Finite Group Databasebeta

← #14673872

Subgroups — #14673872

Order 2816.

346 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10622151C212yesmaximal, complemented
2C2×#10622156C212yesmaximal
3#13069504C211yesmaximal, characteristic
4#13068773C211yesmaximal, characteristic, complemented
5C11×#1376C211yesmaximal, characteristic, complemented
6C2×#66957C2211yescharacteristic
7C2×C11×M32C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622723—21no—
10C2×#66883C2211yescharacteristic
11C2×#66881—21no—
12C2×#66881C2212yes—
13#10622548—21no—
14C2×#66869—21no—
15#10622156—24no—
16#10622151—24no—
17C2×#4339—21no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11C2311yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C4⋊Dic11—22no—
22C2×C4⋊Dic11—42no—
23C2×#4318—21no—
24C2×Dic44Q811yescharacteristic
25#66957—22no—
26#66957—22no—
27C2×D88Q811yescharacteristic
28C2×#4314—21no—
29C11×M32—22no—
30C11×M32D414yes—
31C2×C11×C16—22no—
32C4×C8×C11—22no—
33(C2×D11)⋊C8—42no—
34#66883—22no—
35#66881—22no—
36#66881—22no—
37#66881—42no—
38#66869—42no—
39#13533—111nomaximal, Sylow
40C22×C4×C11—21no—
41C22×C4×C11C2×D411yescharacteristic
42C2×C22⋊D11—41no—
43C22×Dic11—42no—
44#4339—41no—
45#4339—41no—
46#4339—41no—
47#4339—41no—
48C2×D44—21no—
49C2×C4×D11—41no—
50C2×Dic22—21no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11SD1612yes—
54C2×C8×C11C2×D412yes—
55C2×C8×C11C2×Q811yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C2×C8×C11#4112yes—
58C42×C11—21no—
59C42×C11SD1612yes—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62C4⋊Dic11—84no—
63#4318—41no—
64#4318—41no—
65C2×C11⋊C8—41no—
66Dic44—22no—
67D88—22no—
68#4314—42no—
69C11×C16—24no—
70C2×#365—112no—
71C2×#360—112no—
72#1974—111no—
73#1844—111no—
74#1376D1111yescharacteristic, complemented
75C23×C11AGL(1,ℤ/8)11yescharacteristic
76C22×D11—41no—
77C2×C4×C11—24no—
78C2×C4×C11—22no—
79C2×C4×C11C22⋊Q811yescharacteristic
80C2×C4×C11#12311yescharacteristic
81C2×C4×C11#12711yescharacteristic
82C2×C4×C11C2×SD1611yescharacteristic
83C2×C4×C11C2×SD1611yescharacteristic
84C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
85C22⋊D11—81no—
86C22⋊D11—81no—
87C2×Dic11—41no—
88C2×Dic11—84no—
89C2×Dic11—82no—
90D44—41no—
91D44—41no—
92C4×D11—81no—
93C4×D11—81no—
94Dic22—41no—
95Dic22—41no—
96C8×C11—22no—
97C8×C11C22⋊Q812yes—
98C8×C11#12312yes—
99C11⋊C8—81no—
100C2×#135—111no—
101C2×M32C2×D1112yes—
102C2×#108—111no—
103C2×#106—112no—
104C2×#106—221no—
105C2×#104—221no—
106#408—221no—
107C2×C4×C8C2×D1111yescharacteristic
108#384—221no—
109#365—224no—
110#360—224no—
111C22×C11—22no—
112C22×C11#47611yescharacteristic
113C22×C11#48111yescharacteristic
114C22×C11#49611yescharacteristic
115C2×D11—81no—
116C2×D11—82no—
117C4×C11—24no—
118C4×C11#39911yescharacteristic
119C4×C11#47611yescharacteristic
120C4×C11#48111yescharacteristic
121C4×C11#49211yescharacteristic
122Dic11—81no—
123Dic11—162no—
124C2×#41—221no—
125#135—222no—
126#135—222no—
127C2×Q16—111no—
128C2×SD16—221no—
129C2×D8—111no—
130C2×M16—221no—
131C22×C8D4411yescharacteristic
132C22×C8C22×D1111yescharacteristic
133C2×C4⋊C4—222no—
134C2×C4⋊C4—442no—
135C2×C42D4411yescharacteristic
136M32—22no—
137M32D4414yes—
138C2×C16—22no—
139#108—222no—
140#106—222no—
141#106—222no—
142#106—442no—
143#104—442no—
144C22⋊C8—442no—
145C4×C8—22no—
146C2×C11—21no—
147C2×C11—21no—
148C2×C11#209411yescharacteristic
149C2×C11#223012yes—
150D11—161no—
151#41—441no—
152#41—441no—
153#41—441no—
154#41—441no—
155C2×Q8—221no—
156C2×D4—221no—
157C2×D4—441no—
158C22×C4—21no—
159C22×C4—441no—
160C22×C4—442no—
161C22×C4C2×D4411yescharacteristic
162Q16—222no—
163SD16—442no—
164D8—222no—
165M16—441no—
166M16—441no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—441no—
170C2×C8#431412yes—
171C2×C8C2×D4412yes—
172C2×C8#434111yescharacteristic
173C2×C8#434112yes—
174C2×C8Q8×D1111yescharacteristic
175C4⋊C4—442no—
176C4⋊C4—442no—
177C4⋊C4—884no—
178C42—21no—
179C42#431412yes—
180C16—24no—
181C11#1353311yescharacteristic, complemented, Sylow
182C23—441no—
183C23#6696111yescharacteristic
184Q8—441no—
185Q8—441no—
186D4—441no—
187D4—441no—
188D4—881no—
189D4—881no—
190C2×C4—24no—
191C2×C4—22no—
192C2×C4—441no—
193C2×C4—881no—
194C2×C4—881no—
195C2×C4—884no—
196C2×C4—882no—
197C2×C4#6692711yescharacteristic
198C2×C4#6693911yescharacteristic
199C2×C4#6695011yescharacteristic
200C2×C4C2×#431411yescharacteristic
201C2×C4C2×#431411yescharacteristic
202C2×C4#6696111yescharacteristic
203C8—22no—
204C8—881no—
205C8#6693912yes—
206C8#6695012yes—
207C22—22no—
208C22—881no—
209C22—882no—
210C22#1062232511yescharacteristic
211C22#1062234811yescharacteristic
212C22#1062245511yescharacteristic
213C4—24no—
214C4—881no—
215C4—1762no—
216C4#1062229011yescharacteristic
217C4#1062230611yescharacteristic
218C4#1062234811yescharacteristic
219C4#1062245511yescharacteristic
220C2—21no—
221C2—21no—
222C2—1761no—
223C2#1307014811yescharacteristic
224C2#1307078812yes—
subgroupG/H
centerC22#10622455
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11#476
prime radicalC2×#66957C22
hypercenter#1376D11
hypocenterC11#13533
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
1. C2×#10622151C2semidirect
4. #13068773C2semidirect
5. C11×#1376C2semidirect
74. #1376D11semidirect
181. C11#13533semidirect

Maximal subgroups

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

subgroupindex
C2×#106221512
C2×#106221562
#130695042
#130687732
C11×#13762
#1353311