Finite Group Databasebeta

← #15756505

Subgroups — #15756505

Order 3328.

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

normal subgroups only

This group has 378 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#13114832C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic
3#13112739C212yesmaximal
4#13112694C212yesmaximal
5C13×#2356C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C13×#391—21no—
8C13×#387—22no—
9C13×#383C412yes—
10C13×#382C2211yescharacteristic
11C4×C13×C4⋊C4—21no—
12C4×C13×C4⋊C4C2211yescharacteristic
13C13×#376C412yes—
14C2×#88076—21no—
15#11718586C2212yes—
16#11718585C2212yes—
17#11718122—21no—
18#11718120—22no—
19C22×Q8×C13D411yescharacteristic
20C4×Q8×C13—22no—
21C4×Q8×C13—22no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4D412yes—
26C2×C42×C13—22no—
27C2×C42×C13—21no—
28C2×C42×C13C2×C412yes—
29C2×C42×C13C2311yescharacteristic
30C2×#6099—22no—
31C13×#95—22no—
32C13×#95—22no—
33C13×#95—22no—
34C13×#95—21no—
35C13×#95C2×C411yescharacteristic
36C13×#95C2×C411yescharacteristic
37C13×#95C2×C412yes—
38#88076—42no—
39C22⋊#1055—22no—
40C4⋊#1055—22no—
41C4⋊#1055—22no—
42C4⋊#1055—22no—
43C4×#1055—22no—
44#8768—131nomaximal, Sylow
45C2×Q8×C13—22no—
46C2×Q8×C13—22no—
47C2×Q8×C13—21no—
48C2×Q8×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C13×C4⋊C4—22no—
58C13×C4⋊C4—24no—
59C13×C4⋊C4—42no—
60C13×C4⋊C4—42no—
61C42×C13—22no—
62C42×C13—22no—
63C42×C13—44no—
64C42×C13—41no—
65C42×C13—41no—
66C42×C13#4112yes—
67C42×C13#4112yes—
68#6099—42no—
69#6099—42no—
70C2×#1055—42no—
71C2×#1055—42no—
72#2356D1311yescharacteristic
73#1801—131no—
74#1461—131no—
75#1303—132no—
76#1286—132no—
77C23×C13C2×C22⋊C411yescharacteristic
78Q8×C13—42no—
79Q8×C13—42no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13#11711yescharacteristic
97C2×C4×C13#11711yescharacteristic
98C2×C4×C13#12312yes—
99C2×C4×C13#12312yes—
100C2×C4×C13#13512yes—
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C13#13711yescharacteristic
103#1055—82no—
104#1055—82no—
105C2×C4×Q8C2×D1311yescharacteristic
106#431—132no—
107#423—132no—
108C2×#101—261no—
109#391—21no—
110#387—22no—
111#383Dic1312yes—
112#382C2×D1311yescharacteristic
113C4×C4⋊C4—21no—
114C4×C4⋊C4C2×D1311yescharacteristic
115#376Dic1312yes—
116#343—261no—
117#324—262no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13#38111yescharacteristic
121C22×C13#41611yescharacteristic
122C22×C13#41711yescharacteristic
123C4×C13—22no—
124C4×C13—21no—
125C4×C13—21no—
126C4×C13—42no—
127C4×C13—42no—
128C4×C13—42no—
129C4×C13—81no—
130C4×C13—82no—
131C4×C13#48212yes—
132C4×C13#48512yes—
133C22×Q8C22⋊D1311yescharacteristic
134C2×M16—262no—
135C4×Q8—22no—
136C4×Q8—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C22⋊D1312yes—
140C2×C4⋊C4C22⋊D1311yescharacteristic
141C2×C42—22no—
142C2×C42—21no—
143C2×C42C2×Dic1312yes—
144C2×C42C22×D1311yescharacteristic
145C4⋊C8—262no—
146C4⋊C8—262no—
147C4⋊C8—262no—
148#101—522no—
149C22⋊C8—262no—
150C4×C8—262no—
151#95—22no—
152#95—22no—
153#95—22no—
154#95—21no—
155#95C2×Dic1311yescharacteristic
156#95C2×Dic1312yes—
157#95C2×Dic1311yescharacteristic
158C2×C13—21no—
159C2×C13—21no—
160C2×C13#182511yescharacteristic
161C2×C13#182711yescharacteristic
162C2×C13#183011yescharacteristic
163C2×Q8—22no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—21no—
167C22×C4—21no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4C22⋊Dic1312yes—
171C22×C4C22⋊Dic1312yes—
172C22×C4C22×Dic1311yescharacteristic
173C22×C4C2×C22⋊D1311yescharacteristic
174C22×C4C2×C22⋊D1311yescharacteristic
175M16—522no—
176M16—522no—
177C2×C8—522no—
178C2×C8—522no—
179C4⋊C4—22no—
180C4⋊C4—24no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C42—22no—
184C42—22no—
185C42—44no—
186C42—41no—
187C42—41no—
188C42#612712yes—
189C42#612712yes—
190C13#876811yescharacteristic, complemented, Sylow
191C23C2×C22⋊Dic1311yescharacteristic
192Q8—42no—
193Q8—42no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4#8818011yescharacteristic
211C2×C4#8818011yescharacteristic
212C2×C4#8818312yes—
213C2×C4#8818312yes—
214C2×C4#8820311yescharacteristic
215C2×C4#8820412yes—
216C2×C4#8820511yescharacteristic
217C8—1042no—
218C8—1042no—
219C22—21no—
220C22—21no—
221C22#1171887211yescharacteristic
222C22#1171889311yescharacteristic
223C22#1171889411yescharacteristic
224C4—22no—
225C4—21no—
226C4—21no—
227C4—42no—
228C4—42no—
229C4—42no—
230C4—81no—
231C4—82no—
232C4#1171865712yes—
233C4#1171866412yes—
234C2—21no—
235C2—21no—
236C2#1311493111yescharacteristic
237C2#1311494011yescharacteristic
238C2#1311495011yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2356C2
socleC22×C13#381
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2356D13
hypocenterC13#8768
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
190. C13#8768semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131131602
#131127392
#131126942
C13×#23562
#876813