Finite Group Databasebeta

← #14666187

Subgroups — #14666187

Order 2816.

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

normal subgroups only

This group has 424 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#13073989C211yesmaximal, characteristic, complemented
2#13069840C211yesmaximal, characteristic
3#13067621C212yesmaximal
4#13066623C212yesmaximal, complemented
5C11×#1325C211yesmaximal, characteristic, complemented
6#10623041C2211yescharacteristic
7C2×C4×Dic22—21no—
8C11×#384C2211yescharacteristic
9#10622598—22no—
10#10622596—21no—
11#10622596C2212yes—
12#10622587—22no—
13#10622579—21no—
14C2×#66869—21no—
15#10622349—22no—
16C11×#324C2212yes—
17#10622168C2211yescharacteristic
18#10622108—22no—
19C2×#4339—21no—
20C22×Dic22—21no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C11×C4⋊C4C2311yescharacteristic
24C2×C42×C11D411yescharacteristic
25#66983—22no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—21no—
28C2×C4⋊Dic11D412yes—
29C2×Dic11⋊C4—22no—
30C2×C4×Dic11—22no—
31C2×#4318—21no—
32#66950—41no—
33#66948—41no—
34C4×Dic22—42no—
35C4×Dic22—42no—
36C11×C22⋊C8—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#12153—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—24no—
62C2×Dic22—21no—
63C2×Dic22—42no—
64C2×Dic22—42no—
65C2×C8×C11—42no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—44no—
68C11×C4⋊C4—41no—
69C42×C11—21no—
70C42×C11D812yes—
71(C2×D11)⋊C4—42no—
72C4⋊Dic11—22no—
73C4⋊Dic11—42no—
74C4⋊Dic11—42no—
75C4⋊Dic11—81no—
76Dic11⋊C4—42no—
77Dic11⋊C4—42no—
78C4×Dic11—44no—
79#4318—41no—
80#4318—41no—
81C2×C11⋊C8—41no—
82#2582—111no—
83#2039—111no—
84#1610—112no—
85#1346—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×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C22⋊D11—81no—
101C22⋊D11—81no—
102C2×Dic11—24no—
103C2×Dic11—42no—
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—41no—
108C2×Dic11—42no—
109D44—41no—
110D44—41no—
111D44—82no—
112C4×D11—81no—
113C4×D11—81no—
114Dic22—48no—
115Dic22—41no—
116Dic22—41no—
117C8×C11—82no—
118C11⋊C8—81no—
119#537—111no—
120C2×C4×Q8—221no—
121#480—222no—
122C2×#104—221no—
123#417—221no—
124#398—112no—
125#398—221no—
126#391—222no—
127#389—222no—
128#384C2×D1111yescharacteristic
129#343—111no—
130#327—222no—
131#324C2×D1112yes—
132C22×C11—21no—
133C22×C11—21no—
134C22×C11#44711yescharacteristic
135C22×C11#45411yescharacteristic
136C22×C11B(4,𝔽2)11yescharacteristic
137C2×D11—81no—
138C2×D11—81no—
139C2×D11—81no—
140C4×C11—24no—
141C4×C11—21no—
142C4×C11—21no—
143C4×C11—42no—
144C4×C11—81no—
145Dic11—44no—
146Dic11—81no—
147Dic11—82no—
148C2×#41—221no—
149C22×Q8—221no—
150C2×M16—221no—
151C22⋊Q8—441no—
152#121—222no—
153#121—441no—
154C4×Q8—442no—
155C4×Q8—442no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—112no—
158C2×C4⋊C4—221no—
159C2×C4⋊C4—222no—
160C2×C4⋊C4—221no—
161C2×C4⋊C4D4411yescharacteristic
162C2×C4⋊C4C22×D1111yescharacteristic
163C2×C42—222no—
164C2×C42D4411yescharacteristic
165#107—442no—
166#104—442no—
167#103—441no—
168#102—441no—
169#102—442no—
170C22⋊C8—22no—
171#95—112no—
172#95—222no—
173#95—221no—
174#95—222no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#159811yescharacteristic
178C2×C11#219811yescharacteristic
179C2×C11#220511yescharacteristic
180D11—161no—
181#41—441no—
182#41—441no—
183#41—441no—
184#41—441no—
185C2×Q8—224no—
186C2×Q8—221no—
187C2×Q8—442no—
188C2×Q8—442no—
189C2×D4—221no—
190C2×D4—222no—
191C2×D4—441no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—222no—
195C22×C4—222no—
196C22×C4—441no—
197C22×C4C2×D4411yescharacteristic
198C22×C4D4×D1112yes—
199M16—441no—
200M16—441no—
201C2×C8—42no—
202C2×C8—441no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—44no—
206C4⋊C4—222no—
207C4⋊C4—442no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C4⋊C4—881no—
212C22⋊C4—442no—
213C42—21no—
214C42—444no—
215C42D8812yes—
216C11#1215311yescharacteristic, complemented, Sylow
217C23—441no—
218C23#6693511yescharacteristic
219Q8—448no—
220Q8—441no—
221Q8—441no—
222D4—441no—
223D4—441no—
224D4—882no—
225D4—881no—
226D4—881no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—224no—
237C2×C4—442no—
238C2×C4—442no—
239C2×C4—442no—
240C2×C4—441no—
241C2×C4—442no—
242C2×C4—442no—
243C2×C4—881no—
244C2×C4—881no—
245C2×C4C2×D8811yescharacteristic
246C2×C4#6696111yescharacteristic
247C8—82no—
248C8—881no—
249C22—21no—
250C22—21no—
251C22—881no—
252C22—881no—
253C22—881no—
254C22#1062234511yescharacteristic
255C22#1062235411yescharacteristic
256C22#1062236611yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—81no—
262C4—444no—
263C4—882no—
264C4—881no—
265C2—21no—
266C2—21no—
267C2—1761no—
268C2#1306755311yescharacteristic
269C2#1307061411yescharacteristic
270C2#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#12153
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. #13073989C2semidirect
4. #13066623C2semidirect
5. C11×#1325C2semidirect
86. #1325D11semidirect
216. C11#12153semidirect

Maximal subgroups

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

subgroupindex
#130739892
#130698402
#130676212
#130666232
C11×#13252
#1215311