Finite Group Databasebeta

← #16782233

Subgroups — #16782233

Order 3328.

418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 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#13130737C211yesmaximal, characteristic
2#13130733C211yesmaximal, characteristic
3#13129684C212yesmaximal
4#13129684C212yesmaximal
5#13117329C211yesmaximal, characteristic
6C2×#88126C2211yescharacteristic
7#11719135C2212yes—
8#11719126C2212yes—
9C4×C13×C4⋊C4C411yescharacteristic, complemented
10#11718651—21no—
11#11718639—21no—
12C4×#6103C2211yescharacteristic
13C4×#6103C2211yescharacteristic
14C4×C4⋊Dic13C411yescharacteristic, complemented
15#11718593C411yescharacteristic, complemented
16C42×Dic13C411yescharacteristic, complemented
17#11718331—21no—
18#11718316—21no—
19#11718291—21no—
20#11718291—21no—
21#11718289—21no—
22#11718289—21no—
23C22×C4×D13C2311yescharacteristic
24C2×C22⋊#261—22no—
25C2×#6122—22no—
26C2×C13×C4⋊C4—21no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×#6103—21no—
31C2×#6103—21no—
32C2×#6103D411yescharacteristic
33C2×#6103D411yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×#6101D411yescharacteristic
36C2×#6101D411yescharacteristic
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42#88126—24no—
43(C2×#261)⋊C4—24no—
44#88111—24no—
45C13×#95—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#8740—131nomaximal, Sylow
52C23×D13C2×D411yescharacteristic
53C22×#261—42no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C2×C4×D13—41no—
65C2×C4×D13—41no—
66C2×C4×D13#4114yes—
67C22⋊#261—42no—
68C22⋊#261—42no—
69#6122—42no—
70#6122—42no—
71C2×#1057—42no—
72C13×C4⋊C4—42no—
73C42×C13—22no—
74C42×C13—41no—
75C42×C13—41no—
76#6103—22no—
77#6103—22no—
78#6103—42no—
79#6103—42no—
80C4⋊Dic13—42no—
81#6101—22no—
82#6101—22no—
83C4×Dic13—22no—
84C4×Dic13—42no—
85C4×Dic13—42no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88#2298—131no—
89#1822—131no—
90#1820—131no—
91#1284—132no—
92#1284—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94C22×D13—21no—
95C22×D13—21no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13#12312yes—
99C2×#261—82no—
100C2×#261—82no—
101C2×#261—82no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13#11712yes—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—22no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13#12312yes—
128C4×D13—44no—
129#1057—82no—
130C2×#117—131no—
131#407—132no—
132#388—261no—
133#388—261no—
134#387—261no—
135#387—261no—
136#381—132no—
137C4×C4⋊C4—131no—
138C4×C4⋊C4#26111yescharacteristic, complemented
139C4×C22⋊C4—131no—
140C4×C22⋊C4—131no—
141#376—131no—
142C43—131no—
143#343—261no—
144#343—261no—
145#342—261no—
146#342—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13#38111yescharacteristic
150C22×C13#41011yescharacteristic
151C22×C13#41011yescharacteristic
152C2×D13—22no—
153C2×D13—22no—
154C2×D13—22no—
155C2×D13—81no—
156C2×D13—81no—
157#261—162no—
158C4×C13—22no—
159C4×C13—42no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—81no—
163Dic13—22no—
164Dic13—42no—
165Dic13—41no—
166Dic13—41no—
167Dic13—81no—
168C23×C4—131no—
169C2×M16—262no—
170#117—264no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—261no—
175C2×C22⋊C4—131no—
176C2×C22⋊C4—131no—
177C2×C22⋊C4—261no—
178C2×C22⋊C4—261no—
179C2×C22⋊C4—262no—
180C2×C42—131no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—261no—
184C2×C42—261no—
185C2×C42C2×#26111yescharacteristic
186C2×C42C2×#26111yescharacteristic
187C2×C42C2×#26111yescharacteristic
188C22⋊C8—264no—
189#95—21no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—264no—
195#95—261no—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13#182011yescharacteristic
199C2×C13#182711yescharacteristic
200C2×C13#182711yescharacteristic
201D13—42no—
202C24—131no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—131no—
206C22×C4—134no—
207C22×C4—131no—
208C22×C4—131no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4—521no—
212C22×C4—521no—
213C22×C4—522no—
214C22×C4C22⋊#26111yescharacteristic
215C22×C4C22⋊#26111yescharacteristic
216C22×C4C22×#26111yescharacteristic
217M16—522no—
218M16—522no—
219C2×C8—522no—
220C4⋊C4—42no—
221C4⋊C4—262no—
222C4⋊C4—262no—
223C4⋊C4—522no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C22⋊C4—522no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—522no—
230C42—22no—
231C42—41no—
232C42—41no—
233C42—262no—
234C42—521no—
235C42—521no—
236C42—522no—
237C42—522no—
238C13#874011yescharacteristic, complemented, Sylow
239C23—132no—
240C23—261no—
241C23—261no—
242C23—521no—
243C23—521no—
244C23C2×C22⋊#26111yescharacteristic
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—132no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—524no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—1042no—
272C2×C4—1042no—
273C2×C4—1042no—
274C2×C4#8823712yes—
275C8—1042no—
276C22—21no—
277C22—21no—
278C22—262no—
279C22—262no—
280C22—262no—
281C22—1041no—
282C22—1041no—
283C22#1171913511yescharacteristic
284C22#1171914211yescharacteristic
285C22#1171915611yescharacteristic
286C4—22no—
287C4—42no—
288C4—41no—
289C4—41no—
290C4—81no—
291C4—262no—
292C4—522no—
293C4—521no—
294C4—521no—
295C4—1041no—
296C4—2082no—
297C2—21no—
298C2—21no—
299C2—522no—
300C2#1313073411yescharacteristic
301C2#1313074511yescharacteristic
302C2#1313074611yescharacteristic
subgroupG/H
centerC22#11719135
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC22×C13#381
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#8740
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. C4×C13×C4⋊C4C4semidirect
14. C4×C4⋊Dic13C4semidirect
15. #11718593C4semidirect
16. C42×Dic13C4semidirect
138. C4×C4⋊C4#261semidirect
238. C13#8740semidirect

Maximal subgroups

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

subgroupindex
#131307372
#131307332
#131296842
#131173292
#874013