Finite Group Databasebeta

← #16846111

Subgroups — #16846111

Order 3968.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11758513C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic, complemented
3#14521054C211yesmaximal, characteristic
4C2×#11758412C211yesmaximal, characteristic, complemented
5#14520810C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#418C211yesmaximal, characteristic
8C22×D4×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12C2×C22⋊Dic31—22no—
13#11758513—22no—
14#11758513C414yescomplemented
15#11758503C2211yescharacteristic
16C2×C4×Dic31C2211yescharacteristic
17C2×#92474C2211yescharacteristic
18#11758464—22no—
19#11758454—22no—
20C4×Dic62—22no—
21C31×#102—22no—
22#11758420—22no—
23#11758412—22no—
24C24×C31—21no—
25C2×D4×C31—21no—
26C2×D4×C31—21no—
27C2×D4×C31—21no—
28C2×D4×C31—21no—
29C2×D4×C31—21no—
30C2×D4×C31C2×C412yes—
31C22×C4×C31C2311yescharacteristic
32C22×Dic31—21no—
33C22×Dic31D412yes—
34C2×Dic62—21no—
35C2×Dic62—21no—
36C2×Dic62—21no—
37C2×Dic62—21no—
38C2×Dic62C2×C412yes—
39C2×Dic62D412yes—
40M16×C31—21no—
41M16×C31—21no—
42C2×C8×C31—21no—
43C4⋊C4×C31D412yes—
44C22⋊C4×C31—21no—
45C42×C31—21no—
46C22⋊Dic31—21no—
47C22⋊Dic31—28no—
48C4⋊Dic31D412yes—
49Dic31⋊C4—24no—
50C4×Dic31—24no—
51C4×Dic31—21no—
52C4×Dic31—21no—
53C4×Dic31C2×C412yes—
54#92474—21no—
55#92474—21no—
56C2×C31⋊C8—21no—
57C23×C31—22no—
58C23×C31—44no—
59C23×C31—41no—
60C23×C31—41no—
61C23×C31C2×D411yescharacteristic
62D4×C31—22no—
63D4×C31—22no—
64D4×C31—41no—
65D4×C31—41no—
66C2×C4×C31—22no—
67C2×C4×C31C22×C411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31#4111yescharacteristic
72C2×C4×C31#4111yescharacteristic
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—42no—
78C2×Dic31C22⋊C414yes—
79Dic62—22no—
80Dic62—22no—
81Dic62—22no—
82Dic62—22no—
83C8×C31—41no—
84C31⋊C8—41no—
85#1888—311nomaximal, Sylow
86C22×C31—22no—
87C22×C31—44no—
88C22×C31—42no—
89C22×C31—82no—
90C22×C31—82no—
91C22×C31C2×C22⋊C411yescharacteristic
92C22×C31#12011yescharacteristic
93C22×C31#12311yescharacteristic
94C4×C31—42no—
95C4×C31C4×D411yescharacteristic
96C4×C31C4×D411yescharacteristic
97C4×C31#12111yescharacteristic
98C4×C31#12111yescharacteristic
99Dic31—24no—
100Dic31—42no—
101Dic31—42no—
102C2×#124—311no—
103#519—311no—
104#418—311no—
105#418D3111yescharacteristic
106C2×#101—311no—
107#339—311no—
108#339—311no—
109C2×C31—21no—
110C2×C31—21no—
111C2×C31—82no—
112C2×C31#38611yescharacteristic
113C2×C31#45412yes—
114C22×Q8—311no—
115C22×D4C2×D3111yescharacteristic
116C2×M16—311no—
117C2×M16C2×D3111yescharacteristic
118#124—314no—
119#124—622no—
120C4×Q8—622no—
121C4×Q8—622no—
122#117—311no—
123#117—622no—
124#117C2×D3111yescharacteristic
125C2×C22⋊C4—622no—
126C2×C42—311no—
127#102—22no—
128#102—622no—
129#101—622no—
130C31#188811yescharacteristic, complemented, Sylow
131C24—21no—
132C2×Q8—312no—
133C2×Q8—312no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C2×Q8—621no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4C4×D3112yes—
144C22×C4—312no—
145C22×C4—621no—
146C22×C4C22×D3111yescharacteristic
147M16—21no—
148M16—21no—
149M16—621no—
150M16—621no—
151C2×C8—21no—
152C2×C8—621no—
153C4⋊C4—312no—
154C4⋊C4—624no—
155C4⋊C4C22⋊D3112yes—
156C22⋊C4—21no—
157C22⋊C4—628no—
158C22⋊C4—621no—
159C42—21no—
160C42—312no—
161C42—624no—
162C42—621no—
163C42—621no—
164C23—22no—
165C23—44no—
166C23—41no—
167C23—41no—
168C23D4×D3111yescharacteristic
169Q8—622no—
170Q8—622no—
171Q8—622no—
172Q8—622no—
173D4—22no—
174D4—22no—
175D4—41no—
176D4—41no—
177C2×C4—22no—
178C2×C4—314no—
179C2×C4—622no—
180C2×C4—622no—
181C2×C4—622no—
182C2×C4—622no—
183C2×C4—1242no—
184C2×C4C2×C4×D3111yescharacteristic
185C2×C4#9249511yescharacteristic
186C2×C4D4×D3111yescharacteristic
187C2×C4D4×D3111yescharacteristic
188C2×C4#9249711yescharacteristic
189C2×C4C2×C22⋊D3111yescharacteristic
190C8—41no—
191C8—1241no—
192C22—22no—
193C22—44no—
194C22—42no—
195C22—82no—
196C22—82no—
197C22C22⋊C4×D3111yescharacteristic
198C22#1175846011yescharacteristic
199C22#1175851411yescharacteristic
200C4—42no—
201C4—624no—
202C4—1242no—
203C4—1242no—
204C4(C22⋊D31)⋊C411yescharacteristic
205C4#1175846111yescharacteristic
206C4C4×C22⋊D3111yescharacteristic
207C4#1175851511yescharacteristic
208C2—21no—
209C2—21no—
210C2—82no—
211C2#1452092511yescharacteristic
212C2#1452122012yes—
subgroupG/H
centerC22#11758514
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#418C2
socleC22×C31#120
prime radicalC22×D4×C31C22
cosocleC22×C4×C31C23
hypercenter#418D31
hypocenterC31#1888
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #14521526C2semidirect
4. C2×#11758412C2semidirect
5. #14520810C2semidirect
6. #14520808C2semidirect
14. #11758513C4semidirect
130. C31#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#117585132
#145215262
#145210542
C2×#117584122
#145208102
#145208082
C31×#4182
#188831