Finite Group Databasebeta

← #14656404

Subgroups — #14656404

Order 2816.

950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079536C212yesmaximal, complemented
2#13077011C211yesmaximal, characteristic, complemented
3#13069444C211yesmaximal, characteristic, complemented
4#13067283C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C2×#66927—24no—
8C2×#66927—22no—
9C2×#66927C2212yes—
10C11×#431C2212yes—
11C43×C11C2211yescharacteristic
12C2×#66869—22no—
13#10622537C2211yescharacteristic
14#10622456—24no—
15#10622345—24no—
16#10622308—22no—
17#10622307—22no—
18#10622123—24no—
19C2×#4339—21no—
20C22×D44—28no—
21C22×D44—22no—
22C22×D44—22no—
23C22×D44D414yes—
24C2×C42×C11—22no—
25C2×C42×C11D412yes—
26C2×C42×C11C2311yescharacteristic
27#66983—22no—
28C2×#4318—21no—
29C2×D88—28no—
30#66928—21no—
31#66927—22no—
32#66927—22no—
33#66927—22no—
34#66927—22no—
35#66927—416no—
36#66927—44no—
37#66927—44no—
38#66927D411yescharacteristic, complemented
39C4×D44—22no—
40#66922D411yescharacteristic, complemented
41C11×C4⋊C8D414yescomplemented
42C11×C22⋊C8—22no—
43C4×C8×C11—22no—
44#66885—28no—
45#66869—44no—
46C4⋊(C11⋊C8)—22no—
47#10280—111nomaximal, Sylow
48C23×D11—24no—
49C22×C4×C11—22no—
50C22×C4×C11C2×D412yes—
51C22×C4×C11C2×D411yescharacteristic
52C2×C22⋊D11—41no—
53#4339—42no—
54#4339—42no—
55C2×D44—24no—
56C2×D44—22no—
57C2×D44—21no—
58C2×D44—24no—
59C2×D44—48no—
60C2×D44—432no—
61C2×D44—416no—
62C2×D44—48no—
63C2×D44—42no—
64C2×D44—42no—
65C2×D44—42no—
66C2×D44—42no—
67C2×D44—44no—
68C2×D44—44no—
69C2×C4×D11—41no—
70C2×Dic22—21no—
71C2×C8×C11—24no—
72C42×C11—28no—
73C42×C11—22no—
74C42×C11D814yescomplemented
75C42×C11C2×D411yescharacteristic
76C42×C11C2×D412yes—
77C42×C11#4111yescharacteristic
78(C2×D11)⋊C4—42no—
79C4⋊Dic11—22no—
80#4318—42no—
81C2×C11⋊C8—41no—
82D88—88no—
83#3205—112no—
84#2867—111no—
85#1962—111no—
86#1545—112no—
87#1276D1111yescharacteristic, complemented
88C23×C11#12011yescharacteristic
89C22×D11—48no—
90C22×D11—48no—
91C22×D11—41no—
92C22×D11—44no—
93C22×D11—48no—
94C2×C4×C11—28no—
95C2×C4×C11—24no—
96C2×C4×C11—24no—
97C2×C4×C11#12012yes—
98C2×C4×C11#12112yes—
99C2×C4×C11#12111yescharacteristic
100C2×C4×C11#12711yescharacteristic
101C2×C4×C11C2×D812yes—
102C2×C4×C11AGL(1,ℤ/8)12yes—
103C22⋊D11—82no—
104C2×Dic11—41no—
105D44—44no—
106D44—48no—
107D44—42no—
108D44—84no—
109D44—832no—
110D44—84no—
111D44—84no—
112D44—84no—
113D44—82no—
114D44—82no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—42no—
118C8×C11—44no—
119C11⋊C8—81no—
120#532—111no—
121C2×#127—112no—
122C2×#127—224no—
123C2×#127—222no—
124#493—222no—
125#486—222no—
126#459—224no—
127#447—224no—
128#431C2×D1112yes—
129#423—111no—
130C2×#104—222no—
131C43C2×D1111yescharacteristic
132#331—224no—
133C22×C11—22no—
134C22×C11#39211yescharacteristic
135C22×C11#44712yes—
136C2×D11—816no—
137C2×D11—84no—
138C2×D11—84no—
139C2×D11—82no—
140C2×D11—84no—
141C2×D11—81no—
142C4×C11—28no—
143C4×C11—22no—
144C4×C11#45314yes—
145C4×C11#45912yes—
146C4×C11#49311yescharacteristic
147C4×C11#49611yescharacteristic
148Dic11—81no—
149C2×#41—221no—
150C22×D4—114no—
151C22×D4—228no—
152C22×D4—222no—
153C22×D4—222no—
154C2×D8—228no—
155C2×M16—221no—
156C4⋊Q8—111no—
157#127—111no—
158#127—222no—
159#127—222no—
160#127—222no—
161#127—222no—
162#127—4416no—
163#127—444no—
164#127—444no—
165#124—221no—
166#121—222no—
167C4×D4—222no—
168C2×C42—22no—
169C2×C42D4412yes—
170C2×C42C22×D1111yescharacteristic
171C4⋊C8—222no—
172C4⋊C8D4414yescomplemented
173#104—444no—
174#102—228no—
175C22⋊C8—22no—
176C4×C8—22no—
177C2×C11—22no—
178C2×C11#200212yes—
179C2×C11#201111yescharacteristic
180D11—161no—
181D11—164no—
182C24—224no—
183#41—442no—
184#41—442no—
185C2×Q8—221no—
186C2×D4—224no—
187C2×D4—222no—
188C2×D4—221no—
189C2×D4—224no—
190C2×D4—448no—
191C2×D4—4432no—
192C2×D4—4416no—
193C2×D4—448no—
194C2×D4—441no—
195C2×D4—442no—
196C2×D4—442no—
197C2×D4—442no—
198C2×D4—442no—
199C2×D4—444no—
200C2×D4—444no—
201C22×C4—22no—
202C22×C4—441no—
203C22×C4C2×D4411yescharacteristic
204C22×C4D4×D1112yes—
205D8—888no—
206M16—442no—
207C2×C8—24no—
208C2×C8—441no—
209C4⋊C4—222no—
210C22⋊C4—442no—
211C42—28no—
212C42—22no—
213C42D8814yescomplemented
214C42C2×D4412yes—
215C42D4×D1111yescharacteristic
216C42#434311yescharacteristic
217C11#1028011yescharacteristic, complemented, Sylow
218C23—448no—
219C23—448no—
220C23—441no—
221C23—444no—
222C23—448no—
223C23#6693511yescharacteristic
224Q8—442no—
225D4—444no—
226D4—448no—
227D4—442no—
228D4—884no—
229D4—8832no—
230D4—884no—
231D4—882no—
232D4—882no—
233D4—882no—
234D4—884no—
235D4—884no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—24no—
239C2×C4—441no—
240C2×C4—881no—
241C2×C4—881no—
242C2×C4#6692711yescharacteristic
243C2×C4#6693512yes—
244C2×C4#6694812yes—
245C2×C4#6694811yescharacteristic
246C2×C4C2×D8812yes—
247C2×C4#6696112yes—
248C8—44no—
249C8—881no—
250C22—22no—
251C22—8816no—
252C22—884no—
253C22—882no—
254C22—884no—
255C22—881no—
256C22—884no—
257C22#1062228411yescharacteristic
258C22#1062234512yes—
259C4—28no—
260C4—22no—
261C4—881no—
262C4#1062230811yescharacteristic
263C4#1062232511yescharacteristic
264C4#1062243514yes—
265C4#1062245612yes—
266C2—22no—
267C2—1764no—
268C2—1761no—
269C2#1306963412yes—
270C2#1306968911yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#392
hypercenter#1276D11
hypocenterC11#10280
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #13079536C2semidirect
2. #13077011C2semidirect
3. #13069444C2semidirect
4. #13067283C2semidirect
5. C11×#1276C2semidirect
38. #66927D4semidirect
40. #66922D4semidirect
41. C11×C4⋊C8D4semidirect
74. C42×C11D8semidirect
87. #1276D11semidirect
172. C4⋊C8D44semidirect
213. C42D88semidirect
217. C11#10280semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130770112
#130694442
#130672832
C11×#12762
#1028011