Finite Group Databasebeta

← #13118826

Subgroups — #13118826

Order 1664.

668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×D4×Dic13C212yesmaximal, complemented
2C2×#88132C212yesmaximal, complemented
3C13×#392C211yesmaximal, characteristic
4#11718883C212yesmaximal, complemented
5#11718881C212yesmaximal, complemented
6#11718608C211yesmaximal, characteristic, complemented
7#11718607C211yesmaximal, characteristic, complemented
8#11718605C212yesmaximal, complemented
9#11718314C212yesmaximal, complemented
10C22×D4×C13C2212yes—
11C22×D4×C13C2211yescharacteristic
12C23×Dic13C2212yes—
13C23×Dic13C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2211yescharacteristic
22D4×Dic13—28no—
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2212yes—
27#88132—28no—
28C13×#95C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2211yescharacteristic
33C24×C13C2312yes—
34C24×C13C2311yescharacteristic
35C2×D4×C13—24no—
36C2×D4×C13—24no—
37C2×D4×C13—24no—
38C2×D4×C13—24no—
39C2×D4×C13—41no—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×Dic13—24no—
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—42no—
47C22×Dic13—41no—
48C22×Dic13C2312yes—
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C22×Dic13C2312yes—
52C2×Dic26—24no—
53C2×Dic26—41no—
54C13×C22⋊C4—24no—
55C13×C22⋊C4—41no—
56C22⋊Dic13—24no—
57C22⋊Dic13—22no—
58C22⋊Dic13—24no—
59C22⋊Dic13—24no—
60C22⋊Dic13—24no—
61C4⋊Dic13D418yescomplemented
62#6101—24no—
63#6101—24no—
64C4×Dic13—24no—
65#2463—131nomaximal, Sylow
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13#4112yes—
77C23×C13#4114yes—
78C23×C13C2411yescharacteristic
79D4×C13—216no—
80D4×C13—44no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13C2×D414yes—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—48no—
99C2×Dic13—44no—
100C2×Dic13C2×D414yes—
101C2×Dic13C2×D414yes—
102Dic26—44no—
103C2×C22⋊Q8—132no—
104C2×C4×D4—132no—
105#394—132no—
106#393—131no—
107#392D1311yescharacteristic
108#388—132no—
109#387—132no—
110#386—132no—
111#385—131no—
112C22×C13—24no—
113C22×C13—24no—
114C22×C13—22no—
115C22×C13—24no—
116C22×C13—24no—
117C22×C13—42no—
118C22×C13—42no—
119C22×C13—42no—
120C22×C13—41no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13—41no—
124C22×C13C22×D412yes—
125C22×C13C2×#4111yescharacteristic
126C22×C13C2×#4112yes—
127C22×C13H(5,𝔽2)11yescharacteristic
128C22×C132−1+411yescharacteristic
129C4×C13—24no—
130C4×C13—41no—
131C4×C13—41no—
132Dic13—24no—
133Dic13—24no—
134Dic13—42no—
135Dic13—42no—
136C22×Q8—131no—
137C22×D4C2×D1312yes—
138C22×D4C2×D1311yescharacteristic
139C23×C4—131no—
140C23×C4—132no—
141C22⋊Q8—268no—
142C4×D4—268no—
143C2×C4⋊C4—132no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—132no—
146C2×C22⋊C4—132no—
147C2×C22⋊C4—132no—
148C2×C22⋊C4—132no—
149C2×C22⋊C4—131no—
150C2×C22⋊C4—132no—
151C2×C22⋊C4C2×D1312yes—
152C2×C22⋊C4C2×D1311yescharacteristic
153C2×C42—132no—
154#95—132no—
155#95—132no—
156#95—132no—
157#95—131no—
158#95C2×D1311yescharacteristic
159C2×C13—42no—
160C2×C13—44no—
161C2×C13#52512yes—
162C2×C13#53911yescharacteristic
163C2×C13D4211yescharacteristic
164C2×C13#54812yes—
165C2×C13#55111yescharacteristic
166C24C22×D1312yes—
167C24C22×D1311yescharacteristic
168C2×Q8—264no—
169C2×Q8—521no—
170C2×D4—24no—
171C2×D4—24no—
172C2×D4—24no—
173C2×D4—24no—
174C2×D4—41no—
175C22×C4—132no—
176C22×C4—132no—
177C22×C4—132no—
178C22×C4—132no—
179C22×C4—264no—
180C22×C4—264no—
181C22×C4—264no—
182C22×C4—521no—
183C22×C4—522no—
184C22×C4C22×D1311yescharacteristic
185C22×C4C22×D1311yescharacteristic
186C22×C4C22×D1312yes—
187C4⋊C4—138no—
188C4⋊C4—264no—
189C4⋊C4—264no—
190C22⋊C4—24no—
191C22⋊C4—41no—
192C22⋊C4—264no—
193C22⋊C4—264no—
194C22⋊C4—264no—
195C22⋊C4—262no—
196C22⋊C4—264no—
197C42—264no—
198C13#246311yescharacteristic, complemented, Sylow
199C23—22no—
200C23—22no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23#612912yes—
210C23#612914yes—
211C23C23×D1311yescharacteristic
212Q8—524no—
213D4—216no—
214D4—44no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—134no—
222C2×C4—134no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—524no—
234C2×C4—528no—
235C2×C4D4×D1314yes—
236C22—24no—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—22no—
241C22—42no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22C2×D4×D1312yes—
249C22C2×#612911yescharacteristic
250C22C2×#612912yes—
251C22#8825111yescharacteristic
252C22#8825711yescharacteristic
253C4—24no—
254C4—41no—
255C4—41no—
256C4—264no—
257C4—264no—
258C4—522no—
259C4—522no—
260C2—42no—
261C2—44no—
262C2#1171929112yes—
263C2#1171929211yescharacteristic
264C2#1171930312yes—
265C2#1171930711yescharacteristic
266C2#1171942211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
Fitting, prime radicalC13×#392C2
hypercenter#392D13
hypocenterC13#2463
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic13C2semidirect
2. C2×#88132C2semidirect
4. #11718883C2semidirect
5. #11718881C2semidirect
6. #11718608C2semidirect
7. #11718607C2semidirect
8. #11718605C2semidirect
9. #11718314C2semidirect
61. C4⋊Dic13D4semidirect
198. C13#2463semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881322
C13×#3922
#117188832
#117188812
#117186082
#117186072
#117186052
#117183142
#246313