Finite Group Databasebeta

← #14665643

Subgroups — #14665643

Order 2816.

230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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#13070480C211yesmaximal, characteristic
2#13067440C211yesmaximal, characteristic
3#13067434C211yesmaximal, characteristic, complemented
4#13066681C211yesmaximal, characteristic, complemented
5#13066587C211yesmaximal, characteristic, complemented
6#13066538C211yesmaximal, characteristic, complemented
7C11×#1333C211yesmaximal, characteristic
8C4×C11×D8C2211yescharacteristic
9C2×#66891C411yescharacteristic
10D4×C11⋊C8—21no—
11#10622443—21no—
12C4×Dic44C2211yescharacteristic
13C11×#346C2211yescharacteristic
14C11×#334C2211yescharacteristic
15#10622200C411yescharacteristic
16D4⋊(C11⋊C8)—21no—
17#10622130C411yescharacteristic
18#10622127C411yescharacteristic
19#10622122—21no—
20#10622099C2211yescharacteristic
21#10622095C2211yescharacteristic
22#10622093C2211yescharacteristic
23C2×C11×D8C2×C411yescharacteristic
24C4×D4×C11—21no—
25C22×C11⋊C8—41no—
26C2×Dic44C2×C411yescharacteristic
27C4×Dic22—21no—
28C2×C11×C16—21no—
29C11×#107C2×C411yescharacteristic
30C11×C4⋊C8—21no—
31C11×#102—21no—
32C4×C8×C11C2311yescharacteristic
33C22⋊(C11⋊C8)—41no—
34#66891C814yescomplemented
35#66882C2×C411yescharacteristic
36#66880—21no—
37Dic11⋊C8—41no—
38C8×Dic11—41no—
39C2×C11⋊C16C2×C411yescharacteristic
40C2×C11⋊C16C2×C411yescharacteristic
41C4⋊(C11⋊C8)—21no—
42C4×C11⋊C8D411yescharacteristic
43C4×C11⋊C8D411yescharacteristic
44#12065—111nomaximal, Sylow
45C2×D4×C11—21no—
46C22×C4×C11—41no—
47C2×Dic22—21no—
48C11×D8—21no—
49C11×D8C2×C812yes—
50C2×C8×C11—41no—
51C2×C8×C11C22×C411yescharacteristic
52C2×C8×C11#4111yescharacteristic
53C11×C4⋊C4—21no—
54C11×C22⋊C4—41no—
55C42×C11C2×D411yescharacteristic
56C4⋊Dic11—21no—
57Dic11⋊C4—41no—
58C4×Dic11—41no—
59C2×C11⋊C8—21no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8—41no—
62C2×C11⋊C8—82no—
63Dic44—21no—
64Dic44C2×C812yescomplemented
65C11×C16—41no—
66C11⋊C16—21no—
67C11⋊C16C2×C812yescomplemented
68#2175—111no—
69#1580—111no—
70#1579—111no—
71#1368—111no—
72#1334—111no—
73#1333D1111yescharacteristic
74#1313—111no—
75C23×C11—41no—
76D4×C11—22no—
77D4×C11—41no—
78C2×C4×C11—41no—
79C2×C4×C11—81no—
80C2×C4×C11—81no—
81C2×C4×C11C4×D411yescharacteristic
82C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
83C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
84C2×Dic11—41no—
85C2×Dic11—41no—
86Dic22—22no—
87Dic22—41no—
88C8×C11—21no—
89C8×C11—81no—
90C8×C11C22×C811yescharacteristic
91C8×C11#13111yescharacteristic
92C11⋊C8—41no—
93C11⋊C8—41no—
94C11⋊C8—81no—
95C2×SD32—111no—
96C8×Q8—221no—
97C4×Q16—111no—
98C4×D8C2×D1111yescharacteristic
99C8×D4—221no—
100#366—111no—
101#358—111no—
102#357—111no—
103#346—111no—
104#346C2×D1111yescharacteristic
105#334—111no—
106#334C2×D1111yescharacteristic
107Q8⋊C8—221no—
108D4⋊C8—221no—
109#322—111no—
110C22×C11—42no—
111C22×C11—81no—
112C22×C11—81no—
113C22×C11#44211yescharacteristic
114C4×C11—21no—
115C4×C11—21no—
116C4×C11—81no—
117C4×C11C8×D411yescharacteristic
118C4×C11#44411yescharacteristic
119Dic11—42no—
120Dic11—81no—
121C2×Q16—111no—
122C2×D8C4×D1111yescharacteristic
123C22×C8—441no—
124C4×Q8—221no—
125C4×D4—21no—
126SD32—114no—
127C2×C16—21no—
128C2×C16—111no—
129C2×C16—111no—
130#107—111no—
131#107C4×D1111yescharacteristic
132C4⋊C8—21no—
133C4⋊C8—221no—
134C4⋊C8—441no—
135#103—221no—
136#102—21no—
137C22⋊C8—441no—
138C4×C8—111no—
139C4×C8—111no—
140C4×C8—441no—
141C4×C8C22×D1111yescharacteristic
142C2×C11—82no—
143C2×C11#158011yescharacteristic
144C2×C11#218011yescharacteristic
145C2×C11AGL(1,ℤ/16)11yescharacteristic
146C2×Q8—221no—
147C2×D4—21no—
148C22×C4—41no—
149Q16—112no—
150Q16—221no—
151D8—21no—
152D8C8×D1112yes—
153C2×C8—41no—
154C2×C8—221no—
155C2×C8—221no—
156C2×C8—441no—
157C2×C8—882no—
158C2×C8C2×C4×D1111yescharacteristic
159C2×C8#434111yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—221no—
162C4⋊C4—441no—
163C22⋊C4—41no—
164C42—441no—
165C42D4×D1111yescharacteristic
166C16—41no—
167C16—112no—
168C16—221no—
169C11#1206511yescharacteristic, complemented, Sylow
170C23—41no—
171Q8—222no—
172Q8—441no—
173D4—22no—
174D4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—441no—
179C2×C4—441no—
180C2×C4(C22⋊D11)⋊C411yescharacteristic
181C2×C4#6696411yescharacteristic
182C2×C4#6696711yescharacteristic
183C8—21no—
184C8—81no—
185C8—441no—
186C8—441no—
187C8—881no—
188C8C2×C8×D1111yescharacteristic
189C8#6696011yescharacteristic
190C22—42no—
191C22—81no—
192C22—81no—
193C22#1062239811yescharacteristic
194C4—21no—
195C4—21no—
196C4—81no—
197C4—442no—
198C4—881no—
199C4(C22⋊D11)⋊C811yescharacteristic
200C4#1062243611yescharacteristic
201C2—82no—
202C2#1306743711yescharacteristic
203C2#1307050411yescharacteristic
204C2#1307051711yescharacteristic
subgroupG/H
centerC22#10622398
commutatorC8×C11C22×C8
FrattiniC4×C8C22×D11
FittingC11×#1333C2
socleC22×C11#442
prime radicalC2×C11×D8C2×C4
cosocleC4×C8×C11C23
hypercenter#1333D11
hypocenterC11#12065
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

Complements

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

NH ≅ G/Ntype
3. #13067434C2semidirect
4. #13066681C2semidirect
5. #13066587C2semidirect
6. #13066538C2semidirect
34. #66891C8semidirect
64. Dic44C2×C8semidirect
67. C11⋊C16C2×C8semidirect
169. C11#12065semidirect

Maximal subgroups

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

subgroupindex
#130704802
#130674402
#130674342
#130666812
#130665872
#130665382
C11×#13332
#1206511