Finite Group Databasebeta

← #16786910

Subgroups — #16786910

Order 3328.

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

normal subgroups only

This group has 524 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#13130073C212yesmaximal, complemented
2#13129777C212yesmaximal, complemented
3#13129764C212yesmaximal, complemented
4#13117558C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88194C411yescharacteristic
7C2×C4×D52C2211yescharacteristic
8D13⋊(C22⋊C8)—22no—
9#11718882C2211yescharacteristic
10#11718874—22no—
11#11718649C411yescharacteristic
12#11718638C2211yescharacteristic
13#11718617—22no—
14#11718593C411yescharacteristic
15#11718287—22no—
16#11718285C2214yes—
17C22×D4×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C22×C22⋊D13—22no—
20C22×D52C2×C411yescharacteristic
21C22×C4×D13D412yes—
22C2×D13⋊C8—42no—
23C4×D4×C13—42no—
24C2×C13×C4⋊C4C2×C411yescharacteristic
25C2×C13×C22⋊C4—21no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—22no—
28#88194—22no—
29#88194C814yescomplemented
30C2×#6103—22no—
31C2×#6103D412yes—
32C2×C4⋊Dic13C2311yescharacteristic
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C4×D52—42no—
36C22⋊#1057—24no—
37#88111—42no—
38#88071—21no—
39#88071—21no—
40#88071—22no—
41#11479—131nomaximal, Sylow
42C24×C13—21no—
43C23×D13C22⋊C412yes—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13C2×C812yescomplemented
48C22×C4×C13—21no—
49C22×C4×C13—42no—
50C22×C4×C13—82no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—28no—
55C2×C22⋊D13—82no—
56C2×C22⋊D13—82no—
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13C2×D412yes—
60C2×D52—41no—
61C2×D52—41no—
62C2×D52C2×C812yes—
63C2×D52M1612yes—
64C2×C4×D13—22no—
65C2×C4×D13—22no—
66C2×C4×D13—82no—
67C2×#1057—44no—
68D13⋊C8—84no—
69C13×C4⋊C4—41no—
70C13×C22⋊C4—42no—
71C42×C13—22no—
72C22⋊Dic13—82no—
73#6103—42no—
74#6103—82no—
75C4⋊Dic13—41no—
76C4×Dic13—21no—
77C4×Dic13—41no—
78C4×Dic13C2×C812yescomplemented
79#2328—131no—
80#1459—132no—
81#1324—132no—
82#1318—132no—
83C23×C13—22no—
84C23×C13—42no—
85C23×C13—42no—
86C23×C13—41no—
87C23×C13—41no—
88C23×C13C2×C22⋊C411yescharacteristic
89C22×D13—22no—
90C22×D13—22no—
91C22×D13—42no—
92C22×D13—42no—
93C22×D13C22⋊C814yes—
94D4×C13—42no—
95D4×C13—42no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—42no—
102C2×C4×C13—41no—
103C2×C4×C13—84no—
104C2×C4×C13#9912yes—
105C2×C4×C13C22×C811yescharacteristic
106C2×C4×C13C2×M1611yescharacteristic
107C22⋊D13—88no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—42no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116D52—42no—
117D52—42no—
118C4×D13—44no—
119C4×D13—82no—
120#1057—84no—
121C2×#127—131no—
122C2×C4×D4—131no—
123C2×C4×D4#26111yescharacteristic
124C2×C22⋊C8—262no—
125#390—131no—
126#390—131no—
127#386—262no—
128#386—262no—
129#382—131no—
130#376—131no—
131#324—134no—
132#323—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—44no—
136C22×C13—42no—
137C22×C13—82no—
138C22×C13—81no—
139C22×C13—81no—
140C22×C13C2×C22⋊C811yescharacteristic
141C22×C13C2×#9911yescharacteristic
142C22×C13#41311yescharacteristic
143C2×D13—24no—
144C2×D13—42no—
145C2×D13—42no—
146C2×D13—44no—
147C2×D13—82no—
148C4×C13—22no—
149C4×C13—21no—
150C4×C13—21no—
151C4×C13—41no—
152C4×C13—81no—
153Dic13—42no—
154Dic13—42no—
155Dic13—81no—
156C22×D4—131no—
157C22×D4—262no—
158C22×D4C2×#26111yescharacteristic
159C23×C4—21no—
160C23×C4—132no—
161C22×C8—522no—
162#127—134no—
163#127—262no—
164C4×D4—42no—
165C4×D4—522no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4C2×#26111yescharacteristic
168C2×C22⋊C4—21no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—262no—
171C2×C22⋊C4—262no—
172C2×C42—131no—
173C2×C42—131no—
174C2×C42C2×#26111yescharacteristic
175C22⋊C8—264no—
176C22⋊C8—522no—
177#95—262no—
178#95—261no—
179#95—261no—
180C2×C13—21no—
181C2×C13—21no—
182C2×C13—82no—
183C2×C13#145911yescharacteristic
184C2×C13#212711yescharacteristic
185C2×C13#213411yescharacteristic
186D13—44no—
187C24—21no—
188C24—132no—
189C2×D4—21no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—132no—
193C2×D4—132no—
194C2×D4—268no—
195C2×D4—521no—
196C2×D4—521no—
197C2×D4—1042no—
198C2×D4—1042no—
199C2×D4D13⋊C812yescomplemented
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—82no—
203C22×C4—132no—
204C22×C4—261no—
205C22×C4—262no—
206C22×C4—262no—
207C22×C4—261no—
208C22×C4—1042no—
209C22×C4C22⋊#26111yescharacteristic
210C22×C4C22⋊#26111yescharacteristic
211C22×C4C22×#26111yescharacteristic
212C2×C8—524no—
213C2×C8—1044no—
214C4⋊C4—41no—
215C4⋊C4—521no—
216C22⋊C4—42no—
217C22⋊C4—522no—
218C22⋊C4—1042no—
219C22⋊C4—1042no—
220C42—22no—
221C42—132no—
222C42—261no—
223C42—521no—
224C13#1147911yescharacteristic, complemented, Sylow
225C23—22no—
226C23—42no—
227C23—42no—
228C23—41no—
229C23—41no—
230C23—134no—
231C23—262no—
232C23—262no—
233C23—522no—
234C23—522no—
235C23C2×C22⋊#26111yescharacteristic
236D4—42no—
237D4—42no—
238D4—522no—
239D4—522no—
240D4—1048no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—84no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—524no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—522no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—1042no—
259C2×C4#8811912yes—
260C2×C4C2×D13⋊C811yescharacteristic
261C2×C4D13⋊M1611yescharacteristic
262C8—1044no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22—42no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22—264no—
271C22—524no—
272C22—522no—
273C22—522no—
274C22—1042no—
275C22D13⋊(C22⋊C8)11yescharacteristic
276C22#1171913211yescharacteristic
277C22C2×#8811911yescharacteristic
278C4—21no—
279C4—21no—
280C4—22no—
281C4—41no—
282C4—81no—
283C4—522no—
284C4—522no—
285C4—1041no—
286C2—21no—
287C2—21no—
288C2—82no—
289C2—524no—
290C2#1313007111yescharacteristic
291C2#1313111111yescharacteristic
292C2#1313113511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC22×C13C2×#99
prime radicalC2×#88194C4
cosocleC2×C4⋊Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#11479
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13130073C2semidirect
2. #13129777C2semidirect
3. #13129764C2semidirect
29. #88194C8semidirect
47. C2×D4×C13C2×C8semidirect
78. C4×Dic13C2×C8semidirect
199. C2×D4D13⋊C8semidirect
224. C13#11479semidirect

Maximal subgroups

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

subgroupindex
#131300732
#131297772
#131297642
#131175582
#1147913