Finite Group Databasebeta

← #14667131

Subgroups — #14667131

Order 2816.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#13080055C211yesmaximal, characteristic
2#13070830C212yesmaximal, complemented
3#13066606C212yesmaximal, complemented
4#13066569C211yesmaximal, characteristic, complemented
5C11×#2103C211yesmaximal, characteristic, complemented
6#10623066—21no—
7C11×#430C2211yescharacteristic
8C11×#424C2211yescharacteristic
9#10622748C2212yes—
10#10622728—21no—
11#10622460—22no—
12#10622456—22no—
13C11×#344—21no—
14C11×#341—21no—
15C11×#338C2211yescharacteristic
16#10622191C2212yes—
17#10622133—22no—
18#10622132—22no—
19C2×C11×M16—21no—
20C2×C11×M16—21no—
21C2×C11×M16C2311yescharacteristic
22C22×C8×C11D411yescharacteristic
23C11×#117D411yescharacteristic
24#66983—22no—
25C2×D88—21no—
26C2×D88D412yes—
27#66947—42no—
28#66937—42no—
29#66927—21no—
30C4×D44—22no—
31#66923—21no—
32C11×#108—22no—
33C11×C4⋊C8—22no—
34#66885—22no—
35#66885—22no—
36#66882—21no—
37#66881D412yes—
38#66876—22no—
39#12304—111nomaximal, Sylow
40C22×C4×C11C2×D411yescharacteristic
41C2×C22⋊D11—42no—
42C2×D44—22no—
43C2×D44—42no—
44C2×C4×D11—42no—
45C11×M16—41no—
46C11×M16—41no—
47C11×M16—41no—
48C11×M16—41no—
49C11×M16—41no—
50C2×C8×C11—21no—
51C2×C8×C11—41no—
52C2×C8×C11—41no—
53C2×C8×C11—41no—
54C2×C8×C11C2×D412yes—
55C11×C4⋊C4—21no—
56C11×C22⋊C4SD1612yes—
57C42×C11—21no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60C4⋊Dic11—22no—
61Dic11⋊C4—42no—
62D88—42no—
63D88—81no—
64C11⋊C16—42no—
65#3259—111no—
66#2238—112no—
67#2103D1111yescharacteristic, complemented
68#1341—112no—
69#1328—111no—
70C23×C11C2×SD1611yescharacteristic
71C22×D11—42no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11#12011yescharacteristic
76C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
77C22⋊D11—162no—
78C2×Dic11—42no—
79D44—42no—
80D44—42no—
81D44—162no—
82C4×D11—162no—
83C8×C11—22no—
84C8×C11—41no—
85C8×C11—81no—
86C8×C11—81no—
87#540—221no—
88#478—222no—
89#469—112no—
90#466—221no—
91#459—222no—
92#430C2×D1111yescharacteristic
93#424C2×D1111yescharacteristic
94#365—222no—
95#361—222no—
96#349—112no—
97#344—21no—
98#341—21no—
99#338C2×D1111yescharacteristic
100C22×C11—21no—
101C22×C11—41no—
102C22×C11#45011yescharacteristic
103C2×D11—82no—
104C2×D11—82no—
105C2×D11—82no—
106C4×C11—21no—
107C4×C11—42no—
108C4×C11#45411yescharacteristic
109C4×C11#45811yescharacteristic
110Dic11—82no—
111C2×D8—112no—
112C2×D8—221no—
113C2×M16—21no—
114C2×M16—21no—
115C2×M16C22×D1111yescharacteristic
116C22×C8C22⋊D1111yescharacteristic
117#127—221no—
118#125—221no—
119#123—442no—
120#121—222no—
121#121—442no—
122C4×D4—222no—
123#117C22⋊D1111yescharacteristic
124M32—222no—
125#108—22no—
126#107—221no—
127#106—112no—
128C4⋊C8—22no—
129#102—222no—
130#102—222no—
131C2×C11—21no—
132C2×C11—41no—
133C2×C11#161611yescharacteristic
134D11—162no—
135C2×D4—222no—
136C2×D4—442no—
137C2×D4—442no—
138C22×C4—442no—
139C22×C4C2×C22⋊D1111yescharacteristic
140D8—442no—
141D8—881no—
142M16—41no—
143M16—41no—
144M16—41no—
145M16—41no—
146M16—41no—
147C2×C8—21no—
148C2×C8—41no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8D4×D1112yes—
152C4⋊C4—21no—
153C4⋊C4—222no—
154C4⋊C4—442no—
155C22⋊C4—442no—
156C22⋊C4—442no—
157C22⋊C4#432512yes—
158C42—21no—
159C16—442no—
160C11#1230411yescharacteristic, complemented, Sylow
161C23—442no—
162C23C2×#432511yescharacteristic
163D4—442no—
164D4—442no—
165D4—1762no—
166D4—1762no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—442no—
171C2×C4—1762no—
172C2×C4#6699011yescharacteristic
173C2×C4#6700211yescharacteristic
174C8—22no—
175C8—41no—
176C8—81no—
177C8—81no—
178C22—21no—
179C22—41no—
180C22—882no—
181C22—882no—
182C22—882no—
183C22#1062265911yescharacteristic
184C4—21no—
185C4—42no—
186C4—882no—
187C4#1062266611yescharacteristic
188C4#1062267511yescharacteristic
189C2—21no—
190C2—41no—
191C2—1762no—
192C2#1306765211yescharacteristic
subgroupG/H
centerC2#13067652
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#2103C2
socleC2×C11#1616
prime radical#13080055C2
hypercenter#2103D11
hypocenterC11#12304
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
2. #13070830C2semidirect
3. #13066606C2semidirect
4. #13066569C2semidirect
5. C11×#2103C2semidirect
67. #2103D11semidirect
160. C11#12304semidirect

Maximal subgroups

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

subgroupindex
#130800552
#130708302
#130666062
#130665692
C11×#21032
#1230411