Finite Group Databasebeta

← #13115986

Subgroups — #13115986

Order 1664.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#88144C211yesmaximal, characteristic
2C2×#88056C211yesmaximal, characteristic
3#11718635C211yesmaximal, characteristic
4C2×#88050C211yesmaximal, characteristic
5C13×#340C211yesmaximal, characteristic
6#11718142C211yesmaximal, characteristic
7#11718121C211yesmaximal, characteristic
8C22×Dic26C2211yescharacteristic
9C22×C8×C13C2211yescharacteristic
10C2×C13×C4⋊C4C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic13—21no—
13C2×C4⋊Dic13C2211yescharacteristic
14C2×#6101—21no—
15C2×C4×Dic13C2211yescharacteristic
16C22×#1055C2211yescharacteristic
17#88144—22no—
18#88144—22no—
19#88071—21no—
20#88071—21no—
21#88056—22no—
22#88050—22no—
23C22×C4×C13—21no—
24C22×C4×C13—21no—
25C22×C4×C13C2311yescharacteristic
26C22×Dic13—21no—
27C22×Dic13—21no—
28C22×Dic13D411yescharacteristic
29C22×Dic13D411yescharacteristic
30C2×Dic26—21no—
31C2×Dic26—21no—
32C2×Dic26—21no—
33C2×Dic26—21no—
34C2×Dic26—21no—
35C2×Dic26Q812yes—
36C2×C8×C13—21no—
37C2×C8×C13—21no—
38C2×C8×C13—21no—
39C13×C4⋊C4—21no—
40C13×C4⋊C4—21no—
41C13×C4⋊C4—21no—
42C13×C4⋊C4D412yes—
43C4⋊Dic13—24no—
44C4⋊Dic13—21no—
45C4⋊Dic13D412yes—
46#6101—24no—
47C4×Dic13—21no—
48C4×Dic13—21no—
49C2×#1055—21no—
50C2×#1055—21no—
51C2×#1055—21no—
52#2026—131nomaximal, Sylow
53C23×C13C2×D411yescharacteristic
54C2×C4×C13—22no—
55C2×C4×C13—41no—
56C2×C4×C13—41no—
57C2×C4×C13—41no—
58C2×C4×C13—41no—
59C2×C4×C13—41no—
60C2×C4×C13C2×D411yescharacteristic
61C2×C4×C13C2×D411yescharacteristic
62C2×C4×C13C2×Q811yescharacteristic
63C2×C4×C13#4111yescharacteristic
64C2×C4×C13#4111yescharacteristic
65C2×C4×C13#4111yescharacteristic
66C2×Dic13—21no—
67C2×Dic13—21no—
68C2×Dic13—22no—
69C2×Dic13—22no—
70C2×Dic13—21no—
71C2×Dic13—21no—
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—41no—
75C2×Dic13—41no—
76C2×Dic13—41no—
77C2×Dic13—41no—
78Dic26—22no—
79Dic26—22no—
80Dic26—41no—
81Dic26—41no—
82C8×C13—41no—
83#1055—41no—
84C2×#125—131no—
85C2×#103—131no—
86C2×#103—131no—
87#391—131no—
88#340—131no—
89#340D1311yescharacteristic
90#336—131no—
91C22×C13#12011yescharacteristic
92C22×C13C22⋊Q811yescharacteristic
93C22×C13#12411yescharacteristic
94C22×C13#13511yescharacteristic
95C22×C13#13511yescharacteristic
96C22×C13#13711yescharacteristic
97C22×C13#13711yescharacteristic
98C4×C13—42no—
99C4×C13—81no—
100C4×C13C22⋊Q811yescharacteristic
101C4×C13C22⋊Q811yescharacteristic
102C4×C13#12411yescharacteristic
103C4×C13#12411yescharacteristic
104Dic13—42no—
105Dic13—41no—
106Dic13—41no—
107Dic13—42no—
108C22×Q8—131no—
109C22×C8—131no—
110C22×C8C2×D1311yescharacteristic
111#125—262no—
112#125—262no—
113C2×C4⋊C4—131no—
114C2×C4⋊C4—261no—
115C2×C4⋊C4—261no—
116C2×C4⋊C4C2×D1311yescharacteristic
117C2×C4⋊C4C2×D1311yescharacteristic
118C2×C42—131no—
119#103—262no—
120#103—262no—
121#95—261no—
122#95—261no—
123C2×C13#39311yescharacteristic
124C2×C13#45211yescharacteristic
125C2×C13#45211yescharacteristic
126C2×C13#47911yescharacteristic
127C2×C13#47911yescharacteristic
128C2×C13#48811yescharacteristic
129C2×C13#49111yescharacteristic
130C2×Q8—132no—
131C2×Q8—261no—
132C2×Q8—261no—
133C2×Q8—261no—
134C2×Q8—261no—
135C2×Q8—261no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—131no—
139C22×C4—131no—
140C22×C4—261no—
141C22×C4—261no—
142C22×C4C22×D1311yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—261no—
147C2×C8—261no—
148C2×C8—261no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—132no—
153C4⋊C4—264no—
154C4⋊C4—264no—
155C4⋊C4—261no—
156C4⋊C4D5212yes—
157C42—261no—
158C42—261no—
159C13#202611yescharacteristic, complemented, Sylow
160C23D4×D1311yescharacteristic
161Q8—262no—
162Q8—262no—
163Q8—521no—
164Q8—521no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—261no—
172C2×C4—261no—
173C2×C4—262no—
174C2×C4—262no—
175C2×C4—261no—
176C2×C4—261no—
177C2×C4—261no—
178C2×C4—261no—
179C2×C4—521no—
180C2×C4—521no—
181C2×C4—521no—
182C2×C4—521no—
183C2×C4C2×D5211yescharacteristic
184C2×C4#612711yescharacteristic
185C2×C4#612711yescharacteristic
186C2×C4D4×D1311yescharacteristic
187C2×C4#612911yescharacteristic
188C2×C4Q8×D1311yescharacteristic
189C8—41no—
190C8—521no—
191C22#8813611yescharacteristic
192C22#8813911yescharacteristic
193C22#8815011yescharacteristic
194C22#8816611yescharacteristic
195C22#8816911yescharacteristic
196C22#8817011yescharacteristic
197C22#8817211yescharacteristic
198C4—42no—
199C4—81no—
200C4—521no—
201C4—521no—
202C4—522no—
203C4—522no—
204C4#8812911yescharacteristic
205C4#8813911yescharacteristic
206C4#8815011yescharacteristic
207C4#8815111yescharacteristic
208C2#1171833411yescharacteristic
209C2#1171842911yescharacteristic
210C2#1171844411yescharacteristic
211C2#1171845811yescharacteristic
212C2#1171847111yescharacteristic
213C2#1171851811yescharacteristic
214C2#1171853811yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#340C2
socle, prime radicalC23×C13C2×D4
hypercenter#340D13
hypocenterC13#2026
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
159. C13#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#881442
C2×#880562
#117186352
C2×#880502
C13×#3402
#117181422
#117181212
#202613