Finite Group Databasebeta

← #14658562

Subgroups — #14658562

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#13067285C212yesmaximal
3#13066476C212yesmaximal, complemented
4#13066461C211yesmaximal, characteristic, complemented
5C11×#1849C211yesmaximal, characteristic, complemented
6C2×#66927C2211yescharacteristic
7C2×C11×#108—21no—
8C2×C11×#108—21no—
9C11×#423C2212yes—
10C2×C11×#97C2211yescharacteristic
11C2×#66885—21no—
12C2×#66885—21no—
13#10622549C2211yescharacteristic
14#10622538C2212yes—
15#10622123—24no—
16C22×D44—21no—
17C22×D44—22no—
18C2×C11×M16—22no—
19C22×C8×C11D411yescharacteristic
20C22×C8×C11D411yescharacteristic
21C2×C42×C11C2311yescharacteristic
22C2×C4⋊Dic11—21no—
23#66927—22no—
24#66927—21no—
25#66927D412yes—
26C11×#108—42no—
27C11×#108—42no—
28C11×C4⋊C8—22no—
29C11×C4⋊C8—22no—
30C11×#97—22no—
31C11⋊#95—22no—
32C22⋊(C11⋊C8)—22no—
33#66885—42no—
34#66885—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—
51C11×M16—42no—
52C11×M16—42no—
53C2×C8×C11—21no—
54C2×C8×C11—21no—
55C2×C8×C11—21no—
56C2×C8×C11—21no—
57C2×C8×C11—42no—
58C2×C8×C11D812yes—
59C2×C8×C11SD1612yes—
60C42×C11C2×D411yescharacteristic
61C42×C11#4111yescharacteristic
62C42×C11#4112yes—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C2×C11⋊C8—42no—
66#1961—111no—
67#1849D1111yescharacteristic, complemented
68#1545—112no—
69#1286—112no—
70#1281—111no—
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#431—112no—
99C2×#108—21no—
100C2×#108—21no—
101#423C2×D1112yes—
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—222no—
123C22×D4—221no—
124C2×M16—22no—
125C22×C8C22⋊D1111yescharacteristic
126C22×C8C22⋊D1111yescharacteristic
127#127—112no—
128#127—222no—
129#127—221no—
130C2×C4⋊C4—221no—
131C2×C42C22×D1111yescharacteristic
132#108—42no—
133#108—42no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—222no—
137#102—442no—
138#102—442no—
139C22⋊C8—222no—
140#97—22no—
141C4×C8—222no—
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—442no—
152C2×D4—441no—
153C2×D4—441no—
154C2×D4—441no—
155C2×D4—441no—
156C2×D4—441no—
157C2×D4—884no—
158C22×C4—441no—
159C22×C4#434312yes—
160C22×C4C2×C22⋊D1111yescharacteristic
161M16—42no—
162M16—42no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—42no—
168C2×C8—442no—
169C2×C8#432312yes—
170C2×C8#432512yes—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C42#433912yes—
174C42D4×D1111yescharacteristic
175C42#434111yescharacteristic
176C11#1063111yescharacteristic, complemented, Sylow
177C23—442no—
178C23—884no—
179C23—881no—
180C23—881no—
181C23#6700011yescharacteristic
182D4—442no—
183D4—442no—
184D4—884no—
185D4—884no—
186D4—881no—
187D4—881no—
188C2×C4—42no—
189C2×C4—882no—
190C2×C4—881no—
191C2×C4#6694712yes—
192C2×C4#6695112yes—
193C2×C4#6698211yescharacteristic
194C2×C4C2×#432311yescharacteristic
195C2×C4#6698511yescharacteristic
196C2×C4#6699111yescharacteristic
197C2×C4C2×#432511yescharacteristic
198C2×C4#6699511yescharacteristic
199C8—22no—
200C8—22no—
201C8—82no—
202C8—882no—
203C22—22no—
204C22—882no—
205C22—884no—
206C22—1762no—
207C22—1762no—
208C22#1062260611yescharacteristic
209C22#1062270111yescharacteristic
210C22#1062270211yescharacteristic
211C4—22no—
212C4—22no—
213C4—1761no—
214C4#1062258011yescharacteristic
215C4#1062258111yescharacteristic
216C4#1062268511yescharacteristic
217C4#1062269611yescharacteristic
218C2—21no—
219C2—21no—
220C2—1762no—
221C2#1307002011yescharacteristic
222C2#1307007412yes—
subgroupG/H
centerC22#10622606
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1849C2
socleC22×C11#397
prime radicalC2×#66927C22
hypercenter#1849D11
hypocenterC11#10631
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

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

NH ≅ G/Ntype
3. #13066476C2semidirect
4. #13066461C2semidirect
5. C11×#1849C2semidirect
67. #1849D11semidirect
176. C11#10631semidirect

Maximal subgroups

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

subgroupindex
#130694402
#130672852
#130664762
#130664612
C11×#18492
#1063111