Finite Group Databasebeta

← #13120951

Subgroups — #13120951

Order 1664.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#88151C211yesmaximal, characteristic
2C2×#88150C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic, complemented
4#11718648C212yesmaximal
5#11718645C212yesmaximal, complemented
6#11718641C211yesmaximal, characteristic, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718328C212yesmaximal
9D13×#95C211yesmaximal, characteristic
10#11718317C212yesmaximal, complemented
11#11718317C211yesmaximal, characteristic, complemented
12C22×C4×D13C2211yescharacteristic
13C22×C4×D13C2212yes—
14C22×Dic26C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2211yescharacteristic
25C2×#6101C2211yescharacteristic
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28#88151—24no—
29#88150—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2312yes—
48C2×C4×D13—42no—
49C2×C4×D13—42no—
50C2×C4×D13—42no—
51C2×C4×D13D414yes—
52C2×C4×D13Q818yescomplemented
53C2×Dic26—22no—
54C2×Dic26—22no—
55C2×Dic26—42no—
56C2×Dic26—42no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—42no—
60#6103—22no—
61#6103—22no—
62#6103—24no—
63C4⋊Dic13—24no—
64C4⋊Dic13—42no—
65#6101—22no—
66#6101—22no—
67#6101—42no—
68#6101—42no—
69#2659—131nomaximal, Sylow
70C23×C13C2411yescharacteristic
71C22×D13—22no—
72C22×D13—21no—
73C22×D13—21no—
74C22×D13C2×D412yes—
75C22×D13C2×Q814yes—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×Q814yes—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13C2×D412yes—
101C2×Dic13C2×Q814yes—
102C4×D13—44no—
103C4×D13—48no—
104Dic26—44no—
105Dic26—44no—
106C2×C22⋊Q8—131no—
107C2×C22⋊Q8—131no—
108#398—131no—
109#398—132no—
110#398D1311yescharacteristic, complemented
111#395—131no—
112#395—132no—
113#395—131no—
114#380—132no—
115#380—132no—
116C2×#95—131no—
117C22×C13C22×D411yescharacteristic
118C22×C13C22×Q812yes—
119C22×C13H(5,𝔽2)11yescharacteristic
120C22×C13H(5,𝔽2)12yes—
121C22×C132−1+411yescharacteristic
122C2×D13—22no—
123C2×D13—22no—
124C2×D13—24no—
125C2×D13—24no—
126C2×D13C4⋊Q814yes—
127C4×C13—22no—
128C4×C13—24no—
129C4×C13—41no—
130C4×C13—41no—
131C4×C13—42no—
132Dic13—22no—
133Dic13—24no—
134Dic13—41no—
135Dic13—42no—
136Dic13—41no—
137C22×Q8—131no—
138C22×Q8—131no—
139C23×C4—131no—
140C23×C4—132no—
141C22⋊Q8—264no—
142C22⋊Q8—264no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—132no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C4⋊C4C2×D1311yescharacteristic
151C2×C4⋊C4C2×D1312yes—
152C2×C22⋊C4—131no—
153C2×C22⋊C4—131no—
154C2×C22⋊C4—132no—
155#95—131no—
156#95—132no—
157#95—132no—
158#95—132no—
159#95—132no—
160#95C2×D1311yescharacteristic
161#95C2×D1312yes—
162C2×C13C2×C4⋊Q811yescharacteristic
163C2×C13#53411yescharacteristic
164C2×C13#53711yescharacteristic
165C2×C13#54312yes—
166C2×C13#54412yes—
167D13—24no—
168C24—131no—
169C2×Q8—262no—
170C2×Q8—262no—
171C2×Q8—522no—
172C2×Q8—522no—
173C22×C4—132no—
174C22×C4—131no—
175C22×C4—134no—
176C22×C4—138no—
177C22×C4—131no—
178C22×C4—131no—
179C22×C4—132no—
180C22×C4—522no—
181C22×C4—522no—
182C22×C4—522no—
183C22×C4C22×D1311yescharacteristic
184C22×C4C22×D1312yes—
185C22×C4C22×D1311yescharacteristic
186C22×C4C22×D1311yescharacteristic
187C22×C4C22×D1312yes—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—262no—
192C4⋊C4—264no—
193C4⋊C4—262no—
194C4⋊C4—522no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C22⋊C4—262no—
198C22⋊C4—264no—
199C22⋊C4—262no—
200C13#265911yescharacteristic, complemented, Sylow
201C23—132no—
202C23—134no—
203C23—261no—
204C23—262no—
205C23—261no—
206C23C23×D1311yescharacteristic
207Q8—524no—
208Q8—524no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—132no—
221C2×C4—134no—
222C2×C4—262no—
223C2×C4—262no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—262no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—528no—
234C2×C4—524no—
235C2×C4D4×D1312yes—
236C2×C4Q8×D1314yes—
237C22—134no—
238C22—262no—
239C22—264no—
240C22—262no—
241C22—264no—
242C22C2×D4×D1311yescharacteristic
243C22#8825111yescharacteristic
244C22C2×Q8×D1312yes—
245C22#8825612yes—
246C22#8825711yescharacteristic
247C4—24no—
248C4—22no—
249C4—41no—
250C4—42no—
251C4—41no—
252C4—264no—
253C4—262no—
254C4—521no—
255C4—522no—
256C4—521no—
257C2—264no—
258C2#1171931311yescharacteristic
259C2#1171933912yes—
260C2#1171935811yescharacteristic
261C2#1171939412yes—
262C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2659
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C13×#398C2semidirect
5. #11718645C2semidirect
6. #11718641C2semidirect
7. #11718640C2semidirect
10. #11718317C2semidirect
11. #11718317C2semidirect
52. C2×C4×D13Q8semidirect
110. #398D13semidirect
200. C13#2659semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×#881502
C13×#3982
#117186482
#117186452
#117186412
#117186402
#117183282
D13×#952
#117183172
#265913