Finite Group Databasebeta

← #15772450

Subgroups — #15772450

Order 3328.

380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 87 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#13113170C211yesmaximal, characteristic
2#13113150C211yesmaximal, characteristic
3#13112784C212yesmaximal
4#13112766C212yesmaximal
5C13×#2484C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic
8C13×#400—21no—
9C13×#398—21no—
10C13×#387—21no—
11C13×#387—21no—
12C13×#385C411yescharacteristic
13C13×#385C2211yescharacteristic
14C13×#381C411yescharacteristic
15C13×#381C411yescharacteristic
16C13×#381C2211yescharacteristic
17#11718587—21no—
18#11718586—21no—
19#11718120—21no—
20#11718120—21no—
21#11718117C2212yes—
22#11718117C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
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⋊C4—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4C2311yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C13×#95—21no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C4⋊#1055—41no—
53C4⋊#1055—41no—
54#88043—41no—
55C4×#1055—41no—
56#11544—131nomaximal, Sylow
57C24×C13C22×C411yescharacteristic
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13—42no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C2×#1055—42no—
93C2×#1055—42no—
94#2484D1311yescharacteristic
95#1464—131no—
96#1458—131no—
97#1326—132no—
98#1317—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#13112yes—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
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—82no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137#1055—82no—
138#1055—82no—
139C2×#117C2×D1311yescharacteristic
140C22×C4⋊C4Dic1311yescharacteristic
141#432—261no—
142#431—261no—
143#400—21no—
144#398—21no—
145#387—21no—
146#387—21no—
147#385Dic1311yescharacteristic
148#385C2×D1311yescharacteristic
149#381Dic1311yescharacteristic
150#381Dic1311yescharacteristic
151#381C2×D1311yescharacteristic
152#324—261no—
153#324—261no—
154#323—132no—
155#323—132no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13#40811yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13#41311yescharacteristic
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—42no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—81no—
175C4×C13—81no—
176C4×C13—81no—
177C23×C4C2×Dic1311yescharacteristic
178C23×C4C2×Dic1311yescharacteristic
179C23×C4C2×Dic1311yescharacteristic
180#117—41no—
181#117—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4C22⋊D1311yescharacteristic
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4C2×Dic1311yescharacteristic
191C2×C22⋊C4C2×Dic1311yescharacteristic
192C2×C22⋊C4C2×Dic1311yescharacteristic
193C2×C22⋊C4C22×D1311yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C4⋊C8—521no—
197C4⋊C8—521no—
198C22⋊C8—262no—
199C22⋊C8—262no—
200#97—521no—
201C4×C8—521no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—42no—
213C2×C13#146811yescharacteristic
214C2×C13#212011yescharacteristic
215C2×C13#212311yescharacteristic
216C24C22×Dic1311yescharacteristic
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1311yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C22⋊C4—22no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C13#1154411yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23#8820212yes—
259C23C2×C22⋊Dic1311yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—82no—
290C2×C4#8807411yescharacteristic
291C2×C4#8807411yescharacteristic
292C8—1042no—
293C8—1042no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22C2×#8807411yescharacteristic
302C22#1171889511yescharacteristic
303C22#1171889811yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4—81no—
314C4—81no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1311318411yescharacteristic
319C2#1311647711yescharacteristic
320C2#1311649011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutator, prime radicalC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2484C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2484D13
hypocenterC13#11544
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2484

Complements

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

NH ≅ G/Ntype
253. C13#11544semidirect

Maximal subgroups

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

subgroupindex
#131131702
#131131502
#131127842
#131127662
C13×#24842
#1154413