Finite Group Databasebeta

← #14666346

Subgroups — #14666346

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#13069840C211yesmaximal, characteristic
3#13067587C212yesmaximal
4#13066647C212yesmaximal, complemented
5C11×#1325C211yesmaximal, characteristic, complemented
6#10623041C2211yescharacteristic
7C2×#66941—22no—
8C11×#384C2211yescharacteristic
9#10622592—21no—
10#10622592C2212yes—
11#10622586—22no—
12#10622579—21no—
13C4×C4⋊Dic11—21no—
14C2×#66869—21no—
15#10622351—22no—
16C11×#324C2212yes—
17#10622168C2211yescharacteristic
18#10622108—22no—
19C2×#4339—21no—
20C22×Dic22—21no—
21C22×Dic22D412yes—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C4⋊C4C2311yescharacteristic
25C2×C42×C11D411yescharacteristic
26#66983—22no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11—21no—
29C2×Dic11⋊C4—22no—
30C2×Dic11⋊C4—22no—
31C2×C4×Dic11—22no—
32C2×#4318—21no—
33C2×#4314—42no—
34#66950—41no—
35#66948—41no—
36#66941—48no—
37C11×C22⋊C8—22no—
38C11⋊#95—21no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41#66880—42no—
42#66874—41no—
43#66873—41no—
44#66869—42no—
45#12180—111nomaximal, Sylow
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C2×C22⋊D11—41no—
51C22×Dic11—22no—
52C22×Dic11—22no—
53#4339—41no—
54#4339—41no—
55#4339—41no—
56#4339—41no—
57C2×D44—21no—
58C2×D44—22no—
59C2×C4×D11—41no—
60C2×Dic22—21no—
61C2×Dic22—42no—
62C2×Dic22—44no—
63C2×Dic22—44no—
64C2×Dic22—81no—
65C2×C8×C11—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—44no—
68C11×C4⋊C4—41no—
69C42×C11—21no—
70C42×C11SD1612yescomplemented
71(C2×D11)⋊C4—42no—
72C4⋊Dic11—24no—
73C4⋊Dic11—24no—
74C4⋊Dic11—22no—
75Dic11⋊C4—44no—
76Dic11⋊C4—44no—
77C4×Dic11—44no—
78#4318—41no—
79#4318—41no—
80C2×C11⋊C8—41no—
81#4314—84no—
82#2551—111no—
83#2039—111no—
84#1604—112no—
85#1354—112no—
86#1325D1111yescharacteristic, complemented
87C23×C11#12011yescharacteristic
88C22×D11—41no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—21no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—41no—
98C2×C4×C11C2×SD1611yescharacteristic
99C2×C4×C11#13711yescharacteristic
100C22⋊D11—81no—
101C22⋊D11—81no—
102C2×Dic11—24no—
103C2×Dic11—24no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—41no—
109D44—41no—
110D44—41no—
111D44—82no—
112C4×D11—81no—
113C4×D11—81no—
114Dic22—44no—
115Dic22—41no—
116Dic22—41no—
117Dic22—82no—
118Dic22—84no—
119C8×C11—82no—
120C11⋊C8—81no—
121#537—111no—
122C2×C4⋊Q8—222no—
123#448—222no—
124C2×#104—221no—
125#417—221no—
126#395—112no—
127#395—221no—
128#389—222no—
129#384C2×D1111yescharacteristic
130C4×C4⋊C4—221no—
131#343—111no—
132#327—222no—
133#324C2×D1112yes—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11#44811yescharacteristic
137C22×C11#45411yescharacteristic
138C22×C11B(4,𝔽2)11yescharacteristic
139C2×D11—81no—
140C2×D11—81no—
141C2×D11—81no—
142C4×C11—24no—
143C4×C11—21no—
144C4×C11—21no—
145C4×C11—42no—
146C4×C11—81no—
147Dic11—44no—
148Dic11—44no—
149Dic11—81no—
150C2×#41—221no—
151C22×Q8—112no—
152C22×Q8—221no—
153C2×SD16—442no—
154C2×M16—221no—
155C4⋊Q8—448no—
156C22⋊Q8—441no—
157#121—222no—
158#121—441no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4—221no—
162C2×C4⋊C4—222no—
163C2×C4⋊C4—222no—
164C2×C4⋊C4D4411yescharacteristic
165C2×C4⋊C4C22×D1111yescharacteristic
166C2×C42—222no—
167C2×C42D4411yescharacteristic
168#104—442no—
169#103—441no—
170#103—442no—
171#102—441no—
172C22⋊C8—22no—
173#95—112no—
174#95—221no—
175#95—222no—
176C2×C11—21no—
177C2×C11—21no—
178C2×C11#159911yescharacteristic
179C2×C11#219611yescharacteristic
180C2×C11#220511yescharacteristic
181D11—161no—
182#41—441no—
183#41—441no—
184#41—441no—
185#41—441no—
186C2×Q8—221no—
187C2×Q8—442no—
188C2×Q8—444no—
189C2×Q8—444no—
190C2×Q8—881no—
191C2×D4—221no—
192C2×D4—222no—
193C2×D4—441no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4—441no—
199C22×C4C2×D4411yescharacteristic
200C22×C4D4×D1112yes—
201SD16—884no—
202M16—441no—
203M16—441no—
204C2×C8—42no—
205C2×C8—441no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—44no—
209C4⋊C4—224no—
210C4⋊C4—224no—
211C4⋊C4—222no—
212C4⋊C4—444no—
213C4⋊C4—444no—
214C22⋊C4—442no—
215C42—21no—
216C42—444no—
217C42#431412yescomplemented
218C11#1218011yescharacteristic, complemented, Sylow
219C23—441no—
220C23#6693511yescharacteristic
221Q8—441no—
222Q8—441no—
223Q8—444no—
224Q8—882no—
225Q8—884no—
226D4—441no—
227D4—441no—
228D4—882no—
229D4—881no—
230D4—881no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—224no—
241C2×C4—224no—
242C2×C4—442no—
243C2×C4—442no—
244C2×C4—442no—
245C2×C4—442no—
246C2×C4—441no—
247C2×C4—881no—
248C2×C4—881no—
249C2×C4C2×#431411yescharacteristic
250C2×C4#6696211yescharacteristic
251C8—82no—
252C8—881no—
253C22—21no—
254C22—21no—
255C22—881no—
256C22—881no—
257C22—881no—
258C22#1062235111yescharacteristic
259C22#1062235411yescharacteristic
260C22#1062236611yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—81no—
266C4—444no—
267C4—444no—
268C4—881no—
269C2—21no—
270C2—21no—
271C2—1761no—
272C2#1306755811yescharacteristic
273C2#1307060211yescharacteristic
274C2#1307064711yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#1325D11
hypocenterC11#12180
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
1. #13073645C2semidirect
4. #13066647C2semidirect
5. C11×#1325C2semidirect
70. C42×C11SD16semidirect
86. #1325D11semidirect
217. C42#4314semidirect
218. C11#12180semidirect

Maximal subgroups

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

subgroupindex
#130736452
#130698402
#130675872
#130666472
C11×#13252
#1218011