Finite Group Databasebeta

← #14667488

Subgroups — #14667488

Order 2816.

288 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 69 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#13081499C211yesmaximal, characteristic
2#13070663C211yesmaximal, characteristic
3#13067983C211yesmaximal, characteristic
4#13066674C211yesmaximal, characteristic
5#13066596C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×#2241C211yesmaximal, characteristic
8#10623253—21no—
9C11×#500C2211yescharacteristic
10C11×#494C2211yescharacteristic
11C2×#66893—21no—
12#10622707—21no—
13#10622704—21no—
14#10622488—22no—
15#10622487—21no—
16#10622486—21no—
17C4×Dic44C2211yescharacteristic
18C8×Dic22C2211yescharacteristic
19C11×#358—22no—
20C4×C11×C16C2211yescharacteristic
21#10622202—21no—
22#10622185—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C11×C4⋊Q8—21no—
29#66997—42no—
30C2×Dic44D411yescharacteristic
31#66941—22no—
32#66941—41no—
33#66940—22no—
34#66940—41no—
35C4×Dic22—21no—
36C4×Dic22D411yescharacteristic
37C2×C11×C16—21no—
38C11×#107—21no—
39C11×#107D412yes—
40C4×C8×C11C2311yescharacteristic
41#66893—42no—
42#66882D411yescharacteristic
43#66880—21no—
44Dic11⋊C8—21no—
45C8×Dic11—21no—
46C2×C11⋊C16—21no—
47#66874—22no—
48#66874—41no—
49#66872—41no—
50#66871—22no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12358—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×Q8×C11—41no—
56C2×Dic22—21no—
57C2×Dic22—42no—
58C2×Dic22D811yescharacteristic
59C11×Q16—42no—
60C11×Q16—41no—
61C11×Q16—41no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—22no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C42×C11C2×D411yescharacteristic
69C4⋊Dic11—21no—
70C4⋊Dic11D811yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—42no—
73Dic11⋊C4—42no—
74Dic11⋊C4—41no—
75C4×Dic11—21no—
76C4×Dic11—42no—
77C4×Dic11—41no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80Dic44—21no—
81Dic44SD1612yes—
82C11×C16—41no—
83C11⋊C16—41no—
84Q8×Q16—111no—
85#2241D1111yescharacteristic
86#2209—111no—
87#1670—111no—
88#1365—111no—
89Q8⋊C16—111no—
90#1332—111no—
91Q8×C11—81no—
92Q8×C11—81no—
93Q8×C11—161no—
94C2×C4×C11—42no—
95C2×C4×C11—81no—
96C2×C4×C11#12011yescharacteristic
97C2×C4×C11C2×D811yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—41no—
102C2×Dic11—41no—
103Dic22—21no—
104Dic22—22no—
105Dic22—41no—
106Dic22—162no—
107Dic22Q3212yescomplemented
108C8×C11—21no—
109C8×C11C2×SD1611yescharacteristic
110C8×C11#13711yescharacteristic
111C11⋊C8—41no—
112C11⋊C8—81no—
113Q82—221no—
114C2×Q32—221no—
115#500—221no—
116#500C2×D1111yescharacteristic
117#494C2×D1111yescharacteristic
118#477—221no—
119#477—222no—
120#475—221no—
121C8×Q8—111no—
122C4×Q16—111no—
123C4×Q16—221no—
124C4⋊C16—111no—
125#358—22no—
126#358—221no—
127C4×C16C2×D1111yescharacteristic
128#335—111no—
129#332—221no—
130C22×C11#44711yescharacteristic
131C4×C11—21no—
132C4×C11—82no—
133C4×C11—161no—
134C4×C11#44811yescharacteristic
135C4×C11#45411yescharacteristic
136C4×C11C2×Q3211yescharacteristic
137C4×C11#51011yescharacteristic
138Dic11—22no—
139Dic11—42no—
140Dic11—41no—
141Dic11—81no—
142C2×Q16—21no—
143C2×Q16—21no—
144C2×Q16—111no—
145C4⋊Q8—21no—
146C4⋊Q8—21no—
147C4⋊Q8—222no—
148C4⋊Q8—441no—
149C4⋊Q8—442no—
150C4×Q8—111no—
151C4×Q8—222no—
152C4×Q8—221no—
153C4×Q8—441no—
154Q32—442no—
155C2×C16—21no—
156C2×C16—221no—
157#107—21no—
158#107—111no—
159#107—222no—
160#107C22⋊D1112yes—
161#106—441no—
162C4⋊C8—111no—
163C4⋊C8—221no—
164C4⋊C8—221no—
165#103—222no—
166#103—221no—
167#103—441no—
168C4×C8—221no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#162711yescharacteristic
171C2×C11#218811yescharacteristic
172C2×C11#219411yescharacteristic
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—111no—
176C2×Q8—221no—
177C2×Q8—442no—
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—112no—
182Q16—221no—
183C2×C8—221no—
184C2×C8—441no—
185C2×C8D4×D1111yescharacteristic
186C2×C8C2×C22⋊D1111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—111no—
192C4⋊C4—221no—
193C4⋊C4—221no—
194C4⋊C4—442no—
195C4⋊C4—442no—
196C4⋊C4—441no—
197C42—221no—
198C42—442no—
199C42—441no—
200C42D4×D1111yescharacteristic
201C16—41no—
202C16—441no—
203C11#1235811yescharacteristic, complemented, Sylow
204Q8—81no—
205Q8—81no—
206Q8—112no—
207Q8—161no—
208Q8—221no—
209Q8—222no—
210Q8—441no—
211Q8—1762no—
212C2×C4—42no—
213C2×C4—81no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4—441no—
217C2×C4—441no—
218C2×C4D8×D1111yescharacteristic
219C2×C4#6696411yescharacteristic
220C2×C4#6699011yescharacteristic
221C8—21no—
222C8—441no—
223C8—881no—
224C8SD16×D1111yescharacteristic
225C8#6696811yescharacteristic
226C22#1062276911yescharacteristic
227C4—21no—
228C4—82no—
229C4—161no—
230C4—222no—
231C4—442no—
232C4—441no—
233C4—881no—
234C4D11×Q3211yescharacteristic
235C4#1062253111yescharacteristic
236C4#1062267511yescharacteristic
237C4#1062278311yescharacteristic
238C2#1306771611yescharacteristic
239C2#1307054811yescharacteristic
240C2#1307058611yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2241C2
socle, prime radicalC22×C11#447
hypercenter#2241D11
hypocenterC11#12358
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

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
#130814992
#130706632
#130679832
#130666742
#130665962
#130665812
C11×#22412
#1235811