Finite Group Databasebeta

← #14658563

Subgroups — #14658563

Order 2816.

362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069440C211yesmaximal, characteristic
2#13068791C211yesmaximal, characteristic, complemented
3#13067283C212yesmaximal
4#13066475C212yesmaximal, complemented
5C11×#1281C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C11×#431C2212yes—
8C2×C11×#97C2211yescharacteristic
9C2×#66885—21no—
10C2×#66885—21no—
11C2×#66883—21no—
12C2×#66883—21no—
13#10622549C2211yescharacteristic
14#10622537C2212yes—
15#10622123—24no—
16C22×D44—21no—
17C22×D44—22no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11D411yescharacteristic
20C2×C42×C11C2311yescharacteristic
21C2×C4⋊Dic11—21no—
22C2×#4318—22no—
23#66927—22no—
24#66927—21no—
25#66927D412yes—
26C11×C4⋊C8—22no—
27C11×C22⋊C8—22no—
28C11×#97—22no—
29C4×C8×C11—22no—
30C11⋊#95—22no—
31#66885—42no—
32#66885—42no—
33#66883—42no—
34#66883—42no—
35C4⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37#10631—111nomaximal, Sylow
38C23×D11—41no—
39C22×C4×C11C2×D411yescharacteristic
40C22×C4×C11#4112yes—
41C22×Dic11—41no—
42C2×D44—22no—
43C2×D44—24no—
44C2×D44—41no—
45C2×D44—42no—
46C2×D44—41no—
47C2×D44—41no—
48C2×D44—41no—
49C2×D44—41no—
50C2×D44—84no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11—42no—
56C2×C8×C11D812yes—
57C2×C8×C11SD1612yes—
58C42×C11C2×D411yescharacteristic
59C42×C11#4111yescharacteristic
60C42×C11#4112yes—
61C4⋊Dic11—41no—
62C4⋊Dic11—41no—
63#4318—42no—
64#4318—42no—
65C2×C11⋊C8—42no—
66#1961—111no—
67#1849—111no—
68#1545—112no—
69#1286—112no—
70#1281D1111yescharacteristic, complemented
71C23×C11#12411yescharacteristic
72C22×D11—42no—
73C22×D11—84no—
74C22×D11—81no—
75C22×D11—81no—
76C2×C4×C11—42no—
77C2×C4×C11#12111yescharacteristic
78C2×C4×C11#12312yes—
79C2×C4×C11#12311yescharacteristic
80C2×C4×C11#12612yes—
81C2×C4×C11C2×D811yescharacteristic
82C2×C4×C11C2×SD1611yescharacteristic
83C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
84C2×C4×C11#13711yescharacteristic
85C2×Dic11—82no—
86C2×Dic11—81no—
87D44—42no—
88D44—42no—
89D44—84no—
90D44—84no—
91D44—81no—
92D44—81no—
93C8×C11—22no—
94C8×C11—22no—
95C8×C11—82no—
96C11⋊C8—82no—
97C2×#127—111no—
98#431C2×D1112yes—
99C2×#108—221no—
100C2×#108—221no—
101#423—112no—
102C2×#102—221no—
103C2×#102—221no—
104C2×#97C2×D1111yescharacteristic
105#382—111no—
106#331—224no—
107C22×C11—22no—
108C22×C11#39711yescharacteristic
109C22×C11#48611yescharacteristic
110C22×C11#48911yescharacteristic
111C2×D11—82no—
112C2×D11—84no—
113C2×D11—162no—
114C2×D11—162no—
115C4×C11—22no—
116C4×C11—22no—
117C4×C11#45911yescharacteristic
118C4×C11#46111yescharacteristic
119C4×C11#48011yescharacteristic
120C4×C11#48111yescharacteristic
121Dic11—161no—
122C22×D4—221no—
123C22×D4—222no—
124C2×M16—222no—
125C22×C8D4411yescharacteristic
126C22×C8D4411yescharacteristic
127#127—112no—
128#127—222no—
129#127—221no—
130C2×C4⋊C4—221no—
131C2×C42C22×D1111yescharacteristic
132#108—442no—
133#108—442no—
134C4⋊C8—22no—
135C4⋊C8—222no—
136C4⋊C8—222no—
137#102—442no—
138#102—442no—
139C22⋊C8—22no—
140#97—22no—
141C4×C8—22no—
142#95—222no—
143C2×C11—21no—
144C2×C11—21no—
145C2×C11#207111yescharacteristic
146C2×C11#208112yes—
147D11—162no—
148C24—441no—
149C2×D4—224no—
150C2×D4—222no—
151C2×D4—441no—
152C2×D4—442no—
153C2×D4—441no—
154C2×D4—441no—
155C2×D4—441no—
156C2×D4—441no—
157C2×D4—884no—
158C22×C4—441no—
159C22×C4C2×D4411yescharacteristic
160C22×C4#433912yes—
161M16—442no—
162M16—442no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—42no—
168C2×C8—442no—
169C2×C8#431412yes—
170C2×C8D8812yes—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C42D4×D1111yescharacteristic
174C42#434112yes—
175C42#434311yescharacteristic
176C11#1063111yescharacteristic, complemented, Sylow
177C23—442no—
178C23—884no—
179C23—881no—
180C23—881no—
181C23#6692811yescharacteristic
182D4—442no—
183D4—442no—
184D4—884no—
185D4—884no—
186D4—881no—
187D4—881no—
188C2×C4—42no—
189C2×C4—882no—
190C2×C4—881no—
191C2×C4#6693612yes—
192C2×C4#6693911yescharacteristic
193C2×C4#6694811yescharacteristic
194C2×C4#6695112yes—
195C2×C4C2×#431411yescharacteristic
196C2×C4C2×D8811yescharacteristic
197C2×C4#6696111yescharacteristic
198C2×C4#6696211yescharacteristic
199C8—22no—
200C8—22no—
201C8—82no—
202C8—882no—
203C22—22no—
204C22—882no—
205C22—884no—
206C22—1762no—
207C22—1762no—
208C22#1062228711yescharacteristic
209C22#1062230711yescharacteristic
210C22#1062232711yescharacteristic
211C4—22no—
212C4—22no—
213C4—1761no—
214C4#1062234811yescharacteristic
215C4#1062234911yescharacteristic
216C4#1062245411yescharacteristic
217C4#1062245611yescharacteristic
218C2—21no—
219C2—21no—
220C2—1762no—
221C2#1307002111yescharacteristic
222C2#1307007512yes—
subgroupG/H
centerC22#10622287
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1281C2
socleC22×C11#397
prime radicalC2×#66927C22
hypercenter#1281D11
hypocenterC11#10631
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
2. #13068791C2semidirect
4. #13066475C2semidirect
5. C11×#1281C2semidirect
70. #1281D11semidirect
176. C11#10631semidirect

Maximal subgroups

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

subgroupindex
#130694402
#130687912
#130672832
#130664752
C11×#12812
#1063111