Finite Group Databasebeta

← #14651597

Subgroups — #14651597

Order 2816.

726 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 103 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#13071951C211yesmaximal, characteristic
2#13068561C212yesmaximal
3#13066946C211yesmaximal, characteristic, complemented
4#13066469C212yesmaximal, complemented
5C11×#2313C211yesmaximal, characteristic, complemented
6C22×#4339C2211yescharacteristic
7C22×C11×C4⋊C4C2211yescharacteristic
8C2×#66982—21no—
9C11×#387—24no—
10C11×#381—21no—
11C11×#380—21no—
12C4×C11×C22⋊C4C2212yes—
13#10622826—21no—
14#10622824C2211yescharacteristic
15#10622820C2212yes—
16#10622604C412yescomplemented
17#10622602—22no—
18#10622592C412yescomplemented
19C2×#66869—24no—
20#10622166—22no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×C22⋊D11—21no—
25C2×#4339—22no—
26C2×#4339—22no—
27C2×#4339—44no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C22×Dic22C2×C411yescharacteristic
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4—22no—
34C2×C11×C4⋊C4C2×C412yes—
35C2×C11×C4⋊C4D412yes—
36C2×C11×C22⋊C4—22no—
37C2×C42×C11D414yes—
38C2×C22⋊Dic11—21no—
39#66982—44no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×Dic11⋊C4—22no—
43C2×#4318—22no—
44C11×#95—22no—
45C11×#95—24no—
46C11×#95—22no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95C2×C412yes—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52#66869—48no—
53#9480—111nomaximal, Sylow
54C24×C11C2×D411yescharacteristic
55C23×D11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—24no—
61C22×C4×C11—42no—
62C22×C4×C11—42no—
63C22×C4×C11—42no—
64C22×C4×C11C22⋊C412yes—
65C22×C4×C11C22⋊C412yes—
66C22×C4×C11C22×C411yescharacteristic
67C22×C4×C11C2×D412yes—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11#4112yes—
70C2×C22⋊D11—24no—
71C2×C22⋊D11—42no—
72C2×C22⋊D11—41no—
73C2×C22⋊D11—41no—
74C22×Dic11—21no—
75C22×Dic11—22no—
76#4339—28no—
77#4339—44no—
78#4339—44no—
79#4339—44no—
80C2×D44—22no—
81C2×D44—42no—
82C2×C4×D11—42no—
83C2×C4×D11—42no—
84C2×C4×D11—42no—
85C2×Dic22—22no—
86C2×Dic22—42no—
87C11×C4⋊C4—24no—
88C11×C4⋊C4—24no—
89C11×C4⋊C4—82no—
90C11×C22⋊C4—44no—
91C42×C11—44no—
92C22⋊Dic11—42no—
93(C2×D11)⋊C4—44no—
94(C2×D11)⋊C4—44no—
95Dic11⋊C4—44no—
96#4318—44no—
97C2×C11⋊C8—42no—
98#2406—111no—
99#2313D1111yescharacteristic, complemented
100#1789—112no—
101#1463—111no—
102#1284—112no—
103C23×C11—22no—
104C23×C11—22no—
105C23×C11—41no—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11#12011yescharacteristic
108C23×C11#12311yescharacteristic
109C22×D11—22no—
110C22×D11—41no—
111C22×D11—42no—
112C22×D11—41no—
113C22×D11—42no—
114C2×C4×C11—24no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—22no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—42no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—81no—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12112yes—
132C22⋊D11—44no—
133C22⋊D11—44no—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140D44—24no—
141D44—42no—
142C4×D11—48no—
143Dic22—24no—
144Dic22—42no—
145C11⋊C8—82no—
146C22×#41—111no—
147C2×#123—221no—
148C22×C4⋊C4C2×D1111yescharacteristic
149C2×#104—224no—
150#407—112no—
151#395—112no—
152#394—112no—
153#387—24no—
154#386—221no—
155#385—222no—
156#381—21no—
157#381—111no—
158#380—21no—
159C4×C22⋊C4C2×D1112yes—
160#324—222no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11—44no—
169C22×C11#38611yescharacteristic
170C22×C11#42112yes—
171C22×C11B(4,𝔽2)12yes—
172C2×D11—44no—
173C2×D11—42no—
174C2×D11—82no—
175C2×D11—81no—
176C2×D11—81no—
177C4×C11—22no—
178C4×C11—22no—
179C4×C11—42no—
180C4×C11—42no—
181C4×C11—84no—
182Dic11—42no—
183Dic11—82no—
184C2×#41—222no—
185C2×#41—222no—
186C2×#41—444no—
187C22×Q8—111no—
188C22×D4—111no—
189C22×D4—221no—
190C23×C4—221no—
191C23×C4C22⋊D1111yescharacteristic
192C23×C4C22⋊D1111yescharacteristic
193C23×C4C22×D1111yescharacteristic
194C2×M16—222no—
195#123—444no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—222no—
200C2×C4⋊C4C4×D1112yes—
201C2×C4⋊C4D4412yes—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—221no—
204C2×C22⋊C4—222no—
205C2×C22⋊C4—222no—
206C2×C42C22⋊D1114yes—
207#104—448no—
208C22⋊C8—222no—
209C22⋊C8—222no—
210#95—22no—
211#95—24no—
212#95—22no—
213#95—112no—
214#95—222no—
215#95—221no—
216C2×C11—22no—
217C2×C11—22no—
218C2×C11—41no—
219C2×C11#188911yescharacteristic
220C2×C11#189711yescharacteristic
221C2×C11#191211yescharacteristic
222D11—82no—
223C24—221no—
224C24C2×C22⋊D1111yescharacteristic
225#41—228no—
226#41—444no—
227#41—444no—
228#41—444no—
229C2×Q8—222no—
230C2×Q8—442no—
231C2×D4—224no—
232C2×D4—222no—
233C2×D4—442no—
234C2×D4—442no—
235C2×D4—441no—
236C2×D4—441no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—24no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—221no—
246C22×C4—222no—
247C22×C4—442no—
248C22×C4—442no—
249C22×C4—442no—
250C22×C4(C2×D11)⋊C412yes—
251C22×C4(C2×D11)⋊C412yes—
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4C2×D4411yescharacteristic
254C22×C4#433912yes—
255C22×C4C2×C22⋊D1112yes—
256M16—444no—
257C2×C8—442no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—82no—
261C4⋊C4—444no—
262C22⋊C4—44no—
263C22⋊C4—444no—
264C22⋊C4—444no—
265C22⋊C4—442no—
266C42—44no—
267C11#948011yescharacteristic, complemented, Sylow
268C23—22no—
269C23—22no—
270C23—41no—
271C23—222no—
272C23—441no—
273C23—442no—
274C23—441no—
275C23—442no—
276C23C2×(C2×D11)⋊C411yescharacteristic
277C23#6698211yescharacteristic
278C23#6700611yescharacteristic
279Q8—224no—
280Q8—442no—
281D4—224no—
282D4—442no—
283D4—444no—
284D4—444no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—81no—
301C2×C4—222no—
302C2×C4—448no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4C4×C22⋊D1112yes—
309C2×C4#6698312yes—
310C8—882no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—44no—
319C22—444no—
320C22—442no—
321C22—882no—
322C22—881no—
323C22—881no—
324C22#1062261812yes—
325C22#1062282611yescharacteristic
326C22#1062285712yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—84no—
332C4—442no—
333C4—882no—
334C2—22no—
335C2—22no—
336C2—41no—
337C2—882no—
338C2#1306902411yescharacteristic
339C2#1306906411yescharacteristic
340C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2313C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#2313D11
hypocenterC11#9480
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
3. #13066946C2semidirect
4. #13066469C2semidirect
5. C11×#2313C2semidirect
16. #10622604C4semidirect
18. #10622592C4semidirect
99. #2313D11semidirect
267. C11#9480semidirect

Maximal subgroups

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

subgroupindex
#130719512
#130685612
#130669462
#130664692
C11×#23132
#948011