Finite Group Databasebeta

← #13120582

Subgroups — #13120582

Order 1664.

632 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 157 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×C13×#123C211yesmaximal, characteristic, complemented
2C2×#88193C211yesmaximal, characteristic
3C2×#88183C211yesmaximal, characteristic, complemented
4C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
5#11718881C211yesmaximal, characteristic, complemented
6#11718655C212yesmaximal, complemented
7#11718645C212yesmaximal, complemented
8#11718622C212yesmaximal, complemented
9#11718619C211yesmaximal, characteristic, complemented
10#11718609C212yesmaximal, complemented
11#11718603C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C22×C22⋊D13C2211yescharacteristic
16C23×Dic13C2211yescharacteristic
17C23×Dic13C2211yescharacteristic
18C13×#123—24no—
19C2×C13×C4⋊C4C2212yes—
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2212yes—
22C2×C22⋊Dic13C2211yescharacteristic
23C2×C22⋊Dic13C2211yescharacteristic
24C2×C22⋊Dic13C2212yes—
25#88193—24no—
26#88183—24no—
27C2×#6103C2212yes—
28C2×#6103C2211yescharacteristic
29C2×#6103C2212yes—
30C2×C4⋊Dic13—24no—
31C2×C4⋊Dic13C2212yes—
32C2×C4⋊Dic13C2212yes—
33C2×#6101C2212yes—
34C2×#6101C2211yescharacteristic
35C2×#6101C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2212yes—
39C24×C13C2311yescharacteristic
40C24×C13C2311yescharacteristic
41C23×D13C2311yescharacteristic
42C2×D4×C13—22no—
43C2×D4×C13—22no—
44C2×D4×C13—22no—
45C22×C4×C13—22no—
46C22×C4×C13—22no—
47C22×C4×C13D414yescomplemented
48C22×C4×C13C2312yes—
49C22×C4×C13C2311yescharacteristic
50C22×C4×C13C2312yes—
51C2×C22⋊D13—22no—
52C2×C22⋊D13—22no—
53C2×C22⋊D13—22no—
54C2×C22⋊D13—22no—
55C2×C22⋊D13—42no—
56C22×Dic13—22no—
57C22×Dic13—42no—
58C22×Dic13—42no—
59C22×Dic13D414yes—
60C22×Dic13C2311yescharacteristic
61C22×Dic13C2312yes—
62C22×Dic13C2312yes—
63C22×Dic13C2311yescharacteristic
64C22×Dic13C2311yescharacteristic
65C13×C4⋊C4—24no—
66C13×C22⋊C4—22no—
67C13×C22⋊C4—24no—
68C22⋊Dic13—22no—
69C22⋊Dic13—22no—
70C22⋊Dic13—42no—
71#6103—24no—
72#6103—22no—
73#6103—42no—
74C4⋊Dic13—24no—
75C4⋊Dic13—24no—
76#6101—24no—
77#6101—22no—
78#6101—42no—
79#2618—131nomaximal, Sylow
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13C2×D412yes—
88C23×C13C2×D412yes—
89C23×C13#4112yes—
90C23×C13C2411yescharacteristic
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—22no—
95C22×D13—22no—
96D4×C13—44no—
97C2×C4×C13—28no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13C2×D414yes—
107C22⋊D13—44no—
108C22⋊D13—44no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—21no—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—22no—
115C2×Dic13—21no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—22no—
120C2×Dic13—44no—
121C2×Dic13—44no—
122C2×Dic13C2×D412yes—
123C2×Dic13C2×D412yes—
124C2×#123—131no—
125C2×#123D1311yescharacteristic, complemented
126C2×#121—131no—
127C22×C4⋊C4—131no—
128#398—132no—
129#396—132no—
130#396—132no—
131#394—132no—
132#386—131no—
133#386—131no—
134#380—131no—
135C22×C13—22no—
136C22×C13—22no—
137C22×C13—24no—
138C22×C13—24no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—41no—
142C22×C13—42no—
143C22×C13—42no—
144C22×C13#12114yes—
145C22×C13C22×D411yescharacteristic
146C22×C13C22×D411yescharacteristic
147C22×C13C2×#4111yescharacteristic
148C22×C13H(5,𝔽2)12yes—
149C22×C132−1+412yes—
150C2×D13—41no—
151C2×D13—41no—
152C2×D13—41no—
153C2×D13—42no—
154C2×D13—42no—
155C4×C13—24no—
156C4×C13—41no—
157C4×C13—42no—
158Dic13—22no—
159Dic13—22no—
160Dic13—41no—
161Dic13—42no—
162Dic13—42no—
163C22×D4—131no—
164C22×D4—131no—
165C22×D4C2×D1311yescharacteristic
166C23×C4—131no—
167C23×C4—131no—
168C23×C4C2×D1311yescharacteristic
169#123—24no—
170#123—264no—
171#121—264no—
172C2×C4⋊C4—132no—
173C2×C4⋊C4—132no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—132no—
176C2×C4⋊C4—132no—
177C2×C4⋊C4—264no—
178C2×C4⋊C4C2×D1312yes—
179C2×C22⋊C4—131no—
180C2×C22⋊C4—131no—
181C2×C22⋊C4—131no—
182C2×C22⋊C4—132no—
183C2×C22⋊C4—132no—
184C2×C22⋊C4—132no—
185C2×C22⋊C4C2×D1311yescharacteristic
186C2×C22⋊C4C2×D1312yes—
187#95—132no—
188#95—132no—
189#95—132no—
190C2×C13—24no—
191C2×C13—81no—
192C2×C13C2×#12111yescharacteristic
193C2×C13#53411yescharacteristic
194C2×C13#53611yescharacteristic
195C2×C13#53712yes—
196C2×C13#53912yes—
197D13—81no—
198C24—131no—
199C24C22×D1311yescharacteristic
200C24C22×D1311yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—262no—
205C2×D4—262no—
206C2×D4—262no—
207C2×D4—262no—
208C2×D4—522no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—134no—
214C22×C4—132no—
215C22×C4—132no—
216C22×C4—131no—
217C22×C4—262no—
218C22×C4—522no—
219C22×C4—522no—
220C22×C4C22⋊D1314yescomplemented
221C22×C4C22×D1312yes—
222C22×C4C22×D1311yescharacteristic
223C22×C4C22×D1312yes—
224C4⋊C4—24no—
225C4⋊C4—264no—
226C4⋊C4—264no—
227C4⋊C4—262no—
228C4⋊C4—264no—
229C4⋊C4—522no—
230C22⋊C4—22no—
231C22⋊C4—24no—
232C22⋊C4—262no—
233C22⋊C4—262no—
234C22⋊C4—262no—
235C22⋊C4—264no—
236C22⋊C4—522no—
237C22⋊C4—522no—
238C13#261811yescharacteristic, complemented, Sylow
239C23—22no—
240C23—22no—
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23—21no—
246C23—261no—
247C23—261no—
248C23—262no—
249C23—262no—
250C23—261no—
251C23D4×D1312yes—
252C23#612912yes—
253C23C2×C22⋊D1312yes—
254C23C23×D1311yescharacteristic
255D4—44no—
256D4—524no—
257D4—524no—
258C2×C4—28no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4—261no—
272C2×C4—262no—
273C2×C4—261no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—262no—
279C2×C4—261no—
280C2×C4—524no—
281C2×C4—524no—
282C2×C4C2×C22⋊D1314yes—
283C22—24no—
284C22—22no—
285C22—22no—
286C22—24no—
287C22—41no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—42no—
292C22—521no—
293C22—522no—
294C22—521no—
295C22—521no—
296C22—522no—
297C22#8819314yes—
298C22C2×D4×D1311yescharacteristic
299C22C2×#612911yescharacteristic
300C22#8825612yes—
301C22#8825712yes—
302C22C22×C22⋊D1311yescharacteristic
303C4—24no—
304C4—41no—
305C4—42no—
306C4—262no—
307C4—262no—
308C4—521no—
309C4—522no—
310C4—522no—
311C2—24no—
312C2—81no—
313C2—1041no—
314C2#1171935311yescharacteristic
315C2#1171935811yescharacteristic
316C2#1171937012yes—
317C2C2×#8819311yescharacteristic
318C2#1171953812yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#123C2
prime radicalC2×#88193C2
hypercenterC2×#123D13
hypocenterC13#2618
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C13×#123C2semidirect
3. C2×#88183C2semidirect
4. C22×C4⋊Dic13C2semidirect
5. #11718881C2semidirect
6. #11718655C2semidirect
7. #11718645C2semidirect
8. #11718622C2semidirect
9. #11718619C2semidirect
10. #11718609C2semidirect
11. #11718603C2semidirect
47. C22×C4×C13D4semidirect
125. C2×#123D13semidirect
220. C22×C4C22⋊D13semidirect
238. C13#2618semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1232
C2×#881932
C2×#881832
C22×C4⋊Dic132
#117188812
#117186552
#117186452
#117186222
#117186192
#117186092
#117186032
#261813