Finite Group Databasebeta

← C31×#9428 #21466187

Subgroups — C31×#9428 #21466187

Order 7936.

620 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3151C211yesmaximal, characteristic
2C31×#2380C211yesmaximal, characteristic, complemented
3C31×#1555C211yesmaximal, characteristic, complemented
4C31×#1514C212yesmaximal, complemented
5C31×#1288C212yesmaximal, complemented
6C2×C31×AGL(1,ℤ/8)—22no—
7C31×#532C2211yescharacteristic
8C2×C31×#127C2211yescharacteristic
9C31×#496—22no—
10C31×#493C412yescomplemented
11C31×#492C412yescomplemented
12C31×#432C2212yes—
13C4×M16×C31C2211yescharacteristic
14C31×#386—22no—
15C31×#386—24no—
16C31×#383C2212yes—
17C31×#331—22no—
18C31×#327—24no—
19C2×#41×C31—21no—
20C22×D4×C31—22no—
21C22×D4×C31D412yes—
22C23×C4×C31—22no—
23C31×AGL(1,ℤ/8)—44no—
24C31×AGL(1,ℤ/8)—44no—
25C2×SD16×C31—24no—
26C2×D8×C31—24no—
27C2×M16×C31—21no—
28C31×C4⋊Q8C2×C411yescharacteristic, complemented
29C31×#127—22no—
30C31×#127C2×C412yes—
31C31×#127C2×C411yescharacteristic, complemented
32C31×#127D412yes—
33C31×#124—21no—
34C31×#121—22no—
35C4×D4×C31—22no—
36C2×C22⋊C4×C31—24no—
37C2×C22⋊C4×C31—22no—
38C2×C42×C31C2311yescharacteristic
39C31×C4⋊C8—22no—
40C31×C22⋊C8—22no—
41C31×#97—21no—
42C31×#97—22no—
43C4×C8×C31C2×C412yescomplemented
44C31×#95—22no—
45C31×#95—22no—
46C31×#95D414yes—
47C24×C31—22no—
48#41×C31—42no—
49#41×C31—42no—
50C2×Q8×C31—21no—
51C2×D4×C31—21no—
52C2×D4×C31—24no—
53C2×D4×C31—22no—
54C2×D4×C31—24no—
55C2×D4×C31—22no—
56C2×D4×C31—42no—
57C2×D4×C31—42no—
58C2×D4×C31—41no—
59C2×D4×C31—82no—
60C2×D4×C31—82no—
61C2×D4×C31C22⋊C414yes—
62C22×C4×C31—24no—
63C22×C4×C31—41no—
64C22×C4×C31—84no—
65C22×C4×C31—82no—
66C22×C4×C31C2×D411yescharacteristic
67C22×C4×C31C2×D412yes—
68SD16×C31—48no—
69D8×C31—48no—
70M16×C31—24no—
71C2×C8×C31—22no—
72C2×C8×C31—42no—
73C4⋊C4×C31—22no—
74C22⋊C4×C31—42no—
75C22⋊C4×C31—84no—
76C22⋊C4×C31—82no—
77C42×C31C22×C411yescharacteristic
78C42×C31C2×D411yescharacteristic
79C42×C31#4112yes—
80#9428C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31—24no—
82C23×C31—44no—
83C23×C31—44no—
84C23×C31—42no—
85C23×C31—42no—
86C23×C31—41no—
87C23×C31#12011yescharacteristic
88Q8×C31—42no—
89D4×C31—44no—
90D4×C31—42no—
91D4×C31—82no—
92D4×C31—84no—
93D4×C31—84no—
94D4×C31—82no—
95D4×C31—82no—
96C2×C4×C31—22no—
97C2×C4×C31—42no—
98C2×C4×C31—48no—
99C2×C4×C31—41no—
100C2×C4×C31—44no—
101C2×C4×C31—81no—
102C2×C4×C31—81no—
103C2×C4×C31—88no—
104C2×C4×C31C2×C22⋊C411yescharacteristic
105C2×C4×C31C4×D412yes—
106C2×C4×C31#12112yes—
107C2×C4×C31#12311yescharacteristic
108C8×C31—24no—
109C8×C31—82no—
110#3151C2×C3111yescharacteristic
111#2380C2×C3111yescharacteristic, complemented
112#1555C2×C3111yescharacteristic, complemented
113#1514C2×C3112yescomplemented
114#1288C2×C3112yescomplemented
115C22×C31—22no—
116C22×C31—44no—
117C22×C31—48no—
118C22×C31—82no—
119C22×C31—82no—
120C22×C31—84no—
121C22×C31—81no—
122C22×C31—82no—
123C22×C31#38611yescharacteristic
124C22×C31#45312yes—
125C4×C31—21no—
126C4×C31—21no—
127C4×C31—22no—
128C4×C31—22no—
129C4×C31—84no—
130C4×C31—81no—
131C2×AGL(1,ℤ/8)—22no—
132#532C22×C3111yescharacteristic
133C2×#127C22×C3111yescharacteristic
134#496—22no—
135#493C4×C3112yescomplemented
136#492C4×C3112yescomplemented
137#432C22×C3112yes—
138C4×M16C22×C3111yescharacteristic
139#386—22no—
140#386—24no—
141#383C22×C3112yes—
142#331—22no—
143#327—24no—
144C2×C31—22no—
145C2×C31—84no—
146C2×C31—161no—
147C2×C31#188711yescharacteristic
148C2×C31#190412yes—
149C2×#41—21no—
150C22×D4—22no—
151C22×D4D4×C3112yes—
152C23×C4—22no—
153AGL(1,ℤ/8)—44no—
154AGL(1,ℤ/8)—44no—
155C2×SD16—24no—
156C2×D8—24no—
157C2×M16—21no—
158C4⋊Q8C2×C4×C3111yescharacteristic, complemented
159#127—22no—
160#127C2×C4×C3112yes—
161#127C2×C4×C3111yescharacteristic, complemented
162#127D4×C3112yes—
163#124—21no—
164#121—22no—
165C4×D4—22no—
166C2×C22⋊C4—24no—
167C2×C22⋊C4—22no—
168C2×C42C23×C3111yescharacteristic
169C4⋊C8—22no—
170C22⋊C8—22no—
171#97—21no—
172#97—22no—
173C4×C8C2×C4×C3112yescomplemented
174#95—22no—
175#95—22no—
176#95D4×C3114yes—
177C31#942811yescharacteristic, direct product factor, Sylow
178C24—22no—
179#41—42no—
180#41—42no—
181C2×Q8—21no—
182C2×D4—21no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—24no—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—41no—
190C2×D4—82no—
191C2×D4—82no—
192C2×D4C22⋊C4×C3114yes—
193C22×C4—24no—
194C22×C4—41no—
195C22×C4—84no—
196C22×C4—82no—
197C22×C4C2×D4×C3111yescharacteristic
198C22×C4C2×D4×C3112yes—
199SD16—48no—
200D8—48no—
201M16—24no—
202C2×C8—22no—
203C2×C8—42no—
204C4⋊C4—22no—
205C22⋊C4—42no—
206C22⋊C4—84no—
207C22⋊C4—82no—
208C42C22×C4×C3111yescharacteristic
209C42C2×D4×C3111yescharacteristic
210C42#41×C3112yes—
211C23—24no—
212C23—44no—
213C23—44no—
214C23—42no—
215C23—42no—
216C23—41no—
217C23C31×#12011yescharacteristic
218Q8—42no—
219D4—44no—
220D4—42no—
221D4—82no—
222D4—84no—
223D4—84no—
224D4—82no—
225D4—82no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—48no—
229C2×C4—44no—
230C2×C4—41no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—88no—
234C2×C4C2×C22⋊C4×C3111yescharacteristic
235C2×C4C4×D4×C3112yes—
236C2×C4C31×#12112yes—
237C2×C4C31×#12311yescharacteristic
238C8—24no—
239C8—82no—
240C22—22no—
241C22—44no—
242C22—48no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—81no—
247C22—82no—
248C22C31×#38611yescharacteristic
249C22C31×#45312yes—
250C4—21no—
251C4—21no—
252C4—22no—
253C4—22no—
254C4—84no—
255C4—81no—
256C2—22no—
257C2—84no—
258C2—161no—
259C2C31×#188711yescharacteristic
260C2C31×#190412yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2380C2semidirect
3. C31×#1555C2semidirect
4. C31×#1514C2semidirect
5. C31×#1288C2semidirect
10. C31×#493C4semidirect
11. C31×#492C4semidirect
28. C31×C4⋊Q8C2×C4semidirect
31. C31×#127C2×C4semidirect
43. C4×C8×C31C2×C4semidirect
80. #9428C31direct (N × H)
111. #2380C2×C31semidirect
112. #1555C2×C31semidirect
113. #1514C2×C31semidirect
114. #1288C2×C31semidirect
135. #493C4×C31semidirect
136. #492C4×C31semidirect
158. C4⋊Q8C2×C4×C31semidirect
161. #127C2×C4×C31semidirect
173. C4×C8C2×C4×C31semidirect
177. C31#9428direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31512
C31×#23802
C31×#15552
C31×#15142
C31×#12882
#942831