Finite Group Databasebeta

← #16844729

Subgroups — #16844729

Order 3968.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#14521607C211yesmaximal, characteristic
2#14521367C211yesmaximal, characteristic, complemented
3#14520984C211yesmaximal, characteristic, complemented
4#14520784C211yesmaximal, characteristic, complemented
5#14520783C211yesmaximal, characteristic, complemented
6#14520772C211yesmaximal, characteristic, complemented
7C31×#481C211yesmaximal, characteristic, complemented
8C2×D4×D31—21no—
9C31×#121C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic, complemented
11#11758516—21no—
12#11758514—21no—
13#11758507C2211yescharacteristic
14C2×(C2×D31)⋊C4—21no—
15C2×(C2×D31)⋊C4C2211yescharacteristic
16C2×Dic31⋊C4—21no—
17#11758471—21no—
18#11758460—21no—
19#11758459—21no—
20C31×#106—21no—
21C31×#102—21no—
22C31×C22⋊C8C2211yescharacteristic, complemented
23C31⋊#95C2211yescharacteristic, complemented
24C22⋊(C31⋊C8)C2211yescharacteristic, complemented
25#11758397—21no—
26#11758396—21no—
27C23×D31—21no—
28C23×D31D411yescharacteristic
29C2×D4×C31—21no—
30C2×D4×C31D411yescharacteristic
31C22×C4×C31—21no—
32C22×C4×C31C2311yescharacteristic
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C22×Dic31—21no—
37C22×Dic31D411yescharacteristic
38D4×D31—42no—
39D4×D31—42no—
40C2×D124—21no—
41C2×D124D411yescharacteristic
42C2×C4×D31—21no—
43C2×C8×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31—21no—
46C4⋊C4×C31D411yescharacteristic
47C22⋊C4×C31—21no—
48C22⋊Dic31—21no—
49(C2×D31)⋊C4—21no—
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—21no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—42no—
54C4⋊Dic31D411yescharacteristic
55Dic31⋊C4—21no—
56Dic31⋊C4—42no—
57C2×C31⋊C8—21no—
58C23×C31—21no—
59C23×C31C2×D411yescharacteristic
60C22×D31—21no—
61C22×D31—21no—
62C22×D31—21no—
63C22×D31—42no—
64C22×D31—41no—
65C22×D31—41no—
66C22×D31—81no—
67C22×D31—81no—
68C22×D31SD1612yes—
69D4×C31—41no—
70D4×C31—41no—
71D4×C31—41no—
72C2×C4×C31—21no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C22⋊D31—42no—
80C22⋊D31—41no—
81C22⋊D31—41no—
82C22⋊D31—81no—
83C2×Dic31—22no—
84C2×Dic31—21no—
85C2×Dic31—21no—
86C2×Dic31—41no—
87C2×Dic31—41no—
88C2×Dic31—41no—
89D124—41no—
90D124—42no—
91C4×D31—42no—
92C8×C31—41no—
93C31⋊C8—41no—
94#1613—311nomaximal, Sylow
95C22×C31—21no—
96C22×C31—21no—
97C22×C31—41no—
98C22×C31—41no—
99C22×C31—41no—
100C22×C31#12011yescharacteristic
101C22×C31C2×SD1611yescharacteristic
102C22×C31AGL(1,ℤ/8)11yescharacteristic
103C2×D31—22no—
104C2×D31—41no—
105C2×D31—41no—
106C2×D31—42no—
107C2×D31—41no—
108C2×D31—41no—
109C2×D31—41no—
110C2×D31—81no—
111C2×D31—84no—
112C4×C31—21no—
113C4×C31—21no—
114C4×C31—41no—
115C4×C31—81no—
116Dic31—42no—
117Dic31—41no—
118Dic31—41no—
119#534—311no—
120#481—311no—
121#481D3111yescharacteristic, complemented
122#399—311no—
123#327—311no—
124#327—311no—
125#323—311no—
126C2×C31—21no—
127C2×C31—21no—
128C2×C31—81no—
129C2×C31#45011yescharacteristic
130C2×C31#45311yescharacteristic
131C2×C31#45811yescharacteristic
132D31—42no—
133D31—81no—
134C22×D4—621no—
135#123—621no—
136#123—621no—
137#121—311no—
138#121—621no—
139#121C2×D3111yescharacteristic
140#120—621no—
141#120—621no—
142C2×C4⋊C4—621no—
143C2×C4⋊C4C2×D3111yescharacteristic, complemented
144C2×C22⋊C4—311no—
145C2×C22⋊C4—621no—
146#106—21no—
147#106—621no—
148#102—21no—
149#102—621no—
150C22⋊C8—311no—
151C22⋊C8C2×D3111yescharacteristic, complemented
152#95—311no—
153C31#161311yescharacteristic, complemented, Sylow
154C24—311no—
155C24—621no—
156C2×D4—21no—
157C2×D4—311no—
158C2×D4—621no—
159C2×D4—621no—
160C2×D4—621no—
161C2×D4—621no—
162C2×D4—1242no—
163C2×D4—1242no—
164C2×D4C22⋊D3111yescharacteristic
165C22×C4—21no—
166C22×C4—311no—
167C22×C4—621no—
168C22×C4—621no—
169C22×C4C22×D3111yescharacteristic
170C2×C8—21no—
171C2×C8—621no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—311no—
175C4⋊C4—621no—
176C4⋊C4—1242no—
177C4⋊C4C22⋊D3111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—621no—
180C22⋊C4—621no—
181C22⋊C4—621no—
182C22⋊C4—621no—
183C22⋊C4—621no—
184C22⋊C4—1242no—
185C23—21no—
186C23—312no—
187C23—621no—
188C23—621no—
189C23—621no—
190C23—1241no—
191C23—1241no—
192C23—1242no—
193C23—2481no—
194C23—2481no—
195C23D4×D3111yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—1241no—
200D4—1242no—
201D4—1242no—
202D4—1241no—
203D4—1241no—
204D4—2481no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—622no—
211C2×C4—621no—
212C2×C4—621no—
213C2×C4—1242no—
214C2×C4—1241no—
215C2×C4—1241no—
216C2×C4—1241no—
217C2×C4D4×D3111yescharacteristic
218C2×C4C2×C22⋊D3111yescharacteristic
219C8—41no—
220C8—1241no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—622no—
227C22—1242no—
228C22—1241no—
229C22—1241no—
230C22—1241no—
231C22—1241no—
232C22—1241no—
233C22—2481no—
234C22—2484no—
235C22SD16×D3111yescharacteristic
236C22#1175849111yescharacteristic
237C22#1175851411yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—1242no—
243C4—1241no—
244C4—1241no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—1242no—
249C2—2481no—
250C2#1452119811yescharacteristic
251C2#1452121511yescharacteristic
252C2#1452123811yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#481C2
socleC22×C31#120
prime radical#14521607C2
hypercenter#481D31
hypocenterC31#1613
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #14521367C2semidirect
3. #14520984C2semidirect
4. #14520784C2semidirect
5. #14520783C2semidirect
6. #14520772C2semidirect
7. C31×#481C2semidirect
10. C2×C4⋊C4×C31C22semidirect
22. C31×C22⋊C8C22semidirect
23. C31⋊#95C22semidirect
24. C22⋊(C31⋊C8)C22semidirect
121. #481D31semidirect
143. C2×C4⋊C4C2×D31semidirect
151. C22⋊C8C2×D31semidirect
153. C31#1613semidirect

Maximal subgroups

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

subgroupindex
#145216072
#145213672
#145209842
#145207842
#145207832
#145207722
C31×#4812
#161331