Finite Group Databasebeta

← #13121765

Subgroups — #13121765

Order 1664.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#88148C212yesmaximal
2C13×#389C211yesmaximal, characteristic, complemented
3#11718654C212yesmaximal, complemented
4#11718650C212yesmaximal, complemented
5#11718645C212yesmaximal, complemented
6#11718600C211yesmaximal, characteristic
7#11718589C211yesmaximal, characteristic, complemented
8#11718335C212yesmaximal, complemented
9#11718329C212yesmaximal, complemented
10C22×D52C2211yescharacteristic
11C22×C4×D13C2212yes—
12C2×C13×C4⋊C4C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C42×C13C2211yescharacteristic
16C2×#6103C2212yes—
17C2×#6103C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26#88148—28no—
27C13×#95C2212yes—
28#88071C2212yes—
29#88071C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32C23×D13C2312yes—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C22×C4×C13C2311yescharacteristic
38C22×Dic13C2312yes—
39C22×Dic13C2312yes—
40C22×Dic13C2312yes—
41C2×D52—41no—
42C2×D52—41no—
43C2×D52D414yes—
44C2×C4×D13—24no—
45C2×C4×D13—42no—
46C2×C4×D13—42no—
47C13×C4⋊C4—24no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—41no—
50C42×C13—41no—
51#6103—24no—
52#6103—24no—
53#6103—24no—
54#6103—24no—
55#6103—24no—
56C4⋊Dic13—22no—
57C4⋊Dic13—41no—
58C4⋊Dic13—41no—
59#6101—24no—
60#6101—42no—
61#2724—131nomaximal, Sylow
62C23×C13C2411yescharacteristic
63C22×D13—22no—
64C22×D13—22no—
65C22×D13—22no—
66C22×D13—22no—
67C22×D13—22no—
68C22×D13—22no—
69C22×D13C2×D414yes—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13C2×D412yes—
83C2×C4×C13#4112yes—
84C2×C4×C13#4112yes—
85C2×Dic13—22no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94D52—44no—
95C4×D13—48no—
96C2×#123—132no—
97#398—132no—
98#397—132no—
99#397—132no—
100#390—131no—
101#389—131no—
102#389D1311yescharacteristic, complemented
103#385—132no—
104#385—132no—
105C22×C13C22×D411yescharacteristic
106C22×C13C2×#4111yescharacteristic
107C22×C13C2×#4111yescharacteristic
108C22×C13H(5,𝔽2)11yescharacteristic
109C22×C13H(5,𝔽2)11yescharacteristic
110C22×C132−1+411yescharacteristic
111C22×C132−1+411yescharacteristic
112C2×D13—24no—
113C2×D13—24no—
114C2×D13—24no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—42no—
118C2×D13—42no—
119C4×C13—22no—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—42no—
123C4×C13—42no—
124Dic13—42no—
125Dic13—42no—
126Dic13—42no—
127C22×D4—131no—
128C23×C4—132no—
129#123—268no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4C2×D1312yes—
136C2×C4⋊C4C2×D1311yescharacteristic
137C2×C4⋊C4C2×D1311yescharacteristic
138C2×C22⋊C4—132no—
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—132no—
142C2×C22⋊C4—132no—
143C2×C42C2×D1311yescharacteristic
144#95—132no—
145#95—132no—
146#95—132no—
147#95—132no—
148#95C2×D1312yes—
149C2×C13#53411yescharacteristic
150C2×C13#53911yescharacteristic
151C2×C13#53911yescharacteristic
152C2×C13#54711yescharacteristic
153C2×C13#54711yescharacteristic
154C2×C13#55911yescharacteristic
155C2×C13#56311yescharacteristic
156D13—44no—
157C24—132no—
158C2×D4—134no—
159C2×D4—521no—
160C2×D4—521no—
161C22×C4—132no—
162C22×C4—132no—
163C22×C4—132no—
164C22×C4—264no—
165C22×C4—522no—
166C22×C4—522no—
167C22×C4C22×D1312yes—
168C22×C4C22×D1312yes—
169C22×C4C22×D1311yescharacteristic
170C22×C4C22×D1311yescharacteristic
171C22×C4C22×D1311yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—24no—
174C4⋊C4—41no—
175C4⋊C4—264no—
176C4⋊C4—262no—
177C4⋊C4—522no—
178C4⋊C4—521no—
179C4⋊C4—521no—
180C22⋊C4—264no—
181C22⋊C4—264no—
182C22⋊C4—264no—
183C22⋊C4—264no—
184C22⋊C4—264no—
185C42—41no—
186C13#272411yescharacteristic, complemented, Sylow
187C23—134no—
188C23—262no—
189C23—262no—
190C23—262no—
191C23—262no—
192C23—262no—
193C23—262no—
194C23C23×D1311yescharacteristic
195D4—524no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—262no—
209C2×C4—262no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—262no—
217C2×C4—528no—
218C2×C4#612712yes—
219C2×C4D4×D1312yes—
220C2×C4#613112yes—
221C22—264no—
222C22—264no—
223C22—264no—
224C22—522no—
225C22—522no—
226C22—522no—
227C22—522no—
228C22C2×#612711yescharacteristic
229C22C2×D4×D1311yescharacteristic
230C22#8825111yescharacteristic
231C22C2×#613111yescharacteristic
232C22#8825411yescharacteristic
233C22#8825611yescharacteristic
234C22#8825711yescharacteristic
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—522no—
241C4—522no—
242C4—522no—
243C2—524no—
244C2#1171922011yescharacteristic
245C2#1171925611yescharacteristic
246C2#1171929011yescharacteristic
247C2#1171931011yescharacteristic
248C2#1171935011yescharacteristic
249C2#1171940411yescharacteristic
250C2#1171943111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#389C2
prime radicalC22×D52C22
hypercenter#389D13
hypocenterC13#2724
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C13×#389C2semidirect
3. #11718654C2semidirect
4. #11718650C2semidirect
5. #11718645C2semidirect
7. #11718589C2semidirect
8. #11718335C2semidirect
9. #11718329C2semidirect
102. #389D13semidirect
186. C13#2724semidirect

Maximal subgroups

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

subgroupindex
C2×#881482
C13×#3892
#117186542
#117186502
#117186452
#117186002
#117185892
#117183352
#117183292
#272413