Finite Group Databasebeta

← #13120964

Subgroups — #13120964

Order 1664.

598 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 137 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×#88184C211yesmaximal, characteristic, complemented
3#11718884C212yesmaximal, complemented
4C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
5#11718652C211yesmaximal, characteristic, complemented
6#11718651C212yesmaximal, complemented
7#11718644C211yesmaximal, characteristic, complemented
8#11718621C211yesmaximal, characteristic, complemented
9#11718620C212yesmaximal, complemented
10#11718618C212yesmaximal, complemented
11#11718614C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2212yes—
15C22×C22⋊D13C2212yes—
16C22×D52C2211yescharacteristic
17C13×#123—24no—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2211yescharacteristic
21C2×C13×C22⋊C4C2211yescharacteristic
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2212yes—
24C2×C22⋊Dic13C2212yes—
25#88184—24no—
26C2×#6103C2212yes—
27C2×#6103C2212yes—
28C2×#6103C2212yes—
29C2×#6103C2212yes—
30C2×C4⋊Dic13C2211yescharacteristic
31C2×#6101C2212yes—
32C2×C4×Dic13C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C24×C13C2311yescharacteristic
39C23×D13C2312yes—
40C2×D4×C13—22no—
41C2×D4×C13—42no—
42C22×C4×C13—42no—
43C22×C4×C13D414yescomplemented
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C22×C4×C13C2311yescharacteristic
49C2×C22⋊D13—24no—
50C2×C22⋊D13—24no—
51C2×C22⋊D13—42no—
52C2×C22⋊D13—42no—
53C2×C22⋊D13—42no—
54C2×C22⋊D13—42no—
55C22×Dic13C2312yes—
56C22×Dic13C2312yes—
57C22×Dic13C2312yes—
58C2×D52—22no—
59C2×D52—42no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C13×C22⋊C4—22no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4—22no—
65C22⋊Dic13—24no—
66C22⋊Dic13—42no—
67#6103—24no—
68#6103—24no—
69#6103—42no—
70#6103—42no—
71C4⋊Dic13—22no—
72#6101—42no—
73C4×Dic13—42no—
74#2661—131nomaximal, Sylow
75C23×C13—22no—
76C23×C13—21no—
77C23×C13—21no—
78C23×C13—22no—
79C23×C13—21no—
80C23×C13—22no—
81C23×C13—21no—
82C23×C13—21no—
83C23×C13—22no—
84C23×C13C2×D412yes—
85C23×C13C2411yescharacteristic
86C22×D13—22no—
87C22×D13—22no—
88C22×D13—22no—
89C22×D13—22no—
90C22×D13—22no—
91C22×D13—22no—
92C22×D13—22no—
93D4×C13—44no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—22no—
103C2×C4×C13—44no—
104C2×C4×C13C2×D412yes—
105C2×C4×C13C2×D412yes—
106C22⋊D13—48no—
107C22⋊D13—48no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13#4114yes—
117D52—44no—
118C2×#123D1311yescharacteristic, complemented
119C2×#121—131no—
120#398—131no—
121#397—131no—
122#394—131no—
123#394—132no—
124#392—132no—
125#392—131no—
126#390—132no—
127#388—132no—
128C4×C22⋊C4—131no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13C22×D411yescharacteristic
140C22×C13C2×#4112yes—
141C22×C13H(5,𝔽2)12yes—
142C22×C13H(5,𝔽2)11yescharacteristic
143C22×C13H(5,𝔽2)11yescharacteristic
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—42no—
150C2×D13—42no—
151C4×C13—22no—
152C4×C13—22no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156Dic13—24no—
157Dic13—42no—
158Dic13—42no—
159C22×D4—132no—
160C22×D4—132no—
161C22×D4—131no—
162C22×D4C2×D1311yescharacteristic
163C23×C4C2×D1311yescharacteristic
164#123—24no—
165#121—264no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4C2×D1311yescharacteristic
169C2×C4⋊C4C2×D1311yescharacteristic
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4C2×D1311yescharacteristic
177C2×C22⋊C4C2×D1311yescharacteristic
178C2×C22⋊C4C2×D1311yescharacteristic
179C2×C42—132no—
180#95—131no—
181#95—131no—
182#95—132no—
183#95—132no—
184C2×C13—42no—
185C2×C13—81no—
186C2×C13#53211yescharacteristic
187C2×C13#53411yescharacteristic
188C2×C13#53511yescharacteristic
189C2×C13#53812yes—
190C2×C13#54012yes—
191D13—82no—
192C24—132no—
193C24C22×D1311yescharacteristic
194C24C22×D1311yescharacteristic
195C2×D4—22no—
196C2×D4—42no—
197C2×D4—264no—
198C2×D4—264no—
199C2×D4—262no—
200C2×D4—522no—
201C2×D4—522no—
202C2×D4—522no—
203C2×D4—522no—
204C2×D4—522no—
205C22×C4—42no—
206C22×C4—132no—
207C22×C4—132no—
208C22×C4—132no—
209C22×C4C22⋊D1314yescomplemented
210C22×C4C22×D1311yescharacteristic
211C22×C4C22×D1311yescharacteristic
212C22×C4C22×D1311yescharacteristic
213C22×C4C22×D1311yescharacteristic
214C22×C4C22×D1311yescharacteristic
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—262no—
218C4⋊C4—522no—
219C22⋊C4—22no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—264no—
223C22⋊C4—264no—
224C22⋊C4—264no—
225C22⋊C4—522no—
226C22⋊C4—522no—
227C22⋊C4—522no—
228C42—522no—
229C13#266111yescharacteristic, complemented, Sylow
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—262no—
240C23—262no—
241C23—262no—
242C23—262no—
243C23—262no—
244C23—262no—
245C23—262no—
246C23C2×C22⋊D1312yes—
247C23C23×D1311yescharacteristic
248D4—44no—
249D4—524no—
250D4—528no—
251D4—528no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—44no—
262C2×C4—134no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4C2×C22⋊D1312yes—
272C2×C4C2×C22⋊D1312yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22—42no—
282C22—42no—
283C22—522no—
284C22—522no—
285C22—522no—
286C22—522no—
287C22—522no—
288C22—522no—
289C22—522no—
290C22#8825112yes—
291C22#41×D1312yes—
292C22#8825611yescharacteristic
293C22#8825611yescharacteristic
294C22C22×C22⋊D1311yescharacteristic
295C4—22no—
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—264no—
301C4—522no—
302C4—522no—
303C2—42no—
304C2—81no—
305C2—1042no—
306C2#1171936212yes—
307C2#1171936812yes—
308C2#1171950911yescharacteristic
309C2#1171953511yescharacteristic
310C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#123C2
hypercenterC2×#123D13
hypocenterC13#2661
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
2. C2×#88184C2semidirect
3. #11718884C2semidirect
4. C4×C22⋊Dic13C2semidirect
5. #11718652C2semidirect
6. #11718651C2semidirect
7. #11718644C2semidirect
8. #11718621C2semidirect
9. #11718620C2semidirect
10. #11718618C2semidirect
11. #11718614C2semidirect
43. C22×C4×C13D4semidirect
118. C2×#123D13semidirect
209. C22×C4C22⋊D13semidirect
229. C13#2661semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1232
C2×#881842
#117188842
C4×C22⋊Dic132
#117186522
#117186512
#117186442
#117186212
#117186202
#117186182
#117186142
#266113