Finite Group Databasebeta

← #13120629

Subgroups — #13120629

Order 1664.

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

normal subgroups only

This group has 548 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×#88146C211yesmaximal, characteristic, complemented
2C2×#88138C211yesmaximal, characteristic
3C13×#399C211yesmaximal, characteristic, complemented
4#11718653C211yesmaximal, characteristic, complemented
5#11718652C212yesmaximal, complemented
6#11718633C212yesmaximal, complemented
7#11718620C212yesmaximal, complemented
8#11718618C212yesmaximal, complemented
9#11718614C211yesmaximal, characteristic, complemented
10#11718335C211yesmaximal, characteristic, complemented
11#11718328C211yesmaximal, characteristic, complemented
12C22×C22⋊D13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×D52C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×C4×Dic13C2212yes—
31#88146—24no—
32#88138—24no—
33C13×#95C2211yescharacteristic
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—22no—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—24no—
47C2×C22⋊D13—42no—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C2×D52—22no—
53C2×D52—42no—
54C2×C4×D13—24no—
55C2×C4×D13D414yes—
56C13×C4⋊C4—22no—
57C13×C4⋊C4—42no—
58C13×C22⋊C4—22no—
59C13×C22⋊C4—42no—
60C22⋊Dic13—42no—
61#6103—24no—
62#6103—22no—
63#6103—42no—
64#6103—42no—
65#6103—42no—
66C4⋊Dic13—22no—
67#6101—22no—
68#6101—24no—
69#6101—42no—
70C4×Dic13—24no—
71#2624—131nomaximal, Sylow
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13—21no—
77C23×C13C2411yescharacteristic
78C22×D13—22no—
79C22×D13—21no—
80C22×D13—22no—
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—22no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—21no—
87C22×D13C2×D412yes—
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×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13C2×D412yes—
98C22⋊D13—44no—
99C22⋊D13—44no—
100C2×Dic13—22no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13C2×D412yes—
109C2×Dic13#4114yes—
110D52—44no—
111C4×D13—28no—
112C2×#121—131no—
113C2×#117—131no—
114#399—131no—
115#399D1311yescharacteristic, complemented
116#397—131no—
117#397—131no—
118#394—132no—
119#394—132no—
120#390—132no—
121#389—132no—
122#380—131no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13C22×D411yescharacteristic
129C22×C13C2×#4112yes—
130C22×C13H(5,𝔽2)12yes—
131C22×C13H(5,𝔽2)11yescharacteristic
132C22×C132−1+411yescharacteristic
133C2×D13—22no—
134C2×D13—22no—
135C2×D13—22no—
136C2×D13—42no—
137C2×D13—42no—
138C2×D13—41no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—42no—
142C2×D13—42no—
143C4×C13—22no—
144C4×C13—41no—
145C4×C13—42no—
146C4×C13—42no—
147Dic13—41no—
148Dic13—42no—
149Dic13—42no—
150Dic13#12314yes—
151C22×D4—131no—
152C22×D4—131no—
153C22×D4—131no—
154C23×C4—131no—
155#121—264no—
156#117—264no—
157C2×C4⋊C4—131no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4C2×D1311yescharacteristic
162C2×C4⋊C4C2×D1312yes—
163C2×C22⋊C4—132no—
164C2×C22⋊C4—131no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4C2×D1311yescharacteristic
170C2×C22⋊C4C2×D1312yes—
171C2×C42—132no—
172#95—131no—
173#95—132no—
174#95—132no—
175#95C2×D1311yescharacteristic
176C2×C13—81no—
177C2×C13C2×#12311yescharacteristic
178C2×C13#53511yescharacteristic
179C2×C13#53711yescharacteristic
180C2×C13#54012yes—
181C2×C13#54212yes—
182D13—42no—
183D13—81no—
184C24—131no—
185C24—131no—
186C24C22×D1311yescharacteristic
187C2×D4—262no—
188C2×D4—262no—
189C2×D4—264no—
190C2×D4—262no—
191C2×D4—522no—
192C2×D4—522no—
193C22×C4—131no—
194C22×C4—134no—
195C22×C4—132no—
196C22×C4—132no—
197C22×C4—131no—
198C22×C4—264no—
199C22×C4C22×D1311yescharacteristic
200C22×C4C22×D1312yes—
201C22×C4C22×D1312yes—
202C22×C4C22×D1311yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—262no—
206C4⋊C4—264no—
207C4⋊C4—262no—
208C4⋊C4—522no—
209C22⋊C4—22no—
210C22⋊C4—42no—
211C22⋊C4—264no—
212C22⋊C4—262no—
213C22⋊C4—522no—
214C22⋊C4—522no—
215C22⋊C4—522no—
216C22⋊C4—522no—
217C42—264no—
218C13#262411yescharacteristic, complemented, Sylow
219C23—21no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—132no—
225C23—262no—
226C23—261no—
227C23—262no—
228C23—261no—
229C23—261no—
230C23—262no—
231C23—261no—
232C23—262no—
233C23—261no—
234C23C23×D1311yescharacteristic
235D4—524no—
236D4—524no—
237D4—524no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—132no—
248C2×C4—134no—
249C2×C4—268no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4D4×D1312yes—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—42no—
263C22—41no—
264C22—262no—
265C22—262no—
266C22—262no—
267C22—522no—
268C22—522no—
269C22—521no—
270C22—522no—
271C22—521no—
272C22—522no—
273C22—521no—
274C22C2×D4×D1311yescharacteristic
275C22#8825112yes—
276C22#8825411yescharacteristic
277C22#41×D1312yes—
278C22#8825611yescharacteristic
279C4—22no—
280C4—42no—
281C4—42no—
282C4—41no—
283C4—134no—
284C4—522no—
285C4—522no—
286C4—521no—
287C2—81no—
288C2—522no—
289C2—1041no—
290C2#1171933411yescharacteristic
291C2#1171934512yes—
292C2D13×#12311yescharacteristic
293C2#1171936812yes—
294C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radicalC2×#88138C2
hypercenter#399D13
hypocenterC13#2624
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88146C2semidirect
3. C13×#399C2semidirect
4. #11718653C2semidirect
5. #11718652C2semidirect
6. #11718633C2semidirect
7. #11718620C2semidirect
8. #11718618C2semidirect
9. #11718614C2semidirect
10. #11718335C2semidirect
11. #11718328C2semidirect
115. #399D13semidirect
218. C13#2624semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×#881382
C13×#3992
#117186532
#117186522
#117186332
#117186202
#117186182
#117186142
#117183352
#117183282
#262413