Finite Group Databasebeta

← #14668039

Subgroups — #14668039

Order 2816.

232 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 65 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#13070871C211yesmaximal, characteristic
2#13070518C211yesmaximal, characteristic, complemented
3#13067987C211yesmaximal, characteristic, complemented
4#13067973C211yesmaximal, characteristic
5#13066689C211yesmaximal, characteristic, complemented
6#13066666C211yesmaximal, characteristic, complemented
7C11×#1361C211yesmaximal, characteristic
8C11×#493C2211yescharacteristic
9C2×#66891—21no—
10C2×#66891—21no—
11#10622688—21no—
12#10622464—21no—
13#10622312C2211yescharacteristic
14C8×Dic22C2211yescharacteristic
15C11×C4⋊C16C2211yescharacteristic
16C11×#335C2211yescharacteristic
17#10622182—21no—
18Dic11⋊C16—21no—
19C16×Dic11—21no—
20#10622124—21no—
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×D8—21no—
24C2×C11×D8—21no—
25C11×#127—21no—
26C2×#4324—41no—
27C2×Dic44—21no—
28C2×Dic44—21no—
29#66922—21no—
30C4×Dic22D411yescharacteristic
31C2×C11×C16—21no—
32C11×C4⋊C8—21no—
33C4×C8×C11C2311yescharacteristic
34#66896—41no—
35#66891—42no—
36#66891—42no—
37#66881—41no—
38#66880—41no—
39Dic11⋊C8—21no—
40C8×Dic11—21no—
41C2×C11⋊C16D411yescharacteristic
42C2×C11⋊C16D411yescharacteristic
43C4⋊(C11⋊C8)—21no—
44C4⋊(C11⋊C8)D411yescharacteristic
45#12441—111nomaximal, Sylow
46C2×D4×C11—41no—
47C2×D4×C11—41no—
48C2×D4×C11—41no—
49C2×Dic22—41no—
50C2×Dic22D811yescharacteristic
51C11×D8—41no—
52C11×D8—41no—
53C11×D8—81no—
54C2×C8×C11—41no—
55C2×C8×C11C2×D411yescharacteristic
56C2×C8×C11#4111yescharacteristic
57C42×C11C2×D411yescharacteristic
58#4324—82no—
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61C4⋊Dic11D811yescharacteristic
62Dic11⋊C4—21no—
63C4×Dic11—21no—
64C2×C11⋊C8—21no—
65C2×C11⋊C8—41no—
66Dic44—41no—
67Dic44—41no—
68Dic44—81no—
69C11×C16—41no—
70C11⋊C16—21no—
71C11⋊C16SD1612yescomplemented
72#2248—111no—
73Q8×C16—111no—
74#1670—111no—
75#1668—111no—
76#1372—111no—
77#1362—111no—
78#1361D1111yescharacteristic
79C23×C11—81no—
80D4×C11—81no—
81D4×C11—81no—
82D4×C11—81no—
83D4×C11—81no—
84D4×C11—161no—
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11C2×D811yescharacteristic
87C2×C4×C11#13511yescharacteristic
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—81no—
91Dic22—21no—
92Dic22—81no—
93Dic22—81no—
94Dic22SD3212yescomplemented
95C8×C11—21no—
96C8×C11—81no—
97C8×C11C2×SD1611yescharacteristic
98C8×C11AGL(1,ℤ/8)11yescharacteristic
99C11⋊C8—41no—
100C11⋊C8—81no—
101C2×SD32—221no—
102C2×SD32—221no—
103#494—111no—
104#493C2×D1111yescharacteristic
105#475—221no—
106#460—221no—
107C8×Q8—111no—
108C4⋊C16—221no—
109C4⋊C16C2×D1111yescharacteristic
110C4×C16—111no—
111C4×C16—221no—
112#335—111no—
113#335C2×D1111yescharacteristic
114#332—221no—
115#331—221no—
116C22×C11—161no—
117C22×C11—161no—
118C22×C11—161no—
119C22×C11#46611yescharacteristic
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—21no—
132C2×D8—21no—
133C4⋊Q8—221no—
134#127—21no—
135C4×Q8—111no—
136SD32—442no—
137SD32—442no—
138C2×C16—21no—
139C2×C16—111no—
140C2×C16—111no—
141#106—441no—
142C4⋊C8—21no—
143C4⋊C8—111no—
144C4⋊C8—221no—
145C4⋊C8—221no—
146#103—441no—
147#102—441no—
148C4×C8—221no—
149C4×C8C22×D1111yescharacteristic
150C2×C11—321no—
151C2×C11#166811yescharacteristic
152C2×C11#221711yescharacteristic
153C2×C11#222311yescharacteristic
154C2×Q8—111no—
155C2×Q8—441no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—441no—
160Q16—441no—
161Q16—881no—
162SD16—882no—
163D8—41no—
164D8—41no—
165D8—81no—
166C2×C8—41no—
167C2×C8—221no—
168C2×C8—441no—
169C2×C8#433911yescharacteristic
170C2×C8D4×D1111yescharacteristic
171C4⋊C4—111no—
172C4⋊C4—221no—
173C4⋊C4—441no—
174C4⋊C4—441no—
175C42—221no—
176C42D4×D1111yescharacteristic
177C16—41no—
178C16—112no—
179C16—221no—
180C11#1244111yescharacteristic, complemented, Sylow
181C23—81no—
182Q8—112no—
183Q8—221no—
184Q8—881no—
185Q8—881no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—881no—
194C2×C4#6693711yescharacteristic
195C2×C4D8×D1111yescharacteristic
196C2×C4#6696911yescharacteristic
197C8—21no—
198C8—81no—
199C8—441no—
200C8—881no—
201C8#6696411yescharacteristic
202C8SD16×D1111yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1062238811yescharacteristic
207C4—21no—
208C4—222no—
209C4—441no—
210C4—1761no—
211C4#1062236211yescharacteristic
212C4#1062237511yescharacteristic
213C4#1062252511yescharacteristic
214C4D11×SD3211yescharacteristic
215C2—321no—
216C2#1306797511yescharacteristic
217C2#1307071111yescharacteristic
218C2#1307074511yescharacteristic
subgroupG/H
centerC22#10622388
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1361C2
socleC22×C11#466
prime radicalC11×#493C22
hypercenter#1361D11
hypocenterC11#12441
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
2. #13070518C2semidirect
3. #13067987C2semidirect
5. #13066689C2semidirect
6. #13066666C2semidirect
71. C11⋊C16SD16semidirect
94. Dic22SD32semidirect
180. C11#12441semidirect

Maximal subgroups

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

subgroupindex
#130708712
#130705182
#130679872
#130679732
#130666892
#130666662
C11×#13612
#1244111