Finite Group Databasebeta

← C31×#10299 #21467058

Subgroups — C31×#10299 #21467058

Order 7936.

576 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3229C212yesmaximal
2C31×#2868C211yesmaximal, characteristic
3C31×#1994C211yesmaximal, characteristic
4C31×#1546C212yesmaximal
5C31×#1276C211yesmaximal, characteristic
6C31×#533C2211yescharacteristic
7C2×C31×C4⋊Q8—22no—
8C2×C31×C4⋊Q8C2212yes—
9C31×#498—22no—
10C31×#487—22no—
11C31×#483—24no—
12C31×#475—24no—
13C31×#431C2212yes—
14C31×#423C2211yescharacteristic
15C31×#384—24no—
16C43×C31C2211yescharacteristic
17C31×#339—22no—
18C31×#332—24no—
19C22×Q8×C31—22no—
20C2×M16×C31—21no—
21C31×C4⋊Q8—22no—
22C31×C4⋊Q8—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—22no—
25C31×C4⋊Q8—44no—
26C31×C4⋊Q8—44no—
27C31×C4⋊Q8D412yes—
28C31×#125—21no—
29C31×C22⋊Q8—22no—
30C4×Q8×C31—22no—
31C31×#117—21no—
32C2×C4⋊C4×C31—28no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31D414yes—
35C2×C42×C31—22no—
36C2×C42×C31D412yes—
37C2×C42×C31C2311yescharacteristic
38C31×#106—28no—
39C31×C4⋊C8—22no—
40C31×C4⋊C8D414yes—
41C31×#103—28no—
42C31×C22⋊C8—22no—
43C4×C8×C31—22no—
44C2×Q8×C31—22no—
45C2×Q8×C31—42no—
46C2×Q8×C31—42no—
47C2×Q8×C31—44no—
48C2×Q8×C31—44no—
49C22×C4×C31—22no—
50C22×C4×C31—24no—
51C22×C4×C31C2×D412yes—
52C22×C4×C31C2×D411yescharacteristic
53M16×C31—42no—
54C2×C8×C31—24no—
55C2×C8×C31—41no—
56C4⋊C4×C31—24no—
57C4⋊C4×C31—22no—
58C4⋊C4×C31—24no—
59C4⋊C4×C31—22no—
60C4⋊C4×C31—416no—
61C4⋊C4×C31—42no—
62C4⋊C4×C31—42no—
63C4⋊C4×C31—42no—
64C22⋊C4×C31—41no—
65C42×C31—28no—
66C42×C31—22no—
67C42×C31—41no—
68C42×C31SD1614yes—
69C42×C31C2×D411yescharacteristic
70C42×C31C2×D412yes—
71C42×C31#4111yescharacteristic
72#10299C3111yesmaximal, characteristic, direct product factor, Sylow
73C23×C31#12011yescharacteristic
74Q8×C31—44no—
75Q8×C31—84no—
76Q8×C31—82no—
77Q8×C31—82no—
78C2×C4×C31—28no—
79C2×C4×C31—24no—
80C2×C4×C31—24no—
81C2×C4×C31—42no—
82C2×C4×C31—44no—
83C2×C4×C31—48no—
84C2×C4×C31#12012yes—
85C2×C4×C31#12112yes—
86C2×C4×C31#12111yescharacteristic
87C2×C4×C31#12711yescharacteristic
88C2×C4×C31C2×SD1612yes—
89C2×C4×C31AGL(1,ℤ/8)12yes—
90C8×C31—44no—
91C8×C31—81no—
92#3229C2×C3112yes—
93#2868C2×C3111yescharacteristic
94#1994C2×C3111yescharacteristic
95#1546C2×C3112yes—
96#1276C2×C3111yescharacteristic
97C22×C31—22no—
98C22×C31#39211yescharacteristic
99C22×C31#45012yes—
100C4×C31—28no—
101C4×C31—22no—
102C4×C31—82no—
103C4×C31—84no—
104C4×C31#45614yes—
105C4×C31#46012yes—
106C4×C31#49211yescharacteristic
107C4×C31#49611yescharacteristic
108#533C22×C3111yescharacteristic
109C2×C4⋊Q8—22no—
110C2×C4⋊Q8C22×C3112yes—
111#498—22no—
112#487—22no—
113#483—24no—
114#475—24no—
115#431C22×C3112yes—
116#423C22×C3111yescharacteristic
117#384—24no—
118C43C22×C3111yescharacteristic
119#339—22no—
120#332—24no—
121C2×C31—22no—
122C2×C31#200512yes—
123C2×C31#201411yescharacteristic
124C22×Q8—22no—
125C2×M16—21no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—44no—
131C4⋊Q8—44no—
132C4⋊Q8D4×C3112yes—
133#125—21no—
134C22⋊Q8—22no—
135C4×Q8—22no—
136#117—21no—
137C2×C4⋊C4—28no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4D4×C3114yes—
140C2×C42—22no—
141C2×C42D4×C3112yes—
142C2×C42C23×C3111yescharacteristic
143#106—28no—
144C4⋊C8—22no—
145C4⋊C8D4×C3114yes—
146#103—28no—
147C22⋊C8—22no—
148C4×C8—22no—
149C31#1029911yescharacteristic, direct product factor, Sylow
150C2×Q8—22no—
151C2×Q8—42no—
152C2×Q8—42no—
153C2×Q8—44no—
154C2×Q8—44no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4C2×D4×C3112yes—
158C22×C4C2×D4×C3111yescharacteristic
159M16—42no—
160C2×C8—24no—
161C2×C8—41no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—24no—
165C4⋊C4—22no—
166C4⋊C4—416no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C22⋊C4—41no—
171C42—28no—
172C42—22no—
173C42—41no—
174C42SD16×C3114yes—
175C42C2×D4×C3111yescharacteristic
176C42C2×D4×C3112yes—
177C42#41×C3111yescharacteristic
178C23C31×#12011yescharacteristic
179Q8—44no—
180Q8—84no—
181Q8—82no—
182Q8—82no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—48no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4C31×#12012yes—
190C2×C4C31×#12112yes—
191C2×C4C31×#12111yescharacteristic
192C2×C4C31×#12711yescharacteristic
193C2×C4C2×SD16×C3112yes—
194C2×C4C31×AGL(1,ℤ/8)12yes—
195C8—44no—
196C8—81no—
197C22—22no—
198C22C31×#39211yescharacteristic
199C22C31×#45012yes—
200C4—28no—
201C4—22no—
202C4—82no—
203C4—84no—
204C4C31×#45614yes—
205C4C31×#46012yes—
206C4C31×#49211yescharacteristic
207C4C31×#49611yescharacteristic
208C2—22no—
209C2C31×#200512yes—
210C2C31×#201411yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
72. #10299C31direct (N × H)
149. C31#10299direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#32292
C31×#28682
C31×#19942
C31×#15462
C31×#12762
#1029931