Finite Group Databasebeta

← C31×#32879 #21489638

Subgroups — C31×#32879 #21489638

Order 7936.

3876 conjugacy classes of subgroups; only the 438 normal subgroups are shown.

normal subgroups only

This group has 3876 conjugacy classes of subgroups — too many to draw. Only its 438 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×Q8×C31C211yesmaximal, characteristic, complemented
2C2×C31×#448C216yesmaximal, complemented
3C31×#2847C211yesmaximal, characteristic
4C31×#1787C216yesmaximal, complemented
5C31×#1779C211yesmaximal, characteristic, complemented
6C23×Q8×C31—224no—
7C23×Q8×C31—23no—
8C23×Q8×C31C2216yes—
9C24×C4×C31—21no—
10C24×C4×C31C2211yescharacteristic
11C22×SD16×C31C2214yescomplemented
12C2×C31×#121C2213yes—
13C2×C31×#120—21no—
14C31×#448—224no—
15C2×C31×#103C22112yescomplemented
16C2×C31×C22⋊C8C2216yes—
17C31×#386—23no—
18C31×#380C2213yes—
19C25×C31D411yescharacteristic
20C22×Q8×C31—2128no—
21C22×Q8×C31—248no—
22C22×Q8×C31—224no—
23C22×Q8×C31—248no—
24C22×Q8×C31—212no—
25C22×Q8×C31—26no—
26C22×Q8×C31D4124yescomplemented
27C22×Q8×C31C2314yes—
28C22×D4×C31—23no—
29C22×D4×C31C2311yescharacteristic
30C23×C4×C31—224no—
31C23×C4×C31—26no—
32C23×C4×C31—212no—
33C23×C4×C31D413yes—
34C23×C4×C31C2313yes—
35C2×SD16×C31—224no—
36C22×C8×C31C2314yes—
37C31×#121—212no—
38C31×#120—44no—
39C2×C4⋊C4×C31C2313yes—
40C2×C22⋊C4×C31—23no—
41C2×C22⋊C4×C31—23no—
42C31×#103—224no—
43C31×C22⋊C8—212no—
44C31×#95—23no—
45C24×C31—26no—
46C24×C31—26no—
47C24×C31—21no—
48C24×C31SD1614yescomplemented
49C24×C31C2×D413yes—
50C2×Q8×C31—2192no—
51C2×Q8×C31—296no—
52C2×Q8×C31—248no—
53C2×Q8×C31—296no—
54C2×Q8×C31—224no—
55C2×Q8×C31—212no—
56C2×Q8×C31C2×D4124yes—
57C2×D4×C31—26no—
58C2×D4×C31—46no—
59C2×D4×C31—46no—
60C2×D4×C31—46no—
61C22×C4×C31—264no—
62C22×C4×C31—248no—
63C22×C4×C31—232no—
64C22×C4×C31—224no—
65C22×C4×C31—26no—
66C22×C4×C31—24no—
67C22×C4×C31—212no—
68C22×C4×C31—212no—
69C22×C4×C31—23no—
70C22×C4×C31C2×D413yes—
71C22×C4×C31C2×D4112yes—
72C22×C4×C31C2411yescharacteristic
73SD16×C31—416no—
74C2×C8×C31—212no—
75C4⋊C4×C31—26no—
76C22⋊C4×C31—46no—
77C22⋊C4×C31—46no—
78#32879C3111yesmaximal, characteristic, direct product factor, Sylow
79C23×C31—28no—
80C23×C31—224no—
81C23×C31—26no—
82C23×C31—26no—
83C23×C31—224no—
84C23×C31—43no—
85C23×C31—41no—
86C23×C31—43no—
87C23×C31#12016yes—
88C23×C31C2×SD1616yes—
89C23×C31#13716yes—
90C23×C31C22×D411yescharacteristic
91Q8×C31—296no—
92Q8×C31—224no—
93Q8×C31#120116yescomplemented
94D4×C31—44no—
95D4×C31—812no—
96C2×C4×C31—296no—
97C2×C4×C31—224no—
98C2×C4×C31—224no—
99C2×C4×C31—26no—
100C2×C4×C31—224no—
101C2×C4×C31—43no—
102C2×C4×C31—43no—
103C2×C4×C31—43no—
104C2×C4×C31#12016yes—
105C2×C4×C31C22×D416yes—
106C8×C31—44no—
107C24×Q8C2×C3111yescharacteristic, complemented
108C2×#448C2×C3116yescomplemented
109#2847C2×C3111yescharacteristic
110#1787C2×C3116yescomplemented
111#1779C2×C3111yescharacteristic, complemented
112C22×C31—232no—
113C22×C31—26no—
114C22×C31—212no—
115C22×C31—26no—
116C22×C31—212no—
117C22×C31—81no—
118C22×C31—83no—
119C22×C31—83no—
120C22×C31#448112yescomplemented
121C22×C31C2×#12013yes—
122C22×C31C22×SD1611yescharacteristic
123C22×C31C2×#13713yes—
124C4×C31—216no—
125C4×C31—26no—
126C4×C31—83no—
127C4×C31C2×#12014yes—
128C23×Q8—224no—
129C23×Q8—23no—
130C23×Q8C22×C3116yes—
131C24×C4—21no—
132C24×C4C22×C3111yescharacteristic
133C22×SD16C22×C3114yescomplemented
134C2×#121C22×C3113yes—
135C2×#120—21no—
136#448—224no—
137C2×#103C22×C31112yescomplemented
138C2×C22⋊C8C22×C3116yes—
139#386—23no—
140#380C22×C3113yes—
141C2×C31—212no—
142C2×C31—161no—
143C2×C31#284611yescharacteristic
144C2×C31C2×#44813yes—
145C2×C31#300413yes—
146C25D4×C3111yescharacteristic
147C22×Q8—2128no—
148C22×Q8—248no—
149C22×Q8—224no—
150C22×Q8—248no—
151C22×Q8—212no—
152C22×Q8—26no—
153C22×Q8D4×C31124yescomplemented
154C22×Q8C23×C3114yes—
155C22×D4—23no—
156C22×D4C23×C3111yescharacteristic
157C23×C4—224no—
158C23×C4—26no—
159C23×C4—212no—
160C23×C4D4×C3113yes—
161C23×C4C23×C3113yes—
162C2×SD16—224no—
163C22×C8C23×C3114yes—
164#121—212no—
165#120—44no—
166C2×C4⋊C4C23×C3113yes—
167C2×C22⋊C4—23no—
168C2×C22⋊C4—23no—
169#103—224no—
170C22⋊C8—212no—
171#95—23no—
172C31#3287911yescharacteristic, direct product factor, Sylow
173C24—26no—
174C24—26no—
175C24—21no—
176C24SD16×C3114yescomplemented
177C24C2×D4×C3113yes—
178C2×Q8—2192no—
179C2×Q8—296no—
180C2×Q8—248no—
181C2×Q8—296no—
182C2×Q8—224no—
183C2×Q8—212no—
184C2×Q8C2×D4×C31124yes—
185C2×D4—26no—
186C2×D4—46no—
187C2×D4—46no—
188C2×D4—46no—
189C22×C4—264no—
190C22×C4—248no—
191C22×C4—232no—
192C22×C4—224no—
193C22×C4—26no—
194C22×C4—24no—
195C22×C4—212no—
196C22×C4—212no—
197C22×C4—23no—
198C22×C4C2×D4×C3113yes—
199C22×C4C2×D4×C31112yes—
200C22×C4C24×C3111yescharacteristic
201SD16—416no—
202C2×C8—212no—
203C4⋊C4—26no—
204C22⋊C4—46no—
205C22⋊C4—46no—
206C23—28no—
207C23—224no—
208C23—224no—
209C23—26no—
210C23—26no—
211C23—43no—
212C23—41no—
213C23—43no—
214C23C31×#12016yes—
215C23C2×SD16×C3116yes—
216C23C31×#13716yes—
217C23C22×D4×C3111yescharacteristic
218Q8—296no—
219Q8—224no—
220Q8C31×#120116yescomplemented
221D4—44no—
222D4—812no—
223C2×C4—296no—
224C2×C4—224no—
225C2×C4—224no—
226C2×C4—26no—
227C2×C4—224no—
228C2×C4—43no—
229C2×C4—43no—
230C2×C4—43no—
231C2×C4C31×#12016yes—
232C2×C4C22×D4×C3116yes—
233C8—44no—
234C22—232no—
235C22—26no—
236C22—212no—
237C22—26no—
238C22—212no—
239C22—81no—
240C22—83no—
241C22—83no—
242C22C31×#448112yescomplemented
243C22C2×C31×#12013yes—
244C22C22×SD16×C3111yescharacteristic
245C22C2×C31×#13713yes—
246C4—216no—
247C4—26no—
248C4—83no—
249C4C2×C31×#12014yes—
250C2—212no—
251C2—161no—
252C2C31×#284611yescharacteristic
253C2C2×C31×#44813yes—
254C2C31×#300413yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C24×Q8×C31C2semidirect
2. C2×C31×#448C2semidirect
4. C31×#1787C2semidirect
5. C31×#1779C2semidirect
11. C22×SD16×C31C22semidirect
15. C2×C31×#103C22semidirect
26. C22×Q8×C31D4semidirect
48. C24×C31SD16semidirect
78. #32879C31direct (N × H)
93. Q8×C31#120semidirect
107. C24×Q8C2×C31semidirect
108. C2×#448C2×C31semidirect
110. #1787C2×C31semidirect
111. #1779C2×C31semidirect
120. C22×C31#448semidirect
133. C22×SD16C22×C31semidirect
137. C2×#103C22×C31semidirect
153. C22×Q8D4×C31semidirect
172. C31#32879direct (N × H)
176. C24SD16×C31semidirect
220. Q8C31×#120semidirect
242. C22C31×#448semidirect

Maximal subgroups

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

subgroupindex
C24×Q8×C312
C2×C31×#4482
C31×#28472
C31×#17872
C31×#17792
#3287931