Finite Group Databasebeta

← #13120954

Subgroups — #13120954

Order 1664.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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×#88198C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic
5#11718645C212yesmaximal
6#11718640C211yesmaximal, characteristic
7#11718637C212yesmaximal
8#11718318C212yesmaximal
9#11718317C211yesmaximal, characteristic
10#11718311C212yesmaximal
11#11718309C211yesmaximal, characteristic
12C22×Q8×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16#88198—24no—
17C2×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊Dic13C2212yes—
19C2×#6101C2211yescharacteristic
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2212yes—
29#88143—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C2×Q8×C13—22no—
38C2×Q8×C13—42no—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C2×Dic26—22no—
51C2×Dic26—42no—
52C13×C4⋊C4—22no—
53C13×C4⋊C4—42no—
54C4⋊Dic13—22no—
55C4⋊Dic13—42no—
56#6101—22no—
57#6101—22no—
58#6101—22no—
59#6101—22no—
60#6101—24no—
61#6101—24no—
62#6101—42no—
63#6101—42no—
64C4×Dic13D414yes—
65C4×Dic13Q818yescomplemented
66#2660—131nomaximal, Sylow
67C23×C13C2411yescharacteristic
68Q8×C13—44no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13C2×D412yes—
81C2×C4×C13C2×Q814yes—
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13—21no—
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13C2×D412yes—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×Q814yes—
97C2×Dic13C2×Q814yes—
98Dic26—44no—
99C2×C4⋊Q8—131no—
100C2×#125—131no—
101#398—132no—
102#398—132no—
103#395—131no—
104#395—131no—
105#395—131no—
106#395D1311yescharacteristic
107#384—132no—
108#382—132no—
109#376—131no—
110C22×C13C22×D411yescharacteristic
111C22×C13C22×Q812yes—
112C22×C13H(5,𝔽2)12yes—
113C22×C132−1+411yescharacteristic
114C22×C132−1+411yescharacteristic
115C4×C13—22no—
116C4×C13—24no—
117C4×C13—41no—
118C4×C13—42no—
119C4×C13—41no—
120Dic13—22no—
121Dic13—24no—
122Dic13—42no—
123Dic13—41no—
124Dic13—41no—
125Dic13C4⋊Q814yes—
126C22×Q8—131no—
127C22×Q8C2×D1311yescharacteristic
128C4⋊Q8—264no—
129#125—264no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4C2×D1311yescharacteristic
141C2×C4⋊C4C2×D1312yes—
142C2×C42—131no—
143C2×C42—132no—
144#95—131no—
145#95—132no—
146#95—132no—
147#95—132no—
148#95—132no—
149#95C2×D1311yescharacteristic
150#95C2×D1312yes—
151C2×C13C2×C4⋊Q811yescharacteristic
152C2×C13#53511yescharacteristic
153C2×C13#53611yescharacteristic
154C2×C13#54412yes—
155C2×C13#54412yes—
156C2×Q8—22no—
157C2×Q8—42no—
158C2×Q8—262no—
159C2×Q8—522no—
160C22×C4—131no—
161C22×C4—132no—
162C22×C4—131no—
163C22×C4—131no—
164C22×C4—132no—
165C22×C4—131no—
166C22×C4C22×D1311yescharacteristic
167C22×C4C22×D1312yes—
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1311yescharacteristic
170C22×C4C22×D1312yes—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—264no—
178C4⋊C4—264no—
179C4⋊C4—262no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C4⋊C4—522no—
183C42—134no—
184C42—138no—
185C13#266011yescharacteristic, complemented, Sylow
186C23C23×D1311yescharacteristic
187Q8—44no—
188Q8—524no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—132no—
201C2×C4—134no—
202C2×C4—132no—
203C2×C4—134no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—261no—
209C2×C4—261no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4D4×D1312yes—
217C2×C4Q8×D1314yes—
218C22C2×D4×D1311yescharacteristic
219C22#8825112yes—
220C22C2×Q8×D1312yes—
221C22#8825411yescharacteristic
222C22#8825711yescharacteristic
223C4—22no—
224C4—24no—
225C4—41no—
226C4—42no—
227C4—41no—
228C4—134no—
229C4—264no—
230C4—262no—
231C4—521no—
232C4—522no—
233C4—521no—
234C2#1171929711yescharacteristic
235C2#1171932812yes—
236C2#1171933311yescharacteristic
237C2D13×C4⋊Q811yescharacteristic
238C2#1171943412yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2660
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
65. C4×Dic13Q8semidirect
185. C13#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881432
C13×#3952
#117188902
#117186452
#117186402
#117186372
#117183182
#117183172
#117183112
#117183092
#266013