Finite Group Databasebeta

← #13119996

Subgroups — #13119996

Order 1664.

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

normal subgroups only

This group has 532 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×D4×Dic13C211yesmaximal, characteristic
2C2×#88143C211yesmaximal, characteristic, complemented
3C13×#394C211yesmaximal, characteristic
4#11718883C211yesmaximal, characteristic
5#11718647C211yesmaximal, characteristic, complemented
6#11718612C212yesmaximal, complemented
7#11718605C212yesmaximal, complemented
8#11718603C212yesmaximal, complemented
9#11718603C212yesmaximal, complemented
10#11718320C211yesmaximal, characteristic, complemented
11#11718310C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×Dic13C2212yes—
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2212yes—
16C2×C13×C22⋊C4C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20D4×Dic13—24no—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2211yescharacteristic
24C2×#6101C2211yescharacteristic
25C2×#6101C2211yescharacteristic
26C2×#6101C2211yescharacteristic
27C2×#6101C2212yes—
28C2×C4×Dic13C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88143—24no—
31C13×#95C2211yescharacteristic
32#88071C2211yescharacteristic
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2312yes—
38C2×D4×C13—24no—
39C2×D4×C13—22no—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—24no—
47C22×Dic13C2312yes—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C13×C4⋊C4—22no—
54C13×C22⋊C4—24no—
55C13×C22⋊C4—42no—
56C22⋊Dic13—24no—
57C22⋊Dic13—24no—
58C22⋊Dic13—42no—
59C4⋊Dic13—22no—
60C4⋊Dic13—22no—
61#6101—22no—
62#6101—22no—
63#6101—22no—
64#6101—22no—
65#6101—24no—
66C4×Dic13—42no—
67C4×Dic13D414yes—
68#2562—131nomaximal, Sylow
69C23×C13—22no—
70C23×C13—22no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13#4114yes—
76C23×C13C2411yescharacteristic
77D4×C13—28no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13C2×D412yes—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—48no—
102C2×Dic13C2×D412yes—
103C2×Dic13C2×D412yes—
104C2×Dic13#4114yes—
105C2×#125—131no—
106C2×C4×D4—131no—
107#400—131no—
108#400—131no—
109#394—131no—
110#394D1311yescharacteristic
111#388—132no—
112#388—132no—
113#380—132no—
114#380—132no—
115C4×C4⋊C4—131no—
116C22×C13—24no—
117C22×C13—24no—
118C22×C13—24no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—42no—
122C22×C13—42no—
123C22×C13C22×D411yescharacteristic
124C22×C13C2×#4112yes—
125C22×C13C2×#4112yes—
126C22×C13H(5,𝔽2)11yescharacteristic
127C22×C132−1+411yescharacteristic
128C4×C13—22no—
129C4×C13—41no—
130C4×C13—41no—
131C4×C13—42no—
132Dic13—22no—
133Dic13—41no—
134Dic13—42no—
135Dic13—41no—
136Dic13—42no—
137Dic13#12414yes—
138C22×D4C2×D1311yescharacteristic
139C23×C4—132no—
140#125—264no—
141C4×D4—264no—
142C2×C4⋊C4—131no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—131no—
147C2×C4⋊C4—131no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C22⋊C4—132no—
151C2×C22⋊C4—132no—
152C2×C22⋊C4—132no—
153C2×C22⋊C4C2×D1312yes—
154C2×C22⋊C4C2×D1312yes—
155C2×C42—131no—
156C2×C42—132no—
157#95—131no—
158#95—132no—
159#95—132no—
160#95—132no—
161#95—132no—
162#95C2×D1311yescharacteristic
163C2×C13—44no—
164C2×C13#52511yescharacteristic
165C2×C13C2×#12411yescharacteristic
166C2×C13#53711yescharacteristic
167C2×C13#55212yes—
168C2×C13#55312yes—
169C24C22×D1312yes—
170C2×D4—24no—
171C2×D4—22no—
172C22×C4—131no—
173C22×C4—131no—
174C22×C4—132no—
175C22×C4—132no—
176C22×C4—131no—
177C22×C4—131no—
178C22×C4—264no—
179C22×C4—264no—
180C22×C4—264no—
181C22×C4C22×D1312yes—
182C22×C4C22×D1311yescharacteristic
183C22×C4C22×D1311yescharacteristic
184C22×C4C22×D1311yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—264no—
191C4⋊C4—262no—
192C4⋊C4—262no—
193C22⋊C4—24no—
194C22⋊C4—42no—
195C22⋊C4—264no—
196C22⋊C4—264no—
197C22⋊C4—522no—
198C42—134no—
199C42—522no—
200C13#256211yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#612914yes—
208C23C23×D1311yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—132no—
220C2×C4—134no—
221C2×C4—132no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—528no—
236C2×C4D4×D1312yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D1311yescharacteristic
245C22C2×#612912yes—
246C22#8825111yescharacteristic
247C22#41×D1312yes—
248C22#8825711yescharacteristic
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—134no—
254C4—262no—
255C4—521no—
256C4—522no—
257C4—521no—
258C4—522no—
259C2—44no—
260C2#1171929111yescharacteristic
261C2#1171930612yes—
262C2#1171931311yescharacteristic
263C2#1171935512yes—
264C2D13×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2562
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88143C2semidirect
5. #11718647C2semidirect
6. #11718612C2semidirect
7. #11718605C2semidirect
8. #11718603C2semidirect
9. #11718603C2semidirect
10. #11718320C2semidirect
11. #11718310C2semidirect
200. C13#2562semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881432
C13×#3942
#117188832
#117186472
#117186122
#117186052
#117186032
#117183202
#117183102
#256213