Finite Group Databasebeta

← #14656907

Subgroups — #14656907

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#13071909C211yesmaximal, characteristic
2#13069597C211yesmaximal, characteristic
3#13067116C212yesmaximal
4#13066518C212yesmaximal
5C11×#1274C211yesmaximal, characteristic
6#10623001C2211yescharacteristic
7C2×C4×Dic22—21no—
8C11×#431C2212yes—
9C11×#376C2211yescharacteristic
10C4×C4⋊Dic11—21no—
11C4×C4⋊Dic11C2212yes—
12#10622537C2211yescharacteristic
13#10622274—22no—
14#10622269—22no—
15#10622161—21no—
16#10622161—21no—
17#10622105—22no—
18#10622105—22no—
19C22×Dic22—21no—
20C2×C42×C11D411yescharacteristic
21C2×C42×C11D411yescharacteristic
22C2×C42×C11C2311yescharacteristic
23#66979—21no—
24C2×C4⋊Dic11—21no—
25C2×C4⋊Dic11—22no—
26C2×C4⋊Dic11—22no—
27#66977—22no—
28C2×Dic11⋊C4—22no—
29C2×C4×Dic11—22no—
30C2×#4318—21no—
31#66923—21no—
32#66922Q812yescomplemented
33C4×Dic22—22no—
34C4×Dic22—42no—
35C4×Dic22—42no—
36C11×C4⋊C8—22no—
37C11×C22⋊C8—22no—
38C4×C8×C11—22no—
39C11×#95—22no—
40C11⋊#95—21no—
41C11⋊#95—21no—
42C11⋊#95D412yes—
43C11⋊#95D412yes—
44C4⋊(C11⋊C8)—22no—
45#10371—111nomaximal, Sylow
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D412yes—
49C22×C4×C11C2×D411yescharacteristic
50C22×Dic11—22no—
51C22×Dic11—22no—
52C2×Dic22—22no—
53C2×Dic22—42no—
54C2×Dic22—44no—
55C2×C8×C11—42no—
56C42×C11—21no—
57C42×C11—21no—
58C42×C11SD1612yes—
59C42×C11Q1612yes—
60C42×C11C2×Q811yescharacteristic
61C42×C11#4112yes—
62C42×C11#4111yescharacteristic
63C22⋊Dic11—41no—
64C4⋊Dic11—22no—
65C4⋊Dic11—22no—
66C4⋊Dic11—42no—
67C4⋊Dic11—44no—
68C4⋊Dic11—44no—
69Dic11⋊C4—44no—
70Dic11⋊C4—42no—
71C4×Dic11—41no—
72C4×Dic11—42no—
73C4×Dic11—42no—
74#4318—41no—
75#4318—41no—
76C2×C11⋊C8—41no—
77#2399—111no—
78#1995—111no—
79#1503—112no—
80#1303—112no—
81#1274D1111yescharacteristic
82C23×C11#12011yescharacteristic
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—42no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11C22⋊Q812yes—
89C2×C4×C11C22⋊Q811yescharacteristic
90C2×C4×C11#12411yescharacteristic
91C2×C4×C11#12412yes—
92C2×C4×C11C2×SD1611yescharacteristic
93C2×C4×C11C2×Q1611yescharacteristic
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C11#13711yescharacteristic
96C2×Dic11—24no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103Dic22—48no—
104Dic22—82no—
105C8×C11—82no—
106C11⋊C8—81no—
107#533—111no—
108C2×C4×Q8—221no—
109#431C2×D1112yes—
110#423—111no—
111#398—222no—
112#395—222no—
113C4×C4⋊C4—112no—
114C4×C4⋊C4—221no—
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—42no—
128C4×C11#47511yescharacteristic
129C4×C11#47711yescharacteristic
130C4×C11#48711yescharacteristic
131C4×C11#48911yescharacteristic
132Dic11—44no—
133Dic11—82no—
134Dic11—82no—
135C22×Q8—221no—
136C2×M16—221no—
137C4⋊Q8—112no—
138#125—221no—
139C22⋊Q8—222no—
140C4×Q8—222no—
141C4×Q8—442no—
142C4×Q8—442no—
143#117—221no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—222no—
148C2×C42—222no—
149C2×C42D4411yescharacteristic
150C2×C42D4411yescharacteristic
151C2×C42C22×D1111yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—222no—
154C22⋊C8—22no—
155C4×C8—22no—
156#95—22no—
157#95—112no—
158#95—112no—
159#95—221no—
160#95—221no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11#202411yescharacteristic
164C2×C11#203112yes—
165C2×Q8—222no—
166C2×Q8—442no—
167C2×Q8—444no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—222no—
171C22×C4—222no—
172C22×C4C2×D4411yescharacteristic
173C22×C4D4×D1112yes—
174M16—441no—
175M16—441no—
176C2×C8—42no—
177C2×C8—441no—
178C4⋊C4—222no—
179C4⋊C4—222no—
180C4⋊C4—444no—
181C4⋊C4—442no—
182C4⋊C4—444no—
183C4⋊C4—444no—
184C4⋊C4—442no—
185C22⋊C4—441no—
186C42—21no—
187C42—21no—
188C42—441no—
189C42—442no—
190C42—442no—
191C42#431412yes—
192C42Dic4412yes—
193C42#433912yes—
194C42#434111yescharacteristic
195C42Q8×D1111yescharacteristic
196C11#1037111yescharacteristic, complemented, Sylow
197C23#6693511yescharacteristic
198Q8—448no—
199Q8—882no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—224no—
206C2×C4—442no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4#6692811yescharacteristic
213C2×C4#6693812yes—
214C2×C4#6694912yes—
215C2×C4#6695011yescharacteristic
216C2×C4C2×#431411yescharacteristic
217C2×C4C2×Dic4411yescharacteristic
218C2×C4#6696111yescharacteristic
219C2×C4#6696211yescharacteristic
220C8—82no—
221C8—881no—
222C22—22no—
223C22#1062228611yescharacteristic
224C22#1062234411yescharacteristic
225C22#1062235211yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—444no—
231C4—882no—
232C4—882no—
233C4#1062229411yescharacteristic
234C4#1062232711yescharacteristic
235C4#1062246311yescharacteristic
236C4#1062246411yescharacteristic
237C2—21no—
238C2—21no—
239C2#1306975811yescharacteristic
240C2#1306978712yes—
subgroupG/H
centerC2×C4#66928
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1274C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1274D11
hypocenterC11#10371
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
32. #66922Q8semidirect
196. C11#10371semidirect

Maximal subgroups

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

subgroupindex
#130719092
#130695972
#130671162
#130665182
C11×#12742
#1037111