Finite Group Databasebeta

← #14650448

Subgroups — #14650448

Order 2816.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079760C211yesmaximal, characteristic
2#13077553C211yesmaximal, characteristic
3#13069437C211yesmaximal, characteristic
4#13067181C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic
6#13066446C211yesmaximal, characteristic
7C11×#1546C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×#66899—21no—
13C2×#66899—21no—
14#10622735—21no—
15#10622732—21no—
16#10622707—22no—
17#10622706C412yescomplemented
18#10622692C412yescomplemented
19#10622584—22no—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23#10622441—22no—
24#10622441—22no—
25C11×#332—22no—
26#10622105—22no—
27C22×Q8×C11—21no—
28C2×C11×M16—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8—21no—
32C11×C4⋊Q8C2×C412yes—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C42×C11C2311yescharacteristic
36#66979—21no—
37C2×C4⋊Dic11—21no—
38#66977—21no—
39#66977D412yes—
40C22×C11⋊C8D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42#66923—21no—
43#66922C2×C411yescharacteristic
44#66922C2×C411yescharacteristic
45C4×Dic22—21no—
46C4×Dic22D412yes—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8D412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52#66899—42no—
53#66899—42no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57#66879—22no—
58Dic11⋊C8—24no—
59C8×Dic11—22no—
60#66874—24no—
61#66872—24no—
62C4⋊(C11⋊C8)—21no—
63#66867—21no—
64#66867—21no—
65C4×C11⋊C8C2×C412yes—
66#9292—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—41no—
78C2×Dic22—21no—
79C2×Dic22C22⋊C412yes—
80C11×M16—41no—
81C11×M16—41no—
82C2×C8×C11—22no—
83C2×C8×C11—41no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11#4111yescharacteristic
92C22⋊Dic11—22no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11C22⋊C412yes—
99Dic11⋊C4—22no—
100Dic11⋊C4—22no—
101C4×Dic11—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8SD1612yes—
109#3229—111no—
110#2961—111no—
111#1960—111no—
112#1546D1111yescharacteristic
113#1518—111no—
114#1286—111no—
115#1275—111no—
116C23×C11#12111yescharacteristic
117Q8×C11—42no—
118Q8×C11—42no—
119Q8×C11—81no—
120Q8×C11—81no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12311yescharacteristic
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11#13511yescharacteristic
134C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C11#13711yescharacteristic
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—81no—
139C2×Dic11—81no—
140C2×Dic11—81no—
141Dic22—42no—
142Dic22—81no—
143C8×C11—42no—
144C8×C11—81no—
145C11⋊C8—22no—
146C11⋊C8—42no—
147C11⋊C8—41no—
148#533—111no—
149C2×C4⋊Q8C2×D1111yescharacteristic
150#498—112no—
151#487—112no—
152#483—222no—
153#475—222no—
154#446—222no—
155#446—222no—
156#431—111no—
157#431C2×D1111yescharacteristic
158#424—221no—
159#423C2×D1111yescharacteristic
160C2×#103—221no—
161C2×#103—221no—
162#405—221no—
163C2×#97—111no—
164#382—111no—
165#332—22no—
166#328—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#38611yescharacteristic
170C22×C11#46011yescharacteristic
171C22×C11#46411yescharacteristic
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—82no—
177C4×C11C4×SD1611yescharacteristic
178C4×C11#44011yescharacteristic
179C4×C11#44811yescharacteristic
180C4×C11#44911yescharacteristic
181Dic11—42no—
182Dic11—42no—
183Dic11—161no—
184C22×Q8—21no—
185C2×M16—21no—
186C22×C8—111no—
187C22×C8—111no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—111no—
192C4⋊Q8—111no—
193C4⋊Q8C4×D1112yes—
194#125—221no—
195C22⋊Q8—112no—
196C22⋊Q8—221no—
197C4×Q8—112no—
198C4×Q8—221no—
199#117—221no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—221no—
203C2×C42C22×D1111yescharacteristic
204#106—224no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—224no—
208C4⋊C8—221no—
209C4⋊C8C22⋊D1112yes—
210#103—224no—
211#103—442no—
212#103—442no—
213C22⋊C8—21no—
214C22⋊C8—221no—
215#97—222no—
216#97—221no—
217#97—221no—
218C4×C8—21no—
219C4×C8—112no—
220C4×C8—222no—
221#95—221no—
222#95—221no—
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#188011yescharacteristic
226C2×C11#190211yescharacteristic
227C2×C11#190911yescharacteristic
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—112no—
235C2×Q8—221no—
236C22×C4—41no—
237C22×C4—441no—
238C22×C4#433911yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241M16—41no—
242M16—41no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—112no—
246C2×C8—221no—
247C2×C8—221no—
248C2×C8—222no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—221no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—112no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—222no—
260C4⋊C4—221no—
261C4⋊C4—222no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C22⋊C4—222no—
265C42—222no—
266C42C2×C4×D1111yescharacteristic
267C42D4×D1111yescharacteristic
268C42#434111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C11#929211yescharacteristic, complemented, Sylow
271C23#6693711yescharacteristic
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276Q8—442no—
277Q8—881no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—222no—
284C2×C4—222no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4C22⋊C4×D1111yescharacteristic
289C2×C4(C22⋊D11)⋊C411yescharacteristic
290C2×C4#6693611yescharacteristic
291C2×C4#6696411yescharacteristic
292C2×C4#6696511yescharacteristic
293C2×C4SD16×D1111yescharacteristic
294C2×C4#6696811yescharacteristic
295C2×C4C4×C22⋊D1111yescharacteristic
296C2×C4#6699011yescharacteristic
297C2×C4#6699111yescharacteristic
298C8—42no—
299C8—81no—
300C8—222no—
301C8—442no—
302C8—441no—
303C22—21no—
304C22—21no—
305C22#1062237511yescharacteristic
306C22#1062238011yescharacteristic
307C22#1062256911yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—82no—
313C4—442no—
314C4—442no—
315C4—1761no—
316C4#1062237011yescharacteristic
317C4#1062237111yescharacteristic
318C4#1062277111yescharacteristic
319C4#1062278311yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306896811yescharacteristic
323C2#1306909211yescharacteristic
324C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1546C2
socleC22×C11#386
prime radicalC23×C11#121
cosocleC2×C42×C11C23
hypercenter#1546D11
hypocenterC11#9292
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
17. #10622706C4semidirect
18. #10622692C4semidirect
270. C11#9292semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130775532
#130694372
#130671812
#130664762
#130664462
C11×#15462
#929211