Finite Group Databasebeta

← #13125482

Subgroups — #13125482

Order 1664.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#11719267C212yesmaximal, complemented
2C4×C13×D8C211yesmaximal, characteristic, complemented
3#11718818C211yesmaximal, characteristic, complemented
4#11718812C211yesmaximal, characteristic, complemented
5#11718675C212yesmaximal, complemented
6#11718544C211yesmaximal, characteristic, complemented
7#11718539C211yesmaximal, characteristic, complemented
8#11718443C212yesmaximal, complemented
9#11718425C212yesmaximal, complemented
10C4×D104C211yesmaximal, characteristic, complemented
11#11718350C211yesmaximal, characteristic, complemented
12C2×C13×D8C2211yescharacteristic
13C4×D4×C13C2212yes—
14#88194C2212yes—
15#88192C2212yes—
16C2×#6104C2212yes—
17#88184—22no—
18#88183—22no—
19C2×D104C2211yescharacteristic
20C2×#6094C2211yescharacteristic
21C2×C8×D13C2211yescharacteristic
22#88149C2212yes—
23#88144C2212yes—
24#88138—22no—
25#88137—22no—
26C4×D52C2212yes—
27#88126C2211yescharacteristic
28C13×#107C2211yescharacteristic
29C13×#102C2212yes—
30C4×C8×C13C2211yescharacteristic
31#88072C2212yes—
32#88061C2212yes—
33#88058C2211yescharacteristic
34#88055C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36#88049C2212yes—
37#88048C2212yes—
38#88043C2211yescharacteristic
39C2×D4×C13C2312yes—
40C22×C4×C13—22no—
41C2×C22⋊D13—22no—
42C2×C22⋊D13—22no—
43C2×C22⋊D13—22no—
44C2×D52—22no—
45C2×D52C2312yes—
46C2×C4×D13—22no—
47C2×C4×D13C2311yescharacteristic
48C13×D8—22no—
49C2×C8×C13C2311yescharacteristic
50C2×C8×C13C2311yescharacteristic
51C13×C4⋊C4C2312yes—
52C13×C22⋊C4—22no—
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55#6104—24no—
56#6103—22no—
57#6103—22no—
58#6103D411yescharacteristic
59#6103D411yescharacteristic
60C4⋊Dic13—22no—
61C4⋊Dic13C2312yes—
62#6101—22no—
63#6101D411yescharacteristic
64#6101D411yescharacteristic
65C4×Dic13C2311yescharacteristic
66C2×#1055C2311yescharacteristic
67C2×#1055C2311yescharacteristic
68D104—22no—
69#6094—22no—
70C8×D13—22no—
71#3176—131nomaximal, Sylow
72C23×C13—22no—
73C22×D13—22no—
74C22×D13C2×D411yescharacteristic
75D4×C13—22no—
76D4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—82no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D411yescharacteristic
81C2×C4×C13C2411yescharacteristic
82C22⋊D13—82no—
83C22⋊D13—82no—
84C22⋊D13—82no—
85C2×Dic13—22no—
86C2×Dic13C2×D411yescharacteristic
87C2×Dic13C2×D411yescharacteristic
88C2×Dic13C2×D411yescharacteristic
89D52—22no—
90D52—22no—
91D52—82no—
92C4×D13—21no—
93C4×D13—21no—
94C4×D13—82no—
95C8×C13—21no—
96C8×C13#4112yes—
97#1055—21no—
98#1055#4112yes—
99#540—132no—
100#499—131no—
101#493—131no—
102#490—132no—
103#469—132no—
104#466—131no—
105#466—131no—
106#442—132no—
107C4×D8—131no—
108C4×D8D1311yescharacteristic, complemented
109#405—131no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13—42no—
113C22×C13C22×D411yescharacteristic
114C2×D13—21no—
115C2×D13—21no—
116C2×D13—21no—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C4×C13—21no—
121C4×C13—21no—
122C4×C13—42no—
123C4×C13C2×#4111yescharacteristic
124C4×C13C2×#4111yescharacteristic
125Dic13—21no—
126Dic13—21no—
127Dic13—21no—
128Dic13—42no—
129C2×D8—132no—
130C2×D8—131no—
131C2×D8C2×D1311yescharacteristic
132C2×M16—131no—
133C22×C8—131no—
134#127—132no—
135#125—132no—
136#123—262no—
137#123—262no—
138#121—132no—
139#121—132no—
140#121—262no—
141#121—262no—
142C4×D4—132no—
143C4×D4C2×D1312yes—
144#117—131no—
145#107—131no—
146#107C2×D1311yescharacteristic
147#106—132no—
148#102—132no—
149#102—132no—
150#102—132no—
151#102C2×D1312yes—
152#97—131no—
153#97—131no—
154C4×C8—131no—
155C4×C8C2×D1311yescharacteristic
156C2×C13—82no—
157C2×C13#53211yescharacteristic
158C2×C13#57611yescharacteristic
159C2×C13#57611yescharacteristic
160D13—41no—
161D13—82no—
162C2×D4—132no—
163C2×D4—262no—
164C2×D4—262no—
165C2×D4—262no—
166C2×D4—262no—
167C2×D4C22×D1312yes—
168C22×C4—22no—
169C22×C4—131no—
170C22×C4—262no—
171D8—22no—
172D8—264no—
173D8—262no—
174M16—262no—
175C2×C8—131no—
176C2×C8—131no—
177C2×C8—262no—
178C2×C8C22×D1311yescharacteristic
179C2×C8C22×D1311yescharacteristic
180C4⋊C4—131no—
181C4⋊C4—131no—
182C4⋊C4—132no—
183C4⋊C4—262no—
184C4⋊C4—262no—
185C4⋊C4C22×D1312yes—
186C22⋊C4—22no—
187C22⋊C4—131no—
188C22⋊C4—131no—
189C22⋊C4—262no—
190C22⋊C4—262no—
191C22⋊C4—262no—
192C42—131no—
193C42C22×D1311yescharacteristic
194C13#317611yescharacteristic, complemented, Sylow
195C23—22no—
196C23—131no—
197C23—262no—
198D4—22no—
199D4—22no—
200D4—262no—
201D4—262no—
202D4—1042no—
203D4—1042no—
204D4—1042no—
205D4—1042no—
206C2×C4—22no—
207C2×C4—82no—
208C2×C4—131no—
209C2×C4—131no—
210C2×C4—131no—
211C2×C4—261no—
212C2×C4—261no—
213C2×C4—262no—
214C2×C4—1042no—
215C2×C4D4×D1311yescharacteristic
216C2×C4D4×D1311yescharacteristic
217C2×C4C23×D1311yescharacteristic
218C8—21no—
219C8—132no—
220C8—261no—
221C8#612712yes—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—261no—
226C22—261no—
227C22—261no—
228C22—522no—
229C22—522no—
230C22—522no—
231C22C2×D4×D1311yescharacteristic
232C4—21no—
233C4—21no—
234C4—42no—
235C4—261no—
236C4—261no—
237C4—261no—
238C4—522no—
239C4C2×#612711yescharacteristic
240C4#41×D1311yescharacteristic
241C2—82no—
242C2—521no—
243C2—1042no—
244C2#1171925311yescharacteristic
245C2#1171946211yescharacteristic
246C2#1171947411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC4×C13×D8C2
socleC22×C13C22×D4
hypercenterC4×D8D13
hypocenterC13#3176
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11719267C2semidirect
2. C4×C13×D8C2semidirect
3. #11718818C2semidirect
4. #11718812C2semidirect
5. #11718675C2semidirect
6. #11718544C2semidirect
7. #11718539C2semidirect
8. #11718443C2semidirect
9. #11718425C2semidirect
10. C4×D104C2semidirect
11. #11718350C2semidirect
108. C4×D8D13semidirect
194. C13#3176semidirect

Maximal subgroups

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

subgroupindex
#117192672
C4×C13×D82
#117188182
#117188122
#117186752
#117185442
#117185392
#117184432
#117184252
C4×D1042
#117183502
#317613