Finite Group Databasebeta

← #14656906

Subgroups — #14656906

Order 2816.

416 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 99 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#13067115C212yesmaximal
3#13066517C212yesmaximal
4#13066445C211yesmaximal, characteristic
5C11×#1995C211yesmaximal, characteristic
6C11×#533C2211yescharacteristic
7C2×C4×Dic22—21no—
8C11×#423C2211yescharacteristic
9C11×#376C2211yescharacteristic
10C4×C4⋊Dic11—21no—
11C4×C4⋊Dic11C2212yes—
12#10622538C2212yes—
13#10622274—22no—
14#10622269—22no—
15C11×#339—21no—
16C11×#339—21no—
17#10622176—22no—
18#10622176—22no—
19C22×Dic22—21no—
20C2×C11×M16—21no—
21C11×C4⋊Q8Q812yescomplemented
22C11×#125—21no—
23C11×C22⋊Q8—22no—
24C4×Q8×C11—22no—
25C11×#117—21no—
26C2×C42×C11D411yescharacteristic
27C2×C42×C11D411yescharacteristic
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11—22no—
31C2×C4⋊Dic11—22no—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—22no—
34C4×Dic22—42no—
35C4×Dic22—42no—
36C11×C4⋊C8—22no—
37C11×#95—22no—
38C11⋊#95—21no—
39C11⋊#95—21no—
40C11⋊#95D412yes—
41C11⋊#95D412yes—
42C22⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44C4×C11⋊C8—22no—
45#10371—111nomaximal, Sylow
46C2×Q8×C11—22no—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11C2×D412yes—
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—22no—
52C22×Dic11—22no—
53C2×Dic22—42no—
54C2×Dic22—44no—
55C11×M16—41no—
56C11×M16—41no—
57C2×C8×C11—41no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—22no—
60C11×C4⋊C4—42no—
61C11×C22⋊C4—41no—
62C42×C11—21no—
63C42×C11—21no—
64C42×C11—41no—
65C42×C11SD1612yes—
66C42×C11Q1612yes—
67C42×C11C2×Q811yescharacteristic
68C42×C11#4111yescharacteristic
69C42×C11#4112yes—
70C4⋊Dic11—42no—
71C4⋊Dic11—44no—
72C4⋊Dic11—44no—
73Dic11⋊C4—44no—
74C4×Dic11—42no—
75C4×Dic11—42no—
76C2×C11⋊C8—42no—
77#2399—111no—
78#1995D1111yescharacteristic
79#1503—112no—
80#1303—112no—
81#1274—111no—
82C23×C11#12011yescharacteristic
83Q8×C11—82no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—42no—
90C2×C4×C11C22⋊Q812yes—
91C2×C4×C11C22⋊Q811yescharacteristic
92C2×C4×C11#12412yes—
93C2×C4×C11#12411yescharacteristic
94C2×C4×C11C2×SD1611yescharacteristic
95C2×C4×C11C2×Q1611yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C11#13711yescharacteristic
98C2×Dic11—24no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104Dic22—48no—
105C8×C11—81no—
106C11⋊C8—82no—
107#533C2×D1111yescharacteristic
108C2×C4×Q8—221no—
109#431—112no—
110#423C2×D1111yescharacteristic
111#398—222no—
112#395—222no—
113C4×C4⋊C4—112no—
114C4×C4⋊C4—221no—
115#376C2×D1111yescharacteristic
116#339—21no—
117#339—21no—
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—82no—
129C4×C11#47511yescharacteristic
130C4×C11#47711yescharacteristic
131C4×C11#48711yescharacteristic
132C4×C11#48911yescharacteristic
133Dic11—44no—
134Dic11—82no—
135C22×Q8—221no—
136C2×M16—21no—
137C4⋊Q8Dic2212yescomplemented
138#125—21no—
139C22⋊Q8—22no—
140C4×Q8—22no—
141C4×Q8—442no—
142C4×Q8—442no—
143#117—21no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—221no—
146C2×C4⋊C4—222no—
147C2×C4⋊C4—222no—
148C2×C42—222no—
149C2×C42C22⋊D1111yescharacteristic
150C2×C42C22⋊D1111yescharacteristic
151C2×C42C22×D1111yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—222no—
154C22⋊C8—222no—
155C4×C8—222no—
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—22no—
166C2×Q8—442no—
167C2×Q8—444no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—222no—
171C22×C4—222no—
172C22×C4D4×D1112yes—
173C22×C4C2×C22⋊D1111yescharacteristic
174M16—41no—
175M16—41no—
176C2×C8—41no—
177C2×C8—442no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—444no—
182C4⋊C4—442no—
183C4⋊C4—444no—
184C4⋊C4—444no—
185C22⋊C4—41no—
186C42—21no—
187C42—21no—
188C42—41no—
189C42—442no—
190C42—442no—
191C42#432512yes—
192C42#432612yes—
193C42C2×Dic2211yescharacteristic
194C42#433911yescharacteristic
195C42#434112yes—
196C11#1037111yescharacteristic, complemented, Sylow
197C23#6699011yescharacteristic
198Q8—82no—
199Q8—448no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—224no—
207C2×C4—442no—
208C2×C4—442no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4#6693112yes—
213C2×C4#6693812yes—
214C2×C4#6697711yescharacteristic
215C2×C4#6698911yescharacteristic
216C2×C4C2×#432511yescharacteristic
217C2×C4C2×#432611yescharacteristic
218C2×C4#6700211yescharacteristic
219C2×C4#6700411yescharacteristic
220C8—81no—
221C8—882no—
222C22—22no—
223C22#1062256011yescharacteristic
224C22#1062265911yescharacteristic
225C22#1062266311yescharacteristic
226C4—22no—
227C4—22no—
228C4—42no—
229C4—42no—
230C4—82no—
231C4—444no—
232C4—882no—
233C4#1062263311yescharacteristic
234C4#1062263411yescharacteristic
235C4#1062266811yescharacteristic
236C4#1062269411yescharacteristic
237C2—21no—
238C2—21no—
239C2#1306975711yescharacteristic
240C2#1306978612yes—
subgroupG/H
centerC2×C4#66989
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1995C2
socleC22×C11#393
prime radicalC23×C11#120
hypercenter#1995D11
hypocenterC11#10371
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
21. C11×C4⋊Q8Q8semidirect
137. C4⋊Q8Dic22semidirect
196. C11#10371semidirect

Maximal subgroups

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

subgroupindex
#130719092
#130671152
#130665172
#130664452
C11×#19952
#1037111