Finite Group Databasebeta

← #16846017

Subgroups — #16846017

Order 3968.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#11758474C211yesmaximal, characteristic
2C2×C4⋊C4×D31C211yesmaximal, characteristic
3C2×#11758404C211yesmaximal, characteristic, complemented
4C2×#11758398C211yesmaximal, characteristic, complemented
5C2×(C2×D31)⋊C8C211yesmaximal, characteristic
6#14520811C211yesmaximal, characteristic, complemented
7C31×#340C211yesmaximal, characteristic, complemented
8C22×C4×D31—21no—
9C22×C4×D31C2211yescharacteristic
10C22×Dic62C2211yescharacteristic
11C22×C8×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×(C2×D31)⋊C4—21no—
15C2×C4⋊Dic31—21no—
16C2×C4⋊Dic31C2211yescharacteristic
17C2×Dic31⋊C4—21no—
18C22×C31⋊C8C2211yescharacteristic
19#11758474—22no—
20#11758474C414yescomplemented
21C4⋊C4×D31—22no—
22C4⋊C4×D31—22no—
23(C2×D31)⋊C8—22no—
24#11758404—22no—
25#11758398—22no—
26C23×D31D411yescharacteristic
27C22×C4×C31—21no—
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31—21no—
32C22×Dic31D411yescharacteristic
33C2×C4×D31—21no—
34C2×C4×D31—21no—
35C2×C4×D31—21no—
36C2×C4×D31—21no—
37C2×C4×D31—24no—
38C2×C4×D31—42no—
39C2×C4×D31—42no—
40C2×C4×D31C2×C412yes—
41C2×C4×D31D412yes—
42C2×Dic62—21no—
43C2×Dic62—21no—
44C2×Dic62—21no—
45C2×Dic62—21no—
46C2×Dic62—21no—
47C2×Dic62C2×C412yescomplemented
48C2×C8×C31—21no—
49C2×C8×C31—21no—
50C2×C8×C31—21no—
51C4⋊C4×C31—21no—
52C4⋊C4×C31—21no—
53C4⋊C4×C31C2×C412yescomplemented
54C4⋊C4×C31D412yes—
55(C2×D31)⋊C4—24no—
56C4⋊Dic31—21no—
57C4⋊Dic31—24no—
58C4⋊Dic31D412yes—
59Dic31⋊C4—24no—
60C2×C31⋊C8—21no—
61C2×C31⋊C8—21no—
62C2×C31⋊C8—21no—
63C23×C31C2×D411yescharacteristic
64C22×D31—21no—
65C22×D31—21no—
66C22×D31—21no—
67C22×D31—21no—
68C22×D31C22⋊C412yes—
69C22×D31SD1612yes—
70C22×D31Q1612yes—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C22×C411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31#4111yescharacteristic
82C2×C4×C31#4111yescharacteristic
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31—22no—
86C2×Dic31—22no—
87C2×Dic31—41no—
88C2×Dic31—41no—
89C2×Dic31—41no—
90C2×Dic31—41no—
91C2×Dic31C22⋊C412yes—
92C4×D31—22no—
93C4×D31—22no—
94C4×D31—22no—
95C4×D31—22no—
96C4×D31—48no—
97Dic62—22no—
98Dic62—22no—
99Dic62—41no—
100Dic62—41no—
101C8×C31—41no—
102C31⋊C8—41no—
103#1872—311nomaximal, Sylow
104C22×C31C2×C22⋊C411yescharacteristic
105C22×C31#12011yescharacteristic
106C22×C31#12311yescharacteristic
107C22×C31C2×SD1611yescharacteristic
108C22×C31C2×Q1611yescharacteristic
109C22×C31AGL(1,ℤ/8)11yescharacteristic
110C22×C31#13711yescharacteristic
111C2×D31—22no—
112C2×D31—22no—
113C2×D31—22no—
114C2×D31—22no—
115C2×D31—22no—
116C2×D31—22no—
117C2×D31#10314yescomplemented
118C4×C31—42no—
119C4×C31—42no—
120C4×C31C4×D411yescharacteristic
121C4×C31C4×D411yescharacteristic
122C4×C31#12111yescharacteristic
123C4×C31#12111yescharacteristic
124Dic31—22no—
125Dic31—42no—
126Dic31—42no—
127C2×C22⋊Q8—311no—
128C22×C4⋊C4—311no—
129C2×#103—311no—
130C2×#103—311no—
131C2×C22⋊C8—311no—
132#340—311no—
133#340D3111yescharacteristic, complemented
134C2×C31#38611yescharacteristic
135C2×C31C2×#10311yescharacteristic
136C2×C31#41711yescharacteristic
137C2×C31#45011yescharacteristic
138C2×C31#45111yescharacteristic
139C2×C31#48311yescharacteristic
140C2×C31#48411yescharacteristic
141D31—24no—
142C22×Q8—311no—
143C23×C4—311no—
144C23×C4—621no—
145C22×C8—311no—
146C22×C8C2×D3111yescharacteristic
147C22⋊Q8—314no—
148C22⋊Q8—622no—
149C2×C4⋊C4—311no—
150C2×C4⋊C4—622no—
151C2×C4⋊C4—621no—
152C2×C4⋊C4—621no—
153C2×C4⋊C4—622no—
154C2×C4⋊C4C2×D3111yescharacteristic
155C2×C4⋊C4C2×D3111yescharacteristic
156C2×C22⋊C4—621no—
157#103—622no—
158#103—622no—
159C22⋊C8—622no—
160C31#187211yescharacteristic, complemented, Sylow
161C24—311no—
162C2×Q8—312no—
163C2×Q8—621no—
164C2×Q8—621no—
165C2×Q8—621no—
166C2×Q8—621no—
167C2×Q8—621no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—311no—
171C22×C4—312no—
172C22×C4—312no—
173C22×C4—624no—
174C22×C4—621no—
175C22×C4—621no—
176C22×C4—621no—
177C22×C4—621no—
178C22×C4—621no—
179C22×C4—621no—
180C22×C4—1242no—
181C22×C4—1242no—
182C22×C4C22×D3111yescharacteristic
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—621no—
187C2×C8—621no—
188C2×C8—621no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—312no—
192C4⋊C4—624no—
193C4⋊C4—624no—
194C4⋊C4—621no—
195C4⋊C4C4×D3112yescomplemented
196C4⋊C4D12412yes—
197C22⋊C4—624no—
198C23—312no—
199C23—312no—
200C23—312no—
201C23—621no—
202C23—621no—
203C23—621no—
204C23—621no—
205C23D4×D3111yescharacteristic
206Q8—622no—
207Q8—622no—
208Q8—1241no—
209Q8—1241no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—312no—
217C2×C4—621no—
218C2×C4—621no—
219C2×C4—622no—
220C2×C4—622no—
221C2×C4—622no—
222C2×C4—622no—
223C2×C4—622no—
224C2×C4—622no—
225C2×C4—1248no—
226C2×C4—1241no—
227C2×C4—1241no—
228C2×C4—1241no—
229C2×C4—1241no—
230C2×C4C2×C4×D3111yescharacteristic
231C2×C4C2×D12411yescharacteristic
232C2×C4#9249511yescharacteristic
233C2×C4D4×D3111yescharacteristic
234C2×C4D4×D3111yescharacteristic
235C2×C4#9249911yescharacteristic
236C8—41no—
237C8—1241no—
238C22—314no—
239C22—622no—
240C22—622no—
241C22—622no—
242C22—622no—
243C22—622no—
244C22—622no—
245C22C22⋊C4×D3111yescharacteristic
246C22#1175845911yescharacteristic
247C22#1175847111yescharacteristic
248C22#1175848811yescharacteristic
249C22SD16×D3111yescharacteristic
250C22#1175849211yescharacteristic
251C22Q16×D3111yescharacteristic
252C4—42no—
253C4—42no—
254C4—622no—
255C4—1242no—
256C4—1242no—
257C4C4×D12411yescharacteristic
258C4#1175846111yescharacteristic
259C4#1175847011yescharacteristic
260C4#1175847211yescharacteristic
261C2—624no—
262C2#1452092711yescharacteristic
263C2#103×D3111yescharacteristic
264C2#1452104711yescharacteristic
265C2#1452120111yescharacteristic
266C2#1452120611yescharacteristic
267C2#1452138111yescharacteristic
268C2#1452138611yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#340C2
socleC23×C31C2×D4
prime radicalC23×D31D4
cosocleC22×C4×C31C23
hypercenter#340D31
hypocenterC31#1872
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. C2×#11758404C2semidirect
4. C2×#11758398C2semidirect
6. #14520811C2semidirect
7. C31×#340C2semidirect
20. #11758474C4semidirect
47. C2×Dic62C2×C4semidirect
53. C4⋊C4×C31C2×C4semidirect
117. C2×D31#103semidirect
133. #340D31semidirect
160. C31#1872semidirect
195. C4⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584742
C2×C4⋊C4×D312
C2×#117584042
C2×#117583982
C2×(C2×D31)⋊C82
#145208112
C31×#3402
#187231