Finite Group Databasebeta

← #14656275

Subgroups — #14656275

Order 2816.

474 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079961C211yesmaximal, characteristic
2#13078423C212yesmaximal
3#13069551C211yesmaximal, characteristic
4#13067070C212yesmaximal
5C11×#1292C211yesmaximal, characteristic
6#10623001C2212yes—
7C2×C4×Dic22C2211yescharacteristic
8C11×#423C2212yes—
9C2×C11×C4⋊C8C2211yescharacteristic
10#10622734—22no—
11#10622733—22no—
12#10622729—22no—
13C2×C4×C11⋊C8C2211yescharacteristic
14#10622464—22no—
15#10622463—22no—
16#10622463—22no—
17#10622462—22no—
18#10622442—24no—
19#10622188—22no—
20#10622122—24no—
21C22×Dic22D411yescharacteristic
22C2×C11×M16—22no—
23C22×C8×C11D412yes—
24C2×C42×C11C2311yescharacteristic
25#66979—22no—
26C2×C4⋊Dic11D411yescharacteristic
27#66977—22no—
28#66977—22no—
29C2×Dic11⋊C4—21no—
30C2×C4×Dic11—21no—
31C22×C11⋊C8—21no—
32C2×Dic44—22no—
33#66923—22no—
34#66922D412yes—
35#66922D412yes—
36C4×Dic22—22no—
37C4×Dic22—22no—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×C4⋊C8—22no—
41C11×C4⋊C8—22no—
42C11×C4⋊C8D414yes—
43#66882—22no—
44#66882—24no—
45#66881—24no—
46#66880—24no—
47#66880—24no—
48#66880—24no—
49C4×C11⋊C8—22no—
50#10259—111nomaximal, Sylow
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11C2×D411yescharacteristic
53C22×C4×C11#4111yescharacteristic
54C22×Dic11—21no—
55C22×Dic11—21no—
56C2×Dic22—22no—
57C2×Dic22—22no—
58C2×Dic22—22no—
59C2×Dic22—21no—
60C2×Dic22—22no—
61C2×Dic22Q1612yescomplemented
62C11×M16—42no—
63C11×M16—42no—
64C2×C8×C11—24no—
65C2×C8×C11—22no—
66C2×C8×C11—42no—
67C42×C11C2×D412yes—
68C42×C11C2×D412yes—
69C22⋊Dic11—42no—
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11—22no—
73C4⋊Dic11—22no—
74C4⋊Dic11—22no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77Dic11⋊C4—42no—
78C4×Dic11—41no—
79C4×Dic11—42no—
80C4×Dic11—41no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—41no—
83C2×C11⋊C8—41no—
84Dic44—82no—
85#3249—111no—
86#3078—112no—
87#1984—111no—
88#1493—112no—
89#1292D1111yescharacteristic
90C23×C11#12111yescharacteristic
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—41no—
94C2×C4×C11#12012yes—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11#12112yes—
97C2×C4×C11#12711yescharacteristic
98C2×C4×C11C2×Q1611yescharacteristic
99C2×C4×C11#13511yescharacteristic
100C2×C4×C11#13712yes—
101C2×Dic11—22no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108Dic22—24no—
109Dic22—42no—
110Dic22—44no—
111Dic22—42no—
112Dic22—42no—
113C8×C11—44no—
114C8×C11—42no—
115C11⋊C8—42no—
116#533—112no—
117C2×C4×Q8—111no—
118#479—224no—
119#477—222no—
120#477—222no—
121#475—222no—
122#467—222no—
123#462—222no—
124#428—222no—
125#423C2×D1112yes—
126C2×C4⋊C8C2×D1111yescharacteristic
127#419—222no—
128C2×C4×C8—111no—
129#336—222no—
130Q8⋊C8—224no—
131C22×C11—21no—
132C22×C11—21no—
133C22×C11#39211yescharacteristic
134C22×C11#46711yescharacteristic
135C22×C11#47011yescharacteristic
136C4×C11—21no—
137C4×C11—22no—
138C4×C11#45112yes—
139C4×C11#45212yes—
140C4×C11#45511yescharacteristic
141C4×C11#45611yescharacteristic
142Dic11—42no—
143Dic11—82no—
144Dic11—82no—
145Dic11—81no—
146C22×Q8—111no—
147C2×Q16—222no—
148C2×M16—22no—
149C22×C8—221no—
150C22×C8D4412yes—
151C4⋊Q8—112no—
152C4⋊Q8—112no—
153#125—222no—
154C22⋊Q8—222no—
155C22⋊Q8—222no—
156C4×Q8—222no—
157C4×Q8—222no—
158C4×Q8—222no—
159C4×Q8—222no—
160#117—222no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—221no—
163C2×C42—221no—
164C2×C42C22×D1111yescharacteristic
165#107—224no—
166#107—222no—
167#106—224no—
168C4⋊C8—22no—
169C4⋊C8—22no—
170C4⋊C8D4414yes—
171#103—224no—
172#103—224no—
173#103—224no—
174C4×C8—222no—
175C2×C11—21no—
176C2×C11—21no—
177C2×C11#200111yescharacteristic
178C2×C11#200711yescharacteristic
179C2×C11#201711yescharacteristic
180C2×Q8—112no—
181C2×Q8—221no—
182C2×Q8—222no—
183C2×Q8—222no—
184C2×Q8—222no—
185C2×Q8—222no—
186C22×C4—221no—
187C22×C4—221no—
188C22×C4C2×D4411yescharacteristic
189C22×C4D4×D1111yescharacteristic
190C22×C4#434311yescharacteristic
191Q16—882no—
192M16—42no—
193M16—42no—
194C2×C8—22no—
195C2×C8—24no—
196C2×C8—42no—
197C2×C8—222no—
198C2×C8—441no—
199C2×C8—441no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—222no—
203C4⋊C4—222no—
204C4⋊C4—222no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C4⋊C4—442no—
208C22⋊C4—442no—
209C42—441no—
210C42—441no—
211C42—442no—
212C42C2×D4412yes—
213C42D4×D1112yes—
214C11#1025911yescharacteristic, complemented, Sylow
215C23#6694811yescharacteristic
216Q8—224no—
217Q8—444no—
218Q8—442no—
219Q8—442no—
220Q8—442no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—222no—
225C2×C4—441no—
226C2×C4—441no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4#6692711yescharacteristic
232C2×C4#6693511yescharacteristic
233C2×C4#6693512yes—
234C2×C4#6694812yes—
235C2×C4#6696511yescharacteristic
236C2×C4#6696812yes—
237C2×C4Q16×D1111yescharacteristic
238C8—42no—
239C8—44no—
240C8—442no—
241C22—21no—
242C22—21no—
243C22#1062228411yescharacteristic
244C22#1062248111yescharacteristic
245C22#1062250011yescharacteristic
246C4—21no—
247C4—22no—
248C4—442no—
249C4—882no—
250C4—881no—
251C4—882no—
252C4#1062235911yescharacteristic
253C4#1062236511yescharacteristic
254C4#1062239612yes—
255C4#1062242112yes—
256C2—21no—
257C2—21no—
258C2#1306962711yescharacteristic
259C2#1306966511yescharacteristic
260C2#1306972111yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1292D11
hypocenterC11#10259
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
61. C2×Dic22Q16semidirect
214. C11#10259semidirect

Maximal subgroups

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

subgroupindex
#130799612
#130784232
#130695512
#130670702
C11×#12922
#1025911