Finite Group Databasebeta

← #14666370

Subgroups — #14666370

Order 2816.

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

normal subgroups only

This group has 372 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#13076888C211yesmaximal, characteristic, complemented
2#13069845C211yesmaximal, characteristic
3#13067587C212yesmaximal
4#13066647C212yesmaximal, complemented
5C11×#1324C211yesmaximal, characteristic, complemented
6#10623041C2211yescharacteristic
7C11×#382C2211yescharacteristic
8#10622599—21no—
9#10622592C2212yes—
10#10622579—21no—
11#10622549—21no—
12C2×#66869—21no—
13#10622351—22no—
14#10622273—22no—
15#10622269—22no—
16C11×#324C2212yes—
17#10622168C2211yescharacteristic
18#10622108—22no—
19C2×#4339—21no—
20C22×Dic22D412yes—
21C2×C11×C4⋊C4D411yescharacteristic
22C2×C11×C4⋊C4C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66983—22no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28C2×Dic11⋊C4—22no—
29C2×#4318—21no—
30C2×#4314—42no—
31#66950—41no—
32#66948—41no—
33C11×C22⋊C8—22no—
34C11×#95—22no—
35C11⋊#95—22no—
36C11⋊#95—22no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95D412yes—
40#66880—42no—
41#66874—41no—
42#66873—41no—
43#66869—42no—
44#12184—111nomaximal, Sylow
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C2×D411yescharacteristic
48C22×C4×C11C2×D412yes—
49C2×C22⋊D11—41no—
50C22×Dic11—22no—
51C22×Dic11—22no—
52#4339—41no—
53#4339—41no—
54#4339—41no—
55#4339—41no—
56C2×D44—21no—
57C2×D44—22no—
58C2×C4×D11—41no—
59C2×Dic22—21no—
60C2×Dic22—42no—
61C2×Dic22—82no—
62C2×C8×C11—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C42×C11—21no—
66C42×C11SD1612yescomplemented
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—22no—
69C4⋊Dic11—81no—
70C4⋊Dic11—81no—
71C4⋊Dic11—81no—
72Dic11⋊C4—82no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—41no—
76#4314—84no—
77#2844—111no—
78#2040—111no—
79#1604—112no—
80#1354—112no—
81#1324D1111yescharacteristic, complemented
82C23×C11#12011yescharacteristic
83C22×D11—41no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—41no—
93C2×C4×C11C2×SD1611yescharacteristic
94C2×C4×C11#13711yescharacteristic
95C22⋊D11—81no—
96C22⋊D11—81no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—41no—
103C2×Dic11—42no—
104D44—41no—
105D44—41no—
106D44—82no—
107C4×D11—81no—
108C4×D11—81no—
109Dic22—41no—
110Dic22—41no—
111Dic22—44no—
112Dic22—82no—
113C8×C11—82no—
114C11⋊C8—81no—
115#537—111no—
116#448—222no—
117C2×#104—221no—
118#417—221no—
119#400—222no—
120#400—221no—
121#395—112no—
122#395—222no—
123#382—221no—
124#382C2×D1111yescharacteristic
125#343—111no—
126#327—222no—
127#324C2×D1112yes—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#44811yescharacteristic
131C22×C11#45411yescharacteristic
132C22×C11B(4,𝔽2)11yescharacteristic
133C2×D11—81no—
134C2×D11—81no—
135C2×D11—81no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—42no—
139C4×C11—42no—
140C4×C11—81no—
141Dic11—82no—
142Dic11—81no—
143Dic11—82no—
144C2×#41—221no—
145C22×Q8—112no—
146C2×SD16—442no—
147C2×M16—221no—
148C22⋊Q8—441no—
149#121—222no—
150#121—441no—
151C2×C4⋊C4—221no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—221no—
154C2×C4⋊C4—222no—
155C2×C4⋊C4D4411yescharacteristic
156C2×C4⋊C4C22×D1111yescharacteristic
157C2×C42D4411yescharacteristic
158#104—442no—
159#103—441no—
160#103—442no—
161#102—441no—
162C22⋊C8—22no—
163#95—22no—
164#95—112no—
165#95—222no—
166#95—222no—
167#95—221no—
168#95—222no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11#159911yescharacteristic
172C2×C11#219911yescharacteristic
173C2×C11#220311yescharacteristic
174D11—161no—
175#41—441no—
176#41—441no—
177#41—441no—
178#41—441no—
179C2×Q8—221no—
180C2×Q8—442no—
181C2×Q8—882no—
182C2×D4—221no—
183C2×D4—222no—
184C2×D4—441no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—222no—
188C22×C4—222no—
189C22×C4—441no—
190C22×C4C2×D4411yescharacteristic
191C22×C4D4×D1112yes—
192SD16—884no—
193M16—441no—
194M16—441no—
195C2×C8—42no—
196C2×C8—441no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—222no—
200C4⋊C4—882no—
201C4⋊C4—881no—
202C4⋊C4—881no—
203C4⋊C4—881no—
204C22⋊C4—442no—
205C42—21no—
206C42#431412yescomplemented
207C11#1218411yescharacteristic, complemented, Sylow
208C23—441no—
209C23#6693511yescharacteristic
210Q8—441no—
211Q8—441no—
212Q8—444no—
213Q8—882no—
214D4—441no—
215D4—441no—
216D4—882no—
217D4—881no—
218D4—881no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—441no—
233C2×C4—442no—
234C2×C4—442no—
235C2×C4—881no—
236C2×C4—881no—
237C2×C4C2×#431411yescharacteristic
238C2×C4#6696211yescharacteristic
239C8—82no—
240C8—881no—
241C22—21no—
242C22—21no—
243C22—881no—
244C22—881no—
245C22—881no—
246C22#1062235111yescharacteristic
247C22#1062235411yescharacteristic
248C22#1062236611yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—81no—
254C4—882no—
255C4—882no—
256C4—881no—
257C2—21no—
258C2—21no—
259C2—1761no—
260C2#1306755811yescharacteristic
261C2#1307061911yescharacteristic
262C2#1307063911yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1324C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#1324D11
hypocenterC11#12184
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
1. #13076888C2semidirect
4. #13066647C2semidirect
5. C11×#1324C2semidirect
66. C42×C11SD16semidirect
81. #1324D11semidirect
206. C42#4314semidirect
207. C11#12184semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130698452
#130675872
#130666472
C11×#13242
#1218411