Finite Group Databasebeta

← #14650479

Subgroups — #14650479

Order 2816.

470 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079760C211yesmaximal, characteristic
2#13069597C211yesmaximal, characteristic
3#13067288C211yesmaximal, characteristic
4#13067179C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066445C211yesmaximal, characteristic
7C11×#2327C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C11—21no—
10#10623001C2211yescharacteristic
11C11×#391—21no—
12C11×#387—22no—
13C11×#387—22no—
14C11×#382C2211yescharacteristic
15C11×#376C2211yescharacteristic
16#10622707—22no—
17#10622706C412yescomplemented
18#10622692C412yescomplemented
19#10622584—22no—
20#10622538C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622185—22no—
24#10622161—21no—
25#10622161—21no—
26#10622090—22no—
27C22×Q8×C11—21no—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8C2×C412yes—
31C11×C4⋊Q8D412yes—
32C4×Q8×C11—42no—
33C4×Q8×C11—42no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—22no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4D412yes—
38C2×C42×C11—22no—
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11C2311yescharacteristic
42#66979—21no—
43#66977—21no—
44#66977—21no—
45C2×#4318—21no—
46#66923—21no—
47#66922C2×C411yescharacteristic
48#66922C2×C411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×#95—24no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D412yes—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)—21no—
58#66874—24no—
59#66872—24no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8C2×C412yes—
66#9296—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—22no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C2×Dic22—21no—
81C2×Dic22—21no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—44no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4C22⋊C414yes—
89C42×C11—21no—
90C42×C11—21no—
91C42×C11—21no—
92C42×C11—44no—
93C42×C11SD1612yes—
94C42×C11C22×C411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C22⋊Dic11—41no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105C4×Dic11—41no—
106#4318—41no—
107#4318—41no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#3229—111no—
112#2327D1111yescharacteristic
113#1995—111no—
114#1546—111no—
115#1518—111no—
116#1286—111no—
117#1274—111no—
118C23×C11#12011yescharacteristic
119Q8×C11—42no—
120Q8×C11—42no—
121Q8×C11—42no—
122Q8×C11—42no—
123C2×C4×C11—24no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—41no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—41no—
148C2×Dic11—41no—
149Dic22—42no—
150Dic22—81no—
151C11⋊C8—42no—
152C11⋊C8—81no—
153C11⋊C8—81no—
154#533—111no—
155C2×C4⋊Q8C2×D1111yescharacteristic
156C2×C4×Q8—21no—
157#498—112no—
158#487—112no—
159#483—222no—
160#475—222no—
161#431—111no—
162#431—111no—
163#423—111no—
164#391—21no—
165#387—22no—
166#387—22no—
167#382C2×D1111yescharacteristic
168#376C2×D1111yescharacteristic
169#339—221no—
170#339—221no—
171#332—222no—
172#328—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#38611yescharacteristic
176C22×C11#45011yescharacteristic
177C22×C11#45211yescharacteristic
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—42no—
183C4×C11—44no—
184C4×C11—82no—
185C4×C11—81no—
186C4×C11C4×SD1611yescharacteristic
187C4×C11#44011yescharacteristic
188C4×C11#46111yescharacteristic
189C4×C11#46311yescharacteristic
190Dic11—81no—
191Dic11—81no—
192C22×Q8—21no—
193C2×M16—221no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—111no—
197C4⋊Q8—111no—
198C4⋊Q8C4×D1112yes—
199C4⋊Q8D4412yes—
200#125—221no—
201C22⋊Q8—221no—
202C22⋊Q8—221no—
203C4×Q8—42no—
204C4×Q8—42no—
205C4×Q8—221no—
206C4×Q8—221no—
207#117—221no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C22⋊D1112yes—
212C2×C42—22no—
213C2×C42C22⋊D1111yescharacteristic
214C2×C42C22⋊D1111yescharacteristic
215C2×C42C22×D1111yescharacteristic
216#106—224no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221#103—224no—
222C22⋊C8—221no—
223C22⋊C8—221no—
224C4×C8—112no—
225C4×C8—221no—
226#95—24no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95C22⋊D1112yes—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#187711yescharacteristic
234C2×C11#190511yescharacteristic
235C2×C11#191211yescharacteristic
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—221no—
243C2×Q8—221no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4C2×C22⋊D1111yescharacteristic
249C22×C4C2×C22⋊D1111yescharacteristic
250C22×C4C2×C22⋊D1111yescharacteristic
251M16—441no—
252M16—441no—
253C2×C8—222no—
254C2×C8—441no—
255C2×C8—441no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—44no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—441no—
267C4⋊C4—441no—
268C4⋊C4(C2×D11)⋊C414yes—
269C22⋊C4—441no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—44no—
274C42—441no—
275C42#432412yes—
276C42C2×C4×D1111yescharacteristic
277C42C2×D4411yescharacteristic
278C42#433911yescharacteristic
279C42#433911yescharacteristic
280C11#929611yescharacteristic, complemented, Sylow
281C23#6700611yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—42no—
285Q8—42no—
286Q8—442no—
287Q8—881no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4C2×(C2×D11)⋊C411yescharacteristic
305C2×C4C4×C22⋊D1111yescharacteristic
306C2×C4C4×C22⋊D1111yescharacteristic
307C2×C4#6698211yescharacteristic
308C2×C4#6698311yescharacteristic
309C2×C4#6698311yescharacteristic
310C2×C4#6698511yescharacteristic
311C2×C4C2×#432411yescharacteristic
312C2×C4#6700311yescharacteristic
313C2×C4#6700411yescharacteristic
314C8—442no—
315C8—881no—
316C8—881no—
317C22—21no—
318C22—21no—
319C22#1062282611yescharacteristic
320C22#1062283111yescharacteristic
321C22#1062285211yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—44no—
328C4—82no—
329C4—81no—
330C4—881no—
331C4—881no—
332C4#1062262911yescharacteristic
333C4C4×#432411yescharacteristic
334C4#1062263111yescharacteristic
335C4#1062263211yescharacteristic
336C2—21no—
337C2—21no—
338C2#1306895011yescharacteristic
339C2#1306911011yescharacteristic
340C2#1306915311yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2327C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#2327D11
hypocenterC11#9296
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
17. #10622706C4semidirect
18. #10622692C4semidirect
280. C11#9296semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130695972
#130672882
#130671792
#130664742
#130664452
C11×#23272
#929611