Finite Group Databasebeta

← #16847721

Subgroups — #16847721

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#14521786C211yesmaximal, characteristic, complemented
2#14521240C211yesmaximal, characteristic, complemented
3#14521237C211yesmaximal, characteristic, complemented
4#14521216C211yesmaximal, characteristic, complemented
5#14520838C211yesmaximal, characteristic, complemented
6#14520835C211yesmaximal, characteristic, complemented
7C31×#353C211yesmaximal, characteristic, complemented
8#11758561C2211yescharacteristic
9C31×#127C2211yescharacteristic
10#11758516—21no—
11#11758516—21no—
12#11758516—21no—
13#11758514—21no—
14#11758514C2211yescharacteristic
15#11758512—21no—
16#11758512C2211yescharacteristic
17#11758509—21no—
18#11758463—21no—
19#11758459—21no—
20#11758453—21no—
21C31×#99C2211yescharacteristic
22C31×#99C2211yescharacteristic
23#11758421C2211yescharacteristic
24#11758394—21no—
25#11758394—21no—
26#11758393—21no—
27C23×D31D411yescharacteristic
28C2×D4×C31—21no—
29C2×D4×C31—21no—
30C2×D4×C31D411yescharacteristic, complemented
31C2×D4×C31C2311yescharacteristic
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C2×C22⋊D31—21no—
37C22×Dic31—21no—
38C22×Dic31D411yescharacteristic, complemented
39#92497—41no—
40D4×D31—41no—
41#92495—21no—
42C2×D124—41no—
43C22⋊C4×C31—21no—
44C22⋊C4×C31—21no—
45C42×C31D411yescharacteristic, complemented
46C22⋊Dic31—21no—
47C22⋊Dic31—21no—
48C22⋊Dic31D411yescharacteristic
49C22⋊Dic31D411yescharacteristic, complemented
50#92480—41no—
51#92479—41no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—21no—
54(C2×D31)⋊C4—21no—
55(C2×D31)⋊C4—41no—
56(C2×D31)⋊C4—41no—
57C4⋊Dic31—41no—
58Dic31⋊C4—21no—
59Dic31⋊C4—21no—
60Dic31⋊C4—21no—
61#92474—21no—
62C23×C31—21no—
63C23×C31C2×D411yescharacteristic
64C23×C31C2×D411yescharacteristic
65C22×D31—21no—
66C22×D31—21no—
67C22×D31—21no—
68C22×D31—41no—
69C22×D31—81no—
70D4×C31—41no—
71D4×C31—41no—
72D4×C31—81no—
73D4×C31—81no—
74C2×C4×C31—21no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C2×D411yescharacteristic
78C22⋊D31—41no—
79C22⋊D31—41no—
80C22⋊D31—41no—
81C22⋊D31—81no—
82C22⋊D31—81no—
83C22⋊D31—81no—
84C2×Dic31—21no—
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—21no—
88C2×Dic31—21no—
89C2×Dic31—41no—
90C2×Dic31—81no—
91D124—21no—
92D124—82no—
93C4×D31—41no—
94Dic62—21no—
95C31⋊C8—41no—
96#2200—311nomaximal, Sylow
97C22×C31—21no—
98C22×C31—21no—
99C22×C31—41no—
100C22×C31—41no—
101C22×C31—41no—
102C22×C31—41no—
103C22×C31—41no—
104C22×C31#12011yescharacteristic
105C2×D31—41no—
106C2×D31—41no—
107C2×D31—42no—
108C2×D31—41no—
109C2×D31—41no—
110C2×D31—81no—
111C2×D31—81no—
112C2×D31—81no—
113C4×C31—21no—
114C4×C31—41no—
115C4×C31—81no—
116C4×C31—81no—
117Dic31—41no—
118Dic31—41no—
119Dic31—41no—
120Dic31—41no—
121#560—311no—
122#458—311no—
123B(4,𝔽2)—311no—
124#453—311no—
125#353D3111yescharacteristic, complemented
126#352—311no—
127AΣL(1,𝔽16)—311no—
128C2×C31—21no—
129C2×C31—41no—
130C2×C31—41no—
131C2×C31—81no—
132C2×C31B(4,𝔽2)11yescharacteristic
133D31—81no—
134D31—81no—
135H(5,𝔽2)—311no—
136AGL(1,ℤ/8)—621no—
137#127C2×D3111yescharacteristic
138#126—621no—
139#123—311no—
140#123—621no—
141#123—621no—
142#121—621no—
143#121—621no—
144#121—621no—
145#120—311no—
146#120—621no—
147#120—621no—
148#104—621no—
149#100—311no—
150#99—621no—
151#99—621no—
152#99C2×D3111yescharacteristic
153#99C2×D3111yescharacteristic
154C31#220011yescharacteristic, complemented, Sylow
155C24—311no—
156#41—621no—
157#41—1241no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—621no—
161C2×D4—621no—
162C2×D4—621no—
163C2×D4—621no—
164C2×D4—621no—
165C2×D4—1241no—
166C2×D4—1241no—
167C2×D4D12411yescharacteristic, complemented
168C2×D4C22×D3111yescharacteristic
169C22×C4—311no—
170C22×C4—621no—
171SD16—1241no—
172D8—1241no—
173M16—621no—
174C4⋊C4—621no—
175C4⋊C4—621no—
176C4⋊C4—621no—
177C4⋊C4—1241no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—311no—
181C22⋊C4—311no—
182C22⋊C4—621no—
183C22⋊C4—621no—
184C22⋊C4—621no—
185C22⋊C4—621no—
186C22⋊C4—621no—
187C22⋊C4—1241no—
188C22⋊C4—1241no—
189C42D12411yescharacteristic, complemented
190C23—21no—
191C23—621no—
192C23—621no—
193C23—621no—
194C23—1241no—
195C23—2481no—
196C23D4×D3111yescharacteristic
197C23D4×D3111yescharacteristic
198Q8—621no—
199D4—41no—
200D4—41no—
201D4—81no—
202D4—81no—
203D4—621no—
204D4—1241no—
205D4—1241no—
206D4—1241no—
207D4—2482no—
208D4—2481no—
209D4—2481no—
210D4—2481no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—621no—
215C2×C4—621no—
216C2×C4—621no—
217C2×C4—621no—
218C2×C4—621no—
219C2×C4—1241no—
220C2×C4—1241no—
221C2×C4—2481no—
222C2×C4C2×D12411yescharacteristic
223C8—1241no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—1241no—
232C22—1241no—
233C22—1242no—
234C22—1241no—
235C22—1241no—
236C22—2481no—
237C22—2481no—
238C22—2481no—
239C22#1175845911yescharacteristic
240C4—21no—
241C4—41no—
242C4—81no—
243C4—81no—
244C4—1241no—
245C4—1241no—
246C4—1241no—
247C4—1241no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—2481no—
253C2—2481no—
254C2#1452123711yescharacteristic
subgroupG/H
centerC2#14521237
commutator, cosocleC2×D4×C31C23
FrattiniC2×D4C22×D31
FittingC31×#353C2
socleC2×C31B(4,𝔽2)
hypercenter#353D31
hypocenterC31#2200
LCSG ▷ C2×D4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
1. #14521786C2semidirect
2. #14521240C2semidirect
3. #14521237C2semidirect
4. #14521216C2semidirect
5. #14520838C2semidirect
6. #14520835C2semidirect
7. C31×#353C2semidirect
30. C2×D4×C31D4semidirect
38. C22×Dic31D4semidirect
45. C42×C31D4semidirect
49. C22⋊Dic31D4semidirect
125. #353D31semidirect
154. C31#2200semidirect
167. C2×D4D124semidirect
189. C42D124semidirect

Maximal subgroups

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

subgroupindex
#145217862
#145212402
#145212372
#145212162
#145208382
#145208352
C31×#3532
#220031