Finite Group Databasebeta

← #16847719

Subgroups — #16847719

Order 3968.

260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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#14521789C211yesmaximal, characteristic, complemented
2#14521238C211yesmaximal, characteristic, complemented
3#14521237C211yesmaximal, characteristic, complemented
4#14521219C211yesmaximal, characteristic, complemented
5#14520841C211yesmaximal, characteristic, complemented
6#14520837C211yesmaximal, characteristic, complemented
7C31×#352C211yesmaximal, characteristic, complemented
8#11758561C2211yescharacteristic
9C31×#123C2211yescharacteristic
10#11758517C2211yescharacteristic
11#11758514C2211yescharacteristic
12#11758507—21no—
13#11758506—21no—
14#11758485—21no—
15#11758475—21no—
16#11758472—21no—
17#11758461—21no—
18#11758460—21no—
19#11758459—21no—
20#11758459—21no—
21C31×#100C2211yescharacteristic
22C31×#99C2211yescharacteristic
23#11758422C2211yescharacteristic
24#11758413—21no—
25#11758394—21no—
26#11758394—21no—
27C23×D31D411yescharacteristic
28C2×D4×C31C2311yescharacteristic
29C22×C4×C31D411yescharacteristic, complemented
30C2×C22⋊D31—21no—
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35#92497—41no—
36D4×D31—41no—
37#92495—21no—
38C2×D124—21no—
39C2×D124—21no—
40C2×D124—41no—
41C2×D124D411yescharacteristic, complemented
42C2×C4×D31—21no—
43M16×C31—21no—
44C4⋊C4×C31—21no—
45C22⋊C4×C31—21no—
46C22⋊C4×C31—21no—
47C22⋊C4×C31D411yescharacteristic, complemented
48C22⋊Dic31—21no—
49C22⋊Dic31D411yescharacteristic
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—21no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—21no—
54(C2×D31)⋊C4—41no—
55(C2×D31)⋊C4—41no—
56C4⋊Dic31—21no—
57Dic31⋊C4—21no—
58Dic31⋊C4—41no—
59C4×Dic31D411yescharacteristic, complemented
60D248—41no—
61#92470—41no—
62C23×C31C2×D411yescharacteristic
63C23×C31C2×D411yescharacteristic
64C22×D31—21no—
65C22×D31—21no—
66C22×D31—21no—
67C22×D31—21no—
68C22×D31—41no—
69C22×D31—81no—
70D4×C31—41no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31C2×D411yescharacteristic
76C22⋊D31—41no—
77C22⋊D31—41no—
78C22⋊D31—41no—
79C22⋊D31—81no—
80C22⋊D31—81no—
81C22⋊D31—81no—
82C2×Dic31—21no—
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31—21no—
86C2×Dic31—41no—
87D124—21no—
88D124—41no—
89D124—81no—
90D124—81no—
91D124—82no—
92C4×D31—41no—
93C4×D31—81no—
94Dic62—21no—
95C8×C31—41no—
96#2200—311nomaximal, Sylow
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—41no—
100C22×C31—41no—
101C22×C31#12011yescharacteristic
102C2×D31—41no—
103C2×D31—41no—
104C2×D31—41no—
105C2×D31—41no—
106C2×D31—42no—
107C2×D31—41no—
108C2×D31—41no—
109C2×D31—41no—
110C2×D31—81no—
111C2×D31—81no—
112C2×D31—81no—
113C4×C31—21no—
114C4×C31—41no—
115C4×C31—41no—
116C4×C31—81no—
117Dic31—41no—
118Dic31—41no—
119Dic31—41no—
120Dic31—81no—
121#560—311no—
122#458—311no—
123B(4,𝔽2)—311no—
124#453—311no—
125#353—311no—
126#352D3111yescharacteristic, complemented
127AΣL(1,𝔽16)—311no—
128C2×C31—21no—
129C2×C31—41no—
130C2×C31—41no—
131C2×C31B(4,𝔽2)11yescharacteristic
132D31—81no—
133D31—81no—
134D31—81no—
135H(5,𝔽2)—311no—
136AGL(1,ℤ/8)—621no—
137#127—311no—
138#126—621no—
139#123—621no—
140#123—621no—
141#123C2×D3111yescharacteristic
142#121—621no—
143#121—621no—
144#121—621no—
145#120—311no—
146#120—621no—
147#120—621no—
148#104—621no—
149#100C2×D3111yescharacteristic
150#99—311no—
151#99—621no—
152#99—621no—
153#99C2×D3111yescharacteristic
154C31#220011yescharacteristic, complemented, Sylow
155C24—311no—
156#41—621no—
157#41—1241no—
158C2×D4—311no—
159C2×D4—621no—
160C2×D4—621no—
161C2×D4—621no—
162C2×D4—621no—
163C2×D4—621no—
164C2×D4—621no—
165C2×D4—621no—
166C2×D4—1241no—
167C2×D4—1241no—
168C2×D4C22×D3111yescharacteristic
169C22×C4—621no—
170C22×C4D12411yescharacteristic, complemented
171SD16—1241no—
172D8—1241no—
173M16—21no—
174C4⋊C4—21no—
175C4⋊C4—621no—
176C4⋊C4—621no—
177C4⋊C4—1241no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—311no—
181C22⋊C4—621no—
182C22⋊C4—621no—
183C22⋊C4—621no—
184C22⋊C4—621no—
185C22⋊C4—621no—
186C22⋊C4—1241no—
187C22⋊C4—1241no—
188C22⋊C4D12411yescharacteristic, complemented
189C42—311no—
190C23—621no—
191C23—621no—
192C23—621no—
193C23—621no—
194C23—1241no—
195C23—2481no—
196C23C2×D12411yescharacteristic
197C23D4×D3111yescharacteristic
198Q8—621no—
199D4—41no—
200D4—621no—
201D4—1241no—
202D4—1241no—
203D4—1241no—
204D4—1241no—
205D4—2481no—
206D4—2481no—
207D4—2482no—
208D4—2481no—
209D4—2481no—
210D4—2481no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—621no—
216C2×C4—621no—
217C2×C4—621no—
218C2×C4—621no—
219C2×C4—1241no—
220C2×C4—1241no—
221C2×C4—2481no—
222C2×C4D4×D3111yescharacteristic
223C8—41no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—1241no—
229C22—1241no—
230C22—1241no—
231C22—1241no—
232C22—1242no—
233C22—1241no—
234C22—1241no—
235C22—1241no—
236C22—2481no—
237C22—2481no—
238C22—2481no—
239C22#1175845911yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—81no—
244C4—1241no—
245C4—1241no—
246C4—1241no—
247C4—2481no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—2481no—
252C2—2481no—
253C2—2481no—
254C2#1452123711yescharacteristic
subgroupG/H
centerC2#14521237
commutator, cosocleC2×D4×C31C23
FrattiniC2×D4C22×D31
FittingC31×#352C2
socleC2×C31B(4,𝔽2)
hypercenter#352D31
hypocenterC31#2200
LCSG ▷ C2×D4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #14521789C2semidirect
2. #14521238C2semidirect
3. #14521237C2semidirect
4. #14521219C2semidirect
5. #14520841C2semidirect
6. #14520837C2semidirect
7. C31×#352C2semidirect
29. C22×C4×C31D4semidirect
41. C2×D124D4semidirect
47. C22⋊C4×C31D4semidirect
59. C4×Dic31D4semidirect
126. #352D31semidirect
154. C31#2200semidirect
170. C22×C4D124semidirect
188. C22⋊C4D124semidirect

Maximal subgroups

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

subgroupindex
#145217892
#145212382
#145212372
#145212192
#145208412
#145208372
C31×#3522
#220031