Finite Group Databasebeta

← #16846207

Subgroups — #16846207

Order 3968.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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#14521527C211yesmaximal, characteristic, complemented
2#14521066C211yesmaximal, characteristic
3#14521058C211yesmaximal, characteristic, complemented
4#14521023C211yesmaximal, characteristic
5#14520820C211yesmaximal, characteristic, complemented
6#14520806C211yesmaximal, characteristic, complemented
7C2×C31×#137C211yesmaximal, characteristic
8C2×#41×C31C2211yescharacteristic
9C22×Q8×C31C2211yescharacteristic
10C31×#137—22no—
11C31×#137—22no—
12C2×Q16×C31C412yescomplemented
13C2×SD16×C31C412yescomplemented
14C2×M16×C31C2211yescharacteristic
15Q8×Dic31—22no—
16Q8×Dic31—22no—
17#11758503—22no—
18#11758503C2211yescharacteristic
19#11758503C2211yescharacteristic
20#11758503C2211yescharacteristic
21C2×#92474C2211yescharacteristic
22#11758425—22no—
23#11758423—22no—
24#11758422—22no—
25#41×C31—21no—
26#41×C31—21no—
27#41×C31—21no—
28#41×C31—21no—
29C2×Q8×C31—21no—
30C2×Q8×C31—21no—
31C2×Q8×C31—21no—
32C2×Q8×C31C2×C411yescharacteristic
33C2×Q8×C31C2×C412yes—
34C2×Q8×C31D412yes—
35C2×Q8×C31D412yes—
36C2×D4×C31—21no—
37C2×D4×C31C2×C411yescharacteristic
38C22×C4×C31—21no—
39C22×C4×C31—21no—
40C22×C4×C31C2311yescharacteristic
41Q16×C31—24no—
42SD16×C31—24no—
43M16×C31—21no—
44M16×C31—21no—
45C2×C8×C31C2×C412yes—
46C22⋊Dic31—21no—
47C22⋊Dic31—21no—
48C22⋊Dic31D412yes—
49C4⋊Dic31—24no—
50C4⋊Dic31—21no—
51C4⋊Dic31—21no—
52C4⋊Dic31—21no—
53C4×Dic31—24no—
54C4×Dic31—21no—
55C4×Dic31—21no—
56C4×Dic31D412yes—
57#92474—21no—
58#92474—21no—
59C2×C31⋊C8—21no—
60C23×C31—21no—
61C23×C31C2×D411yescharacteristic
62Q8×C31—22no—
63Q8×C31—22no—
64Q8×C31—22no—
65Q8×C31—21no—
66Q8×C31—21no—
67Q8×C31C22⋊C414yes—
68D4×C31—21no—
69D4×C31—21no—
70D4×C31—41no—
71D4×C31—41no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31—21no—
76C2×C4×C31—41no—
77C2×C4×C31—41no—
78C2×C4×C31C22×C411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31#4111yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C2×Dic31—22no—
85C2×Dic31—22no—
86C2×Dic31—41no—
87C8×C31—22no—
88C31⋊C8—41no—
89#1905—311nomaximal, Sylow
90C22×C31—41no—
91C22×C31—41no—
92C22×C31—81no—
93C22×C31C4×D411yescharacteristic
94C22×C31#12011yescharacteristic
95C22×C31#12111yescharacteristic
96C4×C31—24no—
97C4×C31—41no—
98C4×C31C2×C22⋊C411yescharacteristic
99C4×C31C4×D411yescharacteristic
100C4×C31#12111yescharacteristic
101C4×C31#12311yescharacteristic
102Dic31—42no—
103Dic31—42no—
104Dic31—81no—
105C2×#137D3111yescharacteristic
106#519—311no—
107#421—311no—
108#419—311no—
109#410—311no—
110#344—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×Q8C2×D3111yescharacteristic
119#137—22no—
120#137—22no—
121C2×Q16Dic3112yescomplemented
122C2×SD16Dic3112yescomplemented
123C2×M16—311no—
124C2×M16C2×D3111yescharacteristic
125C4×Q8—622no—
126C4×Q8—622no—
127#117—311no—
128#117—311no—
129#117—311no—
130#117—622no—
131#104—622no—
132#103—622no—
133#99—622no—
134C31#190511yescharacteristic, complemented, Sylow
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×Dic3111yescharacteristic
143C2×Q8C2×Dic3112yes—
144C2×Q8C22⋊D3112yes—
145C2×Q8C22⋊D3112yes—
146C2×D4—21no—
147C2×D4C2×Dic3111yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4C22×D3111yescharacteristic
151Q16—24no—
152SD16—24no—
153M16—21no—
154M16—21no—
155M16—621no—
156M16—621no—
157C2×C8—621no—
158C2×C8C2×Dic3112yes—
159C4⋊C4—624no—
160C4⋊C4—621no—
161C4⋊C4—621no—
162C4⋊C4—621no—
163C22⋊C4—312no—
164C22⋊C4—621no—
165C22⋊C4—621no—
166C42—312no—
167C42—624no—
168C42—621no—
169C42—621no—
170C23—21no—
171C23D4×D3111yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—21no—
176Q8—21no—
177Q8C22⋊Dic3114yes—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—622no—
189C2×C4—622no—
190C2×C4—1241no—
191C2×C4D4×D3111yescharacteristic
192C2×C4#9249711yescharacteristic
193C2×C4#9249711yescharacteristic
194C2×C4C22×Dic3111yescharacteristic
195C2×C4C2×C22⋊D3111yescharacteristic
196C2×C4C2×C22⋊D3111yescharacteristic
197C8—22no—
198C8—1241no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22D4×Dic3111yescharacteristic
203C22#1175851411yescharacteristic
204C22#1175851611yescharacteristic
205C4—24no—
206C4—41no—
207C4—1242no—
208C4—1242no—
209C4—2481no—
210C4D4×Dic3111yescharacteristic
211C4#1175851211yescharacteristic
212C4#1175851611yescharacteristic
213C4C2×C22⋊Dic3111yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#1452092911yescharacteristic
subgroupG/H
centerC2#14520929
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#137C2
socleC2×C31#386
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenterC2×#137D31
hypocenterC31#1905
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. #14521527C2semidirect
3. #14521058C2semidirect
5. #14520820C2semidirect
6. #14520806C2semidirect
12. C2×Q16×C31C4semidirect
13. C2×SD16×C31C4semidirect
121. C2×Q16Dic31semidirect
122. C2×SD16Dic31semidirect
134. C31#1905semidirect

Maximal subgroups

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

subgroupindex
#145215272
#145210662
#145210582
#145210232
#145208202
#145208062
C2×C31×#1372
#190531