Finite Group Databasebeta

← #13119784

Subgroups — #13119784

Order 1664.

676 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 171 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×#88150C212yesmaximal, complemented
2C2×#88142C211yesmaximal, characteristic, complemented
3C2×#88135C211yesmaximal, characteristic
4C2×#88132C212yesmaximal, complemented
5C13×#399C211yesmaximal, characteristic, complemented
6#11718653C211yesmaximal, characteristic, complemented
7#11718637C212yesmaximal, complemented
8#11718618C212yesmaximal
9#11718610C211yesmaximal, characteristic, complemented
10#11718338C211yesmaximal, characteristic, complemented
11#11718310C211yesmaximal, characteristic, complemented
12C22×C22⋊D13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2212yes—
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C22⋊C4C2212yes—
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C22⋊Dic13C2212yes—
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26C2×#6101C2212yes—
27C2×#6101C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30C2×#6101C2212yes—
31C2×C4×Dic13C2212yes—
32C2×C4×Dic13C2211yescharacteristic
33#88150—28no—
34#88142—24no—
35#88135—24no—
36#88132—28no—
37C13×#95C2211yescharacteristic
38#88071C2211yescharacteristic
39C24×C13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2312yes—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13Q814yescomplemented
48C22×Dic13—24no—
49C22×Dic13—22no—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—24no—
57C2×Dic26—24no—
58C2×Dic26—24no—
59C2×Dic26—24no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—24no—
62C13×C22⋊C4—24no—
63C13×C22⋊C4—22no—
64C22⋊Dic13—24no—
65#6103—22no—
66#6103—24no—
67#6103—24no—
68C4⋊Dic13—24no—
69C4⋊Dic13—22no—
70#6101—24no—
71#6101—22no—
72#6101—24no—
73#6101—24no—
74#6101D418yescomplemented
75C4×Dic13—24no—
76C4×Dic13D414yes—
77#2542—131nomaximal, Sylow
78C23×C13—22no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—22no—
82C23×C13C2×Q812yes—
83C23×C13C2411yescharacteristic
84C22×D13—22no—
85C22×D13—21no—
86C22×D13—21no—
87C22×D13—22no—
88C22×D13C2×Q812yes—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13C2×D412yes—
98C2×C4×C13C2×D414yes—
99C22⋊D13—28no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—22no—
107C2×Dic13—44no—
108C2×Dic13C2×D414yes—
109C2×Dic13C2×D412yes—
110C2×Dic13C2×D412yes—
111C2×Dic13C2×D414yes—
112C2×Dic13C2×Q812yes—
113C2×Dic13#4112yes—
114C4×D13—44no—
115Dic26—48no—
116C2×C4⋊Q8—131no—
117C2×C22⋊Q8—132no—
118C2×C22⋊Q8—132no—
119C2×C4×D4—131no—
120#399—131no—
121#399—131no—
122#399—131no—
123#399D1311yescharacteristic, complemented
124#390—132no—
125#384—132no—
126C4×C4⋊C4—131no—
127C22×C13—22no—
128C22×C13—24no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13—42no—
132C22×C13C22×D411yescharacteristic
133C22×C13C22×D412yes—
134C22×C13C22×Q811yescharacteristic
135C22×C13C2×#4111yescharacteristic
136C22×C132−1+412yes—
137C2×D13—22no—
138C2×D13—24no—
139C2×D13—41no—
140C2×D13—41no—
141C2×D13—42no—
142C4×C13—22no—
143C4×C13—24no—
144C4×C13—42no—
145C4×C13—41no—
146Dic13—24no—
147Dic13—42no—
148Dic13—41no—
149Dic13C22⋊Q814yescomplemented
150Dic13#12714yes—
151C22×Q8—132no—
152C22×D4—131no—
153C23×C4—131no—
154C23×C4—131no—
155C4⋊Q8—264no—
156C22⋊Q8—268no—
157C22⋊Q8—268no—
158C4×D4—264no—
159C2×C4⋊C4—132no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—132no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—132no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4C2×D1312yes—
167C2×C4⋊C4C2×D1311yescharacteristic
168C2×C22⋊C4—132no—
169C2×C22⋊C4—131no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4C2×D1311yescharacteristic
173C2×C22⋊C4C2×D1312yes—
174C2×C42—131no—
175C2×C42—132no—
176#95—131no—
177#95C2×D1311yescharacteristic
178C2×C13—42no—
179C2×C13C2×C22⋊Q811yescharacteristic
180C2×C13C2×#12711yescharacteristic
181C2×C13#53611yescharacteristic
182C2×C13#54712yes—
183C2×C13D4×Q812yes—
184D13—42no—
185C24—131no—
186C24C22×D1311yescharacteristic
187C2×Q8—264no—
188C2×Q8—264no—
189C2×Q8—264no—
190C2×D4—134no—
191C2×D4—262no—
192C2×D4—262no—
193C22×C4—131no—
194C22×C4—131no—
195C22×C4—132no—
196C22×C4—132no—
197C22×C4—131no—
198C22×C4—262no—
199C22×C4—264no—
200C22×C4—262no—
201C22×C4—264no—
202C22×C4C22×D1312yes—
203C22×C4C22×D1311yescharacteristic
204C22×C4C22×D1311yescharacteristic
205C22×C4C22×D1312yes—
206C4⋊C4—24no—
207C4⋊C4—22no—
208C4⋊C4—138no—
209C4⋊C4—262no—
210C4⋊C4—264no—
211C4⋊C4—264no—
212C4⋊C4—264no—
213C4⋊C4—264no—
214C4⋊C4—262no—
215C22⋊C4—22no—
216C22⋊C4—24no—
217C22⋊C4—264no—
218C22⋊C4—264no—
219C22⋊C4—262no—
220C22⋊C4—264no—
221C42—134no—
222C42—264no—
223C13#254211yescharacteristic, complemented, Sylow
224C23—22no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—132no—
229C23—262no—
230C23—261no—
231C23—261no—
232C23—262no—
233C23Q8×D1312yes—
234C23C23×D1311yescharacteristic
235Q8—528no—
236D4—268no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—134no—
248C2×C4—132no—
249C2×C4—132no—
250C2×C4—134no—
251C2×C4—262no—
252C2×C4—262no—
253C2×C4—261no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—524no—
259C2×C4—524no—
260C2×C4D4×D1312yes—
261C2×C4D4×D1314yes—
262C22—22no—
263C22—24no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—262no—
268C22—264no—
269C22—521no—
270C22—522no—
271C22—521no—
272C22C2×D4×D1311yescharacteristic
273C22C2×D4×D1312yes—
274C22C2×Q8×D1311yescharacteristic
275C22#41×D1311yescharacteristic
276C22#8825712yes—
277C4—22no—
278C4—24no—
279C4—41no—
280C4—42no—
281C4—134no—
282C4—134no—
283C4—264no—
284C4—521no—
285C4—522no—
286C2—42no—
287C2—522no—
288C2D13×C22⋊Q811yescharacteristic
289C2#1171933712yes—
290C2#1171935311yescharacteristic
291C2#1171936012yes—
292C2D13×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radicalC22×C22⋊D13C22
hypercenter#399D13
hypocenterC13#2542
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88150C2semidirect
2. C2×#88142C2semidirect
4. C2×#88132C2semidirect
5. C13×#399C2semidirect
6. #11718653C2semidirect
7. #11718637C2semidirect
9. #11718610C2semidirect
10. #11718338C2semidirect
11. #11718310C2semidirect
47. C2×C22⋊D13Q8semidirect
74. #6101D4semidirect
123. #399D13semidirect
149. Dic13C22⋊Q8semidirect
223. C13#2542semidirect

Maximal subgroups

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

subgroupindex
C2×#881502
C2×#881422
C2×#881352
C2×#881322
C13×#3992
#117186532
#117186372
#117186182
#117186102
#117183382
#117183102
#254213