Finite Group Databasebeta

← #14650488

Subgroups — #14650488

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#13071365C211yesmaximal, characteristic
2#13069598C211yesmaximal, characteristic
3#13067297C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13066475C211yesmaximal, characteristic
6#13066444C211yesmaximal, characteristic
7C11×#3209C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C11×#494C412yescomplemented
11C11×#487C412yescomplemented
12C11×#462—22no—
13C11×#451—22no—
14C11×#431C2211yescharacteristic
15#10622843—22no—
16#10622598—21no—
17#10622594—22no—
18C4⋊C4×Dic11—21no—
19#10622549C2211yescharacteristic
20#10622545C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622184—22no—
24#10622176—22no—
25#10622170—21no—
26#10622170—21no—
27C22×Q8×C11D412yes—
28C2×C11×Q16—24no—
29C11×C4⋊Q8—21no—
30C11×C4⋊Q8—21no—
31C11×C4⋊Q8C2×C411yescharacteristic
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×C4⋊Q8C2×C412yes—
34C11×C4⋊Q8D412yes—
35C11×#125—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11C2311yescharacteristic
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—22no—
46C2×C4×Dic11—22no—
47C2×C4×Dic11D411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49C2×#4318—21no—
50C11×C4⋊C8—21no—
51C11×#103—24no—
52C11×C22⋊C8—21no—
53C4×C8×C11C2×C412yes—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D412yes—
60C22⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65#9297—111nomaximal, Sylow
66C2×Q8×C11—22no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—82no—
70C2×Q8×C11C22⋊C414yes—
71C22×C4×C11—22no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—22no—
78C11×Q16—84no—
79C2×C8×C11—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C42×C11C22×C411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—82no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11—82no—
103C4×Dic11Q1612yescomplemented
104#4318—41no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#3209D1111yescharacteristic
109#2331—111no—
110#1995—111no—
111#1548—111no—
112#1518—111no—
113#1286—111no—
114#1274—111no—
115C23×C11#12011yescharacteristic
116Q8×C11—44no—
117Q8×C11—42no—
118Q8×C11—82no—
119Q8×C11—81no—
120C2×C4×C11—24no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
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—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—42no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—42no—
144C2×Dic11—41no—
145C2×Dic11—42no—
146C8×C11—42no—
147C11⋊C8—81no—
148C11⋊C8—81no—
149#533C2×D1111yescharacteristic
150C2×C4⋊Q8C2×D1111yescharacteristic
151#494Dic1112yescomplemented
152#487Dic1112yescomplemented
153#462—22no—
154#451—22no—
155#431—111no—
156#431C2×D1111yescharacteristic
157#423—111no—
158#391—222no—
159#389—221no—
160#387—222no—
161#382—111no—
162C4×C4⋊C4—221no—
163#376—111no—
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—44no—
178C4×C11—81no—
179C4×C11—81no—
180C4×C11C4×Q1611yescharacteristic
181C4×C11#44111yescharacteristic
182C4×C11#46211yescharacteristic
183C4×C11#46411yescharacteristic
184Dic11—42no—
185Dic11—82no—
186Dic11—81no—
187C22×Q8C22⋊D1112yes—
188C2×Q16—24no—
189C2×M16—221no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8C2×Dic1111yescharacteristic
193C4⋊Q8C2×Dic1111yescharacteristic
194C4⋊Q8C2×Dic1112yes—
195C4⋊Q8C22⋊D1112yes—
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—222no—
206C2×C42—111no—
207C2×C42—111no—
208C2×C42—222no—
209C2×C42C22×D1111yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—24no—
215C22⋊C8—21no—
216C22⋊C8—221no—
217C4×C8—221no—
218C4×C8C2×Dic1112yes—
219#95—112no—
220#95—222no—
221#95—222no—
222#95—221no—
223#95—221no—
224#95—221no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11#187811yescharacteristic
228C2×C11#190511yescharacteristic
229C2×C11#191111yescharacteristic
230C2×Q8—22no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—82no—
234C2×Q8C22⋊Dic1114yes—
235C22×C4—22no—
236C22×C4—221no—
237C22×C4—222no—
238C22×C4—221no—
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242Q16—84no—
243M16—441no—
244M16—441no—
245C2×C8—22no—
246C2×C8—441no—
247C2×C8—441no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—882no—
261C22⋊C4—41no—
262C42—41no—
263C42—112no—
264C42—221no—
265C42—221no—
266C42—221no—
267C42—882no—
268C42#434111yescharacteristic
269C42#434111yescharacteristic
270C42C22×Dic1111yescharacteristic
271C42C2×C22⋊D1111yescharacteristic
272C11#929711yescharacteristic, complemented, Sylow
273C23#6699011yescharacteristic
274Q8—44no—
275Q8—42no—
276Q8—82no—
277Q8—81no—
278C2×C4—24no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—222no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—442no—
289C2×C4—441no—
290C2×C4—442no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—442no—
294C2×C4Q16×D1111yescharacteristic
295C2×C4#6697111yescharacteristic
296C2×C4#6697111yescharacteristic
297C2×C4#6697211yescharacteristic
298C2×C4D4×Dic1111yescharacteristic
299C2×C4D4×Dic1111yescharacteristic
300C2×C4#6698811yescharacteristic
301C2×C4#6699211yescharacteristic
302C2×C4#6699211yescharacteristic
303C2×C4C2×C22⋊Dic1111yescharacteristic
304C8—42no—
305C8—881no—
306C8—881no—
307C22—21no—
308C22—21no—
309C22#1062279911yescharacteristic
310C22#1062280011yescharacteristic
311C22#1062283311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—44no—
317C4—81no—
318C4—81no—
319C4—442no—
320C4—882no—
321C4—881no—
322C4#1062279511yescharacteristic
323C4Q16×Dic1111yescharacteristic
324C4#1062279711yescharacteristic
325C4#1062279811yescharacteristic
326C2—21no—
327C2—21no—
328C2#1306895911yescharacteristic
329C2#1306911211yescharacteristic
330C2#1306914911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#3209C2
socleC22×C11#386
prime radicalC23×C11#120
cosocleC2×C42×C11C23
hypercenter#3209D11
hypocenterC11#9297
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
10. C11×#494C4semidirect
11. C11×#487C4semidirect
103. C4×Dic11Q16semidirect
151. #494Dic11semidirect
152. #487Dic11semidirect
272. C11#9297semidirect

Maximal subgroups

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

subgroupindex
#130713652
#130695982
#130672972
#130671802
#130664752
#130664442
C11×#32092
#929711