Finite Group Databasebeta

← #14656972

Subgroups — #14656972

Order 2816.

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

normal subgroups only

This group has 352 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#13074273C211yesmaximal, characteristic
2#13069561C211yesmaximal, characteristic
3#13067167C211yesmaximal, characteristic
4#13066509C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic
6#13066473C211yesmaximal, characteristic
7C11×#1506C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C11×#376C2211yescharacteristic
11#10622550C2211yescharacteristic
12C4×C4⋊Dic11C2211yescharacteristic
13#10622546—21no—
14#10622541—21no—
15#10622539C2211yescharacteristic
16C4×#4318C2211yescharacteristic
17#10622274—21no—
18#10622270—21no—
19#10622267—21no—
20#10622260—21no—
21C11×#328—21no—
22C11×#328—21no—
23#10622176—21no—
24#10622176—21no—
25#10622170—21no—
26#10622170—21no—
27C11×C4⋊Q8Q811yescharacteristic
28C11×C4⋊Q8Q811yescharacteristic
29C11×#125—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C4×Q8×C11—21no—
33C4×Q8×C11—21no—
34C11×#117—21no—
35C2×C42×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11D411yescharacteristic
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#95—21no—
51C11×#95D411yescharacteristic
52C11×#95D411yescharacteristic
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62#66867—21no—
63#66867—21no—
64C4×C11⋊C8—21no—
65#10381—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×C8×C11—41no—
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C42×C11—42no—
86C42×C11—41no—
87C42×C11C2×Q811yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C42×C11#4111yescharacteristic
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—81no—
97Dic11⋊C4—81no—
98C4×Dic11—41no—
99C4×Dic11—41no—
100#4318—22no—
101#4318—41no—
102C2×C11⋊C8—41no—
103C2×C11⋊C8—41no—
104#2606—111no—
105#1986—111no—
106#1515—111no—
107#1506D1111yescharacteristic
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—
144C8×C11—81no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147#533C2×D1111yescharacteristic
148#432—111no—
149#432C2×D1111yescharacteristic
150C4×M16—111no—
151#398—221no—
152#398—221no—
153#389—221no—
154#389—221no—
155#387—221no—
156#387—221no—
157#383—111no—
158C4×C4⋊C4—111no—
159#376C2×D1111yescharacteristic
160#339—221no—
161#339—221no—
162#328—21no—
163#328—21no—
164#328—221no—
165#328—221no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39311yescharacteristic
169C22×C11#45511yescharacteristic
170C22×C11#45611yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11—81no—
181Dic11—42no—
182Dic11—81no—
183Dic11—81no—
184Dic11—81no—
185C2×M16—221no—
186C4⋊Q8Dic2211yescharacteristic
187C4⋊Q8Dic2211yescharacteristic
188#125—21no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191C4×Q8—21no—
192C4×Q8—21no—
193#117—21no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C42—21no—
202C2×C42—111no—
203C2×C42—111no—
204C2×C42C22×D1111yescharacteristic
205C4⋊C8—21no—
206C4⋊C8—221no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209#97—21no—
210#97—221no—
211#97—221no—
212C4×C8—221no—
213#95—21no—
214#95—111no—
215#95—111no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95C22⋊D1111yescharacteristic
222#95C22⋊D1111yescharacteristic
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#202811yescharacteristic
226C2×C11#203111yescharacteristic
227C2×C11#203111yescharacteristic
228C2×Q8—21no—
229C2×Q8—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—221no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4D4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239M16—222no—
240M16—441no—
241C2×C8—41no—
242C2×C8—441no—
243C2×C8—441no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—442no—
251C4⋊C4—442no—
252C4⋊C4—442no—
253C4⋊C4—442no—
254C4⋊C4—442no—
255C4⋊C4—881no—
256C4⋊C4—881no—
257C22⋊C4—41no—
258C42—42no—
259C42—41no—
260C42—441no—
261C42—441no—
262C42C2×Dic2211yescharacteristic
263C42#433911yescharacteristic
264C42#434111yescharacteristic
265C42#434111yescharacteristic
266C11#1038111yescharacteristic, complemented, Sylow
267C23#6699011yescharacteristic
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—222no—
283C2×C4—441no—
284C2×C4—441no—
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#6693111yescharacteristic
295C2×C4#6693111yescharacteristic
296C2×C4#6693811yescharacteristic
297C2×C4#6693811yescharacteristic
298C2×C4#6697711yescharacteristic
299C2×C4#6698911yescharacteristic
300C8—81no—
301C8—442no—
302C8—881no—
303C22—21no—
304C22—21no—
305C22#1062256011yescharacteristic
306C22#1062281511yescharacteristic
307C22#1062281811yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4—442no—
319C4—881no—
320C4—881no—
321C4—881no—
322C2—21no—
323C2—21no—
324C2#1306977511yescharacteristic
325C2#1306978811yescharacteristic
326C2#1306979011yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1506C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1506D11
hypocenterC11#10381
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
266. C11#10381semidirect

Maximal subgroups

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

subgroupindex
#130742732
#130695612
#130671672
#130665092
#130664822
#130664732
C11×#15062
#1038111