Finite Group Databasebeta

← #13119139

Subgroups — #13119139

Order 1664.

624 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C2×#88147C211yesmaximal, characteristic
3C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
4C13×#398C211yesmaximal, characteristic, complemented
5#11718654C211yesmaximal, characteristic, complemented
6#11718644C211yesmaximal, characteristic, complemented
7#11718633C212yesmaximal, complemented
8#11718335C211yesmaximal, characteristic, complemented
9#11718328C212yesmaximal, complemented
10#11718328C211yesmaximal, characteristic, complemented
11#11718325C212yesmaximal, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13C2212yes—
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29#88148—28no—
30#88147—24no—
31C4⋊C4×D13—24no—
32C13×#95C2212yes—
33C13×#95C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37#88071C2211yescharacteristic
38C23×D13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2312yes—
48C22×Dic13C2311yescharacteristic
49C2×D52—22no—
50C2×D52—22no—
51C2×D52D414yes—
52C2×C4×D13—24no—
53C2×C4×D13—24no—
54C2×C4×D13—24no—
55C2×C4×D13—24no—
56C2×C4×D13—22no—
57C2×C4×D13—24no—
58C2×C4×D13D414yes—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—24no—
62#6103—22no—
63#6103—24no—
64#6103—24no—
65#6103—24no—
66#6103—22no—
67C4⋊Dic13—22no—
68#6101—24no—
69#6101—24no—
70#6101—24no—
71C4×Dic13—22no—
72#2486—131nomaximal, Sylow
73C23×C13C2411yescharacteristic
74C22×D13—22no—
75C22×D13—22no—
76C22×D13—21no—
77C22×D13—22no—
78C22×D13—21no—
79C22×D13—22no—
80C22×D13C2×D412yes—
81C22×D13C2×D412yes—
82C22×D13C2×D412yes—
83C22×D13#4112yes—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13C2×D412yes—
96C2×C4×C13C2×D412yes—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13C2×D412yes—
106C2×Dic13#4114yes—
107D52—28no—
108C4×D13—28no—
109C4×D13—48no—
110C4×D13—44no—
111C2×#123—132no—
112C2×C4×D4—131no—
113C22×C4⋊C4—131no—
114#398—131no—
115#398D1311yescharacteristic, complemented
116#397—131no—
117#397—131no—
118#389—132no—
119#381—132no—
120#380—132no—
121#380—131no—
122C22×C13C22×D411yescharacteristic
123C22×C13C22×D411yescharacteristic
124C22×C13C2×#4111yescharacteristic
125C22×C13C2×#4112yes—
126C22×C132−1+412yes—
127C2×D13—22no—
128C2×D13—22no—
129C2×D13—24no—
130C2×D13—24no—
131C2×D13—22no—
132C2×D13—24no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—42no—
136C2×D13#12114yes—
137C4×C13—22no—
138C4×C13—22no—
139C4×C13—42no—
140C4×C13—41no—
141C4×C13—42no—
142Dic13—42no—
143Dic13—41no—
144Dic13—42no—
145Dic13#12314yescomplemented
146C22×D4—131no—
147C23×C4—131no—
148C23×C4—132no—
149C23×C4—131no—
150#123—268no—
151C4×D4—264no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—264no—
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C4⋊C4C2×D1311yescharacteristic
159C2×C4⋊C4C2×D1312yes—
160C2×C22⋊C4—131no—
161C2×C22⋊C4—131no—
162C2×C22⋊C4—132no—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—132no—
165C2×C42—131no—
166#95—132no—
167#95—131no—
168#95—132no—
169#95—132no—
170#95C2×D1312yes—
171#95C2×D1311yescharacteristic
172C2×C13C2×#12111yescharacteristic
173C2×C13C2×#12311yescharacteristic
174C2×C13#53611yescharacteristic
175C2×C13#54712yes—
176C2×C13#55212yes—
177D13—24no—
178D13—42no—
179C24—131no—
180C24—131no—
181C2×D4—134no—
182C2×D4—262no—
183C2×D4—262no—
184C22×C4—131no—
185C22×C4—134no—
186C22×C4—131no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—264no—
190C22×C4—262no—
191C22×C4—264no—
192C22×C4—264no—
193C22×C4—264no—
194C22×C4—264no—
195C22×C4C22×D1311yescharacteristic
196C22×C4C22×D1312yes—
197C22×C4C22×D1312yes—
198C22×C4C22×D1311yescharacteristic
199C22×C4C22×D1311yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—24no—
203C4⋊C4—264no—
204C4⋊C4—264no—
205C4⋊C4—262no—
206C4⋊C4—264no—
207C22⋊C4—262no—
208C22⋊C4—264no—
209C22⋊C4—264no—
210C22⋊C4—264no—
211C22⋊C4—262no—
212C42—262no—
213C13#248611yescharacteristic, complemented, Sylow
214C23—132no—
215C23—132no—
216C23—132no—
217C23—132no—
218C23—262no—
219C23—262no—
220C23—261no—
221C23—262no—
222C23—262no—
223C23—261no—
224C23C23×D1311yescharacteristic
225D4—268no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—132no—
238C2×C4—134no—
239C2×C4—268no—
240C2×C4—261no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—262no—
248C2×C4—524no—
249C2×C4—528no—
250C2×C4D4×D1312yes—
251C2×C4D4×D1312yes—
252C22—134no—
253C22—262no—
254C22—264no—
255C22—262no—
256C22—264no—
257C22—262no—
258C22—264no—
259C22—521no—
260C22—521no—
261C22—522no—
262C22C2×D4×D1311yescharacteristic
263C22C2×D4×D1311yescharacteristic
264C22#8825412yes—
265C22#41×D1311yescharacteristic
266C22#41×D1312yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—41no—
272C4—134no—
273C4—521no—
274C4—522no—
275C4—522no—
276C2—264no—
277C2—522no—
278C2D13×#12111yescharacteristic
279C2#1171933612yes—
280C2D13×#12311yescharacteristic
281C2#1171939812yes—
282C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC22×D52C22
hypercenter#398D13
hypocenterC13#2486
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D13C2semidirect
4. C13×#398C2semidirect
5. #11718654C2semidirect
6. #11718644C2semidirect
7. #11718633C2semidirect
8. #11718335C2semidirect
9. #11718328C2semidirect
10. #11718328C2semidirect
11. #11718325C2semidirect
115. #398D13semidirect
145. Dic13#123semidirect
213. C13#2486semidirect

Maximal subgroups

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

subgroupindex
C2×#881482
C2×#881472
C2×C4⋊C4×D132
C13×#3982
#117186542
#117186442
#117186332
#117183352
#117183282
#117183252
#248613