Finite Group Databasebeta

← #13113337

Subgroups — #13113337

Order 1664.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#11719311C211yesmaximal, characteristic
2#11718387C211yesmaximal, characteristic, complemented
3D13×#95C211yesmaximal, characteristic, complemented
4C13×#327C211yesmaximal, characteristic, complemented
5#11718129C211yesmaximal, characteristic, complemented
6#11718059C211yesmaximal, characteristic, complemented
7#11718044C211yesmaximal, characteristic, complemented
8C2×#6129C411yescharacteristic, complemented
9C22×C4×D13—21no—
10C22×C4×D13C2211yescharacteristic
11C13×#121C2211yescharacteristic
12#88192C411yescharacteristic, complemented
13#88191—21no—
14D4×Dic13—21no—
15#88178C2211yescharacteristic
16C2×#6094—21no—
17#88151C411yescharacteristic, complemented
18#88146C411yescharacteristic, complemented
19#88137—21no—
20#88135—21no—
21C13×C22⋊C8C2211yescharacteristic
22C13×#95C2211yescharacteristic
23#88071—21no—
24#88071C2211yescharacteristic
25C22⋊#1055C2211yescharacteristic
26#88060—21no—
27C23×D13D411yescharacteristic
28C2×D4×C13—21no—
29C2×D4×C13C2×C411yescharacteristic, complemented
30C22×C4×C13—21no—
31C22×C4×C13C2311yescharacteristic
32C2×C22⋊D13—21no—
33C2×C22⋊D13—21no—
34C22×Dic13—21no—
35C22×Dic13—21no—
36C22×Dic13D411yescharacteristic
37#6129—42no—
38C2×C4×D13—24no—
39C2×C4×D13—42no—
40C2×C4×D13—42no—
41C2×C4×D13—42no—
42C2×C4×D13C2×C411yescharacteristic
43C2×C4×D13C2×C411yescharacteristic
44C2×C4×D13D411yescharacteristic
45C2×C4×D13D411yescharacteristic
46C2×Dic26C2×C411yescharacteristic, complemented
47C2×C8×C13—21no—
48C13×C4⋊C4C2×C411yescharacteristic, complemented
49C13×C22⋊C4—21no—
50C22⋊Dic13—21no—
51C22⋊Dic13—21no—
52#6103—21no—
53#6103—21no—
54C4⋊Dic13—21no—
55C4⋊Dic13C2×C411yescharacteristic, complemented
56#6101—21no—
57C4×Dic13—21no—
58C2×#1055—21no—
59#6094—42no—
60#1504—131nomaximal, Sylow
61C23×C13—21no—
62C23×C13C2×D411yescharacteristic
63C22×D13—21no—
64C22×D13—21no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13C22⋊C411yescharacteristic
68C22×D13C22⋊C411yescharacteristic
69D4×C13—41no—
70D4×C13—41no—
71D4×C13—41no—
72C2×C4×C13—22no—
73C2×C4×C13—21no—
74C2×C4×C13—41no—
75C2×C4×C13—41no—
76C2×C4×C13—41no—
77C2×C4×C13C22×C411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C22⋊D13—42no—
80C22⋊D13—42no—
81C2×Dic13—22no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—41no—
85C2×Dic13—42no—
86C2×Dic13—41no—
87C2×Dic13—41no—
88C2×Dic13C22⋊C411yescharacteristic
89C2×Dic13C22⋊C411yescharacteristic
90C4×D13—22no—
91C4×D13—22no—
92C4×D13—41no—
93C4×D13—41no—
94C4×D13—48no—
95Dic26—41no—
96C8×C13—41no—
97#1055—41no—
98#525—131no—
99#407—131no—
100C2×#95—131no—
101#328—131no—
102#328—131no—
103#327—131no—
104#327D1311yescharacteristic, complemented
105C22×C13—21no—
106C22×C13—21no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—41no—
110C22×C13C2×C22⋊C411yescharacteristic
111C22×C13AGL(1,ℤ/8)11yescharacteristic
112C22×C13#13711yescharacteristic
113C2×D13—24no—
114C2×D13—24no—
115C2×D13—21no—
116C2×D13—21no—
117C2×D13—21no—
118C2×D13—21no—
119C2×D13#9912yes—
120C2×D13#10412yes—
121C4×C13—21no—
122C4×C13—21no—
123C4×C13—42no—
124C4×C13—41no—
125Dic13—21no—
126Dic13—21no—
127Dic13—42no—
128Dic13—41no—
129Dic13—41no—
130C2×#41—131no—
131C23×C4—131no—
132C23×C4—261no—
133C2×M16—261no—
134#123—261no—
135C22⋊Q8—131no—
136C22⋊Q8—131no—
137#121—131no—
138#121C2×D1311yescharacteristic
139#120—261no—
140C4×D4—261no—
141C4×D4—261no—
142#117—131no—
143C22⋊C8—131no—
144C22⋊C8—261no—
145C22⋊C8C2×D1311yescharacteristic
146#95—131no—
147#95—261no—
148#95C2×D1311yescharacteristic
149C2×C13—21no—
150C2×C13—21no—
151C2×C13—81no—
152C2×C13C2×#9911yescharacteristic
153C2×C13#41711yescharacteristic
154C2×C13C2×#10411yescharacteristic
155D13—22no—
156D13—22no—
157C24—131no—
158#41—522no—
159C2×Q8—131no—
160C2×D4—21no—
161C2×D4—261no—
162C2×D4—261no—
163C2×D4C4×D1311yescharacteristic, complemented
164C22×C4—21no—
165C22×C4—131no—
166C22×C4—131no—
167C22×C4—131no—
168C22×C4—131no—
169C22×C4—131no—
170C22×C4—264no—
171C22×C4—261no—
172C22×C4—261no—
173C22×C4—522no—
174C22×C4—522no—
175C22×C4—522no—
176C22×C4C22×D1311yescharacteristic
177M16—522no—
178C2×C8—21no—
179C2×C8—261no—
180C4⋊C4—131no—
181C4⋊C4—261no—
182C4⋊C4—261no—
183C4⋊C4C4×D1311yescharacteristic, complemented
184C22⋊C4—21no—
185C22⋊C4—261no—
186C22⋊C4—261no—
187C22⋊C4—261no—
188C22⋊C4—261no—
189C42—261no—
190C13#150411yescharacteristic, complemented, Sylow
191C23—21no—
192C23—131no—
193C23—131no—
194C23—262no—
195C23—262no—
196C23—261no—
197C23—261no—
198C23D4×D1311yescharacteristic
199Q8—521no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—522no—
204D4—522no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—131no—
211C2×C4—131no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4—528no—
220C2×C4—521no—
221C2×C4—522no—
222C2×C4—521no—
223C2×C4—521no—
224C2×C4C2×C4×D1311yescharacteristic
225C2×C4D4×D1311yescharacteristic
226C8—41no—
227C8—521no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—132no—
234C22—132no—
235C22—264no—
236C22—264no—
237C22—261no—
238C22—261no—
239C22—261no—
240C22—261no—
241C22C22⋊C4×D1311yescharacteristic
242C22#8816511yescharacteristic
243C22#8816911yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—261no—
249C4—261no—
250C4—522no—
251C4—521no—
252C4—521no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—262no—
257C2—262no—
258C2D13×#9911yescharacteristic
259C2#1171843211yescharacteristic
260C2D13×#10411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D13
commutatorC2×C4×C13C22×C4
FrattiniC22×C4C22×D13
FittingC13×#327C2
socleC22×C13C2×C22⋊C4
prime radical#11719311C2
cosocleC22×C4×C13C23
hypercenter#327D13
hypocenterC13#1504
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #11718387C2semidirect
3. D13×#95C2semidirect
4. C13×#327C2semidirect
5. #11718129C2semidirect
6. #11718059C2semidirect
7. #11718044C2semidirect
8. C2×#6129C4semidirect
12. #88192C4semidirect
17. #88151C4semidirect
18. #88146C4semidirect
29. C2×D4×C13C2×C4semidirect
46. C2×Dic26C2×C4semidirect
48. C13×C4⋊C4C2×C4semidirect
55. C4⋊Dic13C2×C4semidirect
104. #327D13semidirect
163. C2×D4C4×D13semidirect
183. C4⋊C4C4×D13semidirect
190. C13#1504semidirect

Maximal subgroups

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

subgroupindex
#117193112
#117183872
D13×#952
C13×#3272
#117181292
#117180592
#117180442
#150413