Finite Group Databasebeta

← #14667494

Subgroups — #14667494

Order 2816.

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

normal subgroups only

This group has 288 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
2#13070844C211yesmaximal, characteristic
3#13070666C211yesmaximal, characteristic
4#13067987C211yesmaximal, characteristic
5#13066675C211yesmaximal, characteristic
6#13066596C211yesmaximal, characteristic
7C11×#1332C211yesmaximal, characteristic
8Q8×Dic22—21no—
9C4×C11×Q16C2211yescharacteristic
10Q16×Dic11—21no—
11C2×#66893—21no—
12#10622634—21no—
13#10622487—21no—
14#10622464—21no—
15#10622407—22no—
16#10622312C2211yescharacteristic
17#10622295C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C4×C11×C16C2211yescharacteristic
20C11×#335C2211yescharacteristic
21#10622141—22no—
22#10622130—21no—
23#10622124—21no—
24C4⋊(C11⋊C16)C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C4×Q8×C11—21no—
27Q8×Dic11—22no—
28C2×Dic44—21no—
29C2×Dic44—21no—
30#66941—22no—
31#66941—42no—
32#66922—21no—
33#66922—21no—
34#66922—41no—
35C4×Dic22—41no—
36C4×Dic22D411yescharacteristic
37C2×C11×C16—21no—
38C11×#107D411yescharacteristic
39C11×C4⋊C8—21no—
40C11×#103—21no—
41C4×C8×C11C2311yescharacteristic
42#66899—22no—
43#66893—42no—
44#66882—21no—
45#66882D412yes—
46#66881—41no—
47#66880—41no—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66871—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12358—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Dic22—42no—
56C2×Dic22—41no—
57C2×Dic22—41no—
58C2×Dic22D811yescharacteristic
59C11×Q16—21no—
60C11×Q16SD1612yes—
61C2×C8×C11—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—21no—
65C11×C4⋊C4—41no—
66C42×C11—41no—
67C42×C11C2×D411yescharacteristic
68C4⋊Dic11—22no—
69C4⋊Dic11—42no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11D811yescharacteristic
74Dic11⋊C4—21no—
75Dic11⋊C4—42no—
76C4×Dic11—21no—
77C4×Dic11—42no—
78C2×C11⋊C8—21no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84Q8×Q16—111no—
85#2241—111no—
86#2209—111no—
87#1670—111no—
88#1365—111no—
89Q8⋊C16—111no—
90#1332D1111yescharacteristic
91Q8×C11—22no—
92Q8×C11—41no—
93C2×C4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—42no—
101C2×Dic11—81no—
102Dic22—21no—
103Dic22—81no—
104Dic22—81no—
105Dic22—162no—
106Dic22—161no—
107Dic22Q3212yescomplemented
108C8×C11—21no—
109C8×C11—81no—
110C8×C11C2×SD1611yescharacteristic
111C8×C11#13711yescharacteristic
112C11⋊C8—41no—
113Q82—221no—
114C2×Q32—221no—
115#500—111no—
116#500—221no—
117#494—111no—
118#477—222no—
119#477—221no—
120#475—221no—
121C8×Q8—111no—
122C4×Q16—221no—
123C4×Q16C2×D1111yescharacteristic
124C4⋊C16—111no—
125#358—222no—
126#358—221no—
127C4×C16C2×D1111yescharacteristic
128#335C2×D1111yescharacteristic
129#332—221no—
130C22×C11#44711yescharacteristic
131C4×C11—21no—
132C4×C11—42no—
133C4×C11—81no—
134C4×C11#44811yescharacteristic
135C4×C11#45411yescharacteristic
136C4×C11C2×Q3211yescharacteristic
137C4×C11#51011yescharacteristic
138Dic11—22no—
139Dic11—41no—
140Dic11—82no—
141Dic11—161no—
142C2×Q16—221no—
143C2×Q16—221no—
144C2×Q16D4411yescharacteristic
145C4⋊Q8—222no—
146C4⋊Q8—221no—
147C4⋊Q8—221no—
148C4⋊Q8—441no—
149C4⋊Q8—442no—
150C4×Q8—21no—
151C4×Q8—111no—
152C4×Q8—222no—
153C4×Q8—441no—
154Q32—442no—
155C2×C16—21no—
156C2×C16—221no—
157#107—112no—
158#107—222no—
159#107—221no—
160#107D4411yescharacteristic
161#106—441no—
162C4⋊C8—21no—
163C4⋊C8—111no—
164C4⋊C8—221no—
165#103—21no—
166#103—222no—
167#103—441no—
168C4×C8—221no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#162711yescharacteristic
171C2×C11#218811yescharacteristic
172C2×C11#219411yescharacteristic
173C2×Q8—21no—
174C2×Q8—111no—
175C2×Q8—442no—
176C2×Q8—441no—
177C2×Q8—441no—
178Q16—21no—
179Q16—442no—
180Q16—441no—
181Q16—441no—
182Q16#431412yes—
183C2×C8—41no—
184C2×C8—221no—
185C2×C8C2×D4411yescharacteristic
186C2×C8D4×D1111yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—41no—
189C4⋊C4—111no—
190C4⋊C4—221no—
191C4⋊C4—222no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4—441no—
197C42—41no—
198C42—221no—
199C42—442no—
200C42D4×D1111yescharacteristic
201C16—41no—
202C16—441no—
203C11#1235811yescharacteristic, complemented, Sylow
204Q8—22no—
205Q8—41no—
206Q8—112no—
207Q8—221no—
208Q8—881no—
209Q8—881no—
210Q8—1761no—
211Q8—1762no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—442no—
217C2×C4—881no—
218C2×C4#6693511yescharacteristic
219C2×C4D8×D1111yescharacteristic
220C2×C4#6696711yescharacteristic
221C8—21no—
222C8—81no—
223C8—441no—
224C8C2×#431411yescharacteristic
225C8#6696211yescharacteristic
226C22#1062238611yescharacteristic
227C4—21no—
228C4—42no—
229C4—81no—
230C4—222no—
231C4—441no—
232C4—882no—
233C4—1761no—
234C4#1062235111yescharacteristic
235C4#1062244011yescharacteristic
236C4#1062252811yescharacteristic
237C4D11×Q3211yescharacteristic
238C2#1306772211yescharacteristic
239C2#1307055111yescharacteristic
240C2#1307058811yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1332C2
socle, prime radicalC22×C11#447
hypercenter#1332D11
hypocenterC11#12358
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
107. Dic22Q32semidirect
203. C11#12358semidirect

Maximal subgroups

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

subgroupindex
Q16×Dic222
#130708442
#130706662
#130679872
#130666752
#130665962
C11×#13322
#1235811