Finite Group Databasebeta

← #16846145

Subgroups — #16846145

Order 3968.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22×#92474C211yesmaximal, characteristic
2C2×#11758423C212yesmaximal, complemented
3#14520909C211yesmaximal, characteristic
4#14520811C212yesmaximal, complemented
5C2×C31×C22⋊Q8C211yesmaximal, characteristic
6C22×Q8×C31C2211yescharacteristic
7C23×C4×C31C2211yescharacteristic
8C31×C22⋊Q8—22no—
9C31×C22⋊Q8C414yescomplemented
10C2×C4⋊C4×C31—21no—
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31—21no—
13C2×C22⋊Dic31—21no—
14C2×C4⋊Dic31C2212yes—
15C2×#92474—22no—
16C2×#92474—24no—
17C22×C31⋊C8C2212yes—
18#11758423—24no—
19C31⋊#95—21no—
20C24×C31D411yescharacteristic
21C2×Q8×C31—21no—
22C2×Q8×C31—22no—
23C2×Q8×C31—22no—
24C2×Q8×C31C2×C412yes—
25C22×C4×C31—22no—
26C22×C4×C31—22no—
27C22×C4×C31—21no—
28C22×C4×C31—21no—
29C22×C4×C31C2×C412yes—
30C22×C4×C31D411yescharacteristic
31C22×C4×C31D412yes—
32C22×C4×C31C2311yescharacteristic
33C22×Dic31—22no—
34C4⋊C4×C31—24no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31C2×C412yes—
37C22⋊C4×C31—24no—
38C22⋊Dic31—42no—
39C4⋊Dic31—22no—
40C4⋊Dic31—22no—
41#92474—28no—
42C2×C31⋊C8—22no—
43C2×C31⋊C8—22no—
44C2×C31⋊C8D414yes—
45C23×C31—22no—
46C23×C31—21no—
47C23×C31—22no—
48C23×C31—21no—
49C23×C31C22⋊C412yes—
50C23×C31C2×D411yescharacteristic
51Q8×C31—24no—
52Q8×C31—41no—
53Q8×C31—41no—
54C2×C4×C31—22no—
55C2×C4×C31—24no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—42no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C22⋊C412yes—
64C2×C4×C31C22×C411yescharacteristic
65C2×C4×C31C2×D412yes—
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31#4112yes—
68C2×Dic31—42no—
69C2×Dic31—42no—
70C2×Dic31—42no—
71C31⋊C8—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#13712yes—
82C22×C31#13711yescharacteristic
83C4×C31—22no—
84C4×C31—42no—
85C4×C31—42no—
86C4×C31C4×D412yes—
87C4×C31#12011yescharacteristic
88C4×C31#12311yescharacteristic
89Dic31—82no—
90C22×M16—311no—
91C2×C22⋊Q8D3111yescharacteristic
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×Q8C2×D3111yescharacteristic
102C23×C4C2×D3111yescharacteristic
103C2×M16—624no—
104C2×M16—622no—
105C22×C8—312no—
106C22⋊Q8—22no—
107C22⋊Q8Dic3114yescomplemented
108C2×C4⋊C4—21no—
109C2×C4⋊C4—312no—
110C2×C4⋊C4C2×D3111yescharacteristic
111C2×C22⋊C4—21no—
112C2×C22⋊C4—621no—
113#103—624no—
114#95—621no—
115C31#189411yescharacteristic, complemented, Sylow
116C24C22⋊D3111yescharacteristic
117C2×Q8—21no—
118C2×Q8—22no—
119C2×Q8—22no—
120C2×Q8C2×Dic3112yes—
121C22×C4—22no—
122C22×C4—22no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—622no—
126C22×C4C2×Dic3112yes—
127C22×C4C22⋊D3111yescharacteristic
128C22×C4C22⋊D3112yes—
129C22×C4C22×D3111yescharacteristic
130M16—628no—
131C2×C8—314no—
132C2×C8—622no—
133C2×C8—622no—
134C4⋊C4—24no—
135C4⋊C4—21no—
136C4⋊C4—622no—
137C4⋊C4—622no—
138C4⋊C4C2×Dic3112yes—
139C22⋊C4—24no—
140C22⋊C4—1242no—
141C23—22no—
142C23—22no—
143C23—21no—
144C23—21no—
145C23C22⋊Dic3112yes—
146C23C2×C22⋊D3111yescharacteristic
147Q8—24no—
148Q8—41no—
149Q8—41no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—1242no—
160C2×C4—1242no—
161C2×C4—1242no—
162C2×C4C22⋊Dic3112yes—
163C2×C4D4×D3112yes—
164C2×C4#9249712yes—
165C2×C4C22×Dic3111yescharacteristic
166C2×C4C2×C22⋊D3111yescharacteristic
167C8—624no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22#1175851612yes—
174C22#1175851912yes—
175C22#1175852611yescharacteristic
176C22#1175852811yescharacteristic
177C22C2×C22⋊Dic3111yescharacteristic
178C4—22no—
179C4—42no—
180C4—42no—
181C4—2482no—
182C4D4×Dic3112yes—
183C4#1175851211yescharacteristic
184C4#1175851411yescharacteristic
185C2—42no—
186C2#1452092911yescharacteristic
187C2#1452105011yescharacteristic
188C2#1452105811yescharacteristic
189C2#1452129712yes—
190C2#1452130512yes—
subgroupG/H
centerC23C2×C22⋊D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×C22⋊Q8C2
socleC23×C31C2×D4
prime radicalC24×C31D4
cosocleC22×C4×C31C23
hypercenterC2×C22⋊Q8D31
hypocenterC31#1894
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#11758423C2semidirect
4. #14520811C2semidirect
9. C31×C22⋊Q8C4semidirect
107. C22⋊Q8Dic31semidirect
115. C31#1894semidirect

Maximal subgroups

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

subgroupindex
C22×#924742
C2×#117584232
#145209092
#145208112
C2×C31×C22⋊Q82
#189431