Finite Group Databasebeta

← #13119742

Subgroups — #13119742

Order 1664.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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×#88150C212yesmaximal, complemented
2C2×#88147C211yesmaximal, characteristic
3C2×#88141C211yesmaximal, characteristic, complemented
4C13×#398C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic
6#11718651C212yesmaximal, complemented
7#11718641C211yesmaximal, characteristic, complemented
8#11718333C211yesmaximal, characteristic
9#11718330C212yesmaximal, complemented
10#11718328C212yesmaximal, complemented
11#11718311C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C22×Dic26C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6101C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28C2×C4×Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88150—28no—
31#88147—24no—
32#88141—24no—
33C13×#95C2211yescharacteristic
34C13×#95C2212yes—
35#88071C2212yes—
36#88071C2211yescharacteristic
37#88071C2212yes—
38C23×D13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C2×D52—24no—
50C2×D52—22no—
51C2×C4×D13—24no—
52C2×C4×D13—24no—
53C2×C4×D13—24no—
54C2×Dic26—22no—
55C2×Dic26—22no—
56C2×Dic26D414yescomplemented
57C13×C4⋊C4—22no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—24no—
60#6103—24no—
61#6103—24no—
62#6103—24no—
63#6103—24no—
64#6103—24no—
65#6101—22no—
66#6101—22no—
67#6101—24no—
68#6101—24no—
69C4×Dic13—22no—
70C4×Dic13—22no—
71C4×Dic13D414yes—
72#2536—131nomaximal, Sylow
73C23×C13C2411yescharacteristic
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13#4114yes—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13C2×D412yes—
93C2×C4×C13C2×D412yes—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13C2×D412yes—
103C2×Dic13C2×D412yes—
104C2×Dic13C2×D412yes—
105C2×Dic13C2×D412yes—
106C2×Dic13#4112yes—
107D52—28no—
108C4×D13—48no—
109Dic26—28no—
110C2×C22⋊Q8—132no—
111C2×C4×Q8—131no—
112C2×C4×D4—131no—
113#398—131no—
114#398D1311yescharacteristic, complemented
115#394—131no—
116#394—131no—
117#388—132no—
118#388—132no—
119#382—131no—
120#380—132no—
121C22×C13C22×D411yescharacteristic
122C22×C13C22×D411yescharacteristic
123C22×C13C2×#4111yescharacteristic
124C22×C13C2×#4112yes—
125C22×C132−1+412yes—
126C2×D13—24no—
127C2×D13—24no—
128C2×D13—24no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13—42no—
132C2×D13—42no—
133C4×C13—22no—
134C4×C13—22no—
135C4×C13—42no—
136C4×C13—41no—
137C4×C13—42no—
138Dic13—22no—
139Dic13—22no—
140Dic13—41no—
141Dic13—42no—
142Dic13#12114yes—
143C22×Q8—131no—
144C22×D4—131no—
145C23×C4—132no—
146C22⋊Q8—268no—
147C4×Q8—264no—
148C4×D4—264no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4C2×D1311yescharacteristic
154C2×C4⋊C4C2×D1311yescharacteristic
155C2×C4⋊C4C2×D1312yes—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—132no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—131no—
164#95—132no—
165#95—132no—
166#95—131no—
167#95C2×D1312yes—
168#95C2×D1311yescharacteristic
169C2×C13C2×#12111yescharacteristic
170C2×C13#52511yescharacteristic
171C2×C13#53611yescharacteristic
172C2×C13#54812yes—
173C2×C13#55212yes—
174D13—44no—
175C24—132no—
176C2×Q8—134no—
177C2×Q8—262no—
178C2×Q8—262no—
179C2×D4—264no—
180C2×D4—262no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—132no—
185C22×C4—131no—
186C22×C4—264no—
187C22×C4—264no—
188C22×C4—264no—
189C22×C4C22×D1312yes—
190C22×C4C22×D1312yes—
191C22×C4C22×D1311yescharacteristic
192C22×C4C22×D1311yescharacteristic
193C22×C4C22×D1311yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—24no—
197C4⋊C4—262no—
198C4⋊C4—264no—
199C4⋊C4—264no—
200C4⋊C4—262no—
201C22⋊C4—264no—
202C22⋊C4—264no—
203C22⋊C4—264no—
204C22⋊C4—264no—
205C22⋊C4—264no—
206C42—134no—
207C42—262no—
208C42—262no—
209C13#253611yescharacteristic, complemented, Sylow
210C23—134no—
211C23—262no—
212C23—262no—
213C23—262no—
214C23—262no—
215C23—262no—
216C23—262no—
217C23C23×D1311yescharacteristic
218Q8—268no—
219D4—268no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—132no—
232C2×C4—132no—
233C2×C4—132no—
234C2×C4—132no—
235C2×C4—132no—
236C2×C4—261no—
237C2×C4—262no—
238C2×C4—261no—
239C2×C4—261no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—528no—
245C2×C4D4×D1312yes—
246C2×C4D4×D1312yes—
247C22—264no—
248C22—264no—
249C22—264no—
250C22—522no—
251C22—522no—
252C22—522no—
253C22—522no—
254C22C2×D4×D1311yescharacteristic
255C22C2×D4×D1311yescharacteristic
256C22#8825412yes—
257C22#41×D1311yescharacteristic
258C22#41×D1312yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—42no—
263C4—41no—
264C4—134no—
265C4—262no—
266C4—262no—
267C4—522no—
268C4—521no—
269C2—524no—
270C2D13×#12111yescharacteristic
271C2#1171933812yes—
272C2#1171936111yescharacteristic
273C2#1171939812yes—
274C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC22×D52C22
hypercenter#398D13
hypocenterC13#2536
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
3. C2×#88141C2semidirect
4. C13×#398C2semidirect
6. #11718651C2semidirect
7. #11718641C2semidirect
9. #11718330C2semidirect
10. #11718328C2semidirect
11. #11718311C2semidirect
56. C2×Dic26D4semidirect
114. #398D13semidirect
209. C13#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881472
C2×#881412
C13×#3982
#117186522
#117186512
#117186412
#117183332
#117183302
#117183282
#117183112
#253613