Finite Group Databasebeta

← #14656270

Subgroups — #14656270

Order 2816.

526 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079961C211yesmaximal, characteristic, complemented
2#13078415C212yesmaximal
3#13069409C211yesmaximal, characteristic
4#13067070C212yesmaximal, complemented
5C11×#1292C211yesmaximal, characteristic, complemented
6C2×C4×D44C2211yescharacteristic
7#10623001C2212yes—
8C11×#423C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10#10622744—22no—
11#10622734—22no—
12#10622729—22no—
13C2×(C2×D11)⋊C8—22no—
14C2×C4×C11⋊C8C2211yescharacteristic
15#10622463—22no—
16#10622462—22no—
17#10622460—24no—
18#10622459—22no—
19#10622455—22no—
20#10622122—24no—
21C22×D44D411yescharacteristic
22C22×C4×D11—21no—
23C2×C11×M16—22no—
24C22×C8×C11D412yes—
25C2×C42×C11C2311yescharacteristic
26C2×(C2×D11)⋊C4—21no—
27#66979—22no—
28C2×C4⋊Dic11D411yescharacteristic
29#66977—22no—
30#66977—22no—
31C22×C11⋊C8—21no—
32C2×Dic44—22no—
33C4×D44—22no—
34C4×D44—22no—
35#66923—22no—
36#66922D412yes—
37#66922D412yes—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8—22no—
42C11×C4⋊C8D414yes—
43#66885—24no—
44#66885—24no—
45(C2×D11)⋊C8—44no—
46#66882—22no—
47#66882—24no—
48#66881—24no—
49#66880—24no—
50C4×C11⋊C8—22no—
51#10258—111nomaximal, Sylow
52C23×D11—21no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×Dic11—21no—
57C2×D44—22no—
58C2×D44—21no—
59C2×D44—22no—
60C2×D44Q1612yescomplemented
61C2×C4×D11—42no—
62C2×C4×D11—42no—
63C2×C4×D11—41no—
64C2×C4×D11—41no—
65C2×Dic22—22no—
66C2×Dic22—22no—
67C11×M16—42no—
68C11×M16—42no—
69C2×C8×C11—22no—
70C2×C8×C11—24no—
71C2×C8×C11—42no—
72C42×C11C2×D412yes—
73C42×C11C2×D412yes—
74C22⋊Dic11—42no—
75(C2×D11)⋊C4—42no—
76C4⋊Dic11—22no—
77C4⋊Dic11—22no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80C4⋊Dic11—22no—
81Dic11⋊C4—42no—
82Dic11⋊C4—42no—
83C4×Dic11—42no—
84C2×C11⋊C8—22no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87Dic44—82no—
88#3249—111no—
89#3077—112no—
90#1954—111no—
91#1493—112no—
92#1292D1111yescharacteristic, complemented
93C23×C11#12111yescharacteristic
94C22×D11—22no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—41no—
98C22×D11—41no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11#12012yes—
103C2×C4×C11#12011yescharacteristic
104C2×C4×C11#12112yes—
105C2×C4×C11#12711yescharacteristic
106C2×C4×C11C2×Q1611yescharacteristic
107C2×C4×C11#13511yescharacteristic
108C2×C4×C11#13712yes—
109C2×Dic11—42no—
110C2×Dic11—42no—
111C2×Dic11—42no—
112C2×Dic11—41no—
113D44—24no—
114D44—42no—
115C4×D11—82no—
116C4×D11—81no—
117C4×D11—81no—
118Dic22—44no—
119Dic22—42no—
120Dic22—42no—
121C8×C11—44no—
122C8×C11—42no—
123C11⋊C8—42no—
124#533—112no—
125C2×C4×D4—111no—
126#478—224no—
127#477—222no—
128#476—222no—
129#474—222no—
130#467—222no—
131#462—222no—
132#428—222no—
133#423C2×D1112yes—
134C2×C4⋊C8C2×D1111yescharacteristic
135#418—222no—
136C2×C22⋊C8—222no—
137C2×C4×C8—111no—
138Q8⋊C8—224no—
139C22×C11—21no—
140C22×C11—21no—
141C22×C11#39211yescharacteristic
142C22×C11#46711yescharacteristic
143C22×C11#47011yescharacteristic
144C2×D11—44no—
145C2×D11—42no—
146C2×D11—82no—
147C2×D11—81no—
148C2×D11—81no—
149C4×C11—21no—
150C4×C11—22no—
151C4×C11#45112yes—
152C4×C11#45212yes—
153C4×C11#45311yescharacteristic
154C4×C11#45411yescharacteristic
155Dic11—82no—
156Dic11—81no—
157Dic11—82no—
158C22×D4—111no—
159C23×C4—221no—
160C2×Q16—222no—
161C2×M16—22no—
162C22×C8—221no—
163C22×C8D4412yes—
164C4⋊Q8—112no—
165C4⋊Q8—112no—
166#125—222no—
167C22⋊Q8—222no—
168C22⋊Q8—222no—
169C4×Q8—222no—
170C4×Q8—222no—
171C4×D4—222no—
172C4×D4—222no—
173#117—222no—
174C2×C4⋊C4—111no—
175C2×C22⋊C4—221no—
176C2×C42C22×D1111yescharacteristic
177#107—224no—
178#107—222no—
179#106—224no—
180C4⋊C8—22no—
181C4⋊C8—22no—
182C4⋊C8D4414yes—
183#103—224no—
184#102—224no—
185#102—224no—
186C22⋊C8—444no—
187C4×C8—222no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#200111yescharacteristic
191C2×C11#200611yescharacteristic
192C2×C11#201711yescharacteristic
193D11—82no—
194C24—221no—
195C2×Q8—222no—
196C2×Q8—222no—
197C2×D4—112no—
198C2×D4—222no—
199C2×D4—221no—
200C2×D4—222no—
201C22×C4—221no—
202C22×C4—442no—
203C22×C4—442no—
204C22×C4—441no—
205C22×C4—441no—
206C22×C4C2×D4411yescharacteristic
207C22×C4D4×D1111yescharacteristic
208C22×C4#434311yescharacteristic
209Q16—882no—
210M16—42no—
211M16—42no—
212C2×C8—24no—
213C2×C8—22no—
214C2×C8—42no—
215C2×C8—222no—
216C2×C8—441no—
217C2×C8—441no—
218C4⋊C4—222no—
219C4⋊C4—222no—
220C4⋊C4—222no—
221C4⋊C4—222no—
222C4⋊C4—222no—
223C4⋊C4—442no—
224C4⋊C4—442no—
225C22⋊C4—442no—
226C22⋊C4—442no—
227C42—442no—
228C42C2×D4412yes—
229C42D4×D1112yes—
230C11#1025811yescharacteristic, complemented, Sylow
231C23—222no—
232C23—442no—
233C23—442no—
234C23—441no—
235C23—441no—
236C23#6694811yescharacteristic
237Q8—444no—
238Q8—442no—
239Q8—442no—
240D4—224no—
241D4—442no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—441no—
249C2×C4—882no—
250C2×C4—881no—
251C2×C4—881no—
252C2×C4#6692711yescharacteristic
253C2×C4#6693511yescharacteristic
254C2×C4#6693512yes—
255C2×C4#6694812yes—
256C2×C4#6696511yescharacteristic
257C2×C4#6696812yes—
258C2×C4Q16×D1111yescharacteristic
259C8—42no—
260C8—44no—
261C8—442no—
262C22—21no—
263C22—21no—
264C22—444no—
265C22—442no—
266C22—882no—
267C22—881no—
268C22—881no—
269C22#1062228411yescharacteristic
270C22#1062248111yescharacteristic
271C22#1062250011yescharacteristic
272C4—21no—
273C4—22no—
274C4—881no—
275C4—882no—
276C4—882no—
277C4#1062236011yescharacteristic
278C4#1062236611yescharacteristic
279C4#1062239612yes—
280C4#1062242112yes—
281C2—21no—
282C2—21no—
283C2—882no—
284C2#1306962711yescharacteristic
285C2#1306966011yescharacteristic
286C2#1306972111yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1292D11
hypocenterC11#10258
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
1. #13079961C2semidirect
4. #13067070C2semidirect
5. C11×#1292C2semidirect
60. C2×D44Q16semidirect
92. #1292D11semidirect
230. C11#10258semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130784152
#130694092
#130670702
C11×#12922
#1025811