Finite Group Databasebeta

← C31×#9426 #21466185

Subgroups — C31×#9426 #21466185

Order 7936.

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

normal subgroups only

This group has 422 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×#3139C211yesmaximal, characteristic
2C31×#2381C211yesmaximal, characteristic
3C31×#1558C211yesmaximal, characteristic
4C31×#1515C212yesmaximal
5C31×#1288C212yesmaximal
6C31×#533C2211yescharacteristic
7C2×C31×C4⋊Q8C2211yescharacteristic
8C31×#491—22no—
9C31×#487C414yescomplemented
10C31×#432C2212yes—
11C31×#419—22no—
12C4×M16×C31C2211yescharacteristic
13C31×#391—22no—
14C31×#387—24no—
15C31×#383C2212yes—
16C31×#333—22no—
17C31×#328—24no—
18C22×Q8×C31D412yes—
19C2×M16×C31—21no—
20C31×C4⋊Q8—22no—
21C31×C4⋊Q8C2×C412yes—
22C31×C4⋊Q8C2×C412yes—
23C31×C4⋊Q8D412yes—
24C31×#125—21no—
25C31×C22⋊Q8—22no—
26C4×Q8×C31—22no—
27C31×#117—21no—
28C2×C4⋊C4×C31—22no—
29C2×C4⋊C4×C31—22no—
30C2×C42×C31—22no—
31C2×C42×C31C2311yescharacteristic
32C31×C4⋊C8—22no—
33C31×#103—28no—
34C31×C22⋊C8—22no—
35C31×#97—21no—
36C31×#97—22no—
37C4×C8×C31C2×C412yes—
38C31×#95—24no—
39C31×#95—22no—
40C31×#95—22no—
41C31×#95D414yes—
42C2×Q8×C31—22no—
43C2×Q8×C31—22no—
44C2×Q8×C31—42no—
45C2×Q8×C31—42no—
46C2×Q8×C31C22⋊C414yes—
47C22×C4×C31—22no—
48C22×C4×C31—24no—
49C22×C4×C31C2×D411yescharacteristic
50C22×C4×C31C2×D412yes—
51M16×C31—42no—
52C2×C8×C31—22no—
53C2×C8×C31—42no—
54C4⋊C4×C31—24no—
55C4⋊C4×C31—24no—
56C4⋊C4×C31—22no—
57C4⋊C4×C31—22no—
58C4⋊C4×C31—42no—
59C4⋊C4×C31—82no—
60C22⋊C4×C31—41no—
61C42×C31—41no—
62C42×C31—82no—
63C42×C31C22×C411yescharacteristic
64C42×C31C2×D411yescharacteristic
65C42×C31#4112yes—
66#9426C3111yesmaximal, characteristic, direct product factor, Sylow
67C23×C31#12011yescharacteristic
68Q8×C31—44no—
69Q8×C31—82no—
70Q8×C31—82no—
71C2×C4×C31—22no—
72C2×C4×C31—24no—
73C2×C4×C31—42no—
74C2×C4×C31—42no—
75C2×C4×C31—42no—
76C2×C4×C31—48no—
77C2×C4×C31—42no—
78C2×C4×C31—44no—
79C2×C4×C31C2×C22⋊C411yescharacteristic
80C2×C4×C31C4×D412yes—
81C2×C4×C31#12112yes—
82C2×C4×C31#12311yescharacteristic
83C8×C31—42no—
84C8×C31—82no—
85#3139C2×C3111yescharacteristic
86#2381C2×C3111yescharacteristic
87#1558C2×C3111yescharacteristic
88#1515C2×C3112yes—
89#1288C2×C3112yes—
90C22×C31—22no—
91C22×C31#38611yescharacteristic
92C22×C31#45512yes—
93C4×C31—21no—
94C4×C31—21no—
95C4×C31—22no—
96C4×C31—22no—
97C4×C31—44no—
98C4×C31—84no—
99C4×C31—82no—
100#533C22×C3111yescharacteristic
101C2×C4⋊Q8C22×C3111yescharacteristic
102#491—22no—
103#487C4×C3114yescomplemented
104#432C22×C3112yes—
105#419—22no—
106C4×M16C22×C3111yescharacteristic
107#391—22no—
108#387—24no—
109#383C22×C3112yes—
110#333—22no—
111#328—24no—
112C2×C31—22no—
113C2×C31#188511yescharacteristic
114C2×C31#190512yes—
115C22×Q8D4×C3112yes—
116C2×M16—21no—
117C4⋊Q8—22no—
118C4⋊Q8C2×C4×C3112yes—
119C4⋊Q8C2×C4×C3112yes—
120C4⋊Q8D4×C3112yes—
121#125—21no—
122C22⋊Q8—22no—
123C4×Q8—22no—
124#117—21no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4—22no—
127C2×C42—22no—
128C2×C42C23×C3111yescharacteristic
129C4⋊C8—22no—
130#103—28no—
131C22⋊C8—22no—
132#97—21no—
133#97—22no—
134C4×C8C2×C4×C3112yes—
135#95—24no—
136#95—22no—
137#95—22no—
138#95D4×C3114yes—
139C31#942611yescharacteristic, direct product factor, Sylow
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8C22⋊C4×C3114yes—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4C2×D4×C3111yescharacteristic
148C22×C4C2×D4×C3112yes—
149M16—42no—
150C2×C8—22no—
151C2×C8—42no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—82no—
158C22⋊C4—41no—
159C42—41no—
160C42—82no—
161C42C22×C4×C3111yescharacteristic
162C42C2×D4×C3111yescharacteristic
163C42#41×C3112yes—
164C23C31×#12011yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—82no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—48no—
174C2×C4—44no—
175C2×C4—42no—
176C2×C4C2×C22⋊C4×C3111yescharacteristic
177C2×C4C4×D4×C3112yes—
178C2×C4C31×#12112yes—
179C2×C4C31×#12311yescharacteristic
180C8—42no—
181C8—82no—
182C22—22no—
183C22C31×#38611yescharacteristic
184C22C31×#45512yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—84no—
191C4—82no—
192C2—22no—
193C2C31×#188511yescharacteristic
194C2C31×#190512yes—
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
9. C31×#487C4semidirect
66. #9426C31direct (N × H)
103. #487C4×C31semidirect
139. C31#9426direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31392
C31×#23812
C31×#15582
C31×#15152
C31×#12882
#942631