Finite Group Databasebeta

← #14667501

Subgroups — #14667501

Order 2816.

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

normal subgroups only

This group has 296 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#13081481C211yesmaximal, characteristic
2#13070844C211yesmaximal, characteristic, complemented
3#13070661C211yesmaximal, characteristic
4#13067987C211yesmaximal, characteristic, complemented
5#13066675C211yesmaximal, characteristic, complemented
6#13066596C211yesmaximal, characteristic, complemented
7C11×#1331C211yesmaximal, characteristic
8#10623074—21no—
9C4×C11×D8C2211yescharacteristic
10D8×Dic11—21no—
11C2×#66891—21no—
12#10622621—21no—
13#10622491—21no—
14#10622464—21no—
15#10622379—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×D8D411yescharacteristic
26C4×D4×C11—21no—
27D4×Dic11—22no—
28C2×C4⋊Dic11—41no—
29#66977—41no—
30C2×Dic44—21no—
31C2×Dic44—21no—
32#66943—22no—
33#66931—42no—
34#66922—21no—
35#66922—21no—
36C4×Dic22D411yescharacteristic
37C2×C11×C16—21no—
38C11×#107D411yescharacteristic
39C11×C4⋊C8—21no—
40C11×#102—21no—
41C4×C8×C11C2311yescharacteristic
42#66896—22no—
43#66891—42no—
44#66882—21no—
45#66882D412yes—
46#66881—41no—
47#66880—41no—
48Dic11⋊C8—21no—
49C8×Dic11—21no—
50C2×C11⋊C16—21no—
51#66872—22no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12359—111nomaximal, Sylow
54C2×D4×C11—21no—
55C22×C4×C11—41no—
56C22×Dic11—42no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×Dic22D811yescharacteristic
60C11×D8—21no—
61C11×D8SD1612yes—
62C2×C8×C11—41no—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C11×C4⋊C4—21no—
66C11×C22⋊C4—41no—
67C42×C11C2×D411yescharacteristic
68C22⋊Dic11—42no—
69C4⋊Dic11—22no—
70C4⋊Dic11—42no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C4⋊Dic11—41no—
74C4⋊Dic11D811yescharacteristic
75Dic11⋊C4—21no—
76Dic11⋊C4—42no—
77C4×Dic11—21no—
78C2×C11⋊C8—21no—
79Dic44—42no—
80Dic44—41no—
81Dic44—41no—
82C11×C16—41no—
83C11⋊C16—41no—
84#3380—111no—
85#2241—111no—
86#2208—111no—
87#1670—111no—
88#1365—111no—
89Q8⋊C16—111no—
90#1331D1111yescharacteristic
91C23×C11—41no—
92D4×C11—22no—
93D4×C11—41no—
94C2×C4×C11—41no—
95C2×C4×C11—81no—
96C2×C4×C11—81no—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C2×D811yescharacteristic
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×Dic11—21no—
101C2×Dic11—21no—
102C2×Dic11—42no—
103C2×Dic11—81no—
104C2×Dic11—162no—
105Dic22—21no—
106Dic22—21no—
107Dic22—81no—
108Dic22—81no—
109Dic22—161no—
110C8×C11—21no—
111C8×C11—81no—
112C8×C11C2×SD1611yescharacteristic
113C8×C11#13711yescharacteristic
114C11⋊C8—41no—
115#554—221no—
116C2×SD32—221no—
117#500—111no—
118#499—221no—
119#494—111no—
120#478—222no—
121#476—221no—
122#475—221no—
123C8×Q8—111no—
124C4×D8—221no—
125C4×D8C2×D1111yescharacteristic
126C4⋊C16—111no—
127#358—222no—
128#358—221no—
129C4×C16C2×D1111yescharacteristic
130#335C2×D1111yescharacteristic
131#332—221no—
132C22×C11—42no—
133C22×C11—81no—
134C22×C11—81no—
135C22×C11#44711yescharacteristic
136C4×C11—21no—
137C4×C11—81no—
138C4×C11#44811yescharacteristic
139C4×C11#45411yescharacteristic
140C4×C11#50811yescharacteristic
141C4×C11#51011yescharacteristic
142Dic11—41no—
143Dic11—41no—
144Dic11—82no—
145Dic11—161no—
146C2×Q16—221no—
147C2×Q16—221no—
148C2×D8D4411yescharacteristic
149C4⋊Q8—221no—
150C4⋊Q8—221no—
151#125—222no—
152C22⋊Q8—442no—
153C22⋊Q8—441no—
154C4×Q8—111no—
155C4×D4—21no—
156C4×D4—222no—
157C2×C4⋊C4—441no—
158SD32—442no—
159C2×C16—21no—
160C2×C16—221no—
161#107—112no—
162#107—221no—
163#107D4411yescharacteristic
164#106—222no—
165#106—441no—
166C4⋊C8—21no—
167C4⋊C8—111no—
168C4⋊C8—221no—
169#103—441no—
170#102—21no—
171#102—222no—
172C4×C8—221no—
173C4×C8C22×D1111yescharacteristic
174C2×C11—82no—
175C2×C11#162711yescharacteristic
176C2×C11#218911yescharacteristic
177C2×C11#219411yescharacteristic
178C2×Q8—111no—
179C2×Q8—441no—
180C2×Q8—441no—
181C2×D4—21no—
182C22×C4—41no—
183C22×C4—442no—
184Q16—442no—
185Q16—441no—
186Q16—441no—
187D8—21no—
188D8#431412yes—
189C2×C8—41no—
190C2×C8—221no—
191C2×C8C2×D4411yescharacteristic
192C2×C8D4×D1111yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—111no—
195C4⋊C4—221no—
196C4⋊C4—222no—
197C4⋊C4—442no—
198C4⋊C4—442no—
199C4⋊C4—441no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C22⋊C4—41no—
203C22⋊C4—442no—
204C42—221no—
205C42D4×D1111yescharacteristic
206C16—41no—
207C16—441no—
208C11#1235911yescharacteristic, complemented, Sylow
209C23—41no—
210Q8—221no—
211Q8—221no—
212Q8—881no—
213Q8—881no—
214Q8—1761no—
215D4—22no—
216D4—41no—
217C2×C4—41no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—221no—
221C2×C4—221no—
222C2×C4—442no—
223C2×C4—881no—
224C2×C4—1762no—
225C2×C4#6693511yescharacteristic
226C2×C4D8×D1111yescharacteristic
227C2×C4#6696711yescharacteristic
228C8—21no—
229C8—81no—
230C8—441no—
231C8C2×#431411yescharacteristic
232C8#6696211yescharacteristic
233C22—42no—
234C22—81no—
235C22—81no—
236C22#1062238611yescharacteristic
237C4—21no—
238C4—81no—
239C4—441no—
240C4—441no—
241C4—882no—
242C4—1761no—
243C4#1062235111yescharacteristic
244C4#1062244011yescharacteristic
245C4#1062252511yescharacteristic
246C4#1062252811yescharacteristic
247C2—82no—
248C2#1306772211yescharacteristic
249C2#1307055711yescharacteristic
250C2#1307058811yescharacteristic
subgroupG/H
centerC22#10622386
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1331C2
socleC22×C11#447
prime radicalC2×C11×D8D4
hypercenter#1331D11
hypocenterC11#12359
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #13070844C2semidirect
4. #13067987C2semidirect
5. #13066675C2semidirect
6. #13066596C2semidirect
208. C11#12359semidirect

Maximal subgroups

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

subgroupindex
#130814812
#130708442
#130706612
#130679872
#130666752
#130665962
C11×#13312
#1235911