Finite Group Databasebeta

← #14667607

Subgroups — #14667607

Order 2816.

366 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 65 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#13080228C211yesmaximal, characteristic
2#13070855C211yesmaximal, characteristic, complemented
3#13070750C211yesmaximal, characteristic, complemented
4#13066658C211yesmaximal, characteristic, complemented
5#13066582C211yesmaximal, characteristic, complemented
6#13066574C211yesmaximal, characteristic, complemented
7C11×#1695C211yesmaximal, characteristic, complemented
8C2×#66961—21no—
9#10623081—21no—
10C11×#500C2211yescharacteristic, complemented
11C11×#476—21no—
12C11×#436C2211yescharacteristic
13#10622747—21no—
14#10622457—21no—
15#10622346—21no—
16#10622345—21no—
17#10622309C2211yescharacteristic
18C4×D88C2211yescharacteristic
19C11×#334C2211yescharacteristic, complemented
20C11×#333—21no—
21#10622130—21no—
22#10622129—21no—
23#10622129—21no—
24#10622127—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic, complemented
26#10622099C2211yescharacteristic, complemented
27C2×#4339—21no—
28C22×D44—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—21no—
31C4×D4×C11D411yescharacteristic
32#66990—41no—
33#66983—21no—
34#66977—21no—
35#66961—42no—
36#66961—42no—
37C2×Dic44D411yescharacteristic
38C2×D88—21no—
39C2×D88D411yescharacteristic
40C2×D88D411yescharacteristic
41C2×#4314—21no—
42C2×#4314—21no—
43#66947—41no—
44#66937—41no—
45C22⋊C4×D11—41no—
46#66928—21no—
47C4×D44—21no—
48C11×#107—21no—
49C11×#107—21no—
50C11×#106—41no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8D411yescharacteristic
53C11×#102—41no—
54C11×C22⋊C8—21no—
55C4×C8×C11C2311yescharacteristic
56#66885—21no—
57#66885—21no—
58#66882D411yescharacteristic
59#66880—21no—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62#12376—111nomaximal, Sylow
63C23×D11—41no—
64C2×Q8×C11—41no—
65C2×D4×C11D811yescharacteristic
66C22×C4×C11—21no—
67C2×C22⋊D11—41no—
68C2×C22⋊D11—41no—
69#4339—42no—
70#4339—81no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44—41no—
74C2×D44—42no—
75C2×D44—81no—
76C2×C4×D11—41no—
77C2×C4×D11—41no—
78C2×Dic22—21no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—21no—
82C2×C8×C11—41no—
83C2×C8×C11C2×D411yescharacteristic
84C2×C8×C11C2×D411yescharacteristic
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4D811yescharacteristic
88C11×C22⋊C4—21no—
89C42×C11C2×D411yescharacteristic
90C22⋊Dic11—41no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—21no—
96Dic11⋊C4—41no—
97Dic44—41no—
98D88—21no—
99D88—41no—
100D88—42no—
101D88SD1612yes—
102#4314—42no—
103#4314—41no—
104#4314—41no—
105C11⋊C16—41no—
106C11⋊C16—41no—
107#3273—111no—
108#2243—111no—
109#2224—111no—
110#1695D1111yescharacteristic, complemented
111#1360—111no—
112#1333—111no—
113#1330—111no—
114C23×C11—21no—
115C22×D11—41no—
116C22×D11—41no—
117C22×D11—82no—
118C22×D11—82no—
119C22×D11—161no—
120Q8×C11—161no—
121D4×C11—41no—
122C2×C4×C11—21no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—81no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11C2×D811yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C22⋊D11—82no—
130C22⋊D11—161no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133D44—22no—
134D44—41no—
135D44—41no—
136D44—41no—
137D44—82no—
138C4×D11—82no—
139C4×D11—161no—
140Dic22—41no—
141Dic22—41no—
142C8×C11—21no—
143C8×C11—41no—
144C8×C11—81no—
145C8×C11C2×SD1611yescharacteristic
146C8×C11AGL(1,ℤ/8)11yescharacteristic
147C2×AGL(1,ℤ/8)—221no—
148#546—221no—
149#500C2×D1111yescharacteristic, complemented
150#495—111no—
151#476—21no—
152#468—221no—
153#463—221no—
154#452—221no—
155#447—221no—
156C4×D8—111no—
157#436C2×D1111yescharacteristic
158#366—221no—
159C4⋊C16—111no—
160#358—221no—
161#357—221no—
162#357—221no—
163#346—111no—
164#334C2×D1111yescharacteristic, complemented
165#333—21no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11#44711yescharacteristic
170C2×D11—42no—
171C2×D11—81no—
172C2×D11—81no—
173C2×D11—81no—
174C2×D11—81no—
175C2×D11—81no—
176C2×D11—164no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—41no—
180C4×C11—161no—
181C4×C11#45011yescharacteristic
182C4×C11#45511yescharacteristic
183Dic11—81no—
184Dic11—81no—
185C2×#41—221no—
186C22×D4—221no—
187AGL(1,ℤ/8)—442no—
188AGL(1,ℤ/8)—442no—
189C2×Q16—111no—
190C2×SD16—221no—
191C2×SD16—221no—
192C2×D8—111no—
193C2×D8—111no—
194C2×D8—221no—
195C2×M16—21no—
196C4⋊Q8—21no—
197#124—221no—
198#123—441no—
199C22⋊Q8—221no—
200#121—221no—
201#121—441no—
202#120—441no—
203C4×D4—221no—
204C4×D4C22⋊D1111yescharacteristic
205C2×C22⋊C4—441no—
206C2×C16—221no—
207C2×C16—221no—
208#107—21no—
209#107—21no—
210#107—111no—
211#106—41no—
212C4⋊C8—21no—
213C4⋊C8C22⋊D1111yescharacteristic
214#103—221no—
215#102—41no—
216#102—221no—
217#102—221no—
218C22⋊C8—21no—
219C4×C8C22×D1111yescharacteristic
220C2×C11—81no—
221C2×C11#163911yescharacteristic
222C2×C11#219111yescharacteristic
223C2×C11#219211yescharacteristic
224D11—82no—
225D11—161no—
226C24—441no—
227#41—442no—
228#41—881no—
229C2×Q8—41no—
230C2×Q8—221no—
231C2×D4—221no—
232C2×D4—221no—
233C2×D4—441no—
234C2×D4—442no—
235C2×D4—441no—
236C2×D4—441no—
237C2×D4—881no—
238C2×D4#432311yescharacteristic
239C22×C4—21no—
240C22×C4—441no—
241C22×C4—441no—
242Q16—441no—
243SD16—442no—
244SD16—441no—
245SD16—441no—
246D8—112no—
247D8—221no—
248D8—441no—
249D8—442no—
250M16—41no—
251M16—41no—
252C2×C8—21no—
253C2×C8—41no—
254C2×C8D4×D1111yescharacteristic
255C2×C8D4×D1111yescharacteristic
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—221no—
259C4⋊C4—441no—
260C4⋊C4#432311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—441no—
263C22⋊C4—441no—
264C22⋊C4—441no—
265C22⋊C4—441no—
266C22⋊C4—441no—
267C42C2×C22⋊D1111yescharacteristic
268C16—441no—
269C16—441no—
270C11#1237611yescharacteristic, complemented, Sylow
271C23—21no—
272C23—441no—
273C23—441no—
274C23—882no—
275C23—882no—
276C23—1761no—
277Q8—161no—
278Q8—441no—
279Q8—441no—
280D4—41no—
281D4—222no—
282D4—441no—
283D4—441no—
284D4—441no—
285D4—882no—
286D4—882no—
287D4—1761no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—882no—
295C2×C4—1761no—
296C2×C4C2×#432311yescharacteristic
297C2×C4#6699011yescharacteristic
298C2×C4#6700211yescharacteristic
299C8—21no—
300C8—41no—
301C8—81no—
302C8SD16×D1111yescharacteristic
303C8#6696711yescharacteristic
304C22—41no—
305C22—41no—
306C22—41no—
307C22—442no—
308C22—881no—
309C22—881no—
310C22—881no—
311C22—881no—
312C22—881no—
313C22—1764no—
314C22#1062264911yescharacteristic
315C4—21no—
316C4—21no—
317C4—41no—
318C4—161no—
319C4—881no—
320C4—881no—
321C4#1062278211yescharacteristic
322C4#1062281511yescharacteristic
323C2—81no—
324C2—882no—
325C2—1761no—
326C2#1306779311yescharacteristic
327C2#1307056611yescharacteristic
328C2#1307057111yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1695C2
socleC22×C11#447
prime radical#13080228C2
hypercenter#1695D11
hypocenterC11#12376
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1695

Complements

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

NH ≅ G/Ntype
2. #13070855C2semidirect
3. #13070750C2semidirect
4. #13066658C2semidirect
5. #13066582C2semidirect
6. #13066574C2semidirect
7. C11×#1695C2semidirect
10. C11×#500C22semidirect
19. C11×#334C22semidirect
25. C4⋊(C11⋊C16)C22semidirect
26. #10622099C22semidirect
110. #1695D11semidirect
149. #500C2×D11semidirect
164. #334C2×D11semidirect
270. C11#12376semidirect

Maximal subgroups

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

subgroupindex
#130802282
#130708552
#130707502
#130666582
#130665822
#130665742
C11×#16952
#1237611