Finite Group Databasebeta

← #14667298

Subgroups — #14667298

Order 2816.

322 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081621C211yesmaximal, characteristic, complemented
2#13070872C211yesmaximal, characteristic
3#13070656C211yesmaximal, characteristic
4#13067977C211yesmaximal, characteristic
5#13066664C211yesmaximal, characteristic, complemented
6#13066596C211yesmaximal, characteristic, complemented
7C11×#1332C211yesmaximal, characteristic, complemented
8#10623098—21no—
9C4×C11×Q16C2211yescharacteristic
10#10622794—21no—
11C2×#66892—21no—
12#10622644—21no—
13C2×#66864—22no—
14#10622486—21no—
15#10622461—21no—
16#10622406—22no—
17#10622312C2211yescharacteristic
18#10622308C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21C11×#335C2211yescharacteristic
22#10622129—21no—
23#10622123—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C4×Q8×C11—21no—
27#66997—22no—
28C2×#4326—22no—
29C2×Dic44—21no—
30C2×Dic44D412yes—
31C2×D88—21no—
32C2×D88—21no—
33C2×#4314—41no—
34#66942—42no—
35#66940—22no—
36#66927—21no—
37#66923—41no—
38#66922—21no—
39C4×Dic22—41no—
40C4×Dic22D411yescharacteristic
41C2×C11×C16—21no—
42C11×#107D411yescharacteristic
43C11×C4⋊C8—21no—
44C11×#103—21no—
45C4×C8×C11C2311yescharacteristic
46#66892—42no—
47#66885—41no—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66874—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#66864—44no—
54#12330—111nomaximal, Sylow
55C2×Q8×C11—21no—
56C2×D44—41no—
57C2×D44—41no—
58C2×D44—41no—
59C2×Dic22—22no—
60C2×Dic22D811yescharacteristic
61C11×Q16—21no—
62C11×Q16—21no—
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
70#4326—82no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11D811yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—42no—
76Dic11⋊C4—42no—
77Dic11⋊C4—42no—
78C4×Dic11—21no—
79C4×Dic11—42no—
80C2×C11⋊C8—21no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84D88—42no—
85D88—41no—
86D88—41no—
87#4314—82no—
88C11×C16—22no—
89C11⋊C16—41no—
90#3395—111no—
91#2248—111no—
92#2207—111no—
93#1668—111no—
94#1362—111no—
95Q8⋊C16—111no—
96#1332D1111yescharacteristic, complemented
97C22×D11—81no—
98Q8×C11—41no—
99Q8×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11—41no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—21no—
106C2×Dic11—21no—
107C2×Dic11—42no—
108D44—81no—
109D44—81no—
110D44—81no—
111D44—81no—
112D44—161no—
113Dic22—21no—
114Dic22—42no—
115Dic22—42no—
116Dic22SD3212yescomplemented
117C8×C11—21no—
118C8×C11—81no—
119C8×C11#13511yescharacteristic
120C8×C11AGL(1,ℤ/8)11yescharacteristic
121C11⋊C8—41no—
122#557—221no—
123C2×SD32—222no—
124C2×SD32—221no—
125#494—111no—
126#494—221no—
127#493—111no—
128#462—222no—
129#462—221no—
130#460—221no—
131C8×Q8—111no—
132C4×Q16—221no—
133C4×Q16C2×D1111yescharacteristic
134C4⋊C16—111no—
135#357—221no—
136C4×C16C2×D1111yescharacteristic
137#335C2×D1111yescharacteristic
138#331—221no—
139C22×C11#44711yescharacteristic
140C2×D11—161no—
141C2×D11—161no—
142C2×D11—161no—
143C4×C11—21no—
144C4×C11—81no—
145C4×C11—81no—
146C4×C11#44911yescharacteristic
147C4×C11#45311yescharacteristic
148C4×C11C2×SD3211yescharacteristic
149C4×C11#51011yescharacteristic
150Dic11—22no—
151Dic11—41no—
152Dic11—82no—
153C2×Q16—112no—
154C2×Q16—222no—
155C2×Q16—221no—
156C2×Q16D4411yescharacteristic
157C2×SD16—441no—
158C2×D8—221no—
159C2×D8—221no—
160C4⋊Q8—222no—
161C4⋊Q8—221no—
162#127—221no—
163#125—441no—
164#125—442no—
165C4×Q8—21no—
166C4×Q8—111no—
167C4×Q8—222no—
168C4×Q8—441no—
169SD32—444no—
170SD32—442no—
171C2×C16—21no—
172C2×C16—221no—
173#107D4411yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—111no—
176C4⋊C8—221no—
177#103—21no—
178#103—222no—
179#102—441no—
180C4×C8—221no—
181C4×C8C22×D1111yescharacteristic
182C2×C11#162111yescharacteristic
183C2×C11#218511yescharacteristic
184C2×C11#219311yescharacteristic
185D11—321no—
186C2×Q8—21no—
187C2×Q8—111no—
188C2×Q8—222no—
189C2×D4—441no—
190C2×D4—441no—
191C2×D4—441no—
192Q16—21no—
193Q16—21no—
194Q16—442no—
195Q16—441no—
196Q16—441no—
197Q16—882no—
198SD16—882no—
199D8—442no—
200D8—441no—
201D8—441no—
202C2×C8—41no—
203C2×C8—221no—
204C2×C8C2×D4411yescharacteristic
205C2×C8D4×D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—111no—
209C4⋊C4—221no—
210C4⋊C4—442no—
211C4⋊C4—442no—
212C4⋊C4—442no—
213C4⋊C4—441no—
214C4⋊C4—441no—
215C42—41no—
216C42—221no—
217C42—442no—
218C42D4×D1111yescharacteristic
219C16—22no—
220C16—441no—
221C11#1233011yescharacteristic, complemented, Sylow
222C23—881no—
223Q8—41no—
224Q8—41no—
225Q8—112no—
226Q8—221no—
227Q8—442no—
228Q8—442no—
229D4—881no—
230D4—881no—
231D4—881no—
232D4—881no—
233D4—1761no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—221no—
237C2×C4—221no—
238C2×C4—442no—
239C2×C4#6693511yescharacteristic
240C2×C4D8×D1111yescharacteristic
241C2×C4#6696711yescharacteristic
242C8—21no—
243C8—81no—
244C8—441no—
245C8#6695711yescharacteristic
246C8#6696111yescharacteristic
247C22—1761no—
248C22—1761no—
249C22—1761no—
250C22#1062238611yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—222no—
255C4—441no—
256C4—882no—
257C4#1062234711yescharacteristic
258C4#1062243511yescharacteristic
259C4D11×SD3211yescharacteristic
260C4#1062253111yescharacteristic
261C2—3521no—
262C2#1306768411yescharacteristic
263C2#1307053411yescharacteristic
264C2#1307058111yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1332D11
hypocenterC11#12330
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. #13081621C2semidirect
5. #13066664C2semidirect
6. #13066596C2semidirect
7. C11×#1332C2semidirect
96. #1332D11semidirect
116. Dic22SD32semidirect
221. C11#12330semidirect

Maximal subgroups

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

subgroupindex
#130816212
#130708722
#130706562
#130679772
#130666642
#130665962
C11×#13322
#1233011