Finite Group Databasebeta

← #14667493

Subgroups — #14667493

Order 2816.

288 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 73 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
1Q8×Dic44C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic
3#13070667C211yesmaximal, characteristic
4#13067986C211yesmaximal, characteristic
5#13066673C211yesmaximal, characteristic
6#13066581C211yesmaximal, characteristic
7C11×Q8⋊C16C211yesmaximal, characteristic
8Q8×Dic22—21no—
9C8×Q8×C11C2211yescharacteristic
10#10622633—21no—
11C2×Dic88—21no—
12#10622463—21no—
13#10622463—22no—
14#10622312C2211yescharacteristic
15C4×Dic44—21no—
16C4×Dic44C2211yescharacteristic
17#10622295—21no—
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622141—21no—
22#10622141—22no—
23#10622120—21no—
24#10622096C2211yescharacteristic
25C4×Q8×C11D411yescharacteristic
26Q8×Dic11—41no—
27C2×Dic44—21no—
28C2×Dic44—21no—
29C2×Dic44D411yescharacteristic
30#66941—42no—
31#66941—41no—
32#66922—22no—
33#66922—21no—
34#66922—21no—
35C4×Dic22—22no—
36C4×Dic22—21no—
37C2×C11×C16—21no—
38C2×C11×C16—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C4×C8×C11—21no—
42C4×C8×C11C2311yescharacteristic
43#66899—41no—
44#66882—22no—
45#66882—21no—
46#66882D411yescharacteristic
47#66882D412yes—
48#66880—22no—
49#66880—21no—
50#66872—41no—
51C4⋊(C11⋊C8)—21no—
52Dic88—42no—
53#12358—111nomaximal, Sylow
54C2×Q8×C11D811yescharacteristic
55C2×Dic22—21no—
56C2×Dic22—42no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×C8×C11—21no—
60C2×C8×C11C2×D411yescharacteristic
61C2×C8×C11C2×D411yescharacteristic
62C11×C4⋊C4—21no—
63C11×C4⋊C4D811yescharacteristic
64C42×C11—21no—
65C42×C11C2×D411yescharacteristic
66C4⋊Dic11—22no—
67C4⋊Dic11—21no—
68C4⋊Dic11—42no—
69C4⋊Dic11—41no—
70C4⋊Dic11—41no—
71C4⋊Dic11—41no—
72Dic11⋊C4—42no—
73Dic11⋊C4—41no—
74C4×Dic11—42no—
75C4×Dic11—41no—
76C2×C11⋊C8—41no—
77Dic44—21no—
78Dic44—42no—
79Dic44—41no—
80Dic44—41no—
81Dic44SD1612yes—
82C11×C16—41no—
83C11×C16—41no—
84Q8×Q16—111no—
85#2241—111no—
86#2209—111no—
87#1670—111no—
88#1365—111no—
89Q8⋊C16D1111yescharacteristic
90#1332—111no—
91Q8×C11—21no—
92Q8×C11Q3212yescomplemented
93C2×C4×C11—21no—
94C2×C4×C11—21no—
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11C2×D811yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×Dic11—41no—
99C2×Dic11—42no—
100C2×Dic11—41no—
101C2×Dic11—81no—
102Dic22—22no—
103Dic22—41no—
104Dic22—81no—
105Dic22—81no—
106Dic22—161no—
107Dic22—162no—
108C8×C11—21no—
109C8×C11—41no—
110C8×C11C2×SD1611yescharacteristic
111C8×C11#13711yescharacteristic
112C11⋊C8—81no—
113Q82—221no—
114C2×Q32—221no—
115#500—111no—
116#500—221no—
117#494—111no—
118#477—222no—
119#477—221no—
120#475—221no—
121C8×Q8C2×D1111yescharacteristic
122C4×Q16—111no—
123C4×Q16—221no—
124C4⋊C16C2×D1111yescharacteristic
125#358—221no—
126#358—222no—
127C4×C16C2×D1111yescharacteristic
128#335—111no—
129#332—221no—
130C22×C11#44711yescharacteristic
131C4×C11—22no—
132C4×C11—21no—
133C4×C11—41no—
134C4×C11#44811yescharacteristic
135C4×C11#45411yescharacteristic
136C4×C11C2×Q3211yescharacteristic
137C4×C11#51011yescharacteristic
138Dic11—42no—
139Dic11—82no—
140Dic11—81no—
141Dic11—161no—
142C2×Q16—111no—
143C2×Q16—221no—
144C2×Q16—221no—
145C4⋊Q8—222no—
146C4⋊Q8—221no—
147C4⋊Q8—221no—
148C4⋊Q8—442no—
149C4⋊Q8—441no—
150C4×Q8—222no—
151C4×Q8—221no—
152C4×Q8—441no—
153C4×Q8D4411yescharacteristic
154Q32—442no—
155C2×C16—21no—
156C2×C16—21no—
157#107—111no—
158#107—112no—
159#107—222no—
160#107—221no—
161#106—441no—
162C4⋊C8—21no—
163C4⋊C8—221no—
164C4⋊C8D4411yescharacteristic
165#103—222no—
166#103—221no—
167#103—441no—
168C4×C8—21no—
169C4×C8C22×D1111yescharacteristic
170C2×C11#162711yescharacteristic
171C2×C11#218811yescharacteristic
172C2×C11#219411yescharacteristic
173C2×Q8—221no—
174C2×Q8—442no—
175C2×Q8—441no—
176C2×Q8—441no—
177C2×Q8D8811yescharacteristic
178Q16—112no—
179Q16—221no—
180Q16—442no—
181Q16—441no—
182Q16—441no—
183C2×C8—21no—
184C2×C8—441no—
185C2×C8D4×D1111yescharacteristic
186C2×C8D4×D1111yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—222no—
189C4⋊C4—221no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C4⋊C4—441no—
193C4⋊C4—441no—
194C4⋊C4—441no—
195C4⋊C4—441no—
196C4⋊C4D8811yescharacteristic
197C42—21no—
198C42—442no—
199C42—441no—
200C42C2×D4411yescharacteristic
201C16—41no—
202C16—41no—
203C11#1235811yescharacteristic, complemented, Sylow
204Q8—21no—
205Q8—222no—
206Q8—441no—
207Q8—881no—
208Q8—881no—
209Q8—1761no—
210Q8—1762no—
211Q8Dic8812yescomplemented
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—441no—
215C2×C4—442no—
216C2×C4—441no—
217C2×C4—881no—
218C2×C4#6693511yescharacteristic
219C2×C4C2×D8811yescharacteristic
220C2×C4#6696111yescharacteristic
221C8—21no—
222C8—41no—
223C8—881no—
224C8SD16×D1111yescharacteristic
225C8#6697111yescharacteristic
226C22#1062234511yescharacteristic
227C4—22no—
228C4—21no—
229C4—41no—
230C4—442no—
231C4—882no—
232C4—881no—
233C4—1761no—
234C4#1062241911yescharacteristic
235C4#1062244011yescharacteristic
236C4C2×Dic8811yescharacteristic
237C4#1062252211yescharacteristic
238C2#1306772111yescharacteristic
239C2#1307055211yescharacteristic
240C2#1307058911yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×Q8⋊C16C2
socle, prime radicalC22×C11#447
hypercenterQ8⋊C16D11
hypocenterC11#12358
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
92. Q8×C11Q32semidirect
203. C11#12358semidirect
211. Q8Dic88semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic442
#130708442
#130706672
#130679862
#130666732
#130665812
C11×Q8⋊C162
#1235811