Finite Group Databasebeta

← #14668202

Subgroups — #14668202

Order 2816.

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

normal subgroups only

This group has 218 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#13070843C211yesmaximal, characteristic, complemented
2D4×C11⋊C16C211yesmaximal, characteristic
3#13068015C211yesmaximal, characteristic
4#13066687C211yesmaximal, characteristic, complemented
5#13066675C211yesmaximal, characteristic, complemented
6#13066665C211yesmaximal, characteristic, complemented
7C11×#1669C211yesmaximal, characteristic
8C11×#494C2211yescharacteristic
9C11×#474—21no—
10C8×D4×C11C2211yescharacteristic
11C22×C11⋊C16—21no—
12#10622621—21no—
13#10622295C2211yescharacteristic
14C11×#335C2211yescharacteristic
15C11×#332—21no—
16#10622202—21no—
17#10622202—21no—
18C22⋊(C11⋊C16)—21no—
19#10622119—21no—
20C4⋊(C11⋊C16)C2211yescharacteristic
21C4×C11⋊C16C2211yescharacteristic
22#10622096C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C22×C8×C11—21no—
26C11×C4⋊Q8—21no—
27C4×D4×C11D411yescharacteristic
28#66922—21no—
29C11×#107—41no—
30C11×C4⋊C8—21no—
31C11×C4⋊C8D411yescharacteristic
32C11×#102—41no—
33C11×C22⋊C8—21no—
34C4×C8×C11C2311yescharacteristic
35#66896—41no—
36#66882—21no—
37#66882—21no—
38C2×C11⋊C16—21no—
39C2×C11⋊C16—42no—
40C2×C11⋊C16D411yescharacteristic
41C2×C11⋊C16D411yescharacteristic
42#66872—41no—
43C4⋊(C11⋊C8)—21no—
44#12469—111nomaximal, Sylow
45C2×Q8×C11—41no—
46C2×D4×C11D811yescharacteristic
47C22×C4×C11—21no—
48C2×Dic22—41no—
49C11×Q16—41no—
50C11×Q16—41no—
51C11×Q16—81no—
52C2×C8×C11—21no—
53C2×C8×C11—41no—
54C2×C8×C11—41no—
55C2×C8×C11—41no—
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11#4111yescharacteristic
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4D811yescharacteristic
61C11×C22⋊C4—21no—
62C42×C11C2×D411yescharacteristic
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C2×C11⋊C8—41no—
66C11⋊C16—21no—
67C11⋊C16—21no—
68C11⋊C16—41no—
69#2241—111no—
70D4×C16—111no—
71#1675—111no—
72#1669D1111yescharacteristic
73#1371—111no—
74#1365—111no—
75#1362—111no—
76C23×C11—21no—
77Q8×C11—81no—
78Q8×C11—81no—
79D4×C11—21no—
80D4×C11Q3212yes—
81C2×C4×C11—21no—
82C2×C4×C11—41no—
83C2×C4×C11—41no—
84C2×C4×C11—81no—
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11C2×D811yescharacteristic
87C2×C4×C11#13511yescharacteristic
88C2×Dic11—81no—
89Dic22—161no—
90C8×C11—21no—
91C8×C11—41no—
92C8×C11—81no—
93C8×C11#13511yescharacteristic
94C8×C11AGL(1,ℤ/8)11yescharacteristic
95C11⋊C8—81no—
96C22×C16—221no—
97#500—111no—
98#494C2×D1111yescharacteristic
99#476—221no—
100#474—21no—
101C8×D4C2×D1111yescharacteristic
102C4⋊C16—111no—
103#358—221no—
104#358—221no—
105C22⋊C16—221no—
106C4×C16—111no—
107#335—111no—
108#335C2×D1111yescharacteristic
109#333—221no—
110#332—21no—
111C22×C11—22no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11#46611yescharacteristic
115C4×C11—21no—
116C4×C11—41no—
117C4×C11—161no—
118C4×C11#46311yescharacteristic
119C4×C11#47111yescharacteristic
120C4×C11C2×Q3211yescharacteristic
121C4×C11#50811yescharacteristic
122Dic11—161no—
123C2×Q16—21no—
124C2×Q16—21no—
125C22×C8—21no—
126C4⋊Q8—21no—
127C4⋊Q8—221no—
128C4×D4C22⋊D1111yescharacteristic
129C2×C16—111no—
130C2×C16—111no—
131C2×C16—221no—
132C2×C16—442no—
133#107—41no—
134#107—221no—
135#107—221no—
136#106—441no—
137C4⋊C8—21no—
138C4⋊C8—221no—
139C4⋊C8C22⋊D1111yescharacteristic
140#102—41no—
141#102—441no—
142C22⋊C8—21no—
143C4×C8C22×D1111yescharacteristic
144C2×C11—42no—
145C2×C11#168111yescharacteristic
146C2×C11#221611yescharacteristic
147C2×C11#222311yescharacteristic
148C2×Q8—41no—
149C2×Q8—441no—
150C2×D4#432311yescharacteristic
151C22×C4—21no—
152Q16—41no—
153Q16—41no—
154Q16—81no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—441no—
160C2×C8D4×D1111yescharacteristic
161C2×C8#434111yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—441no—
165C4⋊C4—441no—
166C4⋊C4#432311yescharacteristic
167C22⋊C4—21no—
168C42C2×C22⋊D1111yescharacteristic
169C16—221no—
170C16—221no—
171C16—441no—
172C11#1246911yescharacteristic, complemented, Sylow
173C23—21no—
174Q8—81no—
175Q8—81no—
176Q8—1761no—
177D4—21no—
178D4#6689312yes—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—81no—
183C2×C4—881no—
184C2×C4C2×#432311yescharacteristic
185C2×C4#6699211yescharacteristic
186C2×C4#6700311yescharacteristic
187C8—21no—
188C8—41no—
189C8—81no—
190C8—881no—
191C8#6696411yescharacteristic
192C8#6696511yescharacteristic
193C22—22no—
194C22—41no—
195C22—41no—
196C22#1062265111yescharacteristic
197C4—21no—
198C4—41no—
199C4—161no—
200C4—1761no—
201C4#1062276611yescharacteristic
202C4C2×#6689311yescharacteristic
203C4#1062280711yescharacteristic
204C4#1062281311yescharacteristic
205C2—42no—
206C2#1306805111yescharacteristic
207C2#1307070511yescharacteristic
208C2#1307074811yescharacteristic
subgroupG/H
centerC22#10622651
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1669C2
socleC22×C11#466
prime radicalC2×D4×C11D8
hypercenter#1669D11
hypocenterC11#12469
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1669

Complements

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

NH ≅ G/Ntype
1. #13070843C2semidirect
4. #13066687C2semidirect
5. #13066675C2semidirect
6. #13066665C2semidirect
172. C11#12469semidirect

Maximal subgroups

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

subgroupindex
#130708432
D4×C11⋊C162
#130680152
#130666872
#130666752
#130666652
C11×#16692
#1246911