Finite Group Databasebeta

← #13118479

Subgroups — #13118479

Order 1664.

800 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 193 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×#88198C211yesmaximal, characteristic, complemented
3C2×#88151C211yesmaximal, characteristic
4C2×#88123C211yesmaximal, characteristic, complemented
5C13×#391C211yesmaximal, characteristic, complemented
6#11718635C211yesmaximal, characteristic, complemented
7C4×#6103C211yesmaximal, characteristic
8#11718329C214yesmaximal
9#11718317C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C2×Q8×D13—24no—
12C2×Q8×D13—24no—
13C2×Q8×D13—24no—
14C22×C4×D13C2212yes—
15C22×C4×D13C2211yescharacteristic
16C22×Dic26C2211yescharacteristic
17C22×Dic26C2212yes—
18C22×Dic26C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C42×C13C2211yescharacteristic
21#88198—24no—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2214yes—
25C2×C4⋊Dic13C2212yes—
26C2×#6101C2214yes—
27C2×C4×Dic13C2211yescharacteristic
28#88151—24no—
29#88123—24no—
30C13×#95C2214yes—
31#88071C2212yes—
32#88071C2214yes—
33C23×D13C2311yescharacteristic
34C2×Q8×C13—22no—
35C2×Q8×C13—22no—
36C2×Q8×C13D414yes—
37C22×C4×C13C2312yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45Q8×D13—232no—
46C2×C4×D13—24no—
47C2×C4×D13—24no—
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×C4×D13—24no—
51C2×C4×D13D414yes—
52C2×Dic26—24no—
53C2×Dic26—22no—
54C2×Dic26—22no—
55C2×Dic26—24no—
56C2×Dic26—24no—
57C2×Dic26—22no—
58C2×Dic26—22no—
59C2×Dic26—22no—
60C2×Dic26D414yes—
61C13×C4⋊C4—22no—
62C42×C13—22no—
63#6103—24no—
64#6103Q818yescomplemented
65C4⋊Dic13—28no—
66C4⋊Dic13—24no—
67#6101—28no—
68C4×Dic13—22no—
69#2434—131nomaximal, Sylow
70C23×C13C2411yescharacteristic
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—22no—
74C22×D13C2×D412yes—
75C22×D13C2×Q814yes—
76Q8×C13—28no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—24no—
83C2×C4×C13C2×D414yes—
84C2×C4×C13C2×D412yes—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D412yes—
87C2×C4×C13C2×Q814yescomplemented
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13C2×D412yes—
98C2×Dic13C2×D414yes—
99C2×Dic13C2×Q814yescomplemented
100C4×D13—216no—
101C4×D13—28no—
102Dic26—216no—
103Dic26—28no—
104Dic26—44no—
105C23×Q8—131no—
106C2×C4⋊Q8—131no—
107C2×C4⋊Q8—131no—
108C2×C22⋊Q8—131no—
109#395—134no—
110#391—131no—
111#391D1311yescharacteristic, complemented
112#385—134no—
113C4×C22⋊C4—131no—
114C22×C13C22×D411yescharacteristic
115C22×C13C22×D411yescharacteristic
116C22×C13C22×D411yescharacteristic
117C22×C13C22×Q812yes—
118C22×C132−1+412yes—
119C2×D13—22no—
120C2×D13—22no—
121C2×D13—24no—
122C2×D13—24no—
123C2×D13C4⋊Q814yescomplemented
124C4×C13—24no—
125C4×C13—24no—
126C4×C13—42no—
127C4×C13#12014yes—
128Dic13—22no—
129Dic13—24no—
130Dic13—24no—
131Dic13—42no—
132C22×Q8—131no—
133C22×Q8—131no—
134C22×Q8—132no—
135C22×Q8—264no—
136C22×Q8—264no—
137C22×Q8—264no—
138C22×Q8C2×D1311yescharacteristic
139C23×C4—131no—
140C23×C4—132no—
141C4⋊Q8—264no—
142C4⋊Q8—264no—
143C22⋊Q8—264no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—134no—
146C2×C4⋊C4—134no—
147C2×C4⋊C4C2×D1311yescharacteristic
148C2×C22⋊C4—132no—
149C2×C22⋊C4—132no—
150C2×C42—131no—
151C2×C42C2×D1311yescharacteristic
152#95—132no—
153#95—134no—
154#95C2×D1314yes—
155C2×C13C2×#12011yescharacteristic
156C2×C13C2×C4⋊Q811yescharacteristic
157C2×C13#53611yescharacteristic
158C2×C13D4×Q812yes—
159C2×C13D4×Q812yes—
160D13—24no—
161C24—131no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—134no—
165C2×Q8—264no—
166C2×Q8—264no—
167C2×Q8—2632no—
168C2×Q8—264no—
169C2×Q8—262no—
170C2×Q8—262no—
171C2×Q8—262no—
172C2×Q8—262no—
173C2×Q8—262no—
174C2×Q8D5214yes—
175C22×C4—132no—
176C22×C4—131no—
177C22×C4—132no—
178C22×C4—134no—
179C22×C4—132no—
180C22×C4—264no—
181C22×C4—264no—
182C22×C4—264no—
183C22×C4—262no—
184C22×C4—262no—
185C22×C4C22×D1312yes—
186C22×C4C22×D1312yes—
187C22×C4C22×D1312yes—
188C22×C4C22×D1311yescharacteristic
189C4⋊C4—22no—
190C4⋊C4—264no—
191C4⋊C4—268no—
192C4⋊C4—268no—
193C22⋊C4—138no—
194C22⋊C4—264no—
195C42—22no—
196C42—262no—
197C13#243411yescharacteristic, complemented, Sylow
198C23—132no—
199C23—134no—
200C23—261no—
201C23—261no—
202C23—262no—
203C23C23×D1311yescharacteristic
204Q8—28no—
205Q8—2616no—
206Q8—268no—
207Q8—524no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—132no—
215C2×C4—134no—
216C2×C4—134no—
217C2×C4—2616no—
218C2×C4—262no—
219C2×C4—261no—
220C2×C4—262no—
221C2×C4—262no—
222C2×C4—261no—
223C2×C4—262no—
224C2×C4—268no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4C2×D5214yes—
229C2×C4C2×D5212yes—
230C2×C4D4×D1312yes—
231C2×C4D4×D1312yes—
232C2×C4Q8×D1314yescomplemented
233C22—134no—
234C22—262no—
235C22—264no—
236C22—264no—
237C22—262no—
238C22C22×D5211yescharacteristic
239C22C2×D4×D1311yescharacteristic
240C22C2×D4×D1311yescharacteristic
241C22C2×Q8×D1312yes—
242C22#8825712yes—
243C4—24no—
244C4—24no—
245C4—42no—
246C4—262no—
247C4—264no—
248C4—264no—
249C4—522no—
250C4#8813614yes—
251C2—264no—
252C2C2×#8813611yescharacteristic
253C2Q8×D5212yes—
254C2#1171933712yes—
255C2#1171938011yescharacteristic
256C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#391C2
prime radicalC23×D13C23
hypercenter#391D13
hypocenterC13#2434
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#88198C2semidirect
4. C2×#88123C2semidirect
5. C13×#391C2semidirect
6. #11718635C2semidirect
9. #11718317C2semidirect
64. #6103Q8semidirect
87. C2×C4×C13C2×Q8semidirect
99. C2×Dic13C2×Q8semidirect
111. #391D13semidirect
123. C2×D13C4⋊Q8semidirect
197. C13#2434semidirect
232. 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×#881982
C2×#881512
C2×#881232
C13×#3912
#117186352
C4×#61032
#117183292
#117183172
#243413