Finite Group Databasebeta

← #14668041

Subgroups — #14668041

Order 2816.

232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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#13070872C211yesmaximal, characteristic
2C16×Dic22C211yesmaximal, characteristic, complemented
3#13067987C211yesmaximal, characteristic, complemented
4#13067977C211yesmaximal, characteristic
5#13066664C211yesmaximal, characteristic, complemented
6#13066661C211yesmaximal, characteristic
7C11×#1372C211yesmaximal, characteristic, complemented
8C2×#66864—21no—
9C2×#66864—21no—
10#10622464—21no—
11#10622461—21no—
12#10622312C2211yescharacteristic
13#10622308C2211yescharacteristic
14C8×Dic22C2211yescharacteristic
15C4×C11×C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17C11×#335C2211yescharacteristic
18Dic11⋊C16—21no—
19C16×Dic11—21no—
20#10622124—21no—
21#10622123—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C2×Dic44—21no—
24C2×Dic44—21no—
25C2×D88—21no—
26C2×D88—21no—
27C2×#4314—41no—
28#66927—21no—
29#66922—21no—
30C4×Dic22D411yescharacteristic
31C2×C11×C16D411yescharacteristic
32C2×C11×C16D411yescharacteristic
33C11×C4⋊C8—21no—
34C11×C4⋊C8—21no—
35C4×C8×C11C2311yescharacteristic
36#66885—41no—
37#66881—41no—
38#66880—41no—
39Dic11⋊C8—21no—
40C8×Dic11—21no—
41C2×C11⋊C16—21no—
42C4⋊(C11⋊C8)D411yescharacteristic
43#66864—42no—
44#66864—42no—
45#12441—111nomaximal, Sylow
46C2×D44—41no—
47C2×D44—41no—
48C2×D44—41no—
49C2×Dic22—41no—
50C2×Dic22D811yescharacteristic
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C42×C11C2×D411yescharacteristic
56C4⋊Dic11—41no—
57C4⋊Dic11—41no—
58C4⋊Dic11D811yescharacteristic
59Dic11⋊C4—21no—
60C4×Dic11—21no—
61C2×C11⋊C8—21no—
62Dic44—41no—
63Dic44—41no—
64Dic44—81no—
65D88—41no—
66D88—41no—
67D88—81no—
68#4314—82no—
69C11×C16—21no—
70C11×C16SD1612yescomplemented
71C11⋊C16—41no—
72#2248—111no—
73Q8×C16—111no—
74#1670—111no—
75#1668—111no—
76#1372D1111yescharacteristic, complemented
77#1362—111no—
78#1361—111no—
79C22×D11—81no—
80C2×C4×C11#12111yescharacteristic
81C2×C4×C11C2×D811yescharacteristic
82C2×C4×C11#13511yescharacteristic
83C2×Dic11—21no—
84C2×Dic11—21no—
85C2×Dic11—81no—
86D44—81no—
87D44—81no—
88D44—81no—
89D44—81no—
90D44—161no—
91Dic22—21no—
92Dic22—81no—
93Dic22—81no—
94Dic22SD3212yescomplemented
95C8×C11—21no—
96C8×C11—81no—
97C8×C11—81no—
98C8×C11C2×SD1611yescharacteristic
99C8×C11AGL(1,ℤ/8)11yescharacteristic
100C11⋊C8—41no—
101C2×SD32—221no—
102C2×SD32—221no—
103#494—111no—
104#493—111no—
105#475—221no—
106#460—221no—
107C8×Q8—111no—
108C4⋊C16—111no—
109C4⋊C16—221no—
110C4×C16—221no—
111C4×C16C2×D1111yescharacteristic
112#335C2×D1111yescharacteristic
113#335C2×D1111yescharacteristic
114#332—221no—
115#331—221no—
116C22×C11#46611yescharacteristic
117C2×D11—161no—
118C2×D11—161no—
119C2×D11—161no—
120C4×C11—21no—
121C4×C11#46011yescharacteristic
122C4×C11#47211yescharacteristic
123C4×C11C2×SD3211yescharacteristic
124C4×C11#50811yescharacteristic
125Dic11—22no—
126Dic11—41no—
127Dic11—161no—
128C2×Q16—221no—
129C2×Q16—221no—
130C2×SD16—441no—
131C2×D8—221no—
132C2×D8—221no—
133C4⋊Q8—221no—
134#127—221no—
135C4×Q8—111no—
136SD32—442no—
137SD32—442no—
138C2×C16—221no—
139C2×C16D4411yescharacteristic
140C2×C16D4411yescharacteristic
141#106—441no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—111no—
145C4⋊C8—221no—
146#103—441no—
147#102—441no—
148C4×C8—221no—
149C4×C8C22×D1111yescharacteristic
150C2×C11#166811yescharacteristic
151C2×C11#221711yescharacteristic
152C2×C11#222311yescharacteristic
153D11—321no—
154C2×Q8—111no—
155C2×Q8—441no—
156C2×D4—441no—
157C2×D4—441no—
158C2×D4—441no—
159Q16—441no—
160Q16—441no—
161Q16—881no—
162SD16—882no—
163D8—441no—
164D8—441no—
165D8—881no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—221no—
169C2×C8C2×D4411yescharacteristic
170C2×C8#434311yescharacteristic
171C4⋊C4—111no—
172C4⋊C4—221no—
173C4⋊C4—441no—
174C4⋊C4—441no—
175C42—221no—
176C42D4×D1111yescharacteristic
177C16—21no—
178C16—441no—
179C16#431412yescomplemented
180C11#1244111yescharacteristic, complemented, Sylow
181C23—881no—
182Q8—112no—
183Q8—221no—
184Q8—881no—
185Q8—881no—
186D4—881no—
187D4—881no—
188D4—881no—
189D4—881no—
190D4—1761no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—881no—
194C2×C4#6694811yescharacteristic
195C2×C4D8×D1111yescharacteristic
196C2×C4#6697211yescharacteristic
197C8—21no—
198C8—81no—
199C8—81no—
200C8—441no—
201C8C2×#431411yescharacteristic
202C8#6696111yescharacteristic
203C22—1761no—
204C22—1761no—
205C22—1761no—
206C22#1062249611yescharacteristic
207C4—21no—
208C4—222no—
209C4—441no—
210C4—1761no—
211C4#1062246111yescharacteristic
212C4#1062251011yescharacteristic
213C4D11×SD3211yescharacteristic
214C4#1062252911yescharacteristic
215C2—3521no—
216C2#1306797711yescharacteristic
217C2#1307071311yescharacteristic
218C2#1307074711yescharacteristic
subgroupG/H
centerC22#10622496
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1372C2
socleC22×C11#466
prime radical#10622308C22
hypercenter#1372D11
hypocenterC11#12441
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
2. C16×Dic22C2semidirect
3. #13067987C2semidirect
5. #13066664C2semidirect
7. C11×#1372C2semidirect
70. C11×C16SD16semidirect
76. #1372D11semidirect
94. Dic22SD32semidirect
179. C16#4314semidirect
180. C11#12441semidirect

Maximal subgroups

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

subgroupindex
#130708722
C16×Dic222
#130679872
#130679772
#130666642
#130666612
C11×#13722
#1244111