Finite Group Databasebeta

← #14534659

Subgroups — #14534659

Order 2176.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587575C211yesmaximal, characteristic
2C2×Q8×Dic17C211yesmaximal, characteristic
3#11762751C212yesmaximal
4#11762749C211yesmaximal, characteristic
5#11762748C211yesmaximal, characteristic
6#11762742C212yesmaximal
7#11762728C211yesmaximal, characteristic
8#11762695C212yesmaximal
9#11762691C212yesmaximal
10#11762676C211yesmaximal, characteristic
11C17×#395C211yesmaximal, characteristic
12C22×Q8×C17C2211yescharacteristic
13C2×C4⋊C4×C17C2212yes—
14C2×C4⋊C4×C17C2211yescharacteristic
15Q8×Dic17—24no—
16C2×C4⋊Dic17C2211yescharacteristic
17C2×C4⋊Dic17C2212yes—
18C2×C4⋊Dic17C2211yescharacteristic
19C2×#63225C2211yescharacteristic
20C2×#63225C2212yes—
21C2×#63225C2211yescharacteristic
22C2×#63225C2211yescharacteristic
23C2×#63225C2211yescharacteristic
24C2×C4×Dic17C2212yes—
25C2×C4×Dic17C2211yescharacteristic
26#10587575—24no—
27C17×#95C2212yes—
28C17×#95C2211yescharacteristic
29#10587502C2212yes—
30#10587502C2212yes—
31#10587502C2212yes—
32#10587502C2212yes—
33#10587502C2212yes—
34#10587502C2212yes—
35#10587502C2211yescharacteristic
36#10587502C2212yes—
37C2×Q8×C17—22no—
38C2×Q8×C17—24no—
39C22×C4×C17C2312yes—
40C22×C4×C17C2311yescharacteristic
41C22×C4×C17C2311yescharacteristic
42C22×C4×C17C2311yescharacteristic
43C22×C4×C17C2312yes—
44C22×Dic17C2312yes—
45C22×Dic17C2312yes—
46C22×Dic17C2311yescharacteristic
47C22×Dic17C2311yescharacteristic
48C22×Dic17C2311yescharacteristic
49C22×Dic17C2311yescharacteristic
50C4⋊C4×C17—22no—
51C4⋊C4×C17—24no—
52C4⋊Dic17—22no—
53C4⋊Dic17—22no—
54C4⋊Dic17—24no—
55#63225—22no—
56#63225—24no—
57#63225—22no—
58#63225—22no—
59#63225—22no—
60C4×Dic17—24no—
61C4×Dic17D414yes—
62C23×C17C2411yescharacteristic
63Q8×C17—28no—
64C2×C4×C17—22no—
65C2×C4×C17—22no—
66C2×C4×C17—22no—
67C2×C4×C17—21no—
68C2×C4×C17—21no—
69C2×C4×C17—22no—
70C2×C4×C17—22no—
71C2×C4×C17—21no—
72C2×C4×C17—22no—
73C2×C4×C17—21no—
74C2×C4×C17—22no—
75C2×C4×C17C2×D412yes—
76C2×C4×C17#4114yes—
77C2×Dic17—21no—
78C2×Dic17—22no—
79C2×Dic17—21no—
80C2×Dic17—22no—
81C2×Dic17—21no—
82C2×Dic17—21no—
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—24no—
86C2×Dic17—21no—
87C2×Dic17—22no—
88C2×Dic17—22no—
89C2×Dic17—21no—
90C2×Dic17C2×D412yes—
91C2×Dic17C2×D412yes—
92#2634—171nomaximal, Sylow
93C22×C17C22×D411yescharacteristic
94C22×C17C2×#4112yes—
95C22×C172−1+411yescharacteristic
96C22×C172−1+412yes—
97C22×C172−1+411yescharacteristic
98C4×C17—22no—
99C4×C17—24no—
100C4×C17—41no—
101C4×C17—41no—
102C4×C17—42no—
103Dic17—22no—
104Dic17—22no—
105Dic17—41no—
106Dic17—41no—
107Dic17—42no—
108Dic17—42no—
109C2×#125—171no—
110C2×C4×Q8—171no—
111#400—171no—
112#400—171no—
113#400—172no—
114#398—172no—
115#395—171no—
116#395D1711yescharacteristic
117#387—172no—
118#387—172no—
119#383—171no—
120C2×C17#52511yescharacteristic
121C2×C17#53611yescharacteristic
122C2×C17#53611yescharacteristic
123C2×C17#54112yes—
124C2×C17#54112yes—
125C22×Q8C2×D1711yescharacteristic
126#125—344no—
127C4×Q8—344no—
128C2×C4⋊C4—172no—
129C2×C4⋊C4—171no—
130C2×C4⋊C4—171no—
131C2×C4⋊C4—171no—
132C2×C4⋊C4—171no—
133C2×C4⋊C4—171no—
134C2×C4⋊C4—171no—
135C2×C4⋊C4—172no—
136C2×C4⋊C4C2×D1711yescharacteristic
137C2×C4⋊C4C2×D1712yes—
138C2×C42—171no—
139C2×C42—172no—
140#95—172no—
141#95—171no—
142#95—172no—
143#95—172no—
144#95—172no—
145#95—172no—
146#95—172no—
147#95—172no—
148#95C2×D1711yescharacteristic
149#95C2×D1712yes—
150C17#263411yescharacteristic, complemented, Sylow
151C2×Q8—22no—
152C2×Q8—24no—
153C22×C4—171no—
154C22×C4—171no—
155C22×C4—172no—
156C22×C4—172no—
157C22×C4—171no—
158C22×C4—171no—
159C22×C4C22×D1712yes—
160C22×C4C22×D1711yescharacteristic
161C22×C4C22×D1711yescharacteristic
162C22×C4C22×D1711yescharacteristic
163C22×C4C22×D1712yes—
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—344no—
167C4⋊C4—342no—
168C4⋊C4—342no—
169C4⋊C4—342no—
170C4⋊C4—342no—
171C4⋊C4—342no—
172C4⋊C4—342no—
173C4⋊C4—344no—
174C42—174no—
175C42—344no—
176C23C23×D1711yescharacteristic
177Q8—28no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—172no—
190C2×C4—172no—
191C2×C4—341no—
192C2×C4—342no—
193C2×C4—341no—
194C2×C4—342no—
195C2×C4—341no—
196C2×C4—341no—
197C2×C4—342no—
198C2×C4—342no—
199C2×C4—341no—
200C2×C4—344no—
201C2×C4—342no—
202C2×C4—342no—
203C2×C4—341no—
204C2×C4D4×D1712yes—
205C2×C4#6325414yes—
206C22C2×D4×D1711yescharacteristic
207C22C2×#6325412yes—
208C22#1058769411yescharacteristic
209C22#1058769412yes—
210C22#1058769711yescharacteristic
211C4—22no—
212C4—24no—
213C4—41no—
214C4—41no—
215C4—42no—
216C4—342no—
217C4—342no—
218C4—681no—
219C4—681no—
220C4—682no—
221C4—682no—
222C2#1176331511yescharacteristic
223C2#1176338211yescharacteristic
224C2#1176338411yescharacteristic
225C2#1176341912yes—
226C2#1176342012yes—
subgroupG/H
center, FrattiniC23C23×D17
commutator, socle, prime radical, cosocleC23×C17C24
FittingC17×#395C2
hypercenter#395D17
hypocenterC17#2634
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
150. C17#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#105875752
C2×Q8×Dic172
#117627512
#117627492
#117627482
#117627422
#117627282
#117626952
#117626912
#117626762
C17×#3952
#263417