Finite Group Databasebeta

← #13120218

Subgroups — #13120218

Order 1664.

468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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×Q8×Dic13C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic
5#11718646C212yesmaximal
6#11718644C211yesmaximal, characteristic
7#11718633C212yesmaximal
8#11718322C211yesmaximal, characteristic
9#11718310C211yesmaximal, characteristic
10#11718308C212yesmaximal
11#11718308C212yesmaximal
12C22×Q8×C13C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2212yes—
15Q8×Dic13—24no—
16C2×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊Dic13C2212yes—
20C2×#6101C2211yescharacteristic
21C2×#6101C2211yescharacteristic
22C2×#6101C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88143—24no—
31C13×#95C2212yes—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C2×Q8×C13—22no—
38C2×Q8×C13—24no—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×C4×C13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C13×C4⋊C4—22no—
51C13×C4⋊C4—24no—
52C4⋊Dic13—22no—
53C4⋊Dic13—22no—
54C4⋊Dic13—24no—
55C4⋊Dic13—42no—
56#6101—22no—
57#6101—24no—
58#6101—22no—
59#6101—22no—
60#6101—22no—
61#6101—42no—
62#6101Q818yescomplemented
63C4×Dic13—24no—
64C4×Dic13—42no—
65C4×Dic13D414yes—
66#2584—131nomaximal, Sylow
67C23×C13C2411yescharacteristic
68Q8×C13—28no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13C2×D412yes—
80C2×C4×C13C2×Q814yes—
81C2×C4×C13#4114yes—
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13—22no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—21no—
94C2×Dic13C2×D412yes—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×Q814yes—
97C2×Dic13C2×Q814yes—
98C2×#125—131no—
99C2×C4×Q8—131no—
100#398—131no—
101#398—131no—
102#395—131no—
103#395D1311yescharacteristic
104#389—132no—
105#389—132no—
106#389—132no—
107#389—132no—
108C4×C4⋊C4—131no—
109C22×C13C22×D411yescharacteristic
110C22×C13C22×Q812yes—
111C22×C13C2×#4112yes—
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C132−1+411yescharacteristic
114C4×C13—22no—
115C4×C13—24no—
116C4×C13—24no—
117C4×C13—41no—
118C4×C13—41no—
119Dic13—22no—
120Dic13—24no—
121Dic13—41no—
122Dic13—42no—
123Dic13—41no—
124Dic13C4⋊Q814yes—
125C22×Q8C2×D1311yescharacteristic
126#125—264no—
127C4×Q8—264no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—131no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—131no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4C2×D1311yescharacteristic
140C2×C4⋊C4C2×D1312yes—
141C2×C42—131no—
142C2×C42—132no—
143C2×C42—132no—
144#95—131no—
145#95—132no—
146#95—132no—
147#95—132no—
148#95C2×D1311yescharacteristic
149#95C2×D1312yes—
150C2×C13#52511yescharacteristic
151C2×C13C2×C4⋊Q811yescharacteristic
152C2×C13#53711yescharacteristic
153C2×C13#55412yes—
154C2×C13#55712yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C22×C4—131no—
158C22×C4—132no—
159C22×C4—131no—
160C22×C4—132no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4C22×D1311yescharacteristic
164C22×C4C22×D1311yescharacteristic
165C22×C4C22×D1311yescharacteristic
166C22×C4C22×D1312yes—
167C22×C4C22×D1312yes—
168C4⋊C4—22no—
169C4⋊C4—24no—
170C4⋊C4—138no—
171C4⋊C4—264no—
172C4⋊C4—262no—
173C4⋊C4—262no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—264no—
179C4⋊C4—522no—
180C4⋊C4—522no—
181C42—134no—
182C42—264no—
183C42—522no—
184C13#258411yescharacteristic, complemented, Sylow
185C23C23×D1311yescharacteristic
186Q8—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—132no—
198C2×C4—134no—
199C2×C4—132no—
200C2×C4—134no—
201C2×C4—262no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—262no—
205C2×C4—262no—
206C2×C4—261no—
207C2×C4—261no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—261no—
211C2×C4—262no—
212C2×C4—261no—
213C2×C4D4×D1312yes—
214C2×C4#612914yes—
215C2×C4Q8×D1314yes—
216C22C2×D4×D1311yescharacteristic
217C22C2×#612912yes—
218C22C2×Q8×D1312yes—
219C22#8825411yescharacteristic
220C22#8825611yescharacteristic
221C4—22no—
222C4—24no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—134no—
227C4—262no—
228C4—264no—
229C4—521no—
230C4—522no—
231C4—521no—
232C2#1171929111yescharacteristic
233C2#1171933411yescharacteristic
234C2#1171934012yes—
235C2#1171942612yes—
236C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2584
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
62. #6101Q8semidirect
184. C13#2584semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881432
C13×#3952
#117188902
#117186462
#117186442
#117186332
#117183222
#117183102
#117183082
#258413