Finite Group Databasebeta

← #14666209

Subgroups — #14666209

Order 2816.

372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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#13069845C211yesmaximal, characteristic
2#13067618C212yesmaximal
3#13066622C212yesmaximal, complemented
4#13066560C211yesmaximal, characteristic, complemented
5C11×#2822C211yesmaximal, characteristic, complemented
6C2×C11×#125—21no—
7#10623041C2211yescharacteristic
8C11×#400—22no—
9C11×#398—21no—
10C11×#398—22no—
11C11×#398C2212yes—
12C11×#382C2211yescharacteristic
13#10622580—22no—
14#10622579—21no—
15C2×#66869—21no—
16#10622168C2211yescharacteristic
17#10622166C2212yes—
18#10622089—22no—
19C2×#4339—21no—
20C11×#125—42no—
21C11×#125—42no—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—22no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D412yes—
29C2×C11×C4⋊C4C2311yescharacteristic
30C2×C42×C11D411yescharacteristic
31#66983—22no—
32C2×#4318—21no—
33#66950—41no—
34#66948—41no—
35C11×#95—22no—
36C11×#95—21no—
37C11×#95—22no—
38C11×#95—22no—
39C11×#95D412yes—
40C22⋊(C11⋊C8)—22no—
41#66874—41no—
42#66873—41no—
43#66873—42no—
44#66871—42no—
45#66869—42no—
46#12157—111nomaximal, Sylow
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11—22no—
50C22×C4×C11—22no—
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D412yes—
53C2×C22⋊D11—41no—
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—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—44no—
65C11×C4⋊C4—42no—
66C11×C4⋊C4—42no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—81no—
71C42×C11—21no—
72C42×C11D812yes—
73(C2×D11)⋊C4—42no—
74C4⋊Dic11—22no—
75#4318—41no—
76#4318—41no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—41no—
79#2822D1111yescharacteristic, complemented
80#2040—111no—
81#1610—112no—
82#1346—112no—
83#1324—111no—
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—42no—
95C2×C4×C11—42no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—41no—
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C22⋊D11—81no—
104C22⋊D11—81no—
105C2×Dic11—41no—
106D44—41no—
107D44—41no—
108D44—82no—
109C4×D11—81no—
110C4×D11—81no—
111Dic22—41no—
112Dic22—41no—
113C11⋊C8—81no—
114C11⋊C8—82no—
115#537—111no—
116C2×#125—21no—
117#480—222no—
118C2×#104—221no—
119#417—221no—
120#400—22no—
121#398—21no—
122#398—22no—
123#398C2×D1112yes—
124#382C2×D1111yescharacteristic
125#343—111no—
126#327—222no—
127#324—112no—
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—82no—
141C4×C11—82no—
142C4×C11—81no—
143Dic11—81no—
144C2×#41—221no—
145C2×M16—221no—
146#125—42no—
147#125—42no—
148C22⋊Q8—441no—
149#121—222no—
150#121—441no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C22⋊D1111yescharacteristic
157C2×C4⋊C4C22⋊D1112yes—
158C2×C4⋊C4C22×D1111yescharacteristic
159C2×C42C22⋊D1111yescharacteristic
160#107—442no—
161#104—442no—
162#103—441no—
163#102—441no—
164#102—442no—
165C22⋊C8—222no—
166#95—22no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95C22⋊D1112yes—
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—22no—
188C22×C4—22no—
189C22×C4—441no—
190C22×C4C2×C22⋊D1111yescharacteristic
191C22×C4C2×C22⋊D1112yes—
192M16—441no—
193M16—441no—
194C2×C8—442no—
195C2×C8—441no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—81no—
205C4⋊C4—222no—
206C22⋊C4—442no—
207C42—21no—
208C42#432312yes—
209C11#1215711yescharacteristic, complemented, Sylow
210C23—441no—
211C23#6700611yescharacteristic
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—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—441no—
235C2×C4—881no—
236C2×C4—881no—
237C2×C4C2×#432311yescharacteristic
238C2×C4#6698511yescharacteristic
239C8—881no—
240C8—882no—
241C22—21no—
242C22—21no—
243C22—881no—
244C22—881no—
245C22—881no—
246C22#1062283011yescharacteristic
247C22#1062285711yescharacteristic
248C22#1062285811yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—881no—
257C2—21no—
258C2—21no—
259C2—1761no—
260C2#1306755111yescharacteristic
261C2#1307062911yescharacteristic
262C2#1307063711yescharacteristic
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2822C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#2822D11
hypocenterC11#12157
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2822

Complements

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

NH ≅ G/Ntype
3. #13066622C2semidirect
4. #13066560C2semidirect
5. C11×#2822C2semidirect
79. #2822D11semidirect
209. C11#12157semidirect

Maximal subgroups

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

subgroupindex
#130698452
#130676182
#130666222
#130665602
C11×#28222
#1215711