Finite Group Databasebeta

← #15772419

Subgroups — #15772419

Order 3328.

348 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 91 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#13116652C212yesmaximal, complemented
2#13112774C212yesmaximal, complemented
3#13112772C212yesmaximal, complemented
4C13×#2929C211yesmaximal, characteristic
5C2×C13×#131C411yescharacteristic
6C23×C8×C13C411yescharacteristic
7C13×#525C411yescharacteristic
8C13×#435—22no—
9C8×D4×C13—22no—
10C13×#424C411yescharacteristic
11C13×#408C2211yescharacteristic
12C13×#407C2211yescharacteristic
13C13×#405C2211yescharacteristic
14#11718145C2214yes—
15#11718058—22no—
16#11718055—22no—
17C2×C13×#41C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C13×#131—42no—
20C2×C13×M16—21no—
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16C2311yescharacteristic
23C22×C8×C13—21no—
24C22×C8×C13—21no—
25C22×C8×C13—21no—
26C22×C8×C13—42no—
27C22×C8×C13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C13×#123—21no—
30C13×C22⋊Q8—21no—
31C13×#121—21no—
32C13×#120—21no—
33C4×D4×C13—22no—
34C13×#117C2×C411yescharacteristic
35C13×C4⋊C8—22no—
36C13×C22⋊C8—22no—
37C13×C22⋊C8—22no—
38C13×#97D412yes—
39C4×C8×C13D412yes—
40#88052—24no—
41#11537—131nomaximal, Sylow
42C24×C13M1611yescharacteristic
43C13×#41—41no—
44C13×#41—41no—
45C2×Q8×C13M1611yescharacteristic
46C2×D4×C13—22no—
47C2×D4×C13—21no—
48C2×D4×C13M1611yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13M1611yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C13×M16—41no—
57C13×M16—42no—
58C13×M16—41no—
59C2×C8×C13—22no—
60C2×C8×C13—21no—
61C2×C8×C13—21no—
62C2×C8×C13—42no—
63C2×C8×C13—42no—
64C2×C8×C13—42no—
65C2×C8×C13—41no—
66C2×C8×C13C22⋊C411yescharacteristic
67C2×C8×C13C22⋊C411yescharacteristic
68C2×C8×C13C2×D412yes—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—21no—
71C13×C22⋊C4—22no—
72C13×C22⋊C4—22no—
73C13×C22⋊C4—21no—
74C42×C13C22⋊C412yes—
75#6090—44no—
76#2929D1311yescharacteristic
77#2166—132no—
78#1321—132no—
79#1320—132no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—41no—
83C23×C13—42no—
84C23×C13C2×M1611yescharacteristic
85Q8×C13—41no—
86D4×C13—41no—
87D4×C13—44no—
88D4×C13—42no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13C2×C22⋊C411yescharacteristic
101C2×C4×C13C2×M1611yescharacteristic
102C8×C13—22no—
103C8×C13—21no—
104C8×C13—41no—
105C8×C13—41no—
106C8×C13#10012yes—
107C2×#131Dic1311yescharacteristic
108C23×C8Dic1311yescharacteristic
109#525Dic1311yescharacteristic
110#435—22no—
111C8×D4—22no—
112#424Dic1311yescharacteristic
113#408C2×D1311yescharacteristic
114#407C2×D1311yescharacteristic
115#405C2×D1311yescharacteristic
116#364—262no—
117#349—134no—
118#347—262no—
119C22×C13—22no—
120C22×C13—21no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—42no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—41no—
127C22×C13—41no—
128C22×C13#40711yescharacteristic
129C4×C13—21no—
130C4×C13—42no—
131C4×C13—41no—
132C4×C13—41no—
133C4×C13#41011yescharacteristic
134C4×C13C2×#10011yescharacteristic
135C2×#41C2×Dic1311yescharacteristic
136C23×C4C2×Dic1311yescharacteristic
137#131—42no—
138C2×M16—21no—
139C2×M16C2×Dic1311yescharacteristic
140C2×M16C22×D1311yescharacteristic
141C22×C8—21no—
142C22×C8—21no—
143C22×C8—21no—
144C22×C8—42no—
145C22×C8C2×Dic1311yescharacteristic
146C22×C8C2×Dic1311yescharacteristic
147#123—21no—
148C22⋊Q8—21no—
149#121—21no—
150#120—21no—
151C4×D4—22no—
152#117C2×Dic1311yescharacteristic
153M32—264no—
154C4⋊C8—22no—
155C22⋊C8—22no—
156C22⋊C8—22no—
157#97C22⋊D1312yes—
158C4×C8C22⋊D1312yes—
159C2×C13—21no—
160C2×C13—42no—
161C2×C13—41no—
162C2×C13—81no—
163C2×C13#146611yescharacteristic
164C24#609911yescharacteristic
165#41—41no—
166#41—41no—
167C2×Q8#609911yescharacteristic
168C2×D4—22no—
169C2×D4—21no—
170C2×D4#609911yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4#609911yescharacteristic
177C22×C4C22×Dic1311yescharacteristic
178M16—41no—
179M16—42no—
180M16—41no—
181C2×C8—22no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8C22⋊Dic1311yescharacteristic
189C2×C8C22⋊Dic1311yescharacteristic
190C2×C8C2×C22⋊D1312yes—
191C4⋊C4—22no—
192C4⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—21no—
196C42C22⋊Dic1312yes—
197C16—524no—
198C13#1153711yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#609911yescharacteristic
204Q8—41no—
205D4—41no—
206D4—44no—
207D4—42no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4C2×#609911yescharacteristic
220C2×C4C2×C22⋊Dic1311yescharacteristic
221C8—21no—
222C8—22no—
223C8—41no—
224C8—41no—
225C8#8807312yes—
226C22—22no—
227C22—21no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22—41no—
235C22#1171886811yescharacteristic
236C4—21no—
237C4—42no—
238C4—41no—
239C4—41no—
240C4C2×#8807311yescharacteristic
241C4#1171890111yescharacteristic
242C2—21no—
243C2—42no—
244C2—41no—
245C2—81no—
246C2#1311317711yescharacteristic
subgroupG/H
centerC4#11718901
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2929C2
socleC2×C13#1466
prime radicalC13×#525C4
cosocleC2×C13×M16C23
hypercenter#2929D13
hypocenterC13#11537
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #13116652C2semidirect
2. #13112774C2semidirect
3. #13112772C2semidirect
198. C13#11537semidirect

Maximal subgroups

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

subgroupindex
#131166522
#131127742
#131127722
C13×#29292
#1153713