Finite Group Databasebeta

← #16778510

Subgroups — #16778510

Order 3328.

636 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 98 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#13130553C212yesmaximal, complemented
2#13129653C212yesmaximal, complemented
3#13129652C212yesmaximal, complemented
4C4×#88194C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88194C411yescharacteristic
7C2×C4×C22⋊D13—22no—
8C2×C4×D52C411yescharacteristic
9C2×#88110—22no—
10#11718882C2211yescharacteristic
11#11718649C2211yescharacteristic
12#11718637C411yescharacteristic
13#11718618—22no—
14C42×Dic13C2211yescharacteristic
15#11718290—22no—
16#11718290C2214yes—
17C22×D4×C13C2×C411yescharacteristic
18C23×C4×C13—21no—
19C22×C22⋊D13—22no—
20C22×D52C2×C411yescharacteristic
21C22×C4×D13—21no—
22C22×#1057—24no—
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#88194—22no—
30C4×C22⋊D13—48no—
31C2×#6103—21no—
32C2×#6103—22no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—22no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13D412yes—
37C2×C4×Dic13D412yes—
38C2×C4×Dic13C2311yescharacteristic
39C4×D52—42no—
40#88110—28no—
41#7637—131nomaximal, Sylow
42C24×C13—21no—
43C23×D13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—41no—
46C2×D4×C13—41no—
47C2×D4×C13M1612yes—
48C22×C4×C13—21no—
49C22×C4×C13—44no—
50C22×C4×C13—42no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C2×C22⋊D13—28no—
55C2×C22⋊D13—44no—
56C2×C22⋊D13—44no—
57C22×Dic13—21no—
58C22×Dic13C22⋊C412yes—
59C22×Dic13C2×D412yes—
60C2×D52—21no—
61C2×D52—41no—
62C2×D52—41no—
63C2×D52M1612yes—
64C2×C4×D13—44no—
65C2×C4×D13—42no—
66C2×#1057—28no—
67C2×#1057—44no—
68C2×#1057—44no—
69C13×C4⋊C4—41no—
70C13×C22⋊C4—42no—
71C42×C13—22no—
72C22⋊Dic13—44no—
73#6103—42no—
74#6103—44no—
75C4⋊Dic13—41no—
76#6101—44no—
77C4×Dic13—21no—
78C4×Dic13—21no—
79C4×Dic13—24no—
80C4×Dic13—24no—
81C4×Dic13—41no—
82C4×#127—131no—
83#1745—132no—
84#1270—132no—
85#1270—132no—
86C23×C13—22no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13—42no—
90C23×C13—42no—
91C23×C13C2×C22⋊C411yescharacteristic
92C22×D13—22no—
93C22×D13—41no—
94C22×D13—41no—
95C22×D13—42no—
96C22×D13—42no—
97D4×C13—42no—
98D4×C13—42no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—22no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—84no—
107C2×C4×C13#10012yes—
108C2×C4×C13C2×M1611yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110C22⋊D13—416no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—41no—
116C2×Dic13—42no—
117C2×Dic13#10414yes—
118C2×Dic13AGL(1,ℤ/8)14yes—
119D52—42no—
120D52—42no—
121C4×D13—84no—
122#1057—48no—
123C2×#127—131no—
124C2×C4×D4—131no—
125C2×C4×D4—262no—
126C2×C4×D4#26111yescharacteristic
127C2×#97—262no—
128#390—131no—
129#390—131no—
130#390—262no—
131#384—131no—
132C43—131no—
133#336—134no—
134#336—262no—
135C22×C13—42no—
136C22×C13—44no—
137C22×C13—81no—
138C22×C13—82no—
139C22×C13—81no—
140C22×C13#40711yescharacteristic
141C22×C13#41011yescharacteristic
142C22×C13C2×#10011yescharacteristic
143C22×C13#41812yes—
144C22×C13C2×#10412yes—
145C2×D13—42no—
146C2×D13—44no—
147C2×D13—81no—
148C2×D13—82no—
149C2×D13—81no—
150C4×C13—22no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—41no—
154C4×C13—81no—
155Dic13—24no—
156Dic13—24no—
157Dic13—81no—
158C22×D4—131no—
159C22×D4—262no—
160C22×D4C2×#26111yescharacteristic
161C23×C4—21no—
162C23×C4—261no—
163C22×C8—264no—
164#127—262no—
165#127—262no—
166C4×D4—42no—
167C4×D4—522no—
168C4×D4—528no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—262no—
171C2×C4⋊C4C2×#26111yescharacteristic
172C2×C22⋊C4—21no—
173C2×C22⋊C4—262no—
174C2×C22⋊C4—262no—
175C2×C22⋊C4—261no—
176C2×C42—132no—
177C2×C42—132no—
178C2×C42—131no—
179C2×C42—131no—
180C2×C42C2×#26111yescharacteristic
181#97—268no—
182C2×C13—82no—
183C2×C13#146611yescharacteristic
184C2×C13#149012yes—
185C2×C13#150512yes—
186C2×C13#152511yescharacteristic
187C2×C13#155511yescharacteristic
188D13—82no—
189C24—21no—
190C24—261no—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4—132no—
195C2×D4—268no—
196C2×D4—261no—
197C2×D4—521no—
198C2×D4—521no—
199C2×D4—524no—
200C2×D4—524no—
201C2×D4#611812yes—
202C22×C4—21no—
203C22×C4—44no—
204C22×C4—42no—
205C22×C4—132no—
206C22×C4—132no—
207C22×C4—261no—
208C22×C4—524no—
209C22×C4—522no—
210C22×C4C22⋊#26111yescharacteristic
211C22×C4C22⋊#26111yescharacteristic
212C22×C4C22×#26111yescharacteristic
213C2×C8—268no—
214C2×C8—524no—
215C2×C8—524no—
216C4⋊C4—41no—
217C4⋊C4—521no—
218C4⋊C4—524no—
219C22⋊C4—42no—
220C22⋊C4—522no—
221C22⋊C4—524no—
222C22⋊C4—524no—
223C42—22no—
224C42—264no—
225C42—264no—
226C42—261no—
227C42—261no—
228C42—521no—
229C13#763711yescharacteristic, complemented, Sylow
230C23—22no—
231C23—41no—
232C23—41no—
233C23—42no—
234C23—42no—
235C23—262no—
236C23—521no—
237C23—521no—
238C23—522no—
239C23—522no—
240C23C2×C22⋊#26111yescharacteristic
241D4—42no—
242D4—42no—
243D4—522no—
244D4—522no—
245D4—5216no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—84no—
254C2×C4—134no—
255C2×C4—134no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—521no—
261C2×C4—522no—
262C2×C4—1044no—
263C2×C4#8812112yes—
264C2×C4C2×#611811yescharacteristic
265C2×C4D13⋊M1611yescharacteristic
266C8—528no—
267C22—42no—
268C22—44no—
269C22—81no—
270C22—81no—
271C22—82no—
272C22—522no—
273C22—524no—
274C22—1041no—
275C22—1041no—
276C22—1042no—
277C22#1171911611yescharacteristic
278C22#1171912711yescharacteristic
279C22#1171913812yes—
280C22D13⋊#10412yes—
281C22C2×#8812111yescharacteristic
282C4—21no—
283C4—21no—
284C4—22no—
285C4—41no—
286C4—81no—
287C4—264no—
288C4—264no—
289C4—1041no—
290C2—82no—
291C2—1042no—
292C2#1313009511yescharacteristic
293C2#1313017612yes—
294C2#1313022612yes—
295C2#1313029011yescharacteristic
296C2#1313036311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC2×#88194C4
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#7637
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #13130553C2semidirect
2. #13129653C2semidirect
3. #13129652C2semidirect
229. C13#7637semidirect

Maximal subgroups

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

subgroupindex
#131305532
#131296532
#131296522
C4×#881942
#763713