Finite Group Databasebeta

← #13119818

Subgroups — #13119818

Order 1664.

576 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 157 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×#88190C211yesmaximal, characteristic
2C2×#88190C211yesmaximal, characteristic
3C2×#88141C211yesmaximal, characteristic, complemented
4C2×#88123C211yesmaximal, characteristic, complemented
5C13×#390C211yesmaximal, characteristic
6#11718635C211yesmaximal, characteristic, complemented
7#11718612C214yesmaximal, complemented
8#11718609C214yesmaximal, complemented
9C4×#6101C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2214yes—
15C2×C42×C13C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2212yes—
19#88190—24no—
20#88190—24no—
21C2×C4⋊Dic13C2214yes—
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×C4×Dic13C2212yes—
25C2×C4×Dic13C2211yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88141—24no—
28#88123—24no—
29#88071C2212yes—
30#88071C2214yes—
31C24×C13C2312yes—
32C2×D4×C13—22no—
33C2×D4×C13—22no—
34C2×D4×C13—22no—
35C22×C4×C13C2312yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2311yescharacteristic
41C22×Dic13C2311yescharacteristic
42C22×Dic13C2312yes—
43C2×Dic26—22no—
44C2×Dic26—22no—
45C2×Dic26—22no—
46C2×Dic26—22no—
47C2×Dic26—22no—
48C2×Dic26D414yes—
49C13×C4⋊C4—22no—
50C13×C22⋊C4—28no—
51C42×C13—22no—
52C22⋊Dic13—28no—
53C22⋊Dic13—24no—
54C22⋊Dic13—24no—
55C4⋊Dic13—28no—
56#6101—24no—
57#6101—24no—
58C4×Dic13—22no—
59C4×Dic13—24no—
60C4×Dic13D414yes—
61#2545—131nomaximal, Sylow
62C23×C13—22no—
63C23×C13—22no—
64C23×C13—24no—
65C23×C13—22no—
66C23×C13—24no—
67C23×C13C2411yescharacteristic
68D4×C13—44no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—24no—
73C2×C4×C13C2×D412yes—
74C2×C4×C13C2×D412yes—
75C2×C4×C13#4114yes—
76C2×C4×C13#4112yes—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13C2×D412yes—
88C2×Dic13C2×D412yes—
89C2×Dic13C2×D414yes—
90Dic26—28no—
91Dic26—44no—
92C2×C4⋊Q8—131no—
93C2×#124—131no—
94C2×#124—131no—
95C2×C4×Q8—131no—
96#396—134no—
97#391—131no—
98#390D1311yescharacteristic
99#388—134no—
100C4×C4⋊C4—131no—
101C22×C13—42no—
102C22×C13—42no—
103C22×C13—42no—
104C22×C13—44no—
105C22×C13—44no—
106C22×C13C22×D411yescharacteristic
107C22×C13C22×D411yescharacteristic
108C22×C13C2×#4111yescharacteristic
109C22×C13C2×#4112yes—
110C22×C132−1+412yes—
111C4×C13—24no—
112C4×C13—42no—
113C4×C13#12114yes—
114Dic13—24no—
115Dic13—22no—
116Dic13—22no—
117Dic13—42no—
118Dic13—42no—
119C22×Q8—131no—
120C22×Q8—131no—
121C22×D4C2×D1311yescharacteristic
122C4⋊Q8—264no—
123#124—264no—
124#124—264no—
125C4×Q8—264no—
126C2×C4⋊C4—132no—
127C2×C4⋊C4—134no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4C2×D1311yescharacteristic
130C2×C22⋊C4—132no—
131C2×C22⋊C4—134no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4C2×D1314yes—
134C2×C42—131no—
135C2×C42—132no—
136C2×C42—131no—
137C2×C42C2×D1311yescharacteristic
138#95—132no—
139#95—134no—
140C2×C13—82no—
141C2×C13C2×#12111yescharacteristic
142C2×C13#53211yescharacteristic
143C2×C13#53611yescharacteristic
144C2×C13#54812yes—
145C2×C13#55612yes—
146C24C22×D1312yes—
147C2×Q8—134no—
148C2×Q8—262no—
149C2×Q8—262no—
150C2×Q8—262no—
151C2×Q8—262no—
152C2×Q8—262no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—132no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4C22×D1312yes—
162C22×C4C22×D1312yes—
163C22×C4C22×D1311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—264no—
166C4⋊C4—268no—
167C4⋊C4—264no—
168C22⋊C4—28no—
169C22⋊C4—264no—
170C22⋊C4—264no—
171C22⋊C4—268no—
172C42—22no—
173C42—134no—
174C42—264no—
175C42—262no—
176C13#254511yescharacteristic, complemented, Sylow
177C23—22no—
178C23—22no—
179C23—22no—
180C23—24no—
181C23—24no—
182C23C23×D1311yescharacteristic
183Q8—268no—
184Q8—524no—
185D4—44no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—24no—
190C2×C4—132no—
191C2×C4—132no—
192C2×C4—134no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—262no—
202C2×C4—262no—
203C2×C4#612712yes—
204C2×C4D4×D1312yes—
205C2×C4D4×D1312yes—
206C2×C4#612914yes—
207C22—42no—
208C22—44no—
209C22—44no—
210C22—42no—
211C22—42no—
212C22C2×#612711yescharacteristic
213C22C2×D4×D1311yescharacteristic
214C22C2×D4×D1311yescharacteristic
215C22C2×#612912yes—
216C22#8825712yes—
217C4—24no—
218C4—42no—
219C4—264no—
220C4—262no—
221C4—262no—
222C4—522no—
223C4—522no—
224C4#8813814yes—
225C2—82no—
226C2C2×#8813811yescharacteristic
227C2#1171924712yes—
228C2#1171930312yes—
229C2#1171938011yescharacteristic
230C2#1171942111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×C13C22
hypercenter#390D13
hypocenterC13#2545
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
3. C2×#88141C2semidirect
4. C2×#88123C2semidirect
6. #11718635C2semidirect
7. #11718612C2semidirect
8. #11718609C2semidirect
9. C4×#6101C2semidirect
176. C13#2545semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
C2×#881412
C2×#881232
C13×#3902
#117186352
#117186122
#117186092
C4×#61012
#254513