Finite Group Databasebeta

← #14652258

Subgroups — #14652258

Order 2816.

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

normal subgroups only

This group has 312 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#13067407C211yesmaximal, characteristic, complemented
2#13067278C211yesmaximal, characteristic
3#13067033C211yesmaximal, characteristic
4#13066899C211yesmaximal, characteristic, complemented
5#13066505C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C11×#423C2211yescharacteristic
10C2×C4×C8×C11C2211yescharacteristic
11#10622538C2211yescharacteristic
12#10622538C2211yescharacteristic
13#10622538C2211yescharacteristic
14C4×#4318C2211yescharacteristic
15C11×D4⋊C8—21no—
16C11×D4⋊C8—21no—
17#10622184C411yescharacteristic
18#10622184C411yescharacteristic
19#10622182C411yescharacteristic
20#10622182C411yescharacteristic
21D4⋊(C11⋊C8)—21no—
22D4⋊(C11⋊C8)—21no—
23#10622118—21no—
24#10622117—21no—
25#10622093—21no—
26C8×C11⋊C8—21no—
27C2×C11×#41—21no—
28C2×C11×M16—21no—
29C22×C8×C11—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#127C2×C411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4318—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C4×C8×C11—21no—
42C4×C8×C11D411yescharacteristic
43C4×C8×C11D411yescharacteristic
44C22⋊(C11⋊C8)—21no—
45C22⋊(C11⋊C8)—21no—
46C22⋊(C11⋊C8)—21no—
47C4⋊(C11⋊C8)C2×C411yescharacteristic
48C4⋊(C11⋊C8)C2×C411yescharacteristic
49C4⋊(C11⋊C8)C2×C411yescharacteristic
50C4⋊(C11⋊C8)C2×C411yescharacteristic
51C4⋊(C11⋊C8)D411yescharacteristic
52C4⋊(C11⋊C8)D411yescharacteristic
53#66867—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58#9586—111nomaximal, Sylow
59C11×#41—81no—
60C11×#41—81no—
61C2×Q8×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11#4111yescharacteristic
68C22×C4×C11#4111yescharacteristic
69C22×C4×C11#4111yescharacteristic
70C11×M16—81no—
71C2×C8×C11—22no—
72C2×C8×C11—22no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—41no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C22⋊C4—41no—
79C11×C22⋊C4—41no—
80C42×C11C22×C411yescharacteristic
81C42×C11C2×D411yescharacteristic
82C42×C11C2×D411yescharacteristic
83C42×C11#4111yescharacteristic
84#4318—22no—
85#4318—41no—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—21no—
88C2×C11⋊C8—21no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—41no—
93#1574—111no—
94#1543—111no—
95#1492D1111yescharacteristic
96#1484—111no—
97#1450—111no—
98#1299—111no—
99#1278—111no—
100C23×C11—41no—
101C23×C11#12611yescharacteristic
102Q8×C11—81no—
103D4×C11—41no—
104D4×C11—41no—
105D4×C11—41no—
106D4×C11—41no—
107D4×C11—81no—
108D4×C11—82no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—41no—
116C2×C4×C11—81no—
117C2×C4×C11—81no—
118C2×C4×C11#11711yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11C4×D411yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11#12411yescharacteristic
124C8×C11—22no—
125C8×C11—22no—
126C8×C11—81no—
127C11⋊C8—42no—
128C11⋊C8—41no—
129C11⋊C8—41no—
130C11⋊C8—41no—
131C11⋊C8—41no—
132C11⋊C8—41no—
133C11⋊C8—41no—
134#532C2×D1111yescharacteristic
135#431—111no—
136#431—111no—
137#431—111no—
138#423C2×D1111yescharacteristic
139C4×M16—111no—
140C2×C4×C8C2×D1111yescharacteristic
141#335—221no—
142#334—221no—
143#333—111no—
144#333—111no—
145#331—111no—
146#331—111no—
147D4⋊C8—21no—
148D4⋊C8—21no—
149D4⋊C8—221no—
150D4⋊C8—221no—
151#322—221no—
152C82—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—81no—
157C22×C11—81no—
158C22×C11—81no—
159C22×C11#38811yescharacteristic
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11—81no—
164C4×C11#44311yescharacteristic
165C4×C11#44311yescharacteristic
166C4×C11#44311yescharacteristic
167C4×C11#44411yescharacteristic
168C4×C11#47111yescharacteristic
169C4×C11#47211yescharacteristic
170C2×#41—21no—
171C2×M16—21no—
172C2×M16—221no—
173C22×C8—21no—
174C4⋊Q8C4×D1111yescharacteristic
175#127C4×D1111yescharacteristic
176#124—21no—
177#121—21no—
178#121—21no—
179C4×D4—21no—
180C4×D4—21no—
181C2×C42C22×D1111yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—111no—
185C4⋊C8—111no—
186C4⋊C8—111no—
187C4⋊C8—111no—
188C4⋊C8—111no—
189C4⋊C8—111no—
190C22⋊C8—221no—
191C22⋊C8—221no—
192C22⋊C8—221no—
193#97—221no—
194C4×C8—21no—
195C4×C8—221no—
196C4×C8—221no—
197C4×C8—221no—
198C4×C8—221no—
199C4×C8C22⋊D1111yescharacteristic
200C4×C8C22⋊D1111yescharacteristic
201C2×C11—41no—
202C2×C11—161no—
203C2×C11#192911yescharacteristic
204C2×C11#193111yescharacteristic
205C2×C11#193711yescharacteristic
206#41—81no—
207#41—81no—
208C2×Q8—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—41no—
213C22×C4—41no—
214C22×C4#433911yescharacteristic
215C22×C4#434111yescharacteristic
216C22×C4#434111yescharacteristic
217M16—81no—
218M16—222no—
219M16—441no—
220C2×C8—22no—
221C2×C8—22no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—221no—
226C2×C8—221no—
227C2×C8—221no—
228C2×C8—221no—
229C2×C8—221no—
230C2×C8—221no—
231C2×C8—441no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C22⋊C4—41no—
235C22⋊C4—41no—
236C42C2×C4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C42#434111yescharacteristic
239C42C2×C22⋊D1111yescharacteristic
240C11#958611yescharacteristic, complemented, Sylow
241C23—41no—
242C23#6693211yescharacteristic
243Q8—81no—
244D4—41no—
245D4—41no—
246D4—41no—
247D4—41no—
248D4—81no—
249D4—82no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4#6693011yescharacteristic
260C2×C4(C22⋊D11)⋊C411yescharacteristic
261C2×C4#6693811yescharacteristic
262C2×C4C4×C22⋊D1111yescharacteristic
263C2×C4#6698811yescharacteristic
264C2×C4#6699111yescharacteristic
265C8—22no—
266C8—22no—
267C8—81no—
268C8—442no—
269C8—441no—
270C8—441no—
271C8—441no—
272C8—441no—
273C8—441no—
274C8—441no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22#1062255711yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—81no—
286C4#1062243711yescharacteristic
287C4#1062243711yescharacteristic
288C4#1062275711yescharacteristic
289C4#1062275811yescharacteristic
290C4#1062277311yescharacteristic
291C4#1062279011yescharacteristic
292C2—41no—
293C2—161no—
294C2#1306926111yescharacteristic
295C2#1306927511yescharacteristic
296C2#1306931711yescharacteristic
subgroupG/H
centerC2×C4#66991
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#388
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1492D11
hypocenterC11#9586
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
1. #13067407C2semidirect
4. #13066899C2semidirect
5. #13066505C2semidirect
6. #13066453C2semidirect
240. C11#9586semidirect

Maximal subgroups

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

subgroupindex
#130674072
#130672782
#130670332
#130668992
#130665052
#130664532
C11×#14922
#958611