Finite Group Databasebeta

← #16844121

Subgroups — #16844121

Order 3968.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#14521581C211yesmaximal, characteristic
2C4⋊C8×D31C211yesmaximal, characteristic, complemented
3C4×#92469C211yesmaximal, characteristic, complemented
4#14520781C211yesmaximal, characteristic, complemented
5#14520779C211yesmaximal, characteristic, complemented
6D4⋊(C31⋊C8)C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic, complemented
8C4×D4×C31C2211yescharacteristic
9#11758515C411yescharacteristic
10#11758513C411yescharacteristic
11C4×C22⋊D31—21no—
12#11758503—21no—
13C2×#92469—21no—
14C2×C8×D31—21no—
15#11758474C411yescharacteristic
16#11758467C411yescharacteristic
17#11758460—21no—
18#11758456—21no—
19C42×D31C2211yescharacteristic
20C4×Dic62C2211yescharacteristic
21C31×C4⋊C8C2211yescharacteristic
22C4×C8×C31C2211yescharacteristic
23#11758403—21no—
24Dic31⋊C8—21no—
25C4⋊(C31⋊C8)C2211yescharacteristic
26C4×C31⋊C8C2211yescharacteristic
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—21no—
29C2×C22⋊D31—21no—
30C2×C4×D31C2×C411yescharacteristic
31C2×C4×D31D411yescharacteristic
32C2×C4×D31D411yescharacteristic
33C2×Dic62C2×C411yescharacteristic
34C2×C8×C31—21no—
35C2×C8×C31—21no—
36C4⋊C4×C31C2×C411yescharacteristic
37C22⋊C4×C31—21no—
38C42×C31C2311yescharacteristic
39C22⋊Dic31—21no—
40C22⋊Dic31—21no—
41C22⋊Dic31—21no—
42(C2×D31)⋊C4—21no—
43C4⋊Dic31—21no—
44C4⋊Dic31—21no—
45C4⋊Dic31C2×C411yescharacteristic
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C4×Dic31C2×C411yescharacteristic
50C4×Dic31D411yescharacteristic
51C4×Dic31D411yescharacteristic
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54#92469—24no—
55C8×D31—42no—
56C23×C31—21no—
57C22×D31C22⋊C411yescharacteristic
58D4×C31—21no—
59D4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31C22×C411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31C2×D411yescharacteristic
66C22⋊D31—42no—
67C2×Dic31—21no—
68C2×Dic31—21no—
69C2×Dic31C22⋊C411yescharacteristic
70C2×Dic31C22⋊C411yescharacteristic
71C2×Dic31C22⋊C411yescharacteristic
72C4×D31—22no—
73C4×D31—21no—
74C4×D31—21no—
75C4×D31—21no—
76C4×D31—21no—
77Dic62—21no—
78Dic62—21no—
79C8×C31—22no—
80C8×C31—41no—
81C31⋊C8—22no—
82C31⋊C8—41no—
83#1483—311nomaximal, Sylow
84C22×C31—41no—
85C22×C31—41no—
86C22×C31—41no—
87C22×C31C2×C22⋊C411yescharacteristic
88C2×D31—21no—
89C2×D31—21no—
90C2×D31#10412yes—
91C4×C31—21no—
92C4×C31—41no—
93C4×C31#13111yescharacteristic
94C4×C31#13111yescharacteristic
95C4×C31AGL(1,ℤ/8)11yescharacteristic
96C4×C31#13711yescharacteristic
97Dic31—21no—
98Dic31—21no—
99Dic31—21no—
100Dic31—41no—
101Dic31—41no—
102#529—311no—
103C2×C4⋊C8—311no—
104C4×M16—311no—
105Q8⋊C8—311no—
106Q8⋊C8—311no—
107D4⋊C8—311no—
108D4⋊C8D3111yescharacteristic, complemented
109C2×C31—81no—
110C2×C31#40811yescharacteristic
111C2×C31#41711yescharacteristic
112C2×C31C2×#10411yescharacteristic
113D31—22no—
114C2×M16—621no—
115C22×C8—621no—
116#126—621no—
117#125—311no—
118#124—311no—
119#123—621no—
120C22⋊Q8—311no—
121#121—311no—
122C4×Q8—311no—
123C4×D4—621no—
124C4×D4C2×D3111yescharacteristic
125#117—621no—
126C2×C42—311no—
127C4⋊C8—311no—
128C4⋊C8—621no—
129C4⋊C8C2×D3111yescharacteristic
130#97—621no—
131C4×C8—311no—
132C4×C8C2×D3111yescharacteristic
133C31#148311yescharacteristic, complemented, Sylow
134C2×Q8—311no—
135C2×D4—621no—
136C2×D4C4×D3111yescharacteristic
137C22×C4—21no—
138C22×C4—311no—
139C22×C4—311no—
140C22×C4—311no—
141M16—624no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—621no—
145C2×C8—621no—
146C2×C8—1242no—
147C4⋊C4—311no—
148C4⋊C4—621no—
149C4⋊C4—621no—
150C4⋊C4—621no—
151C4⋊C4—621no—
152C4⋊C4C4×D3111yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—621no—
155C22⋊C4—621no—
156C22⋊C4—621no—
157C22⋊C4—621no—
158C42—311no—
159C42—311no—
160C42—311no—
161C42—621no—
162C42C22×D3111yescharacteristic
163C23—21no—
164C23—311no—
165Q8—621no—
166Q8—621no—
167D4—21no—
168D4—21no—
169D4—1242no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—311no—
174C2×C4—311no—
175C2×C4—311no—
176C2×C4—622no—
177C2×C4—621no—
178C2×C4—621no—
179C2×C4—621no—
180C2×C4—621no—
181C2×C4—621no—
182C2×C4—621no—
183C2×C4C2×C4×D3111yescharacteristic
184C2×C4D4×D3111yescharacteristic
185C2×C4D4×D3111yescharacteristic
186C8—22no—
187C8—41no—
188C8—622no—
189C8—1241no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—312no—
194C22—621no—
195C22—621no—
196C22C22⋊C4×D3111yescharacteristic
197C4—21no—
198C4—41no—
199C4—621no—
200C4—621no—
201C4—621no—
202C4—1241no—
203C4—1241no—
204C4#1175847811yescharacteristic
205C4#1175848411yescharacteristic
206C4#1175848811yescharacteristic
207C4#1175849211yescharacteristic
208C2—81no—
209C2—622no—
210C2#1452101411yescharacteristic
211C2#1452104711yescharacteristic
212C2#104×D3111yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31C2×C22⋊C4
prime radical#11758515C4
cosocleC42×C31C23
hypercenterD4⋊C8D31
hypocenterC31#1483
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C4⋊C8×D31C2semidirect
3. C4×#92469C2semidirect
4. #14520781C2semidirect
5. #14520779C2semidirect
6. D4⋊(C31⋊C8)C2semidirect
7. C31×D4⋊C8C2semidirect
108. D4⋊C8D31semidirect
133. C31#1483semidirect

Maximal subgroups

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

subgroupindex
#145215812
C4⋊C8×D312
C4×#924692
#145207812
#145207792
D4⋊(C31⋊C8)2
C31×D4⋊C82
#148331