Finite Group Databasebeta

← C31×#1897 #16841830

Subgroups — C31×#1897 #16841830

Order 3968.

358 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C31×#525C211yesmaximal, characteristic
2C2×C31×#117C211yesmaximal, characteristic, complemented
3C2×C31×#104C212yesmaximal, complemented
4C31×#407C211yesmaximal, characteristic, complemented
5C31×#339C212yesmaximal, complemented
6C2×#41×C31C2211yescharacteristic
7C23×C4×C31C2211yescharacteristic
8C2×M16×C31C2212yes—
9C31×#123—21no—
10C31×C22⋊Q8C412yescomplemented
11C31×#121C412yescomplemented
12C31×#120—21no—
13C4×D4×C31—22no—
14C31×#117—24no—
15C31×#117C2211yescharacteristic
16C2×C4⋊C4×C31—21no—
17C2×C22⋊C4×C31—21no—
18C2×C42×C31C2212yes—
19C31×#104—24no—
20C31×C22⋊C8—22no—
21C24×C31D411yescharacteristic
22#41×C31—22no—
23#41×C31—22no—
24C2×Q8×C31C2×C411yescharacteristic
25C2×D4×C31—22no—
26C2×D4×C31—21no—
27C2×D4×C31C2×C411yescharacteristic
28C22×C4×C31—22no—
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31—21no—
32C22×C4×C31C2×C412yes—
33C22×C4×C31D411yescharacteristic
34C22×C4×C31D412yes—
35C22×C4×C31C2311yescharacteristic
36M16×C31—22no—
37M16×C31—22no—
38C2×C8×C31—22no—
39C4⋊C4×C31—24no—
40C4⋊C4×C31—22no—
41C4⋊C4×C31C2×C412yes—
42C22⋊C4×C31—24no—
43C22⋊C4×C31—22no—
44C22⋊C4×C31—21no—
45C22⋊C4×C31—22no—
46C42×C31—22no—
47C42×C31—21no—
48C42×C31D414yescomplemented
49C23×C31—21no—
50C23×C31—21no—
51C23×C31—21no—
52C23×C31—42no—
53C23×C31C22⋊C412yes—
54C23×C31C2×D411yescharacteristic
55Q8×C31—22no—
56D4×C31—22no—
57D4×C31—44no—
58D4×C31—41no—
59D4×C31—41no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—24no—
63C2×C4×C31—24no—
64C2×C4×C31—22no—
65C2×C4×C31—21no—
66C2×C4×C31—24no—
67C2×C4×C31—44no—
68C2×C4×C31—42no—
69C2×C4×C31C22⋊C412yes—
70C2×C4×C31C22×C411yescharacteristic
71C2×C4×C31C2×D412yes—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31#4112yes—
74C8×C31—42no—
75#1897C3111yesmaximal, characteristic, direct product factor, Sylow
76C22×C31—22no—
77C22×C31—22no—
78C22×C31—22no—
79C22×C31—22no—
80C22×C31—42no—
81C22×C31—42no—
82C22×C31—41no—
83C22×C31—42no—
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31#12011yescharacteristic
86C22×C31#12311yescharacteristic
87C4×C31—22no—
88C4×C31—44no—
89C4×C31—41no—
90C4×C31—42no—
91C4×C31C4×D412yes—
92C4×C31#12112yes—
93#525C2×C3111yescharacteristic
94C2×#117C2×C3111yescharacteristic, complemented
95C2×#104C2×C3112yescomplemented
96#407C2×C3111yescharacteristic, complemented
97#339C2×C3112yescomplemented
98C2×C31—21no—
99C2×C31—21no—
100C2×C31—42no—
101C2×C31—81no—
102C2×C31#38611yescharacteristic
103C2×C31#42112yes—
104C2×#41C22×C3111yescharacteristic
105C23×C4C22×C3111yescharacteristic
106C2×M16C22×C3112yes—
107#123—21no—
108C22⋊Q8C4×C3112yescomplemented
109#121C4×C3112yescomplemented
110#120—21no—
111C4×D4—22no—
112#117—24no—
113#117C22×C3111yescharacteristic
114C2×C4⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C42C22×C3112yes—
117#104—24no—
118C22⋊C8—22no—
119C31#189711yescharacteristic, direct product factor, Sylow
120C24D4×C3111yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×C4×C3111yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×C4×C3111yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—21no—
131C22×C4C2×C4×C3112yes—
132C22×C4D4×C3111yescharacteristic
133C22×C4D4×C3112yes—
134C22×C4C23×C3111yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—24no—
139C4⋊C4—22no—
140C4⋊C4C2×C4×C3112yes—
141C22⋊C4—24no—
142C22⋊C4—22no—
143C22⋊C4—21no—
144C22⋊C4—22no—
145C42—22no—
146C42—21no—
147C42D4×C3114yescomplemented
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊C4×C3112yes—
153C23C2×D4×C3111yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—44no—
167C2×C4—42no—
168C2×C4C22⋊C4×C3112yes—
169C2×C4C22×C4×C3111yescharacteristic
170C2×C4C2×D4×C3112yes—
171C2×C4C2×D4×C3111yescharacteristic
172C2×C4#41×C3112yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22C2×C22⋊C4×C3111yescharacteristic
183C22C31×#12011yescharacteristic
184C22C31×#12311yescharacteristic
185C4—22no—
186C4—44no—
187C4—42no—
188C4—41no—
189C4C4×D4×C3112yes—
190C4C31×#12112yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2C31×#38611yescharacteristic
196C2C31×#42112yes—
subgroupG/H
centerC2×C4×C31C2×D4
commutatorC2×C4C22×C4×C31
Frattini, cosocleC22×C4C23×C31
socleC22×C31C2×C22⋊C4
prime radicalC31×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#117C2semidirect
3. C2×C31×#104C2semidirect
4. C31×#407C2semidirect
5. C31×#339C2semidirect
10. C31×C22⋊Q8C4semidirect
11. C31×#121C4semidirect
48. C42×C31D4semidirect
75. #1897C31direct (N × H)
94. C2×#117C2×C31semidirect
95. C2×#104C2×C31semidirect
96. #407C2×C31semidirect
97. #339C2×C31semidirect
108. C22⋊Q8C4×C31semidirect
109. #121C4×C31semidirect
119. C31#1897direct (N × H)
147. C42D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#5252
C2×C31×#1172
C2×C31×#1042
C31×#4072
C31×#3392
#189731