Finite Group Databasebeta

← C31×#7339 #21464098

Subgroups — C31×#7339 #21464098

Order 7936.

356 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 46 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×#1782C211yesmaximal, characteristic
2C31×#1317C212yesmaximal, complemented
3C22×#41×C31C411yescharacteristic
4C2×C31×#99—22no—
5C31×#381C411yescharacteristic
6C31×#381C2211yescharacteristic
7C31×#323—22no—
8C2×#41×C31—41no—
9C2×#41×C31—41no—
10C2×#41×C31—44no—
11C22×Q8×C31C811yescharacteristic, complemented
12C22×D4×C31—21no—
13C22×D4×C31C811yescharacteristic, complemented
14C23×C4×C31—21no—
15C23×C4×C31C2×C411yescharacteristic
16C2×C22⋊C4×C31—21no—
17C2×C22⋊C4×C31D412yes—
18C31×#99—44no—
19C31×C22⋊C8—42no—
20C31×#95—41no—
21C31×#95—41no—
22C24×C31—21no—
23C24×C31C22⋊C411yescharacteristic
24#41×C31—44no—
25#41×C31—44no—
26#41×C31—44no—
27#41×C31—44no—
28C2×Q8×C31—42no—
29C2×Q8×C31—41no—
30C2×D4×C31—24no—
31C2×D4×C31—41no—
32C2×D4×C31—42no—
33C2×D4×C31—41no—
34C2×D4×C31—41no—
35C2×D4×C31—42no—
36C22×C4×C31—21no—
37C22×C4×C31—21no—
38C22×C4×C31—21no—
39C22×C4×C31—22no—
40C22×C4×C31—42no—
41C22×C4×C31—42no—
42C22×C4×C31—42no—
43C22×C4×C31—42no—
44C22×C4×C31—41no—
45C22×C4×C31C2×C811yescharacteristic
46C22×C4×C31M1611yescharacteristic
47C2×C8×C31—82no—
48C22⋊C4×C31—42no—
49C22⋊C4×C31—42no—
50#7339C3111yesmaximal, characteristic, direct product factor, Sylow
51C23×C31—22no—
52C23×C31—22no—
53C23×C31—41no—
54C23×C31—41no—
55C23×C31—81no—
56C23×C31—82no—
57C23×C31C22⋊C811yescharacteristic
58C23×C31#9911yescharacteristic
59C23×C31#10011yescharacteristic
60Q8×C31—42no—
61Q8×C31—42no—
62D4×C31—44no—
63D4×C31—42no—
64D4×C31—42no—
65D4×C31—44no—
66C2×C4×C31—22no—
67C2×C4×C31—21no—
68C2×C4×C31—21no—
69C2×C4×C31—41no—
70C2×C4×C31—42no—
71C2×C4×C31—48no—
72C2×C4×C31—41no—
73C2×C4×C31—42no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31—42no—
77C2×C4×C31—82no—
78C2×C4×C31—81no—
79C2×C4×C31—82no—
80C8×C31—162no—
81#1782C2×C3111yescharacteristic
82#1317C2×C3112yescomplemented
83C22×C31—21no—
84C22×C31—21no—
85C22×C31—41no—
86C22×C31—41no—
87C22×C31—41no—
88C22×C31—42no—
89C22×C31—82no—
90C22×C31—82no—
91C22×C31—82no—
92C22×C31—82no—
93C22×C31#32311yescharacteristic
94C22×C31AΣL(1,𝔽16)12yes—
95C4×C31—41no—
96C4×C31—42no—
97C4×C31—41no—
98C4×C31—82no—
99C4×C31—161no—
100C22×#41C4×C3111yescharacteristic
101C2×#99—22no—
102#381C4×C3111yescharacteristic
103#381C22×C3111yescharacteristic
104#323—22no—
105C2×C31—22no—
106C2×C31—21no—
107C2×C31—41no—
108C2×C31—41no—
109C2×C31—82no—
110C2×C31#131611yescharacteristic
111C2×#41—41no—
112C2×#41—41no—
113C2×#41—44no—
114C22×Q8C8×C3111yescharacteristic, complemented
115C22×D4—21no—
116C22×D4C8×C3111yescharacteristic, complemented
117C23×C4—21no—
118C23×C4C2×C4×C3111yescharacteristic
119C2×C22⋊C4—21no—
120C2×C22⋊C4D4×C3112yes—
121#99—44no—
122C22⋊C8—42no—
123#95—41no—
124#95—41no—
125C31#733911yescharacteristic, direct product factor, Sylow
126C24—21no—
127C24C22⋊C4×C3111yescharacteristic
128#41—44no—
129#41—44no—
130#41—44no—
131#41—44no—
132C2×Q8—42no—
133C2×Q8—41no—
134C2×D4—24no—
135C2×D4—41no—
136C2×D4—42no—
137C2×D4—41no—
138C2×D4—41no—
139C2×D4—42no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4C2×C8×C3111yescharacteristic
150C22×C4M16×C3111yescharacteristic
151C2×C8—82no—
152C22⋊C4—42no—
153C22⋊C4—42no—
154C23—22no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—81no—
159C23—82no—
160C23C31×C22⋊C811yescharacteristic
161C23C31×#9911yescharacteristic
162C23C31×#10011yescharacteristic
163Q8—42no—
164Q8—42no—
165D4—44no—
166D4—42no—
167D4—42no—
168D4—44no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—48no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—42no—
180C2×C4—82no—
181C2×C4—81no—
182C2×C4—82no—
183C8—162no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22C31×#32311yescharacteristic
195C22C31×AΣL(1,𝔽16)12yes—
196C4—41no—
197C4—42no—
198C4—41no—
199C4—82no—
200C4—161no—
201C2—22no—
202C2—21no—
203C2—41no—
204C2—41no—
205C2—82no—
206C2C31×#131611yescharacteristic
subgroupG/H
center, socleC2×C31#1316
commutatorC22×C4C2×C8×C31
Frattini, cosocle#381C22×C31
prime radicalC22×#41×C31C4
LCSG ▷ C22×C4 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C31 ◁ C23×C31 ◁ C24×C31 ◁ C31×#381 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1317C2semidirect
11. C22×Q8×C31C8semidirect
13. C22×D4×C31C8semidirect
50. #7339C31direct (N × H)
82. #1317C2×C31semidirect
114. C22×Q8C8×C31semidirect
116. C22×D4C8×C31semidirect
125. C31#7339direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#17822
C31×#13172
#733931