Finite Group Databasebeta

← #13121179

Subgroups — #13121179

Order 1664.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88189C212yesmaximal
2C2×#88132C212yesmaximal, complemented
3C13×#394C211yesmaximal, characteristic
4#11718640C211yesmaximal, characteristic, complemented
5#11718637C211yesmaximal, characteristic, complemented
6#11718613C212yesmaximal, complemented
7#11718611C212yesmaximal, complemented
8#11718605C212yesmaximal, complemented
9#11718318C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C23×Dic13C2212yes—
12C22×Dic26C2211yescharacteristic
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2212yes—
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19#88189—28no—
20C2×C4⋊Dic13C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101C2212yes—
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27#88132—28no—
28C13×#95C2211yescharacteristic
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2211yescharacteristic
33C24×C13C2312yes—
34C2×D4×C13—24no—
35C2×D4×C13—41no—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×Dic13—24no—
41C22×Dic13—24no—
42C22×Dic13—42no—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C2×Dic26—24no—
48C2×Dic26—41no—
49C13×C4⋊C4—41no—
50C13×C22⋊C4—24no—
51C13×C22⋊C4—24no—
52C22⋊Dic13—24no—
53C22⋊Dic13—24no—
54C22⋊Dic13D418yes—
55C4⋊Dic13—24no—
56C4⋊Dic13—41no—
57#6101—24no—
58#6101—24no—
59#6101—24no—
60#6101—24no—
61C4×Dic13—22no—
62#2680—131nomaximal, Sylow
63C23×C13—22no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13—22no—
69C23×C13C2×D414yes—
70C23×C13C2411yescharacteristic
71D4×C13—44no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13#4112yes—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—48no—
93C2×Dic13C2×D414yes—
94C2×Dic13C2×D414yes—
95Dic26—44no—
96C2×#123—132no—
97C2×C22⋊Q8—132no—
98#398—132no—
99#397—132no—
100#395—131no—
101#394D1311yescharacteristic
102#388—132no—
103#385—132no—
104#384—131no—
105C22×C13—24no—
106C22×C13—24no—
107C22×C13—24no—
108C22×C13—42no—
109C22×C13—42no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13C22×D412yes—
113C22×C13C2×#4111yescharacteristic
114C22×C13H(5,𝔽2)11yescharacteristic
115C22×C132−1+411yescharacteristic
116C22×C132−1+412yes—
117C4×C13—22no—
118C4×C13—41no—
119C4×C13—41no—
120C4×C13—42no—
121Dic13—24no—
122Dic13—24no—
123Dic13—42no—
124Dic13—42no—
125C22×Q8—131no—
126C22×D4C2×D1311yescharacteristic
127C23×C4—132no—
128#123—268no—
129C22⋊Q8—268no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—132no—
134C2×C4⋊C4—132no—
135C2×C4⋊C4—131no—
136C2×C4⋊C4C2×D1311yescharacteristic
137C2×C22⋊C4—132no—
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4C2×D1312yes—
141C2×C22⋊C4C2×D1312yes—
142C2×C42—131no—
143#95—132no—
144#95—132no—
145#95—132no—
146#95—131no—
147#95C2×D1311yescharacteristic
148C2×C13—44no—
149C2×C13#53612yes—
150C2×C13#53911yescharacteristic
151C2×C13D4211yescharacteristic
152C2×C13#54712yes—
153C2×C13#56311yescharacteristic
154C24C22×D1312yes—
155C2×Q8—264no—
156C2×Q8—521no—
157C2×D4—24no—
158C2×D4—41no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—132no—
163C22×C4—264no—
164C22×C4—264no—
165C22×C4—522no—
166C22×C4C22×D1312yes—
167C22×C4C22×D1311yescharacteristic
168C22×C4C22×D1311yescharacteristic
169C22×C4C22×D1311yescharacteristic
170C4⋊C4—41no—
171C4⋊C4—264no—
172C4⋊C4—264no—
173C4⋊C4—264no—
174C4⋊C4—264no—
175C4⋊C4—264no—
176C4⋊C4—521no—
177C22⋊C4—24no—
178C22⋊C4—24no—
179C22⋊C4—138no—
180C22⋊C4—264no—
181C22⋊C4—264no—
182C42—262no—
183C13#268011yescharacteristic, complemented, Sylow
184C23—22no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—22no—
190C23D4×D1314yes—
191C23C23×D1311yescharacteristic
192Q8—524no—
193D4—44no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—134no—
204C2×C4—134no—
205C2×C4—262no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—528no—
216C2×C4#612912yes—
217C22—24no—
218C22—24no—
219C22—24no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22C2×D4×D1312yes—
225C22C2×#612911yescharacteristic
226C22#8825111yescharacteristic
227C22#8825711yescharacteristic
228C22#8825712yes—
229C4—22no—
230C4—41no—
231C4—41no—
232C4—42no—
233C4—264no—
234C4—264no—
235C4—522no—
236C4—522no—
237C2—44no—
238C2#1171929511yescharacteristic
239C2#1171930711yescharacteristic
240C2#1171931612yes—
241C2#1171935312yes—
242C2#1171937711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2680
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88132C2semidirect
4. #11718640C2semidirect
5. #11718637C2semidirect
6. #11718613C2semidirect
7. #11718611C2semidirect
8. #11718605C2semidirect
9. #11718318C2semidirect
183. C13#2680semidirect

Maximal subgroups

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

subgroupindex
C2×#881892
C2×#881322
C13×#3942
#117186402
#117186372
#117186132
#117186112
#117186052
#117183182
#268013