Finite Group Databasebeta

← #15754283

Subgroups — #15754283

Order 3328.

874 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 163 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#13114904C212yesmaximal, complemented
2C2×#11718120C212yesmaximal, complemented
3C2×#11718117C212yesmaximal
4C22×C13×#126C211yesmaximal, characteristic
5C2×C13×#126—24no—
6C2×C13×#126—24no—
7C2×C13×#126—24no—
8C22×C13×C4⋊C4C411yescharacteristic
9C22×C13×C4⋊C4C411yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C22⋊C4C411yescharacteristic
12C22×C13×C22⋊C4C411yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C2×C22⋊#1055C2214yes—
16#11718120—24no—
17#11718117—24no—
18#11718116—24no—
19C25×C13C2×C411yescharacteristic
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2×C411yescharacteristic
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C13×#126—232no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4D414yes—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4—22no—
42C2×C13×C22⋊C4—22no—
43C2×C13×C22⋊C4—22no—
44C2×C13×C22⋊C4D414yes—
45C2×C42×C13—22no—
46C2×C42×C13—22no—
47C2×C42×C13D414yes—
48C22×#1055—24no—
49C22⋊#1055—24no—
50C22⋊#1055—24no—
51#8309—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13—21no—
54C24×C13—24no—
55C24×C13—42no—
56C24×C13—42no—
57C24×C13C22⋊C412yes—
58C24×C13C22×C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—24no—
70C22×C4×C13—24no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13C22⋊C412yes—
76C22×C4×C13C22⋊C412yes—
77C22×C4×C13C22⋊C412yes—
78C22×C4×C13C22⋊C412yes—
79C22×C4×C13C22⋊C412yes—
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D412yes—
83C13×C4⋊C4—28no—
84C13×C4⋊C4—28no—
85C13×C4⋊C4—28no—
86C13×C22⋊C4—28no—
87C13×C22⋊C4—28no—
88C13×C22⋊C4—28no—
89C42×C13—28no—
90C2×#1055—48no—
91C2×#1055—44no—
92C22×#126D1311yescharacteristic
93#1817—132no—
94C2×#324—132no—
95C2×#323—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—24no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—88no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13C2×C22⋊C411yescharacteristic
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13#13114yes—
113C2×C4×C13—24no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—24no—
120C2×C4×C13—24no—
121C2×C4×C13—24no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13#12014yes—
137#1055—84no—
138C2×#126—24no—
139C2×#126—24no—
140C2×#126—24no—
141C22×C4⋊C4Dic1311yescharacteristic
142C22×C4⋊C4Dic1311yescharacteristic
143C22×C4⋊C4C2×D1311yescharacteristic
144C22×C22⋊C4Dic1311yescharacteristic
145C22×C22⋊C4Dic1311yescharacteristic
146C22×C22⋊C4C2×D1311yescharacteristic
147C22×C42C2×D1311yescharacteristic
148C2×C22⋊C8—134no—
149#336—264no—
150#324—264no—
151#323—264no—
152C22×C13—28no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—84no—
161C22×C13—84no—
162C22×C13—84no—
163C22×C13#37911yescharacteristic
164C22×C13#40812yes—
165C22×C13#40812yes—
166C22×C13#40812yes—
167C22×C13#41012yes—
168C22×C13#41312yes—
169C4×C13—24no—
170C4×C13—42no—
171C4×C13—42no—
172C4×C13—42no—
173C4×C13—42no—
174C4×C13—42no—
175C25C2×Dic1311yescharacteristic
176C23×C4C2×Dic1311yescharacteristic
177C23×C4C2×Dic1311yescharacteristic
178C23×C4C2×Dic1311yescharacteristic
179C23×C4C2×Dic1311yescharacteristic
180C23×C4C2×Dic1311yescharacteristic
181C23×C4C22×D1311yescharacteristic
182C22×C8—264no—
183#126—232no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4C22⋊D1314yes—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4C22⋊D1314yes—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42C22⋊D1314yes—
205C22⋊C8—264no—
206C22⋊C8—264no—
207C2×C13—22no—
208C2×C13—22no—
209C2×C13—82no—
210C2×C13#147314yes—
211C2×C13#178011yescharacteristic
212C2×C13#178211yescharacteristic
213C2×C13#178511yescharacteristic
214C24—21no—
215C24—21no—
216C24—24no—
217C24—42no—
218C24—42no—
219C24C22⋊Dic1312yes—
220C24C22×Dic1311yescharacteristic
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊Dic1312yes—
238C22×C4C22⋊Dic1312yes—
239C22×C4C22⋊Dic1312yes—
240C22×C4C22⋊Dic1312yes—
241C22×C4C22⋊Dic1312yes—
242C22×C4C2×C22⋊D1312yes—
243C22×C4C2×C22⋊D1312yes—
244C22×C4C2×C22⋊D1312yes—
245C2×C8—528no—
246C2×C8—524no—
247C4⋊C4—28no—
248C4⋊C4—28no—
249C4⋊C4—28no—
250C22⋊C4—28no—
251C22⋊C4—28no—
252C22⋊C4—28no—
253C42—28no—
254C13#830911yescharacteristic, complemented, Sylow
255C23—22no—
256C23—22no—
257C23—22no—
258C23—24no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—88no—
268C23#8820214yes—
269C23C2×C22⋊Dic1311yescharacteristic
270C23C2×C22⋊Dic1311yescharacteristic
271C23C2×C22⋊Dic1311yescharacteristic
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4#8820714yes—
296C8—1044no—
297C22—28no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—84no—
306C22—84no—
307C22—84no—
308C22#1171889512yes—
309C22#1171889512yes—
310C22#1171889512yes—
311C22#1171889812yes—
312C22#1171890112yes—
313C22#1171890811yescharacteristic
314C4—24no—
315C4—42no—
316C4—42no—
317C4—42no—
318C4—42no—
319C4—42no—
320C2—22no—
321C2—22no—
322C2—82no—
323C2#1311320514yes—
324C2#1311474811yescharacteristic
325C2#1311475411yescharacteristic
326C2#1311476411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC22×C13×#126C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC22×#126D13
hypocenterC13#8309
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #13114904C2semidirect
2. C2×#11718120C2semidirect
254. C13#8309semidirect

Maximal subgroups

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

subgroupindex
#131149042
C2×#117181202
C2×#117181172
C22×C13×#1262
#830913