Finite Group Databasebeta

← C31×#7500 #21464259

Subgroups — C31×#7500 #21464259

Order 7936.

294 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 66 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×#2126C212yesmaximal
2C31×#1962C211yesmaximal, characteristic
3C31×#532C2211yescharacteristic
4C31×#423C411yescharacteristic, complemented
5C2×C31×#104—22no—
6C31×#410—22no—
7C43×C31C411yescharacteristic, complemented
8C31×#354C414yescomplemented
9C31×#353—22no—
10C2×#41×C31D412yes—
11C2×M16×C31—21no—
12C31×C4⋊Q8Q811yescharacteristic
13C31×#127D411yescharacteristic
14C31×#124C2×C412yes—
15C31×#121—41no—
16C4×D4×C31—41no—
17C31×#117—42no—
18C2×C42×C31—21no—
19C2×C42×C31—41no—
20C2×C42×C31C2×C411yescharacteristic
21C31×C4⋊C8—41no—
22C31×#104—44no—
23C31×#99—24no—
24C31×#99—42no—
25#41×C31—42no—
26#41×C31—42no—
27C2×Q8×C31C4⋊C412yes—
28C2×D4×C31—22no—
29C2×D4×C31—41no—
30C2×D4×C31C22⋊C412yes—
31C22×C4×C31—21no—
32C22×C4×C31—22no—
33C22×C4×C31—41no—
34C22×C4×C31C22⋊C411yescharacteristic
35M16×C31—42no—
36C2×C8×C31—41no—
37C4⋊C4×C31—41no—
38C4⋊C4×C31—82no—
39C22⋊C4×C31—42no—
40C22⋊C4×C31—44no—
41C42×C31—21no—
42C42×C31—22no—
43C42×C31—41no—
44C42×C31—44no—
45C42×C31—82no—
46C42×C31C4211yescharacteristic
47C42×C31C4⋊C411yescharacteristic
48#7500C3111yesmaximal, characteristic, direct product factor, Sylow
49C23×C31—22no—
50C23×C31#9911yescharacteristic
51Q8×C31—42no—
52D4×C31—42no—
53D4×C31—82no—
54D4×C31—82no—
55C2×C4×C31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—21no—
59C2×C4×C31—22no—
60C2×C4×C31—42no—
61C2×C4×C31—42no—
62C2×C4×C31—44no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31—84no—
66C2×C4×C31#9511yescharacteristic
67C2×C4×C31#9911yescharacteristic
68C8×C31—81no—
69#2126C2×C3112yes—
70#1962C2×C3111yescharacteristic
71C22×C31—21no—
72C22×C31—41no—
73C22×C31—42no—
74C22×C31—82no—
75C22×C31#34211yescharacteristic
76C4×C31—22no—
77C4×C31—21no—
78C4×C31—41no—
79C4×C31—44no—
80C4×C31—42no—
81C4×C31—164no—
82C4×C31#35311yescharacteristic
83C4×C31#35411yescharacteristic
84#532C22×C3111yescharacteristic
85#423C4×C3111yescharacteristic, complemented
86C2×#104—22no—
87#410—22no—
88C43C4×C3111yescharacteristic, complemented
89#354C4×C3114yescomplemented
90#353—22no—
91C2×C31—21no—
92C2×C31—41no—
93C2×C31—82no—
94C2×C31#139311yescharacteristic
95C2×#41D4×C3112yes—
96C2×M16—21no—
97C4⋊Q8Q8×C3111yescharacteristic
98#127D4×C3111yescharacteristic
99#124C2×C4×C3112yes—
100#121—41no—
101C4×D4—41no—
102#117—42no—
103C2×C42—21no—
104C2×C42—41no—
105C2×C42C2×C4×C3111yescharacteristic
106C4⋊C8—41no—
107#104—44no—
108#99—24no—
109#99—42no—
110C31#750011yescharacteristic, direct product factor, Sylow
111#41—42no—
112#41—42no—
113C2×Q8C4⋊C4×C3112yes—
114C2×D4—22no—
115C2×D4—41no—
116C2×D4C22⋊C4×C3112yes—
117C22×C4—21no—
118C22×C4—22no—
119C22×C4—41no—
120C22×C4C22⋊C4×C3111yescharacteristic
121M16—42no—
122C2×C8—41no—
123C4⋊C4—41no—
124C4⋊C4—82no—
125C22⋊C4—42no—
126C22⋊C4—44no—
127C42—21no—
128C42—22no—
129C42—41no—
130C42—44no—
131C42—82no—
132C42C42×C3111yescharacteristic
133C42C4⋊C4×C3111yescharacteristic
134C23—22no—
135C23C31×#9911yescharacteristic
136Q8—42no—
137D4—42no—
138D4—82no—
139D4—82no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—44no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—84no—
151C2×C4C31×#9511yescharacteristic
152C2×C4C31×#9911yescharacteristic
153C8—81no—
154C22—21no—
155C22—41no—
156C22—42no—
157C22—82no—
158C22C31×#34211yescharacteristic
159C4—22no—
160C4—21no—
161C4—41no—
162C4—44no—
163C4—42no—
164C4—164no—
165C4C31×#35311yescharacteristic
166C4C31×#35411yescharacteristic
167C2—21no—
168C2—41no—
169C2—82no—
170C2C31×#139311yescharacteristic
subgroupG/H
centerC4×C31#354
commutatorC42C42×C31
Frattini, cosocle#532C22×C31
socleC2×C31#1393
prime radicalC31×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#423C4semidirect
7. C43×C31C4semidirect
8. C31×#354C4semidirect
48. #7500C31direct (N × H)
85. #423C4×C31semidirect
88. C43C4×C31semidirect
89. #354C4×C31semidirect
110. C31#7500direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#21262
C31×#19622
#750031