Finite Group Databasebeta

← #13120758

Subgroups — #13120758

Order 1664.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×#88151C211yesmaximal, characteristic, complemented
2C2×#88135C211yesmaximal, characteristic
3C13×#397C211yesmaximal, characteristic, complemented
4#11718641C211yesmaximal, characteristic, complemented
5#11718620C212yesmaximal
6#11718611C212yesmaximal, complemented
7#11718608C211yesmaximal, characteristic, complemented
8#11718335C212yesmaximal, complemented
9#11718325C211yesmaximal, characteristic, complemented
10#11718317C211yesmaximal, characteristic, complemented
11#11718316C212yesmaximal, complemented
12C22×C22⋊D13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×#6101C2211yescharacteristic
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88151—24no—
29#88135—24no—
30C13×#95C2212yes—
31C13×#95C2211yescharacteristic
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2312yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C22×Dic13—22no—
47C22×Dic13—42no—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C2×C4×D13—42no—
54C2×C4×D13D414yes—
55C2×Dic26—22no—
56C2×Dic26—42no—
57C13×C4⋊C4—22no—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—22no—
60C22⋊Dic13—42no—
61#6103—22no—
62#6103—24no—
63#6103—42no—
64C4⋊Dic13—24no—
65C4⋊Dic13—42no—
66#6101—22no—
67#6101—24no—
68C4×Dic13—22no—
69#2638—131nomaximal, Sylow
70C23×C13—21no—
71C23×C13—21no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13#4112yes—
75C23×C13C2411yescharacteristic
76C22×D13—21no—
77C22×D13—21no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13C2×D412yes—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D412yes—
91C22⋊D13—28no—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—44no—
104C2×Dic13C2×D412yes—
105C2×Dic13#4112yes—
106C4×D13—44no—
107Dic26—44no—
108C2×C22⋊Q8—131no—
109C2×C4×D4—131no—
110#398—131no—
111#397—132no—
112#397D1311yescharacteristic, complemented
113#395—131no—
114#394—132no—
115#393—131no—
116#387—132no—
117#385—132no—
118#381—131no—
119C22×C13—22no—
120C22×C13—24no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—42no—
124C22×C13C22×D411yescharacteristic
125C22×C13C2×#4111yescharacteristic
126C22×C13C2×#4111yescharacteristic
127C22×C13H(5,𝔽2)12yes—
128C22×C132−1+412yes—
129C2×D13—22no—
130C2×D13—22no—
131C2×D13—22no—
132C2×D13—42no—
133C2×D13—42no—
134C4×C13—22no—
135C4×C13—42no—
136C4×C13—41no—
137C4×C13—42no—
138Dic13—22no—
139Dic13—22no—
140Dic13—42no—
141Dic13—41no—
142Dic13—42no—
143C22×Q8—131no—
144C22×D4—131no—
145C23×C4—131no—
146C23×C4—131no—
147C22⋊Q8—264no—
148C4×D4—264no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4C2×D1311yescharacteristic
154C2×C22⋊C4—131no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4C2×D1311yescharacteristic
159C2×C22⋊C4C2×D1312yes—
160C2×C42—131no—
161#95—132no—
162#95—131no—
163#95—132no—
164#95—132no—
165#95—132no—
166#95C2×D1311yescharacteristic
167#95C2×D1312yes—
168C2×C13—42no—
169C2×C13#52511yescharacteristic
170C2×C13#53411yescharacteristic
171C2×C13#53611yescharacteristic
172C2×C13#53912yes—
173C2×C13#54212yes—
174D13—42no—
175C24—131no—
176C24C22×D1311yescharacteristic
177C2×Q8—262no—
178C2×Q8—522no—
179C2×D4—262no—
180C2×D4—262no—
181C2×D4—262no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—134no—
185C22×C4—132no—
186C22×C4—132no—
187C22×C4—131no—
188C22×C4—262no—
189C22×C4—522no—
190C22×C4—522no—
191C22×C4C22×D1311yescharacteristic
192C22×C4C22×D1312yes—
193C22×C4C22×D1312yes—
194C22×C4C22×D1311yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—264no—
197C4⋊C4—264no—
198C4⋊C4—262no—
199C4⋊C4—522no—
200C22⋊C4—24no—
201C22⋊C4—22no—
202C22⋊C4—262no—
203C22⋊C4—264no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C42—262no—
207C13#263811yescharacteristic, complemented, Sylow
208C23—21no—
209C23—21no—
210C23—22no—
211C23—22no—
212C23—132no—
213C23—261no—
214C23—261no—
215C23—262no—
216C23—262no—
217C23#612912yes—
218C23C23×D1311yescharacteristic
219Q8—524no—
220D4—268no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—132no—
231C2×C4—132no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—262no—
235C2×C4—261no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—524no—
244C2×C4—524no—
245C2×C4D4×D1312yes—
246C22—22no—
247C22—24no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—262no—
252C22—262no—
253C22—262no—
254C22—522no—
255C22—522no—
256C22C2×D4×D1311yescharacteristic
257C22C2×#612911yescharacteristic
258C22#41×D1311yescharacteristic
259C22#8825612yes—
260C22#8825712yes—
261C4—22no—
262C4—42no—
263C4—42no—
264C4—41no—
265C4—262no—
266C4—262no—
267C4—521no—
268C4—522no—
269C4—522no—
270C2—42no—
271C2—522no—
272C2#1171931111yescharacteristic
273C2#1171935811yescharacteristic
274C2#1171937012yes—
275C2#1171938011yescharacteristic
276C2#1171941512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC22×C22⋊D13C22
hypercenter#397D13
hypocenterC13#2638
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#88151C2semidirect
3. C13×#397C2semidirect
4. #11718641C2semidirect
6. #11718611C2semidirect
7. #11718608C2semidirect
8. #11718335C2semidirect
9. #11718325C2semidirect
10. #11718317C2semidirect
11. #11718316C2semidirect
112. #397D13semidirect
207. C13#2638semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×#881352
C13×#3972
#117186412
#117186202
#117186112
#117186082
#117183352
#117183252
#117183172
#117183162
#263813