Finite Group Databasebeta

← C2×#14521092 #16854297

Subgroups — C2×#14521092 #16854297

Order 3968.

536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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×#92474C211yesmaximal, characteristic
2C22×C4⋊Dic31C211yesmaximal, characteristic
3#14521092C218yesmaximal, direct product factor
4C2×#11758395C212yesmaximal, complemented
5C2×#11758396C212yesmaximal, complemented
6C2×C31×#117C211yesmaximal, characteristic
7C23×C4×C31C2211yescharacteristic
8C23×Dic31—21no—
9C31×#117—22no—
10C31×#117C2214yes—
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31—21no—
14C2×C42×C31—21no—
15C2×C4⋊Dic31—21no—
16C2×C4⋊Dic31—22no—
17C2×C4⋊Dic31C2214yes—
18C2×C4⋊Dic31C2212yes—
19C2×#92474C418yescomplemented
20C2×#92474C2214yes—
21C22×C31⋊C8C2212yes—
22#11758396C2218yescomplemented
23#11758395C2218yescomplemented
24C24×C31D411yescharacteristic
25C22×C4×C31—21no—
26C22×C4×C31—21no—
27C22×C4×C31C2×C414yes—
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D412yes—
30C22×C4×C31Q814yes—
31C22×C4×C31C2311yescharacteristic
32C22×C4×C31C2312yes—
33C22×Dic31—24no—
34C22×Dic31—22no—
35C22×Dic31—44no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31C2312yes—
39C4⋊C4×C31C2312yes—
40C22⋊C4×C31—24no—
41C42×C31—24no—
42C4⋊Dic31—24no—
43C4⋊Dic31—22no—
44C4⋊Dic31C2314yes—
45#92474C2×C4116yescomplemented
46C2×C31⋊C8C2×C418yescomplemented
47C2×C31⋊C8C2314yes—
48C23×C31—22no—
49C23×C31—22no—
50C23×C31C4⋊C414yes—
51C23×C31C2×D412yes—
52C23×C31C2×D411yescharacteristic
53C2×C4×C31—22no—
54C2×C4×C31—22no—
55C2×C4×C31—42no—
56C2×C4×C31—42no—
57C2×C4×C31C4⋊C418yes—
58C2×C4×C31C4⋊C414yes—
59C2×C4×C31C22×C412yes—
60C2×C4×C31C22×C414yes—
61C2×C4×C31C2×D412yes—
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31C2×Q814yes—
64C2×C4×C31C2×Q812yes—
65C2×C4×C31C2411yescharacteristic
66C2×Dic31—24no—
67C2×Dic31—48no—
68C2×Dic31—44no—
69C31⋊C8C22×C418yescomplemented
70C2×#428—311nomaximal, Sylow
71C22×C31—22no—
72C22×C31—22no—
73C22×C31—28no—
74C22×C31C2×C4⋊C414yes—
75C22×C31C2×C4⋊C412yes—
76C22×C31AGL(1,ℤ/8)12yes—
77C22×C31#13712yes—
78C22×C31C22×D411yescharacteristic
79C4×C31—42no—
80C4×C31—42no—
81C4×C31C2×C4⋊C412yes—
82C4×C31C2×C4⋊C414yes—
83C4×C31C23×C411yescharacteristic
84C4×C31C22×Q811yescharacteristic
85Dic31—44no—
86C22×M16—311no—
87C2×#117D3111yescharacteristic
88C22×C4⋊C4—311no—
89#428—318no—
90C2×#107—312no—
91C2×#106—312no—
92C2×C31—24no—
93C2×C31#42814yescomplemented
94C2×C31C22×C4⋊C411yescharacteristic
95C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
96C2×C31C2×#13711yescharacteristic
97C23×C4—621no—
98C23×C4C2×D3111yescharacteristic
99C2×M16—318no—
100C2×M16—314no—
101C22×C8—312no—
102#117—22no—
103#117C2×D3114yes—
104C2×C4⋊C4—312no—
105C2×C4⋊C4—314no—
106C2×C4⋊C4—622no—
107C2×C4⋊C4—621no—
108C2×C4⋊C4C2×D3111yescharacteristic
109C2×C4⋊C4C2×D3111yescharacteristic
110C2×C22⋊C4—21no—
111C2×C42—21no—
112#107—318no—
113#106—318no—
114C31C2×#42811yescharacteristic, complemented, Sylow
115C24C22⋊D3111yescharacteristic
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—624no—
119C22×C4—622no—
120C22×C4—1244no—
121C22×C4Dic6214yes—
122C22×C4C4×D3114yes—
123C22×C4C22⋊D3112yes—
124C22×C4C22⋊D3111yescharacteristic
125C22×C4C22×D3112yes—
126C22×C4C22×D3111yescharacteristic
127M16—3116no—
128C2×C8—318no—
129C2×C8—314no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—314no—
133C4⋊C4—624no—
134C4⋊C4—622no—
135C4⋊C4C22×D3112yes—
136C4⋊C4C22×D3112yes—
137C22⋊C4—24no—
138C42—24no—
139C23—22no—
140C23—22no—
141C23Dic31⋊C414yes—
142C23C2×C22⋊D3112yes—
143C23C2×C22⋊D3111yescharacteristic
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—624no—
149C2×C4—1248no—
150C2×C4—1244no—
151C2×C4Dic31⋊C418yes—
152C2×C4Dic31⋊C414yes—
153C2×C4C2×Dic6214yes—
154C2×C4C2×Dic6212yes—
155C2×C4C2×C4×D3112yes—
156C2×C4C2×C4×D3114yes—
157C2×C4C2×C22⋊D3112yes—
158C2×C4C2×C22⋊D3111yescharacteristic
159C2×C4C23×D3111yescharacteristic
160C8—318no—
161C22—28no—
162C22—22no—
163C22—22no—
164C22C2×Dic31⋊C414yes—
165C22C2×Dic31⋊C412yes—
166C22#1175852612yes—
167C22#1175852812yes—
168C22C22×C22⋊D3111yescharacteristic
169C4—42no—
170C4—42no—
171C4—1244no—
172C4C2×Dic31⋊C412yes—
173C4C2×Dic31⋊C414yes—
174C4C22×Dic6211yescharacteristic
175C4C22×C4×D3111yescharacteristic
176C2—24no—
177C2#1452109214yesdirect product factor
178C2C22×Dic31⋊C411yescharacteristic
179C2C2×#1175852611yescharacteristic
180C2C2×#1175852811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D31
commutatorC4×C31C23×C4
FrattiniC2×C4C23×D31
FittingC2×C31×#117C2
socleC23×C31C2×D4
prime radicalC24×C31D4
cosocleC2×C4×C31C24
hypercenterC2×#117D31
hypocenterC31C2×#428
LCSG ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #14521092C2direct (N × H)
4. C2×#11758395C2semidirect
5. C2×#11758396C2semidirect
19. C2×#92474C4semidirect
22. #11758396C22semidirect
23. #11758395C22semidirect
45. #92474C2×C4semidirect
46. C2×C31⋊C8C2×C4semidirect
69. C31⋊C8C22×C4semidirect
93. C2×C31#428semidirect
114. C31C2×#428semidirect
177. C2#14521092direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#924742
C22×C4⋊Dic312
#145210922
C2×#117583952
C2×#117583962
C2×C31×#1172
C2×#42831