Finite Group Databasebeta

← #14646806

Subgroups — #14646806

Order 2816.

404 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 101 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#13067374C211yesmaximal, characteristic, complemented
3#13067371C211yesmaximal, characteristic, complemented
4#13067349C211yesmaximal, characteristic
5#13067349C211yesmaximal, characteristic
6C11⋊#1309C211yesmaximal, characteristic, complemented
7C11×#1309C211yesmaximal, characteristic, complemented
8C2×#66960C412yes—
9#10623008C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622742C412yes—
14#10622537C2211yescharacteristic
15#10622537C2211yescharacteristic
16C2×C4×C11⋊C8C2211yescharacteristic
17#10622451—21no—
18#10622451—21no—
19#10622447—21no—
20#10622447—21no—
21#10622123—21no—
22#10622123—21no—
23#10622119—21no—
24#10622119—21no—
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C2×#4339C2×C412yes—
30C2×C11×M16—21no—
31C2×C11×M16—21no—
32C2×C11×M16C2×C412yes—
33C2×C42×C11C2311yescharacteristic
34#66983—21no—
35#66983—21no—
36C2×#4318—21no—
37C2×#4318—21no—
38C22×C11⋊C8C2×C411yescharacteristic
39C22×C11⋊C8C2×C411yescharacteristic
40#66960—44no—
41C2×#4313—22no—
42C2×C8×D11—22no—
43#66928Q812yes—
44#66927D411yescharacteristic
45C4×D44—21no—
46C4×D44—21no—
47#66922D411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54(C2×D11)⋊C8—22no—
55(C2×D11)⋊C8—22no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4×C11⋊C8D411yescharacteristic
61C4×C11⋊C8D411yescharacteristic
62C4×C11⋊C8D411yescharacteristic
63C4×C11⋊C8D411yescharacteristic
64#8640—111nomaximal, Sylow
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×C4×C11#4111yescharacteristic
68C2×C22⋊D11—22no—
69#4339—42no—
70#4339—42no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44C4⋊C412yes—
74C2×C4×D11—22no—
75C2×Dic22C4⋊C412yes—
76C11×M16—42no—
77C11×M16—81no—
78C11×M16—81no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C42×C11C2×D411yescharacteristic
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×Q811yescharacteristic
86(C2×D11)⋊C4—22no—
87(C2×D11)⋊C4—22no—
88C4⋊Dic11—21no—
89C4⋊Dic11—21no—
90#4318—81no—
91#4318—81no—
92C2×C11⋊C8—22no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8—41no—
95C2×C11⋊C8—41no—
96C2×C11⋊C8C22⋊C411yescharacteristic
97C2×C11⋊C8C22⋊C411yescharacteristic
98C2×C11⋊C8C22⋊C411yescharacteristic
99C2×C11⋊C8C22⋊C411yescharacteristic
100#4313—44no—
101C8×D11—44no—
102#2931—111no—
103#1567—111no—
104#1566—111no—
105#1560—111no—
106#1560—111no—
107#1309—111no—
108#1309D1111yescharacteristic, complemented
109C23×C11#11711yescharacteristic
110C22×D11—22no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11C2×C4⋊C411yescharacteristic
119C2×C4×C11#12111yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11C22⋊Q811yescharacteristic
122C2×C4×C11C22⋊Q811yescharacteristic
123C22⋊D11—44no—
124C2×Dic11—22no—
125D44—42no—
126D44—41no—
127D44—41no—
128D44—41no—
129D44—41no—
130C4×D11—42no—
131C4×D11—42no—
132Dic22—42no—
133C8×C11—42no—
134C8×C11—81no—
135C8×C11—81no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8—21no—
139C11⋊C8—81no—
140C11⋊C8—81no—
141C11⋊C8#10012yes—
142C2×#131—112no—
143#532—111no—
144#436—221no—
145#436—221no—
146C8×D4—221no—
147C8×D4—221no—
148#423—111no—
149#423—111no—
150#423C2×D1111yescharacteristic
151#423C2×D1111yescharacteristic
152#423C2×D1111yescharacteristic
153#408—112no—
154C2×C4×C8—111no—
155#335—221no—
156#335—221no—
157#334—221no—
158#334—221no—
159#333—221no—
160#333—221no—
161#331—221no—
162#331—221no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#38011yescharacteristic
167C2×D11—42no—
168C2×D11—42no—
169C2×D11—42no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11C2×#10011yescharacteristic
174C4×C11#41311yescharacteristic
175C4×C11#47111yescharacteristic
176C4×C11#47111yescharacteristic
177C4×C11#47211yescharacteristic
178C4×C11#47311yescharacteristic
179Dic11—42no—
180C2×#41—112no—
181#131—444no—
182C2×M16—21no—
183C2×M16—21no—
184C2×M16—222no—
185C2×M16—221no—
186C2×M16—221no—
187C2×M16C4×D1112yes—
188C22×C8—111no—
189C22×C8—111no—
190C22×C8—222no—
191C4⋊Q8—111no—
192#127—111no—
193#124—112no—
194#121—221no—
195#121—221no—
196C4×D4—221no—
197C4×D4—221no—
198C2×C42C22×D1111yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C22⋊C8—222no—
210C22⋊C8—222no—
211C4×C8—111no—
212C4×C8—111no—
213C4×C8—111no—
214C4×C8—111no—
215C2×C11—41no—
216C2×C11#180011yescharacteristic
217C2×C11#181511yescharacteristic
218C2×C11#181611yescharacteristic
219D11—82no—
220#41—442no—
221#41—442no—
222C2×Q8—112no—
223C2×D4—112no—
224C2×D4—222no—
225C2×D4—221no—
226C2×D4—221no—
227C22×C4—222no—
228C22×C4C2×C4×D1111yescharacteristic
229C22×C4#433911yescharacteristic
230C22×C4#433911yescharacteristic
231M16—42no—
232M16—81no—
233M16—81no—
234M16—444no—
235M16—881no—
236M16—881no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8—111no—
243C2×C8—111no—
244C2×C8—222no—
245C2×C8—444no—
246C2×C8—441no—
247C2×C8—441no—
248C2×C8—441no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C22⋊C4—222no—
252C22⋊C4—222no—
253C42D4×D1111yescharacteristic
254C42D4×D1111yescharacteristic
255C42D4×D1111yescharacteristic
256C42Q8×D1111yescharacteristic
257C11#864011yescharacteristic, complemented, Sylow
258C23—222no—
259C23#6692511yescharacteristic
260Q8—442no—
261D4—442no—
262D4—444no—
263D4—441no—
264D4—441no—
265D4—441no—
266D4—441no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—222no—
274C2×C4—442no—
275C2×C4—442no—
276C2×C4C22⋊C4×D1111yescharacteristic
277C2×C4#6693711yescharacteristic
278C2×C4#6693711yescharacteristic
279C2×C4C4⋊C4×D1111yescharacteristic
280C2×C4#6694911yescharacteristic
281C2×C4#6694911yescharacteristic
282C8—42no—
283C8—81no—
284C8—81no—
285C8—112no—
286C8—221no—
287C8—221no—
288C8—221no—
289C8—881no—
290C8—881no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—442no—
295C22—442no—
296C22—442no—
297C22#1062228011yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—442no—
302C4D11×#10011yescharacteristic
303C4#1062236111yescharacteristic
304C4#1062236211yescharacteristic
305C4#1062236411yescharacteristic
306C4#1062236711yescharacteristic
307C4#1062236811yescharacteristic
308C2—41no—
309C2—882no—
310C2#1306860711yescharacteristic
311C2#1306867411yescharacteristic
312C2#1306867911yescharacteristic
subgroupG/H
centerC22#10622280
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1309C2
socleC22×C11#380
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1309D11
hypocenterC11#8640
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1309

Complements

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

NH ≅ G/Ntype
2. #13067374C2semidirect
3. #13067371C2semidirect
6. C11⋊#1309C2semidirect
7. C11×#1309C2semidirect
108. #1309D11semidirect
257. C11#8640semidirect

Maximal subgroups

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

subgroupindex
#130773272
#130673742
#130673712
#130673492
C11⋊#13092
C11×#13092
#864011