Finite Group Databasebeta

← #14656956

Subgroups — #14656956

Order 2816.

360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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#13074259C211yesmaximal, characteristic
2#13067167C211yesmaximal, characteristic
3#13067128C211yesmaximal, characteristic
4#13066510C211yesmaximal, characteristic
5#13066481C211yesmaximal, characteristic
6#13066472C211yesmaximal, characteristic
7C11×#1986C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C4×C11×M16C2211yescharacteristic
10C4×C11×C4⋊C4C2211yescharacteristic
11#10622599—21no—
12#10622592—21no—
13#10622550C2211yescharacteristic
14#10622546—21no—
15#10622545C2211yescharacteristic
16#10622542—21no—
17#10622539C2211yescharacteristic
18#10622539C2211yescharacteristic
19#10622267—21no—
20#10622259—21no—
21C11×#339—21no—
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622176—21no—
26#10622176—21no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8Q811yescharacteristic, complemented
30C11×C4⋊Q8Q811yescharacteristic, complemented
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117—21no—
37C2×C11×C4⋊C4—21no—
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C42×C11C2311yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C11×#97—21no—
46C4×C8×C11—21no—
47C11×#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95D411yescharacteristic
56C11⋊#95D411yescharacteristic
57C11⋊#95D411yescharacteristic
58C11⋊#95D411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60C22⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65#10379—111nomaximal, Sylow
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C2×Dic22—42no—
78C2×Dic22—42no—
79C2×Dic22—81no—
80C11×M16—22no—
81C11×M16—41no—
82C2×C8×C11—41no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11—41no—
93C42×C11—41no—
94C42×C11C2×Q811yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C4⋊Dic11—42no—
99Dic11⋊C4—42no—
100Dic11⋊C4—81no—
101C4×Dic11—42no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2605—111no—
105#1986D1111yescharacteristic
106#1515—111no—
107#1506—111no—
108#1300—111no—
109#1288—111no—
110#1285—111no—
111C23×C11#12011yescharacteristic
112Q8×C11—81no—
113Q8×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—22no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C22⋊Q811yescharacteristic
127C2×C4×C11C22⋊Q811yescharacteristic
128C2×C4×C11C22⋊Q811yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11#12411yescharacteristic
131C2×C4×C11#12411yescharacteristic
132C2×Dic11—22no—
133C2×Dic11—41no—
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—
144Dic22—84no—
145C8×C11—42no—
146C11⋊C8—81no—
147C11⋊C8—81no—
148#533C2×D1111yescharacteristic
149#432—111no—
150#432—111no—
151C4×M16C2×D1111yescharacteristic
152#400—221no—
153#395—221no—
154#391—221no—
155#391—221no—
156#387—221no—
157#387—221no—
158#383—111no—
159C4×C4⋊C4C2×D1111yescharacteristic
160#376—111no—
161#339—21no—
162#339—21no—
163#328—221no—
164#328—221no—
165#328—221no—
166#328—221no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39311yescharacteristic
170C22×C11#45511yescharacteristic
171C22×C11#45611yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—42no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182Dic11—42no—
183Dic11—81no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—221no—
187C2×M16—21no—
188C4⋊Q8Dic2211yescharacteristic, complemented
189C4⋊Q8Dic2211yescharacteristic, complemented
190#125—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195#117—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C42—221no—
201C2×C42C22⋊D1111yescharacteristic
202C2×C42C22⋊D1111yescharacteristic
203C2×C42C22×D1111yescharacteristic
204C4⋊C8—221no—
205C4⋊C8—221no—
206C22⋊C8—221no—
207C22⋊C8—221no—
208#97—21no—
209#97—221no—
210#97—221no—
211C4×C8—21no—
212#95—21no—
213#95—111no—
214#95—111no—
215#95—111no—
216#95—111no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#202811yescharacteristic
227C2×C11#203111yescharacteristic
228C2×C11#203111yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—442no—
232C2×Q8—442no—
233C2×Q8—881no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4—221no—
240C22×C4D4×D1111yescharacteristic
241C22×C4D4×D1111yescharacteristic
242C22×C4C2×C22⋊D1111yescharacteristic
243M16—22no—
244M16—41no—
245C2×C8—41no—
246C2×C8—441no—
247C2×C8—441no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—442no—
256C4⋊C4—442no—
257C4⋊C4—881no—
258C22⋊C4—41no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42—442no—
263C42C2×Dic2211yescharacteristic
264C42#433911yescharacteristic
265C42#434111yescharacteristic
266C42#434111yescharacteristic
267C11#1037911yescharacteristic, complemented, Sylow
268C23#6699011yescharacteristic
269Q8—81no—
270Q8—81no—
271Q8—884no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—222no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4#6693111yescharacteristic
297C2×C4#6693111yescharacteristic
298C2×C4#6693811yescharacteristic
299C2×C4#6693811yescharacteristic
300C2×C4#6697711yescharacteristic
301C2×C4#6698911yescharacteristic
302C8—42no—
303C8—881no—
304C8—881no—
305C22—21no—
306C22—21no—
307C22#1062256011yescharacteristic
308C22#1062267411yescharacteristic
309C22#1062270811yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—442no—
321C4—881no—
322C4—881no—
323C4—881no—
324C2—21no—
325C2—21no—
326C2#1306977711yescharacteristic
327C2#1306978611yescharacteristic
328C2#1306978811yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1986C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1986D11
hypocenterC11#10379
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
29. C11×C4⋊Q8Q8semidirect
30. C11×C4⋊Q8Q8semidirect
188. C4⋊Q8Dic22semidirect
189. C4⋊Q8Dic22semidirect
267. C11#10379semidirect

Maximal subgroups

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

subgroupindex
#130742592
#130671672
#130671282
#130665102
#130664812
#130664722
C11×#19862
#1037911