Finite Group Databasebeta

← #14658611

Subgroups — #14658611

Order 2816.

298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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#13068628C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic
4#13067012C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic
7C11×#1286C211yesmaximal, characteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#382C2211yescharacteristic
12C2×#66888—21no—
13C2×#66874—21no—
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17#10622192—21no—
18#10622167—21no—
19#10622096—22no—
20#10622094—22no—
21C22×Dic22D411yescharacteristic
22C2×C11×M16—21no—
23C2×C11×C4⋊C4—21no—
24C2×C42×C11C2311yescharacteristic
25C2×C4⋊Dic11D411yescharacteristic
26C2×Dic11⋊C4—21no—
27C2×C4×Dic11—21no—
28C2×#4318—21no—
29C22×C11⋊C8—21no—
30C4×Dic22—21no—
31C4×Dic22—21no—
32C4×Dic22—21no—
33C4×Dic22—21no—
34C11×C4⋊C8—21no—
35C11×C4⋊C8—21no—
36C11×C4⋊C8—21no—
37C11×C22⋊C8—21no—
38C4×C8×C11D412yes—
39C11×#95—21no—
40C11×#95—21no—
41C22⋊(C11⋊C8)—21no—
42#66888—42no—
43#66874—42no—
44C4⋊(C11⋊C8)—21no—
45C4⋊(C11⋊C8)—21no—
46C4⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4×C11⋊C8—21no—
50#10639—111nomaximal, Sylow
51C22×C4×C11—41no—
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—21no—
56C22×Dic11—21no—
57C2×Dic22—21no—
58C2×Dic22—21no—
59C2×Dic22—21no—
60C2×Dic22—21no—
61C2×Dic22—21no—
62C2×Dic22D812yes—
63C11×M16—41no—
64C11×M16—41no—
65C2×C8×C11—22no—
66C2×C8×C11—41no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C42×C11C2×D411yescharacteristic
70C42×C11#4111yescharacteristic
71C42×C11#4111yescharacteristic
72C42×C11#4111yescharacteristic
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75Dic11⋊C4—41no—
76Dic11⋊C4—41no—
77C4×Dic11—41no—
78C4×Dic11—41no—
79#4318—41no—
80#4318—41no—
81C2×C11⋊C8—41no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86#1805—111no—
87#1801—111no—
88#1571—111no—
89#1479—111no—
90#1301—111no—
91#1286—111no—
92#1286D1111yescharacteristic
93C23×C11#12311yescharacteristic
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—81no—
97C2×C4×C11—81no—
98C2×C4×C11—81no—
99C2×C4×C11#12111yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12311yescharacteristic
102C2×C4×C11#12411yescharacteristic
103C2×C4×C11#12611yescharacteristic
104C2×C4×C11#12611yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11#13511yescharacteristic
107C2×C4×C11#13711yescharacteristic
108C2×C4×C11#13711yescharacteristic
109C2×Dic11—22no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—81no—
114Dic22—22no—
115Dic22—22no—
116Dic22—41no—
117Dic22—41no—
118C8×C11—42no—
119C8×C11—81no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C11⋊C8—81no—
123C2×C4×Q8—111no—
124#431—111no—
125#431C2×D1111yescharacteristic
126#423—111no—
127#423C2×D1111yescharacteristic
128C2×C4⋊C8—111no—
129C2×#103—221no—
130C2×#101—221no—
131#382C2×D1111yescharacteristic
132#343—221no—
133#340—221no—
134#335—222no—
135Q8⋊C8—222no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11#39711yescharacteristic
139C22×C11#48011yescharacteristic
140C22×C11#48511yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—161no—
146C4×C11#46611yescharacteristic
147C4×C11#47011yescharacteristic
148C4×C11#48011yescharacteristic
149C4×C11#48511yescharacteristic
150Dic11—42no—
151Dic11—81no—
152C22×Q8—111no—
153C2×M16—21no—
154C2×M16—221no—
155C22×C8—221no—
156C4×Q8—221no—
157C4×Q8—221no—
158C4×Q8—221no—
159C4×Q8—221no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—221no—
163C2×C42—221no—
164C2×C42C22×D1111yescharacteristic
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—221no—
169C4⋊C8—221no—
170C4⋊C8—221no—
171C4⋊C8—221no—
172C4⋊C8—221no—
173#103—442no—
174#101—442no—
175C22⋊C8—21no—
176C22⋊C8—221no—
177C4×C8—221no—
178C4×C8D4412yes—
179#95—21no—
180#95—21no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11#207511yescharacteristic
184C2×C11#208011yescharacteristic
185C2×C11#208211yescharacteristic
186C2×Q8—112no—
187C2×Q8—221no—
188C2×Q8—221no—
189C2×Q8—221no—
190C2×Q8—221no—
191C2×Q8—221no—
192C22×C4—41no—
193C22×C4—221no—
194C22×C4—221no—
195C22×C4#433911yescharacteristic
196C22×C4D4×D1111yescharacteristic
197C22×C4#434111yescharacteristic
198M16—41no—
199M16—41no—
200M16—441no—
201M16—441no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—441no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C2×C8—441no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—221no—
212C4⋊C4—221no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C42—441no—
216C42—441no—
217C42C2×D4411yescharacteristic
218C42#433911yescharacteristic
219C42#434111yescharacteristic
220C42#434311yescharacteristic
221C11#1063911yescharacteristic, complemented, Sylow
222C23#6693611yescharacteristic
223Q8—222no—
224Q8—222no—
225Q8—441no—
226Q8—441no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—222no—
233C2×C4—441no—
234C2×C4—441no—
235C2×C4—441no—
236C2×C4—881no—
237C2×C4#6692811yescharacteristic
238C2×C4#6693611yescharacteristic
239C2×C4#6693911yescharacteristic
240C2×C4#6694811yescharacteristic
241C2×C4#6695111yescharacteristic
242C2×C4#6695111yescharacteristic
243C2×C4D8×D1111yescharacteristic
244C2×C4#6696811yescharacteristic
245C2×C4#6696811yescharacteristic
246C2×C4#6697211yescharacteristic
247C8—42no—
248C8—81no—
249C8—881no—
250C8—881no—
251C8—881no—
252C22—21no—
253C22—21no—
254C22#1062228711yescharacteristic
255C22#1062238711yescharacteristic
256C22#1062242711yescharacteristic
257C4—21no—
258C4—21no—
259C4—21no—
260C4—21no—
261C4—161no—
262C4—442no—
263C4—881no—
264C4#1062238711yescharacteristic
265C4#1062242711yescharacteristic
266C4#1062248111yescharacteristic
267C4#1062249611yescharacteristic
268C2—21no—
269C2—21no—
270C2#1307004111yescharacteristic
271C2#1307006811yescharacteristic
272C2#1307008211yescharacteristic
subgroupG/H
centerC22#10622287
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1286C2
socleC22×C11#397
prime radicalC23×C11#123
hypercenter#1286D11
hypocenterC11#10639
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
221. C11#10639semidirect

Maximal subgroups

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

subgroupindex
#130686282
#130686092
#130673912
#130670122
#130665112
#130664742
C11×#12862
#1063911