Finite Group Databasebeta

← #15760673

Subgroups — #15760673

Order 3328.

726 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 111 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#13118490C211yesmaximal, characteristic
2#13114760C211yesmaximal, characteristic, complemented
3#13113364C212yesmaximal
4#13112688C212yesmaximal, complemented
5C13×#2310C211yesmaximal, characteristic, complemented
6C23×Q8×C13C2211yescharacteristic
7C2×C13×#117—21no—
8C2×#88201C412yescomplemented
9C2×#88184C2211yescharacteristic
10C13×#391—24no—
11C13×#381—21no—
12C13×#381C2212yes—
13#11718892—22no—
14#11718891C412yescomplemented
15C2×#88076—22no—
16#11718874—21no—
17#11718874—21no—
18C4×C22⋊Dic13C2211yescharacteristic
19#11718868C2212yes—
20#11718043—24no—
21C22×Q8×C13—22no—
22C22×Q8×C13—22no—
23C22×Q8×C13—44no—
24C22×Q8×C13C2×C412yes—
25C22×Q8×C13D412yes—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C22×C22⋊D13—21no—
30C22×D52C2×C411yescharacteristic
31C13×#117—44no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C42×C13—22no—
35C2×C22⋊Dic13—21no—
36#88201—44no—
37#88184—22no—
38#88184—22no—
39C2×#6103—22no—
40C2×#6103—22no—
41C2×#6103—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×C4×Dic13C2×C412yes—
44C2×#6099—22no—
45C13×#95—24no—
46C13×#95—22no—
47C13×#95D414yes—
48#88076—44no—
49#88071—22no—
50#88071—22no—
51#88071—21no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54#9466—131nomaximal, Sylow
55C24×C13C2×D411yescharacteristic
56C23×D13—21no—
57C2×Q8×C13—24no—
58C2×Q8×C13—24no—
59C2×Q8×C13—24no—
60C2×Q8×C13—24no—
61C2×Q8×C13—42no—
62C2×Q8×C13—42no—
63C2×Q8×C13—44no—
64C2×Q8×C13—44no—
65C2×Q8×C13—48no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—24no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—24no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C412yes—
75C22×C4×C13C22⋊C412yes—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D412yes—
79C22×C4×C13#4112yes—
80C2×C22⋊D13—44no—
81C2×C22⋊D13—41no—
82C2×C22⋊D13—41no—
83C22×Dic13—21no—
84C22×Dic13—22no—
85C2×D52—22no—
86C2×D52—42no—
87C13×C4⋊C4—44no—
88C13×C22⋊C4—44no—
89C42×C13—44no—
90C22⋊Dic13—42no—
91#6103—44no—
92#6103—44no—
93#6103—42no—
94C4⋊Dic13—22no—
95C4×Dic13—42no—
96#6099—44no—
97C2×#1055—42no—
98#2436—131no—
99#2310D1311yescharacteristic, complemented
100#1784—131no—
101#1510—132no—
102#1284—132no—
103C23×C13—22no—
104C23×C13—22no—
105C23×C13—41no—
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13#12011yescharacteristic
108C23×C13#12311yescharacteristic
109C22×D13—42no—
110C22×D13—42no—
111C22×D13—41no—
112C22×D13—42no—
113Q8×C13—48no—
114Q8×C13—48no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—44no—
130C2×C4×C13—44no—
131C2×C4×C13—44no—
132C2×C4×C13#9914yes—
133C2×C4×C13C4×D412yes—
134C2×C4×C13#12112yes—
135C22⋊D13—82no—
136C22⋊D13—82no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—41no—
141C2×Dic13—42no—
142D52—82no—
143#1055—82no—
144C23×Q8C2×D1311yescharacteristic
145C2×#124—132no—
146C2×#121—131no—
147C2×#117—21no—
148C2×#101—262no—
149#407—132no—
150#393—262no—
151#391—24no—
152#391—132no—
153#386—261no—
154#386—261no—
155#381—21no—
156#381C2×D1312yes—
157C4×C22⋊C4—131no—
158#327—264no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—44no—
167C22×C13#38611yescharacteristic
168C22×C13C2×#9912yes—
169C22×C13#45412yes—
170C2×D13—84no—
171C2×D13—81no—
172C2×D13—81no—
173C2×D13—81no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—24no—
177C4×C13—42no—
178C4×C13—84no—
179Dic13—82no—
180Dic13—81no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—44no—
184C22×Q8C4×D1312yes—
185C22×Q8D5212yes—
186C22×D4—131no—
187C22×D4—261no—
188C23×C4C22⋊D1311yescharacteristic
189C23×C4C22⋊D1311yescharacteristic
190C23×C4C22×D1311yescharacteristic
191C2×M16—262no—
192#124—524no—
193#121—262no—
194#121—262no—
195#117—44no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—131no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4—262no—
201C2×C22⋊C4—262no—
202C2×C22⋊C4—261no—
203C2×C42—22no—
204C2×C42—132no—
205#101—524no—
206C22⋊C8—262no—
207C22⋊C8—262no—
208#95—24no—
209#95—22no—
210#95—262no—
211#95—262no—
212#95—261no—
213#95C22⋊D1314yes—
214C2×C13—22no—
215C2×C13—22no—
216C2×C13—41no—
217C2×C13#188811yescharacteristic
218C2×C13#189811yescharacteristic
219C2×C13#191211yescharacteristic
220D13—161no—
221C24—261no—
222C24C2×C22⋊D1311yescharacteristic
223C2×Q8—24no—
224C2×Q8—24no—
225C2×Q8—24no—
226C2×Q8—24no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—44no—
230C2×Q8—44no—
231C2×Q8—48no—
232C2×D4—262no—
233C2×D4—522no—
234C2×D4—524no—
235C2×D4—521no—
236C2×D4—521no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—24no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—261no—
246C22×C4—262no—
247C22×C4#610312yes—
248C22×C4#610312yes—
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4C2×D5211yescharacteristic
251C22×C4#612712yes—
252C22×C4C2×C22⋊D1312yes—
253M16—524no—
254C2×C8—522no—
255C4⋊C4—44no—
256C4⋊C4—262no—
257C22⋊C4—44no—
258C22⋊C4—524no—
259C22⋊C4—522no—
260C22⋊C4—522no—
261C22⋊C4—524no—
262C42—44no—
263C42—522no—
264C13#946611yescharacteristic, complemented, Sylow
265C23—22no—
266C23—22no—
267C23—41no—
268C23—522no—
269C23—522no—
270C23—522no—
271C23—521no—
272C23C2×#610311yescharacteristic
273C23#8818311yescharacteristic
274C23#8820711yescharacteristic
275Q8—48no—
276Q8—48no—
277D4—1042no—
278D4—1042no—
279D4—1042no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—521no—
302C2×C4#8804614yes—
303C2×C4C4×C22⋊D1312yes—
304C2×C4#8818412yes—
305C8—1042no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—44no—
314C22—1044no—
315C22—1041no—
316C22—1041no—
317C22—1041no—
318C22C2×#8804612yes—
319C22#1171887411yescharacteristic
320C22#1171890612yes—
321C4—22no—
322C4—24no—
323C4—22no—
324C4—42no—
325C4—84no—
326C4—1042no—
327C4—1041no—
328C2—22no—
329C2—22no—
330C2—41no—
331C2—2081no—
332C2#1311523911yescharacteristic
333C2#1311528911yescharacteristic
334C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2310C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenter#2310D13
hypocenterC13#9466
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #13114760C2semidirect
4. #13112688C2semidirect
5. C13×#2310C2semidirect
8. C2×#88201C4semidirect
14. #11718891C4semidirect
99. #2310D13semidirect
264. C13#9466semidirect

Maximal subgroups

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

subgroupindex
#131184902
#131147602
#131133642
#131126882
C13×#23102
#946613