Finite Group Databasebeta

← #14656272

Subgroups — #14656272

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#13078417C212yesmaximal
2#13069551C211yesmaximal, characteristic
3#13067071C212yesmaximal
4#13066491C211yesmaximal, characteristic
5C11×#3249C211yesmaximal, characteristic
6C11×#533C2212yes—
7C2×C4×Dic22C2211yescharacteristic
8C11×#477—22no—
9C11×#467—22no—
10C11×#462—22no—
11C2×C11×C4⋊C8C2211yescharacteristic
12#10622707—22no—
13#10622704—22no—
14#10622676—24no—
15#10622617—22no—
16#10622608—22no—
17#10622537C2212yes—
18C2×C4×C11⋊C8C2211yescharacteristic
19#10622188—22no—
20Q8⋊(C11⋊C8)—24no—
21C22×Dic22D411yescharacteristic
22C2×C11×Q16—22no—
23C22×C8×C11D412yes—
24C11×C4⋊Q8D412yes—
25C11×C4⋊Q8D412yes—
26C11×#125—22no—
27C11×C22⋊Q8—22no—
28C11×C22⋊Q8—22no—
29C4×Q8×C11—22no—
30C4×Q8×C11—22no—
31C11×#117—22no—
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11D411yescharacteristic
34C2×Dic11⋊C4—21no—
35C2×C4×Dic11—21no—
36C2×#4318—22no—
37C22×C11⋊C8—21no—
38C4×Dic22—22no—
39C4×Dic22—22no—
40C11×#107—22no—
41C11×C4⋊C8—22no—
42C11×#103—24no—
43#66874—24no—
44#66874—24no—
45#66872—24no—
46#66871—24no—
47C4⋊(C11⋊C8)—22no—
48C4⋊(C11⋊C8)D414yes—
49C4×C11⋊C8—22no—
50#10259—111nomaximal, Sylow
51C2×Q8×C11—22no—
52C2×Q8×C11—22no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×Dic11—21no—
57C22×Dic11—21no—
58C2×Dic22—22no—
59C2×Dic22—21no—
60C2×Dic22—22no—
61C2×Dic22Q1612yescomplemented
62C11×Q16—82no—
63C2×C8×C11—22no—
64C2×C8×C11—42no—
65C11×C4⋊C4—22no—
66C11×C4⋊C4—22no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—22no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C22⋊C4—42no—
72C42×C11—42no—
73C42×C11C2×D412yes—
74C42×C11C2×D412yes—
75C4⋊Dic11—22no—
76Dic11⋊C4—42no—
77C4×Dic11—41no—
78C4×Dic11—41no—
79#4318—42no—
80#4318—42no—
81C2×C11⋊C8—22no—
82C2×C11⋊C8—24no—
83C2×C11⋊C8—41no—
84C2×C11⋊C8—41no—
85#3249D1111yescharacteristic
86#3078—112no—
87#1984—111no—
88#1493—112no—
89#1292—111no—
90C23×C11#12111yescharacteristic
91Q8×C11—44no—
92Q8×C11—42no—
93Q8×C11—42no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—41no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11#12012yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12112yes—
102C2×C4×C11#12711yescharacteristic
103C2×C4×C11C2×Q1611yescharacteristic
104C2×C4×C11#13511yescharacteristic
105C2×C4×C11#13712yes—
106C2×Dic11—22no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109C2×Dic11—42no—
110C2×Dic11—41no—
111Dic22—24no—
112Dic22—42no—
113C8×C11—42no—
114C11⋊C8—42no—
115C11⋊C8—44no—
116#533C2×D1112yes—
117C2×C4×Q8—111no—
118#479—224no—
119#477—22no—
120#477—222no—
121#475—222no—
122#467—22no—
123#462—22no—
124#428—222no—
125#423—112no—
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—82no—
139C4×C11—82no—
140C4×C11#45112yes—
141C4×C11#45212yes—
142C4×C11#45511yescharacteristic
143C4×C11#45611yescharacteristic
144Dic11—42no—
145Dic11—81no—
146C22×Q8—111no—
147C2×Q16—22no—
148C2×M16—222no—
149C22×C8—221no—
150C22×C8C22⋊D1112yes—
151C4⋊Q8C22⋊D1112yes—
152C4⋊Q8C22⋊D1112yes—
153#125—22no—
154C22⋊Q8—22no—
155C22⋊Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—222no—
159C4×Q8—222no—
160#117—22no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—221no—
163C2×C42—221no—
164C2×C42C22×D1111yescharacteristic
165#107—22no—
166#107—224no—
167#106—224no—
168C4⋊C8—22no—
169C4⋊C8—114no—
170C4⋊C8—222no—
171#103—24no—
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—22no—
181C2×Q8—22no—
182C2×Q8—112no—
183C2×Q8—221no—
184C2×Q8—222no—
185C2×Q8—222no—
186C22×C4—221no—
187C22×C4—221no—
188C22×C4D4×D1111yescharacteristic
189C22×C4#434111yescharacteristic
190C22×C4C2×C22⋊D1111yescharacteristic
191Q16—82no—
192M16—442no—
193M16—442no—
194C2×C8—22no—
195C2×C8—42no—
196C2×C8—222no—
197C2×C8—224no—
198C2×C8—441no—
199C2×C8—441no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—222no—
207C4⋊C4—442no—
208C22⋊C4—42no—
209C42—42no—
210C42—441no—
211C42—441no—
212C42D4×D1112yes—
213C42C2×C22⋊D1112yes—
214C11#1025911yescharacteristic, complemented, Sylow
215C23#6699111yescharacteristic
216Q8—44no—
217Q8—42no—
218Q8—42no—
219Q8—224no—
220Q8—442no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—222no—
227C2×C4—441no—
228C2×C4—441no—
229C2×C4—442no—
230C2×C4—441no—
231C2×C4Q16×D1111yescharacteristic
232C2×C4#6697112yes—
233C2×C4#6697211yescharacteristic
234C2×C4#6699012yes—
235C2×C4#6699212yes—
236C2×C4#6699311yescharacteristic
237C2×C4#6700611yescharacteristic
238C8—42no—
239C8—442no—
240C8—444no—
241C22—21no—
242C22—21no—
243C22#1062280111yescharacteristic
244C22#1062280211yescharacteristic
245C22#1062283611yescharacteristic
246C4—21no—
247C4—22no—
248C4—82no—
249C4—82no—
250C4—442no—
251C4—881no—
252C4#1062279912yes—
253C4#1062280012yes—
254C4#1062285511yescharacteristic
255C4#1062285911yescharacteristic
256C2—21no—
257C2—21no—
258C2#1306962311yescharacteristic
259C2#1306966311yescharacteristic
260C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3249C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3249D11
hypocenterC11#10259
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

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
#130784172
#130695512
#130670712
#130664912
C11×#32492
#1025911