Finite Group Databasebeta

← #13120986

Subgroups — #13120986

Order 1664.

498 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 137 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×C13×#123C211yesmaximal, characteristic
2C2×#88178C211yesmaximal, characteristic, complemented
3#11718883C212yesmaximal
4C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
5#11718647C211yesmaximal, characteristic, complemented
6#11718640C211yesmaximal, characteristic, complemented
7#11718633C212yesmaximal, complemented
8#11718613C212yesmaximal, complemented
9#11718610C211yesmaximal, characteristic, complemented
10#11718608C211yesmaximal, characteristic, complemented
11#11718606C212yesmaximal, complemented
12C22×D4×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C13×#123—24no—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2212yes—
23C2×C22⋊Dic13C2212yes—
24C2×C22⋊Dic13C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26#88178—24no—
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×C4×Dic13C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2211yescharacteristic
35#88071C2211yescharacteristic
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C24×C13C2311yescharacteristic
39C2×D4×C13—22no—
40C2×D4×C13—42no—
41C22×C4×C13—42no—
42C22×C4×C13D414yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C22×Dic13C2312yes—
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C22×Dic13C2312yes—
52C2×Dic26—22no—
53C2×Dic26—42no—
54C13×C4⋊C4—22no—
55C13×C4⋊C4—22no—
56C13×C22⋊C4—22no—
57C13×C22⋊C4—22no—
58C13×C22⋊C4—22no—
59C22⋊Dic13—24no—
60C22⋊Dic13—24no—
61C22⋊Dic13—24no—
62C22⋊Dic13—42no—
63C4⋊Dic13—22no—
64#6101—24no—
65#6101—24no—
66#6101—42no—
67C4×Dic13—42no—
68#2663—131nomaximal, Sylow
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13C2×D412yes—
79C23×C13C2411yescharacteristic
80D4×C13—44no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
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—44no—
91C2×C4×C13C2×D412yes—
92C2×C4×C13C2×D412yes—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13#4114yes—
105Dic26—44no—
106C2×#123D1311yescharacteristic
107C2×C22⋊Q8—131no—
108#400—131no—
109#399—131no—
110#397—132no—
111#395—131no—
112#394—132no—
113#393—131no—
114#389—132no—
115#388—132no—
116C4×C22⋊C4—131no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13C22×D411yescharacteristic
128C22×C13C2×#4112yes—
129C22×C13H(5,𝔽2)12yes—
130C22×C132−1+411yescharacteristic
131C22×C132−1+411yescharacteristic
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—41no—
135C4×C13—41no—
136C4×C13—41no—
137Dic13—24no—
138Dic13—42no—
139Dic13—42no—
140Dic13—42no—
141C22×Q8—131no—
142C22×D4C2×D1311yescharacteristic
143C23×C4C2×D1311yescharacteristic
144#123—24no—
145C22⋊Q8—264no—
146C2×C4⋊C4—132no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—132no—
150C2×C4⋊C4C2×D1311yescharacteristic
151C2×C4⋊C4C2×D1311yescharacteristic
152C2×C22⋊C4—132no—
153C2×C22⋊C4—132no—
154C2×C22⋊C4—132no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4C2×D1311yescharacteristic
157C2×C22⋊C4C2×D1311yescharacteristic
158C2×C22⋊C4C2×D1311yescharacteristic
159C2×C42—132no—
160#95—131no—
161#95—131no—
162#95—132no—
163#95—132no—
164#95—132no—
165#95—132no—
166C2×C13—42no—
167C2×C13—81no—
168C2×C13#53211yescharacteristic
169C2×C13#53411yescharacteristic
170C2×C13#53611yescharacteristic
171C2×C13#53912yes—
172C2×C13#54212yes—
173C24C22×D1311yescharacteristic
174C24C22×D1311yescharacteristic
175C2×Q8—262no—
176C2×Q8—522no—
177C2×D4—22no—
178C2×D4—42no—
179C22×C4—42no—
180C22×C4—132no—
181C22×C4—132no—
182C22×C4—132no—
183C22×C4—132no—
184C22×C4C22⋊D1314yes—
185C22×C4C22×D1311yescharacteristic
186C22×C4C22×D1311yescharacteristic
187C22×C4C22×D1311yescharacteristic
188C22×C4C22×D1311yescharacteristic
189C22×C4C22×D1311yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—264no—
193C4⋊C4—264no—
194C4⋊C4—262no—
195C4⋊C4—522no—
196C22⋊C4—22no—
197C22⋊C4—22no—
198C22⋊C4—22no—
199C22⋊C4—264no—
200C22⋊C4—264no—
201C22⋊C4—264no—
202C22⋊C4—522no—
203C42—522no—
204C13#266311yescharacteristic, complemented, Sylow
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23C2×C22⋊D1312yes—
215C23C23×D1311yescharacteristic
216Q8—524no—
217D4—44no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—44no—
228C2×C4—134no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4C2×C22⋊D1312yes—
241C2×C4C2×C22⋊D1312yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—42no—
252C22#8825112yes—
253C22#41×D1312yes—
254C22#8825711yescharacteristic
255C22#8825711yescharacteristic
256C22C22×C22⋊D1311yescharacteristic
257C4—22no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—264no—
263C4—522no—
264C4—522no—
265C4—522no—
266C2—42no—
267C2—81no—
268C2#1171936512yes—
269C2#1171936712yes—
270C2#1171950911yescharacteristic
271C2#1171953011yescharacteristic
272C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#123C2
prime radicalC22×D4×C13C22
hypercenterC2×#123D13
hypocenterC13#2663
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#88178C2semidirect
4. C4×C22⋊Dic13C2semidirect
5. #11718647C2semidirect
6. #11718640C2semidirect
7. #11718633C2semidirect
8. #11718613C2semidirect
9. #11718610C2semidirect
10. #11718608C2semidirect
11. #11718606C2semidirect
204. C13#2663semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1232
C2×#881782
#117188832
C4×C22⋊Dic132
#117186472
#117186402
#117186332
#117186132
#117186102
#117186082
#117186062
#266313