Finite Group Databasebeta

← #14674425

Subgroups — #14674425

Order 2816.

298 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#10622517C211yesmaximal, characteristic, complemented
2C2×#10622087C211yesmaximal, characteristic, complemented
3C2×D352C211yesmaximal, characteristic, complemented
4#13070702C211yesmaximal, characteristic, complemented
5#13066798C211yesmaximal, characteristic, complemented
6#13066795C211yesmaximal, characteristic, complemented
7C11×C22⋊C32C211yesmaximal, characteristic, complemented
8C2×#66957—21no—
9C22×C11×C16C2211yescharacteristic
10#10622728—21no—
11C2×Dic88C2211yescharacteristic
12#10622517—22no—
13#10622517—22no—
14C2×#66864—21no—
15C2×D176C2211yescharacteristic
16C2×D176C2211yescharacteristic
17C2×C11×C32C2211yescharacteristic
18C2×C11×C32C2211yescharacteristic
19#10622147—21no—
20#10622142C2211yescharacteristic
21#10622087—22no—
22D352—22no—
23C2×#4339—41no—
24C22×C8×C11D411yescharacteristic
25#66983—41no—
26C2×Dic44—21no—
27#66957—24no—
28#66957—42no—
29C2×D88—21no—
30C2×D88—21no—
31C2×#4314—41no—
32C2×C11×C16—21no—
33C2×C11×C16—21no—
34C2×C11×C16D411yescharacteristic
35C2×C11×C16C2311yescharacteristic
36#66885—41no—
37#66882—21no—
38Dic88—21no—
39Dic88D412yescomplemented
40#66864—24no—
41D176—21no—
42D176—21no—
43D176—21no—
44D176D412yescomplemented
45C11×C32—21no—
46C11×C32—21no—
47#13663—111nomaximal, Sylow
48C22×C4×C11D811yescharacteristic
49C2×C22⋊D11—81no—
50C2×C22⋊D11—81no—
51#4339—44no—
52#4339—82no—
53C2×D44—41no—
54C2×D44—41no—
55C2×C4×D11—81no—
56C2×Dic22—41no—
57C2×C8×C11—21no—
58C2×C8×C11—21no—
59C2×C8×C11D811yescharacteristic
60C2×C8×C11C2×D411yescharacteristic
61(C2×D11)⋊C4—81no—
62C4⋊Dic11—41no—
63Dic44—22no—
64Dic44—41no—
65D88—22no—
66D88—41no—
67D88—41no—
68D88—41no—
69#4314—44no—
70C11×C16—21no—
71C11×C16C2×D411yescharacteristic
72C11×C16C2×D411yescharacteristic
73C2×#508—111no—
74C2×SD64—111no—
75C2×D32—111no—
76#2215—111no—
77#1416—111no—
78#1415—111no—
79C22⋊C32D1111yescharacteristic, complemented
80C23×C11D1611yescharacteristic
81C22×D11—81no—
82C22×D11—81no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11D1611yescharacteristic
86C2×C4×C11C2×D811yescharacteristic
87C22⋊D11—84no—
88C22⋊D11—162no—
89C2×Dic11—81no—
90C2×Dic11—81no—
91D44—42no—
92D44—81no—
93D44—81no—
94D44—81no—
95C4×D11—84no—
96Dic22—42no—
97Dic22—81no—
98C8×C11—21no—
99C8×C11#12011yescharacteristic
100C8×C11AGL(1,ℤ/8)11yescharacteristic
101C2×#135—221no—
102#508—222no—
103#508—222no—
104C2×Q32—111no—
105C2×SD32—221no—
106C2×D16—111no—
107C2×D16—111no—
108C22×C16C2×D1111yescharacteristic
109#466—221no—
110SD64—222no—
111D32—222no—
112C2×C32C2×D1111yescharacteristic
113C2×C32C2×D1111yescharacteristic
114#366—111no—
115#357—221no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11C2×D1611yescharacteristic
120C2×D11—82no—
121C2×D11—161no—
122C2×D11—161no—
123C2×D11—161no—
124C2×D11—161no—
125C2×D11—161no—
126C4×C11—21no—
127C4×C11#44711yescharacteristic
128C4×C11#50911yescharacteristic
129Dic11—82no—
130Dic11—161no—
131C2×#41—441no—
132#135—224no—
133#135—442no—
134C2×Q16—221no—
135C2×SD16—441no—
136C2×D8—221no—
137C2×D8—221no—
138C22×C8D4411yescharacteristic
139#121—441no—
140Q32—112no—
141Q32—221no—
142SD32—224no—
143D16—112no—
144D16—221no—
145D16—221no—
146D16—221no—
147C2×C16—21no—
148C2×C16—21no—
149C2×C16D4411yescharacteristic
150C2×C16C22×D1111yescharacteristic
151#107—221no—
152#102—441no—
153C32—21no—
154C32—21no—
155C2×C11—41no—
156C2×C11#218411yescharacteristic
157C2×C11#226211yescharacteristic
158C2×C11#226311yescharacteristic
159D11—162no—
160D11—321no—
161#41—444no—
162#41—882no—
163C2×Q8—441no—
164C2×D4—441no—
165C2×D4—441no—
166C2×D4—881no—
167C2×D4—881no—
168C22×C4—881no—
169C22×C4D8811yescharacteristic
170Q16—222no—
171Q16—441no—
172SD16—444no—
173D8—222no—
174D8—441no—
175D8—441no—
176D8—441no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8D8811yescharacteristic
180C2×C8C2×D4411yescharacteristic
181C4⋊C4—441no—
182C22⋊C4—881no—
183C16—21no—
184C16D4×D1111yescharacteristic
185C16D4×D1111yescharacteristic
186C11#1366311yescharacteristic, complemented, Sylow
187C23—881no—
188C23—881no—
189C23D17611yescharacteristic
190Q8—442no—
191Q8—881no—
192D4—442no—
193D4—884no—
194D4—881no—
195D4—881no—
196D4—881no—
197D4—1762no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—884no—
201C2×C4—881no—
202C2×C4—881no—
203C2×C4D17611yescharacteristic
204C2×C4C2×D8811yescharacteristic
205C8—21no—
206C8#6693511yescharacteristic
207C8#6696111yescharacteristic
208C22—21no—
209C22—21no—
210C22—21no—
211C22—882no—
212C22—1761no—
213C22—1761no—
214C22—1761no—
215C22—1761no—
216C22—1761no—
217C22C2×D17611yescharacteristic
218C4—21no—
219C4—882no—
220C4—1761no—
221C4#1062234511yescharacteristic
222C4#1062252111yescharacteristic
223C2—41no—
224C2—3521no—
225C2—1762no—
226C2#1307053011yescharacteristic
227C2#1307092511yescharacteristic
228C2#1307093111yescharacteristic
subgroupG/H
centerC22C2×D176
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×C22⋊C32C2
socleC22×C11C2×D16
hypercenterC22⋊C32D11
hypocenterC11#13663
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C22⋊C32

Complements

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

NH ≅ G/Ntype
1. C2×#10622517C2semidirect
2. C2×#10622087C2semidirect
3. C2×D352C2semidirect
4. #13070702C2semidirect
5. #13066798C2semidirect
6. #13066795C2semidirect
7. C11×C22⋊C32C2semidirect
39. Dic88D4semidirect
44. D176D4semidirect
79. C22⋊C32D11semidirect
186. C11#13663semidirect

Maximal subgroups

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

subgroupindex
C2×#106225172
C2×#106220872
C2×D3522
#130707022
#130667982
#130667952
C11×C22⋊C322
#1366311