Finite Group Databasebeta

← #16847405

Subgroups — #16847405

Order 3968.

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

normal subgroups only

This group has 230 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#14520847C214yesmaximal, complemented
4C31×#413C211yesmaximal, characteristic
5C2×#41×C31C2211yescharacteristic
6C22×Dic62C411yescharacteristic
7C2×M16×C31—21no—
8#11758521C2212yes—
9#11758513C412yes—
10#11758512—21no—
11#11758512—21no—
12#11758503C411yescharacteristic
13#11758501—21no—
14#11758501—21no—
15C2×#92474—21no—
16C31×#101C2212yes—
17C31×#100—21no—
18#11758424C2212yes—
19#11758421—21no—
20#41×C31—41no—
21#41×C31—41no—
22C2×Q8×C31C2311yescharacteristic
23C2×D4×C31C2×C411yescharacteristic
24C2×D4×C31D411yescharacteristic
25C2×D4×C31D411yescharacteristic
26C22×C4×C31C2×C411yescharacteristic
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×Dic31—21no—
30C2×Dic62—21no—
31C2×Dic62—41no—
32C2×Dic62—41no—
33C2×Dic62C2×C412yes—
34M16×C31—22no—
35M16×C31—41no—
36C2×C8×C31—41no—
37C22⋊Dic31—22no—
38C22⋊Dic31—22no—
39C22⋊Dic31—21no—
40C4⋊Dic31—21no—
41Dic31⋊C4—22no—
42Dic31⋊C4—22no—
43C4×Dic31C2×C412yes—
44#92474—22no—
45#92474—41no—
46C2×C31⋊C8—41no—
47C23×C31C22⋊C411yescharacteristic
48C23×C31C22⋊C411yescharacteristic
49C23×C31C22⋊C411yescharacteristic
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×C31C22⋊C411yescharacteristic
61C2×C4×C31C22×C411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31C2×D411yescharacteristic
64C2×Dic31—22no—
65C2×Dic31—22no—
66C2×Dic31—42no—
67Dic62—41no—
68Dic62—41no—
69Dic62—42no—
70C8×C31—42no—
71C31⋊C8—42no—
72#2135—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#9911yescharacteristic
84C4×C31#9911yescharacteristic
85Dic31—42no—
86Dic31—42no—
87#536—311no—
88#413—311no—
89#413D3111yescharacteristic
90#356—314no—
91C2×C31—21no—
92C2×C31—41no—
93C2×C31—41no—
94C2×C31—41no—
95C2×C31C2×#9911yescharacteristic
96C2×#41C2×D3111yescharacteristic
97C22×Q8—311no—
98C2×M16—21no—
99C2×M16—621no—
100C4⋊Q8—312no—
101#124—312no—
102#123—621no—
103#123—621no—
104C22⋊Q8—621no—
105C22⋊Q8—621no—
106#117—311no—
107#101—312no—
108#101C2×D3112yes—
109#100—21no—
110#100—621no—
111C31#213511yescharacteristic, complemented, Sylow
112#41—41no—
113#41—41no—
114C2×Q8—312no—
115C2×Q8—621no—
116C2×Q8—1241no—
117C2×Q8—1241no—
118C2×Q8C22×D3111yescharacteristic
119C2×D4C4×D3111yescharacteristic
120C2×D4D12411yescharacteristic
121C2×D4C22⋊D3111yescharacteristic
122C22×C4—621no—
123C22×C4C4×D3111yescharacteristic
124C22×C4D12411yescharacteristic
125C22×C4C22⋊D3111yescharacteristic
126M16—22no—
127M16—41no—
128M16—622no—
129M16—1241no—
130C2×C8—41no—
131C2×C8—1241no—
132C4⋊C4—621no—
133C4⋊C4—622no—
134C4⋊C4—622no—
135C22⋊C4—621no—
136C22⋊C4—622no—
137C22⋊C4—622no—
138C42—312no—
139C23(C2×D31)⋊C411yescharacteristic
140C23(C2×D31)⋊C411yescharacteristic
141C23(C2×D31)⋊C411yescharacteristic
142Q8—41no—
143Q8—1242no—
144Q8—1241no—
145Q8—1241no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—622no—
156C2×C4—622no—
157C2×C4—1242no—
158C2×C4(C2×D31)⋊C411yescharacteristic
159C2×C4C2×C4×D3111yescharacteristic
160C2×C4C2×D12411yescharacteristic
161C2×C4C2×C22⋊D3111yescharacteristic
162C8—42no—
163C8—1242no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D31)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—1242no—
175C4—1242no—
176C4#1175839411yescharacteristic
177C4#1175839411yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1175839411yescharacteristic
subgroupG/H
centerC2C2×#11758394
commutatorC2×C4×C31C22×C4
FrattiniC2×Q8C22×D31
FittingC31×#413C2
socleC2×C31C2×#99
prime radicalC2×#41×C31C22
cosocleC2×Q8×C31C23
hypercenter#413D31
hypocenterC31#2135
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #14520847C2semidirect
111. C31#2135semidirect

Maximal subgroups

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

subgroupindex
#145216202
#145210332
#145208472
C31×#4132
#213531