Finite Group Databasebeta

← #14673438

Subgroups — #14673438

Order 2816.

310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079144C211yesmaximal, characteristic
2#13070390C211yesmaximal, characteristic
3#13069404C211yesmaximal, characteristic
4#13066731C211yesmaximal, characteristic
5#13066714C211yesmaximal, characteristic
6#13066703C211yesmaximal, characteristic
7C2×C11×#365C211yesmaximal, characteristic
8#10623031—21no—
9C2×C11×M32C2211yescharacteristic
10C2×C11×#108C2211yescharacteristic
11C2×C11×#106C2211yescharacteristic
12#10622737—21no—
13C2×#66883C2211yescharacteristic
14#10622719C2211yescharacteristic
15#10622714C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17#10622577—21no—
18#10622471—21no—
19#10622469—22no—
20#10622468—21no—
21C11×#365—22no—
22#10622194—21no—
23#10622132—21no—
24#10622132—21no—
25C2×C11×M16—21no—
26C22×C8×C11C2311yescharacteristic
27C2×C11×C4⋊C4—21no—
28#66979—21no—
29#66979D411yescharacteristic
30#66977—42no—
31C2×#4318—21no—
32C2×#4318D411yescharacteristic
33#66943—22no—
34#66943—41no—
35#66941—22no—
36#66941—41no—
37C11×M32—21no—
38C11×M32Q812yescomplemented
39C2×C11×C16—21no—
40C11×#108—21no—
41C11×#108—21no—
42C11×#106—21no—
43C11×#106D412yes—
44#66886—42no—
45#66883—21no—
46#66883Q812yescomplemented
47#66882—21no—
48#66881D411yescharacteristic
49#66881D411yescharacteristic
50#66879—21no—
51C8×Dic11—21no—
52#66876—21no—
53#66876—21no—
54C2×C11⋊C16Q812yescomplemented
55#66872—22no—
56#66871—22no—
57#13460—111nomaximal, Sylow
58C22×C4×C11—41no—
59C22×C4×C11C2×D411yescharacteristic
60C2×Dic22—42no—
61C11×M16—41no—
62C11×M16—41no—
63C2×C8×C11—41no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×Q811yescharacteristic
67C2×C8×C11C2×Q811yescharacteristic
68C2×C8×C11C2×Q811yescharacteristic
69C2×C8×C11#4111yescharacteristic
70C11×C4⋊C4—22no—
71C11×C4⋊C4—41no—
72C22⋊Dic11—41no—
73C22⋊Dic11SD1612yes—
74C4⋊Dic11—21no—
75C4⋊Dic11—21no—
76C4⋊Dic11—21no—
77C4⋊Dic11—42no—
78Dic11⋊C4—42no—
79Dic11⋊C4—42no—
80C4×Dic11—21no—
81C4×Dic11—41no—
82#4318—22no—
83#4318—21no—
84#4318—41no—
85#4318SD1612yes—
86C2×C11⋊C8—21no—
87C2×C11⋊C8—41no—
88C11×C16—22no—
89C11⋊C16—22no—
90#3163—111no—
91#2155—111no—
92C2×#365D1111yescharacteristic
93#1953—111no—
94#1389—111no—
95#1383—111no—
96#1378—111no—
97C23×C11C2×SD1611yescharacteristic
98C2×C4×C11—42no—
99C2×C4×C11—161no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C22⋊Q811yescharacteristic
102C2×C4×C11C4⋊Q811yescharacteristic
103C2×C4×C11C2×SD1611yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×C4×C11#13711yescharacteristic
106C2×Dic11—22no—
107C2×Dic11—41no—
108C2×Dic11—41no—
109Dic22—162no—
110C8×C11—81no—
111C8×C11C22⋊Q811yescharacteristic
112C8×C11C22⋊Q811yescharacteristic
113C8×C11C4⋊Q811yescharacteristic
114C8×C11C4⋊Q811yescharacteristic
115C11⋊C8—22no—
116C11⋊C8—42no—
117#544—221no—
118C2×M32—111no—
119C2×M32C2×D1111yescharacteristic
120#501—222no—
121#499—221no—
122#498—221no—
123#430—221no—
124C2×#108—111no—
125C2×#108C2×D1111yescharacteristic
126#428—221no—
127#427—111no—
128C2×#106C2×D1111yescharacteristic
129#405—111no—
130#365—22no—
131#365—221no—
132#365—221no—
133#344—221no—
134C22×C11—41no—
135C22×C11#45011yescharacteristic
136C22×C11#47511yescharacteristic
137C22×C11#49811yescharacteristic
138C4×C11—82no—
139C4×C11#39511yescharacteristic
140C4×C11#44811yescharacteristic
141C4×C11#47611yescharacteristic
142C4×C11#50111yescharacteristic
143Dic11—42no—
144Dic11—81no—
145Dic11—81no—
146C2×M16—21no—
147C2×M16—111no—
148C2×M16—221no—
149C22×C8C22×D1111yescharacteristic
150C4⋊Q8—222no—
151C4⋊Q8—441no—
152#125—222no—
153#125—441no—
154C22⋊Q8—442no—
155#117—111no—
156#117—221no—
157C2×C4⋊C4—21no—
158M32—21no—
159M32—221no—
160M32—221no—
161M32Dic2212yescomplemented
162C2×C16—21no—
163C2×C16—112no—
164#108—21no—
165#108—21no—
166#108—112no—
167#108—221no—
168#108—442no—
169#107—222no—
170#107—221no—
171#106—21no—
172#106—111no—
173#106—111no—
174#106—222no—
175#106C22⋊D1112yes—
176#97—221no—
177C4×C8—221no—
178C2×C11—21no—
179C2×C11—21no—
180C2×C11—21no—
181C2×C11#205811yescharacteristic
182C2×Q8—442no—
183C22×C4—41no—
184C22×C4D4×D1111yescharacteristic
185M16—41no—
186M16—41no—
187M16—112no—
188M16—221no—
189M16—222no—
190M16—441no—
191C2×C8—41no—
192C2×C8—221no—
193C2×C8—441no—
194C2×C8C2×Dic2211yescharacteristic
195C2×C8#433911yescharacteristic
196C2×C8D4×D1111yescharacteristic
197C2×C8Q8×D1111yescharacteristic
198C2×C8Q8×D1111yescharacteristic
199C2×C8C2×C22⋊D1111yescharacteristic
200C4⋊C4—22no—
201C4⋊C4—41no—
202C4⋊C4—221no—
203C4⋊C4—221no—
204C4⋊C4—221no—
205C4⋊C4—442no—
206C4⋊C4—442no—
207C4⋊C4—442no—
208C22⋊C4—112no—
209C22⋊C4—441no—
210C42—221no—
211C42—441no—
212C16—22no—
213C16—222no—
214C11#1346011yescharacteristic, complemented, Sylow
215C23SD16×D1111yescharacteristic
216Q8—1762no—
217C2×C4—42no—
218C2×C4—161no—
219C2×C4—222no—
220C2×C4—441no—
221C2×C4—441no—
222C2×C4#6694111yescharacteristic
223C2×C4#6694911yescharacteristic
224C2×C4SD16×D1111yescharacteristic
225C2×C4#6696711yescharacteristic
226C2×C4#6696811yescharacteristic
227C2×C4#6699011yescharacteristic
228C8—81no—
229C8—222no—
230C8—442no—
231C8#6694111yescharacteristic
232C8#6694911yescharacteristic
233C8#6697711yescharacteristic
234C8#6699711yescharacteristic
235C22—41no—
236C22#1062246711yescharacteristic
237C22#1062246811yescharacteristic
238C22#1062278211yescharacteristic
239C4—82no—
240C4—442no—
241C4—881no—
242C4—881no—
243C4#1062246911yescharacteristic
244C4#1062248311yescharacteristic
245C4#1062259211yescharacteristic
246C4#1062278311yescharacteristic
247C2—21no—
248C2—21no—
249C2—21no—
250C2#1306994711yescharacteristic
subgroupG/H
centerC2#13069947
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#365C2
socleC2×C11#2058
prime radicalC23×C11C2×SD16
hypercenterC2×#365D11
hypocenterC11#13460
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
38. C11×M32Q8semidirect
46. #66883Q8semidirect
54. C2×C11⋊C16Q8semidirect
161. M32Dic22semidirect
214. C11#13460semidirect

Maximal subgroups

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

subgroupindex
#130791442
#130703902
#130694042
#130667312
#130667142
#130667032
C2×C11×#3652
#1346011