Finite Group Databasebeta

← #14674421

Subgroups — #14674421

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×#10622158C211yesmaximal, characteristic, complemented
3C2×#10622157C211yesmaximal, characteristic, complemented
4#13066796C211yesmaximal, characteristic, complemented
5#13066793C211yesmaximal, characteristic, complemented
6C22⋊(C11⋊C32)C211yesmaximal, characteristic, complemented
7C11×#2215C211yesmaximal, characteristic, complemented
8C2×#66957—21no—
9C2×C11×D16C2211yescharacteristic
10C22×C11×C16C2211yescharacteristic
11C11×#466—21no—
12C2×Dic88C2211yescharacteristic
13#10622517—22no—
14#10622517—22no—
15C2×#66864—21no—
16C2×D176C2211yescharacteristic
17C11×#366C2211yescharacteristic
18C11×#357—21no—
19#10622158—22no—
20#10622157—22no—
21C2×C11⋊C32C2211yescharacteristic
22C2×C11⋊C32C2211yescharacteristic
23C2×#4339—41no—
24C2×C11×D8—21no—
25C22×C8×C11D411yescharacteristic
26C11×#121—41no—
27C2×Dic44—21no—
28#66957—24no—
29#66957—42no—
30C2×D88—21no—
31C2×#4314—41no—
32C11×D16—21no—
33C11×D16—21no—
34C2×C11×C16—21no—
35C2×C11×C16—21no—
36C2×C11×C16D411yescharacteristic
37C2×C11×C16C2311yescharacteristic
38C11×#107—21no—
39C11×#102—41no—
40Dic88—21no—
41Dic88D412yescomplemented
42#66864—24no—
43D176—21no—
44D176D412yescomplemented
45C11⋊C32—21no—
46C11⋊C32—21no—
47#13663—111nomaximal, Sylow
48C2×D4×C11—41no—
49C2×D4×C11—81no—
50C22×C4×C11D811yescharacteristic
51C2×C22⋊D11—81no—
52#4339—44no—
53#4339—82no—
54C2×D44—41no—
55C2×C4×D11—81no—
56C2×Dic22—41no—
57C11×D8—41no—
58C11×D8—41no—
59C2×C8×C11—21no—
60C2×C8×C11—21no—
61C2×C8×C11D811yescharacteristic
62C2×C8×C11C2×D411yescharacteristic
63C11×C4⋊C4—41no—
64C11×C22⋊C4—81no—
65Dic44—22no—
66Dic44—41no—
67D88—22no—
68D88—41no—
69#4314—44no—
70C11×C16—21no—
71C11×C16C2×D411yescharacteristic
72C11×C16C2×D411yescharacteristic
73C2×#508—111no—
74C2×SD64—111no—
75C2×D32—111no—
76#2215D1111yescharacteristic, complemented
77#1416—111no—
78#1415—111no—
79C22⋊C32—111no—
80C23×C11—81no—
81C23×C11D1611yescharacteristic
82C22×D11—81no—
83D4×C11—81no—
84D4×C11—81no—
85D4×C11—162no—
86C2×C4×C11—21no—
87C2×C4×C11—21no—
88C2×C4×C11—81no—
89C2×C4×C11D1611yescharacteristic
90C2×C4×C11C2×D811yescharacteristic
91C22⋊D11—84no—
92C2×Dic11—81no—
93D44—42no—
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×D16C2×D1111yescharacteristic
108C22×C16C2×D1111yescharacteristic
109#466—21no—
110SD64—222no—
111D32—222no—
112C2×C32—111no—
113C2×C32—111no—
114#366C2×D1111yescharacteristic
115#357—21no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11—21no—
119C22×C11—161no—
120C22×C11—161no—
121C22×C11—161no—
122C22×C11C2×D1611yescharacteristic
123C2×D11—82no—
124C2×D11—161no—
125C2×D11—161no—
126C4×C11—21no—
127C4×C11—161no—
128C4×C11#44711yescharacteristic
129C4×C11#50911yescharacteristic
130Dic11—82no—
131C2×#41—441no—
132#135—224no—
133#135—442no—
134C2×Q16—221no—
135C2×SD16—441no—
136C2×D8—21no—
137C2×D8—221no—
138C22×C8C22⋊D1111yescharacteristic
139#121—41no—
140Q32—112no—
141Q32—221no—
142SD32—224no—
143D16—21no—
144D16—21no—
145D16—112no—
146D16—221no—
147C2×C16—21no—
148C2×C16—21no—
149C2×C16C22⋊D1111yescharacteristic
150C2×C16C22×D1111yescharacteristic
151#107—21no—
152#102—41no—
153C32—221no—
154C32—221no—
155C2×C11—41no—
156C2×C11—321no—
157C2×C11#218411yescharacteristic
158C2×C11#226211yescharacteristic
159C2×C11#226311yescharacteristic
160D11—162no—
161#41—444no—
162#41—882no—
163C2×Q8—441no—
164C2×D4—41no—
165C2×D4—81no—
166C2×D4—441no—
167C2×D4—881no—
168C22×C4—881no—
169C22×C4#432311yescharacteristic
170Q16—222no—
171Q16—441no—
172SD16—444no—
173D8—41no—
174D8—41no—
175D8—222no—
176D8—441no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8#432311yescharacteristic
180C2×C8C2×C22⋊D1111yescharacteristic
181C4⋊C4—41no—
182C22⋊C4—81no—
183C16—21no—
184C16D4×D1111yescharacteristic
185C16D4×D1111yescharacteristic
186C11#1366311yescharacteristic, complemented, Sylow
187C23—81no—
188C23—881no—
189C23#6689011yescharacteristic
190Q8—442no—
191Q8—881no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—442no—
196D4—884no—
197D4—881no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—81no—
201C2×C4—884no—
202C2×C4—881no—
203C2×C4#6689011yescharacteristic
204C2×C4C2×#432311yescharacteristic
205C8—21no—
206C8#6699011yescharacteristic
207C8#6700211yescharacteristic
208C22—21no—
209C22—21no—
210C22—21no—
211C22—161no—
212C22—161no—
213C22—161no—
214C22—882no—
215C22—1761no—
216C22—1761no—
217C22C2×#6689011yescharacteristic
218C4—21no—
219C4—161no—
220C4—882no—
221C4#1062264911yescharacteristic
222C4#1062280611yescharacteristic
223C2—41no—
224C2—321no—
225C2—1762no—
226C2#1307052711yescharacteristic
227C2#1307092311yescharacteristic
228C2#1307092911yescharacteristic
subgroupG/H
centerC22C2×#66890
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#2215C2
socleC22×C11C2×D16
hypercenter#2215D11
hypocenterC11#13663
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. C2×#10622517C2semidirect
2. C2×#10622158C2semidirect
3. C2×#10622157C2semidirect
4. #13066796C2semidirect
5. #13066793C2semidirect
6. C22⋊(C11⋊C32)C2semidirect
7. C11×#2215C2semidirect
41. Dic88D4semidirect
44. D176D4semidirect
76. #2215D11semidirect
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×#106221582
C2×#106221572
#130667962
#130667932
C22⋊(C11⋊C32)2
C11×#22152
#1366311