Finite Group Databasebeta

← #13122862

Subgroups — #13122862

Order 1664.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88200C211yesmaximal, characteristic, complemented
2C2×#88138C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718622C212yesmaximal, complemented
6#11718620C212yesmaximal, complemented
7#11718610C211yesmaximal, characteristic, complemented
8#11718338C211yesmaximal, characteristic, complemented
9#11718333C212yesmaximal, complemented
10#11718325C211yesmaximal, characteristic, complemented
11#11718318C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C22×D52C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C22⋊Dic13C2212yes—
20#88200—24no—
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2212yes—
28C2×#6101C2211yescharacteristic
29C2×#6101C2212yes—
30C2×#6101C2212yes—
31#88138—24no—
32C13×#95C2212yes—
33C13×#95C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2211yescharacteristic
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C2×Q8×C13—22no—
41C2×Q8×C13—42no—
42C22×C4×C13C2312yes—
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—42no—
49C2×C22⋊D13—42no—
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C2×D52—22no—
55C2×D52—42no—
56C2×C4×D13—42no—
57C2×C4×D13D414yes—
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—
67C4⋊Dic13—42no—
68#6101—22no—
69#6101—24no—
70#6101—42no—
71#2816—131nomaximal, Sylow
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—21no—
76C23×C13—21no—
77C23×C13C2411yescharacteristic
78C22×D13—22no—
79C22×D13—22no—
80C22×D13—21no—
81C22×D13—21no—
82C22×D13—21no—
83C22×D13—22no—
84C22×D13—22no—
85C22×D13—21no—
86C22×D13—21no—
87C22×D13C2×D412yes—
88Q8×C13—44no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13C2×D412yes—
99C22⋊D13—44no—
100C22⋊D13—44no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13C2×D412yes—
111D52—44no—
112C4×D13—44no—
113C2×C22⋊Q8—131no—
114C2×#121—131no—
115#399—131no—
116#399—131no—
117#398—132no—
118#394—132no—
119#394—132no—
120#394—132no—
121#393—131no—
122#393D1311yescharacteristic, complemented
123#381—131no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—41no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C22×C13H(5,𝔽2)12yes—
131C22×C13H(5,𝔽2)12yes—
132C22×C132−1+411yescharacteristic
133C22×C132−1+411yescharacteristic
134C2×D13—22no—
135C2×D13—22no—
136C2×D13—22no—
137C2×D13—42no—
138C2×D13—42no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—41no—
142C2×D13—42no—
143C2×D13—42no—
144C4×C13—22no—
145C4×C13—42no—
146C4×C13—41no—
147C4×C13—42no—
148Dic13—22no—
149Dic13—42no—
150Dic13—41no—
151Dic13—42no—
152C22×Q8C2×D1311yescharacteristic
153C22×D4—131no—
154C22×D4—131no—
155C22×D4—131no—
156C23×C4—131no—
157C22⋊Q8—264no—
158#121—264no—
159C2×C4⋊C4—131no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—132no—
164C2×C22⋊C4—131no—
165C2×C22⋊C4—132no—
166C2×C22⋊C4—132no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4C2×D1311yescharacteristic
171C2×C22⋊C4C2×D1312yes—
172#95—131no—
173#95—132no—
174#95—132no—
175#95C2×D1311yescharacteristic
176#95C2×D1312yes—
177C2×C13—81no—
178C2×C13#53411yescharacteristic
179C2×C13#53511yescharacteristic
180C2×C13#53611yescharacteristic
181C2×C13#56212yes—
182C2×C13#56212yes—
183D13—42no—
184D13—81no—
185C24—131no—
186C24—131no—
187C24C22×D1311yescharacteristic
188C2×Q8—22no—
189C2×Q8—42no—
190C2×D4—262no—
191C2×D4—262no—
192C2×D4—262no—
193C2×D4—522no—
194C2×D4—522no—
195C2×D4—522no—
196C22×C4—131no—
197C22×C4—134no—
198C22×C4—132no—
199C22×C4—131no—
200C22×C4—132no—
201C22×C4—522no—
202C22×C4C22×D1312yes—
203C22×C4C22×D1312yes—
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1311yescharacteristic
206C4⋊C4—262no—
207C4⋊C4—264no—
208C4⋊C4—262no—
209C4⋊C4—522no—
210C4⋊C4—522no—
211C22⋊C4—22no—
212C22⋊C4—42no—
213C22⋊C4—264no—
214C22⋊C4—262no—
215C22⋊C4—522no—
216C22⋊C4—522no—
217C22⋊C4—522no—
218C22⋊C4—522no—
219C13#281611yescharacteristic, complemented, Sylow
220C23—21no—
221C23—22no—
222C23—21no—
223C23—22no—
224C23—21no—
225C23—132no—
226C23—262no—
227C23—261no—
228C23—262no—
229C23—261no—
230C23—261no—
231C23—262no—
232C23—261no—
233C23—262no—
234C23—261no—
235C23C23×D1311yescharacteristic
236Q8—44no—
237D4—524no—
238D4—524no—
239D4—524no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—132no—
250C2×C4—262no—
251C2×C4—262no—
252C2×C4—261no—
253C2×C4—262no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—524no—
260C2×C4D4×D1312yes—
261C22—41no—
262C22—41no—
263C22—42no—
264C22—41no—
265C22—42no—
266C22—262no—
267C22—262no—
268C22—262no—
269C22—522no—
270C22—522no—
271C22—521no—
272C22—521no—
273C22—522no—
274C22—521no—
275C22—522no—
276C22C2×D4×D1311yescharacteristic
277C22#8825112yes—
278C22#8825411yescharacteristic
279C22#8825612yes—
280C22#8825711yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—42no—
285C4—262no—
286C4—522no—
287C4—522no—
288C4—521no—
289C2—81no—
290C2—522no—
291C2—1041no—
292C2#1171929411yescharacteristic
293C2#1171933311yescharacteristic
294C2#1171935212yes—
295C2#1171937911yescharacteristic
296C2#1171938912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC2×#88138C2
hypercenter#393D13
hypocenterC13#2816
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
3. C13×#393C2semidirect
4. #11718892C2semidirect
5. #11718622C2semidirect
6. #11718620C2semidirect
7. #11718610C2semidirect
8. #11718338C2semidirect
9. #11718333C2semidirect
10. #11718325C2semidirect
11. #11718318C2semidirect
122. #393D13semidirect
219. C13#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×#881382
C13×#3932
#117188922
#117186222
#117186202
#117186102
#117183382
#117183332
#117183252
#117183182
#281613