Finite Group Databasebeta

← #13122543

Subgroups — #13122543

Order 1664.

428 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 121 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#11718883C212yesmaximal
3#11718640C211yesmaximal, characteristic, complemented
4#11718638C211yesmaximal, characteristic, complemented
5#11718612C212yesmaximal, complemented
6#11718608C212yesmaximal, complemented
7#11718606C212yesmaximal, complemented
8#11718605C212yesmaximal, complemented
9#11718311C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C13×C22⋊C4C2212yes—
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C4⋊Dic13C2211yescharacteristic
20C2×#6101C2212yes—
21C2×#6101C2212yes—
22C2×C4×Dic13C2212yes—
23C2×C4×Dic13C2211yescharacteristic
24C13×#95C2211yescharacteristic
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31C24×C13C2312yes—
32C2×D4×C13—42no—
33C2×D4×C13—41no—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C2×Dic26—42no—
43C2×Dic26—41no—
44C13×C4⋊C4—41no—
45C13×C22⋊C4—24no—
46C13×C22⋊C4—42no—
47C22⋊Dic13—24no—
48C22⋊Dic13—24no—
49C22⋊Dic13—42no—
50C22⋊Dic13—42no—
51C4⋊Dic13—41no—
52#6101—42no—
53#6101—42no—
54C4×Dic13—22no—
55C4×Dic13—24no—
56#2785—131nomaximal, Sylow
57C23×C13—22no—
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13C2411yescharacteristic
65D4×C13—44no—
66C2×C4×C13—21no—
67C2×C4×C13—21no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13#4112yes—
76C2×Dic13—22no—
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#4114yes—
88Dic26—44no—
89#395—131no—
90#394—132no—
91#394D1311yescharacteristic
92#393—132no—
93#388—132no—
94#388—132no—
95#388—132no—
96#382—131no—
97#382—132no—
98C22×C13—42no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13C2×#4111yescharacteristic
106C22×C13C2×#4112yes—
107C22×C13H(5,𝔽2)11yescharacteristic
108C22×C13H(5,𝔽2)12yes—
109C22×C132−1+411yescharacteristic
110C4×C13—22no—
111C4×C13—42no—
112C4×C13—41no—
113C4×C13—41no—
114Dic13—24no—
115Dic13—42no—
116Dic13—42no—
117Dic13—42no—
118C22×Q8—131no—
119C22×D4C2×D1311yescharacteristic
120C2×C4⋊C4—132no—
121C2×C4⋊C4—132no—
122C2×C4⋊C4—131no—
123C2×C4⋊C4C2×D1311yescharacteristic
124C2×C22⋊C4—132no—
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—132no—
135#95—132no—
136#95—131no—
137#95—132no—
138#95C2×D1311yescharacteristic
139C2×C13—82no—
140C2×C13#53911yescharacteristic
141C2×C13#53912yes—
142C2×C13#55512yes—
143C2×C13#55511yescharacteristic
144C2×C13H(3,𝔽4)11yescharacteristic
145C24C22×D1312yes—
146C2×Q8—522no—
147C2×Q8—521no—
148C2×D4—41no—
149C2×D4—42no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4C22×D1311yescharacteristic
155C22×C4C22×D1312yes—
156C22×C4C22×D1311yescharacteristic
157C22×C4C22×D1311yescharacteristic
158C4⋊C4—41no—
159C4⋊C4—522no—
160C4⋊C4—522no—
161C4⋊C4—521no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—264no—
165C22⋊C4—264no—
166C22⋊C4—522no—
167C22⋊C4—522no—
168C42—264no—
169C42—262no—
170C13#278511yescharacteristic, complemented, Sylow
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23C23×D1311yescharacteristic
179Q8—524no—
180D4—44no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—134no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—262no—
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#612912yes—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C2×#612911yescharacteristic
211C22#8825111yescharacteristic
212C22#8825112yes—
213C22#41×D1312yes—
214C22#8825711yescharacteristic
215C4—22no—
216C4—41no—
217C4—41no—
218C4—42no—
219C4—264no—
220C4—522no—
221C4—522no—
222C4—522no—
223C2—82no—
224C2#1171929911yescharacteristic
225C2#1171930711yescharacteristic
226C2#1171932112yes—
227C2#1171936512yes—
228C2#1171937511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2785
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
3. #11718640C2semidirect
4. #11718638C2semidirect
5. #11718612C2semidirect
6. #11718608C2semidirect
7. #11718606C2semidirect
8. #11718605C2semidirect
9. #11718311C2semidirect
170. C13#2785semidirect

Maximal subgroups

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

subgroupindex
C13×#3942
#117188832
#117186402
#117186382
#117186122
#117186082
#117186062
#117186052
#117183112
#278513