Finite Group Databasebeta

← #14656863

Subgroups — #14656863

Order 2816.

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

normal subgroups only

This group has 416 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#13069593C211yesmaximal, characteristic
2#13067179C212yesmaximal
3#13066474C212yesmaximal
4#13066449C211yesmaximal, characteristic
5C11×#2862C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—21no—
7#10623001C2211yescharacteristic
8C11×#391—24no—
9C11×#382—21no—
10C11×#382C2212yes—
11C43×C11C2211yescharacteristic
12#10622538C2212yes—
13#10622537C2211yescharacteristic
14#10622161—21no—
15#10622161—21no—
16#10622090—24no—
17C22×Q8×C11—22no—
18C11×C4⋊Q8—42no—
19C11×C4⋊Q8—42no—
20C2×C11×C4⋊C4—22no—
21C2×C11×C4⋊C4—22no—
22C2×C42×C11—22no—
23C2×C42×C11D411yescharacteristic
24C2×C42×C11D411yescharacteristic
25C2×C42×C11C2311yescharacteristic
26#66979—21no—
27#66977—22no—
28C2×#4318—21no—
29#66923—21no—
30#66922Q812yescomplemented
31C4×Dic22—22no—
32C11×#95—24no—
33C11×#95—22no—
34C11×#95D414yes—
35C22⋊(C11⋊C8)—22no—
36C4⋊(C11⋊C8)—22no—
37C4⋊(C11⋊C8)—22no—
38C4×C11⋊C8—22no—
39#10363—111nomaximal, Sylow
40C2×Q8×C11—44no—
41C2×Q8×C11—48no—
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11—24no—
45C22×C4×C11C2×D412yes—
46C22×C4×C11C2×D411yescharacteristic
47C2×Dic22—22no—
48C11×C4⋊C4—44no—
49C11×C4⋊C4—42no—
50C11×C4⋊C4—42no—
51C42×C11—21no—
52C42×C11—21no—
53C42×C11—44no—
54C42×C11SD1612yes—
55C42×C11Q1612yes—
56C42×C11C2×Q811yescharacteristic
57C42×C11#4111yescharacteristic
58C42×C11#4112yes—
59C22⋊Dic11—41no—
60C4⋊Dic11—22no—
61C4⋊Dic11—22no—
62Dic11⋊C4—42no—
63C4×Dic11—41no—
64#4318—41no—
65#4318—41no—
66C2×C11⋊C8—42no—
67C2×C11⋊C8—41no—
68#2862D1111yescharacteristic
69#1994—111no—
70#1518—112no—
71#1286—112no—
72#1276—111no—
73C23×C11#12011yescharacteristic
74Q8×C11—88no—
75C2×C4×C11—24no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—42no—
79C2×C4×C11—42no—
80C2×C4×C11—48no—
81C2×C4×C11—44no—
82C2×C4×C11C22⋊Q812yes—
83C2×C4×C11C22⋊Q811yescharacteristic
84C2×C4×C11#12412yes—
85C2×C4×C11#12411yescharacteristic
86C2×C4×C11C2×SD1611yescharacteristic
87C2×C4×C11C2×Q1611yescharacteristic
88C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C11#13711yescharacteristic
90C2×Dic11—42no—
91Dic22—82no—
92C11⋊C8—82no—
93C11⋊C8—81no—
94#533—111no—
95C2×C4⋊Q8—21no—
96#431—112no—
97#423—111no—
98#391—24no—
99#382—21no—
100#382C2×D1112yes—
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—84no—
114C4×C11#47511yescharacteristic
115C4×C11#47711yescharacteristic
116C4×C11#48711yescharacteristic
117C4×C11#48911yescharacteristic
118Dic11—82no—
119C22×Q8—22no—
120C2×M16—221no—
121C4⋊Q8—42no—
122C4⋊Q8—42no—
123C4⋊Q8—112no—
124#125—221no—
125C22⋊Q8—222no—
126C4×Q8—222no—
127#117—221no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C42—22no—
131C2×C42C22⋊D1111yescharacteristic
132C2×C42C22⋊D1111yescharacteristic
133C2×C42C22×D1111yescharacteristic
134C4⋊C8—222no—
135C4⋊C8—222no—
136C22⋊C8—222no—
137C4×C8—222no—
138#95—24no—
139#95—22no—
140#95C22⋊D1114yes—
141C2×C11—21no—
142C2×C11—21no—
143C2×C11#202411yescharacteristic
144C2×C11#203112yes—
145C2×Q8—44no—
146C2×Q8—48no—
147C2×Q8—222no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—24no—
151C22×C4C2×C22⋊D1112yes—
152C22×C4C2×C22⋊D1111yescharacteristic
153M16—441no—
154M16—441no—
155C2×C8—442no—
156C2×C8—441no—
157C4⋊C4—44no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—222no—
161C4⋊C4—222no—
162C4⋊C4—442no—
163C22⋊C4—441no—
164C42—21no—
165C42—21no—
166C42—44no—
167C42—441no—
168C42#432412yes—
169C42#432612yes—
170C42Q8×D1111yescharacteristic
171C42#434311yescharacteristic
172C42#434312yes—
173C11#1036311yescharacteristic, complemented, Sylow
174C23#6700611yescharacteristic
175Q8—88no—
176Q8—882no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—48no—
183C2×C4—44no—
184C2×C4—442no—
185C2×C4#6698511yescharacteristic
186C2×C4C2×#432411yescharacteristic
187C2×C4#6699511yescharacteristic
188C2×C4C2×#432611yescharacteristic
189C2×C4#6699912yes—
190C2×C4#6699911yescharacteristic
191C2×C4#6700012yes—
192C2×C4#6700011yescharacteristic
193C8—882no—
194C8—881no—
195C22—22no—
196C22#1062283111yescharacteristic
197C22#1062284111yescharacteristic
198C22#1062284411yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—84no—
204C4—882no—
205C4#1062270211yescharacteristic
206C4#1062270411yescharacteristic
207C4#1062270611yescharacteristic
208C4#1062270711yescharacteristic
209C2—21no—
210C2—21no—
211C2#1306975411yescharacteristic
212C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2862C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#2862D11
hypocenterC11#10363
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

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
#130695932
#130671792
#130664742
#130664492
C11×#28622
#1036311