Finite Group Databasebeta

← #14651625

Subgroups — #14651625

Order 2816.

542 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 127 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#13077697C211yesmaximal, characteristic, complemented
2#13073521C211yesmaximal, characteristic
3#13067040C212yesmaximal
4#13066476C212yesmaximal, complemented
5C11×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66999—21no—
8C2×C4×D44C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×#101—21no—
11Q8×C11⋊C8—24no—
12#10622604C412yes—
13#10622600—21no—
14#10622596C412yes—
15#10622553—22no—
16#10622549C2211yescharacteristic
17#10622538—22no—
18#10622538C2212yes—
19C11×#343—21no—
20#10622121—24no—
21C22×Q8×C11D411yescharacteristic
22C22×D44C2×C411yescharacteristic
23C22×C4×D11—21no—
24C2×C11×M16—22no—
25C4×Q8×C11—22no—
26C4×Q8×C11—22no—
27C2×C11×C4⋊C4C2×C412yes—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C42×C11D412yes—
30C2×C42×C11C2311yescharacteristic
31#66999—42no—
32#66999—42no—
33C2×(C2×D11)⋊C4—22no—
34C2×(C2×D11)⋊C4—22no—
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×Dic11⋊C4—22no—
39C4×D44—22no—
40C4×D44—22no—
41C11×C4⋊C8—22no—
42C11×C4⋊C8—22no—
43C11×#101—42no—
44C11⋊#95—22no—
45C11⋊#95—21no—
46C11⋊#95C2×C412yes—
47C22⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)—24no—
49C4⋊(C11⋊C8)—22no—
50C4×C11⋊C8—24no—
51C4×C11⋊C8D414yes—
52#9486—111nomaximal, Sylow
53C23×D11—21no—
54C2×Q8×C11—22no—
55C2×Q8×C11—22no—
56C2×Q8×C11D812yes—
57C2×Q8×C11SD1612yes—
58C22×C4×C11C22⋊C412yes—
59C22×C4×C11C22⋊C412yes—
60C22×C4×C11C22×C411yescharacteristic
61C22×C4×C11C2×D411yescharacteristic
62C22×C4×C11C2×D411yescharacteristic
63C22×Dic11—22no—
64C22×Dic11—21no—
65C2×D44—22no—
66C2×D44—42no—
67C2×C4×D11—42no—
68C2×C4×D11—41no—
69C2×C4×D11—41no—
70C2×C4×D11—42no—
71C11×M16—42no—
72C11×M16—42no—
73C2×C8×C11—42no—
74C11×C4⋊C4—24no—
75C11×C4⋊C4—22no—
76C42×C11—22no—
77C42×C11—22no—
78C42×C11C2×D412yes—
79C42×C11#4112yes—
80(C2×D11)⋊C4—44no—
81(C2×D11)⋊C4—44no—
82(C2×D11)⋊C4—41no—
83(C2×D11)⋊C4—41no—
84C4⋊Dic11—22no—
85C4⋊Dic11—41no—
86C4⋊Dic11—41no—
87Dic11⋊C4—44no—
88C2×C11⋊C8—24no—
89#2982—111no—
90#2536—111no—
91#1801D1111yescharacteristic, complemented
92#1486—112no—
93#1286—112no—
94C23×C11C2×C22⋊C411yescharacteristic
95C22×D11—22no—
96C22×D11—41no—
97C22×D11—41no—
98C22×D11—41no—
99C22×D11—41no—
100C22×D11—41no—
101C22×D11—41no—
102Q8×C11—24no—
103Q8×C11—24no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—22no—
107C2×C4×C11—41no—
108C2×C4×C11—41no—
109C2×C4×C11—42no—
110C2×C4×C11#10214yes—
111C2×C4×C11C4×D412yes—
112C2×C4×C11#12011yescharacteristic
113C2×C4×C11#12112yes—
114C2×C4×C11#12311yescharacteristic
115C2×C4×C11C2×D811yescharacteristic
116C2×C4×C11C2×SD1611yescharacteristic
117C2×C4×C11#13512yes—
118C2×Dic11—42no—
119C2×Dic11—42no—
120C2×Dic11—41no—
121C2×Dic11—41no—
122C2×Dic11—42no—
123C2×Dic11—41no—
124D44—24no—
125D44—42no—
126C4×D11—82no—
127C4×D11—82no—
128C8×C11—82no—
129C11⋊C8—44no—
130C2×C22⋊Q8—221no—
131C2×C4×Q8C2×D1111yescharacteristic
132C2×C4×D4—111no—
133C8×Q8—224no—
134#431—112no—
135#431—222no—
136#423C2×D1112yes—
137C2×#101—21no—
138#398—112no—
139#394—112no—
140#388—222no—
141#382—111no—
142#380—221no—
143#343—21no—
144D4⋊C8—224no—
145C22×C11—21no—
146C22×C11—21no—
147C22×C11#38611yescharacteristic
148C22×C11C2×#10211yescharacteristic
149C22×C11#41611yescharacteristic
150C2×D11—42no—
151C2×D11—42no—
152C2×D11—42no—
153C2×D11—81no—
154C2×D11—81no—
155C2×D11—81no—
156C2×D11—81no—
157C4×C11—22no—
158C4×C11—24no—
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—42no—
162C4×C11#46512yes—
163C4×C11#46612yes—
164Dic11—82no—
165Dic11—81no—
166C22×Q8C22⋊D1111yescharacteristic
167C22×D4—111no—
168C23×C4—221no—
169C2×M16—22no—
170C22⋊Q8—442no—
171C22⋊Q8—442no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—222no—
175C4×D4—222no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—222no—
178C2×C4⋊C4—221no—
179C2×C4⋊C4C4×D1112yes—
180C2×C4⋊C4C22⋊D1111yescharacteristic
181C2×C22⋊C4—222no—
182C2×C22⋊C4—222no—
183C2×C22⋊C4—221no—
184C2×C42D4412yes—
185C2×C42C22×D1111yescharacteristic
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—224no—
189C4⋊C8—222no—
190#101—42no—
191C22⋊C8—222no—
192C4×C8—114no—
193C4×C8—224no—
194#95—112no—
195#95—222no—
196#95—221no—
197C2×C11—21no—
198C2×C11—21no—
199C2×C11#189111yescharacteristic
200C2×C11#189311yescharacteristic
201C2×C11#191211yescharacteristic
202D11—82no—
203C24—221no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8#432312yes—
207C2×Q8#432512yes—
208C2×D4—222no—
209C2×D4—442no—
210C22×C4—222no—
211C22×C4—221no—
212C22×C4—441no—
213C22×C4—442no—
214C22×C4—441no—
215C22×C4—442no—
216C22×C4(C2×D11)⋊C412yes—
217C22×C4(C2×D11)⋊C412yes—
218C22×C4C2×C4×D1111yescharacteristic
219C22×C4C2×D4411yescharacteristic
220C22×C4C2×C22⋊D1111yescharacteristic
221M16—42no—
222M16—42no—
223C2×C8—42no—
224C2×C8—224no—
225C4⋊C4—24no—
226C4⋊C4—22no—
227C4⋊C4—222no—
228C4⋊C4—444no—
229C4⋊C4—441no—
230C4⋊C4—441no—
231C22⋊C4—444no—
232C22⋊C4—444no—
233C22⋊C4—441no—
234C22⋊C4—441no—
235C42—22no—
236C42—22no—
237C42D4×D1112yes—
238C42#434112yes—
239C11#948611yescharacteristic, complemented, Sylow
240C23—222no—
241C23—441no—
242C23—441no—
243C23—441no—
244C23—441no—
245C23—441no—
246C23—441no—
247C23C2×(C2×D11)⋊C411yescharacteristic
248Q8—24no—
249Q8—24no—
250D4—224no—
251D4—442no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—442no—
259C2×C4—442no—
260C2×C4—441no—
261C2×C4—442no—
262C2×C4—441no—
263C2×C4—441no—
264C2×C4—882no—
265C2×C4—882no—
266C2×C4#6687314yes—
267C2×C4(C22⋊D11)⋊C412yes—
268C2×C4#6693511yescharacteristic
269C2×C4#6693911yescharacteristic
270C2×C4C2×#432311yescharacteristic
271C2×C4#6699212yes—
272C2×C4C2×#432511yescharacteristic
273C2×C4#6700312yes—
274C8—82no—
275C8—444no—
276C22—21no—
277C22—21no—
278C22—442no—
279C22—442no—
280C22—442no—
281C22—881no—
282C22—881no—
283C22—881no—
284C22—881no—
285C22#1062257111yescharacteristic
286C22C2×#6687311yescharacteristic
287C22#1062261511yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—24no—
292C4—42no—
293C4—882no—
294C4—881no—
295C4#1062265112yes—
296C4#1062266112yes—
297C2—21no—
298C2—21no—
299C2—882no—
300C2#1306903211yescharacteristic
301C2#1306904211yescharacteristic
302C2#1306915111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1801D11
hypocenterC11#9486
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
1. #13077697C2semidirect
4. #13066476C2semidirect
5. C11×#1801C2semidirect
91. #1801D11semidirect
239. C11#9486semidirect

Maximal subgroups

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

subgroupindex
#130776972
#130735212
#130670402
#130664762
C11×#18012
#948611