Finite Group Databasebeta

← #14646771

Subgroups — #14646771

Order 2816.

388 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 101 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#13077328C211yesmaximal, characteristic
2#13067377C212yesmaximal, complemented
3#13067251C211yesmaximal, characteristic
4#13066526C212yesmaximal, complemented
5C11×#1536C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×#67001C412yes—
8C11×#432C2212yes—
9#10622847C412yes—
10#10622625—22no—
11D4×C11⋊C8—22no—
12#10622539C2212yes—
13#10622537C2211yescharacteristic
14C2×C4×C11⋊C8C2211yescharacteristic
15C11×#329—22no—
16#10622178—22no—
17#10622118—22no—
18#10622117—22no—
19C2×C11×#41C2×C412yes—
20C11×C4⋊Q8Q811yescharacteristic
21C11×#127Q811yescharacteristic
22C11×#124D412yes—
23C11×#121—22no—
24C4×D4×C11—22no—
25C2×C42×C11C2311yescharacteristic
26#67001—44no—
27C2×#4318—22no—
28C2×#4318C2×C412yes—
29C22×C11⋊C8—22no—
30C22×C11⋊C8C2×C411yescharacteristic
31C22×C11⋊C8C2×C411yescharacteristic
32C11×C4⋊C8—22no—
33C11×C22⋊C8—22no—
34C11×#97—22no—
35C22⋊(C11⋊C8)—24no—
36C22⋊(C11⋊C8)—22no—
37C4⋊(C11⋊C8)—22no—
38C4⋊(C11⋊C8)—22no—
39#66867—22no—
40C4×C11⋊C8D412yes—
41C4×C11⋊C8D412yes—
42#8632—111nomaximal, Sylow
43C11×#41—42no—
44C11×#41—42no—
45C2×Q8×C11C4⋊C412yes—
46C2×D4×C11—22no—
47C2×D4×C11—22no—
48C2×D4×C11C4⋊C412yes—
49C22×C4×C11—22no—
50C22×C4×C11C22×C411yescharacteristic
51C22×C4×C11#4112yes—
52C2×C8×C11—42no—
53C11×C4⋊C4—22no—
54C11×C22⋊C4—24no—
55C42×C11C2×D412yes—
56C42×C11C2×D411yescharacteristic
57C42×C11C2×Q811yescharacteristic
58#4318—42no—
59#4318—44no—
60C2×C11⋊C8—22no—
61C2×C11⋊C8—22no—
62C2×C11⋊C8—41no—
63C2×C11⋊C8—44no—
64C2×C11⋊C8—42no—
65C2×C11⋊C8C22⋊C412yes—
66C2×C11⋊C8C22⋊C411yescharacteristic
67C2×C11⋊C8C22⋊C411yescharacteristic
68#2931—111no—
69#1568—112no—
70#1536—111no—
71#1536D1111yescharacteristic
72#1307—112no—
73C23×C11—22no—
74C23×C11#11711yescharacteristic
75Q8×C11—42no—
76D4×C11—42no—
77D4×C11—44no—
78D4×C11—44no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—42no—
83C2×C4×C11—42no—
84C2×C4×C11—42no—
85C2×C4×C11C2×C22⋊C411yescharacteristic
86C2×C4×C11C2×C4⋊C411yescharacteristic
87C2×C4×C11#12112yes—
88C2×C4×C11C22⋊Q812yes—
89C8×C11—82no—
90C11⋊C8—21no—
91C11⋊C8—22no—
92C11⋊C8—42no—
93C11⋊C8—82no—
94C11⋊C8#10012yes—
95C2×#131—112no—
96#532C2×D1111yescharacteristic
97#436—222no—
98C8×D4—222no—
99#432—112no—
100#432C2×D1112yes—
101#423—111no—
102#408—112no—
103C2×C4×C8—111no—
104#335—222no—
105#334—222no—
106#329—22no—
107#329—222no—
108C22×C11—21no—
109C22×C11—22no—
110C22×C11—42no—
111C22×C11—44no—
112C22×C11#38011yescharacteristic
113C4×C11—21no—
114C4×C11—22no—
115C4×C11—22no—
116C4×C11—42no—
117C4×C11C2×#10011yescharacteristic
118C4×C11#41311yescharacteristic
119C2×#41C4×D1112yes—
120#131—444no—
121C2×M16—112no—
122C2×M16—222no—
123C22×C8—111no—
124C22×C8—111no—
125C22×C8—222no—
126C4⋊Q8Dic2211yescharacteristic
127#127Dic2211yescharacteristic
128#124C22⋊D1112yes—
129#121—22no—
130C4×D4—22no—
131C2×C42C22×D1111yescharacteristic
132C4⋊C8—22no—
133C4⋊C8—222no—
134C4⋊C8—222no—
135C22⋊C8—22no—
136C22⋊C8—224no—
137C22⋊C8—222no—
138#97—22no—
139#97—222no—
140C4×C8—112no—
141C4×C8—112no—
142C2×C11—41no—
143C2×C11—82no—
144C2×C11#180011yescharacteristic
145C2×C11#181412yes—
146#41—42no—
147#41—42no—
148C2×Q8Dic11⋊C412yes—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4Dic11⋊C412yes—
152C22×C4—22no—
153C22×C4C2×C4×D1111yescharacteristic
154C22×C4#434112yes—
155M16—444no—
156M16—442no—
157C2×C8—42no—
158C2×C8—111no—
159C2×C8—112no—
160C2×C8—111no—
161C2×C8—222no—
162C2×C8—222no—
163C2×C8—444no—
164C2×C8—441no—
165C2×C8—442no—
166C4⋊C4—22no—
167C22⋊C4—24no—
168C42C2×Dic2211yescharacteristic
169C42D4×D1112yes—
170C42C2×C22⋊D1111yescharacteristic
171C11#863211yescharacteristic, complemented, Sylow
172C23—22no—
173C23#6693011yescharacteristic
174Q8—42no—
175D4—42no—
176D4—44no—
177D4—44no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4#6693112yes—
185C2×C4C22⋊C4×D1111yescharacteristic
186C2×C4C2×Dic11⋊C411yescharacteristic
187C2×C4#6699212yes—
188C8—82no—
189C8—112no—
190C8—221no—
191C8—222no—
192C8—442no—
193C8—882no—
194C22—21no—
195C22—22no—
196C22—42no—
197C22—44no—
198C22#1062255511yescharacteristic
199C4—21no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4D11×#10011yescharacteristic
204C4#1062235811yescharacteristic
205C2—41no—
206C2—82no—
207C2#1306860611yescharacteristic
208C2#1306866812yes—
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1536C2
socleC22×C11#380
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1536D11
hypocenterC11#8632
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1536

Complements

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

NH ≅ G/Ntype
2. #13067377C2semidirect
4. #13066526C2semidirect
171. C11#8632semidirect

Maximal subgroups

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

subgroupindex
#130773282
#130673772
#130672512
#130665262
C11×#15362
#863211