Finite Group Databasebeta

← #14658550

Subgroups — #14658550

Order 2816.

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

normal subgroups only

This group has 292 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#13069596C211yesmaximal, characteristic
2#13068769C211yesmaximal, characteristic
3#13067274C211yesmaximal, characteristic
4#13067271C211yesmaximal, characteristic
5#13066511C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×Dic11⋊C8—21no—
13C2×Dic11⋊C8—21no—
14#10622545C2211yescharacteristic
15#10622538C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17#10622193—21no—
18#10622193—21no—
19#10622124—21no—
20#10622120—21no—
21#10622119—21no—
22#10622119—21no—
23C2×C11×M16—21no—
24C22×C8×C11—21no—
25C2×C42×C11C2311yescharacteristic
26#66979—21no—
27#66977—21no—
28#66977—21no—
29C2×C4×Dic11D411yescharacteristic
30C2×C4×Dic11D411yescharacteristic
31C22×C11⋊C8—21no—
32#66923—21no—
33#66922D411yescharacteristic
34#66922D411yescharacteristic
35C4×Dic22—21no—
36C4×Dic22—21no—
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8—21no—
42C11×C22⋊C8—21no—
43C4×C8×C11—21no—
44C11⋊#95—21no—
45C11⋊#95—21no—
46C22⋊(C11⋊C8)—21no—
47Dic11⋊C8—42no—
48Dic11⋊C8—42no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4×C11⋊C8—21no—
53#10628—111nomaximal, Sylow
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×C4×C11#4111yescharacteristic
57C22×Dic11—21no—
58C22×Dic11—21no—
59C2×Dic22—21no—
60C2×Dic22—21no—
61C11×M16—41no—
62C11×M16—41no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C2×C8×C11—41no—
67C2×C8×C11—41no—
68C42×C11C2×D411yescharacteristic
69C42×C11#4111yescharacteristic
70C42×C11#4111yescharacteristic
71C42×C11#4111yescharacteristic
72C22⋊Dic11—41no—
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77Dic11⋊C4—41no—
78Dic11⋊C4—41no—
79C4×Dic11—21no—
80C4×Dic11—21no—
81C4×Dic11—41no—
82C4×Dic11SD1612yes—
83C4×Dic11Q1612yes—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86C2×C11⋊C8—41no—
87C2×C11⋊C8—41no—
88#1995—111no—
89#1843—111no—
90#1542—111no—
91#1542—111no—
92#1301—111no—
93#1301D1111yescharacteristic
94#1274—111no—
95C23×C11#12311yescharacteristic
96C2×C4×C11—41no—
97C2×C4×C11—41no—
98C2×C4×C11#12111yescharacteristic
99C2×C4×C11#12311yescharacteristic
100C2×C4×C11#12311yescharacteristic
101C2×C4×C11#12411yescharacteristic
102C2×C4×C11#12611yescharacteristic
103C2×C4×C11#12611yescharacteristic
104C2×C4×C11C2×SD1611yescharacteristic
105C2×C4×C11C2×Q1611yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C11#13711yescharacteristic
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116Dic22—81no—
117Dic22—81no—
118C8×C11—81no—
119C8×C11—81no—
120C8×C11—81no—
121C11⋊C8—81no—
122C11⋊C8—81no—
123#533—111no—
124#431—111no—
125#431C2×D1111yescharacteristic
126#423C2×D1111yescharacteristic
127C2×C4⋊C8—111no—
128C2×C4⋊C8—221no—
129C2×C4⋊C8—221no—
130C2×C4⋊C8C2×D1111yescharacteristic
131#376—111no—
132#339—221no—
133#339—221no—
134#333—221no—
135#333—221no—
136#332—221no—
137#332—221no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#39711yescharacteristic
141C22×C11#48311yescharacteristic
142C22×C11#48411yescharacteristic
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—21no—
146C4×C11—21no—
147C4×C11#46011yescharacteristic
148C4×C11#46211yescharacteristic
149C4×C11#48711yescharacteristic
150C4×C11#48911yescharacteristic
151Dic11—42no—
152Dic11—42no—
153Dic11—81no—
154Dic11—81no—
155C2×M16—21no—
156C22×C8—21no—
157C22×C8—221no—
158C4⋊Q8—111no—
159C4⋊Q8—111no—
160#125—221no—
161C22⋊Q8—221no—
162C22⋊Q8—221no—
163C4×Q8—221no—
164C4×Q8—221no—
165#117—221no—
166C2×C42—111no—
167C2×C42—111no—
168C2×C42C22×D1111yescharacteristic
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—221no—
175C4⋊C8—221no—
176C4⋊C8—221no—
177C4⋊C8—442no—
178C4⋊C8—442no—
179C22⋊C8—21no—
180C22⋊C8—221no—
181C4×C8—21no—
182C4×C8—221no—
183#95—221no—
184#95—221no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11#207211yescharacteristic
188C2×C11#208011yescharacteristic
189C2×C11#208011yescharacteristic
190C2×Q8—221no—
191C2×Q8—221no—
192C22×C4—221no—
193C22×C4—221no—
194C22×C4#433911yescharacteristic
195C22×C4D4×D1111yescharacteristic
196C22×C4#434311yescharacteristic
197M16—41no—
198M16—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—441no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—221no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C22⋊C4—441no—
215C42—112no—
216C42—112no—
217C42—221no—
218C42—221no—
219C42—441no—
220C42#433911yescharacteristic
221C42#433911yescharacteristic
222C42D4×D1111yescharacteristic
223C42#434111yescharacteristic
224C11#1062811yescharacteristic, complemented, Sylow
225C23#6694711yescharacteristic
226Q8—881no—
227Q8—881no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—441no—
233C2×C4—441no—
234C2×C4—441no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4#6692911yescharacteristic
239C2×C4#6693611yescharacteristic
240C2×C4#6693711yescharacteristic
241C2×C4#6693811yescharacteristic
242C2×C4#6694711yescharacteristic
243C2×C4#6695111yescharacteristic
244C2×C4#6696411yescharacteristic
245C2×C4SD16×D1111yescharacteristic
246C2×C4#6696811yescharacteristic
247C2×C4Q16×D1111yescharacteristic
248C8—81no—
249C8—81no—
250C8—81no—
251C8—881no—
252C8—881no—
253C22—21no—
254C22—21no—
255C22#1062228811yescharacteristic
256C22#1062247511yescharacteristic
257C22#1062249711yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—442no—
263C4—442no—
264C4—881no—
265C4—881no—
266C4#1062237511yescharacteristic
267C4#1062237811yescharacteristic
268C4#1062240511yescharacteristic
269C4#1062240611yescharacteristic
270C2—21no—
271C2—21no—
272C2#1307002811yescharacteristic
273C2#1307007111yescharacteristic
274C2#1307007211yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#397
prime radicalC23×C11#123
hypercenter#1301D11
hypocenterC11#10628
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
224. C11#10628semidirect

Maximal subgroups

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

subgroupindex
#130695962
#130687692
#130672742
#130672712
#130665112
#130664442
C11×#13012
#1062811