Finite Group Databasebeta

← #14667496

Subgroups — #14667496

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#13081484C211yesmaximal, characteristic
2#13070843C211yesmaximal, characteristic, complemented
3#13070658C211yesmaximal, characteristic
4#13066675C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic
7C11×#1670C211yesmaximal, characteristic, complemented
8#10623110—21no—
9C11×#494C2211yescharacteristic
10C11×#475—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66892—21no—
13#10622460—22no—
14#10622455—21no—
15C4×D88—21no—
16C4×D88C2211yescharacteristic
17#10622296—21no—
18#10622295C2211yescharacteristic
19C11×#335C2211yescharacteristic
20C11×#332—21no—
21#10622202—21no—
22#10622202—22no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16—21no—
27C11×C4⋊Q8—21no—
28C4×Q8×C11D411yescharacteristic
29#66999—41no—
30C2×D88D411yescharacteristic
31#66949—42no—
32C4⋊C4×D11—41no—
33C4×D44—22no—
34C4×D44—21no—
35#66923—22no—
36#66922—21no—
37C11×#106—41no—
38C11×C4⋊C8—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#103—41no—
42C4×C8×C11—21no—
43C4×C8×C11C2311yescharacteristic
44#66892—42no—
45#66885—22no—
46#66885—21no—
47#66882—21no—
48#66882D412yes—
49#66882D411yescharacteristic
50#66881—22no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53#12359—111nomaximal, Sylow
54C2×Q8×C11—41no—
55C2×Q8×C11D811yescharacteristic
56C2×D44—21no—
57C2×C4×D11—42no—
58C2×C4×D11—41no—
59C2×Dic22—41no—
60C11×Q16—42no—
61C11×Q16—41no—
62C11×Q16—41no—
63C2×C8×C11—21no—
64C2×C8×C11—41no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4D811yescharacteristic
71C42×C11—21no—
72C42×C11C2×D411yescharacteristic
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—41no—
75C4⋊Dic11—21no—
76C4⋊Dic11—22no—
77C4⋊Dic11—41no—
78Dic11⋊C4—42no—
79Dic11⋊C4—42no—
80D88—21no—
81D88SD1612yes—
82C11⋊C16—41no—
83C11⋊C16—41no—
84#3380—111no—
85#2241—111no—
86#2208—111no—
87#1670D1111yescharacteristic, complemented
88#1365—111no—
89Q8⋊C16—111no—
90#1331—111no—
91C22×D11—41no—
92Q8×C11—21no—
93Q8×C11—21no—
94Q8×C11—81no—
95Q8×C11—81no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—81no—
99C2×C4×C11#12011yescharacteristic
100C2×C4×C11C2×D811yescharacteristic
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×Dic11—41no—
103C2×Dic11—42no—
104D44—22no—
105D44—41no—
106C4×D11—81no—
107C4×D11—81no—
108C4×D11—162no—
109Dic22—161no—
110C8×C11—21no—
111C8×C11—41no—
112C8×C11—81no—
113C8×C11C2×SD1611yescharacteristic
114C8×C11#13711yescharacteristic
115#554—221no—
116C2×SD32—221no—
117#500—111no—
118#499—221no—
119#494C2×D1111yescharacteristic
120#478—222no—
121#476—221no—
122#475—21no—
123C8×Q8C2×D1111yescharacteristic
124C4×D8—111no—
125C4×D8—221no—
126C4⋊C16—111no—
127#358—221no—
128#358—222no—
129C4×C16—111no—
130#335C2×D1111yescharacteristic
131#332—21no—
132C22×C11#44711yescharacteristic
133C2×D11—42no—
134C2×D11—81no—
135C2×D11—81no—
136C4×C11—21no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11—161no—
140C4×C11#44811yescharacteristic
141C4×C11#45411yescharacteristic
142C4×C11#50811yescharacteristic
143C4×C11#51011yescharacteristic
144Dic11—81no—
145Dic11—82no—
146C2×Q16—21no—
147C2×Q16—21no—
148C2×D8—111no—
149C4⋊Q8—21no—
150C4⋊Q8—221no—
151#125—222no—
152C22⋊Q8—442no—
153C22⋊Q8—441no—
154C4×Q8C22⋊D1111yescharacteristic
155C4×D4—222no—
156C4×D4—221no—
157C2×C4⋊C4—441no—
158SD32—442no—
159C2×C16—221no—
160C2×C16—221no—
161#107—111no—
162#107—112no—
163#107—221no—
164#106—41no—
165#106—222no—
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8C22⋊D1111yescharacteristic
169#103—41no—
170#102—222no—
171#102—221no—
172C4×C8—21no—
173C4×C8C22×D1111yescharacteristic
174C2×C11#162711yescharacteristic
175C2×C11#218911yescharacteristic
176C2×C11#219411yescharacteristic
177D11—82no—
178C2×Q8—41no—
179C2×Q8—441no—
180C2×Q8#432311yescharacteristic
181C2×D4—221no—
182C22×C4—442no—
183C22×C4—441no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187D8—112no—
188D8—221no—
189C2×C8—21no—
190C2×C8—41no—
191C2×C8D4×D1111yescharacteristic
192C2×C8D4×D1111yescharacteristic
193C4⋊C4—21no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—221no—
197C4⋊C4—222no—
198C4⋊C4—442no—
199C4⋊C4—442no—
200C4⋊C4—441no—
201C4⋊C4#432311yescharacteristic
202C22⋊C4—442no—
203C22⋊C4—441no—
204C42—21no—
205C42C2×C22⋊D1111yescharacteristic
206C16—441no—
207C16—441no—
208C11#1235911yescharacteristic, complemented, Sylow
209C23—441no—
210Q8—21no—
211Q8—21no—
212Q8—81no—
213Q8—81no—
214Q8—1761no—
215D4—222no—
216D4—441no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—81no—
220C2×C4—441no—
221C2×C4—442no—
222C2×C4—881no—
223C2×C4—881no—
224C2×C4—1762no—
225C2×C4C2×#432311yescharacteristic
226C2×C4#6699011yescharacteristic
227C2×C4#6700211yescharacteristic
228C8—21no—
229C8—41no—
230C8—81no—
231C8SD16×D1111yescharacteristic
232C8#6696811yescharacteristic
233C22—442no—
234C22—881no—
235C22—881no—
236C22#1062264911yescharacteristic
237C4—21no—
238C4—41no—
239C4—41no—
240C4—161no—
241C4—881no—
242C4—882no—
243C4#1062278311yescharacteristic
244C4#1062279211yescharacteristic
245C4#1062280711yescharacteristic
246C4#1062281411yescharacteristic
247C2—882no—
248C2#1306771711yescharacteristic
249C2#1307055411yescharacteristic
250C2#1307058511yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1670C2
socleC22×C11#447
prime radicalC2×D88D4
hypercenter#1670D11
hypocenterC11#12359
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
2. #13070843C2semidirect
4. #13066675C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
7. C11×#1670C2semidirect
87. #1670D11semidirect
208. C11#12359semidirect

Maximal subgroups

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

subgroupindex
#130814842
#130708432
#130706582
#130666752
Q8⋊(C11⋊C16)2
#130665762
C11×#16702
#1235911