Finite Group Databasebeta

← #16847364

Subgroups — #16847364

Order 3968.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521033C211yesmaximal, characteristic
3#14520838C214yesmaximal, complemented
4C31×#410C211yesmaximal, characteristic
5C2×#41×C31C2211yescharacteristic
6C22×Dic62C411yescharacteristic, complemented
7C31×#117—21no—
8#11758521—21no—
9#11758513—21no—
10#11758512C412yescomplemented
11#11758512C2212yes—
12#11758503C411yescharacteristic, complemented
13#11758501—21no—
14#11758501—21no—
15C2×#92474—21no—
16C31×#99—21no—
17C31×#99C2212yes—
18#11758424—21no—
19#11758421C2212yes—
20#41×C31—41no—
21#41×C31—41no—
22C2×Q8×C31D411yescharacteristic
23C2×D4×C31C2×C411yescharacteristic
24C2×D4×C31D411yescharacteristic
25C2×D4×C31C2311yescharacteristic
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×Dic31C2×C412yes—
30C2×Dic62—21no—
31C2×Dic62—21no—
32C2×Dic62—41no—
33C2×Dic62—41no—
34C4⋊C4×C31—41no—
35C22⋊C4×C31—22no—
36C42×C31—41no—
37C22⋊Dic31—22no—
38C22⋊Dic31—22no—
39C22⋊Dic31C2×C412yes—
40C4⋊Dic31—21no—
41Dic31⋊C4—22no—
42Dic31⋊C4—22no—
43C4×Dic31—21no—
44#92474—22no—
45#92474—41no—
46C2×C31⋊C8—41no—
47C23×C31C22⋊C411yescharacteristic
48C23×C31C22×C411yescharacteristic
49C23×C31C2×D411yescharacteristic
50Q8×C31—41no—
51D4×C31—41no—
52D4×C31—41no—
53D4×C31—41no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—42no—
61C2×C4×C31C22⋊C411yescharacteristic
62C2×C4×C31C22⋊C411yescharacteristic
63C2×C4×C31C22⋊C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×Dic31—22no—
66C2×Dic31—22no—
67C2×Dic31—42no—
68Dic62—42no—
69Dic62—41no—
70Dic62—41no—
71C31⋊C8—42no—
72#2123—311nomaximal, Sylow
73C22×C31—21no—
74C22×C31—21no—
75C22×C31—21no—
76C22×C31—41no—
77C22×C31—41no—
78C22×C31—41no—
79C22×C31C2×C22⋊C411yescharacteristic
80C4×C31—21no—
81C4×C31—21no—
82C4×C31—21no—
83C4×C31—82no—
84C4×C31#9911yescharacteristic
85C4×C31#9911yescharacteristic
86Dic31—42no—
87Dic31—42no—
88#536—311no—
89#413—311no—
90#410D3111yescharacteristic
91#352—314no—
92C2×C31—21no—
93C2×C31—41no—
94C2×C31—41no—
95C2×C31—41no—
96C2×C31C2×#9911yescharacteristic
97C2×#41C2×D3111yescharacteristic
98C22×Q8—311no—
99C2×M16—621no—
100C4⋊Q8—621no—
101#124—621no—
102#123—312no—
103#123—312no—
104C22⋊Q8—621no—
105C22⋊Q8—621no—
106#117—21no—
107#117—311no—
108#101—621no—
109#100—312no—
110#99—21no—
111#99C2×D3112yes—
112C31#212311yescharacteristic, complemented, Sylow
113#41—41no—
114#41—41no—
115C2×Q8—621no—
116C2×Q8—621no—
117C2×Q8—1241no—
118C2×Q8—1241no—
119C2×Q8D12411yescharacteristic
120C2×D4C4×D3111yescharacteristic
121C2×D4C22⋊D3111yescharacteristic
122C2×D4C22×D3111yescharacteristic
123C22×C4—312no—
124C22×C4C4×D3111yescharacteristic
125C22×C4D12411yescharacteristic
126C22×C4C22⋊D3111yescharacteristic
127M16—622no—
128M16—1241no—
129C2×C8—1241no—
130C4⋊C4—41no—
131C4⋊C4—622no—
132C4⋊C4—621no—
133C4⋊C4—622no—
134C22⋊C4—22no—
135C22⋊C4—312no—
136C22⋊C4—622no—
137C22⋊C4—622no—
138C42—41no—
139C42—621no—
140C23(C2×D31)⋊C411yescharacteristic
141C23C2×C4×D3111yescharacteristic
142C23C2×C22⋊D3111yescharacteristic
143Q8—41no—
144Q8—1242no—
145Q8—1241no—
146Q8—1241no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—42no—
157C2×C4—622no—
158C2×C4—622no—
159C2×C4—1242no—
160C2×C4(C2×D31)⋊C411yescharacteristic
161C2×C4(C2×D31)⋊C411yescharacteristic
162C2×C4(C2×D31)⋊C411yescharacteristic
163C2×C4C2×D12411yescharacteristic
164C8—1242no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×(C2×D31)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—1242no—
177C4—1242no—
178C4#1175839411yescharacteristic
179C4#1175839411yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1175839411yescharacteristic
subgroupG/H
centerC2C2×#11758394
commutatorC23×C31C22×C4
FrattiniC2×D4C22×D31
FittingC31×#410C2
socleC2×C31C2×#99
prime radicalC2×#41×C31C22
cosocleC2×D4×C31C23
hypercenter#410D31
hypocenterC31#2123
LCSG ▷ C23×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #14520838C2semidirect
6. C22×Dic62C4semidirect
10. #11758512C4semidirect
12. #11758503C4semidirect
112. C31#2123semidirect

Maximal subgroups

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

subgroupindex
#145216202
#145210332
#145208382
C31×#4102
#212331