Finite Group Databasebeta

← #14650486

Subgroups — #14650486

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079564C211yesmaximal, characteristic
2#13069597C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic
4#13067179C211yesmaximal, characteristic
5#13066474C211yesmaximal, characteristic
6#13066445C211yesmaximal, characteristic
7C11×#2331C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#391—22no—
11C11×#389—21no—
12C11×#387—22no—
13C11×#382C2211yescharacteristic
14C4×C11×C4⋊C4—21no—
15C11×#376C2211yescharacteristic
16#10622841—22no—
17#10622705C412yescomplemented
18#10622703—22no—
19#10622694C412yescomplemented
20#10622538C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622184—22no—
24#10622161—21no—
25#10622161—21no—
26#10622090—22no—
27C22×Q8×C11D412yes—
28C11×C4⋊Q8—21no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8C2×C412yes—
31C11×C4⋊Q8D412yes—
32C2×C11×C4⋊C4—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—22no—
36C2×C42×C11—22no—
37C2×C42×C11D411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40C2×#4326—24no—
41#66979—21no—
42#66977—21no—
43#66977—21no—
44C2×#4318—21no—
45#66923—21no—
46#66922C2×C411yescharacteristic
47#66922C2×C411yescharacteristic
48C4×Dic22—21no—
49C4×Dic22—21no—
50C11×#95—22no—
51C11×#95—22no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95D412yes—
56#66899—24no—
57C22⋊(C11⋊C8)—21no—
58C22⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8C2×C412yes—
65#9297—111nomaximal, Sylow
66C2×Q8×C11—22no—
67C2×Q8×C11—82no—
68C2×Q8×C11C22⋊C414yes—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×Dic22—21no—
77C2×Dic22—21no—
78C11×C4⋊C4—22no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C4⋊C4—82no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—82no—
89C42×C11Q1612yescomplemented
90C42×C11C22×C411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C22⋊Dic11—41no—
95#4326—84no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100Dic11⋊C4—41no—
101Dic11⋊C4—41no—
102C4×Dic11—41no—
103#4318—41no—
104#4318—41no—
105C2×C11⋊C8—22no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#3209—111no—
109#2331D1111yescharacteristic
110#1995—111no—
111#1548—111no—
112#1518—111no—
113#1286—111no—
114#1274—111no—
115C23×C11#12011yescharacteristic
116Q8×C11—44no—
117Q8×C11—82no—
118C2×C4×C11—24no—
119C2×C4×C11—22no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—42no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C4×D411yescharacteristic
134C2×C4×C11C4×D411yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12311yescharacteristic
138C2×C4×C11C2×Q1611yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11#13711yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×Dic11—41no—
143C2×Dic11—41no—
144Dic22—42no—
145Dic22—81no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148C11⋊C8—81no—
149#533—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151#494—112no—
152#487—112no—
153#462—222no—
154#451—222no—
155#431—111no—
156#431—111no—
157#423—111no—
158#391—22no—
159#389—21no—
160#387—22no—
161#382C2×D1111yescharacteristic
162C4×C4⋊C4—21no—
163#376C2×D1111yescharacteristic
164#339—221no—
165#339—221no—
166#333—222no—
167#328—222no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11#38611yescharacteristic
171C22×C11#45111yescharacteristic
172C22×C11#45211yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—42no—
178C4×C11—44no—
179C4×C11—82no—
180C4×C11—81no—
181C4×C11C4×Q1611yescharacteristic
182C4×C11#44111yescharacteristic
183C4×C11#46211yescharacteristic
184C4×C11#46411yescharacteristic
185Dic11—81no—
186Dic11—81no—
187C22×Q8C22⋊D1112yes—
188C2×Q16—224no—
189C2×M16—221no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—111no—
193C4⋊Q8—111no—
194C4⋊Q8C4×D1112yes—
195C4⋊Q8D4412yes—
196#125—221no—
197C22⋊Q8—221no—
198C22⋊Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201#117—221no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C42—22no—
207C2×C42C22⋊D1111yescharacteristic
208C2×C42C22⋊D1111yescharacteristic
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—221no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—224no—
215C22⋊C8—221no—
216C22⋊C8—221no—
217C4×C8—112no—
218C4×C8—221no—
219#95—22no—
220#95—22no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C22⋊D1112yes—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#187811yescharacteristic
228C2×C11#190511yescharacteristic
229C2×C11#191111yescharacteristic
230C2×Q8—22no—
231C2×Q8—82no—
232C2×Q8—221no—
233C2×Q8—221no—
234C2×Q8(C2×D11)⋊C414yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4C2×C22⋊D1111yescharacteristic
240C22×C4C2×C22⋊D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242Q16—884no—
243M16—441no—
244M16—441no—
245C2×C8—222no—
246C2×C8—441no—
247C2×C8—441no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—82no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C22⋊C4—441no—
262C42—21no—
263C42—21no—
264C42—21no—
265C42—82no—
266C42—441no—
267C42#432612yescomplemented
268C42C2×C4×D1111yescharacteristic
269C42C2×D4411yescharacteristic
270C42#433911yescharacteristic
271C42#433911yescharacteristic
272C11#929711yescharacteristic, complemented, Sylow
273C23#6700611yescharacteristic
274Q8—44no—
275Q8—82no—
276Q8—442no—
277Q8—881no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4C2×(C2×D11)⋊C411yescharacteristic
295C2×C4C4×C22⋊D1111yescharacteristic
296C2×C4C4×C22⋊D1111yescharacteristic
297C2×C4#6698211yescharacteristic
298C2×C4#6698311yescharacteristic
299C2×C4#6698311yescharacteristic
300C2×C4#6699511yescharacteristic
301C2×C4C2×#432611yescharacteristic
302C2×C4#6700311yescharacteristic
303C2×C4#6700411yescharacteristic
304C8—442no—
305C8—881no—
306C8—881no—
307C22—21no—
308C22—21no—
309C22#1062282611yescharacteristic
310C22#1062284111yescharacteristic
311C22#1062285211yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—44no—
318C4—82no—
319C4—81no—
320C4—881no—
321C4—881no—
322C4#1062264111yescharacteristic
323C4C4×#432611yescharacteristic
324C4#1062264311yescharacteristic
325C4#1062264411yescharacteristic
326C2—21no—
327C2—21no—
328C2#1306895711yescharacteristic
329C2#1306911011yescharacteristic
330C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2331C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#2331D11
hypocenterC11#9297
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2331

Complements

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

NH ≅ G/Ntype
17. #10622705C4semidirect
19. #10622694C4semidirect
89. C42×C11Q16semidirect
267. C42#4326semidirect
272. C11#9297semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130695972
#130672972
#130671792
#130664742
#130664452
C11×#23312
#929711