Finite Group Databasebeta

← #14664350

Subgroups — #14664350

Order 2816.

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

normal subgroups only

This group has 446 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#13073521C211yesmaximal, characteristic
2#13066960C211yesmaximal, characteristic, complemented
3#13066621C212yesmaximal, complemented
4#13066618C212yesmaximal
5C4×C11×#101C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66999—21no—
8C2×C4×D44C411yescharacteristic
9C2×C11×#101—21no—
10C4×C11×M16—21no—
11#10622604C411yescharacteristic
12#10622604C2211yescharacteristic
13#10622600—21no—
14#10622596C411yescharacteristic
15#10622596C2211yescharacteristic
16#10622553—21no—
17#10622553—21no—
18#10622549C411yescharacteristic
19#10622539—21no—
20C11×#343C2212yes—
21#10622166—21no—
22#10622166C2212yes—
23C22×Q8×C11D411yescharacteristic
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
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
35#66999—44no—
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×C4⋊Dic11—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C4×D44—41no—
46C4×D44—41no—
47C11×#101—24no—
48C11×#97—41no—
49C4×C8×C11—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—41no—
57#66867—41no—
58#11778—111nomaximal, Sylow
59C23×D11—21no—
60C2×Q8×C11—22no—
61C2×Q8×C11—22no—
62C2×Q8×C11—41no—
63C22×C4×C11C22⋊C411yescharacteristic
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×D44—41no—
74C2×D44—42no—
75C2×C4×D11—42no—
76C2×C4×D11—42no—
77C2×C4×D11—42no—
78C11×M16—24no—
79C11×M16—42no—
80C2×C8×C11—42no—
81C11×C4⋊C4—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—42no—
96C4⋊Dic11—41no—
97C4⋊Dic11—42no—
98Dic11⋊C4—42no—
99Dic11⋊C4—42no—
100C2×C11⋊C8—42no—
101#2536—111no—
102C4×#101D1111yescharacteristic, complemented
103#1467—111no—
104#1346—112no—
105#1345—112no—
106C23×C11C2×C22⋊C411yescharacteristic
107C22×D11—22no—
108C22×D11—41no—
109C22×D11—41no—
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—41no—
114Q8×C11—44no—
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—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#10412yes—
132C2×C4×C11AGL(1,ℤ/8)12yes—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142D44—42no—
143D44—42no—
144C4×D11—84no—
145C8×C11—44no—
146C11⋊C8—82no—
147C2×C22⋊Q8—221no—
148C2×C4×Q8C2×D1111yescharacteristic
149C2×C4×D4—111no—
150#432—221no—
151C2×#101—21no—
152C4×M16—21no—
153#398—111no—
154#398—111no—
155#394—111no—
156#394—111no—
157#388—221no—
158#388—221no—
159#382—111no—
160#380—221no—
161#343C2×D1112yes—
162#324—112no—
163#324—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11C2×#9911yescharacteristic
167C22×C11#41811yescharacteristic
168C22×C11C2×#10411yescharacteristic
169C2×D11—42no—
170C2×D11—42no—
171C2×D11—42no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—22no—
179C4×C11—22no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184Dic11—81no—
185Dic11—81no—
186Dic11—81no—
187C22×Q8C22⋊D1111yescharacteristic
188C22×D4—111no—
189C23×C4—221no—
190C2×M16—22no—
191C22⋊Q8—444no—
192C4×Q8—41no—
193C4×Q8—41no—
194C4×D4—441no—
195C4×D4—441no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4C4×D1111yescharacteristic
201C2×C4⋊C4D4411yescharacteristic
202C2×C4⋊C4C22×D1111yescharacteristic
203C2×C22⋊C4—221no—
204C2×C22⋊C4—221no—
205C2×C22⋊C4—221no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C42C4×D1111yescharacteristic
209C2×C42D4411yescharacteristic
210C2×C42C22⋊D1111yescharacteristic
211C4⋊C8—441no—
212#101—24no—
213C22⋊C8—222no—
214#97—41no—
215#97—441no—
216C4×C8—41no—
217#95—111no—
218#95—111no—
219#95—221no—
220#95—221no—
221#95—221no—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11#150711yescharacteristic
225C2×C11#212011yescharacteristic
226C2×C11#213311yescharacteristic
227D11—82no—
228C24—221no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×D4—441no—
233C2×D4—442no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—442no—
238C22×C4—442no—
239C22×C4—442no—
240C22×C4(C2×D11)⋊C411yescharacteristic
241C22×C4(C2×D11)⋊C411yescharacteristic
242C22×C4(C2×D11)⋊C411yescharacteristic
243C22×C4(C2×D11)⋊C411yescharacteristic
244C22×C4C2×C4×D1111yescharacteristic
245C22×C4C2×D4411yescharacteristic
246C22×C4C2×C22⋊D1111yescharacteristic
247M16—24no—
248M16—42no—
249C2×C8—42no—
250C2×C8—442no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—441no—
255C4⋊C4—442no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C22⋊C4—442no—
259C22⋊C4—442no—
260C22⋊C4—442no—
261C22⋊C4—441no—
262C22⋊C4—441no—
263C22⋊C4—442no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C11#1177811yescharacteristic, complemented, Sylow
271C23—222no—
272C23—441no—
273C23—441no—
274C23—441no—
275C23—441no—
276C23—441no—
277C23—441no—
278C23C2×(C2×D11)⋊C411yescharacteristic
279Q8—44no—
280D4—442no—
281D4—442no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—884no—
306C2×C4#6686912yes—
307C2×C4#6687011yescharacteristic
308C2×C4#6687011yescharacteristic
309C2×C4#6700212yes—
310C8—44no—
311C8—882no—
312C22—21no—
313C22—21no—
314C22—442no—
315C22—442no—
316C22—442no—
317C22—881no—
318C22—881no—
319C22—881no—
320C22—881no—
321C22C2×#6686911yescharacteristic
322C22C2×#6687011yescharacteristic
323C22#1062261411yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—881no—
333C4—881no—
334C4—881no—
335C2—21no—
336C2—21no—
337C2—882no—
338C2#1306713111yescharacteristic
339C2#1307025811yescharacteristic
340C2#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#11778
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. #13066960C2semidirect
3. #13066621C2semidirect
5. C4×C11×#101C2semidirect
102. C4×#101D11semidirect
270. C11#11778semidirect

Maximal subgroups

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

subgroupindex
#130735212
#130669602
#130666212
#130666182
C4×C11×#1012
#1177811