Finite Group Databasebeta

← #14650398

Subgroups — #14650398

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#13079748C211yesmaximal, characteristic
2#13077710C211yesmaximal, characteristic, complemented
3#13067232C211yesmaximal, characteristic, complemented
4#13067227C211yesmaximal, characteristic
5#13066479C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1496C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#431C2211yescharacteristic
12#10622692C411yescharacteristic
13#10622691C411yescharacteristic
14#10622683C411yescharacteristic
15#10622683C411yescharacteristic
16#10622648—22no—
17#10622622—22no—
18#10622539C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21#10622441—22no—
22#10622333—22no—
23#10622292—21no—
24C8×Dic22—21no—
25C11×D4⋊C8—21no—
26C11×D4⋊C8—21no—
27#10622178—22no—
28#10622103—22no—
29C2×C11×#41—21no—
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#127C2×C411yescharacteristic
32C11×#124—21no—
33C11×#121—21no—
34C11×#121—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C42×C11C2311yescharacteristic
38#66979D412yes—
39#66977—21no—
40#66977—21no—
41C22×C11⋊C8—21no—
42#66923D412yes—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C22⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×#97—21no—
52C4×C8×C11D411yescharacteristic
53C4×C8×C11D411yescharacteristic
54#66896—22no—
55#66896—22no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66879—22no—
59Dic11⋊C8—22no—
60Dic11⋊C8—22no—
61C8×Dic11—22no—
62#66872—22no—
63#66871—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67#66867—21no—
68#66867D412yes—
69C4×C11⋊C8C2×C411yescharacteristic
70C4×C11⋊C8C2×C411yescharacteristic
71#9284—111nomaximal, Sylow
72C11×#41—82no—
73C2×Q8×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C22⋊Dic11—22no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11C22⋊C412yes—
99C4⋊Dic11C22⋊C412yes—
100Dic11⋊C4—22no—
101Dic11⋊C4—22no—
102C4×Dic11—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#3228—111no—
110#2985—111no—
111#1531—111no—
112#1530—111no—
113#1496D1111yescharacteristic
114#1287—111no—
115#1275—111no—
116C23×C11—41no—
117C23×C11#12311yescharacteristic
118Q8×C11—81no—
119D4×C11—42no—
120D4×C11—41no—
121D4×C11—41no—
122D4×C11—81no—
123D4×C11—82no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—82no—
130C2×C4×C11C2×C22⋊C411yescharacteristic
131C2×C4×C11C4×D411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—22no—
138Dic22—41no—
139Dic22—41no—
140Dic22—81no—
141C8×C11—41no—
142C8×C11—41no—
143C8×C11—81no—
144C11⋊C8—41no—
145C11⋊C8—41no—
146C11⋊C8—42no—
147C11⋊C8—42no—
148#533—111no—
149#532C2×D1111yescharacteristic
150#500—111no—
151#498—111no—
152#486—111no—
153#486—111no—
154#482—222no—
155#478—222no—
156#446—222no—
157#446—221no—
158C8×Q8—221no—
159#433—222no—
160#432—111no—
161#432C2×D1111yescharacteristic
162#431—111no—
163#431C2×D1111yescharacteristic
164C2×#97—111no—
165#330—222no—
166#329—222no—
167D4⋊C8—21no—
168D4⋊C8—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11#38611yescharacteristic
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—81no—
182C4×C11#44311yescharacteristic
183C4×C11#44411yescharacteristic
184Dic11—42no—
185Dic11—42no—
186C2×#41—21no—
187C22×C8—221no—
188C4⋊Q8—111no—
189C4⋊Q8—111no—
190C4⋊Q8C4×D1111yescharacteristic
191#127C4×D1111yescharacteristic
192#125—112no—
193#124—21no—
194C22⋊Q8—221no—
195C22⋊Q8—221no—
196#121—21no—
197#121—21no—
198C4×Q8—221no—
199C4×Q8—221no—
200C4×D4—21no—
201C4×D4—21no—
202#117—112no—
203C2×C42C22×D1111yescharacteristic
204#107—222no—
205#106—222no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—222no—
209C4⋊C8—222no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#102—222no—
213#102—222no—
214C22⋊C8—21no—
215C22⋊C8—21no—
216C22⋊C8—221no—
217C22⋊C8—221no—
218#97—21no—
219#97—112no—
220#97—222no—
221#97—221no—
222#97—221no—
223C4×C8—111no—
224C4×C8—111no—
225C4×C8—222no—
226C4×C8C22⋊D1111yescharacteristic
227C4×C8C22⋊D1111yescharacteristic
228C2×C11—41no—
229C2×C11—161no—
230C2×C11#187611yescharacteristic
231C2×C11#190311yescharacteristic
232C2×C11#191211yescharacteristic
233#41—82no—
234C2×Q8—21no—
235C2×Q8—221no—
236C2×Q8—221no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4#433911yescharacteristic
243C22×C4D4×D1111yescharacteristic
244C22×C4#434111yescharacteristic
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—41no—
248C2×C8—222no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—222no—
252C2×C8—441no—
253C2×C8—441no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—112no—
257C4⋊C4—112no—
258C4⋊C4—221no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—222no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—222no—
265C42—222no—
266C42C2×C4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C42D4×D1111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C11#928411yescharacteristic, complemented, Sylow
271C23—41no—
272C23#6693611yescharacteristic
273Q8—81no—
274Q8—441no—
275Q8—441no—
276Q8—881no—
277D4—42no—
278D4—41no—
279D4—41no—
280D4—81no—
281D4—82no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—222no—
289C2×C4—222no—
290C2×C4C22⋊C4×D1111yescharacteristic
291C2×C4(C22⋊D11)⋊C411yescharacteristic
292C2×C4#6693711yescharacteristic
293C2×C4C4×C22⋊D1111yescharacteristic
294C2×C4#6699011yescharacteristic
295C2×C4#6699111yescharacteristic
296C8—41no—
297C8—41no—
298C8—81no—
299C8—442no—
300C8—442no—
301C8—441no—
302C8—441no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1062256911yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—442no—
317C4—442no—
318C4#1062275711yescharacteristic
319C4#1062275811yescharacteristic
320C2—41no—
321C2—161no—
322C2#1306894611yescharacteristic
323C2#1306909311yescharacteristic
324C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1496C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1496D11
hypocenterC11#9284
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #13077710C2semidirect
3. #13067232C2semidirect
5. #13066479C2semidirect
6. #13066446C2semidirect
270. C11#9284semidirect

Maximal subgroups

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

subgroupindex
#130797482
#130777102
#130672322
#130672272
#130664792
#130664462
C11×#14962
#928411