Finite Group Databasebeta

← #14666211

Subgroups — #14666211

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#13076684C211yesmaximal, characteristic, complemented
2#13069845C211yesmaximal, characteristic
3#13067621C212yesmaximal
4#13066623C212yesmaximal, complemented
5C11×#1324C211yesmaximal, characteristic, complemented
6#10623041C2211yescharacteristic
7C2×#66923—21no—
8C11×#382C2211yescharacteristic
9#10622596—21no—
10#10622596C2212yes—
11#10622579—21no—
12C2×#66869—21no—
13#10622349—22no—
14#10622274—22no—
15#10622272—22no—
16C11×#324C2212yes—
17#10622168C2211yescharacteristic
18#10622108—22no—
19C2×#4339—21no—
20C2×C11×C4⋊C4D411yescharacteristic
21C2×C11×C4⋊C4C2311yescharacteristic
22C2×C42×C11D411yescharacteristic
23#66983—22no—
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—21no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11D412yes—
28C2×Dic11⋊C4—22no—
29C2×Dic11⋊C4—22no—
30C2×#4318—21no—
31#66950—41no—
32#66948—41no—
33#66923—42no—
34#66923—42no—
35C11×C22⋊C8—22no—
36C11×#95—22no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40C11⋊#95D412yes—
41#66885—42no—
42#66882—42no—
43#66874—41no—
44#66873—41no—
45#66869—42no—
46#12157—111nomaximal, Sylow
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D412yes—
51C2×C22⋊D11—41no—
52C22×Dic11—22no—
53C22×Dic11—22no—
54#4339—41no—
55#4339—41no—
56#4339—41no—
57#4339—41no—
58C2×D44—21no—
59C2×D44—22no—
60C2×C4×D11—41no—
61C2×Dic22—21no—
62C2×C8×C11—42no—
63C11×C4⋊C4—41no—
64C11×C4⋊C4—41no—
65C42×C11—21no—
66C42×C11D812yes—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—81no—
73Dic11⋊C4—44no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76#4318—41no—
77#4318—41no—
78C2×C11⋊C8—41no—
79#2822—111no—
80#2040—111no—
81#1610—112no—
82#1346—112no—
83#1324D1111yescharacteristic, complemented
84C23×C11#12011yescharacteristic
85C22×D11—41no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—41no—
95C2×C4×C11C2×D811yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C22⋊D11—81no—
98C22⋊D11—81no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—41no—
105C2×Dic11—42no—
106D44—41no—
107D44—41no—
108D44—82no—
109C4×D11—81no—
110C4×D11—81no—
111Dic22—41no—
112Dic22—41no—
113C8×C11—82no—
114C11⋊C8—81no—
115#537—111no—
116C2×#125—221no—
117#480—222no—
118C2×#104—221no—
119#417—221no—
120#400—222no—
121#398—112no—
122#398—222no—
123#398—221no—
124#382C2×D1111yescharacteristic
125#343—111no—
126#327—222no—
127#324C2×D1112yes—
128C22×C11—21no—
129C22×C11—21no—
130C22×C11#44711yescharacteristic
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—
145C2×M16—221no—
146#125—442no—
147#125—442no—
148C22⋊Q8—441no—
149#121—222no—
150#121—441no—
151C2×C4⋊C4—112no—
152C2×C4⋊C4—221no—
153C2×C4⋊C4—222no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—222no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4D4411yescharacteristic
158C2×C4⋊C4C22×D1111yescharacteristic
159C2×C42D4411yescharacteristic
160#107—442no—
161#104—442no—
162#103—441no—
163#102—441no—
164#102—442no—
165C22⋊C8—22no—
166#95—22no—
167#95—112no—
168#95—222no—
169#95—221no—
170#95—222no—
171C2×C11—21no—
172C2×C11—21no—
173C2×C11#159811yescharacteristic
174C2×C11#220111yescharacteristic
175C2×C11#220311yescharacteristic
176D11—161no—
177#41—441no—
178#41—441no—
179#41—441no—
180#41—441no—
181C2×Q8—221no—
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—
192M16—441no—
193M16—441no—
194C2×C8—42no—
195C2×C8—441no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—222no—
199C4⋊C4—442no—
200C4⋊C4—444no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—442no—
205C4⋊C4—881no—
206C22⋊C4—442no—
207C42—21no—
208C42D8812yes—
209C11#1215711yescharacteristic, complemented, Sylow
210C23—441no—
211C23#6693511yescharacteristic
212Q8—441no—
213Q8—441no—
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×D8811yescharacteristic
238C2×C4#6696111yescharacteristic
239C8—82no—
240C8—881no—
241C22—21no—
242C22—21no—
243C22—881no—
244C22—881no—
245C22—881no—
246C22#1062234511yescharacteristic
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#1306755311yescharacteristic
261C2#1307063111yescharacteristic
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#12157
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. #13076684C2semidirect
4. #13066623C2semidirect
5. C11×#1324C2semidirect
83. #1324D11semidirect
209. C11#12157semidirect

Maximal subgroups

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

subgroupindex
#130766842
#130698452
#130676212
#130666232
C11×#13242
#1215711