Finite Group Databasebeta

← #14650403

Subgroups — #14650403

Order 2816.

426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079574C211yesmaximal, characteristic
2#13077694C211yesmaximal, characteristic
3#13067232C211yesmaximal, characteristic, complemented
4#13067228C211yesmaximal, characteristic
5#13067088C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#1287C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622538C2211yescharacteristic
14C2×#66867C2211yescharacteristic
15#10622458—22no—
16#10622451—21no—
17#10622447—21no—
18#10622346—22no—
19#10622340—22no—
20#10622319—22no—
21#10622312C411yescharacteristic
22#10622307C411yescharacteristic
23#10622306C411yescharacteristic
24#10622294C411yescharacteristic
25#10622122—21no—
26#10622122—21no—
27#10622103—22no—
28#10622102—22no—
29C2×#4339D412yes—
30C2×C42×C11C2311yescharacteristic
31#66983—21no—
32#66983—21no—
33#66979—21no—
34#66977—21no—
35#66977—21no—
36C22×C11⋊C8—21no—
37C2×Dic44—22no—
38C2×#4314—22no—
39C2×#4313—22no—
40C2×C8×D11—22no—
41#66928D412yes—
42#66927C2×C411yescharacteristic
43C4×D44—21no—
44C4×D44—21no—
45#66923—21no—
46#66922C2×C411yescharacteristic
47#66922C2×C411yescharacteristic
48#66922C2×C411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C11×#97D412yes—
59C4×C8×C11C2×C411yescharacteristic
60C4×C8×C11C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62#66885—22no—
63(C2×D11)⋊C8—22no—
64(C2×D11)⋊C8—22no—
65#66880—22no—
66C4⋊(C11⋊C8)—21no—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8D411yescharacteristic
70C4×C11⋊C8D411yescharacteristic
71#9285—111nomaximal, Sylow
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11#4111yescharacteristic
74C22×C4×C11#4111yescharacteristic
75C2×C22⋊D11—22no—
76#4339—82no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44C22⋊C412yes—
80C2×C4×D11—22no—
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×Dic22C22⋊C412yes—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—22no—
87C2×C8×C11—41no—
88C42×C11C22×C411yescharacteristic
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C22⋊Dic11—41no—
93(C2×D11)⋊C4—22no—
94(C2×D11)⋊C4—22no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—21no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103C4×Dic11—41no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109Dic44—82no—
110#4314—82no—
111#4313—82no—
112C8×D11—82no—
113#3210—111no—
114#2981—111no—
115#1531—111no—
116#1530—111no—
117#1497—111no—
118#1287D1111yescharacteristic, complemented
119#1275—111no—
120C23×C11#12311yescharacteristic
121C22×D11—22no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11C4×D411yescharacteristic
128C2×C4×C11C4×D411yescharacteristic
129C2×C4×C11#12011yescharacteristic
130C2×C4×C11#12111yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C22⋊D11—82no—
133C2×Dic11—22no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136D44—42no—
137D44—41no—
138D44—41no—
139D44—81no—
140C4×D11—42no—
141C4×D11—42no—
142Dic22—42no—
143Dic22—42no—
144Dic22—41no—
145Dic22—41no—
146C8×C11—42no—
147C8×C11—41no—
148C8×C11—41no—
149C8×C11—81no—
150C11⋊C8—41no—
151C11⋊C8—41no—
152C11⋊C8—42no—
153#533—111no—
154#532—111no—
155#494—111no—
156#492—111no—
157#487—111no—
158#486—111no—
159#464—222no—
160#452—222no—
161#436—221no—
162#435—222no—
163C8×D4—221no—
164#432C2×D1111yescharacteristic
165#432C2×D1111yescharacteristic
166#431—111no—
167#431C2×D1111yescharacteristic
168#408—222no—
169C2×#97—111no—
170#330—222no—
171#329—222no—
172Q8⋊C8—221no—
173Q8⋊C8—221no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#38611yescharacteristic
178C2×D11—42no—
179C2×D11—42no—
180C2×D11—42no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11#44311yescharacteristic
187C4×C11#44411yescharacteristic
188Dic11—42no—
189Dic11—81no—
190Dic11—81no—
191C2×#41—112no—
192C2×Q16—222no—
193C2×SD16—222no—
194C2×M16—222no—
195C22×C8—222no—
196C22×C8—221no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199C4⋊Q8—111no—
200#127—111no—
201#125—221no—
202#124—112no—
203C22⋊Q8—221no—
204C22⋊Q8—221no—
205#121—221no—
206#121—221no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×D4—221no—
210C4×D4—221no—
211#117—221no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—221no—
217#103—222no—
218#102—222no—
219C22⋊C8—21no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C22⋊C8—222no—
223C22⋊C8—222no—
224C22⋊C8—221no—
225#97—21no—
226#97—221no—
227#97—221no—
228#97D4412yes—
229C4×C8—111no—
230C4×C8—111no—
231C4×C8C4×D1111yescharacteristic
232C4×C8C4×D1111yescharacteristic
233C2×C11—41no—
234C2×C11#187611yescharacteristic
235C2×C11#190211yescharacteristic
236C2×C11#191111yescharacteristic
237D11—82no—
238#41—882no—
239C2×Q8—112no—
240C2×Q8—221no—
241C2×Q8—221no—
242C2×D4—112no—
243C2×D4—222no—
244C2×D4—221no—
245C2×D4—221no—
246C22×C4—222no—
247C22×C4#433911yescharacteristic
248C22×C4D4×D1111yescharacteristic
249C22×C4#434311yescharacteristic
250Q16—882no—
251SD16—882no—
252M16—882no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—222no—
258C2×C8—221no—
259C2×C8—221no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—882no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—222no—
272C22⋊C4—222no—
273C22⋊C4—441no—
274C42—441no—
275C42C2×C4×D1111yescharacteristic
276C42C2×D4411yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C11#928511yescharacteristic, complemented, Sylow
280C23—222no—
281C23#6694711yescharacteristic
282Q8—442no—
283Q8—442no—
284Q8—441no—
285Q8—441no—
286D4—442no—
287D4—441no—
288D4—441no—
289D4—881no—
290D4—882no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—222no—
296C2×C4—442no—
297C2×C4—442no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4C4×D4411yescharacteristic
301C2×C4C22⋊C4×D1111yescharacteristic
302C2×C4#6693511yescharacteristic
303C2×C4#6693711yescharacteristic
304C2×C4#6694611yescharacteristic
305C2×C4#6694811yescharacteristic
306C8—42no—
307C8—41no—
308C8—41no—
309C8—81no—
310C8—442no—
311C8—441no—
312C8—441no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—442no—
317C22—442no—
318C22—442no—
319C22#1062227811yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—442no—
326C4—881no—
327C4—881no—
328C4#1062250711yescharacteristic
329C4#1062250811yescharacteristic
330C2—41no—
331C2—882no—
332C2#1306894411yescharacteristic
333C2#1306908811yescharacteristic
334C2#1306914711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1287C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1287D11
hypocenterC11#9285
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1287

Complements

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

NH ≅ G/Ntype
3. #13067232C2semidirect
5. #13067088C2semidirect
6. #13066446C2semidirect
7. C11×#1287C2semidirect
118. #1287D11semidirect
279. C11#9285semidirect

Maximal subgroups

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

subgroupindex
#130795742
#130776942
#130672322
#130672282
#130670882
#130664462
C11×#12872
#928511