Finite Group Databasebeta

← C2×#14521388 #16855601

Subgroups — C2×#14521388 #16855601

Order 3968.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11758523C211yesmaximal, characteristic
2C2×#11758469C211yesmaximal, characteristic
3#14521388C218yesmaximal, direct product factor
4C2×#11758395C211yesmaximal, characteristic, complemented
5C2×#11758405C211yesmaximal, characteristic, complemented
6C2×#11758423C211yesmaximal, characteristic, complemented
7C2×(C2×D31)⋊C8C211yesmaximal, characteristic
8C2×C31×#103C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C22×C4×D31C2211yescharacteristic
11C22×C8×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13#11758523—22no—
14#11758523C2214yes—
15C2×(C2×D31)⋊C4—21no—
16C2×(C2×D31)⋊C4—21no—
17C2×C4⋊Dic31C2211yescharacteristic
18C2×C4⋊Dic31C2211yescharacteristic
19C2×Dic31⋊C4—21no—
20C2×C4×Dic31—21no—
21C22×C31⋊C8C2211yescharacteristic
22#11758469—22no—
23#11758469C2214yes—
24C31×#103C2214yescomplemented
25#11758423C2214yescomplemented
26(C2×D31)⋊C8C2214yes—
27#11758405C2214yescomplemented
28#11758395C2214yescomplemented
29C23×D31D411yescharacteristic
30C2×Q8×C31—21no—
31C2×Q8×C31—22no—
32C2×Q8×C31—22no—
33C2×Q8×C31C2312yes—
34C22×C4×C31—21no—
35C22×C4×C31—21no—
36C22×C4×C31C2311yescharacteristic
37C22×Dic31—21no—
38C22×Dic31—21no—
39C22×Dic31D411yescharacteristic
40C2×C4×D31—22no—
41C2×C4×D31—22no—
42C2×C4×D31D412yes—
43C2×C4×D31C2312yes—
44C2×C8×C31—22no—
45C2×C8×C31C2312yes—
46C4⋊C4×C31—21no—
47C4⋊C4×C31C2312yes—
48(C2×D31)⋊C4—24no—
49(C2×D31)⋊C4—24no—
50C4⋊Dic31—21no—
51C4⋊Dic31—21no—
52C4⋊Dic31C2312yes—
53C4⋊Dic31C2312yes—
54Dic31⋊C4—24no—
55C4×Dic31—24no—
56C2×C31⋊C8—22no—
57C2×C31⋊C8C2312yes—
58C23×C31C2×D411yescharacteristic
59C22×D31—22no—
60C22×D31—22no—
61C22×D31—22no—
62C22×D31C2×D412yes—
63Q8×C31—22no—
64Q8×C31—22no—
65Q8×C31—42no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—42no—
69C2×C4×C31—42no—
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31#4112yes—
72C2×C4×C31#4112yes—
73C2×C4×C31C2411yescharacteristic
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—42no—
78C2×Dic31—42no—
79C2×Dic31C2×D412yes—
80C4×D31—24no—
81C4×D31—22no—
82C4×D31—22no—
83C8×C31—22no—
84C31⋊C8—22no—
85C2×#485—311nomaximal, Sylow
86C22×C31#12312yes—
87C22×C31#13512yes—
88C22×C31#13712yes—
89C22×C31C22×D411yescharacteristic
90C2×D31—22no—
91C2×D31—22no—
92C2×D31—22no—
93C2×D31—44no—
94C4×C31—42no—
95C4×C31—42no—
96C4×C31#12312yes—
97C4×C31C2×#4111yescharacteristic
98C4×C31C2×#4111yescharacteristic
99Dic31—22no—
100Dic31—42no—
101Dic31—42no—
102C2×C22⋊Q8—311no—
103C2×#117—311no—
104#485—318no—
105C2×#107—311no—
106C2×#106—311no—
107C2×#103—311no—
108C2×#103D3111yescharacteristic, complemented
109C2×C22⋊C8—311no—
110C2×C31#48514yescomplemented
111C2×C31C2×#12311yescharacteristic
112C2×C31C2×#13511yescharacteristic
113C2×C31C2×#13711yescharacteristic
114D31—42no—
115C22×Q8C2×D3111yescharacteristic
116C23×C4—311no—
117C22×C8—311no—
118C22×C8C2×D3111yescharacteristic
119C22⋊Q8—314no—
120C22⋊Q8—622no—
121#117—314no—
122#117—622no—
123C2×C4⋊C4—311no—
124C2×C4⋊C4—311no—
125C2×C4⋊C4—621no—
126C2×C4⋊C4C2×D3111yescharacteristic
127C2×C22⋊C4—621no—
128C2×C22⋊C4—621no—
129C2×C42—621no—
130#107—314no—
131#106—314no—
132#103—314no—
133#103C2×D3114yescomplemented
134C22⋊C8—314no—
135C31C2×#48511yescharacteristic, complemented, Sylow
136C24—311no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8C22×D3112yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—311no—
144C22×C4—312no—
145C22×C4—312no—
146C22×C4—622no—
147C22×C4—622no—
148C22×C4—621no—
149C22×C4—621no—
150C22×C4C22×D3111yescharacteristic
151C2×C8—22no—
152C2×C8—312no—
153C2×C8—622no—
154C2×C8C22×D3112yes—
155C4⋊C4—21no—
156C4⋊C4—312no—
157C4⋊C4—312no—
158C4⋊C4—624no—
159C4⋊C4—621no—
160C4⋊C4—621no—
161C4⋊C4C22×D3112yes—
162C22⋊C4—624no—
163C22⋊C4—624no—
164C42—624no—
165C23—312no—
166C23—622no—
167C23—622no—
168C23—622no—
169C23D4×D3111yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—42no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—312no—
178C2×C4—622no—
179C2×C4—624no—
180C2×C4—622no—
181C2×C4—622no—
182C2×C4—622no—
183C2×C4—622no—
184C2×C4—1242no—
185C2×C4—1242no—
186C2×C4#9249512yes—
187C2×C4D4×D3111yescharacteristic
188C2×C4#9249712yes—
189C2×C4C23×D3111yescharacteristic
190C8—22no—
191C8—622no—
192C22—622no—
193C22—622no—
194C22—622no—
195C22—1244no—
196C22#1175846012yes—
197C22#1175849312yes—
198C22#1175849512yes—
199C22C2×D4×D3111yescharacteristic
200C4—42no—
201C4—42no—
202C4—622no—
203C4—1242no—
204C4—1242no—
205C4#1175846012yes—
206C4C2×#9249511yescharacteristic
207C4C2×#9249711yescharacteristic
208C2—1242no—
209C2#1452138814yesdirect product factor
210C2C2×#1175846011yescharacteristic
211C2C2×#1175849311yescharacteristic
212C2C2×#1175849511yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#103C2
socleC23×C31C2×D4
prime radicalC23×D31D4
hypercenterC2×#103D31
hypocenterC31C2×#485
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #14521388C2direct (N × H)
4. C2×#11758395C2semidirect
5. C2×#11758405C2semidirect
6. C2×#11758423C2semidirect
8. C2×C31×#103C2semidirect
24. C31×#103C22semidirect
25. #11758423C22semidirect
27. #11758405C22semidirect
28. #11758395C22semidirect
108. C2×#103D31semidirect
110. C2×C31#485semidirect
133. #103C2×D31semidirect
135. C31C2×#485semidirect
209. C2#14521388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117585232
C2×#117584692
#145213882
C2×#117583952
C2×#117584052
C2×#117584232
C2×(C2×D31)⋊C82
C2×C31×#1032
C2×#48531