Finite Group Databasebeta

← #16844656

Subgroups — #16844656

Order 3968.

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

normal subgroups only

This group has 320 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, complemented
2#14521183C211yesmaximal, characteristic, complemented
3#14520957C211yesmaximal, characteristic, complemented
4#14520786C211yesmaximal, characteristic, complemented
5#14520784C211yesmaximal, characteristic, complemented
6#14520772C211yesmaximal, characteristic, complemented
7C31×#450C211yesmaximal, characteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×C22⋊D31—21no—
10C2×SD16×C31—21no—
11C31×C22⋊Q8C2211yescharacteristic
12C2×C22⋊Dic31—21no—
13#11758524—21no—
14C2×#92479—21no—
15#11758507C2211yescharacteristic
16C2×(C2×D31)⋊C4C2211yescharacteristic
17#11758475—21no—
18#11758472—21no—
19#11758471—21no—
20#11758459—21no—
21(C22⋊D31)⋊C4—21no—
22C31×#102—21no—
23C31×C22⋊C8C2211yescharacteristic
24#11758420—21no—
25C31⋊#95C2211yescharacteristic
26C22⋊(C31⋊C8)C2211yescharacteristic
27C24×C31—21no—
28C23×D31D411yescharacteristic
29C2×Q8×C31D411yescharacteristic, complemented
30C2×D4×C31—21no—
31C2×D4×C31—21no—
32C2×D4×C31—42no—
33C22×C4×C31C2311yescharacteristic
34C2×C22⋊D31—21no—
35C2×C22⋊D31—42no—
36C2×C22⋊D31—42no—
37C2×C22⋊D31—42no—
38C22×Dic31—21no—
39C22×Dic31D411yescharacteristic
40C2×D124—21no—
41C2×D124—21no—
42C2×D124D411yescharacteristic, complemented
43C2×C4×D31—21no—
44SD16×C31—42no—
45C2×C8×C31—21no—
46C4⋊C4×C31—21no—
47C4⋊C4×C31D411yescharacteristic, complemented
48C22⋊C4×C31—21no—
49C22⋊Dic31—42no—
50#92479—42no—
51(C2×D31)⋊C4—21no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—21no—
54(C2×D31)⋊C4—21no—
55(C2×D31)⋊C4—21no—
56(C2×D31)⋊C4—21no—
57C4⋊Dic31D411yescharacteristic, complemented
58Dic31⋊C4—21no—
59C4×Dic31—21no—
60C2×C31⋊C8—21no—
61C23×C31—22no—
62C23×C31—41no—
63C23×C31—41no—
64C23×C31—41no—
65C23×C31—41no—
66C23×C31—41no—
67C23×C31—41no—
68C23×C31C2×D411yescharacteristic
69C22×D31—21no—
70C22×D31—21no—
71C22×D31—21no—
72C22×D31—21no—
73C22×D31—41no—
74C22×D31—41no—
75Q8×C31—41no—
76D4×C31—22no—
77D4×C31—22no—
78D4×C31—41no—
79D4×C31—41no—
80C2×C4×C31—21no—
81C2×C4×C31—21no—
82C2×C4×C31—41no—
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2×D411yescharacteristic
85C22⋊D31—48no—
86C22⋊D31—41no—
87C22⋊D31—41no—
88C2×Dic31—22no—
89C2×Dic31—21no—
90C2×Dic31—21no—
91C2×Dic31—41no—
92C2×Dic31—41no—
93C2×Dic31—41no—
94D124—41no—
95D124—81no—
96D124—81no—
97C4×D31—81no—
98C8×C31—41no—
99C31⋊C8—41no—
100#1600—311nomaximal, Sylow
101C22×C31—21no—
102C22×C31—21no—
103C22×C31—42no—
104C22×C31—42no—
105C22×C31—42no—
106C22×C31—81no—
107C22×C31—81no—
108C22×C31—81no—
109C22×C31—81no—
110C22×C31#12011yescharacteristic
111C22×C31#13511yescharacteristic
112C22×C31AGL(1,ℤ/8)11yescharacteristic
113C2×D31—42no—
114C2×D31—41no—
115C2×D31—41no—
116C2×D31—41no—
117C2×D31—41no—
118C2×D31—41no—
119C2×D31—41no—
120C2×D31—81no—
121C4×C31—21no—
122C4×C31—21no—
123C4×C31—41no—
124C4×C31—41no—
125Dic31—42no—
126Dic31—41no—
127Dic31—41no—
128#538—311no—
129#450D3111yescharacteristic, complemented
130#447—311no—
131#392—311no—
132#328—311no—
133#327—311no—
134#323—311no—
135C2×C31—21no—
136C2×C31—21no—
137C2×C31—82no—
138C2×C31#44911yescharacteristic
139C2×C31#45311yescharacteristic
140C2×C31B(4,𝔽2)11yescharacteristic
141D31—81no—
142D31—81no—
143C22×D4—621no—
144C22×D4C2×D3111yescharacteristic
145C2×SD16—21no—
146C2×D8—621no—
147#126—621no—
148#124—621no—
149#123—621no—
150C22⋊Q8C2×D3111yescharacteristic
151#121—311no—
152#121—621no—
153#120—621no—
154C4×D4—621no—
155C2×C22⋊C4—311no—
156C2×C22⋊C4—621no—
157#102—21no—
158#102—621no—
159C22⋊C8—311no—
160C22⋊C8C2×D3111yescharacteristic
161#95—311no—
162C31#160011yescharacteristic, complemented, Sylow
163C24—21no—
164C24—311no—
165C2×Q8C22⋊D3111yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—42no—
169C2×D4—311no—
170C2×D4—621no—
171C2×D4—621no—
172C2×D4—621no—
173C2×D4—1242no—
174C2×D4—1242no—
175C2×D4—1242no—
176C22×C4—311no—
177C22×C4—621no—
178C22×C4—621no—
179C22×C4C22×D3111yescharacteristic
180SD16—42no—
181D8—1242no—
182C2×C8—21no—
183C2×C8—621no—
184C4⋊C4—21no—
185C4⋊C4—311no—
186C4⋊C4—621no—
187C4⋊C4C22⋊D3111yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—621no—
190C22⋊C4—621no—
191C22⋊C4—621no—
192C22⋊C4—621no—
193C22⋊C4—621no—
194C22⋊C4—621no—
195C22⋊C4—1242no—
196C42—621no—
197C23—22no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—621no—
205C23—621no—
206C23—621no—
207C23—621no—
208C23—1241no—
209C23—1241no—
210C23D4×D3111yescharacteristic
211Q8—41no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—1241no—
217D4—1248no—
218D4—1241no—
219D4—1241no—
220D4—2481no—
221D4—2481no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—622no—
226C2×C4—621no—
227C2×C4—621no—
228C2×C4—1241no—
229C2×C4—1241no—
230C2×C4—1241no—
231C2×C4—2481no—
232C2×C4D4×D3111yescharacteristic
233C2×C4C2×C22⋊D3111yescharacteristic
234C8—41no—
235C8—1241no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22—81no—
245C22—1242no—
246C22—1241no—
247C22—1241no—
248C22—1241no—
249C22—1241no—
250C22—1241no—
251C22—1241no—
252C22—2481no—
253C22#1175849111yescharacteristic
254C22#1175849311yescharacteristic
255C22#1175851411yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—1242no—
261C4—1241no—
262C4—1241no—
263C2—21no—
264C2—21no—
265C2—82no—
266C2—2481no—
267C2—2481no—
268C2#1452119311yescharacteristic
269C2#1452121511yescharacteristic
270C2#1452123511yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#450C2
socleC22×C31#120
hypercenter#450D31
hypocenterC31#1600
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14521639C2semidirect
2. #14521183C2semidirect
3. #14520957C2semidirect
4. #14520786C2semidirect
5. #14520784C2semidirect
6. #14520772C2semidirect
7. C31×#450C2semidirect
29. C2×Q8×C31D4semidirect
42. C2×D124D4semidirect
47. C4⋊C4×C31D4semidirect
57. C4⋊Dic31D4semidirect
129. #450D31semidirect
162. C31#1600semidirect
165. C2×Q8C22⋊D31semidirect
187. C4⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145216392
#145211832
#145209572
#145207862
#145207842
#145207722
C31×#4502
#160031