Finite Group Databasebeta

← #15760664

Subgroups — #15760664

Order 3328.

610 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117439C211yesmaximal, characteristic, complemented
2#13114916C211yesmaximal, characteristic, complemented
3#13113365C212yesmaximal
4#13112689C212yesmaximal, complemented
5C13×#2501C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#123—21no—
8C2×C13×#121C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C13×#399—22no—
11C13×#390C412yescomplemented
12C13×#384C412yescomplemented
13C4×C13×C22⋊C4C2211yescharacteristic
14#11718873—21no—
15#11718872C2212yes—
16C4×C22⋊Dic13—21no—
17#11718868C2212yes—
18#11718642—24no—
19#11718129—24no—
20#11718122—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C13×#123—44no—
27C13×#123—44no—
28C13×#121—22no—
29C13×#121—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C412yes—
36C2×C13×C4⋊C4D412yes—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—21no—
41C2×C42×C13C2×C412yes—
42C2×C22⋊Dic13—22no—
43C2×C4⋊Dic13—22no—
44C2×C4×Dic13—22no—
45C2×#6099—22no—
46C13×#95—21no—
47#88071—22no—
48#88071—22no—
49#88071—22no—
50#88071D414yes—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53#9464—131nomaximal, Sylow
54C24×C13—21no—
55C24×C13C2×D411yescharacteristic
56C2×D4×C13—22no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13—41no—
61C2×D4×C13—41no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4112yes—
77C22×Dic13—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—24no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—44no—
82C13×C4⋊C4—44no—
83C13×C22⋊C4—24no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—42no—
87C42×C13—42no—
88C22⋊Dic13—44no—
89C4⋊Dic13—82no—
90C4×Dic13—82no—
91#6099—44no—
92C2×#1055—42no—
93#2501D1311yescharacteristic
94#2313—131no—
95#1821—131no—
96#1510—132no—
97#1284—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—42no—
104C23×C13—41no—
105C23×C13—42no—
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13#12011yescharacteristic
108C23×C13#12311yescharacteristic
109D4×C13—82no—
110D4×C13—82no—
111D4×C13—82no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—24no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13C4×D412yes—
131C2×C4×C13#12112yes—
132C2×Dic13—44no—
133C2×Dic13—44no—
134C2×Dic13—44no—
135#1055—82no—
136C2×#123—21no—
137C2×#123—21no—
138C2×#121C2×D1311yescharacteristic
139C22×C4⋊C4C2×D1311yescharacteristic
140#407—132no—
141#399—22no—
142#390Dic1312yescomplemented
143#387—264no—
144#384Dic1312yescomplemented
145#381—132no—
146#380—261no—
147C4×C22⋊C4—261no—
148C4×C22⋊C4C2×D1311yescharacteristic
149#343—262no—
150#327—264no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—44no—
159C22×C13—82no—
160C22×C13—82no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13#38611yescharacteristic
165C22×C13#41012yes—
166C22×C13#45312yes—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—44no—
170C4×C13—42no—
171C4×C13—42no—
172C4×C13—81no—
173Dic13—84no—
174C22×D4—21no—
175C22×D4C2×Dic1311yescharacteristic
176C23×C4C22⋊D1311yescharacteristic
177C23×C4C22⋊D1311yescharacteristic
178C23×C4C22×D1311yescharacteristic
179C2×M16—262no—
180#123—44no—
181#123—44no—
182#121—22no—
183#121—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4C2×Dic1311yescharacteristic
190C2×C4⋊C4C2×Dic1312yes—
191C2×C4⋊C4C22⋊D1312yes—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—262no—
197C2×C42—262no—
198C2×C42C2×Dic1312yes—
199C22⋊C8—262no—
200C22⋊C8—262no—
201#95—21no—
202#95—134no—
203#95—262no—
204#95—262no—
205#95—262no—
206C2×C13—22no—
207C2×C13—22no—
208C2×C13—41no—
209C2×C13—161no—
210C2×C13#188711yescharacteristic
211C2×C13#189911yescharacteristic
212C2×C13#191211yescharacteristic
213C24—21no—
214C24C2×C22⋊D1311yescharacteristic
215C2×D4—22no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—264no—
231C22×C4C22⋊Dic1312yes—
232C22×C4C22⋊Dic1312yes—
233C22×C4D4×D1312yes—
234C22×C4#612912yes—
235C22×C4C22×Dic1311yescharacteristic
236C22×C4C2×C22⋊D1311yescharacteristic
237M16—524no—
238C2×C8—522no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—22no—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4—1042no—
245C22⋊C4—24no—
246C22⋊C4—44no—
247C22⋊C4—44no—
248C22⋊C4—42no—
249C22⋊C4—524no—
250C42—42no—
251C42—1042no—
252C13#946411yescharacteristic, complemented, Sylow
253C23—22no—
254C23—22no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—41no—
260C23—42no—
261C23#8818911yescharacteristic
262C23#8819111yescharacteristic
263C23C2×C22⋊Dic1311yescharacteristic
264D4—82no—
265D4—82no—
266D4—82no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—524no—
286C2×C4—524no—
287C2×C4—524no—
288C2×C4D4×Dic1312yes—
289C2×C4#8819312yes—
290C8—1042no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—82no—
300C22—82no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22#1171873812yes—
305C22#1171888111yescharacteristic
306C22#1171890112yes—
307C4—22no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—42no—
312C4—81no—
313C4—1044no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—161no—
318C2#1311523511yescharacteristic
319C2#1311529511yescharacteristic
320C2#1311537411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2501C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2501D13
hypocenterC13#9464
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. #13117439C2semidirect
2. #13114916C2semidirect
4. #13112689C2semidirect
11. C13×#390C4semidirect
12. C13×#384C4semidirect
142. #390Dic13semidirect
144. #384Dic13semidirect
252. C13#9464semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131149162
#131133652
#131126892
C13×#25012
#946413