Finite Group Databasebeta

← #14667297

Subgroups — #14667297

Order 2816.

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

normal subgroups only

This group has 322 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
1#13081622C211yesmaximal, characteristic, complemented
2#13070872C211yesmaximal, characteristic
3#13070657C211yesmaximal, characteristic
4#13067976C211yesmaximal, characteristic
5#13066666C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×Q8⋊C16C211yesmaximal, characteristic, complemented
8#10623101—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622640—21no—
11C2×#66864—22no—
12C2×#66864—21no—
13#10622462—22no—
14#10622462—21no—
15#10622312—21no—
16#10622312C2211yescharacteristic
17C4×Dic44—21no—
18C4×Dic44C2211yescharacteristic
19#10622308C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C4×C11×C16C2211yescharacteristic
22#10622147—21no—
23#10622123—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×#4325—41no—
28C2×Dic44—21no—
29C2×Dic44—22no—
30C2×Dic44D411yescharacteristic
31C2×Dic44D412yes—
32C2×D88—21no—
33C2×D88—21no—
34#66943—42no—
35#66943—41no—
36#66927—21no—
37#66922—22no—
38#66922—21no—
39C4×Dic22—22no—
40C4×Dic22—21no—
41C2×C11×C16—21no—
42C2×C11×C16—21no—
43C11×C4⋊C8—21no—
44C11×C4⋊C8D411yescharacteristic
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66882D411yescharacteristic
48#66880—22no—
49#66880—21no—
50#66873—41no—
51C4⋊(C11⋊C8)—21no—
52#66864—44no—
53#66864—42no—
54#12330—111nomaximal, Sylow
55C2×Q8×C11D811yescharacteristic
56C2×D44—41no—
57C2×D44—41no—
58C2×D44—41no—
59C2×Dic22—21no—
60C2×Dic22—22no—
61C2×C8×C11—21no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—21no—
65C11×C4⋊C4D811yescharacteristic
66C42×C11—21no—
67C42×C11C2×D411yescharacteristic
68#4325—82no—
69C4⋊Dic11—21no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74Dic11⋊C4—42no—
75Dic11⋊C4—41no—
76C4×Dic11—42no—
77C4×Dic11—41no—
78C2×C11⋊C8—41no—
79Dic44—21no—
80Dic44—21no—
81Dic44—42no—
82Dic44—41no—
83Dic44—41no—
84Dic44—82no—
85D88—42no—
86D88—41no—
87D88—41no—
88C11×C16—22no—
89C11×C16—41no—
90#3395—111no—
91#2248—111no—
92#2207—111no—
93#1668—111no—
94#1362—111no—
95Q8⋊C16D1111yescharacteristic, complemented
96#1332—111no—
97C22×D11—81no—
98Q8×C11—21no—
99Q8×C11SD3212yescomplemented
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11#12011yescharacteristic
103C2×C4×C11C2×D811yescharacteristic
104C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—41no—
108D44—81no—
109D44—81no—
110D44—81no—
111D44—81no—
112D44—161no—
113Dic22—41no—
114Dic22—42no—
115Dic22—42no—
116Dic22—41no—
117C8×C11—21no—
118C8×C11—41no—
119C8×C11#13511yescharacteristic
120C8×C11AGL(1,ℤ/8)11yescharacteristic
121C11⋊C8—81no—
122#557—221no—
123C2×SD32—221no—
124C2×SD32—222no—
125#494—111no—
126#494—221no—
127#493—111no—
128#462—222no—
129#462—221no—
130#460—221no—
131C8×Q8C2×D1111yescharacteristic
132C4×Q16—111no—
133C4×Q16—221no—
134C4⋊C16C2×D1111yescharacteristic
135#357—221no—
136C4×C16C2×D1111yescharacteristic
137#335—111no—
138#331—221no—
139C22×C11#44711yescharacteristic
140C2×D11—161no—
141C2×D11—161no—
142C2×D11—161no—
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—41no—
146C4×C11#44911yescharacteristic
147C4×C11#45311yescharacteristic
148C4×C11C2×SD3211yescharacteristic
149C4×C11#51011yescharacteristic
150Dic11—81no—
151Dic11—82no—
152Dic11—81no—
153C2×Q16—111no—
154C2×Q16—112no—
155C2×Q16—222no—
156C2×Q16—221no—
157C2×SD16—441no—
158C2×D8—221no—
159C2×D8—221no—
160C4⋊Q8—222no—
161C4⋊Q8—221no—
162#127—221no—
163#125—442no—
164#125—441no—
165C4×Q8—222no—
166C4×Q8—221no—
167C4×Q8—441no—
168C4×Q8D4411yescharacteristic
169SD32—444no—
170SD32—442no—
171C2×C16—21no—
172C2×C16—21no—
173#107—111no—
174C4⋊C8—21no—
175C4⋊C8—221no—
176C4⋊C8D4411yescharacteristic
177#103—222no—
178#103—221no—
179#102—441no—
180C4×C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11#162111yescharacteristic
183C2×C11#218511yescharacteristic
184C2×C11#219311yescharacteristic
185D11—321no—
186C2×Q8—221no—
187C2×Q8—222no—
188C2×Q8D8811yescharacteristic
189C2×D4—441no—
190C2×D4—441no—
191C2×D4—441no—
192Q16—221no—
193Q16—221no—
194Q16—442no—
195Q16—441no—
196Q16—441no—
197Q16—882no—
198SD16—882no—
199D8—442no—
200D8—441no—
201D8—441no—
202C2×C8—21no—
203C2×C8—441no—
204C2×C8D4×D1111yescharacteristic
205C2×C8D4×D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—221no—
208C4⋊C4—442no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C4⋊C4—441no—
212C4⋊C4—441no—
213C4⋊C4—441no—
214C4⋊C4D8811yescharacteristic
215C42—21no—
216C42—442no—
217C42—441no—
218C42C2×D4411yescharacteristic
219C16—22no—
220C16—41no—
221C11#1233011yescharacteristic, complemented, Sylow
222C23—881no—
223Q8—21no—
224Q8—441no—
225Q8—442no—
226Q8—442no—
227Q8—441no—
228Q8#6686412yescomplemented
229D4—881no—
230D4—881no—
231D4—881no—
232D4—881no—
233D4—1761no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—441no—
237C2×C4—442no—
238C2×C4—441no—
239C2×C4#6693511yescharacteristic
240C2×C4C2×D8811yescharacteristic
241C2×C4#6696111yescharacteristic
242C8—21no—
243C8—41no—
244C8—881no—
245C8#6696711yescharacteristic
246C8#6697211yescharacteristic
247C22—1761no—
248C22—1761no—
249C22—1761no—
250C22#1062234511yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—881no—
255C4—882no—
256C4—881no—
257C4#1062242411yescharacteristic
258C4#1062243511yescharacteristic
259C4C2×#6686411yescharacteristic
260C4#1062252211yescharacteristic
261C2—3521no—
262C2#1306768311yescharacteristic
263C2#1307053511yescharacteristic
264C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socleC22×C11#447
prime radical#10622308C22
hypercenterQ8⋊C16D11
hypocenterC11#12330
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
1. #13081622C2semidirect
5. #13066666C2semidirect
6. #13066581C2semidirect
7. C11×Q8⋊C16C2semidirect
95. Q8⋊C16D11semidirect
99. Q8×C11SD32semidirect
221. C11#12330semidirect
228. Q8#66864semidirect

Maximal subgroups

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

subgroupindex
#130816222
#130708722
#130706572
#130679762
#130666662
#130665812
C11×Q8⋊C162
#1233011