Finite Group Databasebeta

← #16844722

Subgroups — #16844722

Order 3968.

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

normal subgroups only

This group has 232 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#14521636C211yesmaximal, characteristic
2#14521379C211yesmaximal, characteristic, complemented
3#14520975C211yesmaximal, characteristic, complemented
4#14520787C211yesmaximal, characteristic, complemented
5#14520783C211yesmaximal, characteristic, complemented
6#14520772C211yesmaximal, characteristic, complemented
7C31×#480C211yesmaximal, characteristic, complemented
8C31×#121C2211yescharacteristic
9C2×C4⋊C4×C31C2211yescharacteristic
10#11758516—21no—
11#11758514—21no—
12D4×Dic31—21no—
13C2×(C2×D31)⋊C4—21no—
14C2×(C2×D31)⋊C4C2211yescharacteristic
15#11758501C2211yescharacteristic
16#11758475—21no—
17#11758463—21no—
18#11758462—21no—
19C31×#107—21no—
20C31×#102—21no—
21C31×C22⋊C8C2211yescharacteristic
22C31⋊#95—21no—
23C31⋊#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25#11758398—21no—
26#11758396—21no—
27C23×D31D411yescharacteristic
28C2×D4×C31—21no—
29C2×D4×C31D411yescharacteristic
30C22×C4×C31—21no—
31C22×C4×C31C2311yescharacteristic
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C22×Dic31—21no—
35C22×Dic31—21no—
36C22×Dic31D411yescharacteristic
37C2×Dic62D411yescharacteristic
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31D411yescharacteristic
42C22⋊C4×C31—21no—
43C22⋊Dic31—21no—
44C22⋊Dic31—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—42no—
50C4⋊Dic31—21no—
51C4⋊Dic31D411yescharacteristic
52Dic31⋊C4—21no—
53C4×Dic31—21no—
54C2×C31⋊C8—21no—
55C23×C31—21no—
56C23×C31C2×D411yescharacteristic
57C22×D31—21no—
58C22×D31—21no—
59C22×D31—21no—
60C22×D31—41no—
61C22×D31—41no—
62D4×C31—41no—
63D4×C31—41no—
64D4×C31—41no—
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—81no—
73C22⋊D31—81no—
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—21no—
77C2×Dic31—41no—
78C2×Dic31—41no—
79C2×Dic31—41no—
80C2×Dic31—41no—
81C2×Dic31—81no—
82Dic62—41no—
83C8×C31—41no—
84C31⋊C8—41no—
85#1612—311nomaximal, Sylow
86C22×C31—21no—
87C22×C31—21no—
88C22×C31—41no—
89C22×C31—41no—
90C22×C31—41no—
91C22×C31#12011yescharacteristic
92C22×C31#13511yescharacteristic
93C22×C31AGL(1,ℤ/8)11yescharacteristic
94C2×D31—42no—
95C2×D31—41no—
96C2×D31—41no—
97C2×D31—41no—
98C2×D31—81no—
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—41no—
102C4×C31—81no—
103Dic31—41no—
104Dic31—41no—
105Dic31—41no—
106Dic31—81no—
107#538—311no—
108#483—311no—
109#480D3111yescharacteristic, complemented
110#397—311no—
111#328—311no—
112#327—311no—
113#323—311no—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31—81no—
117C2×C31#44911yescharacteristic
118C2×C31#45511yescharacteristic
119C2×C31#45811yescharacteristic
120D31—81no—
121#126—621no—
122#124—621no—
123#123—621no—
124C22⋊Q8—311no—
125#121—621no—
126#121C2×D3111yescharacteristic
127#120—621no—
128C4×D4—621no—
129C2×C4⋊C4C2×D3111yescharacteristic
130C2×C22⋊C4—311no—
131C2×C22⋊C4—621no—
132#107—21no—
133#106—621no—
134#103—621no—
135#102—21no—
136C22⋊C8—311no—
137C22⋊C8C2×D3111yescharacteristic
138#95—311no—
139#95—621no—
140C31#161211yescharacteristic, complemented, Sylow
141C24—311no—
142C2×Q8—311no—
143C2×D4—21no—
144C2×D4—621no—
145C2×D4—621no—
146C2×D4C22⋊D3111yescharacteristic
147C22×C4—21no—
148C22×C4—311no—
149C22×C4—621no—
150C22×C4—621no—
151C22×C4C22×D3111yescharacteristic
152C2×C8—21no—
153C2×C8—621no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—311no—
157C4⋊C4—621no—
158C4⋊C4—621no—
159C4⋊C4C22⋊D3111yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—621no—
162C22⋊C4—621no—
163C22⋊C4—621no—
164C22⋊C4—621no—
165C22⋊C4—621no—
166C22⋊C4—621no—
167C22⋊C4—1242no—
168C42—621no—
169C23—21no—
170C23—621no—
171C23—621no—
172C23—621no—
173C23—1241no—
174C23—1241no—
175C23D4×D3111yescharacteristic
176Q8—1241no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—2481no—
181D4—2481no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—621no—
188C2×C4—621no—
189C2×C4—621no—
190C2×C4—1241no—
191C2×C4—1241no—
192C2×C4—1241no—
193C2×C4—1241no—
194C2×C4—2481no—
195C2×C4D4×D3111yescharacteristic
196C2×C4C2×C22⋊D3111yescharacteristic
197C8—41no—
198C8—1241no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—1242no—
205C22—1241no—
206C22—1241no—
207C22—1241no—
208C22—2481no—
209C22#1175848811yescharacteristic
210C22#1175848911yescharacteristic
211C22#1175851411yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—1241no—
217C4—1241no—
218C4—1241no—
219C4—2481no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—2481no—
224C2#1452119111yescharacteristic
225C2#1452122511yescharacteristic
226C2#1452123811yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#480C2
socleC22×C31#120
prime radical#14521636C2
hypercenter#480D31
hypocenterC31#1612
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #14521379C2semidirect
3. #14520975C2semidirect
4. #14520787C2semidirect
5. #14520783C2semidirect
6. #14520772C2semidirect
7. C31×#480C2semidirect
109. #480D31semidirect
140. C31#1612semidirect

Maximal subgroups

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

subgroupindex
#145216362
#145213792
#145209752
#145207872
#145207832
#145207722
C31×#4802
#161231