Finite Group Databasebeta

← #14656903

Subgroups — #14656903

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#13069597C211yesmaximal, characteristic
2#13067114C212yesmaximal
3#13066519C212yesmaximal
4#13066445C211yesmaximal, characteristic
5C11×#2399C211yesmaximal, characteristic
6C2×C4×Q8×C11—21no—
7#10623001C2211yescharacteristic
8C11×#398—22no—
9C11×#395—22no—
10C4×C11×C4⋊C4—21no—
11C4×C11×C4⋊C4C2212yes—
12C11×#376C2211yescharacteristic
13#10622538C2212yes—
14#10622537C2211yescharacteristic
15#10622161—21no—
16#10622161—21no—
17#10622090—22no—
18#10622090—22no—
19C22×Q8×C11—21no—
20C4×Q8×C11—42no—
21C4×Q8×C11—42no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—21no—
25C2×C11×C4⋊C4—22no—
26C2×C42×C11—22no—
27C2×C42×C11D411yescharacteristic
28C2×C42×C11D411yescharacteristic
29C2×C42×C11C2311yescharacteristic
30#66979—21no—
31#66977—22no—
32C2×#4318—21no—
33#66923—21no—
34#66922Q812yescomplemented
35C4×Dic22—22no—
36C11×#95—21no—
37C11×#95—21no—
38C11×#95—22no—
39C11×#95D412yes—
40C11×#95D412yes—
41C22⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4×C11⋊C8—22no—
45#10371—111nomaximal, Sylow
46C2×Q8×C11—42no—
47C2×Q8×C11—44no—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11C2×D412yes—
53C22×C4×C11C2×D411yescharacteristic
54C2×Dic22—22no—
55C11×C4⋊C4—44no—
56C11×C4⋊C4—44no—
57C11×C4⋊C4—44no—
58C11×C4⋊C4—42no—
59C42×C11—21no—
60C42×C11—21no—
61C42×C11—42no—
62C42×C11—42no—
63C42×C11SD1612yes—
64C42×C11Q1612yes—
65C42×C11C2×Q811yescharacteristic
66C42×C11#4112yes—
67C42×C11#4111yescharacteristic
68C22⋊Dic11—41no—
69C4⋊Dic11—22no—
70C4⋊Dic11—22no—
71Dic11⋊C4—42no—
72C4×Dic11—41no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77#2399D1111yescharacteristic
78#1995—111no—
79#1503—112no—
80#1303—112no—
81#1274—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—48no—
84C2×C4×C11—24no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11—42no—
91C2×C4×C11—42no—
92C2×C4×C11—42no—
93C2×C4×C11—42no—
94C2×C4×C11—42no—
95C2×C4×C11C22⋊Q812yes—
96C2×C4×C11C22⋊Q811yescharacteristic
97C2×C4×C11#12412yes—
98C2×C4×C11#12411yescharacteristic
99C2×C4×C11C2×SD1611yescharacteristic
100C2×C4×C11C2×Q1611yescharacteristic
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C11#13711yescharacteristic
103C2×Dic11—42no—
104Dic22—82no—
105C11⋊C8—82no—
106C11⋊C8—81no—
107#533—111no—
108C2×C4×Q8—21no—
109#431—112no—
110#423—111no—
111#398—22no—
112#395—22no—
113C4×C4⋊C4—21no—
114C4×C4⋊C4C2×D1112yes—
115#376C2×D1111yescharacteristic
116#339—221no—
117#339—221no—
118#328—222no—
119#328—222no—
120C22×C11—22no—
121C22×C11#39311yescharacteristic
122C22×C11#45011yescharacteristic
123C22×C11#45111yescharacteristic
124C4×C11—22no—
125C4×C11—22no—
126C4×C11—42no—
127C4×C11—44no—
128C4×C11—42no—
129C4×C11—82no—
130C4×C11#47511yescharacteristic
131C4×C11#47711yescharacteristic
132C4×C11#48711yescharacteristic
133C4×C11#48911yescharacteristic
134Dic11—82no—
135C22×Q8—21no—
136C2×M16—221no—
137C4⋊Q8—112no—
138#125—221no—
139C22⋊Q8—222no—
140C4×Q8—42no—
141C4×Q8—42no—
142C4×Q8—222no—
143#117—221no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C42—22no—
149C2×C42C22⋊D1111yescharacteristic
150C2×C42C22⋊D1111yescharacteristic
151C2×C42C22×D1111yescharacteristic
152C4⋊C8—222no—
153C4⋊C8—222no—
154C22⋊C8—222no—
155C4×C8—222no—
156#95—21no—
157#95—21no—
158#95—22no—
159#95C22⋊D1112yes—
160#95C22⋊D1112yes—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11#202411yescharacteristic
164C2×C11#203112yes—
165C2×Q8—42no—
166C2×Q8—44no—
167C2×Q8—222no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4C2×C22⋊D1112yes—
173C22×C4C2×C22⋊D1111yescharacteristic
174M16—441no—
175M16—441no—
176C2×C8—442no—
177C2×C8—441no—
178C4⋊C4—44no—
179C4⋊C4—42no—
180C4⋊C4—44no—
181C4⋊C4—44no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—442no—
185C22⋊C4—441no—
186C42—21no—
187C42—21no—
188C42—42no—
189C42—42no—
190C42—441no—
191C42#432412yes—
192C42#432612yes—
193C42Q8×D1111yescharacteristic
194C42#434311yescharacteristic
195C42#434312yes—
196C11#1037111yescharacteristic, complemented, Sylow
197C23#6700611yescharacteristic
198Q8—48no—
199Q8—882no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—442no—
212C2×C4#6698511yescharacteristic
213C2×C4C2×#432411yescharacteristic
214C2×C4#6699511yescharacteristic
215C2×C4C2×#432611yescharacteristic
216C2×C4#6699912yes—
217C2×C4#6699911yescharacteristic
218C2×C4#6700012yes—
219C2×C4#6700011yescharacteristic
220C8—882no—
221C8—881no—
222C22—22no—
223C22#1062283111yescharacteristic
224C22#1062284111yescharacteristic
225C22#1062284411yescharacteristic
226C4—22no—
227C4—22no—
228C4—44no—
229C4—42no—
230C4—42no—
231C4—82no—
232C4—882no—
233C4#1062270211yescharacteristic
234C4#1062270411yescharacteristic
235C4#1062270611yescharacteristic
236C4#1062270711yescharacteristic
237C2—21no—
238C2—21no—
239C2#1306975411yescharacteristic
240C2#1306978512yes—
subgroupG/H
centerC2×C4#67000
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2399C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#2399D11
hypocenterC11#10371
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
34. #66922Q8semidirect
196. C11#10371semidirect

Maximal subgroups

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

subgroupindex
#130695972
#130671142
#130665192
#130664452
C11×#23992
#1037111