Finite Group Databasebeta

← #14646780

Subgroups — #14646780

Order 2816.

388 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 93 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#13077327C211yesmaximal, characteristic
2#13067377C211yesmaximal, characteristic, complemented
3#13067377C211yesmaximal, characteristic, complemented
4#13067250C211yesmaximal, characteristic
5#13067250C211yesmaximal, characteristic
6#13066527C211yesmaximal, characteristic, complemented
7C11×#1307C211yesmaximal, characteristic, complemented
8C2×#66960C412yes—
9#10623008C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622742C412yes—
14#10622539C2211yescharacteristic
15#10622539C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622451—21no—
18#10622451—21no—
19#10622447—21no—
20#10622447—21no—
21#10622118—21no—
22#10622118—21no—
23#10622117—21no—
24#10622117—21no—
25#10622102—22no—
26#10622102—22no—
27C2×#4339C2×C412yes—
28C2×C11×M16C2×C412yes—
29C2×C42×C11C2311yescharacteristic
30#66983—21no—
31#66983—21no—
32C22×C11⋊C8C2×C411yescharacteristic
33C22×C11⋊C8C2×C411yescharacteristic
34#66960—44no—
35C2×#4313—22no—
36C2×C8×D11—22no—
37#66928D412yes—
38#66927Q811yescharacteristic
39C4×D44—21no—
40C4×D44—21no—
41#66922Q811yescharacteristic
42C11×C4⋊C8—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C22⋊C8—21no—
47C11×C22⋊C8—21no—
48C11×#97—21no—
49C11×#97—21no—
50C22⋊(C11⋊C8)—21no—
51C22⋊(C11⋊C8)—21no—
52(C2×D11)⋊C8—22no—
53(C2×D11)⋊C8—22no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56#66867—21no—
57#66867—21no—
58C4×C11⋊C8D411yescharacteristic
59C4×C11⋊C8D411yescharacteristic
60C4×C11⋊C8D411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62#8634—111nomaximal, Sylow
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11#4111yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C2×C22⋊D11—22no—
67#4339—42no—
68#4339—42no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44C4⋊C412yes—
72C2×C4×D11—22no—
73C2×Dic22C4⋊C412yes—
74C11×M16—42no—
75C2×C8×C11—22no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C42×C11C2×D411yescharacteristic
79C42×C11C2×D411yescharacteristic
80C42×C11C2×D411yescharacteristic
81C42×C11C2×Q811yescharacteristic
82(C2×D11)⋊C4—22no—
83(C2×D11)⋊C4—22no—
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C2×C11⋊C8—22no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8C22⋊C411yescharacteristic
91C2×C11⋊C8C22⋊C411yescharacteristic
92C2×C11⋊C8C22⋊C411yescharacteristic
93C2×C11⋊C8C22⋊C411yescharacteristic
94#4313—44no—
95C8×D11—44no—
96#2931—111no—
97#1568—111no—
98#1568—111no—
99#1536—111no—
100#1536—111no—
101#1307—111no—
102#1307D1111yescharacteristic, complemented
103C23×C11#11711yescharacteristic
104C22×D11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11C2×C22⋊C411yescharacteristic
110C2×C4×C11C2×C4⋊C411yescharacteristic
111C2×C4×C11#12111yescharacteristic
112C2×C4×C11#12111yescharacteristic
113C2×C4×C11C22⋊Q811yescharacteristic
114C2×C4×C11C22⋊Q811yescharacteristic
115C22⋊D11—44no—
116C2×Dic11—22no—
117D44—42no—
118D44—42no—
119D44—42no—
120C4×D11—42no—
121C4×D11—42no—
122Dic22—42no—
123C8×C11—42no—
124C8×C11—81no—
125C8×C11—81no—
126C11⋊C8—21no—
127C11⋊C8—21no—
128C11⋊C8—21no—
129C11⋊C8—81no—
130C11⋊C8—81no—
131C11⋊C8#10012yes—
132C2×#131—112no—
133#532—111no—
134#436—221no—
135#436—221no—
136C8×D4—221no—
137C8×D4—221no—
138#432—111no—
139#432—111no—
140#432C2×D1111yescharacteristic
141#432C2×D1111yescharacteristic
142#423C2×D1111yescharacteristic
143#408—112no—
144C2×C4×C8—111no—
145#335—221no—
146#335—221no—
147#334—221no—
148#334—221no—
149#329—222no—
150#329—222no—
151C22×C11—21no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11#38011yescharacteristic
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C4×C11—21no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—21no—
162C4×C11—21no—
163C4×C11C2×#10011yescharacteristic
164C4×C11#41311yescharacteristic
165Dic11—42no—
166C2×#41—112no—
167#131—444no—
168C2×M16—222no—
169C2×M16C4×D1112yes—
170C22×C8—111no—
171C22×C8—111no—
172C22×C8—222no—
173C4⋊Q8—111no—
174#127—111no—
175#124—112no—
176#121—221no—
177#121—221no—
178C4×D4—221no—
179C4×D4—221no—
180C2×C42C22×D1111yescharacteristic
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—21no—
184C4⋊C8—21no—
185C4⋊C8—221no—
186C4⋊C8—221no—
187C22⋊C8—21no—
188C22⋊C8—21no—
189C22⋊C8—222no—
190C22⋊C8—222no—
191C22⋊C8—221no—
192C22⋊C8—221no—
193#97—21no—
194#97—21no—
195#97—221no—
196#97—221no—
197C4×C8—111no—
198C4×C8—111no—
199C4×C8—111no—
200C4×C8—111no—
201C2×C11—41no—
202C2×C11#180011yescharacteristic
203C2×C11#181411yescharacteristic
204C2×C11#181411yescharacteristic
205D11—82no—
206#41—442no—
207#41—442no—
208C2×Q8—112no—
209C2×D4—112no—
210C2×D4—222no—
211C2×D4—221no—
212C2×D4—221no—
213C22×C4—222no—
214C22×C4C2×C4×D1111yescharacteristic
215C22×C4#433911yescharacteristic
216C22×C4#433911yescharacteristic
217M16—42no—
218M16—444no—
219C2×C8—22no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—111no—
223C2×C8—111no—
224C2×C8—111no—
225C2×C8—111no—
226C2×C8—222no—
227C2×C8—444no—
228C2×C8—441no—
229C2×C8—441no—
230C2×C8—441no—
231C4⋊C4—221no—
232C4⋊C4—221no—
233C22⋊C4—222no—
234C22⋊C4—222no—
235C42D4×D1111yescharacteristic
236C42D4×D1111yescharacteristic
237C42D4×D1111yescharacteristic
238C42Q8×D1111yescharacteristic
239C11#863411yescharacteristic, complemented, Sylow
240C23—222no—
241C23#6692511yescharacteristic
242Q8—442no—
243D4—442no—
244D4—442no—
245D4—442no—
246D4—444no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—222no—
252C2×C4—442no—
253C2×C4—442no—
254C2×C4C22⋊C4×D1111yescharacteristic
255C2×C4#6693711yescharacteristic
256C2×C4#6693711yescharacteristic
257C2×C4C4⋊C4×D1111yescharacteristic
258C2×C4#6694911yescharacteristic
259C2×C4#6694911yescharacteristic
260C8—42no—
261C8—81no—
262C8—81no—
263C8—112no—
264C8—221no—
265C8—221no—
266C8—221no—
267C8—881no—
268C8—881no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—442no—
273C22—442no—
274C22—442no—
275C22#1062228011yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—442no—
282C4D11×#10011yescharacteristic
283C4#1062236411yescharacteristic
284C2—41no—
285C2—882no—
286C2#1306860711yescharacteristic
287C2#1306866911yescharacteristic
288C2#1306866911yescharacteristic
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1307C2
socleC22×C11#380
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1307D11
hypocenterC11#8634
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #13067377C2semidirect
3. #13067377C2semidirect
6. #13066527C2semidirect
7. C11×#1307C2semidirect
102. #1307D11semidirect
239. C11#8634semidirect

Maximal subgroups

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

subgroupindex
#130773272
#130673772
#130672502
#130665272
C11×#13072
#863411