Finite Group Databasebeta

← #16856169

Subgroups — #16856169

Order 3968.

552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11758495C214yesmaximal, complemented
2#14521600C211yesmaximal, characteristic
3C4⋊Q8×D31C211yesmaximal, characteristic, complemented
4#14521442C214yesmaximal, complemented
5#14521428C211yesmaximal, characteristic, complemented
6#14521423C211yesmaximal, characteristic, complemented
7#14521422C211yesmaximal, characteristic, complemented
8C4×#92469C211yesmaximal, characteristic, complemented
9C31×#494C211yesmaximal, characteristic, complemented
10C2×#92499C2212yes—
11C2×Q8×D31C2212yes—
12C2×Q16×C31C2214yes—
13C31×C4⋊Q8C2211yescharacteristic
14C31×C4⋊Q8C2211yescharacteristic
15#11758524C2212yes—
16#11758521C2212yes—
17C2×#92482C2214yes—
18C2×#92481C2214yes—
19#11758495—216no—
20C2×#92470C2214yes—
21C2×#92469C2212yes—
22#11758472—22no—
23#11758470—22no—
24C4⋊C4×D31—22no—
25#11758465—22no—
26#11758451C2211yescharacteristic
27C42×D31C2211yescharacteristic
28#11758446C2211yescharacteristic
29C4×C8×C31C2211yescharacteristic
30#11758403C2212yes—
31C4×C31⋊C8C2211yescharacteristic
32C2×Q8×C31C2312yes—
33C2×Q8×C31C2312yes—
34#92499—28no—
35Q8×D31—28no—
36C2×D124—22no—
37C2×D124—22no—
38C2×D124C2312yes—
39C2×C4×D31—22no—
40C2×C4×D31—22no—
41C2×C4×D31D412yes—
42C2×C4×D31C2311yescharacteristic
43C2×Dic62—22no—
44C2×Dic62C2312yes—
45Q16×C31—28no—
46C2×C8×C31C2312yes—
47C4⋊C4×C31—22no—
48C4⋊C4×C31—22no—
49C42×C31C2311yescharacteristic
50#92482—28no—
51#92481—28no—
52(C2×D31)⋊C4—24no—
53C4⋊Dic31—22no—
54Dic31⋊C4—24no—
55C4×Dic31D412yes—
56C4×Dic31C2311yescharacteristic
57C2×C31⋊C8C2312yes—
58#92470—28no—
59#92469D418yescomplemented
60C22×D31—22no—
61C22×D31C2×D411yescharacteristic
62Q8×C31—24no—
63Q8×C31—24no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31C2×D412yes—
67C2×C4×C31C2411yescharacteristic
68C2×Dic31—22no—
69C2×Dic31C2×D412yes—
70C2×Dic31C2×D411yescharacteristic
71D124—24no—
72D124—44no—
73D124—44no—
74C4×D31—24no—
75C4×D31—44no—
76C4×D31—44no—
77C4×D31C2×D414yes—
78Dic62—24no—
79Dic62—44no—
80C8×C31C2×D414yes—
81C31⋊C8C2×D414yes—
82#3152—311nomaximal, Sylow
83C22×C31C22×D411yescharacteristic
84C2×D31—22no—
85C2×D31—42no—
86C2×D31—44no—
87C2×D31#12712yes—
88C4×C31—42no—
89C4×C31—42no—
90C4×C31#13714yescomplemented
91C4×C31C22×D412yes—
92Dic31—22no—
93Dic31—42no—
94Dic31#12712yes—
95C2×#137—314no—
96#532—311no—
97C2×C4⋊Q8—311no—
98#497—314no—
99#494—311no—
100#494D3111yescharacteristic, complemented
101#492—311no—
102#492—311no—
103C4×M16—311no—
104C2×C31C2×#12711yescharacteristic
105C2×C31C2×#13712yes—
106D31—22no—
107D31—82no—
108C2×#41—312no—
109C22×Q8—312no—
110#137—6216no—
111C2×Q16—314no—
112C2×Q16C2×D3114yes—
113C2×SD16—314no—
114C2×SD16—314no—
115C2×M16—312no—
116C4⋊Q8—312no—
117C4⋊Q8—311no—
118C4⋊Q8—622no—
119C4⋊Q8C2×D3111yescharacteristic
120C4⋊Q8C2×D3111yescharacteristic
121#127—311no—
122#124—312no—
123#121—622no—
124C4×D4—622no—
125C2×C4⋊C4—622no—
126C2×C42—311no—
127#97—312no—
128C4×C8—311no—
129C4×C8C2×D3111yescharacteristic
130C31#315211yescharacteristic, complemented, Sylow
131#41—628no—
132C2×Q8—312no—
133C2×Q8—622no—
134C2×Q8—628no—
135C2×Q8C22×D3112yes—
136C2×Q8C22×D3112yes—
137C2×D4—312no—
138C2×D4—622no—
139C2×D4—622no—
140C22×C4—311no—
141C22×C4—312no—
142C22×C4—622no—
143C22×C4—622no—
144Q16—28no—
145Q16—628no—
146SD16—628no—
147SD16—628no—
148M16—318no—
149C2×C8—312no—
150C2×C8C22×D3112yes—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—624no—
154C4⋊C4—622no—
155C22⋊C4—624no—
156C42—312no—
157C42—311no—
158C42C22×D3111yescharacteristic
159C23—311no—
160C23—622no—
161Q8—24no—
162Q8—24no—
163Q8—624no—
164Q8—1244no—
165D4—624no—
166D4—1244no—
167D4—1244no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—311no—
171C2×C4—314no—
172C2×C4—312no—
173C2×C4—624no—
174C2×C4—622no—
175C2×C4—1244no—
176C2×C4—1244no—
177C2×C4D4×D3112yes—
178C2×C4C23×D3111yescharacteristic
179C8—314no—
180C8D4×D3114yes—
181C22—312no—
182C22—622no—
183C22—1242no—
184C22—1244no—
185C22C2×D4×D3111yescharacteristic
186C4—42no—
187C4—42no—
188C4—312no—
189C4—622no—
190C4—1242no—
191C4#1175849514yescomplemented
192C4C2×D4×D3112yes—
193C2—622no—
194C2—2482no—
195C2#127×D3111yescharacteristic
196C2C2×#1175849512yes—
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#494C2
socleC22×C31C22×D4
prime radical#14521600C2
hypercenter#494D31
hypocenterC31#3152
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. C2×#11758495C2semidirect
3. C4⋊Q8×D31C2semidirect
4. #14521442C2semidirect
5. #14521428C2semidirect
6. #14521423C2semidirect
7. #14521422C2semidirect
8. C4×#92469C2semidirect
9. C31×#494C2semidirect
59. #92469D4semidirect
90. C4×C31#137semidirect
100. #494D31semidirect
130. C31#3152semidirect
191. C4#11758495semidirect

Maximal subgroups

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

subgroupindex
C2×#117584952
#145216002
C4⋊Q8×D312
#145214422
#145214282
#145214232
#145214222
C4×#924692
C31×#4942
#315231