Finite Group Databasebeta

← #16846686

Subgroups — #16846686

Order 3968.

284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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#14521602C211yesmaximal, characteristic
2#14521072C211yesmaximal, characteristic
3C42×Dic31C211yesmaximal, characteristic
4#14520810C211yesmaximal, characteristic
5#14520809C211yesmaximal, characteristic
6#14520808C211yesmaximal, characteristic
7C31×#339C211yesmaximal, characteristic
8C2×M16×C31C2211yescharacteristic
9C31×#117C2211yescharacteristic
10C2×C42×C31C2211yescharacteristic
11#11758503C2211yescharacteristic
12C2×C4×Dic31—22no—
13C2×C4×Dic31C2211yescharacteristic
14C2×C4×Dic31C2211yescharacteristic
15C2×#92474C2211yescharacteristic
16#11758467C412yescomplemented
17#11758465C412yescomplemented
18#11758455—22no—
19C4×Dic62—22no—
20Dic31⋊C8—22no—
21C22×C4×C31—21no—
22C22×C4×C31C2311yescharacteristic
23C22×Dic31—21no—
24C22×Dic31D412yes—
25C2×Dic62—22no—
26M16×C31—21no—
27M16×C31—21no—
28C2×C8×C31—21no—
29C4⋊C4×C31C2×C412yes—
30C22⋊C4×C31—21no—
31C42×C31—21no—
32C42×C31—21no—
33C42×C31Q812yescomplemented
34C22⋊Dic31—21no—
35C4⋊Dic31—22no—
36C4⋊Dic31C2×C412yes—
37Dic31⋊C4—22no—
38Dic31⋊C4—22no—
39C4×Dic31—28no—
40C4×Dic31—21no—
41C4×Dic31—21no—
42C4×Dic31C2×C411yescharacteristic
43C4×Dic31C2×C411yescharacteristic
44C4×Dic31D412yes—
45C4×Dic31Q812yescomplemented
46#92474—21no—
47#92474—21no—
48C2×C31⋊C8—21no—
49C23×C31C2×D411yescharacteristic
50C2×C4×C31—24no—
51C2×C4×C31—22no—
52C2×C4×C31—22no—
53C2×C4×C31C22×C411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×Q811yescharacteristic
56C2×C4×C31C2×Q811yescharacteristic
57C2×C4×C31#4111yescharacteristic
58C2×C4×C31#4111yescharacteristic
59C2×Dic31—24no—
60C2×Dic31—22no—
61C2×Dic31—24no—
62C2×Dic31—22no—
63C2×Dic31C22⋊C412yes—
64C2×Dic31C22⋊C412yes—
65Dic62—44no—
66C8×C31—41no—
67C31⋊C8—41no—
68#1994—311nomaximal, Sylow
69C22×C31—22no—
70C22×C31C2×C22⋊C411yescharacteristic
71C22×C31C22⋊Q811yescharacteristic
72C22×C31C22⋊Q811yescharacteristic
73C4×C31—24no—
74C4×C31—42no—
75C4×C31C4×Q811yescharacteristic
76C4×C31C4×Q811yescharacteristic
77C4×C31#12411yescharacteristic
78C4×C31C4⋊Q811yescharacteristic
79Dic31—24no—
80Dic31—22no—
81Dic31—42no—
82Dic31#10414yes—
83#533—311no—
84#423—311no—
85C43—311no—
86#339—311no—
87#339—311no—
88#339—311no—
89#339D3111yescharacteristic
90C2×C31—21no—
91C2×C31—21no—
92C2×C31#39111yescharacteristic
93C2×C31C2×#10412yes—
94C2×M16—311no—
95C2×M16C2×D3111yescharacteristic
96C4⋊Q8—312no—
97#125—312no—
98C22⋊Q8—622no—
99C4×Q8—622no—
100#117—311no—
101#117C2×D3111yescharacteristic
102C2×C42—311no—
103C2×C42—311no—
104C2×C42—622no—
105C2×C42C2×D3111yescharacteristic
106C4⋊C8—622no—
107C31#199411yescharacteristic, complemented, Sylow
108C2×Q8—622no—
109C22×C4—21no—
110C22×C4—312no—
111C22×C4—621no—
112C22×C4C22×D3111yescharacteristic
113M16—21no—
114M16—21no—
115M16—621no—
116M16—621no—
117C2×C8—21no—
118C2×C8—621no—
119C4⋊C4—312no—
120C4⋊C4—622no—
121C4⋊C4—622no—
122C4⋊C4—622no—
123C4⋊C4C4×D3112yes—
124C22⋊C4—21no—
125C22⋊C4—621no—
126C42—21no—
127C42—21no—
128C42—311no—
129C42—311no—
130C42—312no—
131C42—312no—
132C42—628no—
133C42—621no—
134C42—621no—
135C42Dic6212yescomplemented
136C23D4×D3111yescharacteristic
137Q8—1244no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—312no—
142C2×C4—312no—
143C2×C4—624no—
144C2×C4—624no—
145C2×C4—622no—
146C2×C4—622no—
147C2×C4C2×Dic6211yescharacteristic
148C2×C4C2×C4×D3111yescharacteristic
149C2×C4#9249511yescharacteristic
150C2×C4D4×D3111yescharacteristic
151C2×C4#9249711yescharacteristic
152C2×C4Q8×D3111yescharacteristic
153C8—41no—
154C8—1241no—
155C22—22no—
156C22#1175845511yescharacteristic
157C22C22⋊C4×D3111yescharacteristic
158C22#1175847311yescharacteristic
159C4—24no—
160C4—42no—
161C4—314no—
162C4—624no—
163C4—622no—
164C4—1242no—
165C4C4×Dic6211yescharacteristic
166C4#1175846211yescharacteristic
167C4#1175846411yescharacteristic
168C4#1175846511yescharacteristic
169C2—21no—
170C2—21no—
171C2#1452095311yescharacteristic
172C2#104×D3112yes—
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31C2×C22⋊C4
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1994
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
16. #11758467C4semidirect
17. #11758465C4semidirect
33. C42×C31Q8semidirect
45. C4×Dic31Q8semidirect
107. C31#1994semidirect
135. C42Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216022
#145210722
C42×Dic312
#145208102
#145208092
#145208082
C31×#3392
#199431