Finite Group Databasebeta

← #14658560

Subgroups — #14658560

Order 2816.

272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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#13068735C211yesmaximal, 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
12#10622545C2211yescharacteristic
13#10622538C2211yescharacteristic
14C2×C4⋊(C11⋊C8)C2211yescharacteristic
15#10622193—21no—
16#10622193—21no—
17#10622188—21no—
18#10622188—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—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4×C11⋊C8—21no—
51#10630—111nomaximal, Sylow
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×C4×C11#4111yescharacteristic
55C22×Dic11—21no—
56C22×Dic11—21no—
57C2×Dic22—21no—
58C2×Dic22—21no—
59C11×M16—41no—
60C11×M16—41no—
61C2×C8×C11—41no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11—41no—
66C42×C11C2×D411yescharacteristic
67C42×C11#4111yescharacteristic
68C42×C11#4111yescharacteristic
69C42×C11#4111yescharacteristic
70C22⋊Dic11—41no—
71C4⋊Dic11—21no—
72C4⋊Dic11—21no—
73C4⋊Dic11—21no—
74C4⋊Dic11—21no—
75Dic11⋊C4—41no—
76Dic11⋊C4—41no—
77C4×Dic11—21no—
78C4×Dic11—21no—
79C4×Dic11—21no—
80C4×Dic11—21no—
81C4×Dic11—41no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85C2×C11⋊C8—41no—
86#1995—111no—
87#1832—111no—
88#1542—111no—
89#1542—111no—
90#1301—111no—
91#1301D1111yescharacteristic
92#1274—111no—
93C23×C11#12311yescharacteristic
94C2×C4×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11#12111yescharacteristic
97C2×C4×C11#12311yescharacteristic
98C2×C4×C11#12311yescharacteristic
99C2×C4×C11#12411yescharacteristic
100C2×C4×C11#12611yescharacteristic
101C2×C4×C11#12611yescharacteristic
102C2×C4×C11#13511yescharacteristic
103C2×C4×C11#13511yescharacteristic
104C2×C4×C11#13711yescharacteristic
105C2×C4×C11#13711yescharacteristic
106C2×Dic11—41no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109C2×Dic11—41no—
110C2×Dic11—41no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113C2×Dic11—41no—
114Dic22—81no—
115Dic22—81no—
116C8×C11—81no—
117C8×C11—81no—
118C8×C11—81no—
119C11⋊C8—81no—
120C11⋊C8—81no—
121#533—111no—
122#431—111no—
123#431C2×D1111yescharacteristic
124#423C2×D1111yescharacteristic
125C2×C4⋊C8—111no—
126C2×C4⋊C8C2×D1111yescharacteristic
127#376—111no—
128#339—221no—
129#339—221no—
130#336—221no—
131#336—221no—
132#333—221no—
133#333—221no—
134#332—221no—
135#332—221no—
136C22×C11—21no—
137C22×C11—21no—
138C22×C11#39711yescharacteristic
139C22×C11#48511yescharacteristic
140C22×C11#48511yescharacteristic
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11#46411yescharacteristic
146C4×C11#46411yescharacteristic
147C4×C11#48811yescharacteristic
148C4×C11#49111yescharacteristic
149Dic11—81no—
150Dic11—81no—
151Dic11—81no—
152Dic11—81no—
153C2×M16—21no—
154C22×C8—21no—
155C22×C8—221no—
156C4⋊Q8—111no—
157C4⋊Q8—111no—
158#125—221no—
159C22⋊Q8—221no—
160C22⋊Q8—221no—
161C4×Q8—221no—
162C4×Q8—221no—
163#117—221no—
164C2×C42—111no—
165C2×C42—111no—
166C2×C42C22×D1111yescharacteristic
167C4⋊C8—21no—
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—221no—
173C4⋊C8—221no—
174C4⋊C8—221no—
175C22⋊C8—21no—
176C22⋊C8—221no—
177C4×C8—21no—
178C4×C8—221no—
179#95—221no—
180#95—221no—
181C2×C11—21no—
182C2×C11—21no—
183C2×C11#207411yescharacteristic
184C2×C11#208011yescharacteristic
185C2×C11#208011yescharacteristic
186C2×Q8—221no—
187C2×Q8—221no—
188C22×C4—221no—
189C22×C4—221no—
190C22×C4#433911yescharacteristic
191C22×C4D4×D1111yescharacteristic
192C22×C4#434311yescharacteristic
193M16—41no—
194M16—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—441no—
201C2×C8—441no—
202C2×C8—441no—
203C2×C8—441no—
204C4⋊C4—221no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—441no—
209C4⋊C4—441no—
210C22⋊C4—441no—
211C42—221no—
212C42—221no—
213C42—221no—
214C42—221no—
215C42—441no—
216C42#433911yescharacteristic
217C42#433911yescharacteristic
218C42D4×D1111yescharacteristic
219C42#434111yescharacteristic
220C11#1063011yescharacteristic, complemented, Sylow
221C23#6694711yescharacteristic
222Q8—881no—
223Q8—881no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—441no—
227C2×C4—441no—
228C2×C4—441no—
229C2×C4—441no—
230C2×C4—441no—
231C2×C4—441no—
232C2×C4—441no—
233C2×C4—441no—
234C2×C4#6692911yescharacteristic
235C2×C4#6693611yescharacteristic
236C2×C4#6693711yescharacteristic
237C2×C4#6693811yescharacteristic
238C2×C4#6694711yescharacteristic
239C2×C4#6695111yescharacteristic
240C2×C4#6696511yescharacteristic
241C2×C4#6696811yescharacteristic
242C2×C4#6696911yescharacteristic
243C2×C4#6697111yescharacteristic
244C8—81no—
245C8—81no—
246C8—81no—
247C8—881no—
248C8—881no—
249C22—21no—
250C22—21no—
251C22#1062228811yescharacteristic
252C22#1062248011yescharacteristic
253C22#1062250111yescharacteristic
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—881no—
259C4—881no—
260C4—881no—
261C4—881no—
262C4#1062238011yescharacteristic
263C4#1062238111yescharacteristic
264C4#1062241011yescharacteristic
265C4#1062241111yescharacteristic
266C2—21no—
267C2—21no—
268C2#1307003811yescharacteristic
269C2#1307007111yescharacteristic
270C2#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#10630
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
220. C11#10630semidirect

Maximal subgroups

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

subgroupindex
#130695962
#130687352
#130672742
#130672712
#130665112
#130664442
C11×#13012
#1063011