Finite Group Databasebeta

← #13125481

Subgroups — #13125481

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#11719324C212yesmaximal, complemented
2C13×#469C211yesmaximal, characteristic, complemented
3#11718813C211yesmaximal, characteristic, complemented
4#11718812C211yesmaximal, characteristic, complemented
5#11718796C211yesmaximal, characteristic, complemented
6#11718783C211yesmaximal, characteristic, complemented
7#11718699C212yesmaximal, complemented
8#11718530C211yesmaximal, characteristic, complemented
9#11718519C211yesmaximal, characteristic, complemented
10#11718425C212yesmaximal, complemented
11#11718417C212yesmaximal, complemented
12C2×C13×D8C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C13×#121C2212yes—
15#88194C2212yes—
16#88193—22no—
17#88192—22no—
18D4×Dic13C2212yes—
19C2×#6104C2212yes—
20#88184C2212yes—
21#88180C2211yescharacteristic
22C22×#1055C2211yescharacteristic
23C2×D104C2211yescharacteristic
24#88147C2212yes—
25#88144C2212yes—
26#88140—22no—
27#88137—22no—
28C13×#106C2211yescharacteristic
29C13×#102C2212yes—
30#88072C2212yes—
31#88061C2212yes—
32#88057C2211yescharacteristic
33#88055C2211yescharacteristic
34#88055C2211yescharacteristic
35C8×Dic13C2211yescharacteristic
36C8×Dic13C2211yescharacteristic
37#88049C2212yes—
38#88047C2212yes—
39C2×D4×C13—22no—
40C2×D4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C2×C22⋊D13—22no—
43C2×C22⋊D13—22no—
44C2×C22⋊D13—22no—
45C22×Dic13—22no—
46C2×D52C2312yes—
47C2×C4×D13—22no—
48C13×D8—22no—
49C13×M16—22no—
50C2×C8×C13C2311yescharacteristic
51C2×C8×C13C2311yescharacteristic
52C13×C4⋊C4C2312yes—
53C13×C22⋊C4—22no—
54C22⋊Dic13—22no—
55C22⋊Dic13D412yes—
56#6104—24no—
57#6103—22no—
58#6103—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13D412yes—
61C4⋊Dic13C2312yes—
62#6101—22no—
63C4×Dic13C2311yescharacteristic
64C4×Dic13C2311yescharacteristic
65C2×#1055—22no—
66C2×#1055C2311yescharacteristic
67C2×#1055C2311yescharacteristic
68D104—22no—
69#3176—131nomaximal, Sylow
70C23×C13—22no—
71C23×C13C2×D411yescharacteristic
72C22×D13—22no—
73D4×C13—22no—
74D4×C13—22no—
75D4×C13—82no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—82no—
82C22⋊D13—82no—
83C22⋊D13—82no—
84C2×Dic13—22no—
85C2×Dic13—82no—
86C2×Dic13C2×D412yes—
87C2×Dic13C2×D412yes—
88D52—22no—
89D52—22no—
90C4×D13—82no—
91C8×C13—21no—
92C8×C13#4112yes—
93#1055—21no—
94#1055#4112yes—
95#540—132no—
96#499—131no—
97#493—131no—
98#490—132no—
99#469—131no—
100#469D1311yescharacteristic, complemented
101#466—132no—
102#442—131no—
103#442—131no—
104C4×D8—132no—
105#405—131no—
106C22×C13—21no—
107C22×C13—22no—
108C22×C13—42no—
109C22×C13—42no—
110C22×C13—42no—
111C22×C13C22×D411yescharacteristic
112C2×D13—42no—
113C2×D13—42no—
114C2×D13—42no—
115C4×C13—21no—
116C4×C13—42no—
117C4×C13C2×#4111yescharacteristic
118C4×C13C2×#4111yescharacteristic
119Dic13—22no—
120Dic13—22no—
121Dic13—42no—
122C2×D8—132no—
123C2×D8—131no—
124C2×D8C2×D1311yescharacteristic
125C2×M16C2×D1311yescharacteristic
126C22×C8—131no—
127#127—132no—
128#125—132no—
129#123—262no—
130#123—262no—
131#121—132no—
132#121—262no—
133#121—262no—
134#121C2×D1312yes—
135C4×D4—132no—
136C4×D4—132no—
137#117—131no—
138#107—132no—
139#106—131no—
140#106C2×D1311yescharacteristic
141#102—132no—
142#102—132no—
143#102—132no—
144#102C2×D1312yes—
145#97—131no—
146#97—131no—
147C4×C8—131no—
148C4×C8—131no—
149C2×C13—41no—
150C2×C13—82no—
151C2×C13#53211yescharacteristic
152C2×C13#57612yes—
153D13—82no—
154C2×D4—22no—
155C2×D4—132no—
156C2×D4—262no—
157C2×D4—262no—
158C2×D4—262no—
159C2×D4C22×D1312yes—
160C22×C4—262no—
161C22×C4—262no—
162C22×C4C22×D1311yescharacteristic
163D8—22no—
164D8—264no—
165D8—262no—
166M16—22no—
167C2×C8—131no—
168C2×C8—131no—
169C2×C8—262no—
170C2×C8C22×D1311yescharacteristic
171C2×C8C22×D1311yescharacteristic
172C4⋊C4—132no—
173C4⋊C4—132no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4C22×D1312yes—
177C22⋊C4—22no—
178C22⋊C4—132no—
179C22⋊C4—262no—
180C22⋊C4—262no—
181C22⋊C4—262no—
182C42—131no—
183C42—131no—
184C13#317611yescharacteristic, complemented, Sylow
185C23—22no—
186C23—262no—
187C23D4×D1311yescharacteristic
188D4—22no—
189D4—22no—
190D4—82no—
191D4—262no—
192D4—262no—
193D4—1042no—
194D4—1042no—
195D4—1042no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—132no—
200C2×C4—132no—
201C2×C4—262no—
202C2×C4—1042no—
203C2×C4—1042no—
204C2×C4D4×D1311yescharacteristic
205C2×C4C23×D1311yescharacteristic
206C8—21no—
207C8—132no—
208C8—261no—
209C8#612912yes—
210C22—22no—
211C22—21no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—522no—
216C22—522no—
217C22—522no—
218C22C2×D4×D1311yescharacteristic
219C4—21no—
220C4—42no—
221C4—262no—
222C4—262no—
223C4—522no—
224C4C2×#612911yescharacteristic
225C4#41×D1311yescharacteristic
226C2—41no—
227C2—82no—
228C2—1042no—
229C2#1171930111yescharacteristic
230C2#1171947912yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3176
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11719324C2semidirect
2. C13×#469C2semidirect
3. #11718813C2semidirect
4. #11718812C2semidirect
5. #11718796C2semidirect
6. #11718783C2semidirect
7. #11718699C2semidirect
8. #11718530C2semidirect
9. #11718519C2semidirect
10. #11718425C2semidirect
11. #11718417C2semidirect
100. #469D13semidirect
184. C13#3176semidirect

Maximal subgroups

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

subgroupindex
#117193242
C13×#4692
#117188132
#117188122
#117187962
#117187832
#117186992
#117185302
#117185192
#117184252
#117184172
#317613