Finite Group Databasebeta

← #16778558

Subgroups — #16778558

Order 3328.

624 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 122 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#13130753C212yesmaximal, 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×C4⋊#1057—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—44no—
31C4×C22⋊D13—44no—
32C2×#6103—21no—
33C2×#6103—22no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—22no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D412yes—
38C2×C4×Dic13D412yes—
39C2×C4×Dic13C2311yescharacteristic
40C4×D52—42no—
41C4⋊#1057—44no—
42#7651—131nomaximal, Sylow
43C24×C13—21no—
44C23×D13—21no—
45C2×D4×C13—21no—
46C2×D4×C13—41no—
47C2×D4×C13—41no—
48C2×D4×C13M1612yes—
49C22×C4×C13—21no—
50C22×C4×C13—42no—
51C22×C4×C13—44no—
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22×C411yescharacteristic
55C2×C22⋊D13—28no—
56C2×C22⋊D13—44no—
57C2×C22⋊D13—44no—
58C22×Dic13—21no—
59C22×Dic13C22⋊C412yes—
60C22×Dic13C2×D412yes—
61C2×D52—21no—
62C2×D52—41no—
63C2×D52—41no—
64C2×D52M1612yes—
65C2×C4×D13—42no—
66C2×C4×D13—44no—
67C2×#1057—44no—
68C2×#1057—44no—
69C2×#1057—44no—
70C13×C4⋊C4—41no—
71C13×C22⋊C4—42no—
72C42×C13—22no—
73C22⋊Dic13—42no—
74C22⋊Dic13—42no—
75#6103—42no—
76#6103—42no—
77#6103—42no—
78C4⋊Dic13—41no—
79#6101—44no—
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—42no—
83C4×Dic13—41no—
84C4×Dic13D814yes—
85C4×Dic13SD1614yes—
86C4×#127—131no—
87#1831—132no—
88#1270—132no—
89#1270—132no—
90C23×C13—22no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13C2×C22⋊C411yescharacteristic
96C22×D13—22no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—42no—
100C22×D13—42no—
101D4×C13—42no—
102D4×C13—42no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—84no—
110C2×C4×C13#10012yes—
111C2×C4×C13#10214yes—
112C2×C4×C13C2×M1611yescharacteristic
113C2×C4×C13C2×M1611yescharacteristic
114C22⋊D13—416no—
115C2×Dic13—22no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—41no—
120C2×Dic13—42no—
121C2×Dic13#10214yes—
122C2×Dic13C2×D812yes—
123C2×Dic13C2×SD1612yes—
124D52—42no—
125D52—42no—
126C4×D13—84no—
127#1057—84no—
128C2×#127—131no—
129C2×C4×D4—131no—
130C2×C4×D4—262no—
131C2×C4×D4#26111yescharacteristic
132C2×C4⋊C8—262no—
133#390—131no—
134#390—131no—
135#390—262no—
136#384—131no—
137C43—131no—
138#336—134no—
139#336—262no—
140C22×C13—42no—
141C22×C13—44no—
142C22×C13—81no—
143C22×C13—81no—
144C22×C13—82no—
145C22×C13#40711yescharacteristic
146C22×C13#41011yescharacteristic
147C22×C13C2×#10011yescharacteristic
148C22×C13C2×#10212yes—
149C22×C13#42112yes—
150C2×D13—42no—
151C2×D13—44no—
152C2×D13—81no—
153C2×D13—81no—
154C2×D13—82no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—81no—
159C4×C13#33114yes—
160Dic13—24no—
161Dic13—22no—
162Dic13—22no—
163Dic13—81no—
164C22×D4—131no—
165C22×D4—262no—
166C22×D4C2×#26111yescharacteristic
167C23×C4—21no—
168C23×C4—261no—
169C22×C8—264no—
170#127—262no—
171#127—262no—
172C4×D4—42no—
173C4×D4—522no—
174C4×D4—524no—
175C4×D4—524no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4C2×#26111yescharacteristic
179C2×C22⋊C4—21no—
180C2×C22⋊C4—262no—
181C2×C22⋊C4—262no—
182C2×C22⋊C4—261no—
183C2×C42—132no—
184C2×C42—131no—
185C2×C42—132no—
186C2×C42—131no—
187C2×C42C2×#26111yescharacteristic
188C4⋊C8—524no—
189C2×C13—82no—
190C2×C13#146611yescharacteristic
191C2×C13#148612yes—
192C2×C13#151712yes—
193C2×C13#153611yescharacteristic
194C2×C13C2×#33111yescharacteristic
195D13—82no—
196C24—21no—
197C24—261no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—132no—
202C2×D4—268no—
203C2×D4—261no—
204C2×D4—521no—
205C2×D4—521no—
206C2×D4—524no—
207C2×D4—524no—
208C2×D4#611812yes—
209C22×C4—21no—
210C22×C4—44no—
211C22×C4—42no—
212C22×C4—132no—
213C22×C4—132no—
214C22×C4—261no—
215C22×C4—524no—
216C22×C4—522no—
217C22×C4C22⋊#26111yescharacteristic
218C22×C4C22⋊#26111yescharacteristic
219C22×C4C22×#26111yescharacteristic
220C2×C8—524no—
221C2×C8—524no—
222C2×C8—524no—
223C4⋊C4—41no—
224C4⋊C4—521no—
225C4⋊C4—524no—
226C22⋊C4—42no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—522no—
230C22⋊C4—522no—
231C22⋊C4—522no—
232C42—22no—
233C42—134no—
234C42—134no—
235C42—261no—
236C42—261no—
237C42—521no—
238C42—522no—
239C13#765111yescharacteristic, complemented, Sylow
240C23—22no—
241C23—41no—
242C23—41no—
243C23—42no—
244C23—42no—
245C23—262no—
246C23—521no—
247C23—521no—
248C23—522no—
249C23—522no—
250C23C2×C22⋊#26111yescharacteristic
251D4—42no—
252D4—42no—
253D4—522no—
254D4—522no—
255D4—5216no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—84no—
263C2×C4—132no—
264C2×C4—132no—
265C2×C4—134no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—521no—
271C2×C4—522no—
272C2×C4—1044no—
273C2×C4#8811514yes—
274C2×C4#8812112yes—
275C2×C4C2×#611811yescharacteristic
276C2×C4D13⋊M1611yescharacteristic
277C8—1044no—
278C22—42no—
279C22—44no—
280C22—82no—
281C22—81no—
282C22—81no—
283C22—522no—
284C22—524no—
285C22—1042no—
286C22—1041no—
287C22—1041no—
288C22#1171911611yescharacteristic
289C22#1171912711yescharacteristic
290C22C2×#8811512yes—
291C22#1171916612yes—
292C22C2×#8812111yescharacteristic
293C4—21no—
294C4—21no—
295C4—41no—
296C4—81no—
297C4—262no—
298C4—262no—
299C4—264no—
300C4—1041no—
301C4#1171829714yes—
302C2—82no—
303C2—1042no—
304C2#1313009511yescharacteristic
305C2#1313016212yes—
306C2#1313026612yes—
307C2#1313032411yescharacteristic
308C2C2×#1171829711yescharacteristic
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#7651
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. #13130753C2semidirect
2. #13129653C2semidirect
3. #13129652C2semidirect
239. C13#7651semidirect

Maximal subgroups

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

subgroupindex
#131307532
#131296532
#131296522
C4×#881942
#765113