Finite Group Databasebeta

← #13119820

Subgroups — #13119820

Order 1664.

540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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×#88142C212yesmaximal
2C2×#88142C211yesmaximal, characteristic
3C2×#88141C211yesmaximal, characteristic
4C13×#398C211yesmaximal, characteristic
5#11718644C211yesmaximal, characteristic
6#11718641C211yesmaximal, characteristic
7#11718633C212yesmaximal
8#11718322C211yesmaximal, characteristic
9#11718310C211yesmaximal, characteristic
10#11718308C212yesmaximal
11#11718307C212yesmaximal
12C22×Dic26C2212yes—
13C22×Dic26C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×C4⋊Dic13C2211yescharacteristic
19C2×#6101C2211yescharacteristic
20C2×#6101C2211yescharacteristic
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29#88142—28no—
30#88142—24no—
31#88141—24no—
32C13×#95C2212yes—
33C13×#95C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2211yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C2×Dic26—22no—
50C2×Dic26—22no—
51C2×Dic26—24no—
52C2×Dic26—24no—
53C2×Dic26—24no—
54C2×Dic26D414yes—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—24no—
57C13×C4⋊C4—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—24no—
60#6101—22no—
61#6101—24no—
62#6101—22no—
63#6101—24no—
64#6101—24no—
65#6101Q818yescomplemented
66C4×Dic13—22no—
67C4×Dic13—22no—
68C4×Dic13—24no—
69C4×Dic13D414yes—
70#2546—131nomaximal, Sylow
71C23×C13C2411yescharacteristic
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2×Q814yes—
85C2×Dic13—22no—
86C2×Dic13—21no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13C2×D412yes—
95C2×Dic13C2×D412yes—
96C2×Dic13C2×D412yes—
97C2×Dic13C2×D412yes—
98C2×Dic13C2×Q814yes—
99C2×Dic13C2×Q814yes—
100C2×Dic13#4112yes—
101Dic26—28no—
102Dic26—48no—
103C2×C4⋊Q8—131no—
104C2×C4⋊Q8—132no—
105C2×C4×Q8—131no—
106#398—131no—
107#398—131no—
108#398—131no—
109#398D1311yescharacteristic
110#391—132no—
111#389—132no—
112#389—132no—
113C4×C4⋊C4—131no—
114C22×C13C22×D411yescharacteristic
115C22×C13C22×D411yescharacteristic
116C22×C13C22×Q812yes—
117C22×C13C2×#4111yescharacteristic
118C22×C132−1+412yes—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—24no—
122C4×C13—42no—
123C4×C13—41no—
124Dic13—22no—
125Dic13—24no—
126Dic13—42no—
127Dic13—41no—
128Dic13#12114yes—
129Dic13C4⋊Q814yescomplemented
130C22×Q8—131no—
131C22×Q8—132no—
132C4⋊Q8—264no—
133C4⋊Q8—268no—
134C4×Q8—264no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—131no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—132no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—132no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4C2×D1311yescharacteristic
144C2×C4⋊C4C2×D1312yes—
145C2×C4⋊C4C2×D1311yescharacteristic
146C2×C42—131no—
147C2×C42—131no—
148C2×C42—131no—
149C2×C42—132no—
150#95—131no—
151#95—132no—
152#95—132no—
153#95—132no—
154#95C2×D1311yescharacteristic
155#95C2×D1312yes—
156C2×C13C2×#12111yescharacteristic
157C2×C13C2×C4⋊Q811yescharacteristic
158C2×C13#53611yescharacteristic
159C2×C13D4×Q812yes—
160C2×C13#55712yes—
161C2×Q8—134no—
162C2×Q8—262no—
163C2×Q8—262no—
164C2×Q8—264no—
165C2×Q8—264no—
166C2×Q8—264no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—132no—
170C22×C4—131no—
171C22×C4—131no—
172C22×C4—132no—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1312yes—
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C22×C4C22×D1312yes—
178C4⋊C4—22no—
179C4⋊C4—24no—
180C4⋊C4—22no—
181C4⋊C4—138no—
182C4⋊C4—262no—
183C4⋊C4—264no—
184C4⋊C4—264no—
185C4⋊C4—264no—
186C4⋊C4—262no—
187C4⋊C4—264no—
188C4⋊C4—262no—
189C42—134no—
190C42—262no—
191C42—262no—
192C42—264no—
193C13#254611yescharacteristic, complemented, Sylow
194C23C23×D1311yescharacteristic
195Q8—268no—
196Q8—528no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—132no—
208C2×C4—132no—
209C2×C4—132no—
210C2×C4—134no—
211C2×C4—132no—
212C2×C4—132no—
213C2×C4—134no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—262no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4D4×D1312yes—
224C2×C4D4×D1312yes—
225C2×C4Q8×D1314yes—
226C22C2×D4×D1311yescharacteristic
227C22C2×D4×D1311yescharacteristic
228C22C2×Q8×D1312yes—
229C22#41×D1311yescharacteristic
230C22#8825712yes—
231C4—22no—
232C4—24no—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—134no—
237C4—134no—
238C4—262no—
239C4—264no—
240C4—522no—
241C4—521no—
242C2D13×#12111yescharacteristic
243C2#1171933712yes—
244C2#1171935311yescharacteristic
245C2#1171939012yes—
246C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#398C2
hypercenter#398D13
hypocenterC13#2546
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. #6101Q8semidirect
129. Dic13C4⋊Q8semidirect
193. C13#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×#881412
C13×#3982
#117186442
#117186412
#117186332
#117183222
#117183102
#117183082
#117183072
#254613