Finite Group Databasebeta

← #14653262

Subgroups — #14653262

Order 2816.

506 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#10622306C211yesmaximal, characteristic
2#13067289C212yesmaximal, complemented
3#13067285C212yesmaximal
4#13066908C211yesmaximal, characteristic, complemented
5C11×#1837C211yesmaximal, characteristic, complemented
6C22×#4314—22no—
7C2×#66927C2211yescharacteristic
8C2×#66922C2211yescharacteristic
9C11×#423C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11#10622538C2212yes—
12#10622306—22no—
13#10622306C414yes—
14C11×#341—22no—
15#10622123—24no—
16#10622120—24no—
17#10622092—22no—
18C22×D44—21no—
19C22×D44—22no—
20C22×Dic22—21no—
21C2×C11×M16—22no—
22C22×C8×C11D412yes—
23C2×C42×C11C2311yescharacteristic
24C2×C4⋊Dic11—22no—
25C2×#4314—28no—
26C2×#4314—48no—
27#66927—21no—
28#66927—22no—
29#66927C2×C412yes—
30#66922—22no—
31#66922—21no—
32#66922C2×C412yes—
33C11×C4⋊C8—22no—
34C11×C4⋊C8—22no—
35C4×C8×C11C2×C412yes—
36C4×C8×C11D412yes—
37C22⋊(C11⋊C8)—22no—
38C4⋊(C11⋊C8)D414yes—
39C4×C11⋊C8—22no—
40#9777—111nomaximal, Sylow
41C23×D11—41no—
42C22×C4×C11C2×D411yescharacteristic
43C22×C4×C11#4112yes—
44C22×Dic11—41no—
45C2×D44—22no—
46C2×D44—24no—
47C2×D44—42no—
48C2×D44—41no—
49C2×D44—44no—
50C2×D44—84no—
51C2×Dic22—22no—
52C2×Dic22—41no—
53C2×Dic22—44no—
54C11×M16—44no—
55C2×C8×C11—24no—
56C2×C8×C11—42no—
57C2×C8×C11C22⋊C414yes—
58C42×C11C22×C411yescharacteristic
59C42×C11C2×D411yescharacteristic
60C42×C11C2×D412yes—
61C4⋊Dic11—24no—
62C4⋊Dic11—42no—
63C2×C11⋊C8—24no—
64#4314—416no—
65C2×#492—111no—
66#1837D1111yescharacteristic, complemented
67#1546—112no—
68#1545—112no—
69#1452—111no—
70C23×C11#12411yescharacteristic
71C22×D11—42no—
72C22×D11—84no—
73C22×D11—82no—
74C2×C4×C11—24no—
75C2×C4×C11C2×C22⋊C411yescharacteristic
76C2×C4×C11C4×D412yes—
77C2×C4×C11#12112yes—
78C2×C4×C11#12711yescharacteristic
79C2×C4×C11AGL(1,ℤ/8)14yes—
80C2×Dic11—42no—
81C2×Dic11—82no—
82D44—44no—
83D44—84no—
84D44—84no—
85D44—82no—
86Dic22—44no—
87Dic22—82no—
88C8×C11—24no—
89C8×C11—82no—
90C11⋊C8—44no—
91C22×SD16—222no—
92C2×C4⋊Q8—111no—
93C2×#127—111no—
94#492—114no—
95#492—222no—
96#431—112no—
97#423C2×D1112yes—
98C2×C4×C8C2×D1111yescharacteristic
99#341—22no—
100#332—224no—
101#331—224no—
102#322—222no—
103C22×C11—22no—
104C22×C11#39011yescharacteristic
105C22×C11#49012yes—
106C2×D11—82no—
107C2×D11—84no—
108C2×D11—164no—
109C4×C11—22no—
110C4×C11#41812yes—
111C4×C11#47114yes—
112C4×C11#49612yes—
113Dic11—82no—
114C22×Q8—221no—
115C22×D4—222no—
116C22×D4—221no—
117C2×SD16—228no—
118C2×SD16—448no—
119C2×M16—22no—
120C22×C8C22⋊D1112yes—
121C4⋊Q8—112no—
122C4⋊Q8—221no—
123C4⋊Q8—222no—
124#127—112no—
125#127—221no—
126#127—222no—
127C2×C4⋊C4—222no—
128C2×C42C22×D1111yescharacteristic
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—114no—
132C22⋊C8—222no—
133C4×C8—222no—
134C4×C8C4×D1112yes—
135C4×C8D4412yes—
136C2×C11—22no—
137C2×C11#196111yescharacteristic
138C2×C11#197712yes—
139D11—162no—
140C24—441no—
141C2×Q8—222no—
142C2×Q8—441no—
143C2×Q8—444no—
144C2×D4—224no—
145C2×D4—222no—
146C2×D4—442no—
147C2×D4—441no—
148C2×D4—444no—
149C2×D4—884no—
150C22×C4—441no—
151C22×C4#434312yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153SD16—4416no—
154M16—44no—
155C2×C8—24no—
156C2×C8—42no—
157C2×C8—224no—
158C2×C8(C2×D11)⋊C414yes—
159C4⋊C4—224no—
160C4⋊C4—442no—
161C42C2×C4×D1111yescharacteristic
162C42C2×D4411yescharacteristic
163C42D4×D1112yes—
164C11#977711yescharacteristic, complemented, Sylow
165C23—442no—
166C23—884no—
167C23—882no—
168C23#6700011yescharacteristic
169Q8—444no—
170Q8—882no—
171D4—444no—
172D4—884no—
173D4—884no—
174D4—882no—
175C2×C4—24no—
176C2×C4—442no—
177C2×C4—882no—
178C2×C4#6694612yes—
179C2×C4#6694812yes—
180C2×C4C2×(C2×D11)⋊C411yescharacteristic
181C2×C4#6699311yescharacteristic
182C2×C4#6700214yes—
183C8—24no—
184C8—82no—
185C8—444no—
186C22—22no—
187C22—882no—
188C22—884no—
189C22—1764no—
190C22#1062260111yescharacteristic
191C22#1062268012yes—
192C4—22no—
193C4—882no—
194C4#1062251114yes—
195C4#1062261412yes—
196C4#1062267112yes—
197C2—22no—
198C2—1762no—
199C2#1306943911yescharacteristic
200C2#1306951712yes—
subgroupG/H
centerC22#10622601
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1837C2
socleC22×C11#390
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1837D11
hypocenterC11#9777
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
2. #13067289C2semidirect
4. #13066908C2semidirect
5. C11×#1837C2semidirect
66. #1837D11semidirect
164. C11#9777semidirect

Maximal subgroups

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

subgroupindex
C2×#106223062
#130672892
#130672852
#130669082
C11×#18372
#977711