Finite Group Databasebeta

← #13121198

Subgroups — #13121198

Order 1664.

668 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88149C212yesmaximal, complemented
2C2×#88148C212yesmaximal, complemented
3C13×#389C211yesmaximal, characteristic, complemented
4#11718655C212yesmaximal, complemented
5#11718652C212yesmaximal, complemented
6#11718600C211yesmaximal, characteristic, complemented
7#11718600C211yesmaximal, characteristic, complemented
8#11718332C212yesmaximal, complemented
9#11718329C212yesmaximal, complemented
10C22×D52C2212yes—
11C22×D52C2212yes—
12C22×D52C2211yescharacteristic
13C22×D52C2211yescharacteristic
14C22×C4×D13C2212yes—
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2212yes—
29#88149—28no—
30#88148—28no—
31C13×#95C2212yes—
32#88071C2212yes—
33C23×D13C2312yes—
34C23×D13C2312yes—
35C22×C4×C13C2312yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C2×D52—24no—
43C2×D52—24no—
44C2×D52—24no—
45C2×D52—22no—
46C2×D52—41no—
47C2×D52—41no—
48C2×D52—42no—
49C2×D52—41no—
50C2×D52—41no—
51C2×D52—42no—
52C2×D52—42no—
53C2×D52D414yescomplemented
54C2×C4×D13—24no—
55C2×C4×D13—24no—
56C2×C4×D13—42no—
57C13×C4⋊C4—24no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4D414yescomplemented
60C42×C13—41no—
61#6103—24no—
62#6103—24no—
63#6103—24no—
64#6103—24no—
65#6103—24no—
66#6103—24no—
67#6103—42no—
68C4⋊Dic13—41no—
69C4⋊Dic13—41no—
70#6101—24no—
71#2682—131nomaximal, Sylow
72C23×C13C2411yescharacteristic
73C22×D13—22no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13C2×D414yes—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13C2×D414yes—
99C2×C4×C13C2×D412yes—
100C2×C4×C13C2×D412yes—
101C2×C4×C13#4112yes—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108D52—44no—
109D52—48no—
110D52—44no—
111D52—48no—
112C4×D13—48no—
113C2×#123—132no—
114C2×#121—132no—
115#396—132no—
116#394—132no—
117#392—132no—
118#390—131no—
119#390—131no—
120#389D1311yescharacteristic, complemented
121#385—132no—
122C22×C13C22×D411yescharacteristic
123C22×C13C22×D411yescharacteristic
124C22×C13C2×#4111yescharacteristic
125C22×C13H(5,𝔽2)11yescharacteristic
126C22×C13H(5,𝔽2)11yescharacteristic
127C22×C13H(5,𝔽2)11yescharacteristic
128C22×C132−1+411yescharacteristic
129C2×D13—24no—
130C2×D13—24no—
131C2×D13—24no—
132C2×D13—42no—
133C2×D13—42no—
134C2×D13—42no—
135C2×D13—42no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—42no—
140C2×D13—42no—
141C2×D13—42no—
142C2×D13—42no—
143C4×C13—22no—
144C4×C13—22no—
145C4×C13—22no—
146C4×C13—24no—
147C4×C13—42no—
148Dic13—42no—
149Dic13—42no—
150C22×D4—131no—
151C22×D4—132no—
152C22×D4—132no—
153C22×D4—131no—
154C23×C4—132no—
155#123—268no—
156#121—268no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—131no—
160C2×C4⋊C4C2×D1312yes—
161C2×C4⋊C4C2×D1311yescharacteristic
162C2×C4⋊C4C2×D1311yescharacteristic
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C42C2×D1311yescharacteristic
171#95—132no—
172#95C2×D1312yes—
173C2×C13#53411yescharacteristic
174C2×C13#53711yescharacteristic
175C2×C13#53811yescharacteristic
176C2×C13D4211yescharacteristic
177C2×C13#54711yescharacteristic
178C2×C13#55011yescharacteristic
179C2×C13#56211yescharacteristic
180D13—44no—
181D13—82no—
182C24—132no—
183C24—132no—
184C2×D4—134no—
185C2×D4—264no—
186C2×D4—264no—
187C2×D4—264no—
188C2×D4—262no—
189C2×D4—521no—
190C2×D4—521no—
191C2×D4—521no—
192C2×D4—521no—
193C2×D4—522no—
194C2×D4—522no—
195C2×D4—522no—
196C22×C4—132no—
197C22×C4—132no—
198C22×C4—264no—
199C22×C4—264no—
200C22×C4—522no—
201C22×C4C22×D1312yes—
202C22×C4C22×D1312yes—
203C22×C4C22×D1311yescharacteristic
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1311yescharacteristic
206C4⋊C4—24no—
207C4⋊C4—41no—
208C4⋊C4—264no—
209C4⋊C4—521no—
210C4⋊C4—521no—
211C4⋊C4D5214yescomplemented
212C22⋊C4—264no—
213C22⋊C4—264no—
214C22⋊C4—264no—
215C22⋊C4—264no—
216C22⋊C4—264no—
217C22⋊C4—264no—
218C22⋊C4—522no—
219C42—41no—
220C13#268211yescharacteristic, complemented, Sylow
221C23—134no—
222C23—262no—
223C23—262no—
224C23—262no—
225C23—262no—
226C23—262no—
227C23—262no—
228C23—262no—
229C23—262no—
230C23—262no—
231C23—262no—
232C23—262no—
233C23—262no—
234C23—262no—
235C23C23×D1311yescharacteristic
236D4—524no—
237D4—528no—
238D4—524no—
239D4—528no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—528no—
258C2×C4C2×D5212yes—
259C2×C4C2×D5214yes—
260C2×C4D4×D1312yes—
261C2×C4#613112yes—
262C22—264no—
263C22—264no—
264C22—264no—
265C22—522no—
266C22—522no—
267C22—522no—
268C22—522no—
269C22—522no—
270C22—522no—
271C22—522no—
272C22—522no—
273C22—522no—
274C22—522no—
275C22—522no—
276C22C22×D5211yescharacteristic
277C22C2×D4×D1311yescharacteristic
278C22#8825111yescharacteristic
279C22C2×#613111yescharacteristic
280C22#8825411yescharacteristic
281C22#8825611yescharacteristic
282C22#8825611yescharacteristic
283C4—22no—
284C4—24no—
285C4—22no—
286C4—22no—
287C4—42no—
288C4—522no—
289C4—522no—
290C2—524no—
291C2—1042no—
292C2#1171921511yescharacteristic
293C2D4×D5211yescharacteristic
294C2#1171928211yescharacteristic
295C2#1171931011yescharacteristic
296C2#1171934911yescharacteristic
297C2#1171940511yescharacteristic
298C2#1171943111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
hypercenter#389D13
hypocenterC13#2682
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#88149C2semidirect
2. C2×#88148C2semidirect
3. C13×#389C2semidirect
4. #11718655C2semidirect
5. #11718652C2semidirect
6. #11718600C2semidirect
7. #11718600C2semidirect
8. #11718332C2semidirect
9. #11718329C2semidirect
53. C2×D52D4semidirect
59. C13×C4⋊C4D4semidirect
120. #389D13semidirect
211. C4⋊C4D52semidirect
220. C13#2682semidirect

Maximal subgroups

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

subgroupindex
C2×#881492
C2×#881482
C13×#3892
#117186552
#117186522
#117186002
#117183322
#117183292
#268213