Finite Group Databasebeta

← #16844758

Subgroups — #16844758

Order 3968.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#14521639C211yesmaximal, characteristic
2#14521367C211yesmaximal, characteristic, complemented
3#14520984C211yesmaximal, characteristic, complemented
4#14520786C211yesmaximal, characteristic, complemented
5#14520784C211yesmaximal, characteristic, complemented
6#14520772C211yesmaximal, characteristic, complemented
7C31×#484C211yesmaximal, characteristic, complemented
8C31×C22⋊Q8C2211yescharacteristic
9C2×C4⋊C4×C31C2211yescharacteristic
10#11758524—21no—
11#11758507C2211yescharacteristic
12C2×(C2×D31)⋊C4—21no—
13C2×(C2×D31)⋊C4C2211yescharacteristic
14C2×Dic31⋊C4—21no—
15#11758475—21no—
16#11758472—21no—
17#11758471—21no—
18#11758459—21no—
19(C22⋊D31)⋊C4—21no—
20C31×#107—21no—
21C31×#103—21no—
22C31×C22⋊C8C2211yescharacteristic
23C31⋊#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25#11758397—21no—
26#11758396—21no—
27C23×D31D411yescharacteristic
28C2×Q8×C31D411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C22×Dic31—21no—
33C22×Dic31D411yescharacteristic
34C2×D124—21no—
35C2×D124—21no—
36C2×D124D411yescharacteristic
37C2×C4×D31—21no—
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31—21no—
42C4⋊C4×C31D411yescharacteristic
43C22⋊C4×C31—21no—
44(C2×D31)⋊C4—21no—
45(C2×D31)⋊C4—21no—
46(C2×D31)⋊C4—21no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49(C2×D31)⋊C4—21no—
50(C2×D31)⋊C4—42no—
51C4⋊Dic31D411yescharacteristic
52Dic31⋊C4—21no—
53Dic31⋊C4—42no—
54C4×Dic31—21no—
55C2×C31⋊C8—21no—
56C23×C31C2×D411yescharacteristic
57C22×D31—21no—
58C22×D31—21no—
59C22×D31—21no—
60C22×D31—21no—
61C22×D31—41no—
62C22×D31—41no—
63Q8×C31—41no—
64C2×C4×C31—21no—
65C2×C4×C31—21no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31—41no—
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C22⋊D31—41no—
73C22⋊D31—41no—
74C2×Dic31—22no—
75C2×Dic31—21no—
76C2×Dic31—21no—
77C2×Dic31—41no—
78C2×Dic31—41no—
79C2×Dic31—41no—
80D124—41no—
81D124—81no—
82D124—81no—
83C4×D31—81no—
84C8×C31—41no—
85C31⋊C8—41no—
86#1618—311nomaximal, Sylow
87C22×C31—21no—
88C22×C31—21no—
89C22×C31#12011yescharacteristic
90C22×C31#13511yescharacteristic
91C22×C31#13711yescharacteristic
92C2×D31—42no—
93C2×D31—41no—
94C2×D31—41no—
95C2×D31—41no—
96C2×D31—41no—
97C2×D31—41no—
98C2×D31—41no—
99C2×D31—81no—
100C4×C31—21no—
101C4×C31—21no—
102C4×C31—41no—
103C4×C31—41no—
104C4×C31—81no—
105Dic31—42no—
106Dic31—41no—
107Dic31—41no—
108#538—311no—
109#484D3111yescharacteristic, complemented
110#481—311no—
111#399—311no—
112#328—311no—
113#327—311no—
114#323—311no—
115C2×C31—21no—
116C2×C31—21no—
117C2×C31#45211yescharacteristic
118C2×C31#45311yescharacteristic
119C2×C31#45811yescharacteristic
120D31—81no—
121D31—81no—
122#126—621no—
123#124—621no—
124#123—621no—
125C22⋊Q8C2×D3111yescharacteristic
126#121—311no—
127#121—621no—
128#120—621no—
129C4×D4—621no—
130C2×C4⋊C4—621no—
131C2×C4⋊C4C2×D3111yescharacteristic
132C2×C22⋊C4—311no—
133C2×C22⋊C4—621no—
134#107—21no—
135#106—621no—
136#103—21no—
137#102—621no—
138C22⋊C8—311no—
139C22⋊C8C2×D3111yescharacteristic
140#95—311no—
141C31#161811yescharacteristic, complemented, Sylow
142C24—311no—
143C2×Q8C22⋊D3111yescharacteristic
144C2×D4—311no—
145C2×D4—621no—
146C2×D4—621no—
147C2×D4—621no—
148C22×C4—21no—
149C22×C4—311no—
150C22×C4—621no—
151C22×C4—621no—
152C22×C4C22×D3111yescharacteristic
153C2×C8—21no—
154C2×C8—621no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—311no—
159C4⋊C4—621no—
160C4⋊C4—1242no—
161C4⋊C4C22⋊D3111yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—621no—
164C22⋊C4—621no—
165C22⋊C4—621no—
166C22⋊C4—621no—
167C22⋊C4—621no—
168C22⋊C4—621no—
169C22⋊C4—1242no—
170C42—621no—
171C23—621no—
172C23—621no—
173C23—621no—
174C23—621no—
175C23—1241no—
176C23—1241no—
177C23D4×D3111yescharacteristic
178Q8—41no—
179D4—1241no—
180D4—1241no—
181D4—1241no—
182D4—2481no—
183D4—2481no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—622no—
191C2×C4—621no—
192C2×C4—621no—
193C2×C4—1241no—
194C2×C4—1241no—
195C2×C4—1241no—
196C2×C4—2481no—
197C2×C4D4×D3111yescharacteristic
198C2×C4C2×C22⋊D3111yescharacteristic
199C8—41no—
200C8—1241no—
201C22—21no—
202C22—21no—
203C22—1242no—
204C22—1241no—
205C22—1241no—
206C22—1241no—
207C22—1241no—
208C22—1241no—
209C22—1241no—
210C22—2481no—
211C22#1175849511yescharacteristic
212C22#1175849611yescharacteristic
213C22#1175851411yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—1242no—
220C4—1241no—
221C4—1241no—
222C2—21no—
223C2—21no—
224C2—2481no—
225C2—2481no—
226C2#1452121011yescharacteristic
227C2#1452121511yescharacteristic
228C2#1452123811yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#484C2
socleC22×C31#120
prime radical#14521639C2
hypercenter#484D31
hypocenterC31#1618
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #14521367C2semidirect
3. #14520984C2semidirect
4. #14520786C2semidirect
5. #14520784C2semidirect
6. #14520772C2semidirect
7. C31×#484C2semidirect
109. #484D31semidirect
141. C31#1618semidirect

Maximal subgroups

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

subgroupindex
#145216392
#145213672
#145209842
#145207862
#145207842
#145207722
C31×#4842
#161831