Finite Group Databasebeta

← #13120191

Subgroups — #13120191

Order 1664.

564 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 147 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×#88141C211yesmaximal, characteristic, complemented
2C2×#88135C211yesmaximal, characteristic
3C13×#399C211yesmaximal, characteristic, complemented
4#11718653C211yesmaximal, characteristic, complemented
5#11718650C212yesmaximal, complemented
6#11718633C212yesmaximal, complemented
7#11718618C212yesmaximal
8#11718608C211yesmaximal, characteristic, complemented
9#11718607C212yesmaximal, complemented
10#11718334C211yesmaximal, characteristic, complemented
11#11718311C211yesmaximal, characteristic, complemented
12C22×C22⋊D13C2211yescharacteristic
13C23×Dic13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6101C2211yescharacteristic
25C2×#6101C2212yes—
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28C2×C4×Dic13C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88141—24no—
31#88135—24no—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45C2×C22⋊D13Q814yescomplemented
46C22×Dic13—22no—
47C22×Dic13—42no—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53C2×C4×D13—22no—
54C2×C4×D13—42no—
55C2×Dic26—22no—
56C2×Dic26—24no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—42no—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—42no—
61C22⋊Dic13—24no—
62#6103—22no—
63#6103—24no—
64#6103—42no—
65#6101—22no—
66#6101—24no—
67#6101—24no—
68#6101—42no—
69C4×Dic13—24no—
70C4×Dic13D414yes—
71#2580—131nomaximal, Sylow
72C23×C13—21no—
73C23×C13—22no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13C2×Q812yes—
77C23×C13C2411yescharacteristic
78C22×D13—21no—
79C22×D13—22no—
80C22×D13—21no—
81C22×D13—22no—
82C22×D13C2×Q812yes—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13C2×D412yes—
93C22⋊D13—28no—
94C2×Dic13—22no—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—44no—
103C2×Dic13C2×D412yes—
104C2×Dic13C2×D412yes—
105C2×Dic13C2×Q812yes—
106C2×Dic13#4114yes—
107C2×Dic13#4112yes—
108C4×D13—44no—
109Dic26—28no—
110C2×C4×Q8—131no—
111C2×C4×D4—131no—
112#399—131no—
113#399D1311yescharacteristic, complemented
114#393—131no—
115#393—131no—
116#390—132no—
117#389—132no—
118#385—132no—
119#385—132no—
120#382—131no—
121C22×C13—22no—
122C22×C13—24no—
123C22×C13—41no—
124C22×C13—41no—
125C22×C13—42no—
126C22×C13C22×D411yescharacteristic
127C22×C13C22×Q811yescharacteristic
128C22×C13C2×#4111yescharacteristic
129C22×C13C2×#4112yes—
130C22×C13H(5,𝔽2)12yes—
131C2×D13—22no—
132C2×D13—24no—
133C2×D13—41no—
134C2×D13—41no—
135C2×D13—42no—
136C4×C13—22no—
137C4×C13—41no—
138C4×C13—42no—
139C4×C13—42no—
140Dic13—24no—
141Dic13—22no—
142Dic13—41no—
143Dic13—42no—
144Dic13C22⋊Q814yes—
145C22×Q8—131no—
146C22×D4—131no—
147C23×C4—131no—
148C23×C4—131no—
149C4×Q8—264no—
150C4×D4—264no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4—132no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4C2×D1311yescharacteristic
156C2×C4⋊C4C2×D1312yes—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—131no—
159C2×C22⋊C4—132no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4C2×D1311yescharacteristic
162C2×C22⋊C4C2×D1312yes—
163C2×C42—131no—
164C2×C42—132no—
165#95—132no—
166#95—131no—
167#95—132no—
168#95—132no—
169#95C2×D1311yescharacteristic
170C2×C13—42no—
171C2×C13C2×C22⋊Q811yescharacteristic
172C2×C13#52511yescharacteristic
173C2×C13#53511yescharacteristic
174C2×C13#55412yes—
175C2×C13#55912yes—
176D13—42no—
177C24—131no—
178C24C22×D1311yescharacteristic
179C2×Q8—264no—
180C2×Q8—262no—
181C2×D4—134no—
182C2×D4—262no—
183C2×D4—262no—
184C22×C4—131no—
185C22×C4—132no—
186C22×C4—131no—
187C22×C4—132no—
188C22×C4—131no—
189C22×C4—262no—
190C22×C4—262no—
191C22×C4—522no—
192C22×C4—522no—
193C22×C4C22×D1312yes—
194C22×C4C22×D1311yescharacteristic
195C22×C4C22×D1312yes—
196C22×C4C22×D1311yescharacteristic
197C4⋊C4—22no—
198C4⋊C4—42no—
199C4⋊C4—262no—
200C4⋊C4—264no—
201C4⋊C4—264no—
202C4⋊C4—522no—
203C22⋊C4—22no—
204C22⋊C4—42no—
205C22⋊C4—264no—
206C22⋊C4—264no—
207C22⋊C4—262no—
208C22⋊C4—522no—
209C42—134no—
210C42—264no—
211C13#258011yescharacteristic, complemented, Sylow
212C23—21no—
213C23—22no—
214C23—22no—
215C23—21no—
216C23—132no—
217C23—261no—
218C23—262no—
219C23—262no—
220C23—261no—
221C23Q8×D1312yes—
222C23C23×D1311yescharacteristic
223Q8—268no—
224D4—268no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—132no—
235C2×C4—132no—
236C2×C4—132no—
237C2×C4—132no—
238C2×C4—134no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—261no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—524no—
248C2×C4—524no—
249C2×C4D4×D1312yes—
250C22—22no—
251C22—24no—
252C22—41no—
253C22—42no—
254C22—41no—
255C22—262no—
256C22—264no—
257C22—521no—
258C22—522no—
259C22—521no—
260C22C2×D4×D1311yescharacteristic
261C22#8825112yes—
262C22C2×Q8×D1311yescharacteristic
263C22#41×D1311yescharacteristic
264C22#41×D1312yes—
265C4—22no—
266C4—42no—
267C4—42no—
268C4—41no—
269C4—134no—
270C4—264no—
271C4—262no—
272C4—522no—
273C4—521no—
274C2—42no—
275C2—522no—
276C2D13×C22⋊Q811yescharacteristic
277C2#1171934112yes—
278C2#1171936111yescharacteristic
279C2#1171936912yes—
280C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#399C2
prime radicalC22×C22⋊D13C22
hypercenter#399D13
hypocenterC13#2580
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#88141C2semidirect
3. C13×#399C2semidirect
4. #11718653C2semidirect
5. #11718650C2semidirect
6. #11718633C2semidirect
8. #11718608C2semidirect
9. #11718607C2semidirect
10. #11718334C2semidirect
11. #11718311C2semidirect
45. C2×C22⋊D13Q8semidirect
113. #399D13semidirect
211. C13#2580semidirect

Maximal subgroups

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

subgroupindex
C2×#881412
C2×#881352
C13×#3992
#117186532
#117186502
#117186332
#117186182
#117186082
#117186072
#117183342
#117183112
#258013