Finite Group Databasebeta

← #13120600

Subgroups — #13120600

Order 1664.

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

normal subgroups only

This group has 612 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×#88201C211yesmaximal, characteristic, complemented
2C2×#88200C211yesmaximal, characteristic, complemented
3C2×#88149C211yesmaximal, characteristic
4C2×#88126C211yesmaximal, characteristic, complemented
5C13×#391C211yesmaximal, characteristic, complemented
6#11718637C211yesmaximal, characteristic, complemented
7#11718600C211yesmaximal, characteristic, complemented
8#11718337C214yesmaximal, complemented
9#11718333C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×D52C2211yescharacteristic
12C22×D52C2212yes—
13C22×C4×D13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16#88201—24no—
17#88200—24no—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2214yes—
22C2×#6103C2214yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2214yes—
27C2×C4×Dic13C2211yescharacteristic
28#88149—24no—
29#88126—24no—
30C13×#95C2214yes—
31C23×D13C2312yes—
32C23×D13C2311yescharacteristic
33C2×Q8×C13—22no—
34C2×Q8×C13—22no—
35C2×Q8×C13—22no—
36C22×C4×C13C2312yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C2×D52—24no—
44C2×D52—22no—
45C2×D52—22no—
46C2×D52—22no—
47C2×D52—44no—
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×C4×D13D414yes—
51C13×C4⋊C4—22no—
52C42×C13—22no—
53#6103—24no—
54#6103—24no—
55#6103—24no—
56#6103—28no—
57#6103—44no—
58C4⋊Dic13—22no—
59#6101—24no—
60#6101—24no—
61#6101—44no—
62C4×Dic13D414yescomplemented
63#2620—131nomaximal, Sylow
64C23×C13C2411yescharacteristic
65C22×D13—21no—
66C22×D13—21no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—24no—
73C22×D13—24no—
74C22×D13C2×D412yes—
75Q8×C13—44no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—24no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D412yes—
86C2×C4×C13#4112yes—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—24no—
93C2×Dic13C2×D414yes—
94C2×Dic13C2×D412yes—
95D52—48no—
96D52—44no—
97C4×D13—28no—
98C2×#124—131no—
99C2×C22⋊Q8—131no—
100C2×#121—131no—
101C2×#117—131no—
102#396—134no—
103#394—134no—
104#391D1311yescharacteristic, complemented
105#390—131no—
106#384—131no—
107C22×C13C22×D411yescharacteristic
108C22×C13C22×D411yescharacteristic
109C22×C13C2×#4111yescharacteristic
110C22×C13H(5,𝔽2)12yes—
111C22×C132−1+412yes—
112C2×D13—22no—
113C2×D13—22no—
114C2×D13—22no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—44no—
121C2×D13—44no—
122C4×C13—42no—
123C4×C13—42no—
124C4×C13—42no—
125C4×C13#12114yes—
126Dic13—22no—
127Dic13—24no—
128Dic13—42no—
129C22×Q8C2×D1311yescharacteristic
130C22×D4—131no—
131C22×D4—132no—
132C23×C4—131no—
133#124—264no—
134C22⋊Q8—264no—
135#121—264no—
136#117—264no—
137C2×C4⋊C4—132no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—134no—
141C2×C4⋊C4C2×D1311yescharacteristic
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4—132no—
145C2×C22⋊C4—134no—
146C2×C22⋊C4—134no—
147C2×C42—131no—
148C2×C42C2×D1311yescharacteristic
149#95C2×D1314yes—
150C2×C13C2×#12111yescharacteristic
151C2×C13#53511yescharacteristic
152C2×C13#53611yescharacteristic
153C2×C13#53712yes—
154C2×C13#54212yes—
155D13—42no—
156D13—82no—
157C24—131no—
158C24—132no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×D4—264no—
163C2×D4—262no—
164C2×D4—262no—
165C2×D4—262no—
166C2×D4—524no—
167C22×C4—132no—
168C22×C4—131no—
169C22×C4—134no—
170C22×C4—132no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4C22×D1312yes—
174C22×C4C22×D1312yes—
175C22×C4C22×D1312yes—
176C22×C4C22×D1311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—264no—
179C4⋊C4—264no—
180C4⋊C4—262no—
181C4⋊C4—524no—
182C22⋊C4—264no—
183C22⋊C4—264no—
184C22⋊C4—268no—
185C22⋊C4—264no—
186C22⋊C4—524no—
187C42—22no—
188C42—134no—
189C13#262011yescharacteristic, complemented, Sylow
190C23—132no—
191C23—261no—
192C23—261no—
193C23—262no—
194C23—262no—
195C23—262no—
196C23—262no—
197C23—262no—
198C23—264no—
199C23—264no—
200C23C23×D1311yescharacteristic
201Q8—44no—
202D4—528no—
203D4—524no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—24no—
212C2×C4—134no—
213C2×C4—132no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—268no—
219C2×C4—262no—
220C2×C4—264no—
221C2×C4#612712yes—
222C2×C4D4×D1312yes—
223C2×C4D4×D1312yes—
224C22—262no—
225C22—262no—
226C22—262no—
227C22—522no—
228C22—522no—
229C22—522no—
230C22—522no—
231C22—524no—
232C22—524no—
233C22—522no—
234C22C2×#612711yescharacteristic
235C22C2×D4×D1311yescharacteristic
236C22C2×D4×D1311yescharacteristic
237C22#8825412yes—
238C22#8825612yes—
239C4—42no—
240C4—42no—
241C4—42no—
242C4—262no—
243C4—264no—
244C4—522no—
245C4#8813814yes—
246C2—522no—
247C2—1042no—
248C2C2×#8813811yescharacteristic
249C2#1171928712yes—
250C2#1171933412yes—
251C2#1171937911yescharacteristic
252C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#391C2
prime radicalC2×#88149C2
hypercenter#391D13
hypocenterC13#2620
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#88201C2semidirect
2. C2×#88200C2semidirect
4. C2×#88126C2semidirect
5. C13×#391C2semidirect
6. #11718637C2semidirect
7. #11718600C2semidirect
8. #11718337C2semidirect
9. #11718333C2semidirect
62. C4×Dic13D4semidirect
104. #391D13semidirect
189. C13#2620semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
C2×#882002
C2×#881492
C2×#881262
C13×#3912
#117186372
#117186002
#117183372
#117183332
#262013