Finite Group Databasebeta

← #13120079

Subgroups — #13120079

Order 1664.

476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C13×#394C211yesmaximal, characteristic
2#11718881C212yesmaximal
3#11718647C211yesmaximal, characteristic, complemented
4#11718635C211yesmaximal, characteristic, complemented
5#11718612C212yesmaximal, complemented
6#11718608C212yesmaximal, complemented
7#11718604C212yesmaximal, complemented
8C22⋊C4×Dic13C212yesmaximal, complemented
9#11718312C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C23×Dic13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C13×#95C2211yescharacteristic
23#88071C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31C24×C13C2312yes—
32C2×D4×C13—24no—
33C2×D4×C13—41no—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13—24no—
39C22×Dic13—24no—
40C22×Dic13—42no—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×Dic26—22no—
46C2×Dic26—41no—
47C2×Dic26—41no—
48C13×C4⋊C4—41no—
49C13×C22⋊C4—24no—
50C13×C22⋊C4—24no—
51C22⋊Dic13—24no—
52C22⋊Dic13—42no—
53C22⋊Dic13—42no—
54C4⋊Dic13—41no—
55C4×Dic13—24no—
56C4×Dic13—41no—
57#2572—131nomaximal, Sylow
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13#4114yes—
65C23×C13C2411yescharacteristic
66D4×C13—44no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13#4112yes—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—48no—
89C2×Dic13#4114yes—
90Dic26—44no—
91#400—131no—
92#394D1311yescharacteristic
93#393—132no—
94#391—131no—
95#388—132no—
96#386—132no—
97#383—132no—
98#381—132no—
99C4×C22⋊C4—132no—
100C22×C13—24no—
101C22×C13—24no—
102C22×C13—24no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13C2×#4111yescharacteristic
108C22×C13C2×#4112yes—
109C22×C13C2×#4112yes—
110C22×C13H(5,𝔽2)11yescharacteristic
111C22×C13H(5,𝔽2)11yescharacteristic
112C4×C13—22no—
113C4×C13—42no—
114C4×C13—41no—
115C4×C13—41no—
116Dic13—24no—
117Dic13—42no—
118Dic13—42no—
119Dic13—42no—
120C22×Q8—131no—
121C22×D4C2×D1311yescharacteristic
122C23×C4—132no—
123C2×C4⋊C4—131no—
124C2×C4⋊C4C2×D1311yescharacteristic
125C2×C22⋊C4—132no—
126C2×C22⋊C4—132no—
127C2×C22⋊C4—132no—
128C2×C22⋊C4C2×D1312yes—
129C2×C22⋊C4C2×D1312yes—
130C2×C42—132no—
131C2×C42—131no—
132#95—132no—
133#95—132no—
134#95—131no—
135#95—132no—
136#95—132no—
137#95—132no—
138#95—132no—
139#95—132no—
140#95C2×D1311yescharacteristic
141C2×C13—44no—
142C2×C13#52912yes—
143C2×C13#53811yescharacteristic
144C2×C13#55111yescharacteristic
145C2×C13#55112yes—
146C2×C13#55511yescharacteristic
147C24C22×D1312yes—
148C2×Q8—262no—
149C2×Q8—521no—
150C2×Q8—521no—
151C2×D4—24no—
152C2×D4—41no—
153C22×C4—132no—
154C22×C4—132no—
155C22×C4—132no—
156C22×C4—132no—
157C22×C4—264no—
158C22×C4—264no—
159C22×C4—522no—
160C22×C4C22×D1311yescharacteristic
161C22×C4C22×D1312yes—
162C22×C4C22×D1311yescharacteristic
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—521no—
166C22⋊C4—24no—
167C22⋊C4—24no—
168C22⋊C4—264no—
169C22⋊C4—522no—
170C22⋊C4—522no—
171C42—264no—
172C42—521no—
173C13#257211yescharacteristic, complemented, Sylow
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23#612914yes—
181C23C23×D1311yescharacteristic
182Q8—524no—
183D4—44no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—134no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—528no—
206C2×C4#612912yes—
207C22—24no—
208C22—24no—
209C22—24no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#612912yes—
215C22C2×#612911yescharacteristic
216C22#8825111yescharacteristic
217C22#41×D1312yes—
218C22#8825611yescharacteristic
219C4—22no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—264no—
224C4—522no—
225C4—522no—
226C4—522no—
227C2—44no—
228C2#1171929211yescharacteristic
229C2#1171930512yes—
230C2#1171932211yescharacteristic
231C2#1171936312yes—
232C2#1171937511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2572
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
3. #11718647C2semidirect
4. #11718635C2semidirect
5. #11718612C2semidirect
6. #11718608C2semidirect
7. #11718604C2semidirect
8. C22⋊C4×Dic13C2semidirect
9. #11718312C2semidirect
173. C13#2572semidirect

Maximal subgroups

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

subgroupindex
C13×#3942
#117188812
#117186472
#117186352
#117186122
#117186082
#117186042
C22⋊C4×Dic132
#117183122
#257213