Finite Group Databasebeta

← #14672479

Subgroups — #14672479

Order 2816.

566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#10622801C212yesmaximal
2C2×#10622202C212yesmaximal, complemented
3C2×(C2×D11)⋊C16C211yesmaximal, characteristic
4#13066708C211yesmaximal, characteristic, complemented
5C22×C11×Q32C211yesmaximal, characteristic, complemented
6C22×C11×Q16C2212yes—
7C2×#66999—22no—
8C22×C8×D11C2211yescharacteristic
9C2×C11×Q32—24no—
10C2×C11×Q32—22no—
11C22×C11×C16C2211yescharacteristic
12C2×#66899—22no—
13#10622801—24no—
14#10622801—24no—
15C2×#66882C2212yes—
16C22×C11⋊C16C2211yescharacteristic
17#10622202—24no—
18(C2×D11)⋊C16—22no—
19C22×Q8×C11—22no—
20C22×C4×D11D411yescharacteristic
21C2×C11×Q16—22no—
22C2×C11×Q16—22no—
23C2×C11×Q16—22no—
24C2×C11×Q16—22no—
25C2×C11×Q16—22no—
26C2×C11×Q16D414yes—
27C22×C8×C11C2311yescharacteristic
28#66999—28no—
29#66999—44no—
30C2×(C2×D11)⋊C4—42no—
31C2×C4⋊Dic11—22no—
32C2×Dic11⋊C4—42no—
33C22×C11⋊C8D411yescharacteristic
34C2×C8×D11—22no—
35C2×C8×D11—22no—
36C2×C8×D11—21no—
37C2×C8×D11—21no—
38C11×Q32—28no—
39C2×C11×C16—22no—
40C2×C11×C16D412yes—
41#66899—28no—
42#66882—22no—
43#66882D414yes—
44C2×C11⋊C16—21no—
45C2×C11⋊C16—22no—
46#13306—111nomaximal, Sylow
47C23×D11D811yescharacteristic
48C2×Q8×C11—24no—
49C2×Q8×C11—42no—
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11C2×D411yescharacteristic
56C22×Dic11—42no—
57C22×Dic11D811yescharacteristic
58C2×C4×D11—22no—
59C2×C4×D11—21no—
60C2×C4×D11—21no—
61C2×C4×D11—22no—
62C11×Q16—24no—
63C11×Q16—24no—
64C11×Q16—42no—
65C11×Q16—42no—
66C2×C8×C11C2×D412yes—
67C2×C8×C11C2×D412yes—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11#4111yescharacteristic
70(C2×D11)⋊C4—48no—
71C4⋊Dic11—24no—
72C4⋊Dic11—42no—
73Dic11⋊C4—48no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—21no—
76C8×D11—41no—
77C8×D11—42no—
78C8×D11—41no—
79C11×C16—22no—
80C11⋊C16—41no—
81C22×Q32D1111yescharacteristic, complemented
82C2×#467—112no—
83C2×#358—112no—
84C2×C22⋊C16—111no—
85#1380—111no—
86C23×C11C2×D811yescharacteristic
87C22×D11—22no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—22no—
91C22×D11Q3212yescomplemented
92Q8×C11—44no—
93Q8×C11—44no—
94Q8×C11—82no—
95Q8×C11—82no—
96C2×C4×C11—44no—
97C2×C4×C11—82no—
98C2×C4×C11—82no—
99C2×C4×C11#12012yes—
100C2×C4×C11#12111yescharacteristic
101C2×C4×C11#13511yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)12yes—
103C2×Dic11—22no—
104C2×Dic11—21no—
105C2×Dic11—44no—
106C2×Dic11—82no—
107C2×Dic11—82no—
108C4×D11—41no—
109C4×D11—42no—
110C4×D11—41no—
111C8×C11#12011yescharacteristic
112C8×C11#12112yes—
113C8×C11#12711yescharacteristic
114C11⋊C8—41no—
115C22×Q16C2×D1112yes—
116C23×C8—111no—
117C2×C22⋊Q8—222no—
118C2×Q32—24no—
119C2×Q32—22no—
120C22×C16—111no—
121C22×C16C2×D1111yescharacteristic
122#467—224no—
123#467—224no—
124C2×#107—112no—
125C2×#103—222no—
126#358—224no—
127C22⋊C16—222no—
128C22×C11#44712yes—
129C22×C11#46611yescharacteristic
130C22×C11C2×Q3211yescharacteristic
131C22×C11#50811yescharacteristic
132C22×C11#51012yes—
133C2×D11—24no—
134C2×D11—22no—
135C2×D11—42no—
136C2×D11—41no—
137C2×D11—41no—
138C4×C11—84no—
139C4×C11#39211yescharacteristic
140C4×C11#44912yes—
141C4×C11#46911yescharacteristic
142Dic11—41no—
143Dic11—84no—
144C22×Q8—22no—
145C23×C4—111no—
146C2×Q16—22no—
147C2×Q16—22no—
148C2×Q16—22no—
149C2×Q16—22no—
150C2×Q16—22no—
151C2×Q16C22⋊D1114yes—
152C22×C8—111no—
153C22×C8—222no—
154C22×C8—221no—
155C22×C8—221no—
156C22×C8—222no—
157C22×C8C22×D1111yescharacteristic
158C22⋊Q8—228no—
159C22⋊Q8—444no—
160C2×C4⋊C4—222no—
161C2×C4⋊C4—442no—
162C2×C22⋊C4—442no—
163Q32—28no—
164C2×C16—22no—
165C2×C16—222no—
166C2×C16—221no—
167C2×C16C22⋊D1112yes—
168#107—114no—
169#107—222no—
170#103—228no—
171C2×C11#199911yescharacteristic
172C2×C11#218812yes—
173C2×C11#218912yes—
174C2×C11#221611yescharacteristic
175C2×C11#221911yescharacteristic
176D11—42no—
177C24—111no—
178C2×Q8—24no—
179C2×Q8—42no—
180C2×Q8—42no—
181C2×Q8—42no—
182C2×Q8—42no—
183C2×Q8—42no—
184C22×C4—42no—
185C22×C4—111no—
186C22×C4—222no—
187C22×C4—221no—
188C22×C4—222no—
189C22×C4—221no—
190C22×C4—442no—
191C22×C4D4×D1111yescharacteristic
192Q16—24no—
193Q16—24no—
194Q16—42no—
195Q16—42no—
196C2×C8—222no—
197C2×C8—221no—
198C2×C8—442no—
199C2×C8—441no—
200C2×C8—441no—
201C2×C8D4×D1112yes—
202C2×C8#434111yescharacteristic
203C2×C8C2×C22⋊D1112yes—
204C2×C8C2×C22⋊D1111yescharacteristic
205C4⋊C4—224no—
206C4⋊C4—448no—
207C4⋊C4—442no—
208C22⋊C4—448no—
209C16—22no—
210C16—441no—
211C11#1330611yescharacteristic, complemented, Sylow
212C23—112no—
213C23—222no—
214C23—221no—
215C23—222no—
216C23—221no—
217C23D8×D1111yescharacteristic
218Q8—44no—
219Q8—44no—
220Q8—82no—
221Q8—82no—
222C2×C4—44no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—222no—
226C2×C4—221no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4—441no—
230C2×C4—444no—
231C2×C4—882no—
232C2×C4—882no—
233C2×C4#6696412yes—
234C2×C4#6696511yescharacteristic
235C2×C4#6699012yes—
236C2×C4#6699111yescharacteristic
237C8—441no—
238C8#6699212yes—
239C8#6699311yescharacteristic
240C8#6700611yescharacteristic
241C22—222no—
242C22—224no—
243C22—441no—
244C22—441no—
245C22—442no—
246C22D11×Q3211yescharacteristic
247C22#1062253112yes—
248C22#1062253211yescharacteristic
249C22#1062276912yes—
250C22#1062277011yescharacteristic
251C4—84no—
252C4—441no—
253C4—884no—
254C4#1062277112yes—
255C4#1062277211yescharacteristic
256C4#1062283611yescharacteristic
257C2—442no—
258C2#1306961111yescharacteristic
259C2#1307054812yes—
260C2#1307055512yes—
261C2#1307070411yescharacteristic
262C2#1307072111yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC22×C11×Q32C2
socleC23×C11C2×D8
prime radicalC23×D11D8
hypercenterC22×Q32D11
hypocenterC11#13306
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

Complements

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

NH ≅ G/Ntype
2. C2×#10622202C2semidirect
4. #13066708C2semidirect
5. C22×C11×Q32C2semidirect
81. C22×Q32D11semidirect
91. C22×D11Q32semidirect
211. C11#13306semidirect

Maximal subgroups

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

subgroupindex
C2×#106228012
C2×#106222022
C2×(C2×D11)⋊C162
#130667082
C22×C11×Q322
#1330611