Finite Group Databasebeta

← #14663432

Subgroups — #14663432

Order 2816.

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

normal subgroups only

This group has 416 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#13073812C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic
3#13066561C212yesmaximal, complemented
4#13066559C212yesmaximal, complemented
5C11×#1459C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66923C411yescharacteristic
8C2×C11×C22⋊C8—21no—
9#10622834C411yescharacteristic
10#10622834C411yescharacteristic
11#10622823—21no—
12#10622823—21no—
13#10622820—21no—
14#10622590C2211yescharacteristic
15#10622589C2211yescharacteristic
16#10622561—21no—
17#10622561—21no—
18C4×C4⋊Dic11C411yescharacteristic
19C11×#324C2212yes—
20C11×#323—21no—
21#10622166C2212yes—
22#10622163—21no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C8×C11—41no—
27C4×D4×C11—41no—
28C4×D4×C11—41no—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C42×C11C2×C411yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×#4318—41no—
47#66923—41no—
48#66923—41no—
49C11×C22⋊C8—22no—
50C11×C22⋊C8—41no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—41no—
56#11572—111nomaximal, Sylow
57C24×C11C22⋊C411yescharacteristic
58C24×C11C22⋊C411yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—81no—
67C22×C4×C11—81no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×C8×C11—42no—
78C2×C8×C11—82no—
79C11×C4⋊C4—41no—
80C11×C22⋊C4—41no—
81C11×C22⋊C4—41no—
82C42×C11—21no—
83C42×C11—21no—
84C22⋊Dic11—42no—
85C22⋊Dic11—42no—
86C22⋊Dic11—81no—
87C22⋊Dic11—81no—
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—81no—
95Dic11⋊C4—81no—
96C4×Dic11—22no—
97C4×Dic11—22no—
98#4318—82no—
99C2×C11⋊C8—42no—
100#2566—111no—
101#1465—111no—
102#1459D1111yescharacteristic
103#1325—112no—
104#1324—112no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—21no—
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—41no—
114C23×C11#10112yes—
115C23×C11C2×C22⋊C411yescharacteristic
116D4×C11—44no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—81no—
129C2×C4×C11—81no—
130C2×C4×C11#9911yescharacteristic
131C2×C4×C11#9911yescharacteristic
132C2×C4×C11#13112yes—
133C2×Dic11—22no—
134C2×Dic11—41no—
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—41no—
145C8×C11—82no—
146C11⋊C8—82no—
147C2×#125—111no—
148C2×C4×D4C2×D1111yescharacteristic
149#407—221no—
150C2×C22⋊C8—21no—
151#396—221no—
152#396—221no—
153#390—111no—
154#390—111no—
155#385—221no—
156#385—221no—
157#384—111no—
158#382—111no—
159C4×C4⋊C4—111no—
160#324—112no—
161#324C2×D1112yes—
162#323—21no—
163#323—221no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11—22no—
167C22×C11—42no—
168C22×C11—42no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—81no—
175C22×C11—81no—
176C22×C11#40811yescharacteristic
177C22×C11C2×#9911yescharacteristic
178C22×C11C2×#10111yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—22no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185Dic11—42no—
186Dic11—81no—
187Dic11—81no—
188Dic11—81no—
189C22×D4C4×D1111yescharacteristic
190C23×C4D4411yescharacteristic
191C23×C4C22⋊D1111yescharacteristic
192C2×M16—441no—
193C22×C8—41no—
194#125—441no—
195#125—441no—
196C4×D4—41no—
197C4×D4—41no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4C22×D1111yescharacteristic
206C2×C22⋊C4—221no—
207C2×C22⋊C4—221no—
208C2×C22⋊C4—221no—
209C2×C22⋊C4—221no—
210C2×C22⋊C4D4411yescharacteristic
211C2×C22⋊C4C22⋊D1111yescharacteristic
212C2×C42—111no—
213C2×C42—111no—
214C2×C42C4×D1111yescharacteristic
215C22⋊C8—22no—
216C22⋊C8—41no—
217C22⋊C8—222no—
218C22⋊C8—441no—
219#95—221no—
220#95—221no—
221#95—221no—
222C2×C11—21no—
223C2×C11—21no—
224C2×C11—42no—
225C2×C11—81no—
226C2×C11#147211yescharacteristic
227C2×C11#212711yescharacteristic
228C2×C11#213211yescharacteristic
229C24(C2×D11)⋊C411yescharacteristic
230C24(C2×D11)⋊C411yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—221no—
241C22×C4—221no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4(C2×D11)⋊C411yescharacteristic
245C22×C4(C2×D11)⋊C411yescharacteristic
246C22×C4C2×C4×D1111yescharacteristic
247C22×C4C2×D4411yescharacteristic
248C22×C4C2×C22⋊D1111yescharacteristic
249M16—882no—
250C2×C8—42no—
251C2×C8—82no—
252C2×C8—442no—
253C4⋊C4—41no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—442no—
257C4⋊C4—442no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—881no—
261C4⋊C4—881no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—442no—
265C22⋊C4—442no—
266C22⋊C4—881no—
267C22⋊C4—881no—
268C42—21no—
269C42—21no—
270C42—222no—
271C42—222no—
272C11#1157211yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#6688812yes—
283C23C2×(C2×D11)⋊C411yescharacteristic
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—222no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4#6687011yescharacteristic
311C2×C4#6687011yescharacteristic
312C2×C4#6695412yes—
313C8—82no—
314C8—882no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22C2×#6687011yescharacteristic
328C22#1062272311yescharacteristic
329C22C2×#6688811yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—442no—
337C4—881no—
338C4—881no—
339C4—881no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1306697911yescharacteristic
345C2#1307028311yescharacteristic
346C2#1307029911yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1459C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1459D11
hypocenterC11#11572
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13066561C2semidirect
4. #13066559C2semidirect
272. C11#11572semidirect

Maximal subgroups

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

subgroupindex
#130738122
#130669542
#130665612
#130665592
C11×#14592
#1157211