Finite Group Databasebeta

← #15773410

Subgroups — #15773410

Order 3328.

436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114569C211yesmaximal, characteristic
2#13113170C211yesmaximal, characteristic
3#13112860C212yesmaximal
4#13112836C212yesmaximal
5C13×#2611C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C2×#88180—21no—
9C13×#400C411yescharacteristic, complemented
10C13×#399C2211yescharacteristic
11C13×#398C411yescharacteristic, complemented
12C13×#397C2211yescharacteristic
13C13×#389—21no—
14C13×#388—21no—
15C13×#387—21no—
16C13×#385—21no—
17C13×#376C411yescharacteristic, complemented
18#11718587—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C23×C4×C13D411yescharacteristic
24C13×#125—41no—
25C13×#125—41no—
26C13×#117—41no—
27C13×#117—41no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C13×C22⋊C4C2311yescharacteristic
40C2×C42×C13—21no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C22⋊Dic13—22no—
44#88180—24no—
45#88180—42no—
46C2×C4⋊Dic13—41no—
47C2×C4×Dic13—41no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57#88043—41no—
58#11760—131nomaximal, Sylow
59C24×C13C2×D411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—42no—
95C22⋊Dic13—24no—
96C22⋊Dic13—42no—
97C4⋊Dic13—44no—
98C4×Dic13—44no—
99C2×#1055—42no—
100#2611D1311yescharacteristic
101#1740—131no—
102#1464—131no—
103#1352—132no—
104#1344—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13AGL(1,ℤ/8)11yescharacteristic
111C23×C13#13711yescharacteristic
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13#9911yescharacteristic
141C2×C4×C13#9911yescharacteristic
142C2×C4×C13#10412yes—
143C2×Dic13—44no—
144C2×Dic13—82no—
145C2×Dic13—82no—
146#1055—82no—
147C2×#125Dic1311yescharacteristic, complemented
148C2×#117—261no—
149C2×#117C2×D1311yescharacteristic
150#432—261no—
151#400Dic1311yescharacteristic, complemented
152#399C2×D1311yescharacteristic
153#398Dic1311yescharacteristic, complemented
154#397C2×D1311yescharacteristic
155#389—21no—
156#388—21no—
157#387—21no—
158#385—21no—
159#376Dic1311yescharacteristic, complemented
160#342—132no—
161#342—261no—
162#324—261no—
163#323—132no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13C2×#9911yescharacteristic
174C22×C13#41711yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—42no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13—81no—
187Dic13—84no—
188C23×C4C22⋊D1311yescharacteristic
189#125—41no—
190#125—41no—
191#117—41no—
192#117—41no—
193#117—264no—
194#117—522no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—521no—
200C2×C4⋊C4C2×Dic1311yescharacteristic
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C4⋊C4C2×Dic1311yescharacteristic
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—262no—
207C2×C22⋊C4C22⋊D1311yescharacteristic
208C2×C22⋊C4C22×D1311yescharacteristic
209C2×C42—21no—
210C2×C42—521no—
211C2×C42C2×Dic1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C4⋊C8—521no—
214C22⋊C8—262no—
215#97—521no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C2×Dic1311yescharacteristic
222#95C2×Dic1311yescharacteristic
223C2×C13—21no—
224C2×C13—21no—
225C2×C13—41no—
226C2×C13—41no—
227C2×C13#150411yescharacteristic
228C2×C13#212311yescharacteristic
229C2×C13#212611yescharacteristic
230C24C2×C22⋊D1311yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—522no—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22⋊Dic1311yescharacteristic
245C22×C4C22×Dic1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247C2×C8—522no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—524no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—264no—
264C22⋊C4—522no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—42no—
270C42—524no—
271C13#1176011yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#8820311yescharacteristic
277C23#8820511yescharacteristic
278C23C2×C22⋊Dic1311yescharacteristic
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—524no—
308C2×C4—1042no—
309C2×C4—1042no—
310C2×C4#8807411yescharacteristic
311C2×C4#8807411yescharacteristic
312C2×C4#8807712yes—
313C8—1042no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22C2×#8807411yescharacteristic
324C22#1171889311yescharacteristic
325C22C2×#8807711yescharacteristic
326C4—21no—
327C4—21no—
328C4—22no—
329C4—42no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—1044no—
338C2—21no—
339C2—21no—
340C2—41no—
341C2—41no—
342C2#1311334011yescharacteristic
343C2#1311649011yescharacteristic
344C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2611C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2611D13
hypocenterC13#11760
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2611

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
9. C13×#400C4semidirect
11. C13×#398C4semidirect
17. C13×#376C4semidirect
147. C2×#125Dic13semidirect
151. #400Dic13semidirect
153. #398Dic13semidirect
159. #376Dic13semidirect
271. C13#11760semidirect

Maximal subgroups

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

subgroupindex
#131145692
#131131702
#131128602
#131128362
C13×#26112
#1176013