Finite Group Databasebeta

← C31×#9440 #21466199

Subgroups — C31×#9440 #21466199

Order 7936.

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

normal subgroups only

This group has 434 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×#3166C211yesmaximal, characteristic
2C31×#2371C211yesmaximal, characteristic
3C31×#1534C211yesmaximal, characteristic
4C31×#1506C212yesmaximal
5C31×#1300C212yesmaximal
6C31×#533C2211yescharacteristic
7C2×C31×#125C2211yescharacteristic
8C31×#501C414yescomplemented
9C31×#499—22no—
10C31×#432C2212yes—
11C31×#428—22no—
12C4×M16×C31C2211yescharacteristic
13C31×#387—22no—
14C31×#387—22no—
15C4×C4⋊C4×C31—22no—
16C31×#376C2212yes—
17C31×#330—22no—
18C31×#328—22no—
19C31×#328—22no—
20C2×M16×C31—21no—
21C31×C4⋊Q8C2×C412yes—
22C31×#125—21no—
23C31×#125—22no—
24C31×#125C2×C412yes—
25C31×#125D412yes—
26C31×C22⋊Q8—22no—
27C4×Q8×C31—22no—
28C31×#117—21no—
29C2×C4⋊C4×C31—22no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31D412yes—
32C2×C42×C31—22no—
33C2×C42×C31—22no—
34C2×C42×C31C2311yescharacteristic
35C31×#107—24no—
36C31×#106—24no—
37C31×C4⋊C8—22no—
38C31×C22⋊C8—22no—
39C31×#97—22no—
40C31×#97C2×C412yes—
41C4×C8×C31—21no—
42C31×#95—22no—
43C31×#95—22no—
44C31×#95—22no—
45C31×#95D412yes—
46C31×#95D412yes—
47C2×Q8×C31—22no—
48C22×C4×C31—22no—
49C22×C4×C31—22no—
50C22×C4×C31—22no—
51C22×C4×C31C2×D411yescharacteristic
52C22×C4×C31C2×D412yes—
53M16×C31—24no—
54C2×C8×C31—22no—
55C2×C8×C31—42no—
56C4⋊C4×C31—24no—
57C4⋊C4×C31—24no—
58C4⋊C4×C31—22no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—22no—
61C4⋊C4×C31—44no—
62C4⋊C4×C31—42no—
63C4⋊C4×C31C22⋊C414yes—
64C22⋊C4×C31—41no—
65C42×C31—44no—
66C42×C31—44no—
67C42×C31—41no—
68C42×C31C22×C411yescharacteristic
69C42×C31C2×D411yescharacteristic
70C42×C31#4112yes—
71#9440C3111yesmaximal, characteristic, direct product factor, Sylow
72C23×C31#12011yescharacteristic
73Q8×C31—82no—
74C2×C4×C31—22no—
75C2×C4×C31—24no—
76C2×C4×C31—24no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—42no—
80C2×C4×C31—42no—
81C2×C4×C31—42no—
82C2×C4×C31—42no—
83C2×C4×C31—42no—
84C2×C4×C31—42no—
85C2×C4×C31—42no—
86C2×C4×C31C2×C22⋊C411yescharacteristic
87C2×C4×C31C4×D412yes—
88C2×C4×C31#12112yes—
89C2×C4×C31#12311yescharacteristic
90C8×C31—24no—
91C8×C31—82no—
92#3166C2×C3111yescharacteristic
93#2371C2×C3111yescharacteristic
94#1534C2×C3111yescharacteristic
95#1506C2×C3112yes—
96#1300C2×C3112yes—
97C22×C31—22no—
98C22×C31#38611yescharacteristic
99C22×C31#45612yes—
100C4×C31—21no—
101C4×C31—21no—
102C4×C31—22no—
103C4×C31—22no—
104C4×C31—44no—
105C4×C31—44no—
106C4×C31—82no—
107C4×C31—82no—
108#533C22×C3111yescharacteristic
109C2×#125C22×C3111yescharacteristic
110#501C4×C3114yescomplemented
111#499—22no—
112#432C22×C3112yes—
113#428—22no—
114C4×M16C22×C3111yescharacteristic
115#387—22no—
116#387—22no—
117C4×C4⋊C4—22no—
118#376C22×C3112yes—
119#330—22no—
120#328—22no—
121#328—22no—
122C2×C31—22no—
123C2×C31#188611yescharacteristic
124C2×C31#190612yes—
125C2×M16—21no—
126C4⋊Q8C2×C4×C3112yes—
127#125—21no—
128#125—22no—
129#125C2×C4×C3112yes—
130#125D4×C3112yes—
131C22⋊Q8—22no—
132C4×Q8—22no—
133#117—21no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4D4×C3112yes—
137C2×C42—22no—
138C2×C42—22no—
139C2×C42C23×C3111yescharacteristic
140#107—24no—
141#106—24no—
142C4⋊C8—22no—
143C22⋊C8—22no—
144#97—22no—
145#97C2×C4×C3112yes—
146C4×C8—21no—
147#95—22no—
148#95—22no—
149#95—22no—
150#95D4×C3112yes—
151#95D4×C3112yes—
152C31#944011yescharacteristic, direct product factor, Sylow
153C2×Q8—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4C2×D4×C3111yescharacteristic
158C22×C4C2×D4×C3112yes—
159M16—24no—
160C2×C8—22no—
161C2×C8—42no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—44no—
168C4⋊C4—42no—
169C4⋊C4C22⋊C4×C3114yes—
170C22⋊C4—41no—
171C42—44no—
172C42—44no—
173C42—41no—
174C42C22×C4×C3111yescharacteristic
175C42C2×D4×C3111yescharacteristic
176C42#41×C3112yes—
177C23C31×#12011yescharacteristic
178Q8—82no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4C2×C22⋊C4×C3111yescharacteristic
192C2×C4C4×D4×C3112yes—
193C2×C4C31×#12112yes—
194C2×C4C31×#12311yescharacteristic
195C8—24no—
196C8—82no—
197C22—22no—
198C22C31×#38611yescharacteristic
199C22C31×#45612yes—
200C4—21no—
201C4—21no—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—44no—
206C4—82no—
207C4—82no—
208C2—22no—
209C2C31×#188611yescharacteristic
210C2C31×#190612yes—
subgroupG/H
center, socleC22×C31#386
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#120
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
8. C31×#501C4semidirect
71. #9440C31direct (N × H)
110. #501C4×C31semidirect
152. C31#9440direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31662
C31×#23712
C31×#15342
C31×#15062
C31×#13002
#944031