Finite Group Databasebeta

← #14664245

Subgroups — #14664245

Order 2816.

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

normal subgroups only

This group has 444 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#13074193C211yesmaximal, characteristic
2#13068349C211yesmaximal, characteristic
3#13066638C212yesmaximal
4#13066617C212yesmaximal
5C11×#1464C211yesmaximal, characteristic
6C2×C11×#117C2211yescharacteristic
7C2×#66979—21no—
8C2×C4×Dic22C411yescharacteristic, complemented
9C11×#432—21no—
10#10622823—21no—
11#10622596C411yescharacteristic, complemented
12#10622592C411yescharacteristic, complemented
13#10622591—21no—
14#10622566C2211yescharacteristic
15#10622560C2211yescharacteristic
16#10622557—21no—
17#10622550C411yescharacteristic, complemented
18#10622546—21no—
19C11×#324—21no—
20C11×#323C2212yes—
21#10622164—21no—
22#10622164C2212yes—
23C23×C4×C11D411yescharacteristic
24C22×Dic22C2×C411yescharacteristic
25C11×#117—41no—
26C11×#117—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C22⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2311yescharacteristic
31C2×C42×C11C2×C411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36#66979—24no—
37#66979—42no—
38C2×C4⋊Dic11—41no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—41no—
45C4×Dic22—41no—
46C4×Dic22—41no—
47C11×C4⋊C8—41no—
48C11×C22⋊C8—22no—
49C11×#97—41no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11756—111nomaximal, Sylow
59C24×C11C2×D411yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—22no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22×C411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—42no—
76C2×Dic22—41no—
77C2×Dic22—42no—
78C2×C8×C11—42no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C11×C22⋊C4—41no—
82C11×C22⋊C4—41no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C22⋊Dic11—24no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C22⋊Dic11—41no—
91C22⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—44no—
94Dic11⋊C4—42no—
95Dic11⋊C4—41no—
96Dic11⋊C4—41no—
97Dic11⋊C4—42no—
98C4×Dic11—42no—
99C4×Dic11—44no—
100#2599—111no—
101#1740—111no—
102#1464D1111yescharacteristic
103#1351—112no—
104#1344—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11C2×C22⋊C411yescharacteristic
110C23×C11AGL(1,ℤ/8)11yescharacteristic
111C23×C11#13711yescharacteristic
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
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—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11#9911yescharacteristic
129C2×C4×C11#9911yescharacteristic
130C2×C4×C11#10412yes—
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—44no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—82no—
145C2×Dic11—82no—
146Dic22—42no—
147Dic22—42no—
148C8×C11—82no—
149C2×C4×Q8—111no—
150C2×#117—221no—
151C2×#117C2×D1111yescharacteristic
152#432—21no—
153#398—111no—
154#397—111no—
155#395—111no—
156#393—111no—
157#388—221no—
158#387—221no—
159#387—221no—
160#385—221no—
161#383—111no—
162#342—112no—
163#342—221no—
164#324—21no—
165#323C2×D1112yes—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—81no—
175C22×C11C2×#9911yescharacteristic
176C22×C11#41711yescharacteristic
177C22×C11C2×#10411yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—22no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185Dic11—42no—
186Dic11—81no—
187Dic11—81no—
188Dic11—84no—
189Dic11—81no—
190C22×Q8—111no—
191C23×C4D4411yescharacteristic
192C4×Q8—441no—
193C4×Q8—441no—
194#117—41no—
195#117—41no—
196#117—224no—
197#117—442no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—441no—
203C2×C4⋊C4C4×D1111yescharacteristic
204C2×C4⋊C4C22⋊D1111yescharacteristic
205C2×C22⋊C4—222no—
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4D4411yescharacteristic
209C2×C22⋊C4C22×D1111yescharacteristic
210C2×C42—221no—
211C2×C42—441no—
212C2×C42C4×D1111yescharacteristic
213C2×C42C22⋊D1111yescharacteristic
214C4⋊C8—41no—
215C22⋊C8—22no—
216#97—41no—
217#95—111no—
218#95—111no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—41no—
228C2×C11—41no—
229C2×C11#150411yescharacteristic
230C2×C11#212011yescharacteristic
231C2×C11#212911yescharacteristic
232C24C2×D4411yescharacteristic
233C2×Q8—441no—
234C2×Q8—442no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—442no—
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4(C2×D11)⋊C411yescharacteristic
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4(C2×D11)⋊C411yescharacteristic
249C22×C4C2×C4×D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251C2×C8—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—441no—
255C4⋊C4—444no—
256C4⋊C4—442no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—224no—
263C22⋊C4—442no—
264C22⋊C4—442no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—442no—
272C42—444no—
273C11#1175611yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#6696111yescharacteristic
279C23#6696211yescharacteristic
280C23C2×(C2×D11)⋊C411yescharacteristic
281Q8—442no—
282Q8—442no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—222no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—444no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—882no—
313C2×C4—882no—
314C2×C4#6687011yescharacteristic
315C2×C4#6687011yescharacteristic
316C2×C4#6688912yes—
317C8—82no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22C2×#6687011yescharacteristic
328C22#1062274611yescharacteristic
329C22C2×#6688911yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—442no—
338C4—881no—
339C4—881no—
340C4—884no—
341C4—881no—
342C2—21no—
343C2—21no—
344C2—41no—
345C2—41no—
346C2#1306712111yescharacteristic
347C2#1307025811yescharacteristic
348C2#1307029011yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1464C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1464D11
hypocenterC11#11756
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
8. C2×C4×Dic22C4semidirect
11. #10622596C4semidirect
12. #10622592C4semidirect
17. #10622550C4semidirect
273. C11#11756semidirect

Maximal subgroups

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

subgroupindex
#130741932
#130683492
#130666382
#130666172
C11×#14642
#1175611