Finite Group Databasebeta

← #14667456

Subgroups — #14667456

Order 2816.

298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 75 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#13070841C211yesmaximal, characteristic
2#13070656C211yesmaximal, characteristic
3#13067976C211yesmaximal, characteristic
4#13066671C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066580C211yesmaximal, characteristic, complemented
7C11×#3383C211yesmaximal, characteristic, complemented
8C11×#557—21no—
9C11×#500C2211yescharacteristic
10C11×#499—21no—
11C11×#479—22no—
12C11×#475—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×Q16C2211yescharacteristic
16C2×#66892—21no—
17#10622640—21no—
18#10622308C2211yescharacteristic
19#10622129—21no—
20#10622129—22no—
21#10622123—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C11×C4⋊Q8—21no—
27C11×C4⋊Q8—41no—
28C11×#125—22no—
29C11×#125—42no—
30C4×Q8×C11—22no—
31C4×Q8×C11—21no—
32C4×Q8×C11—41no—
33C4×Q8×C11D411yescharacteristic
34C2×#4325—41no—
35C2×D88—21no—
36C2×D88—21no—
37#66927—21no—
38C11×#107—21no—
39C11×#107D411yescharacteristic
40C11×#107D412yes—
41C11×#106—22no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—22no—
45C11×#103—21no—
46C4×C8×C11—21no—
47C4×C8×C11C2311yescharacteristic
48#66892—42no—
49C2×C11⋊C16—21no—
50C2×C11⋊C16—21no—
51#66873—41no—
52C4⋊(C11⋊C8)—21no—
53#12353—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×Q8×C11—41no—
56C2×Q8×C11D811yescharacteristic
57C2×D44—41no—
58C2×D44—41no—
59C2×D44—41no—
60C11×Q16—21no—
61C11×Q16SD1612yescomplemented
62C2×C8×C11—21no—
63C2×C8×C11C2×D411yescharacteristic
64C2×C8×C11C2×D411yescharacteristic
65C11×C4⋊C4—21no—
66C11×C4⋊C4—21no—
67C11×C4⋊C4—22no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—42no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4D811yescharacteristic
74C42×C11—21no—
75C42×C11—42no—
76C42×C11—41no—
77C42×C11C2×D411yescharacteristic
78#4325—82no—
79C2×C11⋊C8—41no—
80D88—42no—
81D88—41no—
82D88—41no—
83C11⋊C16—41no—
84C11⋊C16—41no—
85#3383D1111yescharacteristic, complemented
86#2240—111no—
87#2207—111no—
88#1668—111no—
89#1364—111no—
90Q8⋊C16—111no—
91#1332—111no—
92C22×D11—81no—
93Q8×C11—22no—
94Q8×C11—21no—
95Q8×C11—21no—
96Q8×C11—41no—
97Q8×C11—81no—
98Q8×C11—81no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—41no—
102C2×C4×C11—41no—
103C2×C4×C11—42no—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11C2×D811yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
107D44—81no—
108D44—81no—
109D44—81no—
110D44—81no—
111D44—161no—
112C8×C11—21no—
113C8×C11—41no—
114C8×C11C2×SD1611yescharacteristic
115C8×C11#13711yescharacteristic
116C11⋊C8—81no—
117#557—21no—
118C2×SD32—221no—
119#500C2×D1111yescharacteristic
120#499—21no—
121#493—111no—
122#479—22no—
123#475—21no—
124#460—221no—
125C8×Q8C2×D1111yescharacteristic
126C4×Q16—21no—
127C4×Q16C2×D1111yescharacteristic
128C4⋊C16—111no—
129#357—221no—
130#357—222no—
131C4×C16—111no—
132#335—111no—
133#331—221no—
134C22×C11#44711yescharacteristic
135C2×D11—161no—
136C2×D11—161no—
137C2×D11—161no—
138C4×C11—21no—
139C4×C11—42no—
140C4×C11—41no—
141C4×C11—41no—
142C4×C11—82no—
143C4×C11—81no—
144C4×C11#44811yescharacteristic
145C4×C11#45411yescharacteristic
146C4×C11#50811yescharacteristic
147C4×C11#50911yescharacteristic
148C2×Q16C22⋊D1111yescharacteristic
149C2×SD16—441no—
150C2×D8—221no—
151C2×D8—221no—
152C4⋊Q8—21no—
153C4⋊Q8—41no—
154#127—221no—
155#125—22no—
156#125—42no—
157C4×Q8—22no—
158C4×Q8—21no—
159C4×Q8—41no—
160C4×Q8C22⋊D1111yescharacteristic
161SD32—442no—
162C2×C16—221no—
163C2×C16—221no—
164#107—21no—
165#107C22⋊D1111yescharacteristic
166#107C22⋊D1112yes—
167#106—22no—
168C4⋊C8—21no—
169C4⋊C8—221no—
170C4⋊C8C22⋊D1111yescharacteristic
171#103—22no—
172#103—21no—
173#102—441no—
174C4×C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162711yescharacteristic
177C2×C11#218611yescharacteristic
178C2×C11#219311yescharacteristic
179D11—321no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8#432311yescharacteristic
183C2×D4—441no—
184C2×D4—441no—
185C2×D4—441no—
186Q16—21no—
187Q16#432512yescomplemented
188SD16—882no—
189D8—442no—
190D8—441no—
191D8—441no—
192C2×C8—21no—
193C2×C8—441no—
194C2×C8C2×C22⋊D1111yescharacteristic
195C2×C8C2×C22⋊D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4#432311yescharacteristic
205C42—21no—
206C42—42no—
207C42—41no—
208C42C2×C22⋊D1111yescharacteristic
209C16—441no—
210C16—441no—
211C11#1235311yescharacteristic, complemented, Sylow
212C23—881no—
213Q8—21no—
214Q8—21no—
215Q8—22no—
216Q8—41no—
217Q8—81no—
218Q8—81no—
219D4—881no—
220D4—881no—
221D4—881no—
222D4—881no—
223D4—1761no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4C2×#432311yescharacteristic
230C2×C4#6698511yescharacteristic
231C2×C4#6700611yescharacteristic
232C8—21no—
233C8—41no—
234C8—881no—
235C8C2×#432511yescharacteristic
236C8#6699511yescharacteristic
237C22—1761no—
238C22—1761no—
239C22—1761no—
240C22#1062283011yescharacteristic
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—82no—
246C4—81no—
247C4#1062280611yescharacteristic
248C4#1062280711yescharacteristic
249C4#1062284011yescharacteristic
250C4#1062285811yescharacteristic
251C2—3521no—
252C2#1306771911yescharacteristic
253C2#1307053911yescharacteristic
254C2#1307058011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3383C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#3383D11
hypocenterC11#12353
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
4. #13066671C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066580C2semidirect
7. C11×#3383C2semidirect
61. C11×Q16SD16semidirect
85. #3383D11semidirect
187. Q16#4325semidirect
211. C11#12353semidirect

Maximal subgroups

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

subgroupindex
#130708412
#130706562
#130679762
#130666712
Q8⋊(C11⋊C16)2
#130665802
C11×#33832
#1235311