Finite Group Databasebeta

← #14666343

Subgroups — #14666343

Order 2816.

472 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 59 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#13073645C211yesmaximal, characteristic, complemented
2#13067585C212yesmaximal
3#13066645C212yesmaximal, complemented
4#13066562C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic
6C11×#537C2211yescharacteristic
7C2×#66941—22no—
8C2×C11×#104—21no—
9C11×#417—21no—
10C11×#384C2211yescharacteristic
11#10622653—22no—
12#10622592—21no—
13#10622592C2212yes—
14#10622586—22no—
15C4×C4⋊Dic11—21no—
16C11×#343C2211yescharacteristic
17#10622175—22no—
18#10622166C2212yes—
19C2×C11×#41—21no—
20C22×Dic22—21no—
21C22×Dic22D412yes—
22C2×C11×M16—21no—
23C11×C22⋊Q8—41no—
24C11×#121—22no—
25C11×#121—41no—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4C2311yescharacteristic
29C2×C42×C11D411yescharacteristic
30C2×#4324—42no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×Dic11⋊C4—22no—
34C2×Dic11⋊C4—22no—
35C2×C4×Dic11—22no—
36#66941—48no—
37C11×#104—42no—
38C11×#103—41no—
39C11×#102—41no—
40C11⋊#95—21no—
41C11⋊#95—22no—
42C11⋊#95D412yes—
43C22⋊(C11⋊C8)—22no—
44#66874—42no—
45#12180—111nomaximal, Sylow
46C11×#41—41no—
47C11×#41—41no—
48C11×#41—41no—
49C11×#41—41no—
50C2×Q8×C11—21no—
51C2×D4×C11—21no—
52C2×D4×C11—22no—
53C2×D4×C11—41no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—41no—
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D412yes—
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—42no—
62C2×Dic22—44no—
63C2×Dic22—44no—
64C2×Dic22—81no—
65C11×M16—41no—
66C11×M16—41no—
67C2×C8×C11—41no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—44no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—42no—
73C42×C11—21no—
74C42×C11SD1612yescomplemented
75#4324—84no—
76C4⋊Dic11—24no—
77C4⋊Dic11—24no—
78Dic11⋊C4—44no—
79Dic11⋊C4—44no—
80C4×Dic11—44no—
81C2×C11⋊C8—42no—
82#2551—111no—
83#2039D1111yescharacteristic
84#1604—112no—
85#1354—112no—
86#1325—111no—
87C23×C11—41no—
88C23×C11#12011yescharacteristic
89Q8×C11—41no—
90Q8×C11—41no—
91D4×C11—41no—
92D4×C11—41no—
93D4×C11—82no—
94D4×C11—81no—
95D4×C11—81no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11—22no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—42no—
103C2×C4×C11—42no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11—81no—
107C2×C4×C11—81no—
108C2×C4×C11C2×SD1611yescharacteristic
109C2×C4×C11#13711yescharacteristic
110C2×Dic11—24no—
111C2×Dic11—24no—
112C2×Dic11—42no—
113C2×Dic11—42no—
114C2×Dic11—42no—
115C2×Dic11—42no—
116Dic22—44no—
117Dic22—82no—
118Dic22—84no—
119C8×C11—81no—
120C11⋊C8—82no—
121#537C2×D1111yescharacteristic
122C2×C4⋊Q8—222no—
123#448—222no—
124C2×#104—21no—
125#417—21no—
126#395—112no—
127#395—221no—
128#389—222no—
129#384C2×D1111yescharacteristic
130C4×C4⋊C4—221no—
131#343C2×D1111yescharacteristic
132#327—222no—
133#324—112no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—81no—
137C22×C11—81no—
138C22×C11—81no—
139C22×C11#44811yescharacteristic
140C22×C11#45411yescharacteristic
141C22×C11B(4,𝔽2)11yescharacteristic
142C4×C11—24no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—42no—
146C4×C11—81no—
147C4×C11—81no—
148Dic11—44no—
149Dic11—44no—
150C2×#41—21no—
151C22×Q8—112no—
152C22×Q8—221no—
153C2×SD16—442no—
154C2×M16—21no—
155C4⋊Q8—448no—
156C22⋊Q8—41no—
157#121—22no—
158#121—41no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4—222no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4C22⋊D1111yescharacteristic
165C2×C4⋊C4C22×D1111yescharacteristic
166C2×C42—222no—
167C2×C42C22⋊D1111yescharacteristic
168#104—42no—
169#103—41no—
170#103—442no—
171#102—41no—
172C22⋊C8—222no—
173#95—112no—
174#95—221no—
175#95—222no—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11—161no—
179C2×C11#159911yescharacteristic
180C2×C11#219611yescharacteristic
181C2×C11#220511yescharacteristic
182#41—41no—
183#41—41no—
184#41—41no—
185#41—41no—
186C2×Q8—21no—
187C2×Q8—442no—
188C2×Q8—444no—
189C2×Q8—444no—
190C2×Q8—881no—
191C2×D4—21no—
192C2×D4—22no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—41no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4D4×D1112yes—
200C22×C4C2×C22⋊D1111yescharacteristic
201SD16—884no—
202M16—41no—
203M16—41no—
204C2×C8—41no—
205C2×C8—442no—
206C4⋊C4—22no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—44no—
210C4⋊C4—224no—
211C4⋊C4—224no—
212C4⋊C4—444no—
213C4⋊C4—444no—
214C22⋊C4—42no—
215C42—21no—
216C42—444no—
217C42#432412yescomplemented
218C11#1218011yescharacteristic, complemented, Sylow
219C23—41no—
220C23#6699011yescharacteristic
221Q8—41no—
222Q8—41no—
223Q8—444no—
224Q8—882no—
225Q8—884no—
226D4—41no—
227D4—41no—
228D4—82no—
229D4—81no—
230D4—81no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—224no—
244C2×C4—224no—
245C2×C4—442no—
246C2×C4—442no—
247C2×C4—442no—
248C2×C4—442no—
249C2×C4C2×#432411yescharacteristic
250C2×C4#6700411yescharacteristic
251C8—81no—
252C8—882no—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22#1062264511yescharacteristic
259C22#1062265311yescharacteristic
260C22#1062267511yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—81no—
266C4—81no—
267C4—444no—
268C4—444no—
269C2—21no—
270C2—21no—
271C2—161no—
272C2#1306755511yescharacteristic
273C2#1307059911yescharacteristic
274C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2039C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#537C22
hypercenter#2039D11
hypocenterC11#12180
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #13073645C2semidirect
3. #13066645C2semidirect
4. #13066562C2semidirect
74. C42×C11SD16semidirect
217. C42#4324semidirect
218. C11#12180semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130675852
#130666452
#130665622
C11×#20392
#1218011