Finite Group Databasebeta

← #16786860

Subgroups — #16786860

Order 3328.

438 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 96 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, complemented
2#13129772C212yesmaximal, complemented
3#13129757C212yesmaximal, complemented
4C2×C8×D52C211yesmaximal, characteristic
5C22×C8×D13C411yescharacteristic
6C22×C8×D13C2211yescharacteristic
7C2×C4×D52C411yescharacteristic
8C2×#88098—22no—
9C2×C4×C8×C13C411yescharacteristic
10C2×#88060C411yescharacteristic
11C2×#88060C2211yescharacteristic
12C2×C4⋊#1055C2211yescharacteristic
13C8×D52—22no—
14C8×D52—22no—
15C22⋊#6092C2214yes—
16#11718259—22no—
17C22×D52C811yescharacteristic
18C22×C4×D13C2×C411yescharacteristic
19C22×C4×D13C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C2×C42×C13C2×C411yescharacteristic
23C2×#6103C811yescharacteristic
24C2×#6103C811yescharacteristic
25C2×C4⋊Dic13C811yescharacteristic
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—
34C4×D52—22no—
35C4×D52—22no—
36C2×#6092—24no—
37#88098—44no—
38C4×C8×C13—21no—
39C4×C8×C13—21no—
40#88060—22no—
41#88060—22no—
42C4⋊#1055—22no—
43#11466—131nomaximal, Sylow
44C23×D13C2×C811yescharacteristic
45C23×D13C2×C811yescharacteristic
46C22×C4×C13C2×C811yescharacteristic
47C22×C4×C13C2×C811yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C2×C811yescharacteristic
50C22×Dic13C2×C811yescharacteristic
51C2×D52—22no—
52C2×D52—22no—
53C2×D52—22no—
54C2×C4×D13—21no—
55C2×C4×D13—21no—
56C2×C4×D13—41no—
57C2×C4×D13—41no—
58C2×C4×D13—41no—
59C2×C4×D13—41no—
60C2×C4×D13C22⋊C412yes—
61C2×C4×D13M1612yes—
62C2×C8×C13—22no—
63C2×C8×C13—21no—
64C2×C8×C13—41no—
65C2×C8×C13C22⋊C411yescharacteristic
66C2×C8×C13C22⋊C411yescharacteristic
67C42×C13—21no—
68C42×C13—21no—
69#6103—22no—
70#6103—22no—
71C4⋊Dic13—22no—
72C2×#1055—21no—
73C2×#1055—41no—
74C2×#1055—41no—
75C2×#1055C2×D412yes—
76C8×D13—24no—
77C8×D13—42no—
78C8×D13—42no—
79C8×D13—42no—
80#6092—44no—
81C2×C8×D4—131no—
82#2112—132no—
83#1322—132no—
84#1314—132no—
85C23×C13C22×C811yescharacteristic
86C22×D13—21no—
87C22×D13—21no—
88C22×D13—21no—
89C22×D13—21no—
90C22×D13—41no—
91C22×D13—41no—
92C22×D13—41no—
93C22×D13—41no—
94C22×D13C22⋊C812yes—
95C22×D13M3212yescomplemented
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13M3212yescomplemented
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—21no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13C22⋊C812yes—
109D52—28no—
110C4×D13—22no—
111C4×D13—22no—
112C4×D13—42no—
113C4×D13—42no—
114C4×D13—41no—
115C4×D13—41no—
116C8×C13—21no—
117C8×C13—41no—
118C8×C13#9912yes—
119#1055—22no—
120#1055—41no—
121C23×C8—131no—
122C23×C8—131no—
123C2×C4×D4—131no—
124C2×M32—262no—
125C8×D4—262no—
126C8×D4—262no—
127C2×C4⋊C8—131no—
128C2×C22⋊C8—131no—
129C2×C22⋊C8—131no—
130C2×C4×C8#26111yescharacteristic
131C22⋊C16—134no—
132C22⋊C16—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13C2×C22⋊C811yescharacteristic
136C22×C13C2×M3211yescharacteristic
137C22×C13C2×M3211yescharacteristic
138C2×D13—22no—
139C2×D13—22no—
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—42no—
143C2×D13—42no—
144C2×D13—42no—
145C2×D13—41no—
146C2×D13—41no—
147C2×D13—42no—
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—41no—
151C4×C13C2×#9911yescharacteristic
152C4×C13#41311yescharacteristic
153Dic13—22no—
154Dic13—41no—
155C22×D4—131no—
156C23×C4—131no—
157C23×C4—131no—
158C22×C8—131no—
159C22×C8—132no—
160C22×C8—132no—
161C22×C8—131no—
162C22×C8—261no—
163C22×C8—261no—
164C22×C8—522no—
165C22×C8—522no—
166C22×C8C2×#26111yescharacteristic
167C22×C8C2×#26111yescharacteristic
168C4×D4—262no—
169C4×D4—262no—
170C2×C4⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—131no—
173C2×C42C2×#26111yescharacteristic
174M32—524no—
175C2×C16—264no—
176C4⋊C8—262no—
177C22⋊C8—262no—
178C22⋊C8—262no—
179C4×C8—21no—
180C4×C8—21no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13#145911yescharacteristic
184C2×C13#211211yescharacteristic
185C2×C13#211511yescharacteristic
186D13—42no—
187D13—42no—
188C24—131no—
189C24—131no—
190C2×D4—262no—
191C2×D4—262no—
192C2×D4—262no—
193C22×C4—131no—
194C22×C4—132no—
195C22×C4—132no—
196C22×C4—131no—
197C22×C4—261no—
198C22×C4—261no—
199C22×C4—521no—
200C22×C4—521no—
201C22×C4—521no—
202C22×C4—521no—
203C22×C4D13⋊C811yescharacteristic
204C22×C4D13⋊C811yescharacteristic
205C22×C4C22×#26111yescharacteristic
206C2×C8—22no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—132no—
210C2×C8—264no—
211C2×C8—261no—
212C2×C8—522no—
213C2×C8—522no—
214C2×C8—521no—
215C2×C8—522no—
216C2×C8—521no—
217C2×C8C22⋊#26111yescharacteristic
218C2×C8C22⋊#26111yescharacteristic
219C4⋊C4—262no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C42—21no—
223C42—21no—
224C16—524no—
225C13#1146611yescharacteristic, complemented, Sylow
226C23—132no—
227C23—132no—
228C23—261no—
229C23—261no—
230C23—261no—
231C23—261no—
232C23—521no—
233C23—521no—
234C23—521no—
235C23—521no—
236C23C2×D13⋊C811yescharacteristic
237D4—268no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—132no—
245C2×C4—262no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4#8809812yescomplemented
255C2×C4D13⋊M1611yescharacteristic
256C2×C4C2×C22⋊#26111yescharacteristic
257C8—21no—
258C8—41no—
259C8—262no—
260C8—521no—
261C8#8810712yes—
262C22—21no—
263C22—21no—
264C22—262no—
265C22—262no—
266C22—262no—
267C22—262no—
268C22—522no—
269C22—522no—
270C22—522no—
271C22—522no—
272C22—521no—
273C22—521no—
274C22C2×#8809811yescharacteristic
275C22D13⋊M3211yescharacteristic
276C22D13⋊(C22⋊C8)11yescharacteristic
277C4—22no—
278C4—21no—
279C4—41no—
280C4—262no—
281C4—521no—
282C4C2×#8810711yescharacteristic
283C4#1171913211yescharacteristic
284C2—21no—
285C2—21no—
286C2—522no—
287C2—522no—
288C2#1313007311yescharacteristic
289C2#1313106411yescharacteristic
290C2#1313107311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×C8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC22×D52C8
cosocleC22×#1055C23
hypercenterC2×C4×C8#261
hypocenterC13#11466
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
1. #13131064C2semidirect
2. #13129772C2semidirect
3. #13129757C2semidirect
95. C22×D13M32semidirect
102. C2×C4×C13M32semidirect
225. C13#11466semidirect
254. C2×C4#88098semidirect

Maximal subgroups

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

subgroupindex
#131310642
#131297722
#131297572
C2×C8×D522
#1146613