Finite Group Databasebeta

← #13121845

Subgroups — #13121845

Order 1664.

492 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 137 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
2C2×#88198C211yesmaximal, characteristic, complemented
3C13×#391C211yesmaximal, characteristic, complemented
4#11718655C212yesmaximal, complemented
5#11718601C212yesmaximal, complemented
6#11718334C212yesmaximal, complemented
7#11718333C212yesmaximal
8#11718331C212yesmaximal, complemented
9#11718314C212yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×D52C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C42×C13C2211yescharacteristic
15#88201—24no—
16#88198—24no—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28C13×#95C2212yes—
29C13×#95C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33C23×D13C2312yes—
34C2×Q8×C13—41no—
35C2×Q8×C13—41no—
36C2×Q8×C13D414yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×D52—22no—
46C2×D52—41no—
47C2×D52—41no—
48C2×Dic26—22no—
49C2×Dic26—41no—
50C2×Dic26—41no—
51C13×C4⋊C4—41no—
52C42×C13—41no—
53#6103—24no—
54#6103—24no—
55#6103—24no—
56#6103—24no—
57#6103—42no—
58#6103—42no—
59C4⋊Dic13—24no—
60#6101—24no—
61#6101—24no—
62C4×Dic13—22no—
63C4×Dic13—22no—
64#2731—131nomaximal, Sylow
65C23×C13C2411yescharacteristic
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73Q8×C13—44no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×D412yes—
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#4114yes—
98D52—44no—
99Dic26—44no—
100C2×C4⋊Q8—131no—
101C2×#124—131no—
102#396—132no—
103#394—132no—
104#393—132no—
105#391D1311yescharacteristic, complemented
106#388—132no—
107#388—132no—
108#387—132no—
109C22×C13C22×D411yescharacteristic
110C22×C13C2×#4112yes—
111C22×C13H(5,𝔽2)11yescharacteristic
112C22×C13H(5,𝔽2)11yescharacteristic
113C22×C132−1+412yes—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—42no—
121C4×C13—22no—
122C4×C13—22no—
123C4×C13—22no—
124C4×C13—42no—
125C4×C13—42no—
126Dic13—24no—
127Dic13—42no—
128Dic13—42no—
129C22×Q8—131no—
130C22×Q8C2×D1311yescharacteristic
131C22×D4—131no—
132C4⋊Q8—264no—
133#124—264no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4C2×D1311yescharacteristic
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C42—131no—
145C2×C42—131no—
146C2×C42C2×D1311yescharacteristic
147#95—132no—
148#95—132no—
149#95—132no—
150#95C2×D1312yes—
151#95C2×D1312yes—
152C2×C13#53411yescharacteristic
153C2×C13#54212yes—
154C2×C13#54812yes—
155C2×C13#55511yescharacteristic
156C2×C13#56311yescharacteristic
157D13—82no—
158C24—132no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—262no—
162C2×Q8—521no—
163C2×Q8—521no—
164C2×Q8D5214yes—
165C2×D4—262no—
166C2×D4—521no—
167C2×D4—521no—
168C22×C4—132no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4C22×D1312yes—
172C22×C4C22×D1312yes—
173C22×C4C22×D1311yescharacteristic
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1311yescharacteristic
176C4⋊C4—41no—
177C4⋊C4—264no—
178C4⋊C4—264no—
179C4⋊C4—264no—
180C22⋊C4—264no—
181C22⋊C4—264no—
182C22⋊C4—264no—
183C22⋊C4—264no—
184C22⋊C4—522no—
185C22⋊C4—522no—
186C42—41no—
187C42—262no—
188C42—262no—
189C13#273111yescharacteristic, complemented, Sylow
190C23—262no—
191C23—262no—
192C23—262no—
193C23—262no—
194C23—262no—
195C23—262no—
196C23—262no—
197C23C23×D1311yescharacteristic
198Q8—44no—
199Q8—524no—
200D4—524no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—134no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—262no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4C2×D5212yes—
223C2×C4C2×D5212yes—
224C2×C4C2×D5212yes—
225C22—522no—
226C22—522no—
227C22—522no—
228C22—522no—
229C22—522no—
230C22—522no—
231C22—522no—
232C22C22×D5211yescharacteristic
233C22#8825111yescharacteristic
234C22#8825111yescharacteristic
235C22#8825412yes—
236C22#41×D1312yes—
237C4—22no—
238C4—22no—
239C4—22no—
240C4—42no—
241C4—42no—
242C4—264no—
243C4—522no—
244C4—522no—
245C2—1042no—
246C2#1171919811yescharacteristic
247C2#1171928112yes—
248C2#1171934512yes—
249C2#1171937511yescharacteristic
250C2#1171944011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#391C2
prime radicalC22×D52C22
hypercenter#391D13
hypocenterC13#2731
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#88198C2semidirect
3. C13×#391C2semidirect
4. #11718655C2semidirect
5. #11718601C2semidirect
6. #11718334C2semidirect
8. #11718331C2semidirect
9. #11718314C2semidirect
105. #391D13semidirect
189. C13#2731semidirect

Maximal subgroups

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

subgroupindex
C2×#882012
C2×#881982
C13×#3912
#117186552
#117186012
#117183342
#117183332
#117183312
#117183142
#273113