Finite Group Databasebeta

← C31×#1913 #16841846

Subgroups — C31×#1913 #16841846

Order 3968.

380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 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×#534C211yesmaximal, characteristic
2C31×#518C211yesmaximal, characteristic, complemented
3C2×C31×#99C211yesmaximal, characteristic, complemented
4C2×C31×#99C212yesmaximal, complemented
5C31×#342C212yesmaximal, complemented
6C22×D4×C31C2211yescharacteristic
7C22×D4×C31C2211yescharacteristic
8C31×#123—21no—
9C31×#123C412yescomplemented
10C31×#121—22no—
11C31×#120—21no—
12C31×#120C412yescomplemented
13C4×D4×C31—24no—
14C31×#117—21no—
15C2×C22⋊C4×C31—21no—
16C2×C22⋊C4×C31C2212yes—
17C2×C22⋊C4×C31C2211yescharacteristic
18C2×C22⋊C4×C31C2212yes—
19C31×#99—22no—
20C31×#99—24no—
21C24×C31C2×C411yescharacteristic, complemented
22C24×C31D411yescharacteristic
23C24×C31C2311yescharacteristic
24C2×D4×C31—22no—
25C2×D4×C31—22no—
26C2×D4×C31—22no—
27C2×D4×C31—21no—
28C2×D4×C31—21no—
29C2×D4×C31—22no—
30C2×D4×C31—22no—
31C2×D4×C31C2×C412yes—
32C2×D4×C31D412yes—
33C22×C4×C31—22no—
34C22×C4×C31—22no—
35C22×C4×C31—21no—
36C22×C4×C31—22no—
37C22×C4×C31C2×C411yescharacteristic, complemented
38C22×C4×C31D411yescharacteristic
39C4⋊C4×C31—22no—
40C4⋊C4×C31—22no—
41C22⋊C4×C31—22no—
42C22⋊C4×C31—22no—
43C22⋊C4×C31—22no—
44C22⋊C4×C31—21no—
45C22⋊C4×C31—22no—
46C22⋊C4×C31—22no—
47C22⋊C4×C31—22no—
48C22⋊C4×C31C2×C412yescomplemented
49C22⋊C4×C31D414yescomplemented
50C42×C31—22no—
51C23×C31—21no—
52C23×C31—21no—
53C23×C31—21no—
54C23×C31—22no—
55C23×C31—81no—
56C23×C31—81no—
57C23×C31—81no—
58C23×C31C22⋊C412yes—
59C23×C31C22×C411yescharacteristic
60C23×C31C2×D411yescharacteristic
61C23×C31C2×D411yescharacteristic
62C23×C31C2×D412yes—
63C23×C31#4112yes—
64D4×C31—24no—
65D4×C31—24no—
66D4×C31—41no—
67D4×C31—42no—
68D4×C31—41no—
69D4×C31—82no—
70C2×C4×C31—21no—
71C2×C4×C31—21no—
72C2×C4×C31—22no—
73C2×C4×C31—21no—
74C2×C4×C31—22no—
75C2×C4×C31—24no—
76C2×C4×C31—42no—
77C2×C4×C31—82no—
78C2×C4×C31—82no—
79C2×C4×C31—81no—
80C2×C4×C31—82no—
81C2×C4×C31C22⋊C412yes—
82#1913C3111yesmaximal, characteristic, direct product factor, Sylow
83C22×C31—22no—
84C22×C31—42no—
85C22×C31—41no—
86C22×C31—42no—
87C22×C31—41no—
88C22×C31—41no—
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31—41no—
93C22×C31—81no—
94C22×C31—82no—
95C22×C31C2×C22⋊C411yescharacteristic
96C22×C31C4×D412yes—
97C22×C31#12011yescharacteristic
98C22×C31#12112yes—
99C22×C31#12311yescharacteristic
100C4×C31—22no—
101C4×C31—44no—
102C4×C31—42no—
103C4×C31—41no—
104C4×C31—82no—
105#534C2×C3111yescharacteristic
106#518C2×C3111yescharacteristic, complemented
107C2×#99C2×C3111yescharacteristic, complemented
108C2×#99C2×C3112yescomplemented
109#342C2×C3112yescomplemented
110C2×C31—21no—
111C2×C31—21no—
112C2×C31—22no—
113C2×C31—22no—
114C2×C31—21no—
115C2×C31—42no—
116C2×C31—81no—
117C2×C31#38611yescharacteristic
118C22×D4C22×C3111yescharacteristic
119C22×D4C22×C3111yescharacteristic
120#123—21no—
121#123C4×C3112yescomplemented
122#121—22no—
123#120—21no—
124#120C4×C3112yescomplemented
125C4×D4—24no—
126#117—21no—
127C2×C22⋊C4—21no—
128C2×C22⋊C4C22×C3112yes—
129C2×C22⋊C4C22×C3111yescharacteristic
130C2×C22⋊C4C22×C3112yes—
131#99—22no—
132#99—24no—
133C31#191311yescharacteristic, direct product factor, Sylow
134C24C2×C4×C3111yescharacteristic, complemented
135C24D4×C3111yescharacteristic
136C24C23×C3111yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4C2×C4×C3112yes—
145C2×D4D4×C3112yes—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—22no—
150C22×C4C2×C4×C3111yescharacteristic, complemented
151C22×C4D4×C3111yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—22no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4C2×C4×C3112yescomplemented
162C22⋊C4D4×C3114yescomplemented
163C42—22no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—81no—
169C23—81no—
170C23—81no—
171C23C22⋊C4×C3112yes—
172C23C22×C4×C3111yescharacteristic
173C23C2×D4×C3111yescharacteristic
174C23C2×D4×C3111yescharacteristic
175C23C2×D4×C3112yes—
176C23#41×C3112yes—
177D4—24no—
178D4—24no—
179D4—41no—
180D4—42no—
181D4—41no—
182D4—82no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—82no—
191C2×C4—82no—
192C2×C4—81no—
193C2×C4—82no—
194C2×C4C22⋊C4×C3112yes—
195C22—22no—
196C22—42no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—81no—
206C22—82no—
207C22C2×C22⋊C4×C3111yescharacteristic
208C22C4×D4×C3112yes—
209C22C31×#12011yescharacteristic
210C22C31×#12112yes—
211C22C31×#12311yescharacteristic
212C4—22no—
213C4—44no—
214C4—42no—
215C4—41no—
216C4—82no—
217C2—21no—
218C2—21no—
219C2—22no—
220C2—22no—
221C2—21no—
222C2—42no—
223C2—81no—
224C2C31×#38611yescharacteristic
subgroupG/H
center, socleC2×C31#386
commutatorC23C22×C4×C31
Frattini, cosocleC24C23×C31
prime radicalC31×#534C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#518C2semidirect
3. C2×C31×#99C2semidirect
4. C2×C31×#99C2semidirect
5. C31×#342C2semidirect
9. C31×#123C4semidirect
12. C31×#120C4semidirect
21. C24×C31C2×C4semidirect
37. C22×C4×C31C2×C4semidirect
48. C22⋊C4×C31C2×C4semidirect
49. C22⋊C4×C31D4semidirect
82. #1913C31direct (N × H)
106. #518C2×C31semidirect
107. C2×#99C2×C31semidirect
108. C2×#99C2×C31semidirect
109. #342C2×C31semidirect
121. #123C4×C31semidirect
124. #120C4×C31semidirect
133. C31#1913direct (N × H)
134. C24C2×C4×C31semidirect
150. C22×C4C2×C4×C31semidirect
161. C22⋊C4C2×C4×C31semidirect
162. C22⋊C4D4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#5342
C31×#5182
C2×C31×#992
C31×#3422
#191331