Finite Group Databasebeta

← #14657682

Subgroups — #14657682

Order 2816.

394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079541C211yesmaximal, characteristic
2#13067407C211yesmaximal, characteristic, complemented
3#13067349C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic, complemented
5#13067034C211yesmaximal, characteristic
6#13066506C211yesmaximal, characteristic, complemented
7C11×#1966C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623008C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C2×C11×#101—22no—
12C4×C11×M16C2211yescharacteristic
13#10622840—22no—
14#10622698—21no—
15#10622696—21no—
16#10622696—21no—
17#10622694—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21#10622184—22no—
22#10622123—21no—
23#10622119—21no—
24#10622118—21no—
25#10622117—21no—
26#10622097—22no—
27C22×Q8×C11D412yes—
28C2×#4339—21no—
29C2×C11×M16—21no—
30C2×C11×M16—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×#4325—22no—
39C2×#4325—22no—
40#66983—21no—
41#66983—21no—
42C2×#4318—21no—
43#66928—21no—
44#66927D411yescharacteristic
45C4×D44—21no—
46C4×D44—21no—
47#66922D411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×#101—44no—
51C11×#97—21no—
52C4×C8×C11—21no—
53#66899—22no—
54#66899—22no—
55C22⋊(C11⋊C8)—21no—
56C22⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)D412yes—
60C4⋊(C11⋊C8)D411yescharacteristic
61C4⋊(C11⋊C8)D411yescharacteristic
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10489—111nomaximal, Sylow
65C2×Q8×C11—22no—
66C2×Q8×C11—22no—
67C2×Q8×C11—42no—
68C2×Q8×C11—42no—
69C22×C4×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C2×C22⋊D11—41no—
74#4339—82no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×C4×D11—41no—
79C2×Dic22—21no—
80C11×M16—22no—
81C11×M16—41no—
82C11×M16—42no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93#4325—82no—
94#4325—82no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—41no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99#4318—81no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104#3206—111no—
105#1966D1111yescharacteristic, complemented
106#1574—111no—
107#1560—111no—
108#1548—111no—
109#1484—111no—
110#1299—111no—
111C23×C11#12311yescharacteristic
112C22×D11—41no—
113Q8×C11—42no—
114Q8×C11—42no—
115Q8×C11—82no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—22no—
120C2×C4×C11—21no—
121C2×C4×C11—44no—
122C2×C4×C11—42no—
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11#12411yescharacteristic
129C22⋊D11—82no—
130C2×Dic11—41no—
131D44—41no—
132D44—41no—
133D44—41no—
134D44—41no—
135D44—81no—
136C4×D11—82no—
137Dic22—81no—
138C8×C11—42no—
139C8×C11—81no—
140C11⋊C8—41no—
141C11⋊C8—41no—
142C11⋊C8—42no—
143C11⋊C8—81no—
144#532—111no—
145C2×C4⋊Q8C2×D1111yescharacteristic
146#492—221no—
147#487—221no—
148#461—221no—
149#461—221no—
150#448—222no—
151#431—111no—
152#431—111no—
153#423—111no—
154#423C2×D1111yescharacteristic
155C2×#101—22no—
156C4×M16C2×D1111yescharacteristic
157#335—221no—
158#334—221no—
159#333—221no—
160#333—222no—
161#331—221no—
162D4⋊C8—222no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#39411yescharacteristic
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11#45311yescharacteristic
175C4×C11#45511yescharacteristic
176C4×C11#47111yescharacteristic
177C4×C11#47112yes—
178C4×C11#47311yescharacteristic
179Dic11—81no—
180C2×#41—221no—
181C22×Q8C22⋊D1112yes—
182C2×SD16—222no—
183C2×SD16—222no—
184C2×M16—21no—
185C2×M16—21no—
186C2×M16—221no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—111no—
192#127—111no—
193#124—221no—
194#121—221no—
195#121—221no—
196C4×D4—221no—
197C4×D4—221no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—112no—
204C4⋊C8—111no—
205C4⋊C8—111no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208#103—222no—
209#103—222no—
210#101—44no—
211C22⋊C8—221no—
212C22⋊C8—221no—
213#97—21no—
214C4×C8—21no—
215C4×C8—221no—
216C4×C8—221no—
217C2×C11—41no—
218C2×C11#203711yescharacteristic
219C2×C11#204611yescharacteristic
220C2×C11#205211yescharacteristic
221D11—161no—
222#41—882no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—42no—
226C2×Q8—42no—
227C2×Q8—221no—
228C2×D4—221no—
229C2×D4—221no—
230C2×D4—221no—
231C2×D4—441no—
232C22×C4—22no—
233C22×C4—441no—
234C22×C4#433911yescharacteristic
235C22×C4#433911yescharacteristic
236C22×C4C2×C22⋊D1111yescharacteristic
237SD16—882no—
238SD16—882no—
239M16—22no—
240M16—41no—
241M16—42no—
242M16—881no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—222no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—441no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C22⋊C4—441no—
256C22⋊C4—441no—
257C42D4×D1111yescharacteristic
258C42D4×D1111yescharacteristic
259C42D4×D1111yescharacteristic
260C42#434111yescharacteristic
261C11#1048911yescharacteristic, complemented, Sylow
262C23—441no—
263C23#6698211yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—82no—
267Q8—881no—
268D4—441no—
269D4—441no—
270D4—441no—
271D4—441no—
272D4—881no—
273D4—882no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—441no—
282C2×C4—882no—
283C2×C4#6693611yescharacteristic
284C2×C4#6693711yescharacteristic
285C2×C4#6693711yescharacteristic
286C2×C4#6693811yescharacteristic
287C2×C4#6699011yescharacteristic
288C2×C4#6699211yescharacteristic
289C8—42no—
290C8—81no—
291C8—442no—
292C8—441no—
293C8—441no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—881no—
299C22—881no—
300C22—881no—
301C22#1062257211yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—881no—
307C4#1062236712yes—
308C4#1062236711yescharacteristic
309C4#1062236811yescharacteristic
310C4#1062267411yescharacteristic
311C4#1062269011yescharacteristic
312C2—41no—
313C2—1761no—
314C2#1306982611yescharacteristic
315C2#1306987511yescharacteristic
316C2#1306991511yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1966C2
socleC22×C11#394
prime radical#10623008C22
hypercenter#1966D11
hypocenterC11#10489
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1966

Complements

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

NH ≅ G/Ntype
2. #13067407C2semidirect
4. #13067297C2semidirect
6. #13066506C2semidirect
7. C11×#1966C2semidirect
105. #1966D11semidirect
261. C11#10489semidirect

Maximal subgroups

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

subgroupindex
#130795412
#130674072
#130673492
#130672972
#130670342
#130665062
C11×#19662
#1048911