Finite Group Databasebeta

← #14674422

Subgroups — #14674422

Order 2816.

298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 59 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×#10622532C211yesmaximal, characteristic, complemented
2C2×#10622157C211yesmaximal, characteristic, complemented
3#13070699C211yesmaximal, characteristic, complemented
4#13066797C211yesmaximal, characteristic, complemented
5#13066795C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C32C211yesmaximal, characteristic, complemented
7C2×C11×SD64C211yesmaximal, characteristic, complemented
8C2×#66972—21no—
9C2×C11×Q32C2211yescharacteristic
10C2×C11×D16C2211yescharacteristic
11C2×#66892—21no—
12#10622770—21no—
13#10622532—22no—
14#10622532—22no—
15C2×D176C2211yescharacteristic
16C2×C16×D11C2211yescharacteristic
17C11×SD64—22no—
18C2×C11×C32C2211yescharacteristic
19#10622200—21no—
20#10622157—22no—
21#10622142C2211yescharacteristic
22C2×C11⋊C32C2211yescharacteristic
23C2×#4343—41no—
24C2×C11×Q16—21no—
25C2×C11×D8—21no—
26C2×#4325—41no—
27#66991—41no—
28#66972—24no—
29#66972—42no—
30C2×D88—21no—
31C2×C8×D11D411yescharacteristic
32C11×Q32—21no—
33C11×Q32D412yescomplemented
34C11×D16—21no—
35C11×D16—21no—
36C2×C11×C16C2311yescharacteristic
37#66896—41no—
38#66892—24no—
39#66882—21no—
40C2×C11⋊C16D411yescharacteristic
41D176—21no—
42D176D412yescomplemented
43C16×D11—21no—
44C16×D11—21no—
45C11×C32—21no—
46C11⋊C32—21no—
47#13663—111nomaximal, Sylow
48C2×Q8×C11—41no—
49C2×D4×C11—41no—
50C2×C22⋊D11—81no—
51#4343—44no—
52#4343—82no—
53C2×D44—41no—
54C2×D44—81no—
55C2×C4×D11—81no—
56C2×C4×D11D811yescharacteristic
57C11×Q16—22no—
58C11×Q16—41no—
59C11×D8—41no—
60C11×D8—41no—
61C2×C8×C11C2×D411yescharacteristic
62C22⋊Dic11—81no—
63#4325—44no—
64C4⋊Dic11—41no—
65C2×C11⋊C8D811yescharacteristic
66D88—22no—
67D88—41no—
68C8×D11—21no—
69C8×D11—21no—
70C11×C16C2×D411yescharacteristic
71C11×C16C2×D411yescharacteristic
72C11⋊C16—21no—
73C2×#508—111no—
74C2×SD64D1111yescharacteristic, complemented
75C2×D32—111no—
76#2215—111no—
77#1416—111no—
78#1415—111no—
79C22⋊C32—111no—
80C23×C11—81no—
81C22×D11—81no—
82C22×D11D1611yescharacteristic
83Q8×C11—42no—
84Q8×C11—81no—
85D4×C11—81no—
86D4×C11—81no—
87C2×C4×C11—81no—
88C2×C4×C11C2×D811yescharacteristic
89C22⋊D11—162no—
90C2×Dic11—81no—
91C2×Dic11D1611yescharacteristic
92D44—42no—
93D44—84no—
94D44—81no—
95C4×D11—21no—
96C4×D11—21no—
97C4×D11—84no—
98C8×C11#12011yescharacteristic
99C8×C11AGL(1,ℤ/8)11yescharacteristic
100C11⋊C8—21no—
101C2×#135—221no—
102#508—222no—
103#508—222no—
104C2×Q32C2×D1111yescharacteristic
105C2×SD32—221no—
106C2×D16—111no—
107C2×D16C2×D1111yescharacteristic
108C22×C16—111no—
109#466—221no—
110SD64—22no—
111D32—222no—
112C2×C32—111no—
113C2×C32C2×D1111yescharacteristic
114#366—111no—
115#357—221no—
116C22×C11—161no—
117C22×C11—161no—
118C22×C11—161no—
119C22×C11C2×D1611yescharacteristic
120C2×D11—21no—
121C2×D11—21no—
122C2×D11—21no—
123C2×D11—82no—
124C2×D11—161no—
125C2×D11—161no—
126C4×C11—82no—
127C4×C11#44711yescharacteristic
128C4×C11#50911yescharacteristic
129Dic11—21no—
130Dic11—161no—
131C2×#41—441no—
132#135—224no—
133#135—442no—
134C2×Q16—21no—
135C2×SD16—441no—
136C2×D8—21no—
137C2×D8—221no—
138C22×C8—111no—
139#121—441no—
140Q32—21no—
141Q32C22⋊D1112yescomplemented
142SD32—224no—
143D16—21no—
144D16—21no—
145D16—112no—
146D16—221no—
147C2×C16—111no—
148C2×C16—221no—
149C2×C16—221no—
150C2×C16C22×D1111yescharacteristic
151#107—221no—
152#102—441no—
153C32—21no—
154C32—221no—
155C2×C11—321no—
156C2×C11#218411yescharacteristic
157C2×C11#226211yescharacteristic
158C2×C11#226311yescharacteristic
159D11—41no—
160D11—162no—
161#41—444no—
162#41—882no—
163C2×Q8—41no—
164C2×D4—41no—
165C2×D4—441no—
166C2×D4—881no—
167C2×D4—881no—
168C22×C4—111no—
169C22×C4—881no—
170Q16—22no—
171Q16—41no—
172SD16—444no—
173D8—41no—
174D8—41no—
175D8—222no—
176D8—441no—
177C2×C8—111no—
178C2×C8—221no—
179C2×C8—221no—
180C2×C8D4×D1111yescharacteristic
181C4⋊C4—441no—
182C22⋊C4—881no—
183C16—221no—
184C16D4×D1111yescharacteristic
185C16C2×C22⋊D1111yescharacteristic
186C11#1366311yescharacteristic, complemented, Sylow
187C23—81no—
188C23—111no—
189C23—881no—
190Q8—42no—
191Q8—81no—
192D4—81no—
193D4—81no—
194D4—442no—
195D4—884no—
196D4—881no—
197D4—1762no—
198C2×C4—81no—
199C2×C4—111no—
200C2×C4—221no—
201C2×C4—221no—
202C2×C4—884no—
203C2×C4—881no—
204C2×C4D8×D1111yescharacteristic
205C8—221no—
206C8#6696411yescharacteristic
207C8#6699011yescharacteristic
208C22—161no—
209C22—161no—
210C22—161no—
211C22—221no—
212C22—221no—
213C22—221no—
214C22—882no—
215C22—1761no—
216C22—1761no—
217C22D11×D1611yescharacteristic
218C4—82no—
219C4—221no—
220C4—1761no—
221C4#1062252411yescharacteristic
222C4#1062276911yescharacteristic
223C2—321no—
224C2—441no—
225C2—1762no—
226C2#1307052611yescharacteristic
227C2#1307092411yescharacteristic
228C2#1307093011yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC2×C11×SD64C2
socleC22×C11C2×D16
hypercenterC2×SD64D11
hypocenterC11#13663
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×SD64

Complements

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

NH ≅ G/Ntype
1. C2×#10622532C2semidirect
2. C2×#10622157C2semidirect
3. #13070699C2semidirect
4. #13066797C2semidirect
5. #13066795C2semidirect
6. (C2×D11)⋊C32C2semidirect
7. C2×C11×SD64C2semidirect
33. C11×Q32D4semidirect
42. D176D4semidirect
74. C2×SD64D11semidirect
141. Q32C22⋊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×#106225322
C2×#106221572
#130706992
#130667972
#130667952
(C2×D11)⋊C322
C2×C11×SD642
#1366311