Finite Group Databasebeta

← #14657556

Subgroups — #14657556

Order 2816.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078421C211yesmaximal, characteristic
2#13067390C211yesmaximal, characteristic
3#13067274C211yesmaximal, characteristic
4#13067179C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic
7C11×#1805C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C11×#103—21no—
12C11×#382C2211yescharacteristic
13#10622838—21no—
14#10622635—22no—
15#10622634—21no—
16#10622633—21no—
17#10622577—21no—
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20#10622537C2211yescharacteristic
21C11×#340—21no—
22#10622166—22no—
23#10622124—21no—
24#10622119—21no—
25#10622117—22no—
26#10622090—22no—
27C22×Q8×C11D411yescharacteristic
28C22×C8×C11—21no—
29C4×Q8×C11—21no—
30C4×Q8×C11—21no—
31C4×Q8×C11—21no—
32C4×Q8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C42×C11—21no—
37C2×C42×C11C2311yescharacteristic
38#66979—21no—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42#66923—21no—
43#66922D411yescharacteristic
44#66922D411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×#103—42no—
50C11×#95—21no—
51C11×#95—21no—
52#66899—22no—
53#66899—22no—
54C22⋊(C11⋊C8)—21no—
55C22⋊(C11⋊C8)D412yes—
56#66872—22no—
57#66871—22no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)D412yes—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10471—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11Q1612yes—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C2×Dic22—21no—
78C2×Dic22—21no—
79C2×C8×C11—41no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11—41no—
89C42×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C22⋊Dic11—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99Dic11⋊C4—41no—
100Dic11⋊C4—41no—
101C4×Dic11—41no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107#3078—111no—
108#1805D1111yescharacteristic
109#1571—111no—
110#1542—111no—
111#1518—111no—
112#1461—111no—
113#1286—111no—
114C23×C11#12111yescharacteristic
115Q8×C11—22no—
116Q8×C11—22no—
117Q8×C11—41no—
118Q8×C11—41no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—81no—
126C2×C4×C11—81no—
127C2×C4×C11—81no—
128C2×C4×C11—81no—
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12311yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C2×C4×C11C2×Q1611yescharacteristic
136C2×C4×C11#13511yescharacteristic
137C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C11#13711yescharacteristic
139C2×Dic11—41no—
140C2×Dic11—41no—
141Dic22—81no—
142Dic22—81no—
143C8×C11—81no—
144C11⋊C8—42no—
145C11⋊C8—42no—
146C11⋊C8—81no—
147#533—111no—
148C2×C4×Q8C2×D1111yescharacteristic
149#479—222no—
150#477—221no—
151#475—221no—
152#431—111no—
153#431—111no—
154#428—221no—
155#423—111no—
156C2×C4⋊C8C2×D1111yescharacteristic
157#419—221no—
158C2×#103—21no—
159#382C2×D1111yescharacteristic
160#340—21no—
161#335—222no—
162#333—221no—
163#332—221no—
164#328—222no—
165#324—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39411yescharacteristic
169C22×C11#46711yescharacteristic
170C22×C11#46811yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—42no—
176C4×C11—81no—
177C4×C11—161no—
178C4×C11#44911yescharacteristic
179C4×C11#45111yescharacteristic
180C4×C11#48411yescharacteristic
181C4×C11#48511yescharacteristic
182Dic11—81no—
183Dic11—81no—
184C22×Q8C22⋊D1111yescharacteristic
185C2×M16—221no—
186C22×C8—21no—
187C4⋊Q8—111no—
188C4⋊Q8—111no—
189#125—221no—
190C22⋊Q8—221no—
191C22⋊Q8—221no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×Q8—221no—
197C4×Q8—221no—
198#117—221no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C22⋊D1111yescharacteristic
202C2×C42—21no—
203C2×C42C22×D1111yescharacteristic
204#107—222no—
205#106—222no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—112no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—42no—
213#103—222no—
214#103—222no—
215C22⋊C8—112no—
216C22⋊C8—221no—
217C4×C8—221no—
218C4×C8—221no—
219#95—21no—
220#95—21no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11#203611yescharacteristic
224C2×C11#204911yescharacteristic
225C2×C11#205311yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8#432612yes—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240M16—441no—
241M16—441no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—222no—
246C2×C8—222no—
247C2×C8—441no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—441no—
261C42—41no—
262C42—41no—
263C42—441no—
264C42#433911yescharacteristic
265C42#433911yescharacteristic
266C42D4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C11#1047111yescharacteristic, complemented, Sylow
269C23#6699211yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—881no—
275Q8—881no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4#6693611yescharacteristic
289C2×C4#6693711yescharacteristic
290C2×C4#6693711yescharacteristic
291C2×C4#6693811yescharacteristic
292C2×C4#6698211yescharacteristic
293C2×C4#6698511yescharacteristic
294C2×C4#6699011yescharacteristic
295C2×C4C2×#432611yescharacteristic
296C2×C4#6700311yescharacteristic
297C2×C4#6700411yescharacteristic
298C8—81no—
299C8—442no—
300C8—442no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22#1062257211yescharacteristic
305C22#1062265511yescharacteristic
306C22#1062266411yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—161no—
314C4—881no—
315C4—881no—
316C4#1062258311yescharacteristic
317C4#1062260911yescharacteristic
318C4#1062265011yescharacteristic
319C4#1062266311yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306981911yescharacteristic
323C2#1306989411yescharacteristic
324C2#1306992011yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1805C2
socleC22×C11#394
prime radicalC23×C11#121
hypercenter#1805D11
hypocenterC11#10471
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
268. C11#10471semidirect

Maximal subgroups

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

subgroupindex
#130784212
#130673902
#130672742
#130671792
#130669402
#130664742
C11×#18052
#1047111