Finite Group Databasebeta

← #15758664

Subgroups — #15758664

Order 3328.

756 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 139 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#13123167C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic, complemented
3C2×#11718043C212yesmaximal
4#13112715C212yesmaximal, complemented
5C2×C13×#376C211yesmaximal, characteristic, complemented
6C22×C42×C13—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88184C2211yescharacteristic
9C2×#88183—21no—
10C13×#376—24no—
11C2×C13×#95—21no—
12C2×C13×#95C2212yes—
13#11718874—21no—
14#11718873C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718601—22no—
17#11718600C412yescomplemented
18#11718589C412yescomplemented
19#11718116—22no—
20#11718043—24no—
21C23×C4×C13—22no—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×C22⋊D13—21no—
26C22×D52C2×C411yescharacteristic
27C2×C42×C13—28no—
28C2×C42×C13—24no—
29C2×C42×C13—22no—
30C2×C42×C13—22no—
31C2×C42×C13C2×C412yes—
32C2×C42×C13D412yes—
33C2×C22⋊Dic13—21no—
34#88184—22no—
35#88184—22no—
36#88183—44no—
37C2×#6103—22no—
38C2×#6103—22no—
39C2×#6103—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×C4⋊Dic13C2×C412yes—
42C2×#6101—22no—
43C22×#1055—22no—
44C13×#95—24no—
45C13×#95—22no—
46C13×#95D414yes—
47#88071—22no—
48#88071—21no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9149—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C23×D13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—24no—
57C22×C4×C13—28no—
58C22×C4×C13—21no—
59C22×C4×C13—24no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—42no—
64C22×C4×C13—44no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13#4112yes—
73C2×C22⋊D13—41no—
74C2×C22⋊D13—41no—
75C2×C22⋊D13—42no—
76C2×C22⋊D13—42no—
77C22×Dic13—21no—
78C22×Dic13—22no—
79C2×D52—22no—
80C2×D52—42no—
81C42×C13—216no—
82C42×C13—24no—
83C42×C13—24no—
84C22⋊Dic13—42no—
85#6103—44no—
86#6103—44no—
87#6103—42no—
88C4⋊Dic13—22no—
89C4⋊Dic13—42no—
90#6101—44no—
91C2×#1055—44no—
92C2×#1055—42no—
93#2854—131no—
94C2×#376D1311yescharacteristic, complemented
95#1817—131no—
96C2×#327—132no—
97#1294—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13#12011yescharacteristic
102C23×C13#12311yescharacteristic
103C23×C13#13512yes—
104C23×C13AGL(1,ℤ/8)12yes—
105C22×D13—41no—
106C22×D13—42no—
107C22×D13—41no—
108C22×D13—41no—
109C22×D13—42no—
110C2×C4×C13—24no—
111C2×C4×C13—24no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—28no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—44no—
123C2×C4×C13—48no—
124C2×C4×C13—48no—
125C2×C4×C13—42no—
126C2×C4×C13—44no—
127C2×C4×C13—42no—
128C2×C4×C13#10414yes—
129C2×C4×C13C4×D412yes—
130C2×C4×C13#12112yes—
131C22⋊D13—82no—
132C22⋊D13—82no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139D52—82no—
140#1055—82no—
141C2×#123—261no—
142C2×#121—131no—
143C22×C42—21no—
144C22×C42C2×D1311yescharacteristic
145C2×C22⋊C8—132no—
146#390—132no—
147#389—132no—
148#388—262no—
149#386—261no—
150#380—131no—
151#376—24no—
152C2×#95—21no—
153C2×#95C2×D1312yes—
154#336—262no—
155#327—264no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—24no—
161C22×C13—24no—
162C22×C13#38611yescharacteristic
163C22×C13#41012yes—
164C22×C13#41611yescharacteristic
165C22×C13#41811yescharacteristic
166C22×C13C2×#10412yes—
167C22×C13#44912yes—
168C22×C13#48212yes—
169C2×D13—81no—
170C2×D13—81no—
171C2×D13—81no—
172C2×D13—82no—
173C2×D13—82no—
174C4×C13—24no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—48no—
178C4×C13—42no—
179Dic13—81no—
180Dic13—82no—
181C22×D4—131no—
182C22×D4—261no—
183C23×C4—22no—
184C23×C4C22⋊D1311yescharacteristic
185C23×C4C22⋊D1311yescharacteristic
186C23×C4C22×D1311yescharacteristic
187C22×C8—262no—
188#123—524no—
189#121—262no—
190#121—262no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—132no—
193C2×C4⋊C4—262no—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4—261no—
198C2×C42—24no—
199C2×C42—28no—
200C2×C42—22no—
201C2×C42—22no—
202C2×C42C4×D1312yes—
203C2×C42D5212yes—
204C22⋊C8—262no—
205C22⋊C8—262no—
206#95—24no—
207#95—22no—
208#95—262no—
209#95—261no—
210#95C22⋊D1314yes—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13#150012yes—
214C2×C13#150512yes—
215C2×C13#187511yescharacteristic
216C2×C13#189611yescharacteristic
217C2×C13#189911yescharacteristic
218D13—161no—
219C24—261no—
220C24C2×C22⋊D1311yescharacteristic
221C2×D4—262no—
222C2×D4—522no—
223C2×D4—521no—
224C2×D4—522no—
225C2×D4—522no—
226C2×D4—521no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—28no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—24no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—262no—
241C22×C4—261no—
242C22×C4#610312yes—
243C22×C4#610312yes—
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4C2×D5211yescharacteristic
246C22×C4#612712yes—
247C22×C4C2×C22⋊D1312yes—
248C2×C8—524no—
249C2×C8—522no—
250C4⋊C4—262no—
251C4⋊C4—522no—
252C4⋊C4—524no—
253C22⋊C4—524no—
254C22⋊C4—522no—
255C22⋊C4—522no—
256C22⋊C4—524no—
257C42—216no—
258C42—24no—
259C42—24no—
260C13#914911yescharacteristic, complemented, Sylow
261C23—22no—
262C23—22no—
263C23—521no—
264C23—521no—
265C23—522no—
266C23—522no—
267C23—521no—
268C23C2×#610311yescharacteristic
269C23#8818311yescharacteristic
270C23#8820312yes—
271C23#8820412yes—
272C23#8820711yescharacteristic
273D4—1042no—
274D4—1042no—
275D4—1042no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—28no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—48no—
290C2×C4—48no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—522no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—521no—
300C2×C4#8804514yes—
301C2×C4C4×C22⋊D1312yes—
302C2×C4#8818412yes—
303C8—1042no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—24no—
309C22—24no—
310C22—1041no—
311C22—1041no—
312C22—1041no—
313C22—1042no—
314C22—1042no—
315C22C2×#8804512yes—
316C22#1171866211yescharacteristic
317C22#1171866311yescharacteristic
318C22#1171866412yes—
319C22#1171866712yes—
320C22#1171887411yescharacteristic
321C22#1171889912yes—
322C4—24no—
323C4—22no—
324C4—22no—
325C4—48no—
326C4—42no—
327C4—1041no—
328C4—1042no—
329C2—22no—
330C2—22no—
331C2—2081no—
332C2#1311332012yes—
333C2#1311334312yes—
334C2#1311515811yescharacteristic
335C2#1311527911yescharacteristic
336C2#1311529411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#376C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC2×#376D13
hypocenterC13#9149
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
2. #13114904C2semidirect
4. #13112715C2semidirect
5. C2×C13×#376C2semidirect
17. #11718600C4semidirect
18. #11718589C4semidirect
94. C2×#376D13semidirect
260. C13#9149semidirect

Maximal subgroups

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

subgroupindex
#131231672
#131149042
C2×#117180432
#131127152
C2×C13×#3762
#914913