Finite Group Databasebeta

← #13122979

Subgroups — #13122979

Order 1664.

408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 117 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×#390C211yesmaximal, characteristic
2#11718883C212yesmaximal
3#11718644C211yesmaximal, characteristic, complemented
4#11718640C211yesmaximal, characteristic, complemented
5#11718613C212yesmaximal, complemented
6#11718613C212yesmaximal, complemented
7#11718609C212yesmaximal, complemented
8#11718608C212yesmaximal, complemented
9#11718594C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C13×C22⋊C4C2212yes—
15C2×C42×C13C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2212yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2211yescharacteristic
31C24×C13C2312yes—
32C2×D4×C13—22no—
33C2×D4×C13—41no—
34C2×D4×C13—41no—
35C22×C4×C13C2312yes—
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C2×Dic26—42no—
44C2×Dic26—41no—
45C13×C4⋊C4—41no—
46C13×C22⋊C4—42no—
47C13×C22⋊C4—42no—
48C42×C13—41no—
49C22⋊Dic13—42no—
50C22⋊Dic13—42no—
51C22⋊Dic13—42no—
52C22⋊Dic13—42no—
53C4⋊Dic13—41no—
54#6101—24no—
55#6101—42no—
56#6101—42no—
57#2830—131nomaximal, Sylow
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13C2411yescharacteristic
66D4×C13—44no—
67C2×C4×C13—21no—
68C2×C4×C13—21no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—22no—
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—22no—
89Dic26—44no—
90#398—131no—
91#397—132no—
92#397—132no—
93#396—132no—
94#395—131no—
95#394—132no—
96#393—132no—
97#390D1311yescharacteristic
98#387—132no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13C2×#4111yescharacteristic
107C22×C13H(5,𝔽2)11yescharacteristic
108C22×C13H(5,𝔽2)11yescharacteristic
109C22×C13H(5,𝔽2)12yes—
110C22×C132−1+412yes—
111C4×C13—22no—
112C4×C13—41no—
113C4×C13—41no—
114C4×C13—42no—
115Dic13—42no—
116Dic13—42no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8—131no—
120C22×D4C2×D1311yescharacteristic
121C2×C4⋊C4—132no—
122C2×C4⋊C4—132no—
123C2×C4⋊C4—132no—
124C2×C4⋊C4—131no—
125C2×C4⋊C4C2×D1311yescharacteristic
126C2×C22⋊C4—132no—
127C2×C22⋊C4—132no—
128C2×C22⋊C4—132no—
129C2×C22⋊C4—132no—
130C2×C22⋊C4C2×D1312yes—
131C2×C22⋊C4C2×D1312yes—
132C2×C42C2×D1311yescharacteristic
133#95—132no—
134#95—132no—
135#95—132no—
136#95—132no—
137#95—132no—
138#95—131no—
139#95—131no—
140C2×C13—82no—
141C2×C13#53811yescharacteristic
142C2×C13#54212yes—
143C2×C13#56011yescharacteristic
144C2×C13#56212yes—
145C2×C13#56311yescharacteristic
146C24C22×D1312yes—
147C2×Q8—522no—
148C2×Q8—521no—
149C2×D4—22no—
150C2×D4—41no—
151C2×D4—41no—
152C22×C4—132no—
153C22×C4—132no—
154C22×C4—132no—
155C22×C4—132no—
156C22×C4C22×D1312yes—
157C22×C4C22×D1311yescharacteristic
158C22×C4C22×D1311yescharacteristic
159C22×C4C22×D1311yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—264no—
162C4⋊C4—522no—
163C4⋊C4—522no—
164C4⋊C4—521no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C22⋊C4—522no—
168C22⋊C4—522no—
169C22⋊C4—522no—
170C22⋊C4—522no—
171C42—41no—
172C13#283011yescharacteristic, complemented, Sylow
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23C23×D1311yescharacteristic
181Q8—524no—
182D4—44no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
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—262no—
203C2×C4—262no—
204C2×C4#612712yes—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22C2×#612711yescharacteristic
213C22#8825111yescharacteristic
214C22#8825112yes—
215C22#8825111yescharacteristic
216C22#8825712yes—
217C4—22no—
218C4—41no—
219C4—41no—
220C4—42no—
221C4—522no—
222C4—522no—
223C4—522no—
224C4—522no—
225C2—82no—
226C2#1171919911yescharacteristic
227C2#1171926612yes—
228C2#1171932612yes—
229C2#1171937711yescharacteristic
230C2#1171942511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×C13C22
hypercenter#390D13
hypocenterC13#2830
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
3. #11718644C2semidirect
4. #11718640C2semidirect
5. #11718613C2semidirect
6. #11718613C2semidirect
7. #11718609C2semidirect
8. #11718608C2semidirect
9. #11718594C2semidirect
172. C13#2830semidirect

Maximal subgroups

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

subgroupindex
C13×#3902
#117188832
#117186442
#117186402
#117186132
#117186092
#117186082
#117185942
#283013