Finite Group Databasebeta

← #13121200

Subgroups — #13121200

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×#88193C212yesmaximal, complemented
2C2×#88140C212yesmaximal, complemented
3C13×#390C211yesmaximal, characteristic, complemented
4#11718655C212yesmaximal, complemented
5#11718622C212yesmaximal, complemented
6#11718621C212yesmaximal, complemented
7#11718611C212yesmaximal, complemented
8#11718600C211yesmaximal, characteristic, complemented
9#11718589C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×C22⋊D13C2212yes—
13C23×Dic13C2212yes—
14C22×D52C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2212yes—
18C2×C42×C13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20#88193—28no—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×#6101C2212yes—
30#88140—28no—
31#88071C2212yes—
32#88071C2212yes—
33C24×C13C2312yes—
34C23×D13C2312yes—
35C2×D4×C13—41no—
36C2×D4×C13—41no—
37C2×D4×C13D414yescomplemented
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C2×C22⋊D13—24no—
43C2×C22⋊D13—24no—
44C2×C22⋊D13—24no—
45C2×C22⋊D13—42no—
46C2×C22⋊D13—42no—
47C2×C22⋊D13—42no—
48C22×Dic13—24no—
49C22×Dic13—24no—
50C22×Dic13—42no—
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2312yes—
54C2×D52—22no—
55C2×D52—41no—
56C2×D52—41no—
57C13×C4⋊C4—41no—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—24no—
60C42×C13—41no—
61C22⋊Dic13—24no—
62#6103—24no—
63#6103—24no—
64#6103—24no—
65#6103—42no—
66C4⋊Dic13—24no—
67C4⋊Dic13—41no—
68C4⋊Dic13—41no—
69C4⋊Dic13D414yescomplemented
70#6101—24no—
71#2682—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13C2×D414yes—
79C23×C13C2411yescharacteristic
80C22×D13—22no—
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—22no—
86C22×D13—22no—
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×C13#4112yes—
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—48no—
111C2×Dic13C2×D414yes—
112D52—44no—
113C2×#123—132no—
114C2×#121—132no—
115#396—132no—
116#394—132no—
117#392—132no—
118#390—131no—
119#390D1311yescharacteristic, complemented
120#389—131no—
121#385—132no—
122C22×C13—24no—
123C22×C13—24no—
124C22×C13—24no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C22×C13C22×D411yescharacteristic
131C22×C13C2×#4111yescharacteristic
132C22×C13H(5,𝔽2)11yescharacteristic
133C22×C13H(5,𝔽2)11yescharacteristic
134C22×C13H(5,𝔽2)11yescharacteristic
135C22×C132−1+411yescharacteristic
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—42no—
147Dic13—24no—
148Dic13—42no—
149Dic13—42no—
150C22×D4—132no—
151C22×D4—132no—
152C22×D4—131no—
153C22×D4C2×D1311yescharacteristic
154C23×C4—132no—
155#123—268no—
156#121—268no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—131no—
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⋊C4C2×D1312yes—
169C2×C22⋊C4C2×D1312yes—
170C2×C42C2×D1311yescharacteristic
171#95—132no—
172#95—132no—
173C2×C13—44no—
174C2×C13#53411yescharacteristic
175C2×C13#53711yescharacteristic
176C2×C13#53811yescharacteristic
177C2×C13D4211yescharacteristic
178C2×C13#54711yescharacteristic
179C2×C13#55011yescharacteristic
180C2×C13#56211yescharacteristic
181D13—82no—
182C24—132no—
183C24C22×D1312yes—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—264no—
187C2×D4—264no—
188C2×D4—264no—
189C2×D4—262no—
190C2×D4—521no—
191C2×D4—521no—
192C2×D4—522no—
193C2×D4—522no—
194C2×D4—522no—
195C2×D4D5214yescomplemented
196C22×C4—132no—
197C22×C4—132no—
198C22×C4—132no—
199C22×C4—264no—
200C22×C4—264no—
201C22×C4—522no—
202C22×C4C22×D1312yes—
203C22×C4C22×D1311yescharacteristic
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1311yescharacteristic
206C4⋊C4—41no—
207C4⋊C4—134no—
208C4⋊C4—264no—
209C4⋊C4—264no—
210C4⋊C4—521no—
211C4⋊C4—521no—
212C22⋊C4—24no—
213C22⋊C4—24no—
214C22⋊C4—264no—
215C22⋊C4—264no—
216C22⋊C4—264no—
217C22⋊C4—264no—
218C22⋊C4—522no—
219C42—41no—
220C13#268211yescharacteristic, complemented, Sylow
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—262no—
228C23—262no—
229C23—262no—
230C23—262no—
231C23—262no—
232C23—262no—
233C23—262no—
234C23C2×D5214yes—
235C23C23×D1311yescharacteristic
236D4—44no—
237D4—524no—
238D4—528no—
239D4—528no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—134no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—528no—
259C2×C4C2×D5212yes—
260C2×C4D4×D1312yes—
261C2×C4#612912yes—
262C22—24no—
263C22—24no—
264C22—24no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—522no—
270C22—522no—
271C22—522no—
272C22—522no—
273C22—522no—
274C22—522no—
275C22—522no—
276C22C22×D5211yescharacteristic
277C22C2×D4×D1311yescharacteristic
278C22C2×#612911yescharacteristic
279C22#8825111yescharacteristic
280C22#8825111yescharacteristic
281C22#8825611yescharacteristic
282C22#8825711yescharacteristic
283C4—22no—
284C4—22no—
285C4—22no—
286C4—42no—
287C4—264no—
288C4—522no—
289C4—522no—
290C2—44no—
291C2—1042no—
292C2#1171919811yescharacteristic
293C2D4×D5211yescharacteristic
294C2#1171926011yescharacteristic
295C2#1171930211yescharacteristic
296C2#1171932211yescharacteristic
297C2#1171938911yescharacteristic
298C2#1171942311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
hypercenter#390D13
hypocenterC13#2682
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#88193C2semidirect
2. C2×#88140C2semidirect
3. C13×#390C2semidirect
4. #11718655C2semidirect
5. #11718622C2semidirect
6. #11718621C2semidirect
7. #11718611C2semidirect
8. #11718600C2semidirect
9. #11718589C2semidirect
37. C2×D4×C13D4semidirect
69. C4⋊Dic13D4semidirect
119. #390D13semidirect
195. C2×D4D52semidirect
220. C13#2682semidirect

Maximal subgroups

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

subgroupindex
C2×#881932
C2×#881402
C13×#3902
#117186552
#117186222
#117186212
#117186112
#117186002
#117185892
#268213