Finite Group Databasebeta

← #14656267

Subgroups — #14656267

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#13078409C212yesmaximal
2#13069409C211yesmaximal, characteristic
3#13067071C212yesmaximal, complemented
4#13066491C211yesmaximal, characteristic, complemented
5C11×#3249C211yesmaximal, characteristic, complemented
6C11×#533C2212yes—
7C2×C4×D44C2211yescharacteristic
8C11×#477—22no—
9C11×#467—22no—
10C11×#462—22no—
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×(C2×D11)⋊C8—22no—
13#10622700—22no—
14#10622697—22no—
15#10622679—24no—
16#10622614—22no—
17#10622608—22no—
18#10622537C2212yes—
19C2×C4×C11⋊C8C2211yescharacteristic
20Q8⋊(C11⋊C8)—24no—
21C22×D44D411yescharacteristic
22C22×C4×D11—21no—
23C2×C11×Q16—22no—
24C22×C8×C11D412yes—
25C11×C4⋊Q8D412yes—
26C11×C4⋊Q8D412yes—
27C11×#125—22no—
28C11×C22⋊Q8—22no—
29C11×C22⋊Q8—22no—
30C4×Q8×C11—22no—
31C4×Q8×C11—22no—
32C11×#117—22no—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×#4318—22no—
37C22×C11⋊C8—21no—
38C4×D44—22no—
39C4×D44—22no—
40C11×#107—22no—
41C11×C4⋊C8—22no—
42C11×#103—24no—
43(C2×D11)⋊C8—44no—
44#66873—24no—
45#66873—24no—
46#66872—24no—
47#66871—24no—
48C4⋊(C11⋊C8)—22no—
49C4⋊(C11⋊C8)D414yes—
50C4×C11⋊C8—22no—
51#10258—111nomaximal, Sylow
52C23×D11—21no—
53C2×Q8×C11—22no—
54C2×Q8×C11—22no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—21no—
59C2×D44—22no—
60C2×D44—21no—
61C2×D44—22no—
62C2×D44Q1612yescomplemented
63C2×C4×D11—42no—
64C2×C4×D11—42no—
65C2×C4×D11—41no—
66C2×C4×D11—41no—
67C11×Q16—82no—
68C2×C8×C11—22no—
69C2×C8×C11—42no—
70C11×C4⋊C4—22no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C4⋊C4—22no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—42no—
76C11×C22⋊C4—42no—
77C42×C11—42no—
78C42×C11C2×D412yes—
79C42×C11C2×D412yes—
80(C2×D11)⋊C4—42no—
81C4⋊Dic11—22no—
82#4318—42no—
83#4318—42no—
84C2×C11⋊C8—22no—
85C2×C11⋊C8—24no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88#3249D1111yescharacteristic, complemented
89#3077—112no—
90#1954—111no—
91#1493—112no—
92#1292—111no—
93C23×C11#12111yescharacteristic
94C22×D11—22no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—41no—
98C22×D11—41no—
99Q8×C11—44no—
100Q8×C11—42no—
101Q8×C11—42no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—42no—
107C2×C4×C11#12012yes—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11#12112yes—
110C2×C4×C11#12711yescharacteristic
111C2×C4×C11C2×Q1611yescharacteristic
112C2×C4×C11#13511yescharacteristic
113C2×C4×C11#13712yes—
114C2×Dic11—42no—
115C2×Dic11—41no—
116D44—24no—
117D44—42no—
118C4×D11—82no—
119C4×D11—81no—
120C4×D11—81no—
121C8×C11—42no—
122C11⋊C8—42no—
123C11⋊C8—44no—
124#533C2×D1112yes—
125C2×C4×D4—111no—
126#478—224no—
127#477—22no—
128#476—222no—
129#474—222no—
130#467—22no—
131#462—22no—
132#428—222no—
133#423—112no—
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—82no—
152C4×C11—82no—
153C4×C11#45112yes—
154C4×C11#45212yes—
155C4×C11#45311yescharacteristic
156C4×C11#45411yescharacteristic
157Dic11—81no—
158C22×D4—111no—
159C23×C4—221no—
160C2×Q16—22no—
161C2×M16—222no—
162C22×C8—221no—
163C22×C8C22⋊D1112yes—
164C4⋊Q8C22⋊D1112yes—
165C4⋊Q8C22⋊D1112yes—
166#125—22no—
167C22⋊Q8—22no—
168C22⋊Q8—22no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×D4—222no—
172C4×D4—222no—
173#117—22no—
174C2×C4⋊C4—111no—
175C2×C22⋊C4—221no—
176C2×C42C22×D1111yescharacteristic
177#107—22no—
178#107—224no—
179#106—224no—
180C4⋊C8—22no—
181C4⋊C8—114no—
182C4⋊C8—222no—
183#103—24no—
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—22no—
196C2×Q8—22no—
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×C4D4×D1111yescharacteristic
207C22×C4#434111yescharacteristic
208C22×C4C2×C22⋊D1111yescharacteristic
209Q16—82no—
210M16—442no—
211M16—442no—
212C2×C8—22no—
213C2×C8—42no—
214C2×C8—222no—
215C2×C8—224no—
216C2×C8—441no—
217C2×C8—441no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—222no—
225C22⋊C4—42no—
226C22⋊C4—442no—
227C42—42no—
228C42D4×D1112yes—
229C42C2×C22⋊D1112yes—
230C11#1025811yescharacteristic, complemented, Sylow
231C23—222no—
232C23—442no—
233C23—442no—
234C23—441no—
235C23—441no—
236C23#6699111yescharacteristic
237Q8—44no—
238Q8—42no—
239Q8—42no—
240D4—224no—
241D4—442no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—442no—
248C2×C4—441no—
249C2×C4—882no—
250C2×C4—881no—
251C2×C4—881no—
252C2×C4Q16×D1111yescharacteristic
253C2×C4#6697112yes—
254C2×C4#6697211yescharacteristic
255C2×C4#6699012yes—
256C2×C4#6699212yes—
257C2×C4#6699311yescharacteristic
258C2×C4#6700611yescharacteristic
259C8—42no—
260C8—442no—
261C8—444no—
262C22—21no—
263C22—21no—
264C22—444no—
265C22—442no—
266C22—882no—
267C22—881no—
268C22—881no—
269C22#1062280111yescharacteristic
270C22#1062280211yescharacteristic
271C22#1062283611yescharacteristic
272C4—21no—
273C4—22no—
274C4—82no—
275C4—82no—
276C4—881no—
277C4#1062279912yes—
278C4#1062280012yes—
279C4#1062285411yescharacteristic
280C4#1062285811yescharacteristic
281C2—21no—
282C2—21no—
283C2—882no—
284C2#1306962311yescharacteristic
285C2#1306965811yescharacteristic
286C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3249C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#3249D11
hypocenterC11#10258
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
3. #13067071C2semidirect
4. #13066491C2semidirect
5. C11×#3249C2semidirect
62. C2×D44Q16semidirect
88. #3249D11semidirect
230. C11#10258semidirect

Maximal subgroups

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

subgroupindex
#130784092
#130694092
#130670712
#130664912
C11×#32492
#1025811