Finite Group Databasebeta

← #14667308

Subgroups — #14667308

Order 2816.

362 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081590C211yesmaximal, characteristic
2#13070873C211yesmaximal, characteristic, complemented
3#13067983C211yesmaximal, characteristic, complemented
4#13066663C211yesmaximal, characteristic, complemented
5#13066594C211yesmaximal, characteristic, complemented
6#13066577C211yesmaximal, characteristic, complemented
7C11×#2208C211yesmaximal, characteristic, complemented
8#10623084—21no—
9C2×C11×SD32—21no—
10C11×#494C2211yescharacteristic
11C4×C11×D8C2211yescharacteristic
12C2×#66892—22no—
13#10622764—21no—
14#10622707—21no—
15#10622628—21no—
16#10622485—21no—
17#10622399—22no—
18#10622308C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#358—21no—
22#10622185—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×#4339—41no—
26C2×C11×Q16—21no—
27C2×C11×Q16—21no—
28C2×C11×D8D411yescharacteristic
29C11×C4⋊Q8—21no—
30C4×D4×C11—21no—
31#66993—22no—
32C2×#4323—22no—
33#66983—41no—
34C2×D88—21no—
35C2×D88D412yes—
36#66946—22no—
37#66937—42no—
38#66927—21no—
39C4×Dic22D411yescharacteristic
40C11×SD32—42no—
41C2×C11×C16—21no—
42C11×#107D411yescharacteristic
43C11×#102—21no—
44C4×C8×C11C2311yescharacteristic
45#66892—44no—
46Dic11⋊C8—21no—
47C8×Dic11—21no—
48C2×C11⋊C16—21no—
49#66874—41no—
50#66873—22no—
51#66872—41no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54#12332—111nomaximal, Sylow
55C2×Q8×C11—41no—
56C2×D4×C11—21no—
57C22×C4×C11—41no—
58C2×C22⋊D11—42no—
59C2×C22⋊D11—42no—
60#4339—82no—
61#4339—82no—
62C2×D44—22no—
63C2×D44—41no—
64C2×D44—41no—
65C2×C4×D11—42no—
66C2×Dic22D811yescharacteristic
67C11×Q16—42no—
68C11×Q16—41no—
69C11×Q16—41no—
70C11×D8—21no—
71C11×D8—21no—
72C2×C8×C11C2×D411yescharacteristic
73C2×C8×C11C2×D411yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C22⋊C4—41no—
78C42×C11C2×D411yescharacteristic
79#4323—82no—
80(C2×D11)⋊C4—42no—
81C4⋊Dic11D811yescharacteristic
82Dic11⋊C4—21no—
83C4×Dic11—21no—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—41no—
86D88—42no—
87D88—41no—
88D88—41no—
89C11×C16—41no—
90C11⋊C16—22no—
91#3391—111no—
92#2248—111no—
93#2208D1111yescharacteristic, complemented
94#1670—111no—
95#1361—111no—
96Q8⋊C16—111no—
97#1331—111no—
98C23×C11—41no—
99C22×D11—42no—
100Q8×C11—81no—
101Q8×C11—81no—
102D4×C11—41no—
103D4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11—81no—
106C2×C4×C11—81no—
107C2×C4×C11—81no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C22⋊D11—84no—
112C22⋊D11—162no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115D44—42no—
116D44—42no—
117D44—81no—
118D44—81no—
119D44—161no—
120C4×D11—84no—
121Dic22—21no—
122Dic22SD3212yescomplemented
123C8×C11—21no—
124C8×C11#13511yescharacteristic
125C8×C11AGL(1,ℤ/8)11yescharacteristic
126C11⋊C8—41no—
127C11⋊C8—81no—
128#550—221no—
129C2×SD32—21no—
130C2×SD32—222no—
131#494C2×D1111yescharacteristic
132#493—111no—
133#493—221no—
134#475—221no—
135#459—222no—
136#459—221no—
137C8×Q8—111no—
138C4×D8—221no—
139C4×D8C2×D1111yescharacteristic
140C4⋊C16C2×D1111yescharacteristic
141#358—21no—
142C4×C16—111no—
143#335—111no—
144#332—221no—
145C22×C11—81no—
146C22×C11—81no—
147C22×C11—81no—
148C22×C11#44711yescharacteristic
149C2×D11—82no—
150C2×D11—82no—
151C2×D11—82no—
152C4×C11—21no—
153C4×C11—81no—
154C4×C11—161no—
155C4×C11#44911yescharacteristic
156C4×C11#45311yescharacteristic
157C4×C11C2×SD3211yescharacteristic
158C4×C11#50911yescharacteristic
159Dic11—22no—
160Dic11—41no—
161C2×#41—441no—
162C2×Q16—21no—
163C2×Q16—21no—
164C2×D8—112no—
165C2×D8—222no—
166C2×D8—221no—
167C2×D8C22⋊D1111yescharacteristic
168C4⋊Q8—21no—
169#127—222no—
170#127—221no—
171#121—442no—
172#121—441no—
173C4×Q8—111no—
174C4×D4—21no—
175C4×D4—222no—
176SD32—42no—
177SD32—444no—
178C2×C16—21no—
179C2×C16—221no—
180#107C22⋊D1111yescharacteristic
181#106—441no—
182C4⋊C8—111no—
183C4⋊C8—221no—
184C4⋊C8—221no—
185#103—441no—
186#102—21no—
187#102—222no—
188C4×C8—221no—
189C4×C8C22×D1111yescharacteristic
190C2×C11—161no—
191C2×C11#162111yescharacteristic
192C2×C11#218711yescharacteristic
193C2×C11#219411yescharacteristic
194D11—162no—
195#41—882no—
196#41—882no—
197C2×Q8—41no—
198C2×Q8—111no—
199C2×D4—21no—
200C2×D4—222no—
201C2×D4—442no—
202C2×D4—442no—
203C2×D4—441no—
204C2×D4—441no—
205C22×C4—41no—
206C22×C4—442no—
207Q16—42no—
208Q16—41no—
209Q16—41no—
210D8—21no—
211D8—21no—
212D8—442no—
213D8—441no—
214D8—441no—
215D8—882no—
216C2×C8—221no—
217C2×C8—441no—
218C2×C8D4×D1111yescharacteristic
219C2×C8C2×C22⋊D1111yescharacteristic
220C4⋊C4—21no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—111no—
224C4⋊C4—221no—
225C22⋊C4—41no—
226C22⋊C4—442no—
227C42—221no—
228C42D4×D1111yescharacteristic
229C16—41no—
230C16—222no—
231C11#1233211yescharacteristic, complemented, Sylow
232C23—41no—
233C23—442no—
234Q8—81no—
235Q8—81no—
236Q8—112no—
237Q8—221no—
238D4—41no—
239D4—41no—
240D4—442no—
241D4—442no—
242D4—884no—
243D4—881no—
244D4—881no—
245D4—1761no—
246D4—1762no—
247C2×C4—41no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—221no—
252C2×C4—221no—
253C2×C4—884no—
254C2×C4D8×D1111yescharacteristic
255C2×C4#6696411yescharacteristic
256C2×C4#6699011yescharacteristic
257C8—21no—
258C8—441no—
259C8—881no—
260C8#6698511yescharacteristic
261C8#6700311yescharacteristic
262C22—81no—
263C22—81no—
264C22—81no—
265C22—882no—
266C22—882no—
267C22—882no—
268C22#1062276911yescharacteristic
269C4—21no—
270C4—81no—
271C4—161no—
272C4—222no—
273C4—441no—
274C4D11×SD3211yescharacteristic
275C4#1062252711yescharacteristic
276C4#1062265011yescharacteristic
277C4#1062281111yescharacteristic
278C2—161no—
279C2—1762no—
280C2#1306768011yescharacteristic
281C2#1307054311yescharacteristic
282C2#1307058411yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2208C2
socleC22×C11#447
prime radical#13081590C2
hypercenter#2208D11
hypocenterC11#12332
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
2. #13070873C2semidirect
3. #13067983C2semidirect
4. #13066663C2semidirect
5. #13066594C2semidirect
6. #13066577C2semidirect
7. C11×#2208C2semidirect
93. #2208D11semidirect
122. Dic22SD32semidirect
231. C11#12332semidirect

Maximal subgroups

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

subgroupindex
#130815902
#130708732
#130679832
#130666632
#130665942
#130665772
C11×#22082
#1233211