Finite Group Databasebeta

← #14664160

Subgroups — #14664160

Order 2816.

400 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074476C211yesmaximal, characteristic
2#13066940C211yesmaximal, characteristic, complemented
3#13066645C212yesmaximal, complemented
4#13066618C212yesmaximal
5C4×C11×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66928C411yescharacteristic
8C2×C11×#101—21no—
9C4×C11×M16—21no—
10#10622844—21no—
11#10622605—21no—
12#10622604C411yescharacteristic
13#10622604C2211yescharacteristic
14#10622592C411yescharacteristic
15#10622592C2211yescharacteristic
16#10622553—21no—
17#10622553—21no—
18#10622550C411yescharacteristic
19#10622538—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×Dic22C2×C411yescharacteristic
26C2×C11×M16—22no—
27C4×Q8×C11—41no—
28C4×Q8×C11—41no—
29C2×C11×C4⋊C4C2×C411yescharacteristic
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43#66928—41no—
44#66928—41no—
45C11×#101—24no—
46C11×#97—41no—
47C4×C8×C11—41no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C22⋊(C11⋊C8)—22no—
55C4⋊(C11⋊C8)—41no—
56C4×C11⋊C8—41no—
57#11738—111nomaximal, Sylow
58C23×D11—21no—
59C2×Q8×C11—22no—
60C2×Q8×C11—22no—
61C2×Q8×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C2×D44—41no—
73C2×D44—81no—
74C2×Dic22—41no—
75C2×Dic22—81no—
76C11×M16—24no—
77C11×M16—42no—
78C2×C8×C11—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C4⋊C4—41no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88(C2×D11)⋊C4—42no—
89(C2×D11)⋊C4—41no—
90(C2×D11)⋊C4—41no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—81no—
94(C2×D11)⋊C4—81no—
95Dic11⋊C4—81no—
96Dic11⋊C4—81no—
97C2×C11⋊C8—42no—
98#2632—111no—
99C4×#101D1111yescharacteristic, complemented
100#1461—111no—
101#1354—112no—
102#1345—112no—
103C23×C11C2×C22⋊C411yescharacteristic
104C22×D11—41no—
105C22×D11—41no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111Q8×C11—44no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11#9911yescharacteristic
127C2×C4×C11#9911yescharacteristic
128C2×C4×C11#10412yes—
129C2×C4×C11#13512yes—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139D44—82no—
140Dic22—82no—
141C8×C11—44no—
142C11⋊C8—82no—
143C2×#124—111no—
144C2×C4×Q8C2×D1111yescharacteristic
145#431—221no—
146C2×#101—21no—
147C4×M16—21no—
148#399—221no—
149#395—111no—
150#395—111no—
151#394—111no—
152#394—111no—
153#393—221no—
154#388—221no—
155#388—221no—
156#383—111no—
157#343C2×D1112yes—
158#324—112no—
159#324—221no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11C2×#9911yescharacteristic
163C22×C11#41611yescharacteristic
164C22×C11C2×#10411yescharacteristic
165C2×D11—81no—
166C2×D11—81no—
167C2×D11—81no—
168C2×D11—81no—
169C2×D11—81no—
170C2×D11—81no—
171C2×D11—81no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—41no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—41no—
180Dic11—81no—
181Dic11—81no—
182Dic11—81no—
183C22×Q8—111no—
184C22×Q8C22⋊D1111yescharacteristic
185C22×D4—111no—
186C2×M16—22no—
187#124—441no—
188#124—441no—
189C4×Q8—41no—
190C4×Q8—41no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4—221no—
193C2×C4⋊C4C4×D1111yescharacteristic
194C2×C4⋊C4D4411yescharacteristic
195C2×C4⋊C4C22×D1111yescharacteristic
196C2×C22⋊C4—221no—
197C2×C22⋊C4—221no—
198C2×C22⋊C4—221no—
199C2×C22⋊C4—221no—
200C2×C22⋊C4—221no—
201C2×C22⋊C4—221no—
202C2×C42C4×D1111yescharacteristic
203C2×C42D4411yescharacteristic
204C2×C42C22⋊D1111yescharacteristic
205C4⋊C8—441no—
206#101—24no—
207C22⋊C8—222no—
208#97—41no—
209C4×C8—41no—
210C4×C8—441no—
211#95—111no—
212#95—111no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#150111yescharacteristic
220C2×C11#212211yescharacteristic
221C2×C11#213311yescharacteristic
222D11—161no—
223C24—221no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—441no—
228C2×Q8—881no—
229C2×D4—441no—
230C2×D4—881no—
231C22×C4—221no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4(C2×D11)⋊C411yescharacteristic
236C22×C4(C2×D11)⋊C411yescharacteristic
237C22×C4(C2×D11)⋊C411yescharacteristic
238C22×C4C2×C4×D1111yescharacteristic
239C22×C4C2×D4411yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—24no—
242M16—42no—
243C2×C8—42no—
244C2×C8—442no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—881no—
249C4⋊C4—881no—
250C22⋊C4—442no—
251C22⋊C4—442no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—442no—
255C22⋊C4—881no—
256C22⋊C4—881no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C11#1173811yescharacteristic, complemented, Sylow
264C23—441no—
265C23—441no—
266C23—441no—
267C23—441no—
268C23—441no—
269C23—441no—
270C23—441no—
271C23C2×(C2×D11)⋊C411yescharacteristic
272Q8—44no—
273Q8—882no—
274D4—882no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4#6686912yes—
299C2×C4#6687011yescharacteristic
300C2×C4#6687011yescharacteristic
301C2×C4#6700312yes—
302C8—44no—
303C8—882no—
304C22—21no—
305C22—21no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22—881no—
310C22—881no—
311C22—881no—
312C22—881no—
313C22C2×#6686911yescharacteristic
314C22C2×#6687011yescharacteristic
315C22#1062261511yescharacteristic
316C4—22no—
317C4—22no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—881no—
325C4—881no—
326C4—881no—
327C2—21no—
328C2—21no—
329C2—1761no—
330C2#1306710511yescharacteristic
331C2#1307026711yescharacteristic
332C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC22×D44C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenterC4×#101D11
hypocenterC11#11738
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #13066940C2semidirect
3. #13066645C2semidirect
5. C4×C11×#101C2semidirect
99. C4×#101D11semidirect
263. C11#11738semidirect

Maximal subgroups

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

subgroupindex
#130744762
#130669402
#130666452
#130666182
C4×C11×#1012
#1173811