Finite Group Databasebeta

← #16846144

Subgroups — #16846144

Order 3968.

360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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×#11758501C211yesmaximal, characteristic
2C2×#11758404C212yesmaximal, complemented
3#14520909C211yesmaximal, characteristic
4#14520812C212yesmaximal, complemented
5C22×M16×C31C211yesmaximal, characteristic
6C23×C4×C31C2211yescharacteristic
7C22×Dic62C2211yescharacteristic
8C2×M16×C31—22no—
9C2×M16×C31—24no—
10C22×C8×C31C2212yes—
11C2×C22⋊Dic31—21no—
12C2×C22⋊Dic31—21no—
13C2×C4⋊Dic31C2212yes—
14C2×C4⋊Dic31C2211yescharacteristic
15#11758501—22no—
16#11758501C414yescomplemented
17C2×Dic31⋊C4—21no—
18C31⋊#95—21no—
19#11758404—24no—
20C24×C31D411yescharacteristic
21C22×C4×C31—22no—
22C22×C4×C31—22no—
23C22×C4×C31C2×C412yes—
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D412yes—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31—21no—
28C22×Dic31—21no—
29C22×Dic31—22no—
30C2×Dic62—22no—
31C2×Dic62—22no—
32C2×Dic62—21no—
33C2×Dic62C2×C412yes—
34M16×C31—28no—
35C2×C8×C31—22no—
36C2×C8×C31—22no—
37C2×C8×C31D414yes—
38C22⋊Dic31—24no—
39C22⋊Dic31—42no—
40C4⋊Dic31—21no—
41C4⋊Dic31—22no—
42C4⋊Dic31—22no—
43C4⋊Dic31C2×C412yes—
44Dic31⋊C4—24no—
45C23×C31—22no—
46C23×C31—21no—
47C23×C31—21no—
48C23×C31—22no—
49C23×C31C22⋊C412yes—
50C23×C31C2×D411yescharacteristic
51C2×C4×C31—22no—
52C2×C4×C31—24no—
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31C22⋊C412yes—
56C2×C4×C31C22×C411yescharacteristic
57C2×C4×C31C2×D412yes—
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31#4112yes—
60C2×Dic31—22no—
61C2×Dic31—22no—
62C2×Dic31—42no—
63C2×Dic31—41no—
64C2×Dic31—41no—
65C2×Dic31—42no—
66C2×Dic31—42no—
67C2×Dic31—42no—
68Dic62—24no—
69Dic62—41no—
70Dic62—41no—
71C8×C31—24no—
72#1894—311nomaximal, Sylow
73C22×C31—22no—
74C22×C31—22no—
75C22×C31—22no—
76C22×C31—42no—
77C22×C31—42no—
78C22×C31C2×C22⋊C411yescharacteristic
79C22×C31#12112yes—
80C22×C31AGL(1,ℤ/8)11yescharacteristic
81C22×C31#13711yescharacteristic
82C22×C31#13712yes—
83C4×C31—22no—
84C4×C31C4×D412yes—
85C4×C31#12011yescharacteristic
86C4×C31#12311yescharacteristic
87Dic31—42no—
88Dic31—42no—
89Dic31—82no—
90C22×M16D3111yescharacteristic
91C2×C22⋊Q8—311no—
92C2×#103—312no—
93#380—311no—
94#340—312no—
95C2×C31—42no—
96C2×C31#38611yescharacteristic
97C2×C31#41711yescharacteristic
98C2×C31#41911yescharacteristic
99C2×C31#46812yes—
100C2×C31#47012yes—
101C22×Q8—311no—
102C23×C4C2×D3111yescharacteristic
103C2×M16—22no—
104C2×M16—24no—
105C22×C8C2×D3112yes—
106C22⋊Q8—314no—
107C22⋊Q8—622no—
108C2×C4⋊C4—311no—
109C2×C4⋊C4—312no—
110C2×C4⋊C4—621no—
111C2×C22⋊C4—621no—
112C2×C22⋊C4—621no—
113#103—624no—
114#95—621no—
115C31#189411yescharacteristic, complemented, Sylow
116C24D12411yescharacteristic
117C2×Q8—312no—
118C2×Q8—621no—
119C2×Q8—622no—
120C2×Q8—622no—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—621no—
124C22×C4—621no—
125C22×C4—622no—
126C22×C4C4×D3112yes—
127C22×C4D12411yescharacteristic
128C22×C4C22⋊D3112yes—
129C22×C4C22×D3111yescharacteristic
130M16—28no—
131C2×C8—22no—
132C2×C8—22no—
133C2×C8C22⋊D3114yes—
134C4⋊C4—312no—
135C4⋊C4—624no—
136C4⋊C4—621no—
137C4⋊C4—622no—
138C4⋊C4—622no—
139C22⋊C4—624no—
140C22⋊C4—1242no—
141C23—21no—
142C23—21no—
143C23—22no—
144C23—22no—
145C23(C2×D31)⋊C412yes—
146C23C2×D12411yescharacteristic
147Q8—624no—
148Q8—1241no—
149Q8—1241no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—622no—
155C2×C4—622no—
156C2×C4—1241no—
157C2×C4—1241no—
158C2×C4—1242no—
159C2×C4—1242no—
160C2×C4—1242no—
161C2×C4—1242no—
162C2×C4(C2×D31)⋊C412yes—
163C2×C4C2×C4×D3111yescharacteristic
164C2×C4#9249512yes—
165C2×C4C2×C22⋊D3112yes—
166C2×C4C2×C22⋊D3111yescharacteristic
167C8—24no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22#1175848511yescharacteristic
174C22#1175848612yes—
175C22#1175848611yescharacteristic
176C22C2×(C2×D31)⋊C411yescharacteristic
177C22#1175850712yes—
178C4—22no—
179C4—1242no—
180C4—1242no—
181C4—2482no—
182C4C4×C22⋊D3112yes—
183C4#1175850611yescharacteristic
184C4#1175853011yescharacteristic
185C2—42no—
186C2#1452092811yescharacteristic
187C2#1452105111yescharacteristic
188C2#1452105911yescharacteristic
189C2#1452129512yes—
190C2#1452130712yes—
subgroupG/H
centerC23C2×D124
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC22×M16×C31C2
socleC23×C31C2×D4
prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenterC22×M16D31
hypocenterC31#1894
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#11758404C2semidirect
4. #14520812C2semidirect
16. #11758501C4semidirect
115. C31#1894semidirect

Maximal subgroups

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

subgroupindex
C2×#117585012
C2×#117584042
#145209092
#145208122
C22×M16×C312
#189431