Finite Group Databasebeta

← #14647401

Subgroups — #14647401

Order 2816.

480 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 95 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#13071556C211yesmaximal, characteristic
2C4×#66898C211yesmaximal, characteristic
3#13066501C212yesmaximal, complemented
4#13066470C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C11×#407C2212yes—
8#10622833—21no—
9C2×#66898—21no—
10#10622825C411yescharacteristic, complemented
11#10622824C2211yescharacteristic
12C4×C22⋊Dic11C2212yes—
13C4×C22⋊Dic11C2211yescharacteristic
14C2×C11⋊#95C411yescharacteristic, complemented
15#10622594—21no—
16#10622564—21no—
17C22⋊C4×Dic11—21no—
18#10622550C411yescharacteristic, complemented
19#10622545C411yescharacteristic, complemented
20C11×#324—21no—
21C11×#323—21no—
22#10622164—21no—
23C22×D4×C11D411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—21no—
27C2×C11×M16—22no—
28C4×D4×C11—22no—
29C4×D4×C11—22no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4×Dic11—21no—
40C2×C4×Dic11—21no—
41C2×C4×Dic11—22no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44#66898—24no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—22no—
51C11⋊#95C2×C411yescharacteristic
52C11⋊#95C2×C411yescharacteristic
53C11⋊#95C2×C411yescharacteristic
54C11⋊#95C2×C411yescharacteristic
55#8777—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C2×D411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—81no—
64C22×C4×C11—81no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4112yes—
71C22×C4×C11#4112yes—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C22×Dic11—81no—
80C11×M16—82no—
81C2×C8×C11—42no—
82C11×C4⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C42×C11—21no—
86C42×C11—21no—
87C22⋊Dic11—24no—
88C22⋊Dic11—42no—
89C22⋊Dic11—42no—
90C22⋊Dic11—42no—
91C22⋊Dic11—81no—
92C4⋊Dic11—81no—
93C4×Dic11—42no—
94C4×Dic11—81no—
95C4×Dic11—82no—
96#2353—111no—
97C4×#99—111no—
98#1465D1111yescharacteristic
99#1297—112no—
100#1284—112no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11#10412yes—
110C23×C11C2×C22⋊C411yescharacteristic
111C23×C11#12312yes—
112D4×C11—44no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11#11711yescharacteristic
127C2×C4×C11#11711yescharacteristic
128C2×C4×C11#12312yes—
129C2×Dic11—22no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—44no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—84no—
143C2×Dic11—82no—
144C2×Dic11—82no—
145C8×C11—82no—
146C2×C4×D4C2×D1111yescharacteristic
147C2×#99—221no—
148#407C2×D1112yes—
149#388—221no—
150#387—221no—
151#386—221no—
152#383—111no—
153#381—111no—
154#380—111no—
155C4×C22⋊C4—111no—
156C4×C22⋊C4—112no—
157C4×C22⋊C4—221no—
158#376—111no—
159C2×#95—111no—
160#342—221no—
161#324—21no—
162#323—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—22no—
169C22×C11—42no—
170C22×C11—42no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38111yescharacteristic
176C22×C11C2×#10411yescharacteristic
177C22×C11#42111yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—22no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11—41no—
184Dic11—42no—
185Dic11—81no—
186Dic11—81no—
187Dic11—81no—
188Dic11—84no—
189C22×D4D4411yescharacteristic
190C23×C4—221no—
191C23×C4C4×D1111yescharacteristic
192C23×C4C22×D1111yescharacteristic
193C2×M16—22no—
194C4×D4—22no—
195C4×D4—22no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4C22⋊D1111yescharacteristic
198C2×C22⋊C4—222no—
199C2×C22⋊C4—221no—
200C2×C22⋊C4—221no—
201C2×C22⋊C4—221no—
202C2×C22⋊C4D4411yescharacteristic
203C2×C22⋊C4C22⋊D1111yescharacteristic
204C2×C42—221no—
205C2×C42—221no—
206C2×C42—222no—
207C2×C42C4×D1111yescharacteristic
208#99—224no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211#95—111no—
212#95—111no—
213#95—111no—
214#95—111no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—222no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11—42no—
224C2×C11—42no—
225C2×C11#182611yescharacteristic
226C2×C11#182711yescharacteristic
227C2×C11#182811yescharacteristic
228C24(C2×D11)⋊C411yescharacteristic
229C24C2×D4411yescharacteristic
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—81no—
236C22×C4—81no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4—221no—
241C22×C4—442no—
242C22×C4—442no—
243C22×C4—442no—
244C22×C4—881no—
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4(C2×D11)⋊C411yescharacteristic
247C22×C4(C2×D11)⋊C411yescharacteristic
248C22×C4C2×C4×D1111yescharacteristic
249C22×C4#434112yes—
250C22×C4#434112yes—
251C22×C4C2×C22⋊D1111yescharacteristic
252M16—82no—
253C2×C8—42no—
254C4⋊C4—22no—
255C4⋊C4—881no—
256C22⋊C4—22no—
257C22⋊C4—22no—
258C22⋊C4—224no—
259C22⋊C4—442no—
260C22⋊C4—442no—
261C22⋊C4—442no—
262C22⋊C4—881no—
263C42—21no—
264C42—21no—
265C42—442no—
266C42—881no—
267C42—882no—
268C11#877711yescharacteristic, complemented, Sylow
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23#6688912yes—
278C23#6693912yes—
279C23C2×(C2×D11)⋊C411yescharacteristic
280D4—44no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—222no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—444no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—884no—
308C2×C4—882no—
309C2×C4—882no—
310C2×C4#6693011yescharacteristic
311C2×C4#6693011yescharacteristic
312C2×C4#6698812yes—
313C8—82no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22#1062255611yescharacteristic
327C22C2×#6688911yescharacteristic
328C22#1062275211yescharacteristic
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—442no—
336C4—881no—
337C4—881no—
338C4—881no—
339C4—884no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—42no—
344C2#1306871311yescharacteristic
345C2#1306872111yescharacteristic
346C2#1306872211yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1465C2
socleC22×C11#381
prime radicalC22×D4×C11D4
cosocleC23×C4×C11C23
hypercenter#1465D11
hypocenterC11#8777
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13066501C2semidirect
4. #13066470C2semidirect
10. #10622825C4semidirect
14. C2×C11⋊#95C4semidirect
18. #10622550C4semidirect
19. #10622545C4semidirect
268. C11#8777semidirect

Maximal subgroups

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

subgroupindex
#130715562
C4×#668982
#130665012
#130664702
C11×#14652
#877711