Finite Group Databasebeta

← #14674423

Subgroups — #14674423

Order 2816.

298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 67 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×#10622159C211yesmaximal, characteristic, complemented
2C2×#10622157C211yesmaximal, characteristic, complemented
3#13070702C211yesmaximal, characteristic, complemented
4#13066797C211yesmaximal, characteristic, complemented
5#13066794C211yesmaximal, characteristic, complemented
6C22⋊(C11⋊C32)C211yesmaximal, characteristic, complemented
7C2×C11×#508C211yesmaximal, characteristic, complemented
8C2×C11×#135—21no—
9C11×#508—22no—
10C11×#508—22no—
11C2×C11×Q32C2211yescharacteristic
12C2×C11×SD32—21no—
13C2×C11×D16C2211yescharacteristic
14C22×C11×C16C2211yescharacteristic
15#10622728—21no—
16C2×D176C2211yescharacteristic
17#10622159—22no—
18#10622157—22no—
19#10622147—21no—
20#10622142C2211yescharacteristic
21C2×C11⋊C32C2211yescharacteristic
22C2×C11⋊C32C2211yescharacteristic
23C2×C11×#41—41no—
24C11×#135—24no—
25C11×#135—42no—
26C2×C11×Q16—21no—
27C2×C11×SD16—41no—
28C2×C11×D8—21no—
29C22×C8×C11D411yescharacteristic
30#66983—41no—
31C2×D88—21no—
32C11×Q32—21no—
33C11×Q32D412yescomplemented
34C11×SD32—24no—
35C11×D16—21no—
36C11×D16D412yescomplemented
37C2×C11×C16—21no—
38C2×C11×C16—21no—
39C2×C11×C16D411yescharacteristic
40C2×C11×C16C2311yescharacteristic
41#66885—41no—
42#66882—21no—
43D176—21no—
44D176—21no—
45C11⋊C32—21no—
46C11⋊C32—21no—
47#13663—111nomaximal, Sylow
48C11×#41—44no—
49C11×#41—82no—
50C2×Q8×C11—41no—
51C2×D4×C11—41no—
52C2×D4×C11—81no—
53C22×C4×C11—81no—
54C22×C4×C11D811yescharacteristic
55C2×C22⋊D11—81no—
56C2×D44—41no—
57C11×Q16—22no—
58C11×Q16—41no—
59C11×SD16—44no—
60C11×D8—22no—
61C11×D8—41no—
62C2×C8×C11—21no—
63C2×C8×C11—21no—
64C2×C8×C11D811yescharacteristic
65C2×C8×C11C2×D411yescharacteristic
66(C2×D11)⋊C4—81no—
67C4⋊Dic11—41no—
68D88—41no—
69D88—41no—
70C11×C16—21no—
71C11×C16C2×D411yescharacteristic
72C11×C16C2×D411yescharacteristic
73C2×#508D1111yescharacteristic, complemented
74C2×SD64—111no—
75C2×D32—111no—
76#2215—111no—
77#1416—111no—
78#1415—111no—
79C22⋊C32—111no—
80C23×C11—81no—
81C23×C11D1611yescharacteristic
82C22×D11—81no—
83Q8×C11—42no—
84Q8×C11—81no—
85D4×C11—42no—
86D4×C11—84no—
87D4×C11—81no—
88C2×C4×C11—21no—
89C2×C4×C11—21no—
90C2×C4×C11—84no—
91C2×C4×C11—81no—
92C2×C4×C11D1611yescharacteristic
93C2×C4×C11C2×D811yescharacteristic
94C22⋊D11—162no—
95C2×Dic11—81no—
96D44—81no—
97D44—81no—
98C8×C11—21no—
99C8×C11#12011yescharacteristic
100C8×C11AGL(1,ℤ/8)11yescharacteristic
101C2×#135—21no—
102#508—22no—
103#508—22no—
104C2×Q32C2×D1111yescharacteristic
105C2×SD32—21no—
106C2×D16—111no—
107C2×D16C2×D1111yescharacteristic
108C22×C16C2×D1111yescharacteristic
109#466—221no—
110SD64—222no—
111D32—222no—
112C2×C32—111no—
113C2×C32—111no—
114#366—111no—
115#357—221no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—82no—
120C22×C11—161no—
121C22×C11—161no—
122C22×C11C2×D1611yescharacteristic
123C2×D11—161no—
124C2×D11—161no—
125C2×D11—161no—
126C4×C11—21no—
127C4×C11—82no—
128C4×C11#44711yescharacteristic
129C4×C11#50911yescharacteristic
130Dic11—161no—
131C2×#41—41no—
132#135—24no—
133#135—42no—
134C2×Q16—21no—
135C2×SD16—41no—
136C2×D8—21no—
137C2×D8—221no—
138C22×C8C22⋊D1111yescharacteristic
139#121—441no—
140Q32—21no—
141Q32C22⋊D1112yescomplemented
142SD32—24no—
143D16—21no—
144D16—221no—
145D16—221no—
146D16C22⋊D1112yescomplemented
147C2×C16—21no—
148C2×C16—21no—
149C2×C16C22⋊D1111yescharacteristic
150C2×C16C22×D1111yescharacteristic
151#107—221no—
152#102—441no—
153C32—221no—
154C32—221no—
155C2×C11—41no—
156C2×C11—162no—
157C2×C11#218411yescharacteristic
158C2×C11#226211yescharacteristic
159C2×C11#226311yescharacteristic
160D11—321no—
161#41—44no—
162#41—82no—
163C2×Q8—41no—
164C2×D4—41no—
165C2×D4—81no—
166C2×D4—441no—
167C2×D4—881no—
168C22×C4—81no—
169C22×C4#432311yescharacteristic
170Q16—22no—
171Q16—41no—
172SD16—44no—
173D8—22no—
174D8—41no—
175D8—441no—
176D8—441no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8#432311yescharacteristic
180C2×C8C2×C22⋊D1111yescharacteristic
181C4⋊C4—441no—
182C22⋊C4—881no—
183C16—21no—
184C16C2×C22⋊D1111yescharacteristic
185C16C2×C22⋊D1111yescharacteristic
186C11#1366311yescharacteristic, complemented, Sylow
187C23—81no—
188C23—881no—
189C23#6689011yescharacteristic
190Q8—42no—
191Q8—81no—
192D4—42no—
193D4—84no—
194D4—81no—
195D4—881no—
196D4—881no—
197D4—1762no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—84no—
201C2×C4—81no—
202C2×C4—881no—
203C2×C4#6689011yescharacteristic
204C2×C4C2×#432311yescharacteristic
205C8—21no—
206C8#6698511yescharacteristic
207C8#6700611yescharacteristic
208C22—21no—
209C22—21no—
210C22—21no—
211C22—82no—
212C22—161no—
213C22—161no—
214C22—1761no—
215C22—1761no—
216C22—1761no—
217C22C2×#6689011yescharacteristic
218C4—21no—
219C4—82no—
220C4—1761no—
221C4#1062276011yescharacteristic
222C4#1062283011yescharacteristic
223C2—41no—
224C2—162no—
225C2—3521no—
226C2#1307052811yescharacteristic
227C2#1307092311yescharacteristic
228C2#1307092811yescharacteristic
subgroupG/H
centerC22C2×#66890
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC2×C11×#508C2
socleC22×C11C2×D16
hypercenterC2×#508D11
hypocenterC11#13663
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ C2×#508

Complements

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

NH ≅ G/Ntype
1. C2×#10622159C2semidirect
2. C2×#10622157C2semidirect
3. #13070702C2semidirect
4. #13066797C2semidirect
5. #13066794C2semidirect
6. C22⋊(C11⋊C32)C2semidirect
7. C2×C11×#508C2semidirect
33. C11×Q32D4semidirect
36. C11×D16D4semidirect
73. C2×#508D11semidirect
141. Q32C22⋊D11semidirect
146. D16C22⋊D11semidirect
186. C11#13663semidirect

Maximal subgroups

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

subgroupindex
C2×#106221592
C2×#106221572
#130707022
#130667972
#130667942
C22⋊(C11⋊C32)2
C2×C11×#5082
#1366311