Finite Group Databasebeta

← #15752234

Subgroups — #15752234

Order 3328.

322 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 79 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#13122827C211yesmaximal, characteristic
2#13116400C211yesmaximal, characteristic
3#13116400C211yesmaximal, characteristic
4#13116399C211yesmaximal, characteristic
5#13112660C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C13×#389C2211yescharacteristic
9#11718647—21no—
10#11718643—21no—
11#11718642—21no—
12#11718639—21no—
13#11718596C2211yescharacteristic
14#11718589C2211yescharacteristic
15#11718589C2211yescharacteristic
16#11718320—21no—
17#11718316—21no—
18C13×#336C2211yescharacteristic
19C13×#336C2211yescharacteristic
20#11718143—21no—
21#11718143—21no—
22#11718143—21no—
23#11718143—21no—
24#11718121—21no—
25#11718121—21no—
26#11718116C2211yescharacteristic
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C22×#1055—21no—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7832—131nomaximal, Sylow
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—41no—
65C2×C8×C13—41no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C42×C13—41no—
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85C4⋊Dic13—42no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89#6101—41no—
90C4×Dic13—81no—
91C2×#1055—41no—
92C2×#1055—41no—
93C2×#1055—41no—
94#2810—131no—
95#2100—131no—
96#2100—131no—
97#2100—131no—
98#1271—131no—
99#1271—131no—
100#1271D1311yescharacteristic
101C23×C13#12011yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13#13511yescharacteristic
115C2×C4×C13#13511yescharacteristic
116C2×C4×C13#13511yescharacteristic
117C2×C4×C13#13711yescharacteristic
118C2×C4×C13#13711yescharacteristic
119C2×C4×C13#13711yescharacteristic
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C8×C13—81no—
136C8×C13—81no—
137#1055—81no—
138#400—261no—
139#400—261no—
140#400—261no—
141#389—131no—
142#389—131no—
143#389C2×D1311yescharacteristic
144#387—261no—
145#387—261no—
146#387—261no—
147#384—131no—
148#340—261no—
149#340—261no—
150#340—261no—
151#340—261no—
152#340—261no—
153#340—261no—
154#336—131no—
155#336C2×D1311yescharacteristic
156#336C2×D1311yescharacteristic
157C22×C13#45211yescharacteristic
158C22×C13#45211yescharacteristic
159C22×C13#45211yescharacteristic
160C22×C13#45411yescharacteristic
161C22×C13#45411yescharacteristic
162C22×C13#45411yescharacteristic
163C22×C13#45811yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—81no—
171C4×C13—81no—
172Dic13—81no—
173Dic13—81no—
174Dic13—81no—
175Dic13—81no—
176Dic13—161no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—261no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4D5211yescharacteristic
191C2×C4⋊C4D5211yescharacteristic
192C2×C42—261no—
193C2×C42C22×D1311yescharacteristic
194#95—21no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201#95—261no—
202#95—261no—
203#95—261no—
204C2×C13#161511yescharacteristic
205C2×C13#161511yescharacteristic
206C2×C13#161511yescharacteristic
207C2×C13#163811yescharacteristic
208C2×C13#163811yescharacteristic
209C2×C13#163811yescharacteristic
210C2×C13#165811yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—521no—
218C22×C4C2×D5211yescharacteristic
219C22×C4D4×D1311yescharacteristic
220C22×C4D4×D1311yescharacteristic
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—521no—
228C2×C8—521no—
229C2×C8—521no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—261no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C4⋊C4—522no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C42—41no—
249C42—1041no—
250C13#783211yescharacteristic, complemented, Sylow
251C23#8813611yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—1041no—
277C2×C4—1041no—
278C2×C4—1041no—
279C2×C4#8815811yescharacteristic
280C2×C4#8816311yescharacteristic
281C2×C4#8816611yescharacteristic
282C2×C4#8816911yescharacteristic
283C2×C4#8817011yescharacteristic
284C2×C4#8817211yescharacteristic
285C8—81no—
286C8—81no—
287C8—1041no—
288C22#1171839411yescharacteristic
289C22#1171840311yescharacteristic
290C22#1171841411yescharacteristic
291C22#1171844411yescharacteristic
292C22#1171847111yescharacteristic
293C22#1171848811yescharacteristic
294C22#1171848811yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—1041no—
304C4—1041no—
305C4—1041no—
306C4—1041no—
307C4—2081no—
308C2#1311386811yescharacteristic
309C2#1311386911yescharacteristic
310C2#1311387011yescharacteristic
311C2#1311400911yescharacteristic
312C2#1311401011yescharacteristic
313C2#1311401111yescharacteristic
314C2#1311413911yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13#120
hypercenter#1271D13
hypocenterC13#7832
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
250. C13#7832semidirect

Maximal subgroups

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

subgroupindex
#131228272
#131164002
#131163992
#131126602
#131126582
C13×#12712
#783213