Finite Group Databasebeta

← #14658549

Subgroups — #14658549

Order 2816.

292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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#13069598C211yesmaximal, characteristic
2#13068769C211yesmaximal, characteristic
3#13067273C211yesmaximal, characteristic
4#13066513C211yesmaximal, characteristic
5#13066512C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#1542C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×Dic11⋊C8—21no—
12C2×Dic11⋊C8—21no—
13#10622545C2211yescharacteristic
14#10622538C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C11×#333—21no—
18C11×#332—21no—
19#10622185—21no—
20#10622184—21no—
21#10622170—21no—
22#10622170—21no—
23C22×C8×C11—21no—
24C11×C4⋊Q8D411yescharacteristic
25C11×C4⋊Q8D411yescharacteristic
26C11×#125—21no—
27C11×C22⋊Q8—21no—
28C11×C22⋊Q8—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C11×#117—21no—
32C2×C42×C11C2311yescharacteristic
33C2×C4×Dic11D411yescharacteristic
34C2×C4×Dic11D411yescharacteristic
35C2×#4318—21no—
36C22×C11⋊C8—21no—
37C11×C4⋊C8—21no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C22⋊C8—21no—
41C4×C8×C11—21no—
42C11⋊#95—21no—
43C11⋊#95—21no—
44C22⋊(C11⋊C8)—21no—
45Dic11⋊C8—42no—
46Dic11⋊C8—42no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49C4⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)—21no—
52C4×C11⋊C8—21no—
53#10628—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—21no—
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×C4×C11#4111yescharacteristic
59C22×Dic11—21no—
60C22×Dic11—21no—
61C2×C8×C11—41no—
62C2×C8×C11—41no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C11×C22⋊C4—41no—
72C42×C11—41no—
73C42×C11C2×D411yescharacteristic
74C42×C11#4111yescharacteristic
75C42×C11#4111yescharacteristic
76C42×C11#4111yescharacteristic
77C4×Dic11—21no—
78C4×Dic11—21no—
79C4×Dic11SD1612yes—
80C4×Dic11Q1612yes—
81#4318—41no—
82#4318—41no—
83C2×C11⋊C8—41no—
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#1542D1111yescharacteristic
92#1301—111no—
93#1301—111no—
94#1274—111no—
95C23×C11#12311yescharacteristic
96Q8×C11—81no—
97Q8×C11—81no—
98C2×C4×C11—41no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11#12111yescharacteristic
103C2×C4×C11#12311yescharacteristic
104C2×C4×C11#12311yescharacteristic
105C2×C4×C11#12411yescharacteristic
106C2×C4×C11#12611yescharacteristic
107C2×C4×C11#12611yescharacteristic
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11C2×Q1611yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C11#13711yescharacteristic
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116C2×Dic11—41no—
117C2×Dic11—41no—
118C8×C11—81no—
119C8×C11—81no—
120C11⋊C8—81no—
121C11⋊C8—81no—
122C11⋊C8—81no—
123#533C2×D1111yescharacteristic
124#431—111no—
125#431C2×D1111yescharacteristic
126#423—111no—
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—21no—
135#333—221no—
136#332—21no—
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—81no—
148C4×C11—81no—
149C4×C11#46011yescharacteristic
150C4×C11#46211yescharacteristic
151C4×C11#48711yescharacteristic
152C4×C11#48911yescharacteristic
153Dic11—42no—
154Dic11—42no—
155C2×M16—221no—
156C22×C8—21no—
157C22×C8—221no—
158C4⋊Q8C22⋊D1111yescharacteristic
159C4⋊Q8C22⋊D1111yescharacteristic
160#125—21no—
161C22⋊Q8—21no—
162C22⋊Q8—21no—
163C4×Q8—21no—
164C4×Q8—21no—
165#117—21no—
166C2×C42—111no—
167C2×C42—111no—
168C2×C42C22×D1111yescharacteristic
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—221no—
173C4⋊C8—221no—
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—21no—
191C2×Q8—21no—
192C22×C4—221no—
193C22×C4—221no—
194C22×C4#433911yescharacteristic
195C22×C4D4×D1111yescharacteristic
196C22×C4#434111yescharacteristic
197M16—441no—
198M16—441no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—441no—
204C2×C8—441no—
205C2×C8—441no—
206C2×C8—441no—
207C2×C8—441no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C22⋊C4—41no—
215C42—41no—
216C42—112no—
217C42—112no—
218C42—221no—
219C42—221no—
220C42#433911yescharacteristic
221C42#434111yescharacteristic
222C42#434111yescharacteristic
223C42C2×C22⋊D1111yescharacteristic
224C11#1062811yescharacteristic, complemented, Sylow
225C23#6693611yescharacteristic
226Q8—81no—
227Q8—81no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—441no—
235C2×C4—441no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4#6693211yescharacteristic
239C2×C4#6693211yescharacteristic
240C2×C4#6693811yescharacteristic
241C2×C4SD16×D1111yescharacteristic
242C2×C4#6696711yescharacteristic
243C2×C4Q16×D1111yescharacteristic
244C2×C4#6697111yescharacteristic
245C2×C4#6698211yescharacteristic
246C2×C4#6698811yescharacteristic
247C2×C4#6699211yescharacteristic
248C8—81no—
249C8—81no—
250C8—881no—
251C8—881no—
252C8—881no—
253C22—21no—
254C22—21no—
255C22#1062241811yescharacteristic
256C22#1062242211yescharacteristic
257C22#1062256511yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—81no—
263C4—81no—
264C4—442no—
265C4—442no—
266C4#1062240511yescharacteristic
267C4#1062240811yescharacteristic
268C4#1062277611yescharacteristic
269C4#1062279511yescharacteristic
270C2—21no—
271C2—21no—
272C2#1307002711yescharacteristic
273C2#1307006911yescharacteristic
274C2#1307007011yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1542C2
socleC22×C11#397
prime radicalC23×C11#123
hypercenter#1542D11
hypocenterC11#10628
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

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
#130695982
#130687692
#130672732
#130665132
#130665122
#130664442
C11×#15422
#1062811