Finite Group Databasebeta

← #14664724

Subgroups — #14664724

Order 2816.

358 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 95 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#13079195C211yesmaximal, characteristic
2#13068747C211yesmaximal, characteristic, complemented
3#13066626C214yesmaximal, complemented
4C11×#2163C211yesmaximal, characteristic, complemented
5#10623008—21no—
6C2×C4×C8×C11C2211yescharacteristic
7#10622728—21no—
8#10622728C2212yes—
9#10622549—21no—
10#10622308C411yescharacteristic, complemented
11#10622307—21no—
12C4×D88—21no—
13C4×D88C412yescomplemented
14#10622295C411yescharacteristic, complemented
15C11×C4⋊C16—21no—
16C11×C22⋊C16C2212yes—
17C11×#346—21no—
18#10622189—21no—
19#10622189C2212yes—
20C2×#4339—41no—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C42×C11D411yescharacteristic
24#66983—22no—
25#66983—41no—
26C2×C4⋊Dic11—22no—
27C2×D88—21no—
28C2×D88C2×C412yes—
29#66928—41no—
30#66927—21no—
31C4×D44—22no—
32C4×D44—41no—
33#66922—21no—
34C2×C11×C16—22no—
35C4×C8×C11C2×C411yescharacteristic
36C4×C8×C11C2×C411yescharacteristic
37C4×C8×C11D411yescharacteristic
38C4×C8×C11D411yescharacteristic
39C11⋊#95—41no—
40C11⋊#95—41no—
41#66885—22no—
42#66885—22no—
43#66882—21no—
44#66882C2×C412yes—
45#11858—111nomaximal, Sylow
46C22×C4×C11D811yescharacteristic
47C22×C4×C11D811yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C2×C22⋊D11—42no—
50C22×Dic11—42no—
51#4339—84no—
52C2×D44—22no—
53C2×D44—41no—
54C2×D44—41no—
55C2×C4×D11—42no—
56C2×Dic22—41no—
57C2×C8×C11—41no—
58C2×C8×C11—41no—
59C2×C8×C11C22⋊C411yescharacteristic
60C2×C8×C11C22⋊C411yescharacteristic
61C2×C8×C11C22×C411yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C42×C11C22⋊C411yescharacteristic
64C42×C11C22⋊C411yescharacteristic
65C42×C11SD1611yescharacteristic
66C42×C11SD1611yescharacteristic
67(C2×D11)⋊C4—42no—
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C4⋊Dic11—41no—
73D88—42no—
74D88—42no—
75C11×C16—42no—
76#3169—111no—
77#2163D1111yescharacteristic, complemented
78#1835—111no—
79#1347—114no—
80C23×C11C2×D811yescharacteristic
81C22×D11—42no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—41no—
86C2×C4×C11#10211yescharacteristic
87C2×C4×C11#10211yescharacteristic
88C2×C4×C11#10211yescharacteristic
89C2×C4×C11#10211yescharacteristic
90C2×C4×C11C2×C22⋊C411yescharacteristic
91C2×C4×C11C2×SD1611yescharacteristic
92C22⋊D11—84no—
93C2×Dic11—42no—
94C2×Dic11—82no—
95C2×Dic11—82no—
96C2×Dic11—82no—
97D44—42no—
98D44—42no—
99D44—82no—
100D44—82no—
101C4×D11—84no—
102Dic22—82no—
103C8×C11—21no—
104C8×C11—21no—
105C8×C11—21no—
106C8×C11—21no—
107#532—221no—
108#500—111no—
109#493—111no—
110#486—221no—
111#466—112no—
112#466—221no—
113C4×D8—112no—
114C4×D8—221no—
115C2×C4×C8C2×D1111yescharacteristic
116#382—221no—
117C4⋊C16—21no—
118C22⋊C16C2×D1112yes—
119#346—21no—
120#340—112no—
121#340—221no—
122C22×C11—21no—
123C22×C11—21no—
124C22×C11C2×#10211yescharacteristic
125C22×C11#50912yes—
126C2×D11—82no—
127C2×D11—82no—
128C2×D11—82no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—21no—
132C4×C11—21no—
133C4×C11—21no—
134C4×C11#41011yescharacteristic
135C4×C11#42111yescharacteristic
136Dic11—82no—
137Dic11—162no—
138C2×#41—441no—
139C2×D8—112no—
140C2×D8—221no—
141C22×C8D4411yescharacteristic
142C22×C8C22×D1111yescharacteristic
143C4⋊Q8—221no—
144#127—221no—
145#124—441no—
146#121—222no—
147#121—441no—
148C4×D4—222no—
149C4×D4—441no—
150C2×C4⋊C4—222no—
151C2×C42D4411yescharacteristic
152C2×C16—22no—
153#107—112no—
154#107—221no—
155#102—222no—
156#102—222no—
157C4×C8C4×D1111yescharacteristic
158C4×C8C4×D1111yescharacteristic
159C4×C8C22⋊D1111yescharacteristic
160C4×C8C22⋊D1111yescharacteristic
161#95—441no—
162#95—441no—
163C2×C11—22no—
164C2×C11#151711yescharacteristic
165C2×C11#214011yescharacteristic
166C2×C11#214511yescharacteristic
167D11—162no—
168#41—884no—
169C2×Q8—441no—
170C2×D4—222no—
171C2×D4—442no—
172C2×D4—441no—
173C2×D4—441no—
174C22×C4—442no—
175C22×C4—442no—
176C22×C4D8811yescharacteristic
177C22×C4D8811yescharacteristic
178C22×C4C2×D4411yescharacteristic
179D8—442no—
180D8—442no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8(C2×D11)⋊C411yescharacteristic
184C2×C8(C2×D11)⋊C411yescharacteristic
185C2×C8C2×C4×D1111yescharacteristic
186C2×C8C2×C22⋊D1111yescharacteristic
187C4⋊C4—222no—
188C4⋊C4—442no—
189C4⋊C4—442no—
190C4⋊C4—441no—
191C22⋊C4—442no—
192C22⋊C4—442no—
193C42#431411yescharacteristic
194C42#431411yescharacteristic
195C42(C2×D11)⋊C411yescharacteristic
196C42(C2×D11)⋊C411yescharacteristic
197C16—42no—
198C11#1185811yescharacteristic, complemented, Sylow
199C23—442no—
200C23C2×D8811yescharacteristic
201Q8—882no—
202D4—442no—
203D4—442no—
204D4—882no—
205D4—882no—
206D4—884no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—442no—
212C2×C4—884no—
213C2×C4—882no—
214C2×C4—882no—
215C2×C4—882no—
216C2×C4#6688511yescharacteristic
217C2×C4#6688511yescharacteristic
218C2×C4#6688511yescharacteristic
219C2×C4#6688511yescharacteristic
220C2×C4C2×#431411yescharacteristic
221C2×C4C2×(C2×D11)⋊C411yescharacteristic
222C8—21no—
223C8—21no—
224C8—21no—
225C8—21no—
226C22—21no—
227C22—21no—
228C22—882no—
229C22—882no—
230C22—882no—
231C22#1062252112yes—
232C22C2×#6688511yescharacteristic
233C4—21no—
234C4—21no—
235C4—21no—
236C4—21no—
237C4—21no—
238C4—882no—
239C4—1762no—
240C4#1062261911yescharacteristic
241C4#1062275211yescharacteristic
242C2—22no—
243C2—1762no—
244C2#1306717711yescharacteristic
245C2#1307033311yescharacteristic
246C2#1307035311yescharacteristic
subgroupG/H
centerC22C2×#66885
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2163C2
socleC22×C11C2×#102
prime radical#13079195C2
cosocleC22×C8×C11C23
hypercenter#2163D11
hypocenterC11#11858
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
2. #13068747C2semidirect
3. #13066626C2semidirect
4. C11×#2163C2semidirect
10. #10622308C4semidirect
13. C4×D88C4semidirect
14. #10622295C4semidirect
77. #2163D11semidirect
198. C11#11858semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130687472
#130666262
C11×#21632
#1185811