Finite Group Databasebeta

← #14650438

Subgroups — #14650438

Order 2816.

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

normal subgroups only

This group has 422 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#13079566C211yesmaximal, characteristic
2#13077553C211yesmaximal, characteristic
3#13069588C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic
5#13067179C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#382C2211yescharacteristic
13#10622735—21no—
14#10622732—21no—
15#10622538C2211yescharacteristic
16C2×#66867C2211yescharacteristic
17#10622462—22no—
18#10622441—22no—
19#10622441—22no—
20#10622352—22no—
21#10622312C412yescomplemented
22#10622294C412yescomplemented
23#10622167—21no—
24#10622167—21no—
25#10622124—22no—
26#10622090—22no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11C2311yescharacteristic
31#66979—21no—
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34#66977—21no—
35#66977D412yes—
36C22×C11⋊C8D411yescharacteristic
37C22×C11⋊C8D411yescharacteristic
38C2×Dic44—24no—
39#66923—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43#66922C2×C412yes—
44#66922C2×C411yescharacteristic
45#66922C2×C411yescharacteristic
46C4×Dic22—21no—
47C4×Dic22D412yes—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×C22⋊C8—21no—
52C4×C8×C11C2×C412yes—
53C11×#95—21no—
54C11×#95—21no—
55C22⋊(C11⋊C8)—21no—
56#66880—24no—
57#66879—22no—
58Dic11⋊C8—24no—
59C8×Dic11—22no—
60C4⋊(C11⋊C8)—21no—
61#66867—21no—
62#66867—21no—
63C4×C11⋊C8—21no—
64#9290—111nomaximal, Sylow
65C22×C4×C11—41no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×Dic11—41no—
70C2×Dic22—22no—
71C2×Dic22—21no—
72C2×Dic22—41no—
73C2×Dic22—82no—
74C2×Dic22C22⋊C412yes—
75C11×M16—41no—
76C11×M16—41no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C42×C11C22×C411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11#4111yescharacteristic
85C22⋊Dic11—22no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11—22no—
90C4⋊Dic11—22no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11C22⋊C412yes—
94Dic11⋊C4—22no—
95Dic11⋊C4—22no—
96C4×Dic11—22no—
97C2×C11⋊C8—21no—
98C2×C11⋊C8—21no—
99C2×C11⋊C8—21no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8Q1612yescomplemented
104Dic44—84no—
105#3209—111no—
106#2961—111no—
107#1993—111no—
108#1549—111no—
109#1518—111no—
110#1286D1111yescharacteristic
111#1275—111no—
112C23×C11#12111yescharacteristic
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—81no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
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—42no—
131C2×Dic11—82no—
132Dic22—42no—
133Dic22—44no—
134Dic22—81no—
135Dic22—82no—
136C8×C11—42no—
137C8×C11—42no—
138C11⋊C8—22no—
139C11⋊C8—41no—
140C11⋊C8—81no—
141#533—111no—
142C2×C4⋊Q8—111no—
143#494—112no—
144#487—112no—
145#462—222no—
146#451—222no—
147#446—222no—
148#446—222no—
149#431—111no—
150#431C2×D1111yescharacteristic
151#424—221no—
152#423C2×D1111yescharacteristic
153#405—221no—
154C2×#97—111no—
155#382C2×D1111yescharacteristic
156#340—221no—
157#340—221no—
158#332—222no—
159#328—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#38611yescharacteristic
163C22×C11#46211yescharacteristic
164C22×C11#46411yescharacteristic
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—161no—
170C4×C11C4×Q1611yescharacteristic
171C4×C11#44111yescharacteristic
172C4×C11#45111yescharacteristic
173C4×C11#45211yescharacteristic
174Dic11—42no—
175Dic11—42no—
176Dic11—82no—
177C22×Q8—221no—
178C2×Q16—224no—
179C2×M16—21no—
180C22×C8—111no—
181C22×C8—111no—
182C4⋊Q8—111no—
183C4⋊Q8—111no—
184C4⋊Q8—112no—
185C4⋊Q8—221no—
186C4⋊Q8—221no—
187C4⋊Q8—221no—
188#125—221no—
189C22⋊Q8—112no—
190C22⋊Q8—221no—
191C4×Q8—112no—
192C4×Q8—221no—
193#117—221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C42C22×D1111yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—224no—
201C4⋊C8—221no—
202C4⋊C8D4412yes—
203#103—224no—
204C22⋊C8—21no—
205C22⋊C8—221no—
206#97—222no—
207#97—221no—
208#97—221no—
209C4×C8—222no—
210C4×C8—221no—
211C4×C8C4×D1112yes—
212#95—21no—
213#95—21no—
214C2×C11—21no—
215C2×C11—21no—
216C2×C11#187811yescharacteristic
217C2×C11#190211yescharacteristic
218C2×C11#191011yescharacteristic
219C2×Q8—112no—
220C2×Q8—221no—
221C2×Q8—222no—
222C2×Q8—441no—
223C2×Q8—882no—
224C22×C4—41no—
225C22×C4—441no—
226C22×C4#433911yescharacteristic
227C22×C4D4×D1111yescharacteristic
228C22×C4D4×D1111yescharacteristic
229Q16—884no—
230M16—41no—
231M16—41no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—112no—
235C2×C8—221no—
236C2×C8—221no—
237C2×C8—221no—
238C2×C8—221no—
239C2×C8—221no—
240C2×C8—441no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—112no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4—221no—
247C4⋊C4—222no—
248C4⋊C4—222no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C22⋊C4—222no—
254C42—222no—
255C42C2×C4×D1111yescharacteristic
256C42C2×D4411yescharacteristic
257C42D4×D1111yescharacteristic
258C42#434311yescharacteristic
259C11#929011yescharacteristic, complemented, Sylow
260C23#6693711yescharacteristic
261Q8—442no—
262Q8—444no—
263Q8—881no—
264Q8—882no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—442no—
273C2×C4—882no—
274C2×C4C4×D4411yescharacteristic
275C2×C4C22⋊C4×D1111yescharacteristic
276C2×C4#6693511yescharacteristic
277C2×C4#6694611yescharacteristic
278C2×C4#6694711yescharacteristic
279C2×C4#6694811yescharacteristic
280C2×C4#6696511yescharacteristic
281C2×C4#6696811yescharacteristic
282C2×C4#6696811yescharacteristic
283C2×C4Q16×D1111yescharacteristic
284C8—42no—
285C8—42no—
286C8—222no—
287C8—441no—
288C8—881no—
289C22—21no—
290C22—21no—
291C22#1062227811yescharacteristic
292C22#1062238011yescharacteristic
293C22#1062240611yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—161no—
299C4—442no—
300C4—442no—
301C4—882no—
302C4#1062239611yescharacteristic
303C4#1062242111yescharacteristic
304C4#1062246611yescharacteristic
305C4#1062248611yescharacteristic
306C2—21no—
307C2—21no—
308C2#1306895811yescharacteristic
309C2#1306908811yescharacteristic
310C2#1306914211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1286D11
hypocenterC11#9290
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
21. #10622312C4semidirect
22. #10622294C4semidirect
103. C2×C11⋊C8Q16semidirect
259. C11#9290semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130775532
#130695882
#130673022
#130671792
#130664462
C11×#12862
#929011