Finite Group Databasebeta

← C31×#2849 #16842782

Subgroups — C31×#2849 #16842782

Order 3968.

1102 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 264 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
1C24×C4×C31C211yesmaximal, characteristic, complemented
2C2×C31×#123C212yesmaximal, complemented
3C2×C31×#120C211yesmaximal, characteristic
4C31×#386C214yesmaximal, complemented
5C31×#385C214yesmaximal, complemented
6C31×#381C212yesmaximal, complemented
7C31×#379C211yesmaximal, characteristic, complemented
8C25×C31C2211yescharacteristic
9C22×D4×C31C2211yescharacteristic
10C22×D4×C31C2212yes—
11C23×C4×C31—24no—
12C23×C4×C31—28no—
13C23×C4×C31C2214yes—
14C23×C4×C31C2212yes—
15C31×#123—28no—
16C31×#120—24no—
17C2×C4⋊C4×C31C2214yescomplemented
18C2×C22⋊C4×C31C2211yescharacteristic
19C2×C22⋊C4×C31C2212yes—
20C2×C22⋊C4×C31C2212yes—
21C2×C22⋊C4×C31C2214yes—
22C2×C22⋊C4×C31C2214yescomplemented
23C31×#95C2218yescomplemented
24C24×C31—24no—
25C24×C31—28no—
26C24×C31D414yes—
27C24×C31C2311yescharacteristic
28C24×C31C2311yescharacteristic
29C24×C31C2312yes—
30C2×D4×C31—22no—
31C2×D4×C31—24no—
32C2×D4×C31—24no—
33C2×D4×C31—28no—
34C22×C4×C31—232no—
35C22×C4×C31—28no—
36C22×C4×C31—24no—
37C22×C4×C31—24no—
38C22×C4×C31—216no—
39C22×C4×C31D418yescomplemented
40C22×C4×C31C2312yes—
41C22×C4×C31C2314yes—
42C22×C4×C31C2311yescharacteristic
43C22×C4×C31C2314yes—
44C4⋊C4×C31—28no—
45C22⋊C4×C31—22no—
46C22⋊C4×C31—24no—
47C22⋊C4×C31—24no—
48C22⋊C4×C31—28no—
49C22⋊C4×C31—28no—
50C23×C31—232no—
51C23×C31—28no—
52C23×C31—216no—
53C23×C31—24no—
54C23×C31—24no—
55C23×C31—24no—
56C23×C31—22no—
57C23×C31—21no—
58C23×C31—24no—
59C23×C31C2×D412yes—
60C23×C31C2×D414yes—
61C23×C31C2×D414yes—
62C23×C31#4118yes—
63C23×C31C2411yescharacteristic
64D4×C31—44no—
65D4×C31—48no—
66C2×C4×C31—232no—
67C2×C4×C31—216no—
68C2×C4×C31—24no—
69C2×C4×C31—24no—
70C2×C4×C31—24no—
71C2×C4×C31—21no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—28no—
75C2×C4×C31—24no—
76C2×C4×C31C2×D418yes—
77#2849C3111yesmaximal, characteristic, direct product factor, Sylow
78C22×C31—232no—
79C22×C31—24no—
80C22×C31—24no—
81C22×C31—24no—
82C22×C31—28no—
83C22×C31—216no—
84C22×C31—41no—
85C22×C31—42no—
86C22×C31—44no—
87C22×C31#12014yes—
88C22×C31#12318yescomplemented
89C22×C31C22×D411yescharacteristic
90C22×C31C22×D412yes—
91C22×C31C2×#4114yes—
92C4×C31—28no—
93C4×C31—41no—
94C4×C31—42no—
95C4×C31—44no—
96C24×C4C2×C3111yescharacteristic, complemented
97C2×#123C2×C3112yescomplemented
98C2×#120C2×C3111yescharacteristic
99#386C2×C3114yescomplemented
100#385C2×C3114yescomplemented
101#381C2×C3112yescomplemented
102#379C2×C3111yescharacteristic, complemented
103C2×C31—24no—
104C2×C31—28no—
105C2×C31—81no—
106C2×C31C2×#12011yescharacteristic
107C2×C31C2×#12312yes—
108C2×C31#52514yes—
109C25C22×C3111yescharacteristic
110C22×D4C22×C3111yescharacteristic
111C22×D4C22×C3112yes—
112C23×C4—24no—
113C23×C4—28no—
114C23×C4C22×C3114yes—
115C23×C4C22×C3112yes—
116#123—28no—
117#120—24no—
118C2×C4⋊C4C22×C3114yescomplemented
119C2×C22⋊C4C22×C3111yescharacteristic
120C2×C22⋊C4C22×C3112yes—
121C2×C22⋊C4C22×C3112yes—
122C2×C22⋊C4C22×C3114yes—
123C2×C22⋊C4C22×C3114yescomplemented
124#95C22×C3118yescomplemented
125C31#284911yescharacteristic, direct product factor, Sylow
126C24—24no—
127C24—28no—
128C24D4×C3114yes—
129C24C23×C3111yescharacteristic
130C24C23×C3111yescharacteristic
131C24C23×C3112yes—
132C2×D4—22no—
133C2×D4—24no—
134C2×D4—24no—
135C2×D4—28no—
136C22×C4—232no—
137C22×C4—28no—
138C22×C4—24no—
139C22×C4—24no—
140C22×C4—216no—
141C22×C4D4×C3118yescomplemented
142C22×C4C23×C3112yes—
143C22×C4C23×C3114yes—
144C22×C4C23×C3111yescharacteristic
145C22×C4C23×C3114yes—
146C4⋊C4—28no—
147C22⋊C4—22no—
148C22⋊C4—24no—
149C22⋊C4—24no—
150C22⋊C4—28no—
151C22⋊C4—28no—
152C23—232no—
153C23—28no—
154C23—216no—
155C23—24no—
156C23—24no—
157C23—24no—
158C23—22no—
159C23—21no—
160C23—24no—
161C23C2×D4×C3112yes—
162C23C2×D4×C3114yes—
163C23C2×D4×C3114yes—
164C23#41×C3118yes—
165C23C24×C3111yescharacteristic
166D4—44no—
167D4—48no—
168C2×C4—232no—
169C2×C4—216no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—24no—
178C2×C4C2×D4×C3118yes—
179C22—232no—
180C22—24no—
181C22—24no—
182C22—24no—
183C22—28no—
184C22—216no—
185C22—41no—
186C22—42no—
187C22—44no—
188C22C31×#12014yes—
189C22C31×#12318yescomplemented
190C22C22×D4×C3111yescharacteristic
191C22C22×D4×C3112yes—
192C22C2×#41×C3114yes—
193C4—28no—
194C4—41no—
195C4—42no—
196C4—44no—
197C2—24no—
198C2—28no—
199C2—81no—
200C2C2×C31×#12011yescharacteristic
201C2C2×C31×#12312yes—
202C2C31×#52514yes—
subgroupG/H
center, socleC23×C31C24
commutator, Frattini, cosocleC23C24×C31
prime radicalC2×C31×#120C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×C4×C31C2semidirect
2. C2×C31×#123C2semidirect
4. C31×#386C2semidirect
5. C31×#385C2semidirect
6. C31×#381C2semidirect
7. C31×#379C2semidirect
17. C2×C4⋊C4×C31C22semidirect
22. C2×C22⋊C4×C31C22semidirect
23. C31×#95C22semidirect
39. C22×C4×C31D4semidirect
77. #2849C31direct (N × H)
88. C22×C31#123semidirect
96. C24×C4C2×C31semidirect
97. C2×#123C2×C31semidirect
99. #386C2×C31semidirect
100. #385C2×C31semidirect
101. #381C2×C31semidirect
102. #379C2×C31semidirect
118. C2×C4⋊C4C22×C31semidirect
123. C2×C22⋊C4C22×C31semidirect
124. #95C22×C31semidirect
125. C31#2849direct (N × H)
141. C22×C4D4×C31semidirect
189. C22C31×#123semidirect

Maximal subgroups

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

subgroupindex
C24×C4×C312
C2×C31×#1232
C2×C31×#1202
C31×#3862
C31×#3852
C31×#3812
C31×#3792
#284931