Finite Group Databasebeta

← #13120313

Subgroups — #13120313

Order 1664.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88193C211yesmaximal, characteristic
2C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
3C13×#386C211yesmaximal, characteristic, complemented
4#11718881C211yesmaximal, characteristic, complemented
5#11718874C211yesmaximal, characteristic, complemented
6#11718622C212yesmaximal, complemented
7#11718619C211yesmaximal, characteristic, complemented
8#11718612C212yesmaximal, complemented
9C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
10#11718331C212yesmaximal, complemented
11#11718321C212yesmaximal, complemented
12C22×D4×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C22×C22⋊D13C2211yescharacteristic
16C23×Dic13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2211yescharacteristic
22C2×C22⋊Dic13C2212yes—
23#88193—24no—
24C2×#6103C2211yescharacteristic
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×C4⋊Dic13—24no—
28C2×C4⋊Dic13C2212yes—
29C2×C4⋊Dic13C2212yes—
30C2×#6101C2211yescharacteristic
31C2×C4×Dic13C2212yes—
32C13×#95C2212yes—
33#88071C2212yes—
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C24×C13C2311yescharacteristic
39C23×D13C2311yescharacteristic
40C2×D4×C13—22no—
41C2×D4×C13—22no—
42C2×D4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—24no—
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2312yes—
47C22×C4×C13C2312yes—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—22no—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—42no—
53C22×Dic13—22no—
54C22×Dic13—42no—
55C22×Dic13—42no—
56C22×Dic13D414yes—
57C22×Dic13C2311yescharacteristic
58C22×Dic13C2312yes—
59C22×Dic13C2312yes—
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2311yescharacteristic
62C13×C22⋊C4—22no—
63C13×C22⋊C4—24no—
64C22⋊Dic13—22no—
65C22⋊Dic13—22no—
66C22⋊Dic13—42no—
67#6103—24no—
68#6103—22no—
69#6103—42no—
70C4⋊Dic13—24no—
71C4⋊Dic13—24no—
72#6101—22no—
73C4×Dic13—42no—
74#2591—131nomaximal, Sylow
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—21no—
78C23×C13—22no—
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—22no—
82C23×C13C2×D412yes—
83C23×C13#4112yes—
84C23×C13#4112yes—
85C23×C13C2411yescharacteristic
86C22×D13—21no—
87C22×D13—22no—
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—22no—
91D4×C13—44no—
92C2×C4×C13—28no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13#4114yes—
102C22⋊D13—44no—
103C22⋊D13—44no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—21no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—44no—
116C2×Dic13—44no—
117C2×Dic13C2×D412yes—
118C2×Dic13C2×D412yes—
119C2×#121—131no—
120C22×C4⋊C4—131no—
121#400—132no—
122#394—132no—
123#388—132no—
124#388—132no—
125#386—131no—
126#386—131no—
127#386—131no—
128#386D1311yescharacteristic, complemented
129C4×C22⋊C4—131no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—24no—
133C22×C13—24no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13#12414yes—
140C22×C13C22×D411yescharacteristic
141C22×C13C2×#4111yescharacteristic
142C22×C13C2×#4112yes—
143C22×C13C2×#4111yescharacteristic
144C22×C13H(5,𝔽2)12yes—
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—41no—
148C2×D13—42no—
149C2×D13—42no—
150C4×C13—24no—
151C4×C13—41no—
152C4×C13—42no—
153Dic13—22no—
154Dic13—22no—
155Dic13—41no—
156Dic13—42no—
157Dic13—42no—
158C22×D4—131no—
159C22×D4—131no—
160C22×D4C2×D1311yescharacteristic
161C23×C4—131no—
162C23×C4—131no—
163C23×C4C2×D1311yescharacteristic
164#121—264no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—264no—
169C2×C22⋊C4—131no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4C2×D1311yescharacteristic
176C2×C22⋊C4C2×D1312yes—
177C2×C42—132no—
178#95—132no—
179#95—132no—
180#95—132no—
181#95—132no—
182#95C2×D1312yes—
183C2×C13—24no—
184C2×C13—81no—
185C2×C13#52511yescharacteristic
186C2×C13C2×#12411yescharacteristic
187C2×C13#53411yescharacteristic
188C2×C13#55312yes—
189C2×C13#55312yes—
190D13—81no—
191C24—131no—
192C24C22×D1311yescharacteristic
193C24C22×D1311yescharacteristic
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—262no—
198C2×D4—262no—
199C2×D4—262no—
200C2×D4—262no—
201C2×D4—522no—
202C22×C4—22no—
203C22×C4—24no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—134no—
207C22×C4—131no—
208C22×C4—132no—
209C22×C4—132no—
210C22×C4—262no—
211C22×C4—522no—
212C22×C4—522no—
213C22×C4C22×D1311yescharacteristic
214C22×C4C22×D1312yes—
215C22×C4C22×D1312yes—
216C4⋊C4—264no—
217C4⋊C4—264no—
218C4⋊C4—262no—
219C22⋊C4—22no—
220C22⋊C4—24no—
221C22⋊C4—262no—
222C22⋊C4—262no—
223C22⋊C4—262no—
224C22⋊C4—264no—
225C22⋊C4—522no—
226C22⋊C4—522no—
227C42—522no—
228C13#259111yescharacteristic, complemented, Sylow
229C23—22no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—22no—
234C23—21no—
235C23—22no—
236C23—261no—
237C23—261no—
238C23—262no—
239C23—261no—
240C23—262no—
241C23#612712yes—
242C23D4×D1312yes—
243C23#612912yes—
244C23C23×D1311yescharacteristic
245D4—44no—
246D4—524no—
247D4—524no—
248C2×C4—28no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—132no—
258C2×C4—132no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—261no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—524no—
271C2×C4—524no—
272C2×C4#612914yes—
273C22—24no—
274C22—22no—
275C22—24no—
276C22—22no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—42no—
281C22—41no—
282C22—521no—
283C22—522no—
284C22—521no—
285C22—522no—
286C22—521no—
287C22#8813914yes—
288C22C2×#612711yescharacteristic
289C22C2×D4×D1311yescharacteristic
290C22C2×#612911yescharacteristic
291C22C2×#612912yes—
292C22#8825612yes—
293C4—24no—
294C4—41no—
295C4—42no—
296C4—262no—
297C4—262no—
298C4—521no—
299C4—522no—
300C4—522no—
301C2—24no—
302C2—81no—
303C2—1041no—
304C2C2×#8813911yescharacteristic
305C2#1171927012yes—
306C2#1171929111yescharacteristic
307C2#1171932312yes—
308C2#1171935811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#386C2
prime radicalC2×#88193C2
hypercenter#386D13
hypocenterC13#2591
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic13C2semidirect
3. C13×#386C2semidirect
4. #11718881C2semidirect
5. #11718874C2semidirect
6. #11718622C2semidirect
7. #11718619C2semidirect
8. #11718612C2semidirect
9. C22⋊C4×Dic13C2semidirect
10. #11718331C2semidirect
11. #11718321C2semidirect
128. #386D13semidirect
228. C13#2591semidirect

Maximal subgroups

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

subgroupindex
C2×#881932
C22×C4⋊Dic132
C13×#3862
#117188812
#117188742
#117186222
#117186192
#117186122
C22⋊C4×Dic132
#117183312
#117183212
#259113