Finite Group Databasebeta

← #14650420

Subgroups — #14650420

Order 2816.

410 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079767C211yesmaximal, characteristic
2#13077553C211yesmaximal, characteristic
3#13069590C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622735—21no—
13#10622732—21no—
14#10622706C412yescomplemented
15#10622704—22no—
16#10622691C412yescomplemented
17#10622583—22no—
18#10622549C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622441—22no—
22#10622441—22no—
23C11×#333—22no—
24#10622167—21no—
25#10622167—21no—
26#10622105—22no—
27C22×Q8×C11—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36#66979—21no—
37C2×C4⋊Dic11—21no—
38#66977—21no—
39#66977D412yes—
40C22×C11⋊C8D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42#66923—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8D412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)—21no—
55#66879—22no—
56Dic11⋊C8—24no—
57C8×Dic11—22no—
58#66874—24no—
59#66871—24no—
60C4⋊(C11⋊C8)—21no—
61#66867—21no—
62#66867—21no—
63C4×C11⋊C8C2×C412yes—
64#9288—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—82no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—41no—
73C2×Dic22—21no—
74C2×Dic22C22⋊C412yes—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—22no—
78C2×C8×C11—41no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C42×C11C22×C411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×D411yescharacteristic
86C42×C11#4111yescharacteristic
87C22⋊Dic11—22no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11C22⋊C412yes—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96C4×Dic11—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8Q1612yes—
104#3230—111no—
105#2961—111no—
106#1993—111no—
107#1548D1111yescharacteristic
108#1518—111no—
109#1286—111no—
110#1275—111no—
111C23×C11#12111yescharacteristic
112Q8×C11—82no—
113Q8×C11—82no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—82no—
118C2×C4×C11C2×C22⋊C411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11C2×Q1611yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—81no—
131C2×Dic11—81no—
132C2×Dic11—81no—
133Dic22—42no—
134Dic22—81no—
135C8×C11—42no—
136C8×C11—81no—
137C11⋊C8—22no—
138C11⋊C8—42no—
139C11⋊C8—41no—
140#533—111no—
141C2×C4⋊Q8C2×D1111yescharacteristic
142#500—112no—
143#487—112no—
144#484—222no—
145#477—222no—
146#446—222no—
147#446—222no—
148#431—111no—
149#431C2×D1111yescharacteristic
150#424—221no—
151#423C2×D1111yescharacteristic
152#405—221no—
153C2×#97—111no—
154#382—111no—
155#340—221no—
156#340—221no—
157#333—22no—
158#328—222no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11#38611yescharacteristic
162C22×C11#46211yescharacteristic
163C22×C11#46411yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—82no—
169C4×C11C4×Q1611yescharacteristic
170C4×C11#44111yescharacteristic
171C4×C11#45111yescharacteristic
172C4×C11#45211yescharacteristic
173Dic11—42no—
174Dic11—42no—
175Dic11—161no—
176C22×Q8—21no—
177C2×M16—21no—
178C22×C8—111no—
179C22×C8—111no—
180C4⋊Q8—21no—
181C4⋊Q8—21no—
182C4⋊Q8—21no—
183C4⋊Q8—111no—
184C4⋊Q8—111no—
185C4⋊Q8C4×D1112yes—
186#125—221no—
187C22⋊Q8—112no—
188C22⋊Q8—221no—
189C4×Q8—112no—
190C4×Q8—221no—
191#117—221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—221no—
195C2×C42C22×D1111yescharacteristic
196#107—224no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—224no—
200C4⋊C8—221no—
201C4⋊C8C22⋊D1112yes—
202#103—224no—
203C22⋊C8—21no—
204C22⋊C8—221no—
205#97—222no—
206#97—221no—
207#97—221no—
208C4×C8—21no—
209C4×C8—112no—
210C4×C8—222no—
211#95—221no—
212#95—221no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11#187811yescharacteristic
216C2×C11#190311yescharacteristic
217C2×C11#190911yescharacteristic
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—82no—
221C2×Q8—112no—
222C2×Q8—221no—
223C22×C4—41no—
224C22×C4—441no—
225C22×C4#433911yescharacteristic
226C22×C4D4×D1111yescharacteristic
227C22×C4D4×D1111yescharacteristic
228M16—41no—
229M16—41no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—112no—
233C2×C8—221no—
234C2×C8—221no—
235C2×C8—222no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8—221no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—112no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—222no—
247C4⋊C4—221no—
248C4⋊C4—222no—
249C4⋊C4—441no—
250C4⋊C4—441no—
251C22⋊C4—222no—
252C42—222no—
253C42C2×C4×D1111yescharacteristic
254C42D4×D1111yescharacteristic
255C42#434111yescharacteristic
256C42C2×C22⋊D1111yescharacteristic
257C11#928811yescharacteristic, complemented, Sylow
258C23#6693711yescharacteristic
259Q8—82no—
260Q8—82no—
261Q8—442no—
262Q8—881no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—82no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4—881no—
270C2×C4—881no—
271C2×C4—881no—
272C2×C4C22⋊C4×D1111yescharacteristic
273C2×C4(C22⋊D11)⋊C411yescharacteristic
274C2×C4#6693611yescharacteristic
275C2×C4#6696811yescharacteristic
276C2×C4#6696911yescharacteristic
277C2×C4Q16×D1111yescharacteristic
278C2×C4#6697111yescharacteristic
279C2×C4C4×C22⋊D1111yescharacteristic
280C2×C4#6699011yescharacteristic
281C2×C4#6699111yescharacteristic
282C8—42no—
283C8—81no—
284C8—222no—
285C8—442no—
286C8—441no—
287C22—21no—
288C22—21no—
289C22#1062240611yescharacteristic
290C22#1062241111yescharacteristic
291C22#1062256911yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—82no—
297C4—442no—
298C4—442no—
299C4—1761no—
300C4#1062240211yescharacteristic
301C4#1062240311yescharacteristic
302C4#1062278611yescharacteristic
303C4#1062279911yescharacteristic
304C2—21no—
305C2—21no—
306C2#1306895411yescharacteristic
307C2#1306909911yescharacteristic
308C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1548D11
hypocenterC11#9288
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
14. #10622706C4semidirect
16. #10622691C4semidirect
257. C11#9288semidirect

Maximal subgroups

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

subgroupindex
#130797672
#130775532
#130695902
#130671812
#130664762
#130664462
C11×#15482
#928811