Finite Group Databasebeta

← #16858292

Subgroups — #16858292

Order 3968.

374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 115 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#14521773C211yesmaximal, characteristic, complemented
2#14521704C211yesmaximal, characteristic
3#14521452C211yesmaximal, characteristic, complemented
4#14521386C212yesmaximal, complemented
5#14521372C212yesmaximal, complemented
6#14521335C211yesmaximal, characteristic, complemented
7#14521294C212yesmaximal, complemented
8C4×#92480C211yesmaximal, characteristic, complemented
9#14521126C211yesmaximal, characteristic, complemented
10#14521090C212yesmaximal, complemented
11C31×#474C211yesmaximal, characteristic, complemented
12C2×#92495—21no—
13C31×C4⋊Q8C2211yescharacteristic
14C4×D4×C31C2211yescharacteristic
15#11758524—21no—
16Q8×Dic31—21no—
17#11758515C2212yes—
18C2×#92480C2211yescharacteristic
19#11758501—21no—
20C2×#92469C2212yes—
21#11758475—22no—
22#11758474C2212yes—
23#11758469C2212yes—
24C4⋊C4×D31C2212yes—
25#11758460—22no—
26C4×D124C2211yescharacteristic
27#11758446C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×#107C2212yes—
30C31×C4⋊C8C2211yescharacteristic
31C31×#102C2212yes—
32#11758420C2211yescharacteristic
33(C2×D31)⋊C8C2212yes—
34#11758405C2212yes—
35#11758404C2212yes—
36#11758398C2211yescharacteristic
37#11758396C2211yescharacteristic
38#11758395C2212yes—
39#11758395C2212yes—
40C4×C31⋊C8C2211yescharacteristic
41C2×Q8×C31—21no—
42C2×D4×C31C2311yescharacteristic
43C22×C4×C31—21no—
44C2×C22⋊D31—22no—
45#92495—44no—
46C2×D124D411yescharacteristic
47C2×C4×D31—22no—
48C2×C4×D31C2312yes—
49C2×Dic62—21no—
50C2×Dic62C2311yescharacteristic
51C2×C8×C31C2312yes—
52C4⋊C4×C31—21no—
53C4⋊C4×C31C2312yes—
54C4⋊C4×C31C2311yescharacteristic
55C22⋊C4×C31—21no—
56C42×C31C2311yescharacteristic
57C22⋊Dic31—22no—
58#92480—22no—
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—22no—
61(C2×D31)⋊C4D412yes—
62C4⋊Dic31—21no—
63C4⋊Dic31—22no—
64C4⋊Dic31D411yescharacteristic
65C4⋊Dic31C2312yes—
66C4⋊Dic31C2311yescharacteristic
67Dic31⋊C4—21no—
68Dic31⋊C4—22no—
69C4×Dic31—21no—
70C4×Dic31—22no—
71C2×C31⋊C8C2311yescharacteristic
72C2×C31⋊C8C2311yescharacteristic
73#92469—24no—
74C23×C31—21no—
75C22×D31C2×D412yes—
76Q8×C31—42no—
77D4×C31—21no—
78D4×C31—21no—
79C2×C4×C31—22no—
80C2×C4×C31—21no—
81C2×C4×C31—42no—
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2411yescharacteristic
85C22⋊D31—44no—
86C2×Dic31—21no—
87C2×Dic31—21no—
88C2×Dic31—22no—
89C2×Dic31C2×D412yes—
90D124—22no—
91C4×D31—22no—
92C4×D31—22no—
93C4×D31—44no—
94Dic62—21no—
95Dic62—21no—
96Dic62—42no—
97C8×C31—22no—
98C31⋊C8—21no—
99C31⋊C8#4112yescomplemented
100#3353—311nomaximal, Sylow
101C22×C31—41no—
102C22×C31—41no—
103C22×C31—41no—
104C22×C31C22×D411yescharacteristic
105C2×D31—22no—
106C2×D31—22no—
107C2×D31—22no—
108C4×C31—21no—
109C4×C31—41no—
110C4×C31—42no—
111C4×C31AGL(1,ℤ/8)12yes—
112C4×C31C2×#4111yescharacteristic
113C4×C312−1+411yescharacteristic
114Dic31—22no—
115Dic31—41no—
116Dic31—42no—
117Dic31—41no—
118#556—311no—
119#547—311no—
120#500—311no—
121#484—312no—
122#482—312no—
123#475—311no—
124#474D3111yescharacteristic, complemented
125#468—312no—
126C4×SD16—311no—
127#436—311no—
128#428—312no—
129C2×C31—81no—
130C2×C31#54711yescharacteristic
131C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C31#57811yescharacteristic
133D31—42no—
134C2×#41—621no—
135C2×SD16—311no—
136C2×M16—312no—
137C4⋊Q8—311no—
138C4⋊Q8C2×D3111yescharacteristic
139#126—622no—
140#124—621no—
141#123—622no—
142C22⋊Q8—312no—
143C22⋊Q8—621no—
144#121—312no—
145C4×Q8—311no—
146C4×Q8—621no—
147C4×D4—311no—
148C4×D4C2×D3111yescharacteristic
149#117—312no—
150C2×C4⋊C4—312no—
151#107—312no—
152#107—312no—
153#107C2×D3112yes—
154#106—312no—
155#106—311no—
156C4⋊C8C2×D3111yescharacteristic
157#103—312no—
158#103—311no—
159#102—311no—
160#102C2×D3112yes—
161C22⋊C8—312no—
162C4×C8—311no—
163C31#335311yescharacteristic, complemented, Sylow
164#41—1244no—
165C2×Q8—21no—
166C2×Q8—311no—
167C2×Q8—621no—
168C2×D4—311no—
169C2×D4—622no—
170C2×D4C22×D3111yescharacteristic
171C22×C4—21no—
172C22×C4—312no—
173C22×C4—622no—
174SD16—622no—
175M16—624no—
176C2×C8—311no—
177C2×C8—311no—
178C2×C8C22×D3112yes—
179C4⋊C4—21no—
180C4⋊C4—311no—
181C4⋊C4—311no—
182C4⋊C4—312no—
183C4⋊C4—622no—
184C4⋊C4—622no—
185C4⋊C4—621no—
186C4⋊C4—621no—
187C4⋊C4C22×D3112yes—
188C4⋊C4C22×D3111yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—312no—
191C22⋊C4—622no—
192C22⋊C4—622no—
193C22⋊C4—622no—
194C42—622no—
195C42—621no—
196C42C22×D3111yescharacteristic
197C23—21no—
198C23—312no—
199Q8—42no—
200Q8—621no—
201Q8—621no—
202Q8—1242no—
203D4—21no—
204D4—21no—
205D4—622no—
206D4—1244no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—42no—
210C2×C4—312no—
211C2×C4—622no—
212C2×C4—622no—
213C2×C4—621no—
214C2×C4—621no—
215C2×C4—622no—
216C2×C4—1244no—
217C2×C4D4×D3111yescharacteristic
218C2×C4D4×D3111yescharacteristic
219C2×C4C23×D3111yescharacteristic
220C8—22no—
221C8—312no—
222C8—621no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—622no—
227C22—622no—
228C22—622no—
229C22C2×D4×D3111yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—622no—
234C4—1241no—
235C4—1241no—
236C4—1242no—
237C4#1175848812yes—
238C4#1175856411yescharacteristic
239C4#41×D3111yescharacteristic
240C2—81no—
241C2—1242no—
242C2#1452170111yescharacteristic
243C2C2×#1175848811yescharacteristic
244C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#474C2
socleC22×C31C22×D4
prime radical#14521704C2
hypercenter#474D31
hypocenterC31#3353
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #14521773C2semidirect
3. #14521452C2semidirect
4. #14521386C2semidirect
5. #14521372C2semidirect
6. #14521335C2semidirect
7. #14521294C2semidirect
8. C4×#92480C2semidirect
9. #14521126C2semidirect
10. #14521090C2semidirect
11. C31×#474C2semidirect
99. C31⋊C8#41semidirect
124. #474D31semidirect
163. C31#3353semidirect

Maximal subgroups

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

subgroupindex
#145217732
#145217042
#145214522
#145213862
#145213722
#145213352
#145212942
C4×#924802
#145211262
#145210902
C31×#4742
#335331