Finite Group Databasebeta

← #13118475

Subgroups — #13118475

Order 1664.

800 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×Q8×D13C211yesmaximal, characteristic
2C2×#88150C211yesmaximal, characteristic
3C2×#88142C212yesmaximal, complemented
4C13×#395C211yesmaximal, characteristic, complemented
5#11718890C211yesmaximal, characteristic, complemented
6#11718650C212yesmaximal
7#11718640C211yesmaximal, characteristic, complemented
8#11718329C212yesmaximal
9#11718327C211yesmaximal, characteristic
10#11718317C211yesmaximal, characteristic, complemented
11#11718307C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×Q8×D13—24no—
14C2×Q8×D13—28no—
15C22×C4×D13C2212yes—
16C22×C4×D13C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C22×Dic26C2212yes—
20C2×C13×C4⋊C4C2212yes—
21C2×C13×C4⋊C4C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2212yes—
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28C2×#6101C2211yescharacteristic
29C2×#6101C2211yescharacteristic
30C2×C4×Dic13C2212yes—
31#88150—24no—
32#88142—28no—
33C13×#95C2212yes—
34C13×#95C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2211yescharacteristic
39C23×D13C2311yescharacteristic
40C2×Q8×C13—22no—
41C2×Q8×C13—24no—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2312yes—
46C22×C4×C13C2312yes—
47C22×Dic13C2311yescharacteristic
48C22×Dic13C2311yescharacteristic
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52Q8×D13—232no—
53C2×C4×D13—24no—
54C2×C4×D13—24no—
55C2×C4×D13—24no—
56C2×C4×D13—24no—
57C2×C4×D13D414yes—
58C2×Dic26—22no—
59C2×Dic26—24no—
60C2×Dic26—24no—
61C2×Dic26—24no—
62C2×Dic26—24no—
63C2×Dic26—22no—
64C2×Dic26D418yes—
65C13×C4⋊C4—24no—
66C13×C4⋊C4—22no—
67#6103—22no—
68#6103—22no—
69#6103Q818yescomplemented
70C4⋊Dic13—24no—
71#6101—24no—
72#6101—22no—
73#6101—24no—
74#6101—22no—
75C4×Dic13—24no—
76#2434—131nomaximal, Sylow
77C23×C13C2411yescharacteristic
78C22×D13—22no—
79C22×D13—21no—
80C22×D13—21no—
81C22×D13C2×D412yes—
82C22×D13C2×Q814yes—
83Q8×C13—28no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13C2×D412yes—
95C2×C4×C13C2×D414yes—
96C2×C4×C13C2×Q814yescomplemented
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—21no—
106C2×Dic13C2×D414yes—
107C2×Dic13C2×D414yes—
108C2×Dic13C2×D412yes—
109C2×Dic13C2×Q814yescomplemented
110C4×D13—216no—
111C4×D13—28no—
112Dic26—28no—
113Dic26—216no—
114Dic26—44no—
115C23×Q8—131no—
116C2×C4⋊Q8—132no—
117C2×C22⋊Q8—131no—
118#395—131no—
119#395—131no—
120#395—131no—
121#395D1311yescharacteristic, complemented
122#391—132no—
123#385—132no—
124#385—132no—
125C4×C22⋊C4—131no—
126C22×C13C22×D411yescharacteristic
127C22×C13C22×D412yes—
128C22×C13C22×Q812yes—
129C22×C132−1+411yescharacteristic
130C22×C132−1+411yescharacteristic
131C2×D13—22no—
132C2×D13—22no—
133C2×D13—24no—
134C2×D13—24no—
135C2×D13C4⋊Q814yescomplemented
136C4×C13—22no—
137C4×C13—24no—
138C4×C13—24no—
139C4×C13—41no—
140C4×C13—41no—
141Dic13—24no—
142Dic13—24no—
143Dic13—41no—
144Dic13—41no—
145Dic13#12014yes—
146C22×Q8—132no—
147C22×Q8—131no—
148C22×Q8—131no—
149C22×Q8—264no—
150C22×Q8—268no—
151C22×Q8C2×D1311yescharacteristic
152C23×C4—131no—
153C23×C4—132no—
154C4⋊Q8—268no—
155C22⋊Q8—264no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—132no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4C2×D1311yescharacteristic
162C2×C4⋊C4C2×D1312yes—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—131no—
165C2×C22⋊C4—131no—
166C2×C42—132no—
167#95—131no—
168#95—132no—
169#95—132no—
170#95—132no—
171#95C2×D1311yescharacteristic
172#95C2×D1312yes—
173C2×C13C2×#12011yescharacteristic
174C2×C13C2×C4⋊Q811yescharacteristic
175C2×C13#53611yescharacteristic
176C2×C13D4×Q812yes—
177C2×C13D4×Q812yes—
178D13—24no—
179C24—131no—
180C2×Q8—22no—
181C2×Q8—24no—
182C2×Q8—138no—
183C2×Q8—264no—
184C2×Q8—264no—
185C2×Q8—264no—
186C2×Q8—262no—
187C2×Q8—264no—
188C2×Q8—2632no—
189C2×Q8—262no—
190C22×C4—131no—
191C22×C4—132no—
192C22×C4—132no—
193C22×C4—134no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—264no—
197C22×C4—264no—
198C22×C4—264no—
199C22×C4—264no—
200C22×C4C22×D1311yescharacteristic
201C22×C4C22×D1311yescharacteristic
202C22×C4C22×D1311yescharacteristic
203C22×C4C22×D1312yes—
204C22×C4C22×D1312yes—
205C4⋊C4—22no—
206C4⋊C4—24no—
207C4⋊C4—262no—
208C4⋊C4—264no—
209C4⋊C4—264no—
210C4⋊C4—262no—
211C4⋊C4—264no—
212C22⋊C4—138no—
213C22⋊C4—262no—
214C22⋊C4—262no—
215C42—264no—
216C13#243411yescharacteristic, complemented, Sylow
217C23—132no—
218C23—134no—
219C23—262no—
220C23—261no—
221C23—261no—
222C23C23×D1311yescharacteristic
223Q8—28no—
224Q8—2616no—
225Q8—268no—
226Q8—524no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—134no—
238C2×C4—132no—
239C2×C4—134no—
240C2×C4—134no—
241C2×C4—268no—
242C2×C4—2616no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4D4×D1312yes—
253C2×C4D4×D1314yes—
254C2×C4Q8×D1314yescomplemented
255C22—134no—
256C22—264no—
257C22—262no—
258C22—262no—
259C22—264no—
260C22C2×D4×D1311yescharacteristic
261C22C2×D4×D1312yes—
262C22C2×Q8×D1312yes—
263C22#8825411yescharacteristic
264C22#8825711yescharacteristic
265C4—22no—
266C4—24no—
267C4—24no—
268C4—41no—
269C4—41no—
270C4—134no—
271C4—264no—
272C4—264no—
273C4—521no—
274C4—521no—
275C2—264no—
276C2D13×#12011yescharacteristic
277C2#1171933311yescharacteristic
278C2#1171933712yes—
279C2D13×C4⋊Q811yescharacteristic
280C2#1171943212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#395C2
prime radicalC23×D13C23
hypercenter#395D13
hypocenterC13#2434
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. C2×#88142C2semidirect
4. C13×#395C2semidirect
5. #11718890C2semidirect
7. #11718640C2semidirect
10. #11718317C2semidirect
11. #11718307C2semidirect
69. #6103Q8semidirect
96. C2×C4×C13C2×Q8semidirect
109. C2×Dic13C2×Q8semidirect
121. #395D13semidirect
135. C2×D13C4⋊Q8semidirect
216. C13#2434semidirect
254. C2×C4Q8×D13semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D132
C2×#881502
C2×#881422
C13×#3952
#117188902
#117186502
#117186402
#117183292
#117183272
#117183172
#117183072
#243413