—
70C2×C4×C17—22no—
71C2×C4×C17—22no—
72C2×C4×C17—22no—
73C2×C4×C17—22no—
74C2×C4×C17—22no—
75C2×C4×C17C2×D412yes—
76C2×C4×C17#4112yes—
77C2×Dic17—21no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—22no—
82C2×Dic17—21no—
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—24no—
86C2×Dic17—22no—
87C2×Dic17—22no—
88C2×Dic17—22no—
89C2×Dic17C2×D412yes—
90C2×Dic17C2×D412yes—
91C2×Dic17#4112yes—
92Dic34—28no—
93#2634—171nomaximal, Sylow
94C22×C17C22×D411yescharacteristic
95C22×C17C2×#4111yescharacteristic
96C22×C17C2×#4111yescharacteristic
97C22×C172−1+412yes—
98C22×C172−1+412yes—
99C4×C17—22no—
100C4×C17—22no—
101C4×C17—42no—
102C4×C17—41no—
103C4×C17—42no—
104Dic17—22no—
105Dic17—22no—
106Dic17—22no—
107Dic17—41no—
108Dic17—42no—
109Dic17—42no—
110C2×#125—171no—
111C2×C4×Q8—171no—
112#400—171no—
113#400—171no—
114#400—172no—
115#398—171no—
116#398D1711yescharacteristic
117#395—172no—
118#387—172no—
119#387—172no—
120#383—171no—
121C2×C17#52511yescharacteristic
122C2×C17#53611yescharacteristic
123C2×C17#53611yescharacteristic
124C2×C17#54112yes—
125C2×C17#54112yes—
126C22×Q8—171no—
127#125—344no—
128C4×Q8—344no—
129C2×C4⋊C4—171no—
130C2×C4⋊C4—171no—
131C2×C4⋊C4—172no—
132C2×C4⋊C4—172no—
133C2×C4⋊C4—171no—
134C2×C4⋊C4—172no—
135C2×C4⋊C4C2×D1711yescharacteristic
136C2×C4⋊C4C2×D1711yescharacteristic
137C2×C4⋊C4C2×D1712yes—
138C2×C42—171no—
139C2×C42—171no—
140C2×C42—171no—
141#95—172no—
142#95—172no—
143#95—171no—
144#95—172no—
145#95—172no—
146#95—172no—
147#95—172no—
148#95—172no—
149#95C2×D1711yescharacteristic
150#95C2×D1712yes—
151C17#263411yescharacteristic, complemented, Sylow
152C2×Q8—342no—
153C2×Q8—342no—
154C2×Q8—342no—
155C22×C4—171no—
156C22×C4—171no—
157C22×C4—171no—
158C22×C4—172no—
159C22×C4—171no—
160C22×C4—172no—
161C22×C4C22×D1712yes—
162C22×C4C22×D1711yescharacteristic
163C22×C4C22×D1712yes—
164C22×C4C22×D1711yescharacteristic
165C22×C4C22×D1711yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—24no—
169C4⋊C4—342no—
170C4⋊C4—344no—
171C4⋊C4—344no—
172C4⋊C4—344no—
173C4⋊C4—342no—
174C4⋊C4—342no—
175C42—174no—
176C42—342no—
177C42—342no—
178C23C23×D1711yescharacteristic
179Q8—348no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—172no—
192C2×C4—172no—
193C2×C4—172no—
194C2×C4—341no—
195C2×C4—341no—
196C2×C4—341no—
197C2×C4—342no—
198C2×C4—341no—
199C2×C4—341no—
200C2×C4—342no—
201C2×C4—344no—
202C2×C4—342no—
203C2×C4—342no—
204C2×C4—342no—
205C2×C4—342no—
206C2×C4D4×D1712yes—
207C2×C4#6325412yes—
208C22C2×D4×D1711yescharacteristic
209C22C2×#6325411yescharacteristic
210C22#1058769412yes—
211C22#41×D1711yescharacteristic
212C22#1058769712yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—41no—
217C4—42no—
218C4—342no—
219C4—342no—
220C4—342no—
221C4—681no—
222C4—682no—
223C4—682no—
224C2#1176331911yescharacteristic
225C2#1176338111yescharacteristic
226C2#1176338411yescharacteristic
227C2#1176341812yes—
228C2#1176341912yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#398C2
hypercenter#398D17
hypocenterC17#2634
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
151. C17#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#105875762
C2×#105875732
#117627502
#117627492
#117627482
#117627402
#117627292
#117626962
#117626952
#117626762
C17×#3982
#263417