Finite Group Databasebeta

← #14670340

Subgroups — #14670340

Order 2816.

408 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#10622132C212yesmaximal, complemented
2C2×#10622191C211yesmaximal, characteristic
3#13068649C211yesmaximal, characteristic
4#13066726C212yesmaximal, complemented
5C2×C11×#430C211yesmaximal, characteristic
6C22×C11×M16—21no—
7C22×C11×M16C2211yescharacteristic
8C11×#430—24no—
9C2×C11×#108—21no—
10C2×C11×#108C2212yes—
11#10622825—21no—
12C2×#66882C2211yescharacteristic
13C2×#66881C2211yescharacteristic
14C2×#66876C2212yes—
15#10622191C414yescomplemented
16#10622189—21no—
17#10622132—24no—
18C23×C4×C11D411yescharacteristic
19C2×C11×M16—22no—
20C2×C11×M16—22no—
21C2×C11×M16—24no—
22C2×C11×M16—22no—
23C2×C11×M16—41no—
24C2×C11×M16—42no—
25C2×C11×M16C2×C412yes—
26C2×C11×M16Q812yes—
27C22×C8×C11—41no—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C2×C22⋊Dic11—41no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C11×#108—24no—
34C11×#108—22no—
35C11×#108D414yes—
36C11⋊#95—41no—
37#66882—22no—
38#66881—22no—
39#66876—22no—
40#66876C2×C414yes—
41C2×C11⋊C16—22no—
42#12931—111nomaximal, Sylow
43C24×C11SD1611yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C4⋊C412yes—
49C22×C4×C11SD1611yescharacteristic
50C22×C4×C11SD1612yes—
51C22×C4×C11C2×D411yescharacteristic
52C22×Dic11—41no—
53C22×Dic11—41no—
54C11×M16—24no—
55C11×M16—24no—
56C11×M16—24no—
57C11×M16—44no—
58C11×M16—42no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11—44no—
62C2×C8×C11—42no—
63C2×C8×C11C4⋊C412yes—
64C2×C8×C11C22×C411yescharacteristic
65C2×C8×C11C2×D412yes—
66C2×C8×C11C2×Q811yescharacteristic
67C2×C8×C11#4112yes—
68C22⋊Dic11—82no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C11⋊C16—24no—
74C2×#430D1111yescharacteristic
75C2×#365—112no—
76C2×#349—111no—
77#1809—111no—
78#1387—112no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—41no—
82C23×C11—41no—
83C23×C11#10612yes—
84C23×C11C2×SD1611yescharacteristic
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11#10612yes—
92C2×C4×C11C2×C4⋊C411yescharacteristic
93C2×C4×C11#12011yescharacteristic
94C2×C4×C11#12311yescharacteristic
95C2×C4×C11C2×SD1611yescharacteristic
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C11#13711yescharacteristic
98C2×Dic11—81no—
99C2×Dic11—81no—
100C2×Dic11—81no—
101C2×Dic11—81no—
102C2×Dic11—81no—
103C2×Dic11—81no—
104C8×C11—22no—
105C8×C11—44no—
106C8×C11C4×D412yes—
107C8×C11C22⋊Q812yes—
108C22×M16—21no—
109C22×M16C2×D1111yescharacteristic
110C2×M32—112no—
111#430—24no—
112C2×#108—21no—
113C2×#108C2×D1112yes—
114C2×#107—111no—
115C2×#106—111no—
116#380—221no—
117#365—224no—
118#349—114no—
119#340—221no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—22no—
123C22×C11—42no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—81no—
127C22×C11C2×#10611yescharacteristic
128C22×C11#44811yescharacteristic
129C22×C11#48111yescharacteristic
130C4×C11—22no—
131C4×C11#38511yescharacteristic
132C4×C11#42811yescharacteristic
133C4×C11#45011yescharacteristic
134C4×C11#48311yescharacteristic
135Dic11—161no—
136Dic11—161no—
137C23×C4C22⋊D1111yescharacteristic
138C2×M16—22no—
139C2×M16—22no—
140C2×M16—24no—
141C2×M16—22no—
142C2×M16—41no—
143C2×M16—42no—
144C2×M16Dic2212yes—
145C2×M16C4×D1112yes—
146C22×C8—41no—
147C22×C8C22⋊D1111yescharacteristic
148C22×C8C22×D1111yescharacteristic
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C22⋊C4—441no—
152M32—114no—
153M32—222no—
154C2×C16—222no—
155#108—24no—
156#108—22no—
157#108C22⋊D1114yes—
158#107—222no—
159#106—222no—
160#95—441no—
161C2×C11—21no—
162C2×C11—21no—
163C2×C11—42no—
164C2×C11#185311yescharacteristic
165C2×C11#223811yescharacteristic
166C2×C11#223911yescharacteristic
167C24#432511yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—441no—
173C22×C4—441no—
174C22×C4Dic11⋊C412yes—
175C22×C4#432412yes—
176C22×C4#432511yescharacteristic
177C22×C4C2×C22⋊D1111yescharacteristic
178M16—24no—
179M16—24no—
180M16—24no—
181M16—44no—
182M16—42no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—44no—
186C2×C8—42no—
187C2×C8Dic11⋊C412yes—
188C2×C8C2×Dic2211yescharacteristic
189C2×C8C2×C4×D1111yescharacteristic
190C2×C8#433912yes—
191C2×C8C2×C22⋊D1112yes—
192C4⋊C4—441no—
193C4⋊C4—441no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C22⋊C4—882no—
197C16—224no—
198C11#1293111yescharacteristic, complemented, Sylow
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23#6687212yes—
204C23C2×#432511yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—881no—
212C2×C4—881no—
213C2×C4—881no—
214C2×C4—881no—
215C2×C4—881no—
216C2×C4—881no—
217C2×C4#6687212yes—
218C2×C4C2×Dic11⋊C411yescharacteristic
219C2×C4#6698211yescharacteristic
220C2×C4#6698511yescharacteristic
221C2×C4C2×#432411yescharacteristic
222C2×C4#6699511yescharacteristic
223C2×C4#6700611yescharacteristic
224C8—22no—
225C8—44no—
226C8#6697712yes—
227C8C4×C22⋊D1112yes—
228C22—21no—
229C22—21no—
230C22—22no—
231C22—42no—
232C22—41no—
233C22—41no—
234C22—81no—
235C22C2×#6687211yescharacteristic
236C22#1062258111yescharacteristic
237C22#1062284011yescharacteristic
238C4—22no—
239C4—1761no—
240C4—1761no—
241C4#1062257711yescharacteristic
242C4#1062258411yescharacteristic
243C4#1062282311yescharacteristic
244C4#1062283111yescharacteristic
245C2—21no—
246C2—21no—
247C2—42no—
248C2#1306880911yescharacteristic
249C2#1307083011yescharacteristic
250C2#1307083511yescharacteristic
subgroupG/H
centerC22#10622581
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#430C2
socleC22×C11#481
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC2×#430D11
hypocenterC11#12931
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#10622132C2semidirect
4. #13066726C2semidirect
15. #10622191C4semidirect
198. C11#12931semidirect

Maximal subgroups

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

subgroupindex
C2×#106221322
C2×#106221912
#130686492
#130667262
C2×C11×#4302
#1293111