Finite Group Databasebeta

← #14645552

Subgroups — #14645552

Order 2816.

782 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#10623110C211yesmaximal, characteristic
2#13067302C212yesmaximal, complemented
3#13067040C212yesmaximal
4#13066940C211yesmaximal, characteristic, complemented
5C11×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66999—21no—
8#10623110—24no—
9#10623110—24no—
10C2×#66949—22no—
11C2×C4⋊C4×D11—21no—
12C2×C4×D44C412yes—
13C2×C4×D44C2211yescharacteristic
14C2×#66923C412yes—
15C2×#66922C2211yescharacteristic
16C11×#423C2212yes—
17C2×C11×#101—21no—
18#10622538C2212yes—
19C11×#343—21no—
20#10622166—22no—
21#10622124—24no—
22#10622121—24no—
23C22×Q8×C11D411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
26C22×C4×D11—22no—
27C22×Dic22—21no—
28C2×C11×M16—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C2×C11×C4⋊C4D412yes—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11C2×C412yes—
34C2×C42×C11C2311yescharacteristic
35#66999—28no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C412yes—
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—22no—
42C2×Dic11⋊C4—22no—
43#66949—216no—
44C4⋊C4×D11—28no—
45C4×D44—24no—
46C4×D44—22no—
47C4×D44—24no—
48C4×D44D414yes—
49#66923—24no—
50#66923—24no—
51#66922—22no—
52#66922D414yes—
53C11×C4⋊C8—22no—
54C11×C4⋊C8—22no—
55C11×#101—42no—
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4×C11⋊C8—22no—
59#8398—111nomaximal, Sylow
60C23×D11—21no—
61C2×Q8×C11—22no—
62C2×Q8×C11—22no—
63C2×Q8×C11—21no—
64C2×Q8×C11—21no—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—22no—
72C2×D44—24no—
73C2×D44—21no—
74C2×D44C22⋊C412yes—
75C2×C4×D11—28no—
76C2×C4×D11—24no—
77C2×C4×D11—42no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×C4×D11—84no—
81C2×Dic22—24no—
82C2×Dic22—82no—
83C11×M16—42no—
84C11×M16—42no—
85C2×C8×C11—42no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—24no—
88C42×C11—22no—
89C42×C11—22no—
90C42×C11C2×D412yes—
91C42×C11C2×D412yes—
92(C2×D11)⋊C4—28no—
93(C2×D11)⋊C4—24no—
94C4⋊Dic11—22no—
95C4⋊Dic11—21no—
96C4⋊Dic11—24no—
97C4⋊Dic11C22⋊C414yes—
98C4⋊Dic11C22⋊C412yes—
99Dic11⋊C4—28no—
100Dic11⋊C4—28no—
101C2×C11⋊C8—42no—
102C2×#554—111no—
103#1801D1111yescharacteristic, complemented
104#1549—112no—
105#1486—112no—
106#1461—111no—
107C23×C11C2×C22⋊C411yescharacteristic
108C22×D11—24no—
109C22×D11—22no—
110C22×D11—42no—
111C22×D11—41no—
112C22×D11—41no—
113Q8×C11—42no—
114Q8×C11—42no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C2×C22⋊C411yescharacteristic
124C2×C4×C11#12012yes—
125C2×C4×C11#12012yes—
126C2×C4×C11#13512yes—
127C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C2×Dic11—22no—
130C2×Dic11—24no—
131C2×Dic11—44no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134D44—24no—
135D44—22no—
136D44#10114yescomplemented
137C4×D11—44no—
138C4×D11—44no—
139C4×D11—88no—
140Dic22—84no—
141C8×C11—82no—
142C11⋊C8—82no—
143#554—224no—
144#554—224no—
145C2×C4⋊Q8—111no—
146C2×#125—112no—
147C2×C22⋊Q8—221no—
148C2×C22⋊Q8—222no—
149C2×C4×Q8C2×D1111yescharacteristic
150C2×C4×D4—111no—
151C2×C4×D4—112no—
152C22×C4⋊C4—221no—
153#431—112no—
154#423C2×D1112yes—
155C2×#101—21no—
156#343—21no—
157#332—224no—
158D4⋊C8—224no—
159#324—222no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11#37911yescharacteristic
163C22×C11#41611yescharacteristic
164C22×C11#41711yescharacteristic
165C2×D11—24no—
166C2×D11—44no—
167C2×D11—44no—
168C2×D11—42no—
169C2×D11—42no—
170C4×C11—22no—
171C4×C11—21no—
172C4×C11—42no—
173C4×C11—42no—
174C4×C11C2×#10112yes—
175C4×C11#44912yes—
176C4×C11#45212yes—
177Dic11—44no—
178Dic11—42no—
179C22×Q8—221no—
180C22×Q8C22⋊D1111yescharacteristic
181C22×D4—111no—
182C23×C4—221no—
183C23×C4—222no—
184C2×M16—22no—
185C4⋊Q8—114no—
186C4⋊Q8—222no—
187#125—224no—
188#125—224no—
189C22⋊Q8—2216no—
190C22⋊Q8—228no—
191C4×Q8—22no—
192C4×Q8—22no—
193C4×D4—114no—
194C4×D4—224no—
195C4×D4—224no—
196C4×D4—222no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—112no—
199C2×C4⋊C4—228no—
200C2×C4⋊C4—222no—
201C2×C4⋊C4—222no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4D4412yes—
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C22⋊C4—222no—
206C2×C22⋊C4—221no—
207C2×C42C4×D1112yes—
208C2×C42C22×D1111yescharacteristic
209C4⋊C8—22no—
210C4⋊C8—22no—
211C4⋊C8—222no—
212#101—42no—
213C22⋊C8—222no—
214C4×C8—222no—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11#178411yescharacteristic
218C2×C11#178811yescharacteristic
219C2×C11#179511yescharacteristic
220D11—44no—
221C24—221no—
222C2×Q8—21no—
223C2×Q8—22no—
224C2×Q8—21no—
225C2×Q8—22no—
226C2×Q8—224no—
227C2×Q8—882no—
228C2×D4—112no—
229C2×D4—224no—
230C2×D4—221no—
231C22×C4—228no—
232C22×C4—221no—
233C22×C4—222no—
234C22×C4—224no—
235C22×C4—441no—
236C22×C4—441no—
237C22×C4—442no—
238C22×C4—884no—
239C22×C4(C2×D11)⋊C412yes—
240C22×C4(C2×D11)⋊C412yes—
241C22×C4C2×C4×D1111yescharacteristic
242C22×C4C2×D4411yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244M16—42no—
245M16—42no—
246C2×C8—42no—
247C2×C8—442no—
248C4⋊C4—24no—
249C4⋊C4—22no—
250C4⋊C4—112no—
251C4⋊C4—114no—
252C4⋊C4—228no—
253C4⋊C4—228no—
254C4⋊C4—221no—
255C4⋊C4—222no—
256C4⋊C4—224no—
257C22⋊C4—228no—
258C22⋊C4—224no—
259C42—22no—
260C42—22no—
261C42D4×D1112yes—
262C42D4×D1112yes—
263C11#839811yescharacteristic, complemented, Sylow
264C23—224no—
265C23—222no—
266C23—442no—
267C23—441no—
268C23—441no—
269C23C2×(C2×D11)⋊C411yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—884no—
273D4—114no—
274D4—224no—
275D4—222no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—222no—
284C2×C4—224no—
285C2×C4—444no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—444no—
289C2×C4—444no—
290C2×C4—888no—
291C2×C4C22⋊C4×D1111yescharacteristic
292C2×C4C22⋊C4×D1111yescharacteristic
293C2×C4#6693512yes—
294C2×C4#6698511yescharacteristic
295C2×C4#6699012yes—
296C2×C4#6699511yescharacteristic
297C2×C4#6700312yes—
298C8—82no—
299C8—882no—
300C22—21no—
301C22—21no—
302C22—224no—
303C22—444no—
304C22—444no—
305C22—442no—
306C22—442no—
307C22#1062256811yescharacteristic
308C22#1062257911yescharacteristic
309C22#1062261511yescharacteristic
310C4—22no—
311C4—21no—
312C4—42no—
313C4—42no—
314C4—442no—
315C4—444no—
316C4D11×#10112yes—
317C4#1062265012yes—
318C4#1062266012yes—
319C2—21no—
320C2—21no—
321C2—444no—
322C2#1306853811yescharacteristic
323C2#1306855411yescharacteristic
324C2#1306858711yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1801C2
socleC22×C11#379
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1801D11
hypocenterC11#8398
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
2. #13067302C2semidirect
4. #13066940C2semidirect
5. C11×#1801C2semidirect
103. #1801D11semidirect
136. D44#101semidirect
263. C11#8398semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
#130673022
#130670402
#130669402
C11×#18012
#839811