Finite Group Databasebeta

← C2×#13066803 #14674232

Subgroups — C2×#13066803 #14674232

Order 2816.

302 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622137C211yesmaximal, characteristic, complemented
2C2×#10622143C211yesmaximal, characteristic, complemented
3#13066803C214yesmaximal, direct product factor
4C2×C11×#508C211yesmaximal, characteristic
5C2×C11×#135—21no—
6C11×#508—21no—
7C11×#508—21no—
8C11×#508C412yescomplemented
9C11×#508C2212yes—
10C2×C11×Q32C411yescharacteristic, complemented
11C2×C11×SD32—21no—
12C2×C11×D16C411yescharacteristic, complemented
13C22×C11×C16C2211yescharacteristic
14C2×#66882—21no—
15#10622143—21no—
16#10622143C2212yescomplemented
17#10622137—21no—
18#10622137C2212yescomplemented
19C2×C11⋊C32—21no—
20C2×C11×#41—41no—
21C11×#135—22no—
22C11×#135—22no—
23C11×#135—41no—
24C11×#135—41no—
25C2×C11×Q16—21no—
26C2×C11×SD16—41no—
27C2×C11×D8—21no—
28C22×C8×C11D411yescharacteristic
29C2×C4⋊Dic11—41no—
30C11×Q32—21no—
31C11×Q32C2×C412yescomplemented
32C11×SD32—22no—
33C11×SD32—22no—
34C11×D16—21no—
35C11×D16C2×C412yescomplemented
36C2×C11×C16C2×C411yescharacteristic
37C2×C11×C16C2×C411yescharacteristic
38C2×C11×C16D411yescharacteristic
39C2×C11×C16D411yescharacteristic
40C2×C11×C16D411yescharacteristic
41C2×C11×C16C2311yescharacteristic
42#66882—22no—
43#66882—41no—
44C11⋊C32—22no—
45C2×#1418—111nomaximal, Sylow
46C11×#41—42no—
47C11×#41—42no—
48C11×#41—81no—
49C11×#41—81no—
50C2×Q8×C11—41no—
51C2×D4×C11—41no—
52C2×D4×C11—81no—
53C22×C4×C11—81no—
54C22×C4×C11D811yescharacteristic
55C22×Dic11—81no—
56C11×Q16—22no—
57C11×Q16—41no—
58C11×SD16—42no—
59C11×SD16—42no—
60C11×D8—22no—
61C11×D8—41no—
62C2×C8×C11C22⋊C411yescharacteristic
63C2×C8×C11C22⋊C411yescharacteristic
64C2×C8×C11D811yescharacteristic
65C2×C8×C11SD1611yescharacteristic
66C2×C8×C11SD1611yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C4⋊Dic11—42no—
69C4⋊Dic11—81no—
70C11×C16C22⋊C411yescharacteristic
71C11×C16C22⋊C411yescharacteristic
72C11×C16C22×C411yescharacteristic
73C11×C16C2×D411yescharacteristic
74C2×#508D1111yescharacteristic
75C2×M64—111no—
76C2×#367—111no—
77#1418—114no—
78C23×C11—81no—
79C23×C11D1611yescharacteristic
80Q8×C11—42no—
81Q8×C11—81no—
82D4×C11—42no—
83D4×C11—82no—
84D4×C11—82no—
85D4×C11—81no—
86C2×C4×C11—81no—
87C2×C4×C11—82no—
88C2×C4×C11—82no—
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11#10211yescharacteristic
91C2×C4×C11D1611yescharacteristic
92C2×C4×C11SD3211yescharacteristic
93C2×C4×C11SD3211yescharacteristic
94C2×C4×C11C2×D811yescharacteristic
95C2×Dic11—82no—
96C2×Dic11—162no—
97C8×C11#10211yescharacteristic
98C8×C11#10211yescharacteristic
99C8×C11C2×C22⋊C411yescharacteristic
100C8×C11C2×SD1611yescharacteristic
101C2×#135—21no—
102#508—21no—
103#508—21no—
104#508Dic1112yescomplemented
105#508C2×D1112yes—
106C2×Q32Dic1111yescharacteristic, complemented
107C2×SD32—21no—
108C2×D16Dic1111yescharacteristic, complemented
109C22×C16C2×D1111yescharacteristic
110C2×#107—221no—
111M64—112no—
112M64—221no—
113C2×C32—221no—
114#367—112no—
115#367—221no—
116C22×C11—22no—
117C22×C11—82no—
118C22×C11—162no—
119C22×C11#35711yescharacteristic
120C22×C11#35711yescharacteristic
121C22×C11C2×D1611yescharacteristic
122C4×C11—82no—
123C4×C11#35711yescharacteristic
124C4×C11#35711yescharacteristic
125C4×C11C2×#10211yescharacteristic
126C4×C11C2×SD3211yescharacteristic
127Dic11—162no—
128C2×#41—41no—
129#135—22no—
130#135—22no—
131#135—41no—
132#135—41no—
133C2×Q16—21no—
134C2×SD16—41no—
135C2×D8—21no—
136C22×C8C22⋊D1111yescharacteristic
137C2×C4⋊C4—441no—
138Q32—21no—
139Q32C2×Dic1112yescomplemented
140SD32—22no—
141SD32—22no—
142D16—21no—
143D16C2×Dic1112yescomplemented
144C2×C16C2×Dic1111yescharacteristic
145C2×C16C2×Dic1111yescharacteristic
146C2×C16C22⋊D1111yescharacteristic
147C2×C16C22⋊D1111yescharacteristic
148C2×C16C22⋊D1111yescharacteristic
149C2×C16C22×D1111yescharacteristic
150#107—222no—
151#107—441no—
152C32—222no—
153C2×C11—21no—
154C2×C11—21no—
155C2×C11—162no—
156C2×C11#141812yescomplemented
157C2×C11C2×#35711yescharacteristic
158#41—42no—
159#41—42no—
160#41—81no—
161#41—81no—
162C2×Q8—41no—
163C2×D4—41no—
164C2×D4—81no—
165C22×C4—81no—
166C22×C4—881no—
167C22×C4#432311yescharacteristic
168Q16—22no—
169Q16—41no—
170SD16—42no—
171SD16—42no—
172D8—22no—
173D8—41no—
174C2×C8#432311yescharacteristic
175C2×C8#432411yescharacteristic
176C2×C8#432411yescharacteristic
177C2×C8C22⋊Dic1111yescharacteristic
178C2×C8C22⋊Dic1111yescharacteristic
179C2×C8C2×C22⋊D1111yescharacteristic
180C4⋊C4—442no—
181C4⋊C4—881no—
182C16C22⋊Dic1111yescharacteristic
183C16C22⋊Dic1111yescharacteristic
184C16C22×Dic1111yescharacteristic
185C16C2×C22⋊D1111yescharacteristic
186C11C2×#141811yescharacteristic, complemented, Sylow
187C23—81no—
188C23#6689011yescharacteristic
189Q8—42no—
190Q8—81no—
191D4—42no—
192D4—82no—
193D4—82no—
194D4—81no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—82no—
198C2×C4—882no—
199C2×C4—1762no—
200C2×C4#6689011yescharacteristic
201C2×C4#6689111yescharacteristic
202C2×C4#6689111yescharacteristic
203C2×C4#6689611yescharacteristic
204C2×C4#6689611yescharacteristic
205C2×C4C2×#432311yescharacteristic
206C8#6689611yescharacteristic
207C8#6689611yescharacteristic
208C8C2×#432411yescharacteristic
209C8C2×C22⋊Dic1111yescharacteristic
210C22—22no—
211C22—82no—
212C22—162no—
213C22#1062220011yescharacteristic
214C22#1062220011yescharacteristic
215C22C2×#6689011yescharacteristic
216C4—82no—
217C4—1762no—
218C4#1062220011yescharacteristic
219C4#1062220011yescharacteristic
220C4C2×#6689111yescharacteristic
221C4C2×#6689611yescharacteristic
222C2—21no—
223C2—21no—
224C2—162no—
225C2#1306680312yesdirect product factor
226C2C2×#1062220011yescharacteristic
subgroupG/H
centerC22#10622200
commutatorC11×C16C22×C4
FrattiniC2×C16C22×D11
Fitting, prime radicalC2×C11×#508C2
socleC22×C11#357
cosocleC2×C11×C16C23
hypercenterC2×#508D11
hypocenterC11C2×#1418
LCSG ▷ C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#10622137C2semidirect
2. C2×#10622143C2semidirect
3. #13066803C2direct (N × H)
8. C11×#508C4semidirect
10. C2×C11×Q32C4semidirect
12. C2×C11×D16C4semidirect
16. #10622143C22semidirect
18. #10622137C22semidirect
31. C11×Q32C2×C4semidirect
35. C11×D16C2×C4semidirect
104. #508Dic11semidirect
106. C2×Q32Dic11semidirect
108. C2×D16Dic11semidirect
139. Q32C2×Dic11semidirect
143. D16C2×Dic11semidirect
156. C2×C11#1418semidirect
186. C11C2×#1418semidirect
225. C2#13066803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221372
C2×#106221432
#130668032
C2×C11×#5082
C2×#141811