Finite Group Databasebeta

← #16846245

Subgroups — #16846245

Order 3968.

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

normal subgroups only

This group has 314 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#14521620C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic, complemented
3#14521066C211yesmaximal, characteristic
4C2×#11758412C211yesmaximal, characteristic, complemented
5#14520806C211yesmaximal, characteristic, complemented
6#14520805C211yesmaximal, characteristic, complemented
7C31×#421C211yesmaximal, characteristic
8C2×#41×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758521C412yescomplemented
13#11758513C412yescomplemented
14#11758512—22no—
15#11758503C2211yescharacteristic
16#11758503C2211yescharacteristic
17#11758501—22no—
18C2×#92474C2211yescharacteristic
19#11758464—22no—
20#11758454—22no—
21C4×Dic62—22no—
22C31×#104—22no—
23#11758425—22no—
24#11758412—22no—
25#41×C31—21no—
26#41×C31—21no—
27#41×C31—21no—
28#41×C31—21no—
29C2×Q8×C31C2×C411yescharacteristic
30C2×D4×C31—21no—
31C2×D4×C31C2×C411yescharacteristic
32C22×C4×C31—21no—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31D412yes—
35C2×Dic62—21no—
36C2×Dic62—21no—
37C2×Dic62—21no—
38C2×Dic62—21no—
39C2×Dic62C2×C412yes—
40C2×Dic62D412yes—
41M16×C31—21no—
42M16×C31—21no—
43C2×C8×C31—21no—
44C4⋊C4×C31—21no—
45C22⋊C4×C31—21no—
46C42×C31D412yes—
47C22⋊Dic31—21no—
48C22⋊Dic31—21no—
49C22⋊Dic31—24no—
50C4⋊Dic31—21no—
51C4⋊Dic31—21no—
52Dic31⋊C4—24no—
53Dic31⋊C4—24no—
54C4×Dic31—24no—
55C4×Dic31C2×C412yes—
56C4×Dic31D412yes—
57#92474—21no—
58#92474—21no—
59C2×C31⋊C8—21no—
60C23×C31—21no—
61C23×C31C2×D411yescharacteristic
62Q8×C31—21no—
63Q8×C31—21no—
64D4×C31—21no—
65D4×C31—21no—
66D4×C31—41no—
67D4×C31—41no—
68C2×C4×C31—21no—
69C2×C4×C31—22no—
70C2×C4×C31—41no—
71C2×C4×C31—41no—
72C2×C4×C31C22×C411yescharacteristic
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31#4111yescharacteristic
77C2×C4×C31#4111yescharacteristic
78C2×Dic31—22no—
79C2×Dic31—22no—
80C2×Dic31—22no—
81C2×Dic31—22no—
82C2×Dic31C22⋊C414yes—
83Dic62—22no—
84Dic62—22no—
85Dic62—22no—
86Dic62—22no—
87C8×C31—41no—
88C31⋊C8—41no—
89#1912—311nomaximal, Sylow
90C22×C31—41no—
91C22×C31—42no—
92C22×C31—41no—
93C22×C31C2×C22⋊C411yescharacteristic
94C22×C31#12011yescharacteristic
95C22×C31#12311yescharacteristic
96C4×C31—42no—
97C4×C31—41no—
98C4×C31C4×D411yescharacteristic
99C4×C31C4×D411yescharacteristic
100C4×C31#12111yescharacteristic
101C4×C31#12111yescharacteristic
102Dic31—24no—
103Dic31—42no—
104Dic31—42no—
105#536—311no—
106#519—311no—
107#421—311no—
108#421D3111yescharacteristic
109C2×#101—311no—
110H(3,ℤ/4)—311no—
111H(3,ℤ/4)—311no—
112C2×C31—21no—
113C2×C31—21no—
114C2×C31—21no—
115C2×C31—81no—
116C2×C31#38611yescharacteristic
117C2×#41C2×D3111yescharacteristic
118C22×Q8—311no—
119C2×M16—311no—
120C2×M16C2×D3111yescharacteristic
121C4⋊Q8—312no—
122#124—312no—
123#123—622no—
124C22⋊Q8—622no—
125C4×Q8—622no—
126C4×Q8—622no—
127#117—311no—
128#117—311no—
129#117—622no—
130#117C2×D3111yescharacteristic
131#104—22no—
132#104—622no—
133#101—622no—
134C31#191211yescharacteristic, complemented, Sylow
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—312no—
140C2×Q8—312no—
141C2×Q8—621no—
142C2×Q8—621no—
143C2×Q8—621no—
144C2×Q8—621no—
145C2×Q8C4×D3111yescharacteristic
146C2×D4—21no—
147C2×D4C4×D3111yescharacteristic
148C22×C4—21no—
149C22×C4—312no—
150C22×C4C22×D3111yescharacteristic
151M16—21no—
152M16—21no—
153M16—621no—
154M16—621no—
155C2×C8—21no—
156C2×C8—621no—
157C4⋊C4—21no—
158C4⋊C4—624no—
159C4⋊C4—624no—
160C4⋊C4—621no—
161C4⋊C4—621no—
162C22⋊C4—21no—
163C22⋊C4—624no—
164C22⋊C4—621no—
165C22⋊C4—621no—
166C42—312no—
167C42—312no—
168C42—624no—
169C42C22⋊D3112yes—
170C23—21no—
171C23D4×D3111yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—622no—
175Q8—622no—
176Q8—622no—
177Q8—622no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—314no—
187C2×C4—622no—
188C2×C4—622no—
189C2×C4—622no—
190C2×C4—622no—
191C2×C4C2×C4×D3111yescharacteristic
192C2×C4#9249511yescharacteristic
193C2×C4D4×D3111yescharacteristic
194C2×C4D4×D3111yescharacteristic
195C2×C4#9249711yescharacteristic
196C2×C4C2×C22⋊D3111yescharacteristic
197C8—41no—
198C8—1241no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C22⋊C4×D3111yescharacteristic
203C22#1175846011yescharacteristic
204C22#1175851411yescharacteristic
205C4—42no—
206C4—41no—
207C4—624no—
208C4—1242no—
209C4—1242no—
210C4(C22⋊D31)⋊C411yescharacteristic
211C4#1175846111yescharacteristic
212C4C4×C22⋊D3111yescharacteristic
213C4#1175851511yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1452092511yescharacteristic
subgroupG/H
centerC2#14520925
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#421C2
socleC2×C31#386
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenter#421D31
hypocenterC31#1912
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #14521526C2semidirect
4. C2×#11758412C2semidirect
5. #14520806C2semidirect
6. #14520805C2semidirect
12. #11758521C4semidirect
13. #11758513C4semidirect
134. C31#1912semidirect

Maximal subgroups

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

subgroupindex
#145216202
#145215262
#145210662
C2×#117584122
#145208062
#145208052
C31×#4212
#191231