Finite Group Databasebeta

← #16787037

Subgroups — #16787037

Order 3328.

418 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 76 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#13130087C212yesmaximal
2#13129779C214yesmaximal, complemented
3#13117460C211yesmaximal, characteristic
4C22×C13×C4⋊C4C411yescharacteristic
5C2×#88180C411yescharacteristic
6C2×#88180C2211yescharacteristic
7#11719128—22no—
8#11718871—22no—
9#11718638C412yes—
10#11718637C2212yes—
11#11718634—22no—
12#11718305—22no—
13#11718285C2214yes—
14C23×C4×C13—21no—
15C23×C4×C13C2×C411yescharacteristic
16C2×C13×C4⋊C4—21no—
17C2×C13×C4⋊C4—42no—
18C2×C13×C4⋊C4C2×C412yes—
19C2×C22⋊Dic13—21no—
20C2×C22⋊Dic13D412yes—
21#88180—24no—
22#88180—42no—
23C2×C4⋊Dic13—21no—
24C2×C4⋊Dic13C2×C411yescharacteristic
25C2×C4⋊Dic13C2311yescharacteristic
26C2×#6101—24no—
27C2×C4×Dic13C2×C412yes—
28C2×C4×Dic13D412yes—
29C22⋊#1057—24no—
30#88112—42no—
31#88110—42no—
32#88071—24no—
33#11516—131nomaximal, Sylow
34C24×C13C22⋊C411yescharacteristic
35C22×C4×C13—22no—
36C22×C4×C13—22no—
37C22×C4×C13—22no—
38C22×C4×C13—22no—
39C22×C4×C13—42no—
40C22×C4×C13—82no—
41C22×C4×C13C22⋊C411yescharacteristic
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—22no—
44C22×Dic13C22⋊C412yes—
45C22×Dic13C2×D412yes—
46C2×#1057—44no—
47C13×C4⋊C4—42no—
48C13×C4⋊C4—42no—
49C22⋊Dic13—24no—
50C22⋊Dic13—42no—
51C4⋊Dic13—24no—
52C4⋊Dic13—41no—
53C4⋊Dic13—41no—
54#6101—84no—
55C4×Dic13—22no—
56C4×Dic13—22no—
57C4×Dic13—22no—
58C4×Dic13M1614yes—
59#2317—131no—
60#1464—132no—
61#1325—134no—
62C23×C13—21no—
63C23×C13—21no—
64C23×C13—41no—
65C23×C13—41no—
66C23×C13#10112yes—
67C23×C13C2×C22⋊C411yescharacteristic
68C2×C4×C13—28no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—44no—
74C2×C4×C13—42no—
75C2×C4×C13—84no—
76C2×C4×C13#9912yes—
77C2×C4×C13C2×M1612yes—
78C2×Dic13—24no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—42no—
82C2×Dic13—42no—
83C2×Dic13—42no—
84C2×Dic13—42no—
85#1057—84no—
86C2×#117—131no—
87C2×#117—131no—
88C22×C4⋊C4#26111yescharacteristic
89#432—262no—
90#389—262no—
91#385—262no—
92#384—132no—
93#382—132no—
94#324—134no—
95#323—262no—
96C22×C13—21no—
97C22×C13—21no—
98C22×C13—22no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—41no—
102C22×C13—41no—
103C22×C13#40711yescharacteristic
104C22×C13C2×#9911yescharacteristic
105C22×C13C2×#10111yescharacteristic
106C4×C13—22no—
107C4×C13—22no—
108C4×C13—82no—
109Dic13—44no—
110Dic13—42no—
111Dic13—42no—
112C23×C4—21no—
113C23×C4C2×#26111yescharacteristic
114#117—264no—
115#117—522no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—131no—
120C2×C4⋊C4—261no—
121C2×C4⋊C4—264no—
122C2×C4⋊C4C2×#26112yes—
123C2×C22⋊C4—132no—
124C2×C22⋊C4—261no—
125C2×C42—132no—
126C2×C42—132no—
127C4⋊C8—522no—
128C22⋊C8—264no—
129#97—522no—
130#95—264no—
131C2×C13—21no—
132C2×C13—21no—
133C2×C13—42no—
134C2×C13#146311yescharacteristic
135C2×C13#212811yescharacteristic
136C2×C13#213511yescharacteristic
137C24C22⋊#26111yescharacteristic
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—42no—
143C22×C4—82no—
144C22×C4—132no—
145C22×C4—132no—
146C22×C4—262no—
147C22×C4C22⋊#26111yescharacteristic
148C22×C4C22×#26111yescharacteristic
149C2×C8—524no—
150C4⋊C4—42no—
151C4⋊C4—42no—
152C4⋊C4—264no—
153C4⋊C4—521no—
154C4⋊C4—521no—
155C4⋊C4—1044no—
156C22⋊C4—264no—
157C22⋊C4—522no—
158C42—134no—
159C42—262no—
160C42—262no—
161C42—262no—
162C13#1151611yescharacteristic, complemented, Sylow
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23#8811312yes—
168C23C2×C22⋊#26111yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—44no—
175C2×C4—42no—
176C2×C4—84no—
177C2×C4—264no—
178C2×C4—262no—
179C2×C4—262no—
180C2×C4—522no—
181C2×C4—522no—
182C2×C4—522no—
183C2×C4—522no—
184C2×C4#8811912yes—
185C2×C4D13⋊M1612yes—
186C8—1044no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22#1171912611yescharacteristic
195C22C2×#8811311yescharacteristic
196C22C2×#8811911yescharacteristic
197C4—22no—
198C4—22no—
199C4—82no—
200C4—524no—
201C4—522no—
202C4—522no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2#1313008611yescharacteristic
207C2#1313111511yescharacteristic
208C2#1313113811yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11516
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13129779C2semidirect
162. C13#11516semidirect

Maximal subgroups

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

subgroupindex
#131300872
#131297792
#131174602
#1151613