Finite Group Databasebeta

← #14650396

Subgroups — #14650396

Order 2816.

396 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079754C211yesmaximal, characteristic
2#13077713C211yesmaximal, characteristic, complemented
3#13067232C211yesmaximal, characteristic, complemented
4#13067228C211yesmaximal, characteristic
5#13067084C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1287C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622538C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15#10622460—22no—
16#10622444—21no—
17#10622443—21no—
18#10622350—22no—
19#10622333—22no—
20#10622314—22no—
21#10622307C411yescharacteristic
22#10622307C411yescharacteristic
23#10622295C411yescharacteristic
24#10622293C411yescharacteristic
25#10622121—21no—
26#10622121—21no—
27#10622103—22no—
28#10622102—22no—
29C2×#4339—21no—
30C2×C42×C11C2311yescharacteristic
31#66983—21no—
32#66983—21no—
33#66979D412yes—
34#66977—21no—
35#66977—21no—
36C22×C11⋊C8—21no—
37#66928—21no—
38#66927C2×C411yescharacteristic
39C4×D44—21no—
40C4×D44—21no—
41#66923D412yes—
42#66922C2×C411yescharacteristic
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#97—21no—
54C11×#97D412yes—
55C4×C8×C11C2×C411yescharacteristic
56C4×C8×C11C2×C411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66885—22no—
59#66885—22no—
60#66882—22no—
61#66881—22no—
62#66879—22no—
63Dic11⋊C8—22no—
64Dic11⋊C8—22no—
65C8×Dic11—22no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9284—111nomaximal, Sylow
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C22⋊D11—41no—
76#4339—82no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×C4×D11—41no—
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C22⋊Dic11—22no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C22⋊C412yes—
100C4⋊Dic11C22⋊C412yes—
101Dic11⋊C4—22no—
102Dic11⋊C4—22no—
103C4×Dic11—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#3228—111no—
110#2985—111no—
111#1531—111no—
112#1530—111no—
113#1496—111no—
114#1287D1111yescharacteristic, complemented
115#1275—111no—
116C23×C11#12311yescharacteristic
117C22×D11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C2×C22⋊C411yescharacteristic
123C2×C4×C11C4×D411yescharacteristic
124C2×C4×C11C4×D411yescharacteristic
125C2×C4×C11#12011yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12111yescharacteristic
128C22⋊D11—82no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—41no—
132D44—42no—
133D44—41no—
134D44—41no—
135D44—81no—
136C4×D11—82no—
137Dic22—41no—
138Dic22—41no—
139Dic22—81no—
140Dic22—81no—
141C8×C11—41no—
142C8×C11—41no—
143C8×C11—42no—
144C8×C11—81no—
145C11⋊C8—41no—
146C11⋊C8—41no—
147C11⋊C8—42no—
148#533—111no—
149#532—111no—
150#500—111no—
151#498—111no—
152#486—111no—
153#486—111no—
154#482—222no—
155#478—222no—
156#446—221no—
157#446—222no—
158C8×Q8—221no—
159#433—222no—
160#432C2×D1111yescharacteristic
161#432C2×D1111yescharacteristic
162#431—111no—
163#431C2×D1111yescharacteristic
164C2×#97—111no—
165#330—222no—
166#329—222no—
167D4⋊C8—221no—
168D4⋊C8—221no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11#38611yescharacteristic
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11#44311yescharacteristic
182C4×C11#44411yescharacteristic
183Dic11—42no—
184Dic11—42no—
185Dic11—81no—
186C2×#41—221no—
187C22×C8—221no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190C4⋊Q8—111no—
191#127—111no—
192#125—112no—
193#124—221no—
194C22⋊Q8—221no—
195C22⋊Q8—221no—
196#121—221no—
197#121—221no—
198C4×Q8—221no—
199C4×Q8—221no—
200C4×D4—221no—
201C4×D4—221no—
202#117—112no—
203C2×C42C22×D1111yescharacteristic
204#107—222no—
205#106—222no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—222no—
210C4⋊C8—222no—
211C4⋊C8—221no—
212#102—222no—
213#102—222no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C22⋊C8—21no—
217C22⋊C8—221no—
218#97—21no—
219#97—222no—
220#97—221no—
221#97—221no—
222#97D4412yes—
223C4×C8—111no—
224C4×C8—111no—
225C4×C8—222no—
226C4×C8C4×D1111yescharacteristic
227C4×C8C4×D1111yescharacteristic
228C2×C11—41no—
229C2×C11#187611yescharacteristic
230C2×C11#190311yescharacteristic
231C2×C11#191211yescharacteristic
232D11—161no—
233#41—882no—
234C2×Q8—221no—
235C2×Q8—221no—
236C2×Q8—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—441no—
241C22×C4—441no—
242C22×C4#433911yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C22×C4#434311yescharacteristic
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—222no—
250C2×C8—221no—
251C2×C8—221no—
252C2×C8—441no—
253C2×C8—441no—
254C4⋊C4—112no—
255C4⋊C4—112no—
256C4⋊C4—221no—
257C4⋊C4—222no—
258C4⋊C4—221no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C22⋊C4—222no—
263C22⋊C4—441no—
264C22⋊C4—441no—
265C42—222no—
266C42C2×C4×D1111yescharacteristic
267C42C2×D4411yescharacteristic
268C42D4×D1111yescharacteristic
269C42D4×D1111yescharacteristic
270C11#928411yescharacteristic, complemented, Sylow
271C23—441no—
272C23#6694711yescharacteristic
273Q8—441no—
274Q8—441no—
275Q8—881no—
276Q8—881no—
277D4—442no—
278D4—441no—
279D4—441no—
280D4—881no—
281D4—882no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—222no—
287C2×C4—222no—
288C2×C4—441no—
289C2×C4—882no—
290C2×C4C4×D4411yescharacteristic
291C2×C4C22⋊C4×D1111yescharacteristic
292C2×C4#6693511yescharacteristic
293C2×C4#6693711yescharacteristic
294C2×C4#6694611yescharacteristic
295C2×C4#6694811yescharacteristic
296C8—42no—
297C8—41no—
298C8—41no—
299C8—81no—
300C8—442no—
301C8—441no—
302C8—441no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22#1062227811yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—442no—
316C4—442no—
317C4—881no—
318C4#1062250711yescharacteristic
319C4#1062250811yescharacteristic
320C2—41no—
321C2—1761no—
322C2#1306894411yescharacteristic
323C2#1306909511yescharacteristic
324C2#1306915211yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1287C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1287D11
hypocenterC11#9284
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
2. #13077713C2semidirect
3. #13067232C2semidirect
6. #13066446C2semidirect
7. C11×#1287C2semidirect
114. #1287D11semidirect
270. C11#9284semidirect

Maximal subgroups

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

subgroupindex
#130797542
#130777132
#130672322
#130672282
#130670842
#130664462
C11×#12872
#928411