Finite Group Databasebeta

← #13120040

Subgroups — #13120040

Order 1664.

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

normal subgroups only

This group has 500 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×#88198C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic
3C13×#395C211yesmaximal, characteristic
4#11718890C211yesmaximal, characteristic
5#11718640C211yesmaximal, characteristic
6#11718637C212yesmaximal
7#11718633C212yesmaximal
8#11718317C211yesmaximal, characteristic
9#11718310C211yesmaximal, characteristic
10#11718308C212yesmaximal
11#11718307C212yesmaximal
12C22×Q8×C13C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2212yes—
17#88198—24no—
18C2×C4⋊Dic13C2212yes—
19C2×#6101C2211yescharacteristic
20C2×#6101C2211yescharacteristic
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88141—24no—
31C13×#95C2212yes—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2211yescharacteristic
37C2×Q8×C13—22no—
38C2×Q8×C13—42no—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2311yescharacteristic
50C2×Dic26—22no—
51C2×Dic26—22no—
52C2×Dic26—22no—
53C2×Dic26—42no—
54C2×Dic26Q814yescomplemented
55C13×C4⋊C4—22no—
56C13×C4⋊C4—42no—
57C4⋊Dic13—42no—
58#6101—22no—
59#6101—22no—
60#6101—24no—
61#6101—24no—
62#6101—42no—
63#6101—42no—
64#6101Q818yescomplemented
65C4×Dic13—22no—
66C4×Dic13—22no—
67C4×Dic13—24no—
68C4×Dic13D414yes—
69#2567—131nomaximal, Sylow
70C23×C13C2411yescharacteristic
71Q8×C13—44no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
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×Q814yes—
84C2×C4×C13C2×Q812yes—
85C2×Dic13—21no—
86C2×Dic13—22no—
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×Q814yes—
97C2×Dic13C2×Q812yes—
98C2×Dic13C2×Q812yes—
99C2×Dic13C2×Q814yes—
100C2×Dic13#4112yes—
101Dic26—28no—
102Dic26—44no—
103C2×C4⋊Q8—131no—
104C2×C4×Q8—131no—
105#395—131no—
106#395—131no—
107#395—131no—
108#395D1311yescharacteristic
109#391—132no—
110#389—132no—
111#389—132no—
112#384—132no—
113C4×C4⋊C4—131no—
114C22×C13C22×D411yescharacteristic
115C22×C13C22×Q811yescharacteristic
116C22×C13C22×Q812yes—
117C22×C13C2×#4111yescharacteristic
118C22×C13H(5,𝔽2)12yes—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—24no—
122C4×C13—41no—
123C4×C13—42no—
124Dic13—22no—
125Dic13—24no—
126Dic13—42no—
127Dic13—41no—
128Dic13C22⋊Q814yes—
129Dic13C4⋊Q814yes—
130C22×Q8—131no—
131C22×Q8—131no—
132C22×Q8C2×D1311yescharacteristic
133C4⋊Q8—264no—
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—132no—
143C2×C4⋊C4C2×D1311yescharacteristic
144C2×C4⋊C4C2×D1312yes—
145C2×C42—131no—
146C2×C42—131no—
147C2×C42—131no—
148C2×C42—132no—
149#95—131no—
150#95—132no—
151#95—132no—
152#95—132no—
153#95C2×D1311yescharacteristic
154#95C2×D1312yes—
155C2×C13C2×C22⋊Q811yescharacteristic
156C2×C13C2×C4⋊Q811yescharacteristic
157C2×C13#53511yescharacteristic
158C2×C13#55412yes—
159C2×C13Q8212yes—
160C2×Q8—22no—
161C2×Q8—42no—
162C2×Q8—134no—
163C2×Q8—262no—
164C2×Q8—262no—
165C2×Q8—262no—
166C2×Q8—522no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4—131no—
173C22×C4C22×D1312yes—
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1311yescharacteristic
176C22×C4C22×D1311yescharacteristic
177C22×C4C22×D1312yes—
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—138no—
181C4⋊C4—262no—
182C4⋊C4—264no—
183C4⋊C4—264no—
184C4⋊C4—262no—
185C4⋊C4—522no—
186C4⋊C4—522no—
187C4⋊C4—522no—
188C42—134no—
189C42—262no—
190C42—262no—
191C42—264no—
192C13#256711yescharacteristic, complemented, Sylow
193C23C23×D1311yescharacteristic
194Q8—44no—
195Q8—268no—
196Q8—524no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—132no—
208C2×C4—132no—
209C2×C4—134no—
210C2×C4—132no—
211C2×C4—132no—
212C2×C4—134no—
213C2×C4—132no—
214C2×C4—261no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—261no—
218C2×C4—261no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—262no—
223C2×C4D4×D1312yes—
224C2×C4Q8×D1314yes—
225C2×C4Q8×D1312yes—
226C22C2×D4×D1311yescharacteristic
227C22#8825112yes—
228C22C2×Q8×D1311yescharacteristic
229C22C2×Q8×D1312yes—
230C22#41×D1311yescharacteristic
231C4—22no—
232C4—22no—
233C4—24no—
234C4—41no—
235C4—42no—
236C4—134no—
237C4—134no—
238C4—262no—
239C4—264no—
240C4—521no—
241C4—522no—
242C2#1171929711yescharacteristic
243C2D13×C22⋊Q811yescharacteristic
244C2#1171934112yes—
245C2#1171942712yes—
246C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, prime radical, cosocleC23×C13C24
FittingC13×#395C2
hypercenter#395D13
hypocenterC13#2567
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×Dic26Q8semidirect
64. #6101Q8semidirect
192. C13#2567semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C2×#881412
C13×#3952
#117188902
#117186402
#117186372
#117186332
#117183172
#117183102
#117183082
#117183072
#256713