Finite Group Databasebeta

← #13119281

Subgroups — #13119281

Order 1664.

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

normal subgroups only

This group has 546 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×#88148C211yesmaximal, characteristic
2C2×#88146C211yesmaximal, characteristic, complemented
3C13×#398C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718651C212yesmaximal, complemented
6#11718648C212yesmaximal, complemented
7#11718647C211yesmaximal, characteristic, complemented
8#11718338C211yesmaximal, characteristic, complemented
9#11718326C212yesmaximal
10D13×#95C211yesmaximal, characteristic, complemented
11#11718315C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C22×C4×D13C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×#6103C2212yes—
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2212yes—
26C2×#6101C2211yescharacteristic
27C2×C4×Dic13C2212yes—
28#88148—24no—
29#88146—24no—
30C13×#95C2212yes—
31C13×#95C2211yescharacteristic
32#88071C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×D52—22no—
49C2×D52—24no—
50C2×C4×D13—24no—
51C2×C4×D13—24no—
52C2×C4×D13—24no—
53C2×C4×D13—42no—
54C2×C4×D13D414yes—
55C13×C4⋊C4—22no—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—42no—
58#6103—24no—
59#6103—22no—
60#6103—22no—
61#6103—24no—
62#6103—22no—
63#6103—42no—
64C4⋊Dic13—22no—
65C4⋊Dic13—24no—
66#6101—22no—
67C4×Dic13—24no—
68#2498—131nomaximal, Sylow
69C23×C13C2411yescharacteristic
70C22×D13—22no—
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—21no—
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—21no—
77C22×D13—21no—
78C22×D13C2×D412yes—
79C22×D13#4114yes—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13C2×D412yes—
92C2×C4×C13#4114yes—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13C2×D412yes—
103D52—44no—
104C4×D13—28no—
105C4×D13—48no—
106C2×#123—131no—
107C2×#117—131no—
108#400—131no—
109#399—131no—
110#398D1311yescharacteristic, complemented
111#397—131no—
112#388—132no—
113#387—132no—
114#386—132no—
115#380—132no—
116C2×#95—131no—
117C22×C13C22×D411yescharacteristic
118C22×C13C2×#4112yes—
119C22×C13C2×#4112yes—
120C22×C13H(5,𝔽2)11yescharacteristic
121C22×C132−1+411yescharacteristic
122C2×D13—22no—
123C2×D13—22no—
124C2×D13—24no—
125C2×D13—24no—
126C2×D13—41no—
127C2×D13—41no—
128C2×D13—41no—
129C2×D13—42no—
130C2×D13—42no—
131C2×D13#12314yes—
132C4×C13—22no—
133C4×C13—24no—
134C4×C13—41no—
135C4×C13—42no—
136C4×C13—41no—
137Dic13—22no—
138Dic13—42no—
139Dic13—41no—
140Dic13—42no—
141C22×D4—131no—
142C23×C4—131no—
143C23×C4—132no—
144#123—264no—
145#117—264no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C4⋊C4C2×D1311yescharacteristic
151C2×C4⋊C4C2×D1312yes—
152C2×C22⋊C4—132no—
153C2×C22⋊C4—131no—
154C2×C22⋊C4—131no—
155C2×C22⋊C4—131no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C42—132no—
159#95—132no—
160#95—131no—
161#95—132no—
162#95—132no—
163#95—132no—
164#95C2×D1311yescharacteristic
165#95C2×D1312yes—
166C2×C13C2×#12311yescharacteristic
167C2×C13#53211yescharacteristic
168C2×C13#53711yescharacteristic
169C2×C13#55112yes—
170C2×C13#55212yes—
171D13—24no—
172D13—81no—
173C24—131no—
174C24—131no—
175C2×D4—262no—
176C2×D4—264no—
177C22×C4—131no—
178C22×C4—134no—
179C22×C4—132no—
180C22×C4—132no—
181C22×C4—131no—
182C22×C4—264no—
183C22×C4—264no—
184C22×C4—264no—
185C22×C4—522no—
186C22×C4C22×D1311yescharacteristic
187C22×C4C22×D1311yescharacteristic
188C22×C4C22×D1312yes—
189C22×C4C22×D1311yescharacteristic
190C22×C4C22×D1312yes—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—262no—
195C4⋊C4—262no—
196C4⋊C4—264no—
197C22⋊C4—262no—
198C22⋊C4—264no—
199C22⋊C4—262no—
200C22⋊C4—262no—
201C22⋊C4—264no—
202C22⋊C4—522no—
203C42—264no—
204C13#249811yescharacteristic, complemented, Sylow
205C23—132no—
206C23—134no—
207C23—261no—
208C23—262no—
209C23—261no—
210C23—261no—
211C23—261no—
212C23—262no—
213C23—262no—
214C23—261no—
215C23C23×D1311yescharacteristic
216D4—524no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—132no—
229C2×C4—268no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—528no—
240C2×C4D4×D1312yes—
241C2×C4#613114yes—
242C22—134no—
243C22—262no—
244C22—262no—
245C22—264no—
246C22—264no—
247C22—521no—
248C22—521no—
249C22—522no—
250C22—521no—
251C22—522no—
252C22C2×D4×D1311yescharacteristic
253C22#8825111yescharacteristic
254C22C2×#613112yes—
255C22#41×D1312yes—
256C22#8825711yescharacteristic
257C4—24no—
258C4—22no—
259C4—42no—
260C4—41no—
261C4—41no—
262C4—262no—
263C4—522no—
264C4—521no—
265C4—522no—
266C2—264no—
267C2—1041no—
268C2#1171931311yescharacteristic
269C2#1171934212yes—
270C2D13×#12311yescharacteristic
271C2#1171939912yes—
272C2#1171943011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC22×D52C22
hypercenter#398D13
hypocenterC13#2498
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#88146C2semidirect
3. C13×#398C2semidirect
4. #11718654C2semidirect
5. #11718651C2semidirect
6. #11718648C2semidirect
7. #11718647C2semidirect
8. #11718338C2semidirect
10. D13×#95C2semidirect
11. #11718315C2semidirect
110. #398D13semidirect
204. C13#2498semidirect

Maximal subgroups

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

subgroupindex
C2×#881482
C2×#881462
C13×#3982
#117186542
#117186512
#117186482
#117186472
#117183382
#117183262
D13×#952
#117183152
#249813