Finite Group Databasebeta

← #14650496

Subgroups — #14650496

Order 2816.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079764C211yesmaximal, characteristic
2#13071364C211yesmaximal, characteristic
3#13067302C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066445C211yesmaximal, characteristic
7C11×#1995C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C11×#376C2211yescharacteristic
12#10622694C412yescomplemented
13#10622691C412yescomplemented
14#10622657—22no—
15#10622634—22no—
16#10622549C2211yescharacteristic
17C4×C4⋊Dic11—21no—
18#10622541—21no—
19#10622538C2211yescharacteristic
20#10622538C2211yescharacteristic
21#10622267—22no—
22#10622259—22no—
23C11×#339—21no—
24C11×#339—21no—
25#10622176—22no—
26#10622124—22no—
27C22×Dic22—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8C2×C411yescharacteristic
30C11×C4⋊Q8C2×C411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C11×#117—21no—
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×Dic11⋊C4—22no—
44C2×C4×Dic11—22no—
45#66922—21no—
46#66922—21no—
47#66922C2×C412yes—
48#66922D412yes—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×#95—21no—
52C11×#95—21no—
53#66899—24no—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57C11⋊#95D412yes—
58C22⋊(C11⋊C8)—21no—
59C22⋊(C11⋊C8)—21no—
60#66871—24no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8C2×C412yes—
65#9298—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—22no—
74C22×Dic11—22no—
75C2×Dic22—22no—
76C2×Dic22—22no—
77C2×Dic22—82no—
78C11×M16—41no—
79C11×M16—41no—
80C2×C8×C11—41no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C22⋊C4—41no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—41no—
92C42×C11Q1612yes—
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11#4111yescharacteristic
96C42×C11#4111yescharacteristic
97C4⋊Dic11—22no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11C22⋊C414yes—
103Dic11⋊C4—82no—
104C4×Dic11—82no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107#3230—111no—
108#2331—111no—
109#1995D1111yescharacteristic
110#1549—111no—
111#1518—111no—
112#1286—111no—
113#1274—111no—
114C23×C11#12011yescharacteristic
115Q8×C11—42no—
116Q8×C11—81no—
117C2×C4×C11—22no—
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×C11—41no—
127C2×C4×C11C2×C22⋊C411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11C4×D411yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11C2×Q1611yescharacteristic
134C2×C4×C11#13511yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×C4×C11#13711yescharacteristic
137C2×Dic11—24no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143Dic22—82no—
144Dic22—82no—
145C8×C11—81no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148#533C2×D1111yescharacteristic
149C2×C4⋊Q8—111no—
150#500—112no—
151#487—112no—
152#484—222no—
153#477—222no—
154#431—111no—
155#431—111no—
156#423C2×D1111yescharacteristic
157#391—222no—
158#389—221no—
159#387—222no—
160#382—111no—
161C4×C4⋊C4—221no—
162#376C2×D1111yescharacteristic
163#339—21no—
164#339—21no—
165#332—222no—
166#328—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C22×C11#45111yescharacteristic
171C22×C11#45211yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11C4×Q1611yescharacteristic
181C4×C11#44111yescharacteristic
182C4×C11#46211yescharacteristic
183C4×C11#46411yescharacteristic
184Dic11—44no—
185Dic11—82no—
186C22×Q8—221no—
187C2×M16—21no—
188C4⋊Q8—112no—
189C4⋊Q8—112no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8C4×D1111yescharacteristic
193C4⋊Q8C4×D1111yescharacteristic
194#125—21no—
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199#117—21no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—222no—
204C2×C42—222no—
205C2×C42C22⋊D1111yescharacteristic
206C2×C42C22⋊D1111yescharacteristic
207C2×C42C22×D1111yescharacteristic
208#107—224no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213#103—224no—
214C22⋊C8—221no—
215C22⋊C8—221no—
216C4×C8—112no—
217C4×C8—221no—
218#95—21no—
219#95—21no—
220#95—112no—
221#95—222no—
222#95—222no—
223#95—221no—
224C2×C11—21no—
225C2×C11—21no—
226C2×C11#187811yescharacteristic
227C2×C11#190411yescharacteristic
228C2×C11#191211yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8—882no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—222no—
237C22×C4—222no—
238C22×C4D4×D1111yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—41no—
244C2×C8—222no—
245C2×C8—441no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—114no—
253C4⋊C4—222no—
254C4⋊C4—222no—
255C4⋊C4—222no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—882no—
259C22⋊C4—41no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—41no—
264C42—882no—
265C42#432612yes—
266C42C2×C4×D1111yescharacteristic
267C42#433911yescharacteristic
268C42D4×D1111yescharacteristic
269C42#434111yescharacteristic
270C11#929811yescharacteristic, complemented, Sylow
271C23#6699011yescharacteristic
272Q8—42no—
273Q8—81no—
274Q8—882no—
275Q8—882no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—224no—
287C2×C4—442no—
288C2×C4—442no—
289C2×C4—442no—
290C2×C4—442no—
291C2×C4—442no—
292C2×C4C22⋊C4×D1111yescharacteristic
293C2×C4(C22⋊D11)⋊C411yescharacteristic
294C2×C4#6693611yescharacteristic
295C2×C4#6693711yescharacteristic
296C2×C4C4×C22⋊D1111yescharacteristic
297C2×C4#6699111yescharacteristic
298C2×C4#6699511yescharacteristic
299C2×C4C2×#432611yescharacteristic
300C2×C4#6700311yescharacteristic
301C2×C4#6700411yescharacteristic
302C8—81no—
303C8—442no—
304C8—881no—
305C22—21no—
306C22—21no—
307C22#1062256911yescharacteristic
308C22#1062266011yescharacteristic
309C22#1062266311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4—444no—
319C4—882no—
320C4C4×#432611yescharacteristic
321C4#1062264311yescharacteristic
322C4#1062266711yescharacteristic
323C4#1062270311yescharacteristic
324C2—21no—
325C2—21no—
326C2#1306896011yescharacteristic
327C2#1306910011yescharacteristic
328C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1995C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#1995D11
hypocenterC11#9298
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
12. #10622694C4semidirect
13. #10622691C4semidirect
270. C11#9298semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130713642
#130673022
#130671802
#130664762
#130664452
C11×#19952
#929811