Finite Group Databasebeta

← #14651303

Subgroups — #14651303

Order 2816.

436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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#13078992C211yesmaximal, characteristic
2#13077722C211yesmaximal, characteristic, complemented
3#13067329C212yesmaximal
4#13066489C212yesmaximal, complemented
5C11×#1537C211yesmaximal, characteristic, complemented
6C11×#533C2211yescharacteristic
7C2×#66927C2211yescharacteristic
8C11×#432C2212yes—
9#10622701C414yes—
10#10622680—22no—
11#10622637—24no—
12#10622614—22no—
13#10622613—22no—
14#10622539C2212yes—
15C4×#4318C2211yescharacteristic
16C11×#330—22no—
17#10622123—24no—
18C22×D44—21no—
19C22×D44—22no—
20C11×C4⋊Q8C2×C412yes—
21C11×#125D412yes—
22C11×C22⋊Q8—22no—
23C4×Q8×C11—22no—
24C11×#117D412yes—
25C2×C42×C11C2311yescharacteristic
26C2×#4318—21no—
27#66927—22no—
28#66927—21no—
29#66927C2×C412yes—
30C11×C4⋊C8—22no—
31C11×C22⋊C8—22no—
32C11×#97—22no—
33C22⋊(C11⋊C8)—22no—
34#66873—28no—
35C4⋊(C11⋊C8)—24no—
36C4⋊(C11⋊C8)D414yes—
37#66867—22no—
38#66867—21no—
39#66867—22no—
40C4×C11⋊C8—22no—
41C4×C11⋊C8C2×C412yes—
42#9424—111nomaximal, Sylow
43C23×D11—41no—
44C2×Q8×C11—22no—
45C22×C4×C11C2×D411yescharacteristic
46C22×C4×C11#4112yes—
47C2×D44—22no—
48C2×D44—24no—
49C2×D44—44no—
50C2×D44—41no—
51C2×D44—42no—
52C2×D44—84no—
53C2×C8×C11—42no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—24no—
56C11×C4⋊C4C22⋊C414yes—
57C11×C22⋊C4—22no—
58C42×C11—22no—
59C42×C11C22×C411yescharacteristic
60C42×C11C2×D411yescharacteristic
61C42×C11C2×D412yes—
62#4318—42no—
63C2×C11⋊C8—22no—
64C2×C11⋊C8—24no—
65#3138—111no—
66#2987—111no—
67#1555—112no—
68#1537D1111yescharacteristic, complemented
69#1291—112no—
70C23×C11#12311yescharacteristic
71C22×D11—42no—
72C22×D11—82no—
73C22×D11—84no—
74Q8×C11—82no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—42no—
78C2×C4×C11C2×C22⋊C411yescharacteristic
79C2×C4×C11C4×D412yes—
80C2×C4×C11#12011yescharacteristic
81C2×C4×C11#12112yes—
82D44—44no—
83D44—84no—
84D44—84no—
85D44—82no—
86C8×C11—82no—
87C11⋊C8—42no—
88C11⋊C8—44no—
89#533C2×D1111yescharacteristic
90C2×#127—111no—
91#490—222no—
92#486—114no—
93#446—224no—
94#433—222no—
95#432—112no—
96#432C2×D1112yes—
97#418—222no—
98C4×M16—111no—
99#331—224no—
100#330—22no—
101C22×C11—21no—
102C22×C11—22no—
103C22×C11#38611yescharacteristic
104C2×D11—82no—
105C2×D11—84no—
106C2×D11—164no—
107C4×C11—21no—
108C4×C11—22no—
109C4×C11—22no—
110C4×C11—44no—
111C4×C11#45412yes—
112C22×D4—221no—
113C22×D4—222no—
114C2×M16—221no—
115C4⋊Q8C4×D1112yes—
116#127—112no—
117#127—222no—
118#127—221no—
119#125C22⋊D1112yes—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117D4412yes—
123C2×C42C22×D1111yescharacteristic
124C4⋊C8—22no—
125C4⋊C8—114no—
126C4⋊C8—224no—
127#102—228no—
128C22⋊C8—22no—
129C22⋊C8—222no—
130#97—22no—
131#97—222no—
132#97—222no—
133#97—221no—
134C4×C8—112no—
135C4×C8—222no—
136C2×C11—41no—
137C2×C11#188811yescharacteristic
138C2×C11#190312yes—
139D11—162no—
140C24—441no—
141C2×Q8—22no—
142C2×D4—224no—
143C2×D4—222no—
144C2×D4—444no—
145C2×D4—441no—
146C2×D4—442no—
147C2×D4—884no—
148C22×C4C2×D4411yescharacteristic
149C22×C4#434112yes—
150M16—442no—
151C2×C8—42no—
152C2×C8—224no—
153C2×C8—222no—
154C4⋊C4—22no—
155C4⋊C4—24no—
156C4⋊C4(C2×D11)⋊C414yes—
157C22⋊C4—22no—
158C42—22no—
159C42C2×C4×D1111yescharacteristic
160C42D4×D1112yes—
161C42C2×C22⋊D1111yescharacteristic
162C11#942411yescharacteristic, complemented, Sylow
163C23—442no—
164C23—882no—
165C23—884no—
166C23#6693911yescharacteristic
167Q8—82no—
168D4—444no—
169D4—884no—
170D4—884no—
171D4—882no—
172C2×C4—22no—
173C2×C4—24no—
174C2×C4—42no—
175C2×C4(C22⋊D11)⋊C412yes—
176C2×C4#6693511yescharacteristic
177C2×C4C2×(C2×D11)⋊C411yescharacteristic
178C2×C4#6699212yes—
179C8—82no—
180C8—442no—
181C8—444no—
182C22—22no—
183C22—21no—
184C22—884no—
185C22—882no—
186C22—1764no—
187C22#1062257111yescharacteristic
188C4—22no—
189C4—22no—
190C4—21no—
191C4—44no—
192C4#1062236612yes—
193C2—41no—
194C2—1762no—
195C2#1306901711yescharacteristic
196C2#1306909412yes—
subgroupG/H
centerC22#10622571
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1537C2
socleC22×C11#386
prime radicalC2×#66927C22
cosocleC2×C42×C11C23
hypercenter#1537D11
hypocenterC11#9424
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
2. #13077722C2semidirect
4. #13066489C2semidirect
5. C11×#1537C2semidirect
68. #1537D11semidirect
162. C11#9424semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130777222
#130673292
#130664892
C11×#15372
#942411