Finite Group Databasebeta

← #11776950

Subgroups — #11776950

Order 1152.

308 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 66 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#10593806C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic
3M16×C3⋊Dic3C211yesmaximal, characteristic
4#10590173C211yesmaximal, characteristic, complemented
5#10590172C211yesmaximal, characteristic, complemented
6#10590171C211yesmaximal, characteristic, complemented
7#10590170C211yesmaximal, characteristic, complemented
8C2×#3792—21no—
9C2×C32×M16C411yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×#3748C411yescharacteristic
12C22⋊#622—21no—
13#63779—21no—
14#63777—21no—
15C4⋊#622C2211yescharacteristic
16C4⋊#622C2211yescharacteristic
17C4⋊#622C2211yescharacteristic
18C4⋊#622C2211yescharacteristic
19#63642C411yescharacteristic
20#63642C411yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22C8×C3⋊Dic3C2211yescharacteristic
23Dic3×M16—62no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3⋊Dic3Q811yescharacteristic
27#3792—42no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—21no—
31C2×#622—21no—
32C32×M16—22no—
33C2×C32×C8C2×C411yescharacteristic
34C2×C32×C8C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3Q811yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39#3748—22no—
40C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
41C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
42#1569—91nomaximal, Sylow
43C2×C3×M16—22no—
44C2×C4×Dic3—62no—
45C2×#208—62no—
46#815—62no—
47#815—62no—
48C8×Dic3—62no—
49C8×Dic3—62no—
50C23×C32C4⋊C411yescharacteristic
51C2×C32×C4—21no—
52C2×C32×C4—21no—
53C2×C32×C4C4⋊C411yescharacteristic
54C2×C32×C4C22×C411yescharacteristic
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—41no—
58C2×C3⋊Dic3C4⋊C411yescharacteristic
59C2×C3⋊Dic3C4⋊C411yescharacteristic
60C2×C3⋊Dic3C2×D411yescharacteristic
61C2×C3⋊Dic3C2×Q811yescharacteristic
62#622—41no—
63#622—41no—
64#622—41no—
65#622—41no—
66C32×C8—21no—
67C32×C8M1612yescomplemented
68C3⋊(C3⋊C8)—21no—
69C3⋊(C3⋊C8)M1612yescomplemented
70#432—91no—
71#423—91no—
72C4×M16—91no—
73#335—91no—
74#335—91no—
75#334—91no—
76#334—91no—
77C22×C3×C4—22no—
78C22×Dic3—62no—
79C22×Dic3—62no—
80C3×M16—28no—
81C2×C3×C8—22no—
82C2×C3×C8—22no—
83C4×Dic3—62no—
84C4×Dic3—62no—
85C4×Dic3—62no—
86C4×Dic3—62no—
87#208—68no—
88C2×C3⋊C8—62no—
89C2×C3⋊C8—62no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32—21no—
93C22×C32C2×C4⋊C411yescharacteristic
94C32×C4—21no—
95C32×C4C2×M1611yescharacteristic
96C32×C4C2×M1611yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3⋊Dic3—21no—
100C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
101C3⋊Dic3#13711yescharacteristic
102C2×M16—91no—
103C2×M16—181no—
104C2×M16#15711yescharacteristic
105C2×C42—91no—
106C4⋊C8—91no—
107C4⋊C8—91no—
108C4⋊C8—91no—
109C4⋊C8—91no—
110C4⋊C8—181no—
111C22⋊C8—181no—
112#97—91no—
113#97—91no—
114#97—181no—
115C4×C8—91no—
116C4×C8—91no—
117C23×C3—22no—
118C2×C3×C4—24no—
119C2×C3×C4—24no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—122no—
127C2×Dic3—122no—
128C2×Dic3—124no—
129C3×C8—24no—
130C3×C8—24no—
131C3⋊C8—64no—
132C3⋊C8—64no—
133C2×C32—41no—
134C2×C32#42311yescharacteristic
135C2×C32#42811yescharacteristic
136C2×C32#43011yescharacteristic
137C22×C4—91no—
138C22×C4—91no—
139C22×C4C2×#15711yescharacteristic
140M16—22no—
141M16—182no—
142M16—362no—
143C2×C8—91no—
144C2×C8—91no—
145C2×C8—181no—
146C2×C8—181no—
147C2×C8—181no—
148C2×C8—181no—
149C2×C8C2×#15711yescharacteristic
150C2×C8C2×#15711yescharacteristic
151C42—91no—
152C42—91no—
153C42—91no—
154C42—91no—
155C22×C3—24no—
156C22×C3—22no—
157C22×C3—42no—
158C22×C3—42no—
159C3×C4—24no—
160C3×C4—22no—
161C3×C4—22no—
162Dic3—62no—
163Dic3—62no—
164Dic3—64no—
165Dic3—122no—
166Dic3—122no—
167C32#156911yescharacteristic, complemented, Sylow
168C23C4⋊#15711yescharacteristic
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—91no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C4—361no—
178C2×C4C4⋊#15711yescharacteristic
179C2×C4C22×#15711yescharacteristic
180C8—21no—
181C8—92no—
182C8—181no—
183C8—361no—
184C8—361no—
185C8—361no—
186C8—361no—
187C8#379212yescomplemented
188C2×C3—22no—
189C2×C3—22no—
190C2×C3—22no—
191C2×C3—44no—
192C22—21no—
193C22—21no—
194C22—21no—
195C22C2×C4⋊#15711yescharacteristic
196C4—21no—
197C4—91no—
198C4—91no—
199C4—181no—
200C4—181no—
201C4—181no—
202C4#6428311yescharacteristic
203C4C2×#379211yescharacteristic
204C3—22no—
205C2—41no—
206C2#1059377411yescharacteristic
207C2#1059377611yescharacteristic
208C2#1059380511yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×M16#157
hypocenterC32#1569
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10590173C2semidirect
5. #10590172C2semidirect
6. #10590171C2semidirect
7. #10590170C2semidirect
67. C32×C8M16semidirect
69. C3⋊(C3⋊C8)M16semidirect
167. C32#1569semidirect
187. C8#3792semidirect

Maximal subgroups

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

subgroupindex
#105938062
#105938052
M16×C3⋊Dic32
#105901732
#105901722
#105901712
#105901702
#15699