Finite Group Databasebeta

← #13121860

Subgroups — #13121860

Order 1664.

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

normal subgroups only

This group has 592 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×C13×#124C211yesmaximal, characteristic, complemented
2C2×#88201C211yesmaximal, characteristic, complemented
3#11718891C211yesmaximal, characteristic, complemented
4#11718884C212yesmaximal, complemented
5#11718622C212yesmaximal, complemented
6#11718621C212yesmaximal, complemented
7#11718618C212yesmaximal, complemented
8#11718605C212yesmaximal, complemented
9#11718601C212yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic
12C22×C22⋊D13C2212yes—
13C22×C22⋊D13C2212yes—
14C22×D52C2211yescharacteristic
15C13×#124—24no—
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2212yes—
18C2×C42×C13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21#88201—24no—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33C24×C13C2312yes—
34C23×D13C2312yes—
35C2×Q8×C13—41no—
36C2×Q8×C13—41no—
37C2×Q8×C13D414yescomplemented
38C2×D4×C13—22no—
39C2×D4×C13—41no—
40C2×D4×C13—41no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C2×C22⋊D13—24no—
46C2×C22⋊D13—42no—
47C2×C22⋊D13—42no—
48C2×C22⋊D13—42no—
49C2×C22⋊D13—42no—
50C2×C22⋊D13—42no—
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2312yes—
54C2×D52—22no—
55C2×D52—41no—
56C2×D52—41no—
57C13×C22⋊C4—24no—
58C13×C22⋊C4—24no—
59C42×C13—22no—
60C22⋊Dic13—24no—
61C22⋊Dic13—42no—
62#6103—24no—
63#6103—24no—
64#6103—24no—
65#6103—42no—
66C4⋊Dic13—41no—
67#6101—42no—
68C4×Dic13—22no—
69C4×Dic13—41no—
70#2733—131nomaximal, Sylow
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13C2411yescharacteristic
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86Q8×C13—44no—
87D4×C13—44no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D412yes—
99C2×C4×C13C2×D412yes—
100C22⋊D13—48no—
101C22⋊D13—48no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13#4114yes—
111D52—44no—
112C2×#124—131no—
113C2×#124D1311yescharacteristic, complemented
114#394—132no—
115#392—132no—
116#392—132no—
117#391—131no—
118#390—132no—
119#388—132no—
120#388—132no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13C22×D411yescharacteristic
129C22×C13C2×#4112yes—
130C22×C13H(5,𝔽2)11yescharacteristic
131C22×C13H(5,𝔽2)11yescharacteristic
132C22×C13H(5,𝔽2)12yes—
133C2×D13—42no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—42no—
140C4×C13—22no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—42no—
144Dic13—24no—
145Dic13—42no—
146Dic13—42no—
147C22×Q8C2×D1311yescharacteristic
148C22×D4—132no—
149C22×D4—132no—
150C22×D4—131no—
151C22×D4C2×D1311yescharacteristic
152#124—24no—
153#124—264no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—131no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4C2×D1312yes—
163C2×C22⋊C4C2×D1312yes—
164C2×C42—131no—
165C2×C42—131no—
166C2×C42C2×D1311yescharacteristic
167#95—132no—
168#95—132no—
169#95—132no—
170C2×C13—82no—
171C2×C13#53411yescharacteristic
172C2×C13#53812yes—
173C2×C13#55012yes—
174C2×C13#55511yescharacteristic
175C2×C13H(3,𝔽4)11yescharacteristic
176D13—82no—
177C24—132no—
178C24C22×D1312yes—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8C22⋊D1314yescomplemented
182C2×D4—22no—
183C2×D4—41no—
184C2×D4—41no—
185C2×D4—264no—
186C2×D4—262no—
187C2×D4—521no—
188C2×D4—521no—
189C2×D4—522no—
190C2×D4—522no—
191C2×D4—522no—
192C2×D4—522no—
193C2×D4—522no—
194C22×C4—132no—
195C22×C4—132no—
196C22×C4—132no—
197C22×C4C22×D1312yes—
198C22×C4C22×D1311yescharacteristic
199C22×C4C22×D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201C4⋊C4—522no—
202C4⋊C4—521no—
203C22⋊C4—24no—
204C22⋊C4—24no—
205C22⋊C4—264no—
206C22⋊C4—264no—
207C22⋊C4—264no—
208C22⋊C4—264no—
209C22⋊C4—522no—
210C22⋊C4—522no—
211C42—22no—
212C42—262no—
213C42—521no—
214C13#273311yescharacteristic, complemented, Sylow
215C23—22no—
216C23—22no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—262no—
223C23—262no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23—262no—
228C23—262no—
229C23C23×D1311yescharacteristic
230Q8—44no—
231D4—44no—
232D4—524no—
233D4—528no—
234D4—528no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—134no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4C2×C22⋊D1312yes—
254C2×C4C2×C22⋊D1312yes—
255C2×C4C2×C22⋊D1312yes—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—522no—
264C22—522no—
265C22—522no—
266C22—522no—
267C22—522no—
268C22—522no—
269C22—522no—
270C22#8825111yescharacteristic
271C22#8825111yescharacteristic
272C22#41×D1312yes—
273C22#8825612yes—
274C22C22×C22⋊D1311yescharacteristic
275C4—22no—
276C4—22no—
277C4—22no—
278C4—42no—
279C4—264no—
280C4—522no—
281C4—522no—
282C2—82no—
283C2—1042no—
284C2#1171937511yescharacteristic
285C2#1171938312yes—
286C2#1171938811yescharacteristic
287C2#1171950911yescharacteristic
288C2#1171953912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#124C2
hypercenterC2×#124D13
hypocenterC13#2733
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×C13×#124C2semidirect
2. C2×#88201C2semidirect
3. #11718891C2semidirect
4. #11718884C2semidirect
5. #11718622C2semidirect
6. #11718621C2semidirect
7. #11718618C2semidirect
8. #11718605C2semidirect
9. #11718601C2semidirect
37. C2×Q8×C13D4semidirect
113. C2×#124D13semidirect
181. C2×Q8C22⋊D13semidirect
214. C13#2733semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1242
C2×#882012
#117188912
#117188842
#117186222
#117186212
#117186182
#117186052
#117186012
#273313