Finite Group Databasebeta

← #14666550

Subgroups — #14666550

Order 2816.

460 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 59 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#13075642C211yesmaximal, characteristic
2#13069777C211yesmaximal, characteristic, complemented
3#13067558C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C11×#1319C211yesmaximal, characteristic, complemented
6C2×#67000—21no—
7#10623031C2211yescharacteristic
8C11×#391C2211yescharacteristic
9#10622838—21no—
10#10622604C2212yes—
11#10622552—21no—
12#10622344—22no—
13#10622284—22no—
14#10622283—22no—
15C11×#324C2212yes—
16#10622168C2211yescharacteristic
17#10622161—21no—
18#10622105—22no—
19C22×Q8×C11D411yescharacteristic
20C22×D44—21no—
21C22×D44—21no—
22C22×D44D412yes—
23C2×C11×C4⋊C4C2311yescharacteristic
24C2×C42×C11D411yescharacteristic
25#67000—42no—
26#67000—42no—
27C2×(C2×D11)⋊C4—22no—
28C2×(C2×D11)⋊C4—22no—
29C2×(C2×D11)⋊C4—22no—
30C2×(C2×D11)⋊C4—22no—
31#66979—21no—
32C2×C4⋊Dic11—21no—
33#66977—22no—
34C2×C4×Dic11—21no—
35C2×#4318—21no—
36C2×#4314—42no—
37#66943—41no—
38#66941—41no—
39C11×C22⋊C8—22no—
40C11×#95—22no—
41#66899—41no—
42#66899—41no—
43C11⋊#95D412yes—
44#66885—42no—
45#12212—111nomaximal, Sylow
46C23×D11—22no—
47C2×Q8×C11—21no—
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11SD1612yescomplemented
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D412yes—
55C22×Dic11—22no—
56C2×D44—42no—
57C2×D44—42no—
58C2×D44—42no—
59C2×D44—82no—
60C2×D44—81no—
61C2×D44—81no—
62C2×D44—81no—
63C2×D44—81no—
64C2×Dic22—22no—
65C2×C8×C11—42no—
66C11×C4⋊C4—41no—
67C42×C11—41no—
68C22⋊Dic11—41no—
69(C2×D11)⋊C4—44no—
70(C2×D11)⋊C4—44no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—82no—
74C4⋊Dic11—22no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77C4⋊Dic11—81no—
78Dic11⋊C4—42no—
79C4×Dic11—41no—
80C4×Dic11—42no—
81#4318—41no—
82#4318—41no—
83C2×C11⋊C8—41no—
84#4314—84no—
85#2733—111no—
86#2028—111no—
87#1599—112no—
88#1345—112no—
89#1319D1111yescharacteristic, complemented
90C23×C11#12011yescharacteristic
91C22×D11—42no—
92C22×D11—42no—
93C22×D11—42no—
94C22×D11—42no—
95C22×D11—42no—
96C22×D11—42no—
97C22×D11—42no—
98Q8×C11—42no—
99Q8×C11—81no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—41no—
106C2×C4×C11—41no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11C2×SD1611yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117D44—44no—
118D44—82no—
119D44—84no—
120D44—84no—
121Dic22—82no—
122C8×C11—82no—
123C11⋊C8—81no—
124#544—111no—
125C2×#124—221no—
126#450—222no—
127#419—221no—
128#394—112no—
129#392—222no—
130#391C2×D1111yescharacteristic
131#390—221no—
132#388—222no—
133#343—111no—
134#339—221no—
135#328—222no—
136#324C2×D1112yes—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11#45011yescharacteristic
140C22×C11#45511yescharacteristic
141C22×C11B(4,𝔽2)11yescharacteristic
142C2×D11—82no—
143C2×D11—82no—
144C2×D11—82no—
145C2×D11—82no—
146C2×D11—82no—
147C2×D11—82no—
148C2×D11—82no—
149C4×C11—21no—
150C4×C11—21no—
151C4×C11—42no—
152C4×C11—42no—
153C4×C11—42no—
154Dic11—82no—
155Dic11—81no—
156Dic11—81no—
157C22×Q8D4411yescharacteristic
158C22×D4—112no—
159C22×D4—221no—
160C22×D4—221no—
161C2×SD16—442no—
162C2×M16—221no—
163C4⋊Q8—441no—
164#125—441no—
165#124—442no—
166#124—442no—
167C22⋊Q8—222no—
168#117—221no—
169C2×C4⋊C4—221no—
170C2×C4⋊C4C22×D1111yescharacteristic
171C2×C22⋊C4—222no—
172C2×C22⋊C4—222no—
173C2×C22⋊C4—222no—
174C2×C22⋊C4—222no—
175C2×C42—221no—
176C2×C42D4411yescharacteristic
177#103—441no—
178#103—441no—
179#102—442no—
180C22⋊C8—22no—
181#95—22no—
182#95—112no—
183C2×C11—21no—
184C2×C11—21no—
185C2×C11#160111yescharacteristic
186C2×C11#219911yescharacteristic
187C2×C11#220411yescharacteristic
188D11—162no—
189C24—222no—
190C2×Q8—21no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8—222no—
194C2×Q8#431412yescomplemented
195C2×D4—442no—
196C2×D4—442no—
197C2×D4—442no—
198C2×D4—882no—
199C2×D4—881no—
200C2×D4—881no—
201C2×D4—881no—
202C2×D4—881no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—222no—
206C22×C4C2×D4411yescharacteristic
207C22×C4D4×D1112yes—
208SD16—884no—
209M16—441no—
210M16—441no—
211C2×C8—42no—
212C2×C8—441no—
213C4⋊C4—41no—
214C4⋊C4—222no—
215C4⋊C4—221no—
216C4⋊C4—221no—
217C4⋊C4—442no—
218C4⋊C4—881no—
219C22⋊C4—444no—
220C22⋊C4—444no—
221C22⋊C4—441no—
222C22⋊C4—442no—
223C22⋊C4—442no—
224C22⋊C4—882no—
225C42—41no—
226C42—442no—
227C42—441no—
228C11#1221211yescharacteristic, complemented, Sylow
229C23—442no—
230C23—442no—
231C23—442no—
232C23—442no—
233C23—442no—
234C23—442no—
235C23—442no—
236C23#6693511yescharacteristic
237Q8—42no—
238Q8—81no—
239Q8—882no—
240D4—444no—
241D4—882no—
242D4—884no—
243D4—884no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—442no—
255C2×C4—442no—
256C2×C4—442no—
257C2×C4—441no—
258C2×C4—441no—
259C2×C4C2×#431411yescharacteristic
260C2×C4#6696111yescharacteristic
261C8—82no—
262C8—881no—
263C22—21no—
264C22—21no—
265C22—882no—
266C22—882no—
267C22—882no—
268C22—882no—
269C22—882no—
270C22—882no—
271C22—882no—
272C22#1062234411yescharacteristic
273C22#1062235411yescharacteristic
274C22#1062235911yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—42no—
280C4—882no—
281C4—881no—
282C4—881no—
283C2—21no—
284C2—21no—
285C2—1762no—
286C2#1306757011yescharacteristic
287C2#1307061911yescharacteristic
288C2#1307064411yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11B(4,𝔽2)
prime radical#13075642C2
hypercenter#1319D11
hypocenterC11#12212
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
2. #13069777C2semidirect
3. #13067558C2semidirect
4. #13066620C2semidirect
5. C11×#1319C2semidirect
50. C2×Q8×C11SD16semidirect
89. #1319D11semidirect
194. C2×Q8#4314semidirect
228. C11#12212semidirect

Maximal subgroups

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

subgroupindex
#130756422
#130697772
#130675582
#130666202
C11×#13192
#1221211