Finite Group Databasebeta

← #14735858

Subgroups — #14735858

Order 2816.

824 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 824 conjugacy classes of subgroups — too many to draw. Only its 179 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#13079163C212yesmaximal
2#13078998C211yesmaximal, characteristic
3#13067944C218yesmaximal, complemented
4#13067211C211yesmaximal, characteristic
5#13067211C212yesmaximal
6C11×#3556C211yesmaximal, characteristic
7C11×#564C2214yes—
8C11×#557—22no—
9C11×#557—22no—
10C11×#557—22no—
11C11×#541—24no—
12C11×#541—22no—
13C11×#533C2212yes—
14C11×#533C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16#10622706—22no—
17#10622692—22no—
18#10622691—22no—
19#10622682C2214yes—
20#10622678C2218yes—
21#10622617—22no—
22#10622608—24no—
23C4×#4318C2212yes—
24C4×#4318C2211yescharacteristic
25#10622181C2214yes—
26#10622181C2218yes—
27C22×Dic22—21no—
28C11×C4⋊Q8—22no—
29C11×C4⋊Q8—24no—
30C11×C4⋊Q8D412yes—
31C11×C4⋊Q8D412yes—
32C11×C4⋊Q8D412yes—
33C11×#126—28no—
34C11×#125—22no—
35C11×#125—24no—
36C11×#125—28no—
37C11×#125—28no—
38C11×#125—28no—
39C11×#125C2314yes—
40C11×#125C2312yes—
41C11×C22⋊Q8—22no—
42C11×C22⋊Q8—22no—
43C11×C22⋊Q8—22no—
44C4×Q8×C11—24no—
45C4×Q8×C11—24no—
46C4×Q8×C11—24no—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C11×#117D414yes—
51C11×#117D412yes—
52C2×C42×C11C2311yescharacteristic
53C2×C4⋊Dic11—22no—
54C2×#4318—22no—
55C2×#4318—21no—
56#66922—22no—
57#66922—21no—
58#66922C2312yes—
59#66874—28no—
60#66872—28no—
61#66871—28no—
62#66867C2314yes—
63#66867C2312yes—
64C4×C11⋊C8—22no—
65C4×C11⋊C8—21no—
66#19084—111nomaximal, Sylow
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—22no—
70C22×C4×C11C2×D412yes—
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—41no—
73C2×Dic22—22no—
74C2×Dic22—44no—
75C2×Dic22—41no—
76C11×C4⋊C4—28no—
77C11×C4⋊C4—28no—
78C11×C4⋊C4—28no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—22no—
81C11×C4⋊C4—22no—
82C11×C4⋊C4—24no—
83C11×C4⋊C4—24no—
84C11×C4⋊C4—24no—
85C11×C4⋊C4C2×D414yes—
86C11×C4⋊C4C2×D414yes—
87C11×C4⋊C4C2×D414yes—
88C11×C22⋊C4—24no—
89C11×C22⋊C4—22no—
90C42×C11—28no—
91C42×C11—22no—
92C42×C11—24no—
93C42×C11C2×D412yes—
94C42×C11C2×D411yescharacteristic
95C42×C11C2411yescharacteristic
96C4⋊Dic11—24no—
97C4⋊Dic11—42no—
98#4318—28no—
99#4318—42no—
100C2×C11⋊C8—24no—
101C2×C11⋊C8—22no—
102#3556D1111yescharacteristic
103#3165—112no—
104#3139—111no—
105#1663—118no—
106#1526—111no—
107#1526—112no—
108C23×C11#12011yescharacteristic
109Q8×C11—44no—
110Q8×C11—44no—
111Q8×C11—44no—
112C2×C4×C11—22no—
113C2×C4×C11—24no—
114C2×C4×C11—24no—
115C2×C4×C11—24no—
116C2×C4×C11—24no—
117C2×C4×C11#12011yescharacteristic
118C2×C4×C11#12012yes—
119C2×C4×C11C22×D412yes—
120C2×C4×C11C22×D411yescharacteristic
121C2×Dic11—42no—
122C2×Dic11—82no—
123Dic22—44no—
124Dic22—82no—
125C11⋊C8—28no—
126C11⋊C8—42no—
127#564C2×D1114yes—
128#557—22no—
129#557—22no—
130#557—22no—
131#541—22no—
132#541—24no—
133#533C2×D1111yescharacteristic
134#533C2×D1112yes—
135C2×C4⋊Q8—111no—
136#501—118no—
137#500—222no—
138#498—222no—
139#491—114no—
140#487—222no—
141#428—224no—
142#419—222no—
143C4×M16—111no—
144C4×M16—112no—
145#330—118no—
146#330—114no—
147C22×C11—21no—
148C22×C11—22no—
149C22×C11C2×#12011yescharacteristic
150C4×C11—21no—
151C4×C11—22no—
152C4×C11—44no—
153C4×C11—44no—
154C4×C11—44no—
155C4×C11#45412yes—
156C4×C11#45614yes—
157Dic11—82no—
158C22×Q8—221no—
159C2×M16—222no—
160C2×M16—221no—
161C4⋊Q8—22no—
162C4⋊Q8—24no—
163C4⋊Q8—112no—
164C4⋊Q8—222no—
165C4⋊Q8—221no—
166C4⋊Q8C22⋊D1112yes—
167C4⋊Q8C22⋊D1112yes—
168C4⋊Q8C22⋊D1112yes—
169#126—28no—
170#125—22no—
171#125—24no—
172#125—28no—
173#125—28no—
174#125—28no—
175#125C22×D1112yes—
176#125C22×D1114yes—
177C22⋊Q8—22no—
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C4×Q8—24no—
181C4×Q8—24no—
182C4×Q8—24no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186#117C22⋊D1112yes—
187#117C22⋊D1114yes—
188C2×C4⋊C4—222no—
189C2×C42C22×D1111yescharacteristic
190#107—228no—
191#106—228no—
192#103—228no—
193#97—112no—
194#97—114no—
195C4×C8—221no—
196C4×C8—222no—
197C2×C11—41no—
198C2×C11C2×#45411yescharacteristic
199C2×C11C2×#45612yes—
200C2×Q8—22no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—222no—
204C2×Q8—444no—
205C2×Q8—441no—
206C22×C4—441no—
207C22×C4C2×C22⋊D1112yes—
208C22×C4C2×C22⋊D1111yescharacteristic
209M16—228no—
210M16—442no—
211C2×C8—224no—
212C2×C8—222no—
213C4⋊C4—28no—
214C4⋊C4—28no—
215C4⋊C4—28no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—22no—
219C4⋊C4—24no—
220C4⋊C4—24no—
221C4⋊C4—24no—
222C4⋊C4—224no—
223C4⋊C4—442no—
224C4⋊C4C2×C22⋊D1114yes—
225C4⋊C4C2×C22⋊D1114yes—
226C4⋊C4C2×C22⋊D1114yes—
227C22⋊C4—22no—
228C22⋊C4—24no—
229C42—28no—
230C42—22no—
231C42—24no—
232C42C2×C22⋊D1112yes—
233C42C2×C22⋊D1111yescharacteristic
234C42C23×D1111yescharacteristic
235C11#1908411yescharacteristic, complemented, Sylow
236C23#6700611yescharacteristic
237Q8—44no—
238Q8—44no—
239Q8—44no—
240Q8—444no—
241Q8—882no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—24no—
247C2×C4—442no—
248C2×C4—882no—
249C2×C4#6700611yescharacteristic
250C2×C4#6700612yes—
251C2×C4C22×C22⋊D1112yes—
252C2×C4C22×C22⋊D1111yescharacteristic
253C8—228no—
254C8—442no—
255C22—21no—
256C22—22no—
257C22C2×#6700611yescharacteristic
258C4—21no—
259C4—22no—
260C4—44no—
261C4—44no—
262C4—44no—
263C4—882no—
264C4#1062285812yes—
265C4#1062285914yes—
266C2—41no—
267C2C2×#1062285811yescharacteristic
268C2C2×#1062285912yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3556C2
socleC22×C11C2×#120
prime radicalC23×C11#120
hypercenter#3556D11
hypocenterC11#19084
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
3. #13067944C2semidirect
235. C11#19084semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130789982
#130679442
#130672112
C11×#35562
#1908411