Finite Group Databasebeta

← #14651869

Subgroups — #14651869

Order 2816.

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

normal subgroups only

This group has 428 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#13078711C211yesmaximal, characteristic
2#13067346C211yesmaximal, characteristic, complemented
3#13067042C211yesmaximal, characteristic
4#13066956C211yesmaximal, characteristic
5#13066526C211yesmaximal, characteristic, complemented
6#13066478C211yesmaximal, characteristic, complemented
7C11×#2985C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10C11×#446—22no—
11C11×#446—21no—
12C8×Q8×C11—21no—
13C11×#433—22no—
14C11×#432C2211yescharacteristic
15C11×#431C2211yescharacteristic
16#10622700—21no—
17#10622696—21no—
18#10622659C412yes—
19#10622657C412yes—
20#10622639—22no—
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622537C2211yescharacteristic
24#10622185—21no—
25#10622184—21no—
26#10622106—22no—
27#10622097—21no—
28#10622097—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C11×C4⋊Q8D411yescharacteristic
32C11×C4⋊Q8D411yescharacteristic
33C11×#125—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8C2×C412yes—
36C4×Q8×C11—21no—
37C4×Q8×C11D412yes—
38C11×#117—21no—
39C2×C42×C11C2311yescharacteristic
40C2×#4325—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×C4⋊Dic11C2×C411yescharacteristic
43C2×#4318—21no—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C11×C4⋊C8—22no—
49C11×C4⋊C8—22no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8D412yes—
54C11×#97—22no—
55C11×#97—21no—
56C4×C8×C11—22no—
57C4×C8×C11D411yescharacteristic
58C4×C8×C11D411yescharacteristic
59#66899—22no—
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)C2×C412yes—
62#66873—22no—
63#66871—22no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68#66867—21no—
69#66867—21no—
70#9530—111nomaximal, Sylow
71C23×D11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11C22⋊C412yes—
74C22×C4×C11C22×C411yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×Dic11—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—42no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—81no—
84C2×C4×D11—81no—
85C2×C8×C11—21no—
86C2×C8×C11—22no—
87C2×C8×C11—21no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—22no—
93C11×C4⋊C4C22⋊C412yes—
94C11×C22⋊C4—22no—
95C42×C11—22no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11#4111yescharacteristic
100#4325—44no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—41no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105#4318—81no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109#3110—111no—
110#2985D1111yescharacteristic, complemented
111#1559—111no—
112#1486—111no—
113#1466—111no—
114#1307—111no—
115#1287—111no—
116C23×C11C4×D411yescharacteristic
117C22×D11—22no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—81no—
121C22×D11—81no—
122Q8×C11—42no—
123Q8×C11—41no—
124Q8×C11—41no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11C2×C22⋊C411yescharacteristic
132C2×C4×C11C4×D411yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12311yescharacteristic
137C2×Dic11—41no—
138C2×Dic11—81no—
139D44—22no—
140D44—22no—
141D44—41no—
142D44—41no—
143C4×D11—82no—
144C4×D11—81no—
145C4×D11—81no—
146C8×C11—41no—
147C8×C11—42no—
148C8×C11—41no—
149C11⋊C8—42no—
150C11⋊C8—81no—
151C11⋊C8—81no—
152#533C2×D1111yescharacteristic
153C2×C4×D4—111no—
154#484—112no—
155#474—221no—
156#461—221no—
157#450—112no—
158#446—22no—
159#446—21no—
160C8×Q8—21no—
161#440—222no—
162#433—22no—
163#432—111no—
164#432—111no—
165#432C2×D1111yescharacteristic
166#431C2×D1111yescharacteristic
167#423—111no—
168#333—221no—
169#332—221no—
170D4⋊C8—221no—
171D4⋊C8—221no—
172#323—222no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11#38611yescharacteristic
177C2×D11—42no—
178C2×D11—82no—
179C2×D11—81no—
180C2×D11—81no—
181C2×D11—82no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—21no—
187C4×C11—42no—
188C4×C11—42no—
189C4×C11#47111yescharacteristic
190C4×C11#47211yescharacteristic
191Dic11—81no—
192C22×D4—111no—
193C23×C4—221no—
194C2×SD16—222no—
195C2×M16—221no—
196C4⋊Q8D4411yescharacteristic
197C4⋊Q8D4411yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8C4×D1112yes—
201C4×Q8—21no—
202C4×Q8C22⋊D1112yes—
203C4×D4—221no—
204C4×D4—221no—
205C4×D4—221no—
206C4×D4—221no—
207#117—21no—
208C2×C4⋊C4—111no—
209C2×C22⋊C4—221no—
210C2×C42C22×D1111yescharacteristic
211#107—222no—
212C4⋊C8—22no—
213C4⋊C8—22no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—221no—
217C4⋊C8—221no—
218C4⋊C8—221no—
219C4⋊C8—221no—
220#103—222no—
221#102—222no—
222C22⋊C8—21no—
223C22⋊C8—112no—
224C22⋊C8—221no—
225C22⋊C8C22⋊D1112yes—
226#97—22no—
227#97—21no—
228#97—221no—
229#97—221no—
230C4×C8—22no—
231C4×C8C22⋊D1111yescharacteristic
232C4×C8C22⋊D1111yescharacteristic
233C2×C11—41no—
234C2×C11#189111yescharacteristic
235C2×C11#190511yescharacteristic
236C2×C11#190711yescharacteristic
237D11—82no—
238C24—221no—
239C2×Q8—21no—
240C2×Q8(C2×D11)⋊C412yes—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4—442no—
244C22×C4—221no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4—881no—
248C22×C4—881no—
249C22×C4C2×C4×D1111yescharacteristic
250C22×C4#433911yescharacteristic
251C22×C4C2×C22⋊D1111yescharacteristic
252SD16—444no—
253M16—881no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—21no—
257C2×C8—222no—
258C2×C8—441no—
259C2×C8—441no—
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4(C2×D11)⋊C412yes—
268C22⋊C4—22no—
269C22⋊C4—441no—
270C22⋊C4—441no—
271C42—22no—
272C42C2×D4411yescharacteristic
273C42#433911yescharacteristic
274C42C2×C22⋊D1111yescharacteristic
275C42C2×C22⋊D1111yescharacteristic
276C11#953011yescharacteristic, complemented, Sylow
277C23—222no—
278C23—441no—
279C23—441no—
280C23—881no—
281C23—881no—
282C23C4×C22⋊D1111yescharacteristic
283Q8—42no—
284Q8—41no—
285Q8—41no—
286D4—222no—
287D4—222no—
288D4—441no—
289D4—441no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—441no—
297C2×C4—882no—
298C2×C4—881no—
299C2×C4—881no—
300C2×C4—881no—
301C2×C4C2×(C2×D11)⋊C411yescharacteristic
302C2×C4C4×C22⋊D1111yescharacteristic
303C2×C4#6698211yescharacteristic
304C2×C4#6698311yescharacteristic
305C2×C4#6698311yescharacteristic
306C2×C4#6700611yescharacteristic
307C8—41no—
308C8—42no—
309C8—41no—
310C8—442no—
311C8—881no—
312C8—881no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—442no—
317C22—882no—
318C22—882no—
319C22—881no—
320C22—881no—
321C22#1062282611yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—881no—
330C4#1062275411yescharacteristic
331C4#1062275511yescharacteristic
332C2—41no—
333C2—882no—
334C2#1306903411yescharacteristic
335C2#1306911011yescharacteristic
336C2#1306912411yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2985C2
socleC22×C11#386
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#2985D11
hypocenterC11#9530
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2985

Complements

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

NH ≅ G/Ntype
2. #13067346C2semidirect
5. #13066526C2semidirect
6. #13066478C2semidirect
7. C11×#2985C2semidirect
110. #2985D11semidirect
276. C11#9530semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130673462
#130670422
#130669562
#130665262
#130664782
C11×#29852
#953011