Finite Group Databasebeta

← C4×C31×#99 #16841687

Subgroups — C4×C31×#99 #16841687

Order 3968.

412 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 156 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×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#99C212yesmaximal
3C4×C22⋊C4×C31C212yesmaximal, complemented
4C31×#342C212yesmaximal, complemented
5C22×D4×C31C2211yescharacteristic
6C23×C4×C31C411yescharacteristic, complemented
7C23×C4×C31C2211yescharacteristic
8C4×D4×C31—22no—
9C4×D4×C31—22no—
10C2×C4⋊C4×C31C411yescharacteristic, complemented
11C2×C22⋊C4×C31C411yescharacteristic, complemented
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31C2214yes—
14C2×C42×C31—22no—
15C2×C42×C31C411yescharacteristic, complemented
16C31×#99C418yesdirect product factor
17C31×#95—22no—
18C24×C31C2×C411yescharacteristic
19C24×C31C2311yescharacteristic
20C2×D4×C31—22no—
21C2×D4×C31—22no—
22C2×D4×C31C2×C414yes—
23C22×C4×C31—24no—
24C22×C4×C31—21no—
25C22×C4×C31—21no—
26C22×C4×C31—42no—
27C22×C4×C31—42no—
28C22×C4×C31C2×C411yescharacteristic
29C22×C4×C31C2×C411yescharacteristic
30C22×C4×C31C2×C411yescharacteristic
31C22×C4×C31C2×C411yescharacteristic
32C22×C4×C31C2×C411yescharacteristic
33C22×C4×C31D412yes—
34C22×C4×C31D412yes—
35C4⋊C4×C31—22no—
36C22⋊C4×C31—22no—
37C22⋊C4×C31—24no—
38C22⋊C4×C31—22no—
39C22⋊C4×C31C2×C418yescomplemented
40C42×C31—21no—
41C42×C31—21no—
42C42×C31—44no—
43C23×C31—21no—
44C23×C31—21no—
45C23×C31—41no—
46C23×C31—41no—
47C23×C31—41no—
48C23×C31—41no—
49C23×C31C4212yescomplemented
50C23×C31C22×C411yescharacteristic
51C23×C31C22×C412yes—
52C23×C31C2×D412yes—
53C23×C31#4112yes—
54D4×C31—28no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—24no—
58C2×C4×C31—22no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—28no—
62C2×C4×C31—41no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31—44no—
66C2×C4×C31—44no—
67C2×C4×C31—42no—
68C2×C4×C31—41no—
69C2×C4×C31—41no—
70C2×C4×C31C4212yescomplemented
71C2×C4×C31C22⋊C411yescharacteristic
72C2×C4×C31C22⋊C412yes—
73C2×C4×C31C22⋊C411yescharacteristic
74C4×#99C3111yesmaximal, characteristic, direct product factor, Sylow
75C22×C31—22no—
76C22×C31—21no—
77C22×C31—22no—
78C22×C31—21no—
79C22×C31—22no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—42no—
83C22×C31—42no—
84C22×C31—41no—
85C22×C31—41no—
86C22×C31C2×C4211yescharacteristic
87C22×C31C2×C22⋊C411yescharacteristic
88C22×C31#11711yescharacteristic
89C22×C31C4×D414yes—
90C4×C31—22no—
91C4×C31—21no—
92C4×C31—22no—
93C4×C31—48no—
94C4×C31—41no—
95C4×C31—41no—
96C4×C31#9912yesdirect product factor
97C2×C4×D4C2×C3111yescharacteristic
98C2×#99C2×C3112yes—
99C4×C22⋊C4C2×C3112yescomplemented
100#342C2×C3112yescomplemented
101C2×C31—24no—
102C2×C31—21no—
103C2×C31—21no—
104C2×C31—42no—
105C2×C31C4×C22⋊C411yescharacteristic
106C2×C31C2×#9911yescharacteristic
107C2×C31#41011yescharacteristic
108C22×D4C22×C3111yescharacteristic
109C23×C4C4×C3111yescharacteristic, complemented
110C23×C4C22×C3111yescharacteristic
111C4×D4—22no—
112C4×D4—22no—
113C2×C4⋊C4C4×C3111yescharacteristic, complemented
114C2×C22⋊C4C4×C3111yescharacteristic, complemented
115C2×C22⋊C4C22×C3111yescharacteristic
116C2×C22⋊C4C22×C3114yes—
117C2×C42—22no—
118C2×C42C4×C3111yescharacteristic, complemented
119#99C4×C3118yesdirect product factor
120#95—22no—
121C31C4×#9911yescharacteristic, direct product factor, Sylow
122C24C2×C4×C3111yescharacteristic
123C24C23×C3111yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4C2×C4×C3114yes—
127C22×C4—24no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—42no—
131C22×C4—42no—
132C22×C4C2×C4×C3111yescharacteristic
133C22×C4C2×C4×C3111yescharacteristic
134C22×C4C2×C4×C3111yescharacteristic
135C22×C4C2×C4×C3111yescharacteristic
136C22×C4C2×C4×C3111yescharacteristic
137C22×C4D4×C3112yes—
138C22×C4D4×C3112yes—
139C4⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—24no—
142C22⋊C4—22no—
143C22⋊C4C2×C4×C3118yescomplemented
144C42—21no—
145C42—21no—
146C42—44no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23—41no—
153C23C42×C3112yescomplemented
154C23C22×C4×C3111yescharacteristic
155C23C22×C4×C3112yes—
156C23C2×D4×C3112yes—
157C23#41×C3112yes—
158D4—28no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—28no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—44no—
170C2×C4—44no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4C42×C3112yescomplemented
175C2×C4C22⋊C4×C3111yescharacteristic
176C2×C4C22⋊C4×C3112yes—
177C2×C4C22⋊C4×C3111yescharacteristic
178C22—22no—
179C22—21no—
180C22—22no—
181C22—21no—
182C22—22no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—41no—
189C22C2×C42×C3111yescharacteristic
190C22C2×C22⋊C4×C3111yescharacteristic
191C22C31×#11711yescharacteristic
192C22C4×D4×C3114yes—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—48no—
197C4—41no—
198C4—41no—
199C4C31×#9912yesdirect product factor
200C2—24no—
201C2—21no—
202C2—21no—
203C2—42no—
204C2C4×C22⋊C4×C3111yescharacteristic
205C2C2×C31×#9911yescharacteristic
206C2C31×#41011yescharacteristic
subgroupG/H
centerC2×C4×C31C22⋊C4
commutatorC22C2×C42×C31
Frattini, cosocleC24C23×C31
socleC22×C31C2×C22⋊C4
prime radicalC22×D4×C31C22
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×C22⋊C4×C31C2semidirect
4. C31×#342C2semidirect
6. C23×C4×C31C4semidirect
10. C2×C4⋊C4×C31C4semidirect
11. C2×C22⋊C4×C31C4semidirect
15. C2×C42×C31C4semidirect
16. C31×#99C4direct (N × H)
39. C22⋊C4×C31C2×C4semidirect
49. C23×C31C42semidirect
70. C2×C4×C31C42semidirect
74. C4×#99C31direct (N × H)
96. C4×C31#99direct (N × H)
99. C4×C22⋊C4C2×C31semidirect
100. #342C2×C31semidirect
109. C23×C4C4×C31semidirect
113. C2×C4⋊C4C4×C31semidirect
114. C2×C22⋊C4C4×C31semidirect
118. C2×C42C4×C31semidirect
119. #99C4×C31direct (N × H)
121. C31C4×#99direct (N × H)
143. C22⋊C4C2×C4×C31semidirect
153. C23C42×C31semidirect
174. C2×C4C42×C31semidirect
199. C4C31×#99direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×C312
C2×C31×#992
C4×C22⋊C4×C312
C31×#3422
C4×#9931