Finite Group Databasebeta

← #14651116

Subgroups — #14651116

Order 2816.

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

normal subgroups only

This group has 496 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#13077254C211yesmaximal, characteristic, complemented
2#13074303C211yesmaximal, characteristic
3#13067215C212yesmaximal, complemented
4#13066508C212yesmaximal, complemented
5C11×#1464C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66928C2211yescharacteristic
8C11×#432C2212yes—
9#10622826—21no—
10#10622820—21no—
11#10622613—24no—
12#10622604C411yescharacteristic
13#10622603—21no—
14#10622592C411yescharacteristic
15#10622573C411yescharacteristic
16#10622570—21no—
17#10622560C411yescharacteristic
18#10622553—21no—
19#10622545C2211yescharacteristic
20#10622537—21no—
21C4×#4318C2212yes—
22C11×#324—21no—
23C11×#323—21no—
24#10622102—24no—
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C11×#117—22no—
30C11×#117—22no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C2×#4318—22no—
46#66928—22no—
47#66928—22no—
48C11×C4⋊C8—22no—
49C11×C22⋊C8—22no—
50C11×#97—22no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—24no—
57C4⋊(C11⋊C8)—24no—
58#66867D414yescomplemented
59C4×C11⋊C8—22no—
60#9389—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C23×D11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—41no—
66C22×C4×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C2×C22⋊D11—81no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C2×D44—22no—
80C2×D44—81no—
81C2×Dic22—22no—
82C2×Dic22—81no—
83C2×C8×C11—42no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C22⋊C4—22no—
87C11×C22⋊C4—22no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11C2×D412yes—
91C42×C11#4112yes—
92C22⋊Dic11—81no—
93(C2×D11)⋊C4—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—41no—
96(C2×D11)⋊C4—42no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—81no—
99Dic11⋊C4—81no—
100C4×Dic11—42no—
101#4318—42no—
102#4318—42no—
103C2×C11⋊C8—24no—
104#2921—111no—
105#2610—111no—
106#1527—112no—
107#1464D1111yescharacteristic, complemented
108#1300—112no—
109C23×C11—21no—
110C23×C11—21no—
111C23×C11—21no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11C2×C22⋊C411yescharacteristic
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—41no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11C4×D412yes—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12112yes—
138C2×C4×C11#12311yescharacteristic
139C22⋊D11—84no—
140C2×Dic11—22no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149D44—82no—
150Dic22—82no—
151C8×C11—82no—
152C11⋊C8—44no—
153C2×#124—111no—
154C2×#117C2×D1111yescharacteristic
155#433—224no—
156#432C2×D1112yes—
157#423—221no—
158#407—221no—
159C4×M16—112no—
160#395—111no—
161#394—111no—
162#393—111no—
163#392—111no—
164#390—221no—
165#388—221no—
166#388—221no—
167#386—221no—
168#376—111no—
169#329—224no—
170#324—21no—
171#323—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—42no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—81no—
179C22×C11#38611yescharacteristic
180C22×C11#42111yescharacteristic
181C22×C11#42111yescharacteristic
182C2×D11—81no—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C4×C11—22no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—22no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—41no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199C22×Q8—111no—
200C22×D4—111no—
201C22×D4—221no—
202C23×C4D4411yescharacteristic
203C2×M16—222no—
204#124—222no—
205#124—222no—
206#117—22no—
207#117—22no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4C4×D1111yescharacteristic
210C2×C4⋊C4C22⋊D1111yescharacteristic
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4—221no—
214C2×C22⋊C4—221no—
215C2×C22⋊C4—221no—
216C2×C22⋊C4—221no—
217C2×C22⋊C4C4×D1111yescharacteristic
218C2×C22⋊C4C22⋊D1111yescharacteristic
219C2×C42—221no—
220C2×C42D4411yescharacteristic
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—22no—
223C4⋊C8—224no—
224C22⋊C8—22no—
225C22⋊C8—224no—
226#97—22no—
227#97—114no—
228C4×C8—222no—
229#95—111no—
230#95—111no—
231#95—221no—
232#95—221no—
233#95—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—81no—
237C2×C11#188411yescharacteristic
238C2×C11#189711yescharacteristic
239C2×C11#191411yescharacteristic
240D11—161no—
241C24—221no—
242C24(C2×D11)⋊C411yescharacteristic
243C2×Q8—222no—
244C2×Q8—881no—
245C2×D4—222no—
246C2×D4—442no—
247C2×D4—442no—
248C2×D4—881no—
249C2×D4—881no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257C22×C4(C2×D11)⋊C411yescharacteristic
258C22×C4(C2×D11)⋊C411yescharacteristic
259C22×C4(C2×D11)⋊C411yescharacteristic
260C22×C4C2×C4×D1111yescharacteristic
261C22×C4C2×D4411yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263M16—442no—
264M16—442no—
265C2×C8—42no—
266C2×C8—224no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—881no—
270C22⋊C4—22no—
271C22⋊C4—22no—
272C22⋊C4—442no—
273C22⋊C4—442no—
274C22⋊C4—441no—
275C22⋊C4—441no—
276C22⋊C4—442no—
277C22⋊C4—881no—
278C22⋊C4—881no—
279C42—21no—
280C42—21no—
281C42—442no—
282C42D4×D1112yes—
283C42#434112yes—
284C11#938911yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23—41no—
290C23—441no—
291C23—441no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23C2×(C2×D11)⋊C411yescharacteristic
298Q8—882no—
299D4—882no—
300D4—884no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—222no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4(C22⋊D11)⋊C412yes—
324C2×C4#6693511yescharacteristic
325C2×C4#6693911yescharacteristic
326C2×C4#6699212yes—
327C8—82no—
328C8—444no—
329C22—21no—
330C22—21no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22—881no—
342C22—881no—
343C22#1062257111yescharacteristic
344C22#1062275211yescharacteristic
345C22#1062275211yescharacteristic
346C4—21no—
347C4—21no—
348C4—22no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—442no—
354C4—881no—
355C4—881no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—1761no—
360C2#1306899711yescharacteristic
361C2#1306906211yescharacteristic
362C2#1306916111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1464C2
socleC22×C11#386
prime radical#10622573C4
cosocleC2×C42×C11C23
hypercenter#1464D11
hypocenterC11#9389
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
1. #13077254C2semidirect
3. #13067215C2semidirect
4. #13066508C2semidirect
5. C11×#1464C2semidirect
58. #66867D4semidirect
107. #1464D11semidirect
284. C11#9389semidirect

Maximal subgroups

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

subgroupindex
#130772542
#130743032
#130672152
#130665082
C11×#14642
#938911