Finite Group Databasebeta

← #13115920

Subgroups — #13115920

Order 1664.

406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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×#88198C211yesmaximal, characteristic, complemented
2C22×#6106C211yesmaximal, characteristic
3C22×#6095C211yesmaximal, characteristic
4C2×C13×#103C211yesmaximal, characteristic, complemented
5#11718649C211yesmaximal, characteristic
6C2×#88050C211yesmaximal, characteristic, complemented
7#11718142C211yesmaximal, characteristic, complemented
8C22×Q8×C13C2211yescharacteristic
9C22×D52C2211yescharacteristic
10C22×Dic26C2211yescharacteristic
11C22×C8×C13C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13#88198—22no—
14#88198—22no—
15C2×#6106—22no—
16C2×#6106—22no—
17C2×#6106—22no—
18C2×#6103—22no—
19C2×#6101—22no—
20C2×C4×Dic13C2211yescharacteristic
21C22×#1055C2211yescharacteristic
22C2×#6095—22no—
23C2×#6095—22no—
24C2×#6095—22no—
25C13×#103—22no—
26#88050—22no—
27C23×D13—21no—
28C2×Q8×C13—21no—
29C2×Q8×C13—21no—
30C2×Q8×C13—21no—
31C2×Q8×C13—21no—
32C2×Q8×C13—21no—
33C2×Q8×C13D412yes—
34C22×C4×C13—21no—
35C22×C4×C13—21no—
36C22×C4×C13C2311yescharacteristic
37C22×Dic13—21no—
38C22×Dic13D412yes—
39C2×D52—21no—
40C2×D52—21no—
41C2×D52—21no—
42C2×D52—21no—
43C2×D52—21no—
44C2×D52D412yes—
45C2×Dic26—21no—
46C2×Dic26—21no—
47C2×Dic26—21no—
48C2×Dic26—21no—
49C2×Dic26—21no—
50C2×Dic26D412yes—
51C2×C8×C13—21no—
52C2×C8×C13—21no—
53C2×C8×C13D412yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56#6106—28no—
57#6103—44no—
58#6101—28no—
59C4×Dic13—21no—
60C4×Dic13—21no—
61C2×#1055—21no—
62C2×#1055—21no—
63C2×#1055D412yes—
64#6095—28no—
65#2013—131nomaximal, Sylow
66C23×C13C2×D411yescharacteristic
67C22×D13—22no—
68C22×D13—41no—
69C22×D13—41no—
70C22×D13—42no—
71C22×D13—42no—
72Q8×C13—22no—
73Q8×C13—22no—
74Q8×C13—41no—
75Q8×C13—41no—
76C2×C4×C13—22no—
77C2×C4×C13—41no—
78C2×C4×C13—41no—
79C2×C4×C13—41no—
80C2×C4×C13—42no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×D411yescharacteristic
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×D411yescharacteristic
86C2×C4×C13#4111yescharacteristic
87C2×Dic13—22no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—41no—
91C2×Dic13—41no—
92C2×Dic13SD1614yescomplemented
93D52—22no—
94D52—22no—
95D52—41no—
96D52—41no—
97Dic26—22no—
98Dic26—22no—
99Dic26—41no—
100Dic26—41no—
101C8×C13—22no—
102#1055—22no—
103C22×SD16—131no—
104C22×SD16—131no—
105C2×C4⋊Q8—131no—
106C2×#103—131no—
107C2×#103D1311yescharacteristic, complemented
108#390—131no—
109#336—131no—
110C22×C13#12011yescharacteristic
111C22×C13#12111yescharacteristic
112C22×C13#12711yescharacteristic
113C22×C13C2×SD1612yes—
114C22×C13#13712yes—
115C2×D13—42no—
116C2×D13—44no—
117C2×D13—82no—
118C2×D13—81no—
119C2×D13—81no—
120C4×C13—42no—
121C4×C13—81no—
122C4×C13#12011yescharacteristic
123C4×C13#12011yescharacteristic
124C4×C13#12111yescharacteristic
125C4×C13#12111yescharacteristic
126Dic13—24no—
127Dic13—42no—
128C22×Q8—131no—
129C22×Q8C2×D1311yescharacteristic
130C22×D4—131no—
131C2×SD16—262no—
132C2×SD16—262no—
133C2×SD16—262no—
134C2×SD16—262no—
135C2×SD16—262no—
136C2×SD16—262no—
137C22×C8—131no—
138C22×C8C2×D1311yescharacteristic
139C4⋊Q8—262no—
140C4⋊Q8—262no—
141C2×C4⋊C4—262no—
142C2×C4⋊C4C2×D1311yescharacteristic
143C2×C22⋊C4—262no—
144C2×C42—131no—
145#103—22no—
146#103—262no—
147C2×C13#39211yescharacteristic
148C2×C13#44812yes—
149C2×C13#46112yes—
150C2×C13#49211yescharacteristic
151C2×C13#49711yescharacteristic
152D13—82no—
153C24—261no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—132no—
160C2×Q8—261no—
161C2×Q8—261no—
162C2×Q8—261no—
163C2×Q8—261no—
164C2×Q8—261no—
165C2×Q8D5212yes—
166C2×D4—132no—
167C2×D4—261no—
168C2×D4—261no—
169C2×D4—261no—
170C2×D4—261no—
171C2×D4—261no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—132no—
175C22×C4—261no—
176C22×C4C22×D1311yescharacteristic
177SD16—268no—
178SD16—268no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—132no—
182C2×C8—261no—
183C2×C8—261no—
184C2×C8C22⋊D1312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—268no—
188C22⋊C4—524no—
189C42—261no—
190C42—261no—
191C13#201311yescharacteristic, complemented, Sylow
192C23—262no—
193C23—521no—
194C23—522no—
195C23—522no—
196C23—521no—
197C23D4×D1311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—262no—
203Q8—262no—
204Q8—521no—
205Q8—521no—
206D4—262no—
207D4—262no—
208D4—521no—
209D4—521no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—134no—
216C2×C4—262no—
217C2×C4—262no—
218C2×C4—262no—
219C2×C4—521no—
220C2×C4—521no—
221C2×C4C2×D5211yescharacteristic
222C2×C4#612711yescharacteristic
223C2×C4D4×D1311yescharacteristic
224C2×C4D4×D1311yescharacteristic
225C2×C4D4×D1311yescharacteristic
226C2×C4C2×C22⋊D1311yescharacteristic
227C8—22no—
228C8—262no—
229C22—524no—
230C22—522no—
231C22—1042no—
232C22—1041no—
233C22—1041no—
234C22#8813611yescharacteristic
235C22#8813811yescharacteristic
236C22SD16×D1312yes—
237C22#8817212yes—
238C22#8819411yescharacteristic
239C4—42no—
240C4—81no—
241C4—264no—
242C4—522no—
243C4#8813611yescharacteristic
244C4#8813811yescharacteristic
245C4#8818411yescharacteristic
246C4#8819111yescharacteristic
247C2—1042no—
248C2#1171846712yes—
249C2#1171847912yes—
250C2#1171862111yescharacteristic
251C2#1171883611yescharacteristic
252C2#1171885111yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#103C2
socleC23×C13C2×D4
prime radicalC22×D52C22
hypercenterC2×#103D13
hypocenterC13#2013
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#88198C2semidirect
4. C2×C13×#103C2semidirect
6. C2×#88050C2semidirect
7. #11718142C2semidirect
92. C2×Dic13SD16semidirect
107. C2×#103D13semidirect
191. C13#2013semidirect

Maximal subgroups

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

subgroupindex
C2×#881982
C22×#61062
C22×#60952
C2×C13×#1032
#117186492
C2×#880502
#117181422
#201313