Finite Group Databasebeta

← #14670765

Subgroups — #14670765

Order 2816.

572 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 135 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#13078197C211yesmaximal, characteristic
2C22×#66881C211yesmaximal, characteristic, complemented
3C2×#10622156C212yesmaximal, complemented
4#13066722C212yesmaximal, complemented
5C11×#2112C211yesmaximal, characteristic, complemented
6C23×C8×C11C2211yescharacteristic
7#10623322—21no—
8C22×C4⋊Dic11—21no—
9C2×#66957C2211yescharacteristic
10C2×C11×M32C2212yes—
11#10622729C412yescomplemented
12#10622728C412yescomplemented
13#10622727—22no—
14#10622726—21no—
15#10622719C2211yescharacteristic
16C2×#66881—21no—
17C2×#66881—24no—
18C2×#66881C2212yes—
19C11×C22⋊C16—22no—
20#10622156—24no—
21C23×C4×C11D411yescharacteristic
22C23×Dic11—41no—
23C2×#4339—21no—
24C22×C8×C11—22no—
25C22×C8×C11—22no—
26C22×C8×C11C2×C412yes—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D412yes—
29C22×C8×C11C2311yescharacteristic
30#67006—41no—
31#66983—22no—
32#66982—41no—
33C4×C22⋊D11—42no—
34#66979—21no—
35C2×C4⋊Dic11—24no—
36C2×C4⋊Dic11—22no—
37C2×C4⋊Dic11—42no—
38C2×C4⋊Dic11—41no—
39#66977—22no—
40C2×Dic44C2×C411yescharacteristic, complemented
41#66957—22no—
42#66957—22no—
43C2×D88C2×C411yescharacteristic, complemented
44C2×#4314—21no—
45C11×M32—22no—
46C11×M32—22no—
47C2×C11×C16—22no—
48#66885—22no—
49#66882C2×C412yescomplemented
50#66881—24no—
51#66881—21no—
52#66881—22no—
53#66881D414yescomplemented
54#66880—22no—
55#13001—111nomaximal, Sylow
56C24×C11D811yescharacteristic
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11D811yescharacteristic
63C22×C4×C11SD1612yes—
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—42no—
66C2×C22⋊D11—41no—
67C22×Dic11—44no—
68C22×Dic11—42no—
69C22×Dic11—84no—
70#4339—41no—
71#4339—41no—
72#4339—41no—
73#4339—41no—
74C2×D44—21no—
75C2×C4×D11—41no—
76C2×Dic22—21no—
77C2×C8×C11—24no—
78C2×C8×C11—24no—
79C2×C8×C11—21no—
80C2×C8×C11—21no—
81C2×C8×C11C22⋊C412yes—
82C2×C8×C11C22×C411yescharacteristic
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11C2×D412yes—
85C2×C8×C11#4112yes—
86C22⋊Dic11—42no—
87C22⋊Dic11—41no—
88(C2×D11)⋊C4—42no—
89C4⋊Dic11—22no—
90C4⋊Dic11—24no—
91C4⋊Dic11—44no—
92C4⋊Dic11—42no—
93Dic11⋊C4—42no—
94C4×Dic11—41no—
95Dic44—22no—
96D88—22no—
97#4314—42no—
98C11×C16—42no—
99#3050—111no—
100C22×#106—111no—
101C2×#360—112no—
102#2112D1111yescharacteristic, complemented
103#1386—112no—
104C23×C11—24no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11#10212yes—
108C23×C11C2×D811yescharacteristic
109C22×D11—41no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11#10212yes—
117C2×C4×C11C2×C22⋊C411yescharacteristic
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11#12311yescharacteristic
120C2×C4×C11C2×SD1611yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C11#13711yescharacteristic
123C22⋊D11—84no—
124C22⋊D11—81no—
125C22⋊D11—81no—
126C2×Dic11—42no—
127C2×Dic11—41no—
128C2×Dic11—44no—
129C2×Dic11—88no—
130C2×Dic11—84no—
131D44—41no—
132D44—41no—
133C4×D11—81no—
134C4×D11—81no—
135Dic22—41no—
136Dic22—41no—
137C8×C11—22no—
138C8×C11C4×D412yes—
139C8×C11#12112yes—
140C2×#135—111no—
141C23×C8C2×D1111yescharacteristic
142#525—221no—
143C22×C4⋊C4—221no—
144C2×M32C2×D1112yes—
145#467—112no—
146#466—112no—
147#465—222no—
148#427—111no—
149C2×#106—112no—
150C2×#106—224no—
151C2×#106—221no—
152#416—221no—
153#360—224no—
154C22⋊C16—22no—
155C22×C11—24no—
156C22×C11—24no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11#36014yescomplemented
161C22×C11C2×#10211yescharacteristic
162C22×C11#44711yescharacteristic
163C22×C11#48011yescharacteristic
164C2×D11—81no—
165C2×D11—82no—
166C4×C11—22no—
167C4×C11#38611yescharacteristic
168C4×C11#41711yescharacteristic
169C4×C11#44811yescharacteristic
170C4×C11#48111yescharacteristic
171Dic11—84no—
172Dic11—81no—
173Dic11—82no—
174C2×#41—221no—
175C23×C4—441no—
176C23×C4D4411yescharacteristic
177#135—222no—
178#135—222no—
179C2×Q16—111no—
180C2×SD16—221no—
181C2×D8—111no—
182C22×C8—22no—
183C22×C8—22no—
184C22×C8C4×D1112yes—
185C22×C8D4411yescharacteristic
186C22×C8C22⋊D1112yes—
187C22×C8C22×D1111yescharacteristic
188#123—441no—
189C22⋊Q8—222no—
190#121—222no—
191#120—441no—
192C4×D4—442no—
193#117—221no—
194C2×C4⋊C4—224no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—442no—
197C2×C4⋊C4—441no—
198M32—22no—
199M32—22no—
200C2×C16—22no—
201#107—112no—
202#106—114no—
203#106—224no—
204#106—222no—
205#106—221no—
206#103—222no—
207#102—222no—
208C2×C11—21no—
209C2×C11—24no—
210C2×C11—21no—
211C2×C11#187411yescharacteristic
212C2×C11C2×#36012yes—
213D11—161no—
214C24D8811yescharacteristic
215#41—441no—
216#41—441no—
217#41—441no—
218#41—441no—
219C2×Q8—221no—
220C2×D4—221no—
221C2×D4—442no—
222C2×D4—441no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—444no—
228C22×C4—442no—
229C22×C4—441no—
230C22×C4—884no—
231C22×C4#431412yes—
232C22×C4D8811yescharacteristic
233C22×C4(C2×D11)⋊C412yes—
234C22×C4C2×D4411yescharacteristic
235Q16—222no—
236SD16—442no—
237D8—222no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—24no—
241C2×C8—24no—
242C2×C8(C2×D11)⋊C412yes—
243C2×C8C2×C4×D1111yescharacteristic
244C2×C8D4×D1112yes—
245C2×C8#434112yes—
246C2×C8C2×C22⋊D1111yescharacteristic
247C4⋊C4—224no—
248C4⋊C4—222no—
249C4⋊C4—444no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C22⋊C4—442no—
253C22⋊C4—441no—
254C22⋊C4—442no—
255C42—441no—
256C16—42no—
257C11#1300111yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—24no—
261C23—441no—
262C23#6688512yes—
263C23C2×D8811yescharacteristic
264Q8—441no—
265Q8—441no—
266D4—441no—
267D4—441no—
268D4—881no—
269D4—881no—
270D4—884no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—442no—
278C2×C4—441no—
279C2×C4—444no—
280C2×C4—888no—
281C2×C4—884no—
282C2×C4—881no—
283C2×C4—881no—
284C2×C4#6688512yes—
285C2×C4#6693511yescharacteristic
286C2×C4#6693911yescharacteristic
287C2×C4C2×#431411yescharacteristic
288C2×C4#6696111yescharacteristic
289C2×C4#6696211yescharacteristic
290C2×C4C2×(C2×D11)⋊C411yescharacteristic
291C8—22no—
292C8(C22⋊D11)⋊C412yes—
293C8#6699212yes—
294C22—24no—
295C22—24no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—882no—
300C22—881no—
301C22#1062215614yescomplemented
302C22#1062234511yescharacteristic
303C22#1062234911yescharacteristic
304C22C2×#6688511yescharacteristic
305C4—22no—
306C4—884no—
307C4—882no—
308C4—881no—
309C4#1062234811yescharacteristic
310C4#1062235111yescharacteristic
311C4#1062257111yescharacteristic
312C4#1062274611yescharacteristic
313C2—21no—
314C2—21no—
315C2—24no—
316C2—1761no—
317C2#1306893111yescharacteristic
318C2C2×#1062215612yes—
subgroupG/H
centerC22C2×#66885
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2112C2
socleC22×C11C2×#102
prime radical#13078197C2
cosocleC22×C8×C11C23
hypercenter#2112D11
hypocenterC11#13001
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. C22×#66881C2semidirect
3. C2×#10622156C2semidirect
4. #13066722C2semidirect
5. C11×#2112C2semidirect
11. #10622729C4semidirect
12. #10622728C4semidirect
40. C2×Dic44C2×C4semidirect
43. C2×D88C2×C4semidirect
49. #66882C2×C4semidirect
53. #66881D4semidirect
102. #2112D11semidirect
160. C22×C11#360semidirect
257. C11#13001semidirect
301. C22#10622156semidirect

Maximal subgroups

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

subgroupindex
#130781972
C22×#668812
C2×#106221562
#130667222
C11×#21122
#1300111