Finite Group Databasebeta

← #15779194

Subgroups — #15779194

Order 3328.

614 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114764C212yesmaximal
2#13112963C214yesmaximal, complemented
3C13×#2311C211yesmaximal, characteristic
4C22×C13×#41C2211yescharacteristic
5C2×C13×#117C411yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C13×#391C2212yes—
8C13×#390C412yes—
9C13×#386—22no—
10C13×#380—22no—
11C2×#88076C2214yes—
12C2×#88073—22no—
13#11718868—22no—
14C2×C13×#41—24no—
15C2×C13×#41—42no—
16C2×C13×#41—42no—
17C22×Q8×C13C2311yescharacteristic
18C22×D4×C13C2×C411yescharacteristic
19C22×D4×C13D412yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D412yes—
23C13×#117—42no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—42no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—24no—
30C2×C42×C13C2×C412yes—
31C2×#6099—24no—
32C13×#95—24no—
33#88076—28no—
34#88073—44no—
35C22⋊#1055—44no—
36#12863—131nomaximal, Sylow
37C24×C13C22⋊C412yes—
38C24×C13C22⋊C411yescharacteristic
39C13×#41—416no—
40C2×Q8×C13—41no—
41C2×Q8×C13—41no—
42C2×Q8×C13#4114yes—
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—24no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13—42no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—22no—
52C22×C4×C13—24no—
53C22×C4×C13—24no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13—82no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D412yes—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—84no—
67C42×C13—42no—
68#6099—44no—
69#6099—44no—
70C2×#1055—44no—
71#2311D1311yescharacteristic
72#1785—132no—
73#1394—134no—
74C23×C13—21no—
75C23×C13—21no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—41no—
80C23×C13—41no—
81C23×C13—42no—
82C23×C13—42no—
83C23×C13#9912yes—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—44no—
86D4×C13—48no—
87D4×C13—44no—
88C2×C4×C13—28no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—48no—
96C2×C4×C13—42no—
97C2×C4×C13—44no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—84no—
102C2×C4×C13#9912yes—
103C2×C4×C13#11712yes—
104C2×C4×C13#12314yes—
105#1055—84no—
106C22×#41C2×D1311yescharacteristic
107C2×#117Dic1311yescharacteristic
108C22×C4⋊C4Dic1311yescharacteristic
109C2×#101—134no—
110C2×#100—262no—
111#407—262no—
112#391C2×D1312yes—
113#390Dic1312yes—
114#386—22no—
115#380—22no—
116C22×C13—21no—
117C22×C13—21no—
118C22×C13—22no—
119C22×C13—42no—
120C22×C13—42no—
121C22×C13—44no—
122C22×C13—41no—
123C22×C13—41no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—82no—
128C22×C13#38111yescharacteristic
129C22×C13C2×#9911yescharacteristic
130C22×C13C2×#9911yescharacteristic
131C4×C13—24no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—82no—
135C4×C13—82no—
136C2×#41—24no—
137C2×#41—42no—
138C2×#41—42no—
139C22×Q8C22×D1311yescharacteristic
140C22×D4C2×Dic1311yescharacteristic
141C22×D4C22⋊D1312yes—
142C23×C4—21no—
143C23×C4C2×Dic1311yescharacteristic
144C23×C4C22⋊D1312yes—
145C2×M16—264no—
146#117—42no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—42no—
150C2×C4⋊C4C2×Dic1312yes—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—24no—
153C2×C42C2×Dic1312yes—
154#101—268no—
155#100—524no—
156C22⋊C8—524no—
157#95—24no—
158C2×C13—21no—
159C2×C13—21no—
160C2×C13—42no—
161C2×C13—82no—
162C2×C13#181911yescharacteristic
163C2×C13#213411yescharacteristic
164C2×C13#213511yescharacteristic
165C24C22⋊Dic1312yes—
166C24C22⋊Dic1311yescharacteristic
167#41—416no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8#612714yes—
171C2×D4—24no—
172C2×D4—22no—
173C2×D4—24no—
174C2×D4—41no—
175C2×D4—41no—
176C2×D4—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—24no—
181C22×C4—24no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—82no—
187C22×C4C22⋊Dic1311yescharacteristic
188C22×C4C22×Dic1311yescharacteristic
189C22×C4C2×C22⋊D1312yes—
190M16—524no—
191M16—524no—
192C2×C8—524no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—84no—
198C42—42no—
199C13#1286311yescharacteristic, complemented, Sylow
200C23—21no—
201C23—21no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—41no—
206C23—41no—
207C23—42no—
208C23—42no—
209C23#8807412yes—
210C23C2×C22⋊Dic1311yescharacteristic
211Q8—44no—
212D4—48no—
213D4—44no—
214C2×C4—28no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—48no—
222C2×C4—42no—
223C2×C4—44no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—84no—
228C2×C4#8807412yes—
229C2×C4#8818012yes—
230C2×C4#8818314yes—
231C8—1044no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—42no—
236C22—42no—
237C22—44no—
238C22—41no—
239C22—41no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22#1171887211yescharacteristic
245C22C2×#8807411yescharacteristic
246C22C2×#8807411yescharacteristic
247C4—24no—
248C4—22no—
249C4—22no—
250C4—82no—
251C4—82no—
252C2—21no—
253C2—21no—
254C2—42no—
255C2—82no—
256C2#1311491011yescharacteristic
257C2#1311652811yescharacteristic
258C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#2311C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×Q8×C13C23
hypercenter#2311D13
hypocenterC13#12863
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #13112963C2semidirect
199. C13#12863semidirect

Maximal subgroups

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

subgroupindex
#131147642
#131129632
C13×#23112
#1286313