Finite Group Databasebeta

← #15773848

Subgroups — #15773848

Order 3328.

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

normal subgroups only

This group has 368 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#13120534C211yesmaximal, characteristic
2#13114919C211yesmaximal, characteristic
3#13112864C212yesmaximal, complemented
4#13112843C212yesmaximal, complemented
5C13×#1458C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88124C411yescharacteristic
8C13×#431—21no—
9#11718871—21no—
10#11718868—21no—
11#11718647C2211yescharacteristic
12#11718644C2211yescharacteristic
13#11718633—21no—
14#11718614C411yescharacteristic
15#11718610C411yescharacteristic
16#11718606—21no—
17#11718594—21no—
18#11718593C411yescharacteristic
19C13×#324C2212yes—
20C13×#323—21no—
21#11718122—21no—
22#11718122C2212yes—
23C23×C4×C13D411yescharacteristic
24C13×#117—41no—
25C13×#117—41no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4C2311yescharacteristic
28C2×C13×C22⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13—21no—
41C2×#6099—22no—
42#88124—41no—
43#88124—41no—
44C13×C4⋊C8—41no—
45C13×C22⋊C8—22no—
46C4×C8×C13—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56#11853—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C2×C8×C13—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C22⋊Dic13—42no—
82C22⋊Dic13—42no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85#6101—42no—
86#6101—42no—
87#6101—41no—
88#6101—41no—
89#6101—42no—
90C4×Dic13—42no—
91#6099—42no—
92#6099—42no—
93C2×#1055—42no—
94#2611—131no—
95#1822—131no—
96#1458D1311yescharacteristic
97#1353—132no—
98#1346—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#9911yescharacteristic
121C2×C4×C13#13512yes—
122C2×Dic13—22no—
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—41no—
133C2×Dic13—41no—
134C8×C13—82no—
135#1055—82no—
136C2×#125—131no—
137C2×#117C2×D1311yescharacteristic
138#431—21no—
139#407—261no—
140#400—131no—
141#399—131no—
142#398—131no—
143#397—131no—
144#389—261no—
145#388—261no—
146#387—261no—
147#385—261no—
148#376—131no—
149#343—132no—
150#343—261no—
151#324C2×D1312yes—
152#323—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—81no—
160C22×C13C2×#9911yescharacteristic
161C22×C13#41611yescharacteristic
162C22×C13#42111yescharacteristic
163C4×C13—22no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170Dic13—42no—
171Dic13—81no—
172Dic13—81no—
173Dic13—81no—
174C23×C4D5211yescharacteristic
175C2×M16—262no—
176#125—521no—
177#125—521no—
178#117—41no—
179#117—41no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4D5211yescharacteristic
187C2×C4⋊C4C22×D1311yescharacteristic
188C2×C22⋊C4—261no—
189C2×C22⋊C4—261no—
190C2×C22⋊C4C4×D1311yescharacteristic
191C2×C22⋊C4C22⋊D1311yescharacteristic
192C2×C42—261no—
193C2×C42C4×D1311yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C4⋊C8—41no—
196C22⋊C8—22no—
197C22⋊C8—521no—
198C22⋊C8—521no—
199C4×C8—41no—
200#95—131no—
201#95—131no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—81no—
210C2×C13#151611yescharacteristic
211C2×C13#212311yescharacteristic
212C2×C13#213211yescharacteristic
213C24#610311yescharacteristic
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—41no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4C2×D5211yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228M16—522no—
229M16—522no—
230C2×C8—42no—
231C2×C8—522no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—522no—
250C13#1185311yescharacteristic, complemented, Sylow
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23C2×#610311yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—262no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4#8804611yescharacteristic
284C2×C4#8804611yescharacteristic
285C2×C4#8815812yes—
286C8—82no—
287C8—1042no—
288C22—21no—
289C22—21no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—81no—
295C22C2×#8804611yescharacteristic
296C22#1171877411yescharacteristic
297C22#1171880011yescharacteristic
298C4—22no—
299C4—21no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—522no—
306C4—1041no—
307C4—1041no—
308C4—1041no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2#1311339311yescharacteristic
313C2#1311648911yescharacteristic
314C2#1311651911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1458D13
hypocenterC13#11853
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13112864C2semidirect
4. #13112843C2semidirect
250. C13#11853semidirect

Maximal subgroups

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

subgroupindex
#131205342
#131149192
#131128642
#131128432
C13×#14582
#1185313