Finite Group Databasebeta

← #14674418

Subgroups — #14674418

Order 2816.

294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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×D11×Q32C211yesmaximal, characteristic, complemented
2C2×#10622087C211yesmaximal, characteristic, complemented
3C2×#10622159C211yesmaximal, characteristic, complemented
4#13070703C211yesmaximal, characteristic
5#13066796C211yesmaximal, characteristic, complemented
6(C2×D11)⋊C32C211yesmaximal, characteristic, complemented
7C11×#1416C211yesmaximal, characteristic, complemented
8C2×Q16×D11—21no—
9C2×C11×Q32C2211yescharacteristic
10C2×#66893—21no—
11D11×Q32—22no—
12D11×Q32—22no—
13C2×Dic88C2211yescharacteristic
14C2×D176C2211yescharacteristic
15C2×C16×D11C2211yescharacteristic
16#10622496—21no—
17C2×C11×C32C2211yescharacteristic
18C11×#366C2211yescharacteristic
19#10622159—22no—
20C2×C11⋊C32C2211yescharacteristic
21#10622129—21no—
22#10622087—22no—
23C2×Q8×D11—41no—
24C2×C11×Q16—21no—
25C2×#4326—41no—
26Q16×D11—24no—
27Q16×D11—42no—
28C2×Dic44—21no—
29C2×D88—21no—
30C2×C8×D11D411yescharacteristic
31#66948—41no—
32C11×Q32—21no—
33C11×Q32D412yescomplemented
34C2×C11×C16C2311yescharacteristic
35C11×#107—21no—
36#66893—24no—
37C2×C11⋊C16D411yescharacteristic
38#66873—41no—
39Dic88—21no—
40Dic88D412yescomplemented
41D176—21no—
42D176—21no—
43C16×D11—21no—
44C16×D11—21no—
45C11×C32—21no—
46C11⋊C32—21no—
47#13662—111nomaximal, Sylow
48C2×Q8×C11—41no—
49Q8×D11—44no—
50Q8×D11—82no—
51C2×D44—41no—
52C2×D44—81no—
53C2×C4×D11—81no—
54C2×C4×D11D811yescharacteristic
55C2×Dic22—41no—
56C2×Dic22—81no—
57C11×Q16—22no—
58C11×Q16—41no—
59C2×C8×C11C2×D411yescharacteristic
60C11×C4⋊C4—41no—
61#4326—44no—
62(C2×D11)⋊C4—81no—
63C2×C11⋊C8D811yescharacteristic
64Dic44—22no—
65Dic44—41no—
66D88—41no—
67D88—41no—
68C8×D11—21no—
69C8×D11—21no—
70C11×C16C2×D411yescharacteristic
71C11×C16C2×D411yescharacteristic
72C11⋊C16—21no—
73C22×Q32—111no—
74C2×SD64—111no—
75C2×SD64—111no—
76#2215—111no—
77#1416—111no—
78#1416D1111yescharacteristic, complemented
79C22⋊C32—111no—
80C22×D11—81no—
81C22×D11D1611yescharacteristic
82Q8×C11—42no—
83Q8×C11—81no—
84C2×C4×C11—81no—
85C2×C4×C11—81no—
86C2×C4×C11C2×D811yescharacteristic
87C2×Dic11—81no—
88C2×Dic11D1611yescharacteristic
89D44—81no—
90D44—81no—
91D44—162no—
92C4×D11—21no—
93C4×D11—21no—
94C4×D11—84no—
95Dic22—42no—
96Dic22—84no—
97Dic22—81no—
98C8×C11#12011yescharacteristic
99C8×C11AGL(1,ℤ/8)11yescharacteristic
100C11⋊C8—21no—
101C22×Q16—221no—
102C2×Q32—111no—
103C2×Q32—221no—
104C2×Q32—222no—
105C2×Q32—222no—
106C2×Q32C2×D1111yescharacteristic
107C2×D16—111no—
108C22×C16—111no—
109#466—221no—
110SD64—222no—
111SD64—222no—
112C2×C32—111no—
113C2×C32C2×D1111yescharacteristic
114#366C2×D1111yescharacteristic
115#357—221no—
116C22×C11C2×D1611yescharacteristic
117C2×D11—21no—
118C2×D11—21no—
119C2×D11—161no—
120C2×D11—161no—
121C2×D11—161no—
122C2×D11SD6412yescomplemented
123C4×C11—82no—
124C4×C11—161no—
125C4×C11#44711yescharacteristic
126C4×C11#50911yescharacteristic
127Dic11—21no—
128Dic11—82no—
129C22×Q8—441no—
130C2×Q16—21no—
131C2×Q16—224no—
132C2×Q16—221no—
133C2×Q16—441no—
134C2×Q16—442no—
135C2×D8—221no—
136C22×C8—111no—
137#121—441no—
138Q32—21no—
139Q32—112no—
140Q32—224no—
141Q32—221no—
142Q32D4412yescomplemented
143D16—221no—
144D16—221no—
145C2×C16—111no—
146C2×C16—221no—
147C2×C16—221no—
148C2×C16C22×D1111yescharacteristic
149#107—21no—
150#102—441no—
151C32—21no—
152C32—221no—
153C2×C11#218411yescharacteristic
154C2×C11C2×SD6411yescharacteristic
155C2×C11#226411yescharacteristic
156D11—22no—
157D11—321no—
158C2×Q8—41no—
159C2×Q8—444no—
160C2×Q8—441no—
161C2×Q8—881no—
162C2×Q8—882no—
163C2×D4—441no—
164C2×D4—881no—
165C22×C4—111no—
166C22×C4—881no—
167Q16—22no—
168Q16—41no—
169Q16—222no—
170Q16—444no—
171Q16—441no—
172D8—441no—
173D8—441no—
174C2×C8—111no—
175C2×C8—221no—
176C2×C8—221no—
177C2×C8D4×D1111yescharacteristic
178C4⋊C4—41no—
179C22⋊C4—881no—
180C16—221no—
181C16C2×D4411yescharacteristic
182C16D4×D1111yescharacteristic
183C11#1366211yescharacteristic, complemented, Sylow
184C23—111no—
185C23—881no—
186Q8—42no—
187Q8—81no—
188Q8—442no—
189Q8—884no—
190Q8—881no—
191D4—881no—
192D4—881no—
193D4—1762no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—111no—
197C2×C4—221no—
198C2×C4—221no—
199C2×C4—884no—
200C2×C4—881no—
201C2×C4D8×D1111yescharacteristic
202C8—221no—
203C8#6693511yescharacteristic
204C8#6696711yescharacteristic
205C22—112no—
206C22—221no—
207C22—221no—
208C22—1761no—
209C22—1761no—
210C22—1761no—
211C22D11×D1611yescharacteristic
212C4—82no—
213C4—161no—
214C4—221no—
215C4—882no—
216C4#1062238611yescharacteristic
217C4#1062252711yescharacteristic
218C2—222no—
219C2—3521no—
220C2#1307052911yescharacteristic
221C2D11×SD6411yescharacteristic
222C2#1307093511yescharacteristic
subgroupG/H
centerC22D11×D16
commutator, cosocleC2×C11×C16C23
FrattiniC2×C16C22×D11
FittingC11×#1416C2
socleC22×C11C2×D16
prime radical#13070703C2
hypercenter#1416D11
hypocenterC11#13662
LCSG ▷ C2×C11×C16 ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
1. C2×D11×Q32C2semidirect
2. C2×#10622087C2semidirect
3. C2×#10622159C2semidirect
5. #13066796C2semidirect
6. (C2×D11)⋊C32C2semidirect
7. C11×#1416C2semidirect
33. C11×Q32D4semidirect
40. Dic88D4semidirect
78. #1416D11semidirect
122. C2×D11SD64semidirect
142. Q32D44semidirect
183. C11#13662semidirect

Maximal subgroups

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

subgroupindex
C2×D11×Q322
C2×#106220872
C2×#106221592
#130707032
#130667962
(C2×D11)⋊C322
C11×#14162
#1366211