Finite Group Databasebeta

← #14653220

Subgroups — #14653220

Order 2816.

450 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 127 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#13068754C211yesmaximal, characteristic, complemented
2#13067301C211yesmaximal, characteristic, complemented
3#13067297C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067284C211yesmaximal, characteristic
6#13066899C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C11×#486—21no—
11C11×#486—21no—
12C11×#486C414yes—
13C2×C11×#102—22no—
14C2×C4×C8×C11C2211yescharacteristic
15#10622538C2211yescharacteristic
16#10622538C2211yescharacteristic
17#10622537C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622190—22no—
20#10622185—22no—
21#10622184—22no—
22#10622182—22no—
23#10622182—22no—
24#10622093—21no—
25C8×C11⋊C8—21no—
26C22×Q8×C11—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×C8×C11D412yes—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8C2×C412yes—
35C11×#127—21no—
36C11×#127—21no—
37C11×#127—21no—
38C11×#127C2×C412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4318—21no—
43C2×#4318—21no—
44C11×#102—24no—
45C11×#102—24no—
46C4×C8×C11C2×C412yes—
47C4×C8×C11D411yescharacteristic
48C4×C8×C11D411yescharacteristic
49C22⋊(C11⋊C8)—21no—
50C22⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)D412yes—
56C4⋊(C11⋊C8)D412yes—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59#9769—111nomaximal, Sylow
60C24×C11—41no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C2×Q8×C11—82no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—82no—
73C2×D4×C11—82no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11C22⋊C412yes—
81C2×C8×C11C22⋊C412yes—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C42×C11C22×C411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D411yescharacteristic
90#4318—42no—
91#4318—42no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—22no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96C2×#486D1111yescharacteristic
97#1837—111no—
98#1549—111no—
99#1548—111no—
100#1545—111no—
101#1545—111no—
102#1450—111no—
103C23×C11—42no—
104C23×C11—82no—
105C23×C11—82no—
106C23×C11—82no—
107C23×C11#12411yescharacteristic
108Q8×C11—82no—
109Q8×C11—82no—
110D4×C11—44no—
111D4×C11—82no—
112D4×C11—82no—
113D4×C11—82no—
114D4×C11—82no—
115D4×C11—81no—
116D4×C11—81no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—42no—
120C2×C4×C11—82no—
121C2×C4×C11C2×C22⋊C411yescharacteristic
122C2×C4×C11C4×D411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12711yescharacteristic
127C2×C4×C11#13512yes—
128C2×C4×C11#13512yes—
129C8×C11—22no—
130C8×C11—22no—
131C11⋊C8—42no—
132C11⋊C8—42no—
133C11⋊C8—81no—
134C11⋊C8—81no—
135C2×C4⋊Q8C2×D1111yescharacteristic
136C2×#127C2×D1111yescharacteristic
137#486—21no—
138#486—21no—
139#486Dic1114yes—
140#431—111no—
141#431—111no—
142#423—111no—
143#423—111no—
144C2×#102—22no—
145C2×C4×C8C2×D1111yescharacteristic
146#341—222no—
147#333—222no—
148#332—222no—
149#331—222no—
150#331—222no—
151#322—221no—
152C82—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—82no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—164no—
159C22×C11#39011yescharacteristic
160C22×C11#48812yes—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—82no—
164C4×C11#41612yes—
165C4×C11#47112yes—
166C4×C11#47212yes—
167C4×C11#49511yescharacteristic
168C4×C11#49511yescharacteristic
169C22×Q8—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C2×M16—221no—
174C2×M16—221no—
175C22×C8C22⋊D1112yes—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8C2×Dic1112yes—
180#127—21no—
181#127—21no—
182#127—21no—
183#127C2×Dic1112yes—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C42C22×D1111yescharacteristic
187C4⋊C8—112no—
188C4⋊C8—112no—
189C4⋊C8—221no—
190C4⋊C8—221no—
191C4⋊C8—221no—
192C4⋊C8—221no—
193#102—24no—
194#102—24no—
195C22⋊C8—221no—
196C22⋊C8—221no—
197C4×C8—221no—
198C4×C8—221no—
199C4×C8C2×Dic1112yes—
200C4×C8C22⋊D1111yescharacteristic
201C4×C8C22⋊D1111yescharacteristic
202C2×C11—22no—
203C2×C11—162no—
204C2×C11#195811yescharacteristic
205C2×C11#197711yescharacteristic
206C2×C11#197811yescharacteristic
207C24—41no—
208C2×Q8—22no—
209C2×Q8—41no—
210C2×Q8—82no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—82no—
220C2×D4—82no—
221C22×C4—41no—
222C22×C4#434111yescharacteristic
223C22×C4#434111yescharacteristic
224C22×C4C2×C22⋊D1111yescharacteristic
225M16—442no—
226M16—442no—
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—222no—
230C2×C8—222no—
231C2×C8—441no—
232C2×C8—441no—
233C2×C8C22⋊Dic1112yes—
234C2×C8C22⋊Dic1112yes—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C42D4×D1111yescharacteristic
240C42D4×D1111yescharacteristic
241C42C22×Dic1111yescharacteristic
242C42C2×C22⋊D1111yescharacteristic
243C11#976911yescharacteristic, complemented, Sylow
244C23—42no—
245C23—82no—
246C23—82no—
247C23—82no—
248C23#6698911yescharacteristic
249Q8—82no—
250Q8—82no—
251D4—44no—
252D4—82no—
253D4—82no—
254D4—82no—
255D4—82no—
256D4—81no—
257D4—81no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4D4×Dic1111yescharacteristic
263C2×C4D4×Dic1111yescharacteristic
264C2×C4#6699111yescharacteristic
265C2×C4#6699111yescharacteristic
266C2×C4#6699311yescharacteristic
267C2×C4#6700312yes—
268C2×C4#6700312yes—
269C2×C4C2×C22⋊Dic1111yescharacteristic
270C8—22no—
271C8—22no—
272C8—442no—
273C8—442no—
274C8—881no—
275C8—881no—
276C22—21no—
277C22—21no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22—164no—
282C22#1062266912yes—
283C22#1062283411yescharacteristic
284C4—21no—
285C4—21no—
286C4—82no—
287C4#1062267211yescharacteristic
288C4#1062267211yescharacteristic
289C4#1062277312yes—
290C4#1062279012yes—
291C4#1062284612yes—
292C2—22no—
293C2—162no—
294C2#1306942811yescharacteristic
295C2#1306952111yescharacteristic
296C2#1306952711yescharacteristic
subgroupG/H
centerC22#10622834
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC22×C11#390
prime radicalC2×C11×#127C22
cosocleC2×C42×C11C23
hypercenterC2×#486D11
hypocenterC11#9769
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. #13068754C2semidirect
2. #13067301C2semidirect
3. #13067297C2semidirect
6. #13066899C2semidirect
243. C11#9769semidirect

Maximal subgroups

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

subgroupindex
#130687542
#130673012
#130672972
#130672842
#130668992
C2×C11×#4862
#976911