Finite Group Databasebeta

← #16786772

Subgroups — #16786772

Order 3328.

450 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 102 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#13131064C212yesmaximal
2#13129773C212yesmaximal, complemented
3#13129772C212yesmaximal, complemented
4C2×D13×C4⋊C8C211yesmaximal, characteristic
5C22×C8×D13C411yescharacteristic
6C22×C8×D13C2211yescharacteristic
7C2×C42×D13C411yescharacteristic
8C2×#88098—22no—
9C2×C13×C4⋊C8C411yescharacteristic
10C2×#88054C411yescharacteristic
11C2×#88054C2211yescharacteristic
12C2×C4⋊#1055C2211yescharacteristic
13D13×C4⋊C8—22no—
14D13×C4⋊C8—22no—
15C22⋊#6092C2214yes—
16#11718259—22no—
17C22×C4×D13C811yescharacteristic
18C22×C4×D13C811yescharacteristic
19C22×C4×D13C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×C4×Dic13C811yescharacteristic
24C2×C4×Dic13C811yescharacteristic
25C2×C4×Dic13C2×C411yescharacteristic
26C22×#1055C2×C411yescharacteristic
27C22×#1055C2311yescharacteristic
28C2×C8×D13—21no—
29C2×C8×D13—21no—
30C2×C8×D13—42no—
31C2×C8×D13—42no—
32C2×C8×D13D412yes—
33C2×C8×D13D412yes—
34C42×D13—21no—
35C42×D13—21no—
36C42×D13—21no—
37C42×D13—21no—
38C2×#6092—24no—
39#88098—44no—
40C13×C4⋊C8—22no—
41#88054—22no—
42#88054—22no—
43C4⋊#1055—22no—
44#11440—131nomaximal, Sylow
45C23×D13C2×C811yescharacteristic
46C22×C4×C13C2×C811yescharacteristic
47C22×C4×C13C2×C811yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C2×C811yescharacteristic
50C22×Dic13C2×C811yescharacteristic
51C22×Dic13C2×C811yescharacteristic
52C2×C4×D13—21no—
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—22no—
58C2×C4×D13—21no—
59C2×C4×D13—21no—
60C2×C4×D13—42no—
61C2×C4×D13C22⋊C411yescharacteristic
62C2×C4×D13C22⋊C411yescharacteristic
63C2×C4×D13M1611yescharacteristic
64C2×C4×D13M1611yescharacteristic
65C2×C8×C13—21no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13C22⋊C412yes—
69C42×C13—21no—
70C42×C13—21no—
71C4×Dic13—21no—
72C4×Dic13—21no—
73C4×Dic13—21no—
74C4×Dic13—21no—
75C4×Dic13—21no—
76C4×Dic13—21no—
77C2×#1055—21no—
78C2×#1055—41no—
79C2×#1055—41no—
80C2×#1055C2×D412yes—
81C8×D13—24no—
82C8×D13—42no—
83C8×D13—42no—
84C8×D13—42no—
85#6092—44no—
86C22×C4⋊C8—131no—
87#2112—132no—
88#1322—132no—
89#1322—132no—
90C23×C13C22×C811yescharacteristic
91C22×D13—21no—
92C22×D13—21no—
93C22×D13—22no—
94C22×D13—22no—
95C22×D13C22⋊C811yescharacteristic
96C22×D13C22⋊C811yescharacteristic
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—41no—
103C2×C4×C13M3212yescomplemented
104C2×C4×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13C2×M1611yescharacteristic
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—22no—
109C2×Dic13—21no—
110C2×Dic13—41no—
111C2×Dic13C22⋊C811yescharacteristic
112C2×Dic13C22⋊C811yescharacteristic
113C2×Dic13M3212yescomplemented
114C4×D13—24no—
115C4×D13—24no—
116C4×D13—22no—
117C4×D13—21no—
118C4×D13—21no—
119C4×D13—22no—
120C4×D13—42no—
121C4×D13—42no—
122C4×D13#9912yes—
123C4×D13#10112yes—
124C8×C13—22no—
125C8×C13—41no—
126#1055—22no—
127#1055—41no—
128C23×C8—131no—
129C23×C8—131no—
130C22×C42—131no—
131C2×M32—262no—
132C2×C4⋊C8—131no—
133C2×C4⋊C8—131no—
134C2×C4⋊C8—131no—
135C2×C4⋊C8—262no—
136C2×C4⋊C8—262no—
137C2×C4⋊C8#26111yescharacteristic
138C22⋊C16—134no—
139C22⋊C16—262no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13C2×C22⋊C811yescharacteristic
143C22×C13C2×M3211yescharacteristic
144C22×C13C2×M3211yescharacteristic
145C2×D13—24no—
146C2×D13—24no—
147C2×D13—21no—
148C2×D13—21no—
149C2×D13—21no—
150C2×D13—21no—
151C2×D13#32412yes—
152C2×D13#34912yes—
153C4×C13—22no—
154C4×C13—21no—
155C4×C13—41no—
156C4×C13C2×#9911yescharacteristic
157C4×C13C2×#10111yescharacteristic
158Dic13—22no—
159Dic13—21no—
160Dic13—41no—
161Dic13#32412yes—
162C23×C4—131no—
163C23×C4—131no—
164C23×C4—131no—
165C22×C8—131no—
166C22×C8—132no—
167C22×C8—132no—
168C22×C8—131no—
169C22×C8—261no—
170C22×C8—261no—
171C22×C8—522no—
172C22×C8—522no—
173C22×C8C2×#26111yescharacteristic
174C22×C8C2×#26111yescharacteristic
175C2×C42—131no—
176C2×C42—131no—
177C2×C42—131no—
178C2×C42—261no—
179C2×C42—261no—
180C2×C42—261no—
181C2×C42—261no—
182C2×C42C2×#26111yescharacteristic
183M32—524no—
184C2×C16—264no—
185C4⋊C8—22no—
186C4⋊C8—262no—
187C4⋊C8—262no—
188C4⋊C8—262no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13C2×#32411yescharacteristic
192C2×C13#211211yescharacteristic
193C2×C13C2×#34911yescharacteristic
194D13—22no—
195D13—22no—
196C24—131no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—262no—
205C22×C4—262no—
206C22×C4—262no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4—262no—
212C22×C4—522no—
213C22×C4D13⋊C811yescharacteristic
214C22×C4D13⋊C811yescharacteristic
215C22×C4C22×#26111yescharacteristic
216C2×C8—21no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—132no—
220C2×C8—264no—
221C2×C8—261no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C2×C8—521no—
226C2×C8—521no—
227C2×C8C22⋊#26112yes—
228C42—21no—
229C42—21no—
230C42—261no—
231C42—261no—
232C42—261no—
233C42—261no—
234C42—261no—
235C42—261no—
236C16—524no—
237C13#1144011yescharacteristic, complemented, Sylow
238C23—131no—
239C23—131no—
240C23—262no—
241C23—262no—
242C23—261no—
243C23—261no—
244C23C2×D13⋊C811yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—131no—
252C2×C4—132no—
253C2×C4—132no—
254C2×C4—132no—
255C2×C4—131no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—264no—
259C2×C4—264no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4—521no—
269C2×C4#8809812yescomplemented
270C2×C4D13⋊M1611yescharacteristic
271C2×C4C2×C22⋊#26111yescharacteristic
272C8—22no—
273C8—41no—
274C8—262no—
275C8—521no—
276C22—21no—
277C22—21no—
278C22—132no—
279C22—132no—
280C22—264no—
281C22—264no—
282C22—261no—
283C22—261no—
284C22—261no—
285C22—261no—
286C22C2×#8809811yescharacteristic
287C22D13⋊M3211yescharacteristic
288C22D13⋊(C22⋊C8)11yescharacteristic
289C4—22no—
290C4—21no—
291C4—41no—
292C4—132no—
293C4—262no—
294C4—261no—
295C4—521no—
296C4D13⋊#9911yescharacteristic
297C4D13⋊#10111yescharacteristic
298C2—21no—
299C2—21no—
300C2—262no—
301C2—262no—
302C2D13⋊#32411yescharacteristic
303C2#1313106411yescharacteristic
304C2D13⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C4⋊C8C4
socleC22×C13C2×C22⋊C8
prime radicalC23×D13C2×C8
cosocleC22×#1055C23
hypercenterC2×C4⋊C8#261
hypocenterC13#11440
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13129773C2semidirect
3. #13129772C2semidirect
103. C2×C4×C13M32semidirect
113. C2×Dic13M32semidirect
237. C13#11440semidirect
269. C2×C4#88098semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131297732
#131297722
C2×D13×C4⋊C82
#1144013