Finite Group Databasebeta

← #16786916

Subgroups — #16786916

Order 3328.

440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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#13130078C212yesmaximal, complemented
2#13129778C212yesmaximal, complemented
3#13129765C212yesmaximal
4#13117547C211yesmaximal, characteristic
5C2×#88129C411yescharacteristic
6C2×C4×D52C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8#11719125—22no—
9C13×#376C411yescharacteristic
10#11718600C2211yescharacteristic
11#11718596C2211yescharacteristic
12#11718590C411yescharacteristic
13#11718331—22no—
14#11718329—22no—
15#11718286—22no—
16#11718285C2214yes—
17C22×D52C2×C411yescharacteristic
18C22×C4×D13—21no—
19C22×Dic26C2×C411yescharacteristic
20C2×C42×C13C2×C411yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103—22no—
24C2×#6103—21no—
25C2×#6103—22no—
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13C2×C411yescharacteristic
28C2×C4⋊Dic13C2311yescharacteristic
29C2×#6101D412yes—
30C2×C4×Dic13D412yes—
31#88129—22no—
32#88129C814yescomplemented
33C4×D52—42no—
34C4×Dic26—42no—
35C22⋊#1057—24no—
36#88112—42no—
37C4×#1057—42no—
38C13×#95—21no—
39C13×#95—21no—
40#88071—22no—
41#11480—131nomaximal, Sylow
42C23×D13—21no—
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13C22⋊C411yescharacteristic
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13C22×C411yescharacteristic
48C22×Dic13—21no—
49C22×Dic13C22⋊C412yes—
50C22×Dic13C2×D412yes—
51C2×D52—21no—
52C2×D52—41no—
53C2×D52—41no—
54C2×D52C2×C812yes—
55C2×C4×D13—42no—
56C2×C4×D13—82no—
57C2×Dic26—41no—
58C2×Dic26—41no—
59C2×Dic26C2×C812yes—
60C2×Dic26M1612yes—
61C2×#1057—44no—
62C42×C13—22no—
63C42×C13—21no—
64C42×C13—41no—
65C42×C13C2×C812yes—
66#6103—28no—
67#6103—42no—
68#6103—82no—
69C4⋊Dic13—41no—
70C4⋊Dic13—41no—
71C4⋊Dic13—82no—
72#6101—42no—
73C4×Dic13—22no—
74C4×Dic13—22no—
75#2326—131no—
76#1461—132no—
77#1325—132no—
78#1318—132no—
79C23×C13C2×C22⋊C411yescharacteristic
80C22×D13—22no—
81C22×D13—42no—
82C22×D13—42no—
83C22×D13—41no—
84C22×D13—41no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—21no—
89C2×C4×C13—41no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13#9912yes—
97C2×C4×C13C22×C811yescharacteristic
98C2×C4×C13C2×M1611yescharacteristic
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—41no—
105C2×Dic13C22⋊C814yes—
106D52—42no—
107D52—42no—
108C4×D13—84no—
109Dic26—42no—
110Dic26—42no—
111#1057—84no—
112C2×#124—131no—
113C2×C4×Q8—131no—
114C2×C4×D4—131no—
115#431—262no—
116#391—131no—
117#390—131no—
118#388—262no—
119#385—262no—
120#384—131no—
121#376#26111yescharacteristic
122#324—134no—
123#324—262no—
124C22×C13—21no—
125C22×C13—21no—
126C22×C13C2×C22⋊C811yescharacteristic
127C22×C13C2×#9911yescharacteristic
128C22×C13#41311yescharacteristic
129C2×D13—44no—
130C2×D13—42no—
131C2×D13—82no—
132C2×D13—81no—
133C2×D13—81no—
134C4×C13—22no—
135C4×C13—21no—
136C4×C13—21no—
137C4×C13—42no—
138C4×C13—41no—
139C4×C13—81no—
140Dic13—24no—
141Dic13—42no—
142Dic13—81no—
143C22×Q8—131no—
144C22×D4—131no—
145C23×C4—261no—
146#124—134no—
147#124—262no—
148C4×Q8—522no—
149C4×D4—522no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—131no—
153C2×C4⋊C4—262no—
154C2×C22⋊C4—262no—
155C2×C22⋊C4—261no—
156C2×C22⋊C4—262no—
157C2×C42—132no—
158C2×C42C2×#26111yescharacteristic
159C2×C42C2×#26111yescharacteristic
160C2×C42C2×#26111yescharacteristic
161C4⋊C8—522no—
162C22⋊C8—264no—
163C4×C8—522no—
164#95—21no—
165#95—21no—
166#95—262no—
167C2×C13—21no—
168C2×C13—21no—
169C2×C13#145911yescharacteristic
170C2×C13#212811yescharacteristic
171C2×C13#213311yescharacteristic
172D13—82no—
173C24—261no—
174C2×Q8—132no—
175C2×Q8—132no—
176C2×Q8—521no—
177C2×Q8—521no—
178C2×D4—132no—
179C2×D4—261no—
180C2×D4—521no—
181C2×D4—521no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—132no—
185C22×C4—132no—
186C22×C4—261no—
187C22×C4—522no—
188C22×C4—1042no—
189C22×C4C22⋊#26111yescharacteristic
190C22×C4C22⋊#26111yescharacteristic
191C22×C4C22×#26111yescharacteristic
192C2×C8—524no—
193C4⋊C4—522no—
194C4⋊C4—521no—
195C4⋊C4—521no—
196C4⋊C4—1042no—
197C22⋊C4—268no—
198C22⋊C4—522no—
199C22⋊C4—1042no—
200C42—22no—
201C42—21no—
202C42—41no—
203C42—262no—
204C42—262no—
205C42D13⋊C812yes—
206C13#1148011yescharacteristic, complemented, Sylow
207C23—262no—
208C23—522no—
209C23—522no—
210C23—521no—
211C23—521no—
212C23C2×C22⋊#26111yescharacteristic
213Q8—522no—
214Q8—522no—
215D4—522no—
216D4—522no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—134no—
229C2×C4—262no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—521no—
235C2×C4—1044no—
236C2×C4#8810712yes—
237C2×C4C2×D13⋊C811yescharacteristic
238C2×C4D13⋊M1611yescharacteristic
239C8—1044no—
240C22—21no—
241C22—21no—
242C22—524no—
243C22—522no—
244C22—1042no—
245C22—1041no—
246C22—1041no—
247C22C2×#8810711yescharacteristic
248C22D13⋊(C22⋊C8)11yescharacteristic
249C22#1171913211yescharacteristic
250C4—21no—
251C4—21no—
252C4—22no—
253C4—42no—
254C4—41no—
255C4—81no—
256C4—264no—
257C4—522no—
258C4—1041no—
259C2—21no—
260C2—21no—
261C2—1042no—
262C2#1313007311yescharacteristic
263C2#1313111711yescharacteristic
264C2#1313113311yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#376C4
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C4⋊Dic13C23
hypercenter#376#261
hypocenterC13#11480
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
1. #13130078C2semidirect
2. #13129778C2semidirect
32. #88129C8semidirect
206. C13#11480semidirect

Maximal subgroups

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

subgroupindex
#131300782
#131297782
#131297652
#131175472
#1148013