Finite Group Databasebeta

← #14656867

Subgroups — #14656867

Order 2816.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076994C211yesmaximal, characteristic
2#13069593C211yesmaximal, characteristic
3#13067181C212yesmaximal
4#13066475C212yesmaximal
5C11×#1276C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C2×#66922—21no—
8C11×#431C2212yes—
9C43×C11C2211yescharacteristic
10#10622549—21no—
11#10622549C2212yes—
12#10622542—24no—
13#10622537C2211yescharacteristic
14#10622161—21no—
15#10622161—21no—
16#10622105—24no—
17C22×Dic22—22no—
18C2×C42×C11—22no—
19C2×C42×C11D411yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C42×C11C2311yescharacteristic
22#66979—21no—
23C2×C4⋊Dic11—22no—
24C2×C4⋊Dic11—22no—
25#66977—22no—
26C2×#4318—21no—
27#66923—21no—
28#66922—42no—
29#66922—42no—
30#66922Q812yescomplemented
31C4×Dic22—22no—
32C11×C4⋊C8—22no—
33C11×C22⋊C8—22no—
34C4×C8×C11—22no—
35C11⋊#95—24no—
36C11⋊#95—22no—
37C11⋊#95D414yes—
38C4⋊(C11⋊C8)—22no—
39#10363—111nomaximal, Sylow
40C22×C4×C11—21no—
41C22×C4×C11—21no—
42C22×C4×C11C2×D412yes—
43C22×C4×C11C2×D411yescharacteristic
44C22×Dic11—24no—
45C2×Dic22—22no—
46C2×Dic22—44no—
47C2×Dic22—48no—
48C2×C8×C11—42no—
49C42×C11—21no—
50C42×C11—21no—
51C42×C11—44no—
52C42×C11SD1612yes—
53C42×C11Q1612yes—
54C42×C11C2×Q811yescharacteristic
55C42×C11#4112yes—
56C42×C11#4111yescharacteristic
57C22⋊Dic11—41no—
58C4⋊Dic11—22no—
59C4⋊Dic11—22no—
60C4⋊Dic11—44no—
61C4⋊Dic11—42no—
62C4⋊Dic11—42no—
63Dic11⋊C4—42no—
64C4×Dic11—41no—
65#4318—41no—
66#4318—41no—
67C2×C11⋊C8—41no—
68#2862—111no—
69#1994—111no—
70#1518—112no—
71#1286—112no—
72#1276D1111yescharacteristic
73C23×C11#12011yescharacteristic
74C2×C4×C11—24no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—42no—
78C2×C4×C11—42no—
79C2×C4×C11C22⋊Q812yes—
80C2×C4×C11C22⋊Q811yescharacteristic
81C2×C4×C11#12411yescharacteristic
82C2×C4×C11#12412yes—
83C2×C4×C11C2×SD1611yescharacteristic
84C2×C4×C11C2×Q1611yescharacteristic
85C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C11#13711yescharacteristic
87C2×Dic11—48no—
88C2×Dic11—42no—
89C2×Dic11—44no—
90Dic22—88no—
91Dic22—82no—
92C8×C11—82no—
93C11⋊C8—81no—
94#533—111no—
95C2×C4⋊Q8—221no—
96#431C2×D1112yes—
97#423—111no—
98#391—224no—
99#382—112no—
100#382—221no—
101C43C2×D1111yescharacteristic
102#339—221no—
103#339—221no—
104#328—224no—
105C22×C11—22no—
106C22×C11#39311yescharacteristic
107C22×C11#45011yescharacteristic
108C22×C11#45111yescharacteristic
109C4×C11—24no—
110C4×C11—22no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11#47511yescharacteristic
114C4×C11#47711yescharacteristic
115C4×C11#48711yescharacteristic
116C4×C11#48911yescharacteristic
117Dic11—84no—
118Dic11—82no—
119C22×Q8—222no—
120C2×M16—221no—
121C4⋊Q8—112no—
122C4⋊Q8—442no—
123C4⋊Q8—442no—
124#125—221no—
125C22⋊Q8—222no—
126C4×Q8—222no—
127#117—221no—
128C2×C4⋊C4—222no—
129C2×C4⋊C4—222no—
130C2×C42—22no—
131C2×C42D4411yescharacteristic
132C2×C42D4411yescharacteristic
133C2×C42C22×D1111yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—222no—
136C22⋊C8—22no—
137C4×C8—22no—
138#95—114no—
139#95—224no—
140#95—222no—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11#202411yescharacteristic
144C2×C11#203112yes—
145C2×Q8—222no—
146C2×Q8—444no—
147C2×Q8—448no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—224no—
151C22×C4C2×D4411yescharacteristic
152C22×C4D4×D1112yes—
153M16—441no—
154M16—441no—
155C2×C8—42no—
156C2×C8—441no—
157C4⋊C4—222no—
158C4⋊C4—222no—
159C4⋊C4—444no—
160C4⋊C4—442no—
161C4⋊C4—442no—
162C4⋊C4—442no—
163C22⋊C4—441no—
164C42—21no—
165C42—21no—
166C42—44no—
167C42—441no—
168C42#431412yes—
169C42Dic4412yes—
170C42#433912yes—
171C42#434111yescharacteristic
172C42Q8×D1111yescharacteristic
173C11#1036311yescharacteristic, complemented, Sylow
174C23#6693511yescharacteristic
175Q8—882no—
176Q8—888no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—448no—
183C2×C4—442no—
184C2×C4—444no—
185C2×C4#6692811yescharacteristic
186C2×C4#6693812yes—
187C2×C4#6694912yes—
188C2×C4#6695011yescharacteristic
189C2×C4C2×#431411yescharacteristic
190C2×C4C2×Dic4411yescharacteristic
191C2×C4#6696111yescharacteristic
192C2×C4#6696211yescharacteristic
193C8—82no—
194C8—881no—
195C22—22no—
196C22#1062228611yescharacteristic
197C22#1062234411yescharacteristic
198C22#1062235211yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—884no—
204C4—882no—
205C4#1062229411yescharacteristic
206C4#1062232711yescharacteristic
207C4#1062246311yescharacteristic
208C4#1062246411yescharacteristic
209C2—21no—
210C2—21no—
211C2#1306975811yescharacteristic
212C2#1306978912yes—
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1276D11
hypocenterC11#10363
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
30. #66922Q8semidirect
173. C11#10363semidirect

Maximal subgroups

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

subgroupindex
#130769942
#130695932
#130671812
#130664752
C11×#12762
#1036311