Finite Group Databasebeta

← C31×#9429 #21466188

Subgroups — C31×#9429 #21466188

Order 7936.

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

normal subgroups only

This group has 508 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×#3152C211yesmaximal, characteristic
2C31×#2381C211yesmaximal, characteristic, complemented
3C31×#1558C211yesmaximal, characteristic, complemented
4C31×#1514C212yesmaximal
5C31×#1288C212yesmaximal, complemented
6C2×C31×#137—22no—
7C31×#532C2211yescharacteristic
8C2×C31×C4⋊Q8C2211yescharacteristic
9C31×#497—22no—
10C31×#494C412yescomplemented
11C31×#492C412yescomplemented
12C31×#432C2212yes—
13C4×M16×C31C2211yescharacteristic
14C31×#391—22no—
15C31×#387—24no—
16C31×#383C2212yes—
17C31×#333—22no—
18C31×#327—24no—
19C2×#41×C31—21no—
20C22×Q8×C31D412yes—
21C31×#137—44no—
22C31×#137—44no—
23C2×Q16×C31—24no—
24C2×SD16×C31—24no—
25C2×M16×C31—21no—
26C31×C4⋊Q8—22no—
27C31×C4⋊Q8C2×C411yescharacteristic
28C31×C4⋊Q8C2×C412yes—
29C31×C4⋊Q8D412yes—
30C31×#127C2×C411yescharacteristic
31C31×#124—21no—
32C31×#121—22no—
33C4×D4×C31—22no—
34C2×C4⋊C4×C31—22no—
35C2×C4⋊C4×C31—22no—
36C2×C42×C31—22no—
37C2×C42×C31C2311yescharacteristic
38C31×C4⋊C8—22no—
39C31×C22⋊C8—22no—
40C31×#97—21no—
41C31×#97—22no—
42C4×C8×C31C2×C412yes—
43C31×#95—24no—
44C31×#95—22no—
45C31×#95—22no—
46C31×#95D414yes—
47#41×C31—42no—
48#41×C31—42no—
49C2×Q8×C31—22no—
50C2×Q8×C31—21no—
51C2×Q8×C31—42no—
52C2×Q8×C31—42no—
53C2×Q8×C31C22⋊C414yes—
54C2×D4×C31—21no—
55C2×D4×C31—22no—
56C2×D4×C31—41no—
57C22×C4×C31—22no—
58C22×C4×C31—24no—
59C22×C4×C31—41no—
60C22×C4×C31C2×D411yescharacteristic
61C22×C4×C31C2×D412yes—
62Q16×C31—48no—
63SD16×C31—48no—
64M16×C31—24no—
65C2×C8×C31—22no—
66C2×C8×C31—42no—
67C4⋊C4×C31—24no—
68C4⋊C4×C31—24no—
69C4⋊C4×C31—22no—
70C4⋊C4×C31—82no—
71C22⋊C4×C31—42no—
72C42×C31—82no—
73C42×C31C22×C411yescharacteristic
74C42×C31C2×D411yescharacteristic
75C42×C31#4112yes—
76#9429C3111yesmaximal, characteristic, direct product factor, Sylow
77C23×C31—41no—
78C23×C31#12011yescharacteristic
79Q8×C31—44no—
80Q8×C31—42no—
81Q8×C31—82no—
82D4×C31—42no—
83D4×C31—82no—
84D4×C31—82no—
85C2×C4×C31—22no—
86C2×C4×C31—24no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—42no—
90C2×C4×C31—48no—
91C2×C4×C31—41no—
92C2×C4×C31—44no—
93C2×C4×C31—81no—
94C2×C4×C31—81no—
95C2×C4×C31C2×C22⋊C411yescharacteristic
96C2×C4×C31C4×D412yes—
97C2×C4×C31#12112yes—
98C2×C4×C31#12311yescharacteristic
99C8×C31—24no—
100C8×C31—82no—
101#3152C2×C3111yescharacteristic
102#2381C2×C3111yescharacteristic, complemented
103#1558C2×C3111yescharacteristic, complemented
104#1514C2×C3112yes—
105#1288C2×C3112yescomplemented
106C22×C31—22no—
107C22×C31—81no—
108C22×C31—82no—
109C22×C31#38611yescharacteristic
110C22×C31#45312yes—
111C4×C31—21no—
112C4×C31—21no—
113C4×C31—22no—
114C4×C31—22no—
115C4×C31—44no—
116C4×C31—84no—
117C4×C31—81no—
118C2×#137—22no—
119#532C22×C3111yescharacteristic
120C2×C4⋊Q8C22×C3111yescharacteristic
121#497—22no—
122#494C4×C3112yescomplemented
123#492C4×C3112yescomplemented
124#432C22×C3112yes—
125C4×M16C22×C3111yescharacteristic
126#391—22no—
127#387—24no—
128#383C22×C3112yes—
129#333—22no—
130#327—24no—
131C2×C31—22no—
132C2×C31—161no—
133C2×C31#188711yescharacteristic
134C2×C31#190512yes—
135C2×#41—21no—
136C22×Q8D4×C3112yes—
137#137—44no—
138#137—44no—
139C2×Q16—24no—
140C2×SD16—24no—
141C2×M16—21no—
142C4⋊Q8—22no—
143C4⋊Q8C2×C4×C3111yescharacteristic
144C4⋊Q8C2×C4×C3112yes—
145C4⋊Q8D4×C3112yes—
146#127C2×C4×C3111yescharacteristic
147#124—21no—
148#121—22no—
149C4×D4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C42—22no—
153C2×C42C23×C3111yescharacteristic
154C4⋊C8—22no—
155C22⋊C8—22no—
156#97—21no—
157#97—22no—
158C4×C8C2×C4×C3112yes—
159#95—24no—
160#95—22no—
161#95—22no—
162#95D4×C3114yes—
163C31#942911yescharacteristic, direct product factor, Sylow
164#41—42no—
165#41—42no—
166C2×Q8—22no—
167C2×Q8—21no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8C22⋊C4×C3114yes—
171C2×D4—21no—
172C2×D4—22no—
173C2×D4—41no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—41no—
177C22×C4C2×D4×C3111yescharacteristic
178C22×C4C2×D4×C3112yes—
179Q16—48no—
180SD16—48no—
181M16—24no—
182C2×C8—22no—
183C2×C8—42no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—82no—
188C22⋊C4—42no—
189C42—82no—
190C42C22×C4×C3111yescharacteristic
191C42C2×D4×C3111yescharacteristic
192C42#41×C3112yes—
193C23—41no—
194C23C31×#12011yescharacteristic
195Q8—44no—
196Q8—42no—
197Q8—82no—
198D4—42no—
199D4—82no—
200D4—82no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—48no—
207C2×C4—44no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4C2×C22⋊C4×C3111yescharacteristic
212C2×C4C4×D4×C3112yes—
213C2×C4C31×#12112yes—
214C2×C4C31×#12311yescharacteristic
215C8—24no—
216C8—82no—
217C22—22no—
218C22—81no—
219C22—82no—
220C22C31×#38611yescharacteristic
221C22C31×#45312yes—
222C4—21no—
223C4—21no—
224C4—22no—
225C4—22no—
226C4—44no—
227C4—84no—
228C4—81no—
229C2—22no—
230C2—161no—
231C2C31×#188711yescharacteristic
232C2C31×#190512yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#532C22
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×#2381C2semidirect
3. C31×#1558C2semidirect
5. C31×#1288C2semidirect
10. C31×#494C4semidirect
11. C31×#492C4semidirect
76. #9429C31direct (N × H)
102. #2381C2×C31semidirect
103. #1558C2×C31semidirect
105. #1288C2×C31semidirect
122. #494C4×C31semidirect
123. #492C4×C31semidirect
163. C31#9429direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31522
C31×#23812
C31×#15582
C31×#15142
C31×#12882
#942931