Finite Group Databasebeta

← #11797964

Subgroups — #11797964

Order 1152.

244 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593780C211yesmaximal, characteristic, complemented
2#10593778C211yesmaximal, characteristic, complemented
3#10592610C211yesmaximal, characteristic
4#10590195C211yesmaximal, characteristic, complemented
5#10590192C211yesmaximal, characteristic, complemented
6#10590137C211yesmaximal, characteristic, complemented
7#10590136C211yesmaximal, characteristic, complemented
8D4×#157—21no—
9#64287—21no—
10#64121C2211yescharacteristic
11D8×C3⋊D3C2211yescharacteristic
12#63783—21no—
13#63782—21no—
14#63770C2211yescharacteristic
15#63768C2211yescharacteristic
16#63767C2211yescharacteristic
17#63765C2211yescharacteristic
18C32×D16C411yescharacteristic, complemented
19#63654C411yescharacteristic, complemented
20#63653C411yescharacteristic, complemented
21#63627C411yescharacteristic, complemented
22#63625C2211yescharacteristic
23#4911—62no—
24C22×#157—41no—
25#3830—21no—
26D4×C3⋊D3—21no—
27C22⋊#157—41no—
28#3792—41no—
29C2×#622—41no—
30C4⋊#157—21no—
31C4×#157D411yescharacteristic
32#3788—21no—
33#3787D411yescharacteristic
34C32×D8C2×C411yescharacteristic
35C32×D8C2×C411yescharacteristic, complemented
36#3754—21no—
37#3753—21no—
38#3746C2×C411yescharacteristic, complemented
39#3745C2×C411yescharacteristic
40C8×C3⋊D3C2311yescharacteristic
41#3708—21no—
42C32×C16C2×C411yescharacteristic, complemented
43C3⋊(C3⋊C16)C2×C411yescharacteristic, complemented
44AGL(1,ℤ/16)—91nomaximal, Sylow
45#912—62no—
46D3×D8—62no—
47C3×D16—22no—
48#827—62no—
49#826—62no—
50#800—62no—
51#798—62no—
52C22×C3⋊D3—41no—
53C2×#157—21no—
54C2×#157—41no—
55C2×#157—82no—
56C32×D4—21no—
57C32×D4—21no—
58#638—41no—
59#638—41no—
60C2×C3⋊Dic3—41no—
61C4⋊(C3⋊D3)—21no—
62C4×C3⋊D3C2×D411yescharacteristic
63#634—21no—
64#622—21no—
65#622—41no—
66C32×C8C22×C411yescharacteristic
67C3⋊(C3⋊C8)#4111yescharacteristic
68#509—91no—
69#444—91no—
70#442—91no—
71#365—91no—
72#361—91no—
73#360—91no—
74#347—91no—
75#237—122no—
76D3×D4—122no—
77C3×D8—22no—
78C3×D8—22no—
79#214—122no—
80#213—122no—
81Dic12—62no—
82D24—62no—
83D3×C8—62no—
84C3×C16—22no—
85C3⋊C16—62no—
86C22×C32—41no—
87C22×C32—41no—
88C2×C3⋊D3—41no—
89C2×C3⋊D3—81no—
90C2×C3⋊D3—81no—
91C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
92#157—41no—
93#157—81no—
94C32×C4C4×D411yescharacteristic
95C3⋊Dic3—41no—
96C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
97#135—91no—
98C2×D8—91no—
99#131—181no—
100C4×D4—181no—
101SD32—91no—
102SD32—91no—
103D16—91no—
104D16#15711yescharacteristic, complemented
105M32—91no—
106M32—91no—
107#108—91no—
108#106—91no—
109#104—181no—
110#102—181no—
111#97—91no—
112C22×D3—242no—
113C3×D4—42no—
114C3×D4—42no—
115#67—242no—
116#67—242no—
117C2×Dic3—242no—
118D12—122no—
119C4×D3—62no—
120Dic6—122no—
121C3×C8—22no—
122C3⋊C8—62no—
123C2×C32—81no—
124C2×C32—81no—
125C2×C32#44211yescharacteristic
126C3⋊D3—21no—
127C3⋊D3—81no—
128#41—181no—
129C2×D4—181no—
130C22×C4—361no—
131Q16—91no—
132SD16—181no—
133D8—91no—
134D8—181no—
135D8C2×#15711yescharacteristic
136D8C2×#15711yescharacteristic, complemented
137M16—181no—
138M16—361no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—361no—
142C4⋊C4—181no—
143C22⋊C4—361no—
144C42—91no—
145C16—91no—
146C16—181no—
147C16C2×#15711yescharacteristic, complemented
148C22×C3—82no—
149C22×C3—82no—
150C2×D3—62no—
151C2×D3—242no—
152C2×D3—482no—
153C2×D3—482no—
154C3×C4—22no—
155Dic3—62no—
156Dic3—242no—
157C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
158C23—361no—
159Q8—181no—
160D4—21no—
161D4—21no—
162D4—181no—
163D4—361no—
164D4—361no—
165C2×C4—91no—
166C2×C4—181no—
167C2×C4—361no—
168C2×C4—361no—
169C2×C4—722no—
170C8—91no—
171C8—181no—
172C8—361no—
173C8C22×#15711yescharacteristic
174C2×C3—22no—
175C2×C3—162no—
176C2×C3—162no—
177D3—122no—
178D3—482no—
179C22—41no—
180C22—41no—
181C22—91no—
182C22—361no—
183C22—721no—
184C22—721no—
185C4—91no—
186C4—361no—
187C4—361no—
188C4—721no—
189C4D4×#15711yescharacteristic
190C3—22no—
191C2—81no—
192C2—81no—
193C2—181no—
194C2—721no—
195C2#1059377811yescharacteristic
subgroupG/H
centerC2#10593778
commutatorC32×C8C22×C4
FrattiniC8C22×#157
FittingC32×D16C4
socleC2×C32#442
prime radical#10592610C2
cosocleC8×C3⋊D3C23
hypercenterD16#157
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D16

Complements

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

NH ≅ G/Ntype
1. #10593780C2semidirect
2. #10593778C2semidirect
4. #10590195C2semidirect
5. #10590192C2semidirect
6. #10590137C2semidirect
7. #10590136C2semidirect
18. C32×D16C4semidirect
19. #63654C4semidirect
20. #63653C4semidirect
21. #63627C4semidirect
35. C32×D8C2×C4semidirect
38. #3746C2×C4semidirect
42. C32×C16C2×C4semidirect
43. C3⋊(C3⋊C16)C2×C4semidirect
104. D16#157semidirect
136. D8C2×#157semidirect
147. C16C2×#157semidirect
157. C32AGL(1,ℤ/16)semidirect

Maximal subgroups

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

subgroupindex
#105937802
#105937782
#105926102
#105901952
#105901922
#105901372
#105901362
AGL(1,ℤ/16)9