Finite Group Databasebeta

← #14650402

Subgroups — #14650402

Order 2816.

426 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079572C211yesmaximal, characteristic
2#13067232C211yesmaximal, characteristic, complemented
3#13067227C211yesmaximal, characteristic
4#13067090C211yesmaximal, characteristic, complemented
5#13066477C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#2981C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C11×#436—21no—
11C11×#435—22no—
12C8×D4×C11—21no—
13C11×#432C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#408—22no—
16#10622852—22no—
17#10622705C411yescharacteristic
18#10622694C411yescharacteristic
19#10622689C411yescharacteristic
20#10622683C411yescharacteristic
21#10622667—22no—
22#10622539C2211yescharacteristic
23#10622538C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25#10622178—22no—
26#10622103—22no—
27#10622094—21no—
28#10622094—21no—
29C2×C11×#41D412yes—
30C2×C11×M16—22no—
31C22×C8×C11—22no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#124D412yes—
35C11×#121—21no—
36C11×#121—21no—
37C4×D4×C11—21no—
38C4×D4×C11—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4326—22no—
41C2×#4324—22no—
42#66979—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8—21no—
46#66923—21no—
47#66922C2×C411yescharacteristic
48#66922C2×C411yescharacteristic
49C4×Dic22—21no—
50C4×Dic22—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C22⋊C8—22no—
54C11×C22⋊C8—22no—
55C11×C22⋊C8—21no—
56C11×C22⋊C8—21no—
57C11×#97D412yes—
58C4×C8×C11D411yescharacteristic
59C4×C8×C11D411yescharacteristic
60#66899—22no—
61#66896—22no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67#66867—21no—
68#66867—21no—
69C4×C11⋊C8C2×C411yescharacteristic
70C4×C11⋊C8C2×C411yescharacteristic
71#9285—111nomaximal, Sylow
72C11×#41—82no—
73C2×Q8×C11C22⋊C412yes—
74C2×D4×C11—22no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11C22⋊C412yes—
78C22×C4×C11—22no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C2×Dic22—21no—
83C2×Dic22—21no—
84C11×M16—82no—
85C2×C8×C11—21no—
86C2×C8×C11—21no—
87C2×C8×C11—22no—
88C2×C8×C11—82no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C42×C11C22×C411yescharacteristic
94C42×C11C2×D411yescharacteristic
95C42×C11C2×D411yescharacteristic
96C42×C11C2×D411yescharacteristic
97C22⋊Dic11—41no—
98#4326—82no—
99#4324—82no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104Dic11⋊C4—41no—
105Dic11⋊C4—41no—
106C4×Dic11—41no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#3210—111no—
114#2981D1111yescharacteristic
115#1531—111no—
116#1530—111no—
117#1497—111no—
118#1287—111no—
119#1275—111no—
120C23×C11—22no—
121C23×C11#12311yescharacteristic
122Q8×C11—42no—
123D4×C11—42no—
124D4×C11—41no—
125D4×C11—41no—
126D4×C11—81no—
127D4×C11—82no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C2×C22⋊C411yescharacteristic
136C2×C4×C11C4×D411yescharacteristic
137C2×C4×C11C4×D411yescharacteristic
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×Dic11—41no—
142C2×Dic11—41no—
143Dic22—42no—
144Dic22—41no—
145Dic22—41no—
146C8×C11—41no—
147C8×C11—42no—
148C8×C11—41no—
149C11⋊C8—42no—
150C11⋊C8—41no—
151C11⋊C8—41no—
152C11⋊C8—81no—
153#533—111no—
154#532C2×D1111yescharacteristic
155#494—111no—
156#492—111no—
157#487—111no—
158#486—111no—
159#464—222no—
160#452—222no—
161#436—21no—
162#435—22no—
163C8×D4—21no—
164#432—111no—
165#432C2×D1111yescharacteristic
166#431—111no—
167#431C2×D1111yescharacteristic
168#408—22no—
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—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11#38611yescharacteristic
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—42no—
187C4×C11#44311yescharacteristic
188C4×C11#44411yescharacteristic
189Dic11—81no—
190Dic11—81no—
191C2×#41C22⋊D1112yes—
192C2×Q16—222no—
193C2×SD16—222no—
194C2×M16—22no—
195C22×C8—22no—
196C22×C8—221no—
197C4⋊Q8—111no—
198C4⋊Q8—111no—
199C4⋊Q8C4×D1111yescharacteristic
200#127C4×D1111yescharacteristic
201#125—221no—
202#124D4412yes—
203C22⋊Q8—221no—
204C22⋊Q8—221no—
205#121—21no—
206#121—21no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×D4—21no—
210C4×D4—21no—
211#117—221no—
212C2×C42C22×D1111yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—221no—
216C4⋊C8—221no—
217#103—222no—
218#102—222no—
219C22⋊C8—22no—
220C22⋊C8—22no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224C22⋊C8—221no—
225#97—221no—
226#97—221no—
227#97—221no—
228#97C22⋊D1112yes—
229C4×C8—111no—
230C4×C8—111no—
231C4×C8C22⋊D1111yescharacteristic
232C4×C8C22⋊D1111yescharacteristic
233C2×C11—41no—
234C2×C11—82no—
235C2×C11#187611yescharacteristic
236C2×C11#190211yescharacteristic
237C2×C11#191111yescharacteristic
238#41—82no—
239C2×Q8—221no—
240C2×Q8—221no—
241C2×Q8(C2×D11)⋊C412yes—
242C2×D4—22no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4(C2×D11)⋊C412yes—
246C22×C4—22no—
247C22×C4#433911yescharacteristic
248C22×C4#433911yescharacteristic
249C22×C4C2×C22⋊D1111yescharacteristic
250Q16—882no—
251SD16—882no—
252M16—82no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—82no—
257C2×C8—222no—
258C2×C8—221no—
259C2×C8—221no—
260C2×C8—441no—
261C2×C8—441no—
262C2×C8—441no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C22⋊C4—441no—
274C42—441no—
275C42C2×C4×D1111yescharacteristic
276C42C2×D4411yescharacteristic
277C42C2×C22⋊D1111yescharacteristic
278C42C2×C22⋊D1111yescharacteristic
279C11#928511yescharacteristic, complemented, Sylow
280C23—22no—
281C23#6698211yescharacteristic
282Q8—42no—
283Q8—442no—
284Q8—441no—
285Q8—441no—
286D4—42no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4C2×(C2×D11)⋊C411yescharacteristic
301C2×C4C4×C22⋊D1111yescharacteristic
302C2×C4C4×C22⋊D1111yescharacteristic
303C2×C4#6698311yescharacteristic
304C2×C4#6698311yescharacteristic
305C2×C4#6700611yescharacteristic
306C8—41no—
307C8—42no—
308C8—41no—
309C8—442no—
310C8—441no—
311C8—441no—
312C8—881no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22#1062282611yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—881no—
327C4—881no—
328C4#1062275711yescharacteristic
329C4#1062275811yescharacteristic
330C2—41no—
331C2—82no—
332C2#1306894311yescharacteristic
333C2#1306908911yescharacteristic
334C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2981C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#2981D11
hypocenterC11#9285
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #13067232C2semidirect
4. #13067090C2semidirect
5. #13066477C2semidirect
6. #13066446C2semidirect
279. C11#9285semidirect

Maximal subgroups

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

subgroupindex
#130795722
#130672322
#130672272
#130670902
#130664772
#130664462
C11×#29812
#928511