Finite Group Databasebeta

← #16846151

Subgroups — #16846151

Order 3968.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#14521556C211yesmaximal, characteristic
2C2×C42×D31C211yesmaximal, characteristic, complemented
3C2×#11758425C211yesmaximal, characteristic, complemented
4#14521012C211yesmaximal, characteristic, complemented
5#14520810C211yesmaximal, characteristic, complemented
6#14520809C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C22×C4×D31—21no—
10C22×C4×D31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13#11758523C412yescomplemented
14#11758515C412yescomplemented
15#11758514—21no—
16#11758512—21no—
17C4×C22⋊D31—22no—
18#11758503C2211yescharacteristic
19C2×C4×Dic31—21no—
20C2×C4×Dic31C2211yescharacteristic
21C2×#92474C2211yescharacteristic
22C42×D31—22no—
23C42×D31—22no—
24C31×#104—22no—
25#11758425—22no—
26(C2×D31)⋊C8—22no—
27C23×D31D411yescharacteristic
28#41×C31—21no—
29#41×C31—21no—
30#41×C31—21no—
31#41×C31—21no—
32C2×Q8×C31C2×C411yescharacteristic, complemented
33C2×D4×C31—21no—
34C2×D4×C31C2×C411yescharacteristic, complemented
35C22×C4×C31—21no—
36C22×C4×C31—21no—
37C22×C4×C31C2311yescharacteristic
38C2×C22⋊D31—22no—
39C22×Dic31—21no—
40C22×Dic31D411yescharacteristic
41C2×C4×D31—24no—
42C2×C4×D31—28no—
43C2×C4×D31—21no—
44C2×C4×D31—21no—
45C2×C4×D31—21no—
46C2×C4×D31—21no—
47C2×C4×D31C2×C412yes—
48C2×C4×D31D412yes—
49M16×C31—21no—
50M16×C31—21no—
51C2×C8×C31—21no—
52C42×C31—21no—
53C42×C31D412yescomplemented
54C22⋊Dic31—21no—
55C22⋊Dic31—22no—
56(C2×D31)⋊C4—22no—
57C4⋊Dic31C2×C412yescomplemented
58Dic31⋊C4—22no—
59C4×Dic31—24no—
60C4×Dic31—21no—
61C4×Dic31—21no—
62C4×Dic31D412yescomplemented
63#92474—21no—
64#92474—21no—
65C2×C31⋊C8—21no—
66C23×C31—21no—
67C23×C31C2×D411yescharacteristic
68C22×D31—21no—
69C22×D31—21no—
70C22×D31—24no—
71C22×D31C22⋊C412yes—
72Q8×C31—21no—
73Q8×C31—21no—
74D4×C31—21no—
75D4×C31—21no—
76D4×C31—41no—
77D4×C31—41no—
78C2×C4×C31—24no—
79C2×C4×C31—22no—
80C2×C4×C31—21no—
81C2×C4×C31—41no—
82C2×C4×C31—41no—
83C2×C4×C31C22×C411yescharacteristic
84C2×C4×C31C2×D411yescharacteristic
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2×D411yescharacteristic
87C2×C4×C31#4111yescharacteristic
88C2×C4×C31#4111yescharacteristic
89C22⋊D31—44no—
90C2×Dic31—24no—
91C2×Dic31—21no—
92C2×Dic31—22no—
93C2×Dic31—21no—
94C2×Dic31—22no—
95C2×Dic31C22⋊C412yes—
96C4×D31—216no—
97C4×D31—22no—
98C4×D31—22no—
99C4×D31—22no—
100C4×D31—22no—
101C8×C31—41no—
102C31⋊C8—41no—
103#1896—311nomaximal, Sylow
104C22×C31—22no—
105C22×C31—41no—
106C22×C31—42no—
107C22×C31C2×C22⋊C411yescharacteristic
108C22×C31#12011yescharacteristic
109C22×C31#12311yescharacteristic
110C2×D31—24no—
111C2×D31—24no—
112C2×D31—22no—
113C2×D31—22no—
114C2×D31#10414yescomplemented
115C4×C31—24no—
116C4×C31—41no—
117C4×C31C4×D411yescharacteristic
118C4×C31C4×D411yescharacteristic
119C4×C31#12111yescharacteristic
120C4×C31#12111yescharacteristic
121Dic31—24no—
122Dic31—22no—
123Dic31—42no—
124#525—311no—
125C22×C42—311no—
126C2×#104—311no—
127C2×#104D3111yescharacteristic, complemented
128#407—311no—
129#339—311no—
130#339—311no—
131C2×C31—21no—
132C2×C31—21no—
133C2×C31—81no—
134C2×C31#38611yescharacteristic
135C2×C31C2×#10412yes—
136D31—24no—
137C2×#41C2×D3111yescharacteristic
138C23×C4—311no—
139C23×C4—621no—
140C2×M16—311no—
141C2×M16C2×D3111yescharacteristic
142#123—621no—
143C22⋊Q8—312no—
144#121—312no—
145#120—621no—
146C4×D4—622no—
147#117—311no—
148C2×C42—311no—
149C2×C42—622no—
150C2×C42—621no—
151C2×C42—622no—
152C2×C42C2×D3111yescharacteristic
153#104—22no—
154#104—622no—
155C22⋊C8—622no—
156C31#189611yescharacteristic, complemented, Sylow
157C24—311no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8C4×D3111yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—622no—
165C2×D4C4×D3111yescharacteristic, complemented
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—311no—
169C22×C4—312no—
170C22×C4—312no—
171C22×C4—624no—
172C22×C4—628no—
173C22×C4—621no—
174C22×C4—621no—
175C22×C4—621no—
176C22×C4—621no—
177C22×C4—621no—
178C22×C4C22×D3111yescharacteristic
179M16—21no—
180M16—21no—
181M16—621no—
182M16—621no—
183C2×C8—21no—
184C2×C8—621no—
185C4⋊C4—312no—
186C4⋊C4—622no—
187C22⋊C4—622no—
188C22⋊C4—622no—
189C22⋊C4—621no—
190C42—21no—
191C42—312no—
192C42—624no—
193C42—621no—
194C42—621no—
195C42C22⋊D3112yescomplemented
196C23—21no—
197C23—312no—
198C23—624no—
199C23—621no—
200C23—621no—
201C23D4×D3111yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—1244no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—312no—
215C2×C4—6216no—
216C2×C4—624no—
217C2×C4—621no—
218C2×C4—622no—
219C2×C4—621no—
220C2×C4—622no—
221C2×C4—622no—
222C2×C4—622no—
223C2×C4—622no—
224C2×C4—622no—
225C2×C4C2×C4×D3111yescharacteristic
226C2×C4#9249511yescharacteristic
227C2×C4D4×D3111yescharacteristic
228C2×C4D4×D3111yescharacteristic
229C2×C4#9249711yescharacteristic
230C2×C4C2×C22⋊D3111yescharacteristic
231C8—41no—
232C8—1241no—
233C22—22no—
234C22—41no—
235C22—42no—
236C22—314no—
237C22—624no—
238C22—624no—
239C22—622no—
240C22—622no—
241C22C22⋊C4×D3111yescharacteristic
242C22#1175846011yescharacteristic
243C22#1175851411yescharacteristic
244C4—24no—
245C4—41no—
246C4—624no—
247C4—622no—
248C4—1242no—
249C4(C22⋊D31)⋊C411yescharacteristic
250C4#1175846111yescharacteristic
251C4C4×C22⋊D3111yescharacteristic
252C4#1175851511yescharacteristic
253C2—21no—
254C2—21no—
255C2—81no—
256C2—624no—
257C2#1452092511yescharacteristic
258C2#104×D3112yes—
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC22×C31C2×C22⋊C4
prime radical#14521556C2
cosocleC22×C4×C31C23
hypercenterC2×#104D31
hypocenterC31#1896
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×C42×D31C2semidirect
3. C2×#11758425C2semidirect
4. #14521012C2semidirect
5. #14520810C2semidirect
6. #14520809C2semidirect
7. C2×C31×#104C2semidirect
13. #11758523C4semidirect
14. #11758515C4semidirect
32. C2×Q8×C31C2×C4semidirect
34. C2×D4×C31C2×C4semidirect
53. C42×C31D4semidirect
57. C4⋊Dic31C2×C4semidirect
62. C4×Dic31D4semidirect
114. C2×D31#104semidirect
127. C2×#104D31semidirect
156. C31#1896semidirect
162. C2×Q8C4×D31semidirect
165. C2×D4C4×D31semidirect
195. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145215562
C2×C42×D312
C2×#117584252
#145210122
#145208102
#145208092
C2×C31×#1042
#189631