Finite Group Databasebeta

← C2×C31×#448 #16842931

Subgroups — C2×C31×#448 #16842931

Order 3968.

792 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 248 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
1C23×Q8×C31C211yesmaximal, characteristic, complemented
2C22×SD16×C31C212yesmaximal, complemented
3C2×C31×#121C211yesmaximal, characteristic
4C31×#448C218yesmaximal, direct product factor
5C2×C31×#103C212yesmaximal, complemented
6C2×C31×C22⋊C8C211yesmaximal, characteristic, complemented
7C22×Q8×C31—28no—
8C22×Q8×C31—22no—
9C22×Q8×C31—21no—
10C22×Q8×C31C2212yes—
11C22×Q8×C31C2214yescomplemented
12C22×D4×C31—21no—
13C22×D4×C31C2211yescharacteristic
14C23×C4×C31—21no—
15C23×C4×C31C2211yescharacteristic
16C2×SD16×C31—28no—
17C2×SD16×C31C2218yescomplemented
18C22×C8×C31C2212yes—
19C31×#121—22no—
20C31×#121C2214yes—
21C2×C4⋊C4×C31C2211yescharacteristic
22C2×C22⋊C4×C31—21no—
23C31×#103C2218yescomplemented
24C31×C22⋊C8C2214yescomplemented
25C24×C31—21no—
26C24×C31D411yescharacteristic
27C2×Q8×C31—216no—
28C2×Q8×C31—28no—
29C2×Q8×C31—216no—
30C2×Q8×C31—24no—
31C2×Q8×C31—22no—
32C2×Q8×C31—24no—
33C2×Q8×C31D418yescomplemented
34C2×Q8×C31C2314yes—
35C2×D4×C31—24no—
36C2×D4×C31—24no—
37C2×D4×C31—21no—
38C2×D4×C31—44no—
39C2×D4×C31C2312yes—
40C22×C4×C31—28no—
41C22×C4×C31—24no—
42C22×C4×C31—22no—
43C22×C4×C31—24no—
44C22×C4×C31—21no—
45C22×C4×C31D412yes—
46C22×C4×C31D411yescharacteristic
47C22×C4×C31C2312yes—
48C22×C4×C31C2311yescharacteristic
49SD16×C31—216no—
50C2×C8×C31—24no—
51C2×C8×C31C2314yes—
52C4⋊C4×C31—21no—
53C4⋊C4×C31C2312yes—
54C22⋊C4×C31—24no—
55C23×C31—22no—
56C23×C31—22no—
57C23×C31—22no—
58C23×C31—42no—
59C23×C31—42no—
60C23×C31—42no—
61C23×C31SD1614yescomplemented
62C23×C31C2×D412yes—
63C23×C31C2×D411yescharacteristic
64Q8×C31—216no—
65Q8×C31—28no—
66Q8×C31—24no—
67Q8×C31C2×D418yescomplemented
68D4×C31—24no—
69D4×C31—48no—
70D4×C31—42no—
71C2×C4×C31—216no—
72C2×C4×C31—28no—
73C2×C4×C31—22no—
74C2×C4×C31—24no—
75C2×C4×C31—24no—
76C2×C4×C31—24no—
77C2×C4×C31—22no—
78C2×C4×C31—42no—
79C2×C4×C31C2×D412yes—
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D414yes—
82C2×C4×C31C2411yescharacteristic
83C8×C31—24no—
84C2×#448C3111yesmaximal, characteristic, direct product factor, Sylow
85C22×C31—22no—
86C22×C31—22no—
87C22×C31—28no—
88C22×C31—42no—
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—84no—
92C22×C31#12012yes—
93C22×C31C2×SD1612yes—
94C22×C31C2×SD1614yescomplemented
95C22×C31#13712yes—
96C22×C31C22×D411yescharacteristic
97C4×C31—28no—
98C4×C31—22no—
99C4×C31—42no—
100C4×C31#12012yes—
101C4×C31C22×D412yes—
102C23×Q8C2×C3111yescharacteristic, complemented
103C22×SD16C2×C3112yescomplemented
104C2×#121C2×C3111yescharacteristic
105#448C2×C3118yesdirect product factor
106C2×#103C2×C3112yescomplemented
107C2×C22⋊C8C2×C3111yescharacteristic, complemented
108C2×C31—24no—
109C2×C31—82no—
110C2×C31#44814yesdirect product factor
111C2×C31C2×#12011yescharacteristic
112C2×C31C22×SD1611yescharacteristic
113C2×C31C2×#13711yescharacteristic
114C22×Q8—28no—
115C22×Q8—21no—
116C22×Q8—22no—
117C22×Q8C22×C3112yes—
118C22×Q8C22×C3114yescomplemented
119C22×D4—21no—
120C22×D4C22×C3111yescharacteristic
121C23×C4—21no—
122C23×C4C22×C3111yescharacteristic
123C2×SD16—28no—
124C2×SD16C22×C3118yescomplemented
125C22×C8C22×C3112yes—
126#121—22no—
127#121C22×C3114yes—
128C2×C4⋊C4C22×C3111yescharacteristic
129C2×C22⋊C4—21no—
130#103C22×C3118yescomplemented
131C22⋊C8C22×C3114yescomplemented
132C31C2×#44811yescharacteristic, direct product factor, Sylow
133C24—21no—
134C24D4×C3111yescharacteristic
135C2×Q8—216no—
136C2×Q8—28no—
137C2×Q8—216no—
138C2×Q8—24no—
139C2×Q8—22no—
140C2×Q8—24no—
141C2×Q8D4×C3118yescomplemented
142C2×Q8C23×C3114yes—
143C2×D4—24no—
144C2×D4—24no—
145C2×D4—21no—
146C2×D4—44no—
147C2×D4C23×C3112yes—
148C22×C4—28no—
149C22×C4—22no—
150C22×C4—24no—
151C22×C4—24no—
152C22×C4—21no—
153C22×C4D4×C3111yescharacteristic
154C22×C4D4×C3112yes—
155C22×C4C23×C3112yes—
156C22×C4C23×C3111yescharacteristic
157SD16—216no—
158C2×C8—24no—
159C2×C8C23×C3114yes—
160C4⋊C4—21no—
161C4⋊C4C23×C3112yes—
162C22⋊C4—24no—
163C23—22no—
164C23—22no—
165C23—22no—
166C23—42no—
167C23—42no—
168C23—42no—
169C23SD16×C3114yescomplemented
170C23C2×D4×C3112yes—
171C23C2×D4×C3111yescharacteristic
172Q8—216no—
173Q8—28no—
174Q8—24no—
175Q8C2×D4×C3118yescomplemented
176D4—24no—
177D4—48no—
178D4—42no—
179C2×C4—216no—
180C2×C4—28no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—42no—
187C2×C4C2×D4×C3112yes—
188C2×C4C2×D4×C3111yescharacteristic
189C2×C4C2×D4×C3114yes—
190C2×C4C24×C3111yescharacteristic
191C8—24no—
192C22—28no—
193C22—22no—
194C22—22no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22—84no—
199C22C31×#12012yes—
200C22C2×SD16×C3112yes—
201C22C2×SD16×C3114yescomplemented
202C22C31×#13712yes—
203C22C22×D4×C3111yescharacteristic
204C4—28no—
205C4—22no—
206C4—42no—
207C4C31×#12012yes—
208C4C22×D4×C3112yes—
209C2—24no—
210C2—82no—
211C2C31×#44814yesdirect product factor
212C2C2×C31×#12011yescharacteristic
213C2C22×SD16×C3111yescharacteristic
214C2C2×C31×#13711yescharacteristic
subgroupG/H
center, socleC23×C31C2×D4
commutator, Frattini, cosocleC2×C4C24×C31
prime radicalC2×C31×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×Q8×C31C2semidirect
2. C22×SD16×C31C2semidirect
4. C31×#448C2direct (N × H)
5. C2×C31×#103C2semidirect
6. C2×C31×C22⋊C8C2semidirect
11. C22×Q8×C31C22semidirect
17. C2×SD16×C31C22semidirect
23. C31×#103C22semidirect
24. C31×C22⋊C8C22semidirect
33. C2×Q8×C31D4semidirect
61. C23×C31SD16semidirect
67. Q8×C31C2×D4semidirect
84. C2×#448C31direct (N × H)
94. C22×C31C2×SD16semidirect
102. C23×Q8C2×C31semidirect
103. C22×SD16C2×C31semidirect
105. #448C2×C31direct (N × H)
106. C2×#103C2×C31semidirect
107. C2×C22⋊C8C2×C31semidirect
110. C2×C31#448direct (N × H)
118. C22×Q8C22×C31semidirect
124. C2×SD16C22×C31semidirect
130. #103C22×C31semidirect
131. C22⋊C8C22×C31semidirect
132. C31C2×#448direct (N × H)
141. C2×Q8D4×C31semidirect
169. C23SD16×C31semidirect
175. Q8C2×D4×C31semidirect
201. C22C2×SD16×C31semidirect
211. C2C31×#448direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×C312
C22×SD16×C312
C2×C31×#1212
C31×#4482
C2×C31×#1032
C2×C31×C22⋊C82
C2×#44831