Finite Group Databasebeta

← #16846230

Subgroups — #16846230

Order 3968.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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#14521815C211yesmaximal, characteristic
2#14521623C211yesmaximal, characteristic
3#14521058C211yesmaximal, characteristic, complemented
4#14521022C211yesmaximal, characteristic
5#14520806C211yesmaximal, characteristic, complemented
6#14520805C211yesmaximal, characteristic, complemented
7C31×#419C211yesmaximal, characteristic, complemented
8C22×Q8×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758524C412yescomplemented
13#11758523—22no—
14#11758521C412yescomplemented
15#11758506—22no—
16#11758503C2211yescharacteristic
17#11758503C2211yescharacteristic
18C2×#92474C2211yescharacteristic
19#11758484—22no—
20M16×D31—22no—
21#11758478—22no—
22C31×#103—22no—
23#11758423—22no—
24#11758394—22no—
25C2×Q8×C31—21no—
26C2×Q8×C31—21no—
27C2×Q8×C31—21no—
28C2×Q8×C31—21no—
29C2×Q8×C31—21no—
30C2×Q8×C31C2×C412yes—
31C22×C4×C31—21no—
32C22×C4×C31C2311yescharacteristic
33C2×C22⋊D31D412yes—
34#92495—21no—
35#92495—21no—
36#92495—21no—
37#92495—21no—
38C2×D124C2×C411yescharacteristic
39C2×C4×D31D412yes—
40C2×Dic62C2×C411yescharacteristic
41M16×C31—21no—
42M16×C31—21no—
43C2×C8×C31D412yes—
44C4⋊C4×C31—21no—
45C22⋊C4×C31—21no—
46C42×C31—21no—
47C22⋊Dic31—21no—
48C22⋊Dic31—21no—
49(C2×D31)⋊C4—24no—
50C4⋊Dic31—21no—
51C4⋊Dic31—21no—
52Dic31⋊C4—24no—
53C4×Dic31—21no—
54C4×Dic31C2×C412yes—
55#92474—21no—
56#92474—21no—
57C2×C31⋊C8D412yes—
58#92469—24no—
59C8×D31—24no—
60C23×C31C2×D411yescharacteristic
61C22×D31C22⋊C412yes—
62Q8×C31—22no—
63Q8×C31—22no—
64Q8×C31—41no—
65Q8×C31—41no—
66C2×C4×C31—22no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31—41no—
70C2×C4×C31C22×C411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31#4111yescharacteristic
75C2×C4×C31#4111yescharacteristic
76C22⋊D31—22no—
77C22⋊D31—22no—
78C2×Dic31—22no—
79C2×Dic31—41no—
80C2×Dic31C22⋊C412yes—
81D124—21no—
82D124—21no—
83C4×D31—22no—
84C4×D31—22no—
85Dic62—21no—
86Dic62—21no—
87C8×C31—22no—
88C31⋊C8—22no—
89#1909—311nomaximal, Sylow
90C22×C31—41no—
91C22×C31C2×C22⋊C411yescharacteristic
92C22×C31#12111yescharacteristic
93C22×C31#12111yescharacteristic
94C2×D31—22no—
95C2×D31—42no—
96C4×C31—42no—
97C4×C31—81no—
98C4×C31C4×D411yescharacteristic
99C4×C31C4×D411yescharacteristic
100C4×C31#12011yescharacteristic
101C4×C31#12311yescharacteristic
102Dic31—22no—
103Dic31—42no—
104Dic31—81no—
105#568—311no—
106#536—311no—
107#419—311no—
108#419D3111yescharacteristic, complemented
109#410—311no—
110H(3,ℤ/4)—311no—
111H(3,ℤ/4)—311no—
112C2×C31—21no—
113C2×C31—21no—
114C2×C31—21no—
115C2×C31#38611yescharacteristic
116D31—42no—
117C2×#41—311no—
118C22×Q8C2×D3111yescharacteristic
119#131—622no—
120#131—622no—
121C2×M16—311no—
122C2×M16—622no—
123C2×M16C2×D3111yescharacteristic
124C4⋊Q8—312no—
125#124—312no—
126#123—622no—
127C22⋊Q8—622no—
128#117—311no—
129#117—311no—
130#117C2×D3111yescharacteristic
131#103—22no—
132#103—622no—
133#99—622no—
134C31#190911yescharacteristic, complemented, Sylow
135#41—621no—
136#41—621no—
137#41—621no—
138#41—621no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—21no—
144C2×Q8—311no—
145C2×Q8C4×D3112yes—
146C2×D4—312no—
147C2×D4—311no—
148C22×C4—21no—
149C22×C4—312no—
150C22×C4C22×D3111yescharacteristic
151M16—21no—
152M16—21no—
153M16—624no—
154M16—621no—
155M16—621no—
156C2×C8—312no—
157C2×C8—624no—
158C2×C8C22⋊D3112yes—
159C4⋊C4—21no—
160C4⋊C4—624no—
161C4⋊C4—621no—
162C4⋊C4—621no—
163C22⋊C4—21no—
164C22⋊C4—624no—
165C22⋊C4—621no—
166C22⋊C4—621no—
167C42—21no—
168C42—312no—
169C42—621no—
170C23—312no—
171C23D4×D3111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—621no—
177Q8—621no—
178D4—622no—
179D4—622no—
180D4—621no—
181D4—621no—
182C2×C4—22no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—312no—
187C2×C4—622no—
188C2×C4—622no—
189C2×C4—622no—
190C2×C4—1241no—
191C2×C4C2×C4×D3111yescharacteristic
192C2×C4#9249511yescharacteristic
193C2×C4D4×D3111yescharacteristic
194C2×C4D4×D3111yescharacteristic
195C2×C4#9249711yescharacteristic
196C2×C4C2×C22⋊D3111yescharacteristic
197C8—22no—
198C8—622no—
199C22—41no—
200C22—622no—
201C22—1242no—
202C22C22⋊C4×D3111yescharacteristic
203C22#1175846111yescharacteristic
204C22#1175851511yescharacteristic
205C4—42no—
206C4—81no—
207C4—622no—
208C4—1242no—
209C4—2481no—
210C4(C22⋊D31)⋊C411yescharacteristic
211C4#1175846011yescharacteristic
212C4C4×C22⋊D3111yescharacteristic
213C4#1175851411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—1242no—
218C2#1452092511yescharacteristic
subgroupG/H
centerC2#14520925
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#419C2
socleC2×C31#386
prime radicalC2×#92495C22
cosocleC22×C4×C31C23
hypercenter#419D31
hypocenterC31#1909
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #14521058C2semidirect
5. #14520806C2semidirect
6. #14520805C2semidirect
7. C31×#419C2semidirect
12. #11758524C4semidirect
14. #11758521C4semidirect
108. #419D31semidirect
134. C31#1909semidirect

Maximal subgroups

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

subgroupindex
#145218152
#145216232
#145210582
#145210222
#145208062
#145208052
C31×#4192
#190931