Finite Group Databasebeta

← #16846101

Subgroups — #16846101

Order 3968.

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

normal subgroups only

This group has 324 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×#11758521C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic
3#14521058C211yesmaximal, characteristic
4C2×#11758412C211yesmaximal, characteristic
5#14520810C211yesmaximal, characteristic
6#14520808C211yesmaximal, characteristic
7C31×#419C211yesmaximal, characteristic
8C22×Q8×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758521—22no—
13#11758521C414yescomplemented
14#11758503C2211yescharacteristic
15C2×Dic31⋊C4—22no—
16C2×C4×Dic31C2211yescharacteristic
17C2×#92474C2211yescharacteristic
18#11758464—22no—
19#11758454—22no—
20C4×Dic62—22no—
21C31×#103—22no—
22#11758423—22no—
23#11758412—22no—
24C2×Q8×C31—21no—
25C2×Q8×C31—21no—
26C2×Q8×C31—21no—
27C2×Q8×C31—21no—
28C2×Q8×C31—21no—
29C2×Q8×C31C2×C412yes—
30C22×C4×C31—21no—
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—
47C4⋊Dic31D412yes—
48Dic31⋊C4—24no—
49Dic31⋊C4—28no—
50C4×Dic31—24no—
51C4×Dic31—21no—
52C4×Dic31—21no—
53C4×Dic31C2×C412yes—
54#92474—21no—
55#92474—21no—
56C2×C31⋊C8—21no—
57C23×C31C2×D411yescharacteristic
58Q8×C31—22no—
59Q8×C31—22no—
60Q8×C31—41no—
61Q8×C31—41no—
62C2×C4×C31—22no—
63C2×C4×C31—22no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31C22×C411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31#4111yescharacteristic
71C2×C4×C31#4111yescharacteristic
72C2×Dic31—24no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31C22⋊C414yes—
78Dic62—22no—
79Dic62—22no—
80Dic62—22no—
81Dic62—22no—
82C8×C31—41no—
83C31⋊C8—41no—
84#1886—311nomaximal, Sylow
85C22×C31—22no—
86C22×C31C2×C22⋊C411yescharacteristic
87C22×C31#12011yescharacteristic
88C22×C31#12311yescharacteristic
89C4×C31—42no—
90C4×C31—42no—
91C4×C31C4×D411yescharacteristic
92C4×C31C4×D411yescharacteristic
93C4×C31#12111yescharacteristic
94C4×C31#12111yescharacteristic
95Dic31—24no—
96Dic31—24no—
97Dic31—42no—
98C2×C4⋊Q8—311no—
99#519—311no—
100#419—311no—
101#419D3111yescharacteristic
102C2×#101—311no—
103#339—311no—
104#339—311no—
105C2×C31—21no—
106C2×C31—21no—
107C2×C31#38611yescharacteristic
108C2×C31#45612yes—
109C22×Q8—311no—
110C22×Q8C2×D3111yescharacteristic
111C2×M16—311no—
112C2×M16C2×D3111yescharacteristic
113C4⋊Q8—314no—
114C4⋊Q8—622no—
115C4×Q8—622no—
116C4×Q8—622no—
117#117—311no—
118#117—622no—
119#117C2×D3111yescharacteristic
120C2×C4⋊C4—622no—
121C2×C42—311no—
122#103—22no—
123#103—622no—
124#101—622no—
125C31#188611yescharacteristic, complemented, Sylow
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—312no—
132C2×Q8—312no—
133C2×Q8—621no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C2×Q8C4×D3112yes—
138C22×C4—21no—
139C22×C4—312no—
140C22×C4—621no—
141C22×C4C22×D3111yescharacteristic
142M16—21no—
143M16—21no—
144M16—621no—
145M16—621no—
146C2×C8—21no—
147C2×C8—621no—
148C4⋊C4—312no—
149C4⋊C4—628no—
150C4⋊C4—624no—
151C4⋊C4C22⋊D3112yes—
152C22⋊C4—21no—
153C22⋊C4—621no—
154C42—21no—
155C42—312no—
156C42—624no—
157C42—621no—
158C42—621no—
159C23D4×D3111yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—622no—
165Q8—622no—
166Q8—622no—
167Q8—622no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—314no—
173C2×C4—624no—
174C2×C4—622no—
175C2×C4—622no—
176C2×C4—622no—
177C2×C4—622no—
178C2×C4C2×C4×D3111yescharacteristic
179C2×C4#9249511yescharacteristic
180C2×C4D4×D3111yescharacteristic
181C2×C4D4×D3111yescharacteristic
182C2×C4#9249711yescharacteristic
183C2×C4C2×C22⋊D3111yescharacteristic
184C8—41no—
185C8—1241no—
186C22—22no—
187C22C22⋊C4×D3111yescharacteristic
188C22#1175846011yescharacteristic
189C22#1175851411yescharacteristic
190C4—42no—
191C4—42no—
192C4—624no—
193C4—624no—
194C4—1242no—
195C4(C22⋊D31)⋊C411yescharacteristic
196C4#1175846111yescharacteristic
197C4C4×C22⋊D3111yescharacteristic
198C4#1175851511yescharacteristic
199C2—21no—
200C2—21no—
201C2#1452092511yescharacteristic
202C2#1452123012yes—
subgroupG/H
centerC22#11758514
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#419C2
socleC22×C31#120
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#419D31
hypocenterC31#1886
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
13. #11758521C4semidirect
125. C31#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#117585212
#145215262
#145210582
C2×#117584122
#145208102
#145208082
C31×#4192
#188631