Finite Group Databasebeta

← #16780712

Subgroups — #16780712

Order 3328.

684 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 134 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#13130621C212yesmaximal, complemented
2C2×#11718297C212yesmaximal
3#13129714C212yesmaximal, complemented
4C4×#88194C211yesmaximal, characteristic
5C2×C4×D4×C13C411yescharacteristic
6C2×#88194C2211yescharacteristic
7C2×C4×C22⋊D13—22no—
8C2×C4×D52C411yescharacteristic
9C2×#88112C2214yes—
10C2×#88110—22no—
11#11718882C411yescharacteristic
12#11718649C411yescharacteristic
13#11718637C2211yescharacteristic
14#11718618—22no—
15C42×Dic13C2211yescharacteristic
16#11718297C418yescomplemented
17#11718290—22no—
18C22×D4×C13C2×C411yescharacteristic
19C23×C4×C13—21no—
20C22×C22⋊D13—22no—
21C22×D52C2×C411yescharacteristic
22C22×C4×D13—21no—
23C22×#1057—24no—
24C4×D4×C13—42no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C22⋊C4—21no—
27C2×C42×C13C2×C411yescharacteristic
28C2×C22⋊Dic13—22no—
29#88194—22no—
30#88194C2×C414yes—
31C4×C22⋊D13—48no—
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—
41#88112—24no—
42#88112C2×C418yescomplemented
43#88110—44no—
44#8231—131nomaximal, Sylow
45C24×C13—21no—
46C23×D13—21no—
47C2×D4×C13—21no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13C4212yes—
51C22×C4×C13—21no—
52C22×C4×C13—44no—
53C22×C4×C13—42no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C2×C22⋊D13—28no—
58C2×C22⋊D13—44no—
59C2×C22⋊D13—42no—
60C2×C22⋊D13—42no—
61C22×Dic13—21no—
62C22×Dic13C22⋊C412yes—
63C22×Dic13C2×D412yes—
64C2×D52—21no—
65C2×D52—41no—
66C2×D52—41no—
67C2×D52C4212yes—
68C2×C4×D13—44no—
69C2×C4×D13—42no—
70C2×#1057—28no—
71C2×#1057—44no—
72C2×#1057—44no—
73C13×C4⋊C4—41no—
74C13×C22⋊C4—42no—
75C42×C13—22no—
76C22⋊Dic13—44no—
77#6103—44no—
78#6103—42no—
79C4⋊Dic13—41no—
80#6101—44no—
81C4×Dic13—22no—
82C4×Dic13—24no—
83C4×Dic13—22no—
84C4×Dic13—41no—
85C4×Dic13C22×C412yes—
86C4×Dic13#4112yes—
87C4×#127—131no—
88#1767—132no—
89C2×#331—132no—
90#1296—132no—
91C23×C13—22no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—22no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—42no—
101C22×D13—42no—
102D4×C13—42no—
103D4×C13—42no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—84no—
112C2×C4×C13#10012yes—
113C2×C4×C13C2×C4211yescharacteristic
114C2×C4×C13#11711yescharacteristic
115C22⋊D13—48no—
116C22⋊D13—48no—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—22no—
120C2×Dic13—41no—
121C2×Dic13—42no—
122C2×Dic13C4×D414yes—
123C2×Dic13AGL(1,ℤ/8)14yes—
124C2×Dic13AGL(1,ℤ/8)12yes—
125C2×Dic13#13712yes—
126D52—42no—
127D52—42no—
128C4×D13—84no—
129#1057—48no—
130C2×#127—131no—
131C2×C4×D4—131no—
132C2×C4×D4—262no—
133C2×C4×D4#26111yescharacteristic
134C2×C4⋊C8—134no—
135C2×#97—262no—
136#390—131no—
137#390—131no—
138#390—262no—
139#384—131no—
140C43—131no—
141#336—262no—
142#331—138no—
143C22×C13—42no—
144C22×C13—44no—
145C22×C13—81no—
146C22×C13—82no—
147C22×C13—81no—
148C22×C13C4×C22⋊C411yescharacteristic
149C22×C13C2×#10011yescharacteristic
150C22×C13#41311yescharacteristic
151C22×C13#41712yes—
152C22×C13#41812yes—
153C2×D13—42no—
154C2×D13—44no—
155C2×D13—81no—
156C2×D13—82no—
157C2×D13—81no—
158C4×C13—22no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13—81no—
163Dic13—42no—
164Dic13—81no—
165Dic13#44014yes—
166Dic13#44214yes—
167C22×D4—131no—
168C22×D4—262no—
169C22×D4C2×#26111yescharacteristic
170C23×C4—21no—
171C23×C4—261no—
172C22×C8—264no—
173#127—134no—
174#127—262no—
175C4×D4—42no—
176C4×D4—522no—
177C4×D4—528no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—262no—
180C2×C4⋊C4C2×#26111yescharacteristic
181C2×C22⋊C4—21no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4—262no—
184C2×C22⋊C4—261no—
185C2×C42—131no—
186C2×C42—132no—
187C2×C42—132no—
188C2×C42—131no—
189C2×C42C2×#26111yescharacteristic
190C4⋊C8—138no—
191C4⋊C8—264no—
192#97—524no—
193C2×C13—82no—
194C2×C13#155511yescharacteristic
195C2×C13#155712yes—
196C2×C13#156011yescharacteristic
197C2×C13C4×#10011yescharacteristic
198C2×C13#176212yes—
199D13—82no—
200C24—21no—
201C24—261no—
202C2×D4—21no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—132no—
206C2×D4—268no—
207C2×D4—261no—
208C2×D4—521no—
209C2×D4—521no—
210C2×D4—524no—
211C2×D4—522no—
212C2×D4—522no—
213C2×D4C4×#26112yes—
214C22×C4—21no—
215C22×C4—44no—
216C22×C4—42no—
217C22×C4—132no—
218C22×C4—132no—
219C22×C4—261no—
220C22×C4—524no—
221C22×C4—522no—
222C22×C4C22⋊#26111yescharacteristic
223C22×C4C22⋊#26111yescharacteristic
224C22×C4C22×#26111yescharacteristic
225C2×C8—268no—
226C2×C8—524no—
227C2×C8—524no—
228C4⋊C4—41no—
229C4⋊C4—521no—
230C4⋊C4—524no—
231C22⋊C4—42no—
232C22⋊C4—522no—
233C22⋊C4—524no—
234C22⋊C4—524no—
235C42—22no—
236C42—132no—
237C42—132no—
238C42—262no—
239C42—264no—
240C42—262no—
241C42—521no—
242C13#823111yescharacteristic, complemented, Sylow
243C23—22no—
244C23—41no—
245C23—41no—
246C23—42no—
247C23—42no—
248C23—262no—
249C23—521no—
250C23—521no—
251C23—522no—
252C23—522no—
253C23C2×C22⋊#26111yescharacteristic
254D4—42no—
255D4—42no—
256D4—522no—
257D4—522no—
258D4—528no—
259D4—528no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—84no—
268C2×C4—134no—
269C2×C4—134no—
270C2×C4—132no—
271C2×C4—132no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—521no—
276C2×C4—522no—
277C2×C4—1044no—
278C2×C4#8812112yes—
279C2×C4C2×C4×#26111yescharacteristic
280C2×C4#8823711yescharacteristic
281C8—528no—
282C22—42no—
283C22—44no—
284C22—81no—
285C22—82no—
286C22—81no—
287C22—522no—
288C22—524no—
289C22—1041no—
290C22—1042no—
291C22—1041no—
292C22#1171913211yescharacteristic
293C22C4×C22⋊#26111yescharacteristic
294C22#1171913812yes—
295C22#1171916412yes—
296C22C2×#8812111yescharacteristic
297C4—21no—
298C4—21no—
299C4—22no—
300C4—41no—
301C4—81no—
302C4—134no—
303C4—134no—
304C4—522no—
305C4—1041no—
306C2—82no—
307C2—1042no—
308C2#1313036311yescharacteristic
309C2#1313036712yes—
310C2#1313037311yescharacteristic
311C2C4×#8812111yescharacteristic
312C2#1313060612yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C4×D4×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC2×#88194C22
cosocleC2×C4×Dic13C23
hypercenterC2×C4×D4#261
hypocenterC13#8231
LCSG ▷ C2×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. #13130621C2semidirect
3. #13129714C2semidirect
16. #11718297C4semidirect
42. #88112C2×C4semidirect
242. C13#8231semidirect

Maximal subgroups

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

subgroupindex
#131306212
C2×#117182972
#131297142
C4×#881942
#823113