Finite Group Databasebeta

← #14652260

Subgroups — #14652260

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#13067276C211yesmaximal, characteristic
2#13067066C211yesmaximal, characteristic
3#13067032C211yesmaximal, characteristic
4#13066900C211yesmaximal, characteristic, complemented
5#13066505C211yesmaximal, characteristic, complemented
6#13066452C211yesmaximal, characteristic, complemented
7C11×#1574C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#431C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12#10622538C2211yescharacteristic
13C4×#4318C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#335—21no—
16C11×#334—21no—
17#10622123C411yescharacteristic
18#10622123C411yescharacteristic
19#10622121—21no—
20#10622121—21no—
21#10622121—21no—
22#10622121—21no—
23#10622119C411yescharacteristic
24#10622119C411yescharacteristic
25#10622092—21no—
26C8×C11⋊C8—21no—
27C2×#4339—21no—
28C2×C11×M16—21no—
29C2×C42×C11C2311yescharacteristic
30#66983—21no—
31#66983—21no—
32C2×#4318—21no—
33C22×C11⋊C8—21no—
34#66928—21no—
35#66927C2×C411yescharacteristic
36C4×D44—21no—
37C4×D44—21no—
38#66922C2×C411yescharacteristic
39C11×C4⋊C8—21no—
40C11×C4⋊C8—21no—
41C11×C4⋊C8C2×C411yescharacteristic
42C11×C4⋊C8C2×C411yescharacteristic
43C11×C4⋊C8D411yescharacteristic
44C11×C4⋊C8D411yescharacteristic
45C11×C22⋊C8—21no—
46C11×C22⋊C8—21no—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49C22⋊(C11⋊C8)—21no—
50C4⋊(C11⋊C8)C2×C411yescharacteristic
51C4⋊(C11⋊C8)C2×C411yescharacteristic
52#66867—21no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8D411yescharacteristic
57C4×C11⋊C8D411yescharacteristic
58#9586—111nomaximal, Sylow
59C22×C4×C11#4111yescharacteristic
60C22×C4×C11#4111yescharacteristic
61C22×C4×C11#4111yescharacteristic
62C2×C22⋊D11—41no—
63#4339—81no—
64#4339—81no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44—21no—
68C2×C4×D11—41no—
69C2×Dic22—21no—
70C11×M16—81no—
71C2×C8×C11—21no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—41no—
76C42×C11C22×C411yescharacteristic
77C42×C11C2×D411yescharacteristic
78C42×C11C2×D411yescharacteristic
79C42×C11#4111yescharacteristic
80(C2×D11)⋊C4—41no—
81(C2×D11)⋊C4—41no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84#4318—22no—
85#4318—41no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—21no—
89C2×C11⋊C8—21no—
90C2×C11⋊C8—21no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—41no—
93#1574D1111yescharacteristic, complemented
94#1543—111no—
95#1492—111no—
96#1484—111no—
97#1450—111no—
98#1299—111no—
99#1278—111no—
100C23×C11#12611yescharacteristic
101C22×D11—41no—
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11#11711yescharacteristic
109C2×C4×C11C4×D411yescharacteristic
110C2×C4×C11C4×D411yescharacteristic
111C2×C4×C11#12111yescharacteristic
112C2×C4×C11#12311yescharacteristic
113C2×C4×C11#12411yescharacteristic
114C22⋊D11—82no—
115C2×Dic11—41no—
116D44—41no—
117D44—41no—
118D44—41no—
119D44—41no—
120D44—81no—
121C4×D11—81no—
122C4×D11—81no—
123Dic22—81no—
124C8×C11—41no—
125C8×C11—41no—
126C8×C11—41no—
127C8×C11—41no—
128C8×C11—81no—
129C11⋊C8—22no—
130C11⋊C8—22no—
131C11⋊C8—42no—
132C11⋊C8—41no—
133C11⋊C8—41no—
134#532—111no—
135#431—111no—
136#431C2×D1111yescharacteristic
137#431C2×D1111yescharacteristic
138#423C2×D1111yescharacteristic
139C4×M16—111no—
140C2×C4×C8—111no—
141#335—21no—
142#334—21no—
143#333—111no—
144#333—111no—
145#331—111no—
146#331—111no—
147D4⋊C8—221no—
148D4⋊C8—221no—
149D4⋊C8—221no—
150D4⋊C8—221no—
151#322—221no—
152C82—221no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11#38811yescharacteristic
157C2×D11—81no—
158C2×D11—81no—
159C2×D11—81no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11#44311yescharacteristic
164C4×C11#44311yescharacteristic
165C4×C11#44311yescharacteristic
166C4×C11#44411yescharacteristic
167C4×C11#47111yescharacteristic
168C4×C11#47211yescharacteristic
169Dic11—81no—
170C2×#41—221no—
171C2×M16—21no—
172C2×M16—221no—
173C22×C8—221no—
174C4⋊Q8—111no—
175#127—111no—
176#124—221no—
177#121—221no—
178#121—221no—
179C4×D4—221no—
180C4×D4—221no—
181C2×C42C22×D1111yescharacteristic
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—111no—
185C4⋊C8—111no—
186C4⋊C8C4×D1111yescharacteristic
187C4⋊C8C4×D1111yescharacteristic
188C4⋊C8C22⋊D1111yescharacteristic
189C4⋊C8C22⋊D1111yescharacteristic
190C22⋊C8—21no—
191C22⋊C8—21no—
192C22⋊C8—221no—
193#97—221no—
194C4×C8—21no—
195C4×C8—21no—
196C4×C8—111no—
197C4×C8—111no—
198C4×C8—221no—
199C4×C8—221no—
200C4×C8—221no—
201C2×C11—41no—
202C2×C11#192911yescharacteristic
203C2×C11#193111yescharacteristic
204C2×C11#193711yescharacteristic
205D11—161no—
206#41—881no—
207#41—881no—
208C2×Q8—221no—
209C2×D4—221no—
210C2×D4—221no—
211C2×D4—221no—
212C2×D4—441no—
213C22×C4—441no—
214C22×C4#433911yescharacteristic
215C22×C4#434111yescharacteristic
216C22×C4#434311yescharacteristic
217M16—81no—
218M16—222no—
219M16—441no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—222no—
226C2×C8—222no—
227C2×C8—221no—
228C2×C8—221no—
229C2×C8—221no—
230C2×C8—221no—
231C2×C8—441no—
232C4⋊C4—221no—
233C4⋊C4—221no—
234C22⋊C4—441no—
235C22⋊C4—441no—
236C42C2×C4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C42#434311yescharacteristic
239C42C2×C22⋊D1111yescharacteristic
240C11#958611yescharacteristic, complemented, Sylow
241C23—441no—
242C23#6695111yescharacteristic
243Q8—881no—
244D4—441no—
245D4—441no—
246D4—441no—
247D4—441no—
248D4—881no—
249D4—882no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—441no—
257C2×C4—881no—
258C2×C4—881no—
259C2×C4#6694511yescharacteristic
260C2×C4#6694611yescharacteristic
261C2×C4#6694711yescharacteristic
262C2×C4C4×C22⋊D1111yescharacteristic
263C2×C4#6699211yescharacteristic
264C2×C4#6700011yescharacteristic
265C8—41no—
266C8—41no—
267C8—41no—
268C8—41no—
269C8—81no—
270C8—222no—
271C8—222no—
272C8—442no—
273C8—441no—
274C8—441no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—881no—
279C22—881no—
280C22—881no—
281C22#1062260311yescharacteristic
282C4—21no—
283C4—21no—
284C4—21no—
285C4—881no—
286C4#1062250711yescharacteristic
287C4#1062250811yescharacteristic
288C4#1062275711yescharacteristic
289C4#1062275711yescharacteristic
290C4#1062281211yescharacteristic
291C4#1062281611yescharacteristic
292C2—41no—
293C2—1761no—
294C2#1306926311yescharacteristic
295C2#1306927711yescharacteristic
296C2#1306931911yescharacteristic
subgroupG/H
centerC2×C4#66992
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1574C2
socleC22×C11#388
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1574D11
hypocenterC11#9586
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #13066900C2semidirect
5. #13066505C2semidirect
6. #13066452C2semidirect
7. C11×#1574C2semidirect
93. #1574D11semidirect
240. C11#9586semidirect

Maximal subgroups

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

subgroupindex
#130672762
#130670662
#130670322
#130669002
#130665052
#130664522
C11×#15742
#958611