Finite Group Databasebeta

← #14654390

Subgroups — #14654390

Order 2816.

544 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 83 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#13079367C211yesmaximal, characteristic
2#13078556C212yesmaximal, complemented
3#13066975C212yesmaximal, complemented
4#13066493C211yesmaximal, characteristic, complemented
5C11×#1818C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66983C2212yes—
8C2×C11×C22⋊C8C2211yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10#10622820C2212yes—
11#10622728—22no—
12#10622616—24no—
13#10622614—22no—
14#10622608—22no—
15#10622581—22no—
16#10622580—22no—
17#10622349—22no—
18#10622345—22no—
19C11×#336—22no—
20#10622106—24no—
21C23×C4×C11C2311yescharacteristic
22C22×C22⋊D11—22no—
23C22×D44D412yes—
24C22×C8×C11—21no—
25C22×C8×C11D412yes—
26C11×#117—22no—
27C11×#117—22no—
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C42×C11—21no—
32#66983—22no—
33#66983—22no—
34#66983—22no—
35#66983—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×C4⋊Dic11D412yes—
38C2×#4318—22no—
39C2×D88—22no—
40C11×C22⋊C8—22no—
41C11×C22⋊C8—22no—
42C22⋊(C11⋊C8)—22no—
43C22⋊(C11⋊C8)D414yes—
44#66885—24no—
45#66882—22no—
46#66873—24no—
47#66873—24no—
48#66872—24no—
49#66871—24no—
50#9977—111nomaximal, Sylow
51C24×C11#4111yescharacteristic
52C23×D11—22no—
53C22×C4×C11—21no—
54C22×C4×C11—21no—
55C22×C4×C11—42no—
56C22×C4×C11C2×D412yes—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×C4×C11C2×D412yes—
60C2×C22⋊D11—42no—
61C2×C22⋊D11—42no—
62C2×C22⋊D11—84no—
63C22×Dic11—22no—
64C2×D44—22no—
65C2×D44—22no—
66C2×D44—44no—
67C2×C8×C11—22no—
68C2×C8×C11—42no—
69C2×C8×C11—42no—
70C2×C8×C11—41no—
71C11×C4⋊C4—22no—
72C11×C4⋊C4—22no—
73C11×C22⋊C4—42no—
74C42×C11—41no—
75C42×C11—41no—
76(C2×D11)⋊C4—42no—
77(C2×D11)⋊C4—42no—
78C4⋊Dic11—22no—
79C4⋊Dic11—22no—
80#4318—44no—
81C2×C11⋊C8—24no—
82D88—82no—
83#3186—111no—
84#3094—112no—
85#1818D1111yescharacteristic, complemented
86#1471—112no—
87#1293—111no—
88C23×C11—22no—
89C23×C11—41no—
90C23×C11—41no—
91C23×C11#12112yes—
92C23×C11#12111yescharacteristic
93C22×D11—42no—
94C22×D11—44no—
95C22×D11—82no—
96C22×D11—82no—
97C2×C4×C11—24no—
98C2×C4×C11—22no—
99C2×C4×C11—41no—
100C2×C4×C11—42no—
101C2×C4×C11—42no—
102C2×C4×C11—41no—
103C2×C4×C11—41no—
104C2×C4×C11—42no—
105C2×C4×C11#12012yes—
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11#12711yescharacteristic
108C22⋊D11—84no—
109C22⋊D11—84no—
110C2×Dic11—42no—
111C2×Dic11—82no—
112D44—44no—
113D44—44no—
114C8×C11—42no—
115C8×C11—81no—
116C11⋊C8—44no—
117C2×#121—112no—
118C2×#117C2×D1111yescharacteristic
119#482—224no—
120#481—222no—
121#480—222no—
122#480—222no—
123#466—222no—
124#447—222no—
125#428—222no—
126#418—222no—
127#407—112no—
128C2×C22⋊C8C2×D1111yescharacteristic
129C2×C22⋊C8C2×D1111yescharacteristic
130#336—22no—
131#323—224no—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11—22no—
135C22×C11—22no—
136C22×C11—22no—
137C22×C11—82no—
138C22×C11#39211yescharacteristic
139C22×C11#47212yes—
140C2×D11—82no—
141C2×D11—82no—
142C2×D11—82no—
143C2×D11—164no—
144C4×C11—22no—
145C4×C11—21no—
146C4×C11—81no—
147C4×C11—81no—
148C4×C11#45812yes—
149Dic11—82no—
150C22×D4—112no—
151C22×D4—222no—
152C23×C4C22×D1111yescharacteristic
153C2×D8—222no—
154C2×M16—222no—
155C22×C8—21no—
156C22×C8C22⋊D1112yes—
157#121—222no—
158#121—222no—
159#121—222no—
160#121—222no—
161#117—22no—
162#117—22no—
163C2×C4⋊C4—112no—
164C2×C4⋊C4D4411yescharacteristic
165C2×C4⋊C4D4411yescharacteristic
166C2×C22⋊C4—21no—
167C2×C22⋊C4—222no—
168C2×C42—21no—
169#107—224no—
170#107—222no—
171#106—224no—
172#102—224no—
173#102—224no—
174#102—224no—
175C22⋊C8—22no—
176C22⋊C8—22no—
177C22⋊C8—114no—
178C22⋊C8—222no—
179C2×C11—22no—
180C2×C11—42no—
181C2×C11#201711yescharacteristic
182C2×C11#201811yescharacteristic
183C2×C11#202211yescharacteristic
184D11—162no—
185C24—222no—
186C24#433911yescharacteristic
187C2×D4—222no—
188C2×D4—222no—
189C2×D4—444no—
190C2×D4—442no—
191C2×D4—442no—
192C2×D4—884no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—222no—
197C22×C4C2×D4411yescharacteristic
198C22×C4D4×D1112yes—
199C22×C4D4×D1112yes—
200C22×C4C2×C22⋊D1111yescharacteristic
201D8—882no—
202M16—444no—
203C2×C8—22no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—41no—
207C2×C8—224no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—222no—
211C4⋊C4—222no—
212C22⋊C4—42no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C42—41no—
216C42—41no—
217C11#997711yescharacteristic, complemented, Sylow
218C23—22no—
219C23—41no—
220C23—41no—
221C23—444no—
222C23—442no—
223C23—882no—
224C23—882no—
225C23#6693712yes—
226C23#6698311yescharacteristic
227D4—444no—
228D4—444no—
229D4—884no—
230D4—884no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—442no—
240C2×C4—882no—
241C2×C4#6693512yes—
242C2×C4#6699011yescharacteristic
243C2×C4#6699311yescharacteristic
244C8—42no—
245C8—81no—
246C8—444no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—882no—
254C22—882no—
255C22—882no—
256C22—1764no—
257C22#1062257311yescharacteristic
258C22#1062275512yes—
259C4—21no—
260C4—22no—
261C4—81no—
262C4—81no—
263C4—882no—
264C4#1062266612yes—
265C2—22no—
266C2—42no—
267C2—1762no—
268C2#1306972011yescharacteristic
269C2#1306972511yescharacteristic
270C2#1306974711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1818C2
socleC22×C11#392
prime radical#13079367C2
hypercenter#1818D11
hypocenterC11#9977
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. #13078556C2semidirect
3. #13066975C2semidirect
4. #13066493C2semidirect
5. C11×#1818C2semidirect
85. #1818D11semidirect
217. C11#9977semidirect

Maximal subgroups

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

subgroupindex
#130793672
#130785562
#130669752
#130664932
C11×#18182
#997711