Finite Group Databasebeta

← #14667466

Subgroups — #14667466

Order 2816.

304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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
1Q16×Dic22C211yesmaximal, characteristic, complemented
2#13070840C211yesmaximal, characteristic
3#13070656C211yesmaximal, characteristic
4#13067977C211yesmaximal, characteristic
5#13066675C211yesmaximal, characteristic, complemented
6#13066596C211yesmaximal, characteristic, complemented
7C11×#1332C211yesmaximal, characteristic, complemented
8Q8×Dic22—21no—
9C4×C11×Q16C2211yescharacteristic
10Q16×Dic11—21no—
11C2×#66892—21no—
12#10622634—21no—
13#10622487—21no—
14#10622461—21no—
15#10622407—22no—
16#10622308C2211yescharacteristic
17#10622295C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20C11×#335C2211yescharacteristic
21#10622147—22no—
22#10622129—21no—
23#10622123—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C4×Q8×C11—21no—
27Q8×Dic11—22no—
28C2×D88—21no—
29C2×D88—21no—
30C2×#4314—41no—
31#66941—22no—
32#66941—42no—
33#66927—21no—
34#66922—21no—
35#66922—41no—
36C4×Dic22—41no—
37C4×Dic22D411yescharacteristic
38C2×C11×C16—21no—
39C11×#107D411yescharacteristic
40C11×C4⋊C8—21no—
41C11×#103—21no—
42C4×C8×C11C2311yescharacteristic
43#66899—22no—
44#66892—42no—
45#66885—41no—
46#66882—21no—
47#66882D412yes—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66871—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12354—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×D44—41no—
56C2×D44—41no—
57C2×D44—41no—
58C2×Dic22—42no—
59C2×Dic22—41no—
60C2×Dic22D811yescharacteristic
61C11×Q16—21no—
62C11×Q16SD1612yescomplemented
63C2×C8×C11—41no—
64C2×C8×C11C2×D411yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66C11×C4⋊C4—21no—
67C11×C4⋊C4—41no—
68C42×C11—41no—
69C42×C11C2×D411yescharacteristic
70C4⋊Dic11—22no—
71C4⋊Dic11—42no—
72C4⋊Dic11—41no—
73C4⋊Dic11D811yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—42no—
76C4×Dic11—21no—
77C4×Dic11—42no—
78C2×C11⋊C8—21no—
79D88—42no—
80D88—41no—
81D88—41no—
82#4314—82no—
83C11×C16—41no—
84C11⋊C16—41no—
85Q8×Q16—111no—
86#2240—111no—
87#2207—111no—
88#1668—111no—
89#1365—111no—
90Q8⋊C16—111no—
91#1332D1111yescharacteristic, complemented
92C22×D11—81no—
93Q8×C11—22no—
94Q8×C11—41no—
95C2×C4×C11—41no—
96C2×C4×C11—41no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—42no—
103D44—81no—
104D44—81no—
105D44—81no—
106D44—81no—
107D44—161no—
108Dic22—21no—
109Dic22—162no—
110Dic22—161no—
111Dic22SD3212yescomplemented
112C8×C11—21no—
113C8×C11—81no—
114C8×C11C2×SD1611yescharacteristic
115C8×C11#13711yescharacteristic
116C11⋊C8—41no—
117Q82—221no—
118C2×SD32—221no—
119#500—111no—
120#500—221no—
121#493—111no—
122#477—222no—
123#477—221no—
124#460—221no—
125C8×Q8—111no—
126C4×Q16—221no—
127C4×Q16C2×D1111yescharacteristic
128C4⋊C16—111no—
129#357—222no—
130#357—221no—
131C4×C16C2×D1111yescharacteristic
132#335C2×D1111yescharacteristic
133#331—221no—
134C22×C11#44711yescharacteristic
135C2×D11—161no—
136C2×D11—161no—
137C2×D11—161no—
138C4×C11—21no—
139C4×C11—42no—
140C4×C11—81no—
141C4×C11#44811yescharacteristic
142C4×C11#45411yescharacteristic
143C4×C11C2×SD3211yescharacteristic
144C4×C11#51011yescharacteristic
145Dic11—22no—
146Dic11—41no—
147Dic11—82no—
148C2×Q16D4411yescharacteristic
149C2×SD16—441no—
150C2×D8—221no—
151C2×D8—221no—
152C4⋊Q8—222no—
153C4⋊Q8—221no—
154C4⋊Q8—441no—
155C4⋊Q8—442no—
156#127—221no—
157C4×Q8—21no—
158C4×Q8—111no—
159C4×Q8—222no—
160C4×Q8—441no—
161SD32—442no—
162C2×C16—21no—
163C2×C16—221no—
164#107—112no—
165#107—222no—
166#107—221no—
167#107D4411yescharacteristic
168C4⋊C8—21no—
169C4⋊C8—111no—
170C4⋊C8—221no—
171#103—21no—
172#103—222no—
173#102—441no—
174C4×C8—221no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162711yescharacteristic
177C2×C11#218511yescharacteristic
178C2×C11#219211yescharacteristic
179D11—321no—
180C2×Q8—21no—
181C2×Q8—111no—
182C2×Q8—442no—
183C2×Q8—441no—
184C2×D4—441no—
185C2×D4—441no—
186C2×D4—441no—
187Q16—21no—
188Q16#431412yescomplemented
189SD16—882no—
190D8—442no—
191D8—441no—
192D8—441no—
193C2×C8—41no—
194C2×C8—221no—
195C2×C8C2×D4411yescharacteristic
196C2×C8D4×D1111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—41no—
199C4⋊C4—111no—
200C4⋊C4—221no—
201C4⋊C4—222no—
202C4⋊C4—442no—
203C4⋊C4—442no—
204C4⋊C4—441no—
205C42—41no—
206C42—221no—
207C42—442no—
208C42D4×D1111yescharacteristic
209C16—41no—
210C16—441no—
211C11#1235411yescharacteristic, complemented, Sylow
212C23—881no—
213Q8—22no—
214Q8—41no—
215Q8—112no—
216Q8—221no—
217Q8—1761no—
218Q8—1762no—
219D4—881no—
220D4—881no—
221D4—881no—
222D4—881no—
223D4—1761no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—442no—
229C2×C4#6693511yescharacteristic
230C2×C4D8×D1111yescharacteristic
231C2×C4#6696711yescharacteristic
232C8—21no—
233C8—81no—
234C8—441no—
235C8C2×#431411yescharacteristic
236C8#6696211yescharacteristic
237C22—1761no—
238C22—1761no—
239C22—1761no—
240C22#1062238611yescharacteristic
241C4—21no—
242C4—42no—
243C4—81no—
244C4—222no—
245C4—441no—
246C4—882no—
247C4#1062235111yescharacteristic
248C4#1062244011yescharacteristic
249C4D11×SD3211yescharacteristic
250C4#1062253111yescharacteristic
251C2—3521no—
252C2#1306772211yescharacteristic
253C2#1307053411yescharacteristic
254C2#1307057411yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1332D11
hypocenterC11#12354
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
1. Q16×Dic22C2semidirect
5. #13066675C2semidirect
6. #13066596C2semidirect
7. C11×#1332C2semidirect
62. C11×Q16SD16semidirect
91. #1332D11semidirect
111. Dic22SD32semidirect
188. Q16#4314semidirect
211. C11#12354semidirect

Maximal subgroups

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

subgroupindex
Q16×Dic222
#130708402
#130706562
#130679772
#130666752
#130665962
C11×#13322
#1235411