Finite Group Databasebeta

← C2×#14521276 #16855269

Subgroups — C2×#14521276 #16855269

Order 3968.

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

normal subgroups only

This group has 564 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×#92480C211yesmaximal, characteristic, complemented
2C23×C31⋊C8C211yesmaximal, characteristic, complemented
3C2×#11758501C211yesmaximal, characteristic, complemented
4#14521276C218yesmaximal, direct product factor
5C2×#11758396C211yesmaximal, characteristic, complemented
6C2×#11758398C211yesmaximal, characteristic, complemented
7C2×#11758420C211yesmaximal, characteristic, complemented
8C2×C31×#121C211yesmaximal, characteristic
9C22×D4×C31—21no—
10C22×D4×C31C2211yescharacteristic
11C23×C4×C31C2211yescharacteristic
12C22×Dic62C2211yescharacteristic
13C31×#121—22no—
14C31×#121C2214yes—
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×C22⋊C4×C31—21no—
17C2×C22⋊Dic31—21no—
18C2×#92480—24no—
19C2×#92480C2214yescomplemented
20C2×C4⋊Dic31C2211yescharacteristic
21#11758501—22no—
22#11758501C2214yescomplemented
23C2×Dic31⋊C4—21no—
24C22×C31⋊C8—24no—
25C22×C31⋊C8C2211yescharacteristic
26C22×C31⋊C8C2211yescharacteristic
27C22×C31⋊C8C2214yescomplemented
28#11758420C2214yescomplemented
29#11758398C2214yescomplemented
30#11758396C2214yescomplemented
31C24×C31—21no—
32C24×C31D411yescharacteristic
33C2×D4×C31—24no—
34C2×D4×C31—22no—
35C2×D4×C31—21no—
36C2×D4×C31—22no—
37C2×D4×C31—44no—
38C2×D4×C31C2312yes—
39C22×C4×C31—22no—
40C22×C4×C31—22no—
41C22×C4×C31—21no—
42C22×C4×C31D411yescharacteristic
43C22×C4×C31D412yes—
44C22×C4×C31C2312yes—
45C22×C4×C31C2311yescharacteristic
46C22×Dic31—21no—
47C22×Dic31—21no—
48C2×Dic62—22no—
49C2×Dic62—22no—
50C2×Dic62—21no—
51C2×Dic62C2312yes—
52C4⋊C4×C31—21no—
53C4⋊C4×C31C2312yes—
54C22⋊C4×C31—24no—
55C22⋊Dic31—24no—
56#92480—28no—
57C4⋊Dic31—21no—
58C4⋊Dic31C2312yes—
59Dic31⋊C4—24no—
60C2×C31⋊C8—22no—
61C2×C31⋊C8—28no—
62C2×C31⋊C8D414yescomplemented
63C2×C31⋊C8C2312yes—
64C2×C31⋊C8C2312yes—
65C23×C31—22no—
66C23×C31—22no—
67C23×C31—22no—
68C23×C31—42no—
69C23×C31—42no—
70C23×C31—42no—
71C23×C31SD1614yescomplemented
72C23×C31C2×D412yes—
73C23×C31C2×D411yescharacteristic
74D4×C31—22no—
75D4×C31—22no—
76D4×C31—48no—
77D4×C31—42no—
78C2×C4×C31—22no—
79C2×C4×C31—24no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—42no—
84C2×C4×C31C2×D412yes—
85C2×C4×C31C2×D412yes—
86C2×C4×C31C2×D411yescharacteristic
87C2×C4×C31#4112yes—
88C2×C4×C31C2411yescharacteristic
89C2×Dic31—22no—
90C2×Dic31—22no—
91C2×Dic31—42no—
92C2×Dic31—42no—
93Dic62—22no—
94Dic62—22no—
95Dic62—42no—
96C31⋊C8—22no—
97C31⋊C8C2×D414yescomplemented
98C2×#465—311nomaximal, Sylow
99C22×C31—22no—
100C22×C31—22no—
101C22×C31—28no—
102C22×C31—42no—
103C22×C31—42no—
104C22×C31—42no—
105C22×C31—84no—
106C22×C31#12112yes—
107C22×C31C2×SD1612yes—
108C22×C31C2×SD1614yescomplemented
109C22×C31#13512yes—
110C22×C31C22×D411yescharacteristic
111C4×C31—22no—
112C4×C31—42no—
113C4×C31#12112yes—
114C4×C31C22×D411yescharacteristic
115C4×C31C2×#4111yescharacteristic
116Dic31—42no—
117Dic31—42no—
118C22×SD16—311no—
119C23×C8—311no—
120C2×C22⋊Q8—311no—
121C2×#121D3111yescharacteristic
122#465—318no—
123C2×#106—311no—
124C2×#103—311no—
125C2×#102—311no—
126C2×C31—24no—
127C2×C31—82no—
128C2×C31#46514yescomplemented
129C2×C31C2×#12111yescharacteristic
130C2×C31C22×SD1611yescharacteristic
131C2×C31C2×#13511yescharacteristic
132C22×Q8—311no—
133C22×D4—21no—
134C22×D4C2×D3111yescharacteristic
135C23×C4C2×D3111yescharacteristic
136C2×SD16—314no—
137C2×SD16—624no—
138C22×C8—311no—
139C22×C8—311no—
140C22×C8—314no—
141C22×C8—624no—
142C22⋊Q8—314no—
143C22⋊Q8—622no—
144#121—22no—
145#121C2×D3114yes—
146C2×C4⋊C4—311no—
147C2×C4⋊C4—621no—
148C2×C4⋊C4C2×D3111yescharacteristic
149C2×C22⋊C4—21no—
150C2×C22⋊C4—621no—
151#106—314no—
152#103—314no—
153#102—314no—
154C31C2×#46511yescharacteristic, complemented, Sylow
155C24—21no—
156C24C22⋊D3111yescharacteristic
157C2×Q8—312no—
158C2×Q8—621no—
159C2×Q8—622no—
160C2×Q8—622no—
161C2×D4—24no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—21no—
165C2×D4—44no—
166C2×D4C22×D3112yes—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—621no—
171C22×C4—621no—
172C22×C4C22⋊D3112yes—
173C22×C4C22⋊D3111yescharacteristic
174C22×C4C22×D3112yes—
175C22×C4C22×D3111yescharacteristic
176SD16—628no—
177C2×C8—314no—
178C2×C8—312no—
179C2×C8—312no—
180C2×C8—628no—
181C2×C8—622no—
182C4⋊C4—21no—
183C4⋊C4—312no—
184C4⋊C4—624no—
185C4⋊C4—621no—
186C4⋊C4C22×D3112yes—
187C22⋊C4—24no—
188C22⋊C4—624no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—42no—
193C23—42no—
194C23—42no—
195C23#9248014yescomplemented
196C23C2×C22⋊D3112yes—
197C23C2×C22⋊D3111yescharacteristic
198Q8—622no—
199Q8—622no—
200Q8—1242no—
201D4—22no—
202D4—22no—
203D4—48no—
204D4—42no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—622no—
212C2×C4—622no—
213C2×C4—1242no—
214C2×C4—1242no—
215C2×C4D4×D3112yes—
216C2×C4#9249712yes—
217C2×C4C2×C22⋊D3112yes—
218C2×C4C2×C22⋊D3111yescharacteristic
219C2×C4C23×D3111yescharacteristic
220C8—314no—
221C8—622no—
222C22—28no—
223C22—22no—
224C22—22no—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—84no—
229C22C2×#9248012yes—
230C22C2×#9248014yescomplemented
231C22#1175851612yes—
232C22#1175852712yes—
233C22C22×C22⋊D3111yescharacteristic
234C4—22no—
235C4—42no—
236C4—1242no—
237C4—1242no—
238C4#1175851612yes—
239C4C2×D4×D3111yescharacteristic
240C4C2×#9249711yescharacteristic
241C2—24no—
242C2—82no—
243C2#1452127614yesdirect product factor
244C2C2×#1175851611yescharacteristic
245C2C22×#9248011yescharacteristic
246C2C2×#1175852711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC2×C31×#121C2
socleC23×C31C2×D4
hypercenterC2×#121D31
hypocenterC31C2×#465
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#92480C2semidirect
2. C23×C31⋊C8C2semidirect
3. C2×#11758501C2semidirect
4. #14521276C2direct (N × H)
5. C2×#11758396C2semidirect
6. C2×#11758398C2semidirect
7. C2×#11758420C2semidirect
19. C2×#92480C22semidirect
22. #11758501C22semidirect
27. C22×C31⋊C8C22semidirect
28. #11758420C22semidirect
29. #11758398C22semidirect
30. #11758396C22semidirect
62. C2×C31⋊C8D4semidirect
71. C23×C31SD16semidirect
97. C31⋊C8C2×D4semidirect
108. C22×C31C2×SD16semidirect
128. C2×C31#465semidirect
154. C31C2×#465semidirect
195. C23#92480semidirect
230. C22C2×#92480semidirect
243. C2#14521276direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924802
C23×C31⋊C82
C2×#117585012
#145212762
C2×#117583962
C2×#117583982
C2×#117584202
C2×C31×#1212
C2×#46531