Finite Group Databasebeta

← #15779182

Subgroups — #15779182

Order 3328.

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

normal subgroups only

This group has 642 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#13114754C212yesmaximal
2#13112961C214yesmaximal, complemented
3C13×#2311C211yesmaximal, characteristic
4C22×C13×#41C2211yescharacteristic
5C2×C13×#117C411yescharacteristic, complemented
6C22×C13×C4⋊C4C411yescharacteristic, complemented
7C13×#391C412yescomplemented
8C13×#390C2212yes—
9C13×#386—22no—
10C13×#380—22no—
11C2×#88074—22no—
12C2×#88074C2214yes—
13#11718872—22no—
14C2×C13×#41—24no—
15C2×C13×#41—42no—
16C2×C13×#41—42no—
17C22×Q8×C13C2×C411yescharacteristic
18C22×D4×C13D412yes—
19C22×D4×C13C2311yescharacteristic
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×C22⋊Dic13—24no—
32C13×#95—24no—
33#88074—28no—
34#88074—44no—
35#88071—44no—
36#12859—131nomaximal, Sylow
37C24×C13C22⋊C411yescharacteristic
38C24×C13C2×D412yes—
39C13×#41—416no—
40C2×Q8×C13—22no—
41C2×Q8×C13—41no—
42C2×Q8×C13—41no—
43C2×D4×C13—24no—
44C2×D4×C13—24no—
45C2×D4×C13—42no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13#4114yes—
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⋊C412yes—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—44no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—42no—
66C13×C22⋊C4—42no—
67C13×C22⋊C4—84no—
68C42×C13—42no—
69C22⋊Dic13—44no—
70C22⋊Dic13—44no—
71#2311D1311yescharacteristic
72#1782—132no—
73#1393—134no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13—21no—
77C23×C13—22no—
78C23×C13—41no—
79C23×C13—41no—
80C23×C13—42no—
81C23×C13—42no—
82C23×C13#9912yes—
83C23×C13C2×C22⋊C411yescharacteristic
84C23×C13#12314yes—
85Q8×C13—44no—
86D4×C13—44no—
87D4×C13—48no—
88C2×C4×C13—28no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—48no—
97C2×C4×C13—42no—
98C2×C4×C13—44no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—84no—
103C2×C4×C13#9912yes—
104C2×C4×C13#11712yes—
105C2×Dic13—84no—
106C2×Dic13—84no—
107C2×Dic13—84no—
108C22×#41C2×D1311yescharacteristic
109C2×#117Dic1311yescharacteristic, complemented
110C22×C4⋊C4Dic1311yescharacteristic, complemented
111C2×#99—134no—
112C2×#99—262no—
113#391Dic1312yescomplemented
114#390C2×D1312yes—
115#386—22no—
116#381—262no—
117#380—22no—
118C22×C13—21no—
119C22×C13—21no—
120C22×C13—24no—
121C22×C13—22no—
122C22×C13—42no—
123C22×C13—44no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—41no—
127C22×C13—42no—
128C22×C13—41no—
129C22×C13—82no—
130C22×C13#38111yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#9911yescharacteristic
133C4×C13—22no—
134C4×C13—22no—
135C4×C13—42no—
136C4×C13—82no—
137C4×C13—82no—
138Dic13—164no—
139C2×#41—24no—
140C2×#41—42no—
141C2×#41—42no—
142C22×Q8C2×Dic1311yescharacteristic
143C22×D4C22⋊D1312yes—
144C22×D4C22×D1311yescharacteristic
145C23×C4—21no—
146C23×C4C2×Dic1311yescharacteristic
147C23×C4C22⋊D1312yes—
148#117—42no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4C2×Dic1312yes—
153C2×C22⋊C4—21no—
154C2×C22⋊C4—24no—
155C2×C22⋊C4—264no—
156C2×C42C2×Dic1312yes—
157#99—268no—
158#99—524no—
159#95—24no—
160#95—524no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13—44no—
164C2×C13—42no—
165C2×C13#181911yescharacteristic
166C2×C13#212811yescharacteristic
167C2×C13#212911yescharacteristic
168C24C22⋊Dic1311yescharacteristic
169C24C2×C22⋊D1312yes—
170#41—416no—
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×D4—24no—
175C2×D4—24no—
176C2×D4—42no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4#612714yes—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—82no—
190C22×C4—524no—
191C22×C4C22⋊Dic1312yes—
192C22×C4C22⋊Dic1311yescharacteristic
193C22×C4C22×Dic1311yescharacteristic
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C22⋊C4—42no—
198C22⋊C4—84no—
199C22⋊C4—524no—
200C22⋊C4—524no—
201C42—42no—
202C13#1285911yescharacteristic, complemented, Sylow
203C23—21no—
204C23—21no—
205C23—22no—
206C23—22no—
207C23—41no—
208C23—41no—
209C23—42no—
210C23—42no—
211C23#8807412yes—
212C23#8818314yes—
213C23C2×C22⋊Dic1311yescharacteristic
214Q8—44no—
215D4—44no—
216D4—48no—
217C2×C4—28no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—48no—
226C2×C4—42no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—84no—
232C2×C4—1044no—
233C2×C4—1044no—
234C2×C4—1044no—
235C2×C4#8807412yes—
236C2×C4#8818012yes—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—24no—
241C22—42no—
242C22—44no—
243C22—42no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—41no—
248C22—82no—
249C22#1171887211yescharacteristic
250C22C2×#8807411yescharacteristic
251C22C2×#8807411yescharacteristic
252C4—22no—
253C4—22no—
254C4—42no—
255C4—82no—
256C4—82no—
257C4—2084no—
258C2—21no—
259C2—21no—
260C2—44no—
261C2—42no—
262C2#1311491011yescharacteristic
263C2#1311650811yescharacteristic
264C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2311C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×D4×C13C23
hypercenter#2311D13
hypocenterC13#12859
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. #13112961C2semidirect
5. C2×C13×#117C4semidirect
6. C22×C13×C4⋊C4C4semidirect
7. C13×#391C4semidirect
109. C2×#117Dic13semidirect
110. C22×C4⋊C4Dic13semidirect
113. #391Dic13semidirect
202. C13#12859semidirect

Maximal subgroups

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

subgroupindex
#131147542
#131129612
C13×#23112
#1285913