Finite Group Databasebeta

← #13122840

Subgroups — #13122840

Order 1664.

578 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88184C211yesmaximal, characteristic, complemented
2C2×#88183C211yesmaximal, characteristic, complemented
3C13×#380C211yesmaximal, characteristic, complemented
4#11718655C212yesmaximal, complemented
5#11718652C212yesmaximal, complemented
6#11718622C212yesmaximal, complemented
7#11718621C212yesmaximal, complemented
8#11718338C211yesmaximal, characteristic, complemented
9#11718333C211yesmaximal, characteristic, complemented
10#11718332C211yesmaximal, characteristic, complemented
11#11718320C211yesmaximal, characteristic, complemented
12C23×C4×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C22⋊D13C2212yes—
15C22×D52C2211yescharacteristic
16C22×D52C2212yes—
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2211yescharacteristic
20#88184—24no—
21#88183—24no—
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×#6103C2212yes—
28C2×#6103C2212yes—
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2212yes—
31C2×#6101C2211yescharacteristic
32C2×#6101C2211yescharacteristic
33C13×#95C2211yescharacteristic
34C13×#95C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C23×D13C2312yes—
40C22×C4×C13—42no—
41C22×C4×C13D414yescomplemented
42C22×C4×C13C2312yes—
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—22no—
47C2×C22⋊D13—24no—
48C2×C22⋊D13—42no—
49C2×C22⋊D13—42no—
50C2×C22⋊D13—42no—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2312yes—
54C22×Dic13C2311yescharacteristic
55C2×D52—22no—
56C2×D52—42no—
57C2×D52—42no—
58C2×D52—42no—
59C2×D52—42no—
60C13×C4⋊C4—42no—
61C13×C22⋊C4—42no—
62C22⋊Dic13—22no—
63#6103—22no—
64#6103—22no—
65#6103—24no—
66#6103—42no—
67#6103—42no—
68#6103—42no—
69#6103—42no—
70C4⋊Dic13—22no—
71C4⋊Dic13—42no—
72#6101—22no—
73#6101—22no—
74#2813—131nomaximal, Sylow
75C23×C13—21no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—21no—
79C23×C13C2×D412yes—
80C23×C13C2411yescharacteristic
81C22×D13—21no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—21no—
89C22×D13—22no—
90C22×D13—22no—
91C22×D13—21no—
92C22×D13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—44no—
102C2×C4×C13C2×D412yes—
103C2×C4×C13C2×D412yes—
104C22⋊D13—44no—
105C22⋊D13—48no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—21no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—21no—
116D52—44no—
117D52—48no—
118C2×#123—131no—
119C2×#121—131no—
120#400—131no—
121#399—131no—
122#396—132no—
123#394—132no—
124#394—132no—
125#394—131no—
126#392—132no—
127#392—131no—
128#380D1311yescharacteristic, complemented
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13C22×D411yescharacteristic
135C22×C13H(5,𝔽2)12yes—
136C22×C13H(5,𝔽2)11yescharacteristic
137C22×C13H(5,𝔽2)12yes—
138C22×C132−1+411yescharacteristic
139C2×D13—42no—
140C2×D13—41no—
141C2×D13—42no—
142C2×D13—41no—
143C2×D13—41no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—42no—
150C2×D13—42no—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—42no—
154C4×C13—42no—
155Dic13—41no—
156Dic13—41no—
157Dic13—42no—
158Dic13—41no—
159C22×D4—132no—
160C22×D4—131no—
161C22×D4—131no—
162C22×D4—132no—
163C23×C4C2×D1311yescharacteristic
164#123—264no—
165#121—264no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—132no—
170C2×C4⋊C4C2×D1312yes—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—131no—
174C2×C22⋊C4—131no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4—132no—
177C2×C22⋊C4—132no—
178C2×C22⋊C4—132no—
179C2×C22⋊C4C2×D1312yes—
180#95—132no—
181#95—132no—
182#95C2×D1311yescharacteristic
183#95C2×D1311yescharacteristic
184C2×C13—42no—
185C2×C13#53411yescharacteristic
186C2×C13#53511yescharacteristic
187C2×C13#53711yescharacteristic
188C2×C13#56012yes—
189C2×C13#56212yes—
190D13—82no—
191D13—81no—
192C24—131no—
193C24—132no—
194C24C22×D1311yescharacteristic
195C2×D4—264no—
196C2×D4—262no—
197C2×D4—262no—
198C2×D4—522no—
199C2×D4—522no—
200C2×D4—522no—
201C2×D4—522no—
202C2×D4—522no—
203C2×D4—522no—
204C2×D4—522no—
205C22×C4—42no—
206C22×C4—131no—
207C22×C4—132no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4D5214yescomplemented
211C22×C4C22×D1312yes—
212C22×C4C22×D1312yes—
213C22×C4C22×D1311yescharacteristic
214C22×C4C22×D1311yescharacteristic
215C4⋊C4—42no—
216C4⋊C4—262no—
217C4⋊C4—262no—
218C4⋊C4—262no—
219C4⋊C4—522no—
220C22⋊C4—42no—
221C22⋊C4—262no—
222C22⋊C4—264no—
223C22⋊C4—262no—
224C22⋊C4—262no—
225C22⋊C4—522no—
226C22⋊C4—522no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C13#281311yescharacteristic, complemented, Sylow
230C23—21no—
231C23—22no—
232C23—21no—
233C23—22no—
234C23—261no—
235C23—262no—
236C23—262no—
237C23—262no—
238C23—262no—
239C23—262no—
240C23—261no—
241C23—261no—
242C23—262no—
243C23—262no—
244C23—262no—
245C23—262no—
246C23C2×D5212yes—
247C23C23×D1311yescharacteristic
248D4—524no—
249D4—528no—
250D4—524no—
251D4—528no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—44no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—262no—
267C2×C4—261no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4C2×D5212yes—
272C2×C4C2×D5212yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—522no—
279C22—521no—
280C22—521no—
281C22—522no—
282C22—522no—
283C22—521no—
284C22—522no—
285C22—522no—
286C22—522no—
287C22—522no—
288C22—522no—
289C22—522no—
290C22C22×D5211yescharacteristic
291C22#8825112yes—
292C22#8825111yescharacteristic
293C22#8825411yescharacteristic
294C22#8825612yes—
295C4—22no—
296C4—22no—
297C4—42no—
298C4—42no—
299C4—521no—
300C4—521no—
301C4—521no—
302C4—522no—
303C2—42no—
304C2—1042no—
305C2—1041no—
306C2#1171919811yescharacteristic
307C2#1171921511yescharacteristic
308C2#1171923011yescharacteristic
309C2#1171932512yes—
310C2#1171935212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
hypercenter#380D13
hypocenterC13#2813
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#88184C2semidirect
2. C2×#88183C2semidirect
3. C13×#380C2semidirect
4. #11718655C2semidirect
5. #11718652C2semidirect
6. #11718622C2semidirect
7. #11718621C2semidirect
8. #11718338C2semidirect
9. #11718333C2semidirect
10. #11718332C2semidirect
11. #11718320C2semidirect
41. C22×C4×C13D4semidirect
128. #380D13semidirect
210. C22×C4D52semidirect
229. C13#2813semidirect

Maximal subgroups

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

subgroupindex
C2×#881842
C2×#881832
C13×#3802
#117186552
#117186522
#117186222
#117186212
#117183382
#117183332
#117183322
#117183202
#281313