Finite Group Databasebeta

← C2×#14521186 #16854897

Subgroups — C2×#14521186 #16854897

Order 3968.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×Q8×D31C211yesmaximal, characteristic, complemented
2C22×#92480C211yesmaximal, characteristic, complemented
3C2×#11758515C211yesmaximal, characteristic
4#14521186C218yesmaximal, direct product factor
5C2×#11758404C211yesmaximal, characteristic, complemented
6C2×#11758423C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C31C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C22×D4×C31C2211yescharacteristic
11C22×C22⋊D31—21no—
12C2×Q8×D31—24no—
13C2×Q8×D31—22no—
14C2×Q8×D31—24no—
15C2×Q8×D31C2214yescomplemented
16C22×C4×D31—21no—
17C22×C4×D31C2211yescharacteristic
18C22×Dic62—21no—
19C22×Dic62C2211yescharacteristic
20C2×SD16×C31—24no—
21C2×SD16×C31C2214yescomplemented
22C22×C8×C31C2211yescharacteristic
23C2×C22⋊Dic31—21no—
24#11758515—22no—
25#11758515C2214yes—
26C2×#92480—24no—
27C2×#92480C2214yescomplemented
28C2×C4⋊Dic31C2211yescharacteristic
29C22×C31⋊C8C2211yescharacteristic
30#11758423C2214yescomplemented
31(C2×D31)⋊C8C2214yescomplemented
32#11758404C2214yescomplemented
33C24×C31—21no—
34C23×D31D411yescharacteristic
35C2×Q8×C31—22no—
36C2×Q8×C31—21no—
37C2×Q8×C31D414yescomplemented
38C2×Q8×C31C2312yes—
39C2×D4×C31—22no—
40C2×D4×C31—22no—
41C2×D4×C31—21no—
42C2×D4×C31C2312yes—
43C22×C4×C31—21no—
44C22×C4×C31C2311yescharacteristic
45C2×C22⋊D31—24no—
46C2×C22⋊D31—44no—
47C22×Dic31—21no—
48C22×Dic31—21no—
49C22×Dic31D411yescharacteristic
50Q8×D31—216no—
51Q8×D31—28no—
52Q8×D31—28no—
53C2×C4×D31—28no—
54C2×C4×D31—24no—
55C2×C4×D31—22no—
56C2×C4×D31—22no—
57C2×C4×D31D412yes—
58C2×C4×D31C2312yes—
59C2×Dic62—28no—
60C2×Dic62—21no—
61C2×Dic62—22no—
62C2×Dic62—24no—
63C2×Dic62D414yescomplemented
64C2×Dic62C2312yes—
65SD16×C31—28no—
66C2×C8×C31—22no—
67C2×C8×C31C2312yes—
68C22⋊Dic31—24no—
69#92480—28no—
70C4⋊Dic31—21no—
71C4⋊Dic31C2312yes—
72C2×C31⋊C8—22no—
73C2×C31⋊C8C2312yes—
74C23×C31—22no—
75C23×C31—42no—
76C23×C31—42no—
77C23×C31—42no—
78C23×C31C2×D411yescharacteristic
79C22×D31—22no—
80C22×D31—22no—
81C22×D31SD1614yescomplemented
82C22×D31C2×D412yes—
83Q8×C31—24no—
84Q8×C31—22no—
85Q8×C31C2×D414yescomplemented
86D4×C31—22no—
87D4×C31—22no—
88D4×C31—42no—
89C2×C4×C31—24no—
90C2×C4×C31—22no—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D412yes—
93C2×C4×C31C2×D412yes—
94C2×C4×C31C2411yescharacteristic
95C22⋊D31—48no—
96C2×Dic31—22no—
97C2×Dic31—24no—
98C2×Dic31—22no—
99C2×Dic31—22no—
100C2×Dic31—42no—
101C2×Dic31C2×D412yes—
102C4×D31—216no—
103C4×D31—24no—
104C4×D31—22no—
105C4×D31—22no—
106Dic62—216no—
107Dic62—24no—
108Dic62—22no—
109Dic62C2×D414yescomplemented
110C8×C31—22no—
111C31⋊C8—22no—
112C2×#448—311nomaximal, Sylow
113C22×C31—42no—
114C22×C31—42no—
115C22×C31—42no—
116C22×C31—84no—
117C22×C31#12012yes—
118C22×C31C2×SD1612yes—
119C22×C31#13712yes—
120C22×C31C22×D411yescharacteristic
121C2×D31—22no—
122C2×D31—22no—
123C2×D31—28no—
124C2×D31C2×SD1614yescomplemented
125C4×C31—24no—
126C4×C31#12012yes—
127C4×C31C22×D411yescharacteristic
128C4×C31C22×D411yescharacteristic
129Dic31—22no—
130Dic31—24no—
131Dic31—42no—
132C23×Q8—311no—
133C22×SD16—311no—
134C22×SD16D3111yescharacteristic, complemented
135C2×#121—311no—
136#448—318no—
137C2×#103—311no—
138C2×#103—311no—
139C2×C22⋊C8—311no—
140C2×C31—82no—
141C2×C31#44814yescomplemented
142C2×C31C2×#12011yescharacteristic
143C2×C31C22×SD1611yescharacteristic
144C2×C31C2×#13711yescharacteristic
145D31—24no—
146C22×Q8—314no—
147C22×Q8—311no—
148C22×Q8—621no—
149C22×Q8—622no—
150C22×Q8—624no—
151C22×Q8—624no—
152C22×Q8C2×D3111yescharacteristic
153C22×D4—621no—
154C22×D4C2×D3111yescharacteristic
155C23×C4—311no—
156C23×C4—621no—
157C2×SD16—24no—
158C2×SD16—314no—
159C2×SD16—624no—
160C2×SD16C2×D3114yescomplemented
161C22×C8—311no—
162C22×C8C2×D3111yescharacteristic
163#121—314no—
164#121—622no—
165C2×C4⋊C4—311no—
166C2×C22⋊C4—621no—
167#103—314no—
168#103—314no—
169C22⋊C8—314no—
170C31C2×#44811yescharacteristic, complemented, Sylow
171C24—21no—
172C24—311no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—314no—
176C2×Q8—312no—
177C2×Q8—624no—
178C2×Q8—628no—
179C2×Q8—628no—
180C2×Q8—6216no—
181C2×Q8—628no—
182C2×Q8—621no—
183C2×Q8—622no—
184C2×Q8C22⋊D3114yescomplemented
185C2×Q8C22×D3112yes—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—624no—
190C2×D4—1244no—
191C2×D4C22×D3112yes—
192C22×C4—21no—
193C22×C4—311no—
194C22×C4—312no—
195C22×C4—312no—
196C22×C4—624no—
197C22×C4—628no—
198C22×C4—621no—
199C22×C4—622no—
200C22×C4—622no—
201C22×C4—621no—
202C22×C4C22×D3111yescharacteristic
203SD16—28no—
204SD16—628no—
205C2×C8—22no—
206C2×C8—312no—
207C2×C8—622no—
208C2×C8C22×D3112yes—
209C4⋊C4—312no—
210C4⋊C4—621no—
211C22⋊C4—624no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23—42no—
216C23—314no—
217C23—312no—
218C23—622no—
219C23—622no—
220C23D4×D3111yescharacteristic
221Q8—24no—
222Q8—22no—
223Q8—314no—
224Q8—6216no—
225Q8—624no—
226Q8—622no—
227Q8C2×C22⋊D3114yescomplemented
228D4—22no—
229D4—22no—
230D4—42no—
231D4—1248no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—312no—
235C2×C4—6216no—
236C2×C4—622no—
237C2×C4—624no—
238C2×C4—622no—
239C2×C4—624no—
240C2×C4—622no—
241C2×C4—622no—
242C2×C4—622no—
243C2×C4—1242no—
244C2×C4D4×D3111yescharacteristic
245C2×C4D4×D3112yes—
246C2×C4C2×C22⋊D3112yes—
247C2×C4C23×D3111yescharacteristic
248C8—22no—
249C8—622no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—84no—
254C22—314no—
255C22—628no—
256C22—622no—
257C22—622no—
258C22SD16×D3112yes—
259C22#1175849212yes—
260C22#1175851412yes—
261C22C2×D4×D3111yescharacteristic
262C4—24no—
263C4—622no—
264C4—624no—
265C4—1242no—
266C4#1175851412yes—
267C4C2×D4×D3111yescharacteristic
268C4C22×C22⋊D3111yescharacteristic
269C2—82no—
270C2—624no—
271C2#1452118614yesdirect product factor
272C2C2×#1175851411yescharacteristic
273C2C2×SD16×D3111yescharacteristic
274C2C2×#1175849211yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC22×SD16×C31C2
socleC23×C31C2×D4
prime radicalC2×#11758515C2
hypercenterC22×SD16D31
hypocenterC31C2×#448
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D31C2semidirect
2. C22×#92480C2semidirect
4. #14521186C2direct (N × H)
5. C2×#11758404C2semidirect
6. C2×#11758423C2semidirect
7. C2×(C2×D31)⋊C8C2semidirect
8. C22×SD16×C31C2semidirect
15. C2×Q8×D31C22semidirect
21. C2×SD16×C31C22semidirect
27. C2×#92480C22semidirect
30. #11758423C22semidirect
31. (C2×D31)⋊C8C22semidirect
32. #11758404C22semidirect
37. C2×Q8×C31D4semidirect
63. C2×Dic62D4semidirect
81. C22×D31SD16semidirect
85. Q8×C31C2×D4semidirect
109. Dic62C2×D4semidirect
124. C2×D31C2×SD16semidirect
134. C22×SD16D31semidirect
141. C2×C31#448semidirect
160. C2×SD16C2×D31semidirect
170. C31C2×#448semidirect
184. C2×Q8C22⋊D31semidirect
227. Q8C2×C22⋊D31semidirect
271. C2#14521186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D312
C22×#924802
C2×#117585152
#145211862
C2×#117584042
C2×#117584232
C2×(C2×D31)⋊C82
C22×SD16×C312
C2×#44831