Finite Group Databasebeta

← C31×#7283 #21464042

Subgroups — C31×#7283 #21464042

Order 7936.

402 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1955C211yesmaximal, characteristic
2C4×C31×#99C212yesmaximal
3C2×C4×D4×C31C2211yescharacteristic
4C2×C31×C4⋊C8C411yescharacteristic, complemented
5C2×C31×#99—22no—
6C2×C31×C22⋊C8—22no—
7C2×C31×#97C411yescharacteristic, complemented
8C4×C22⋊C4×C31—22no—
9C31×#342C414yescomplemented
10C22×D4×C31D411yescharacteristic
11C23×C4×C31D412yes—
12C22×C8×C31—21no—
13C22×C8×C31—21no—
14C4×D4×C31—41no—
15C4×D4×C31—41no—
16C2×C4⋊C4×C31Q811yescharacteristic
17C2×C22⋊C4×C31—24no—
18C2×C22⋊C4×C31C2×C412yes—
19C2×C42×C31—42no—
20C2×C42×C31C2×C411yescharacteristic
21C31×C4⋊C8—41no—
22C31×#99—28no—
23C31×C22⋊C8—44no—
24C31×#97—41no—
25C31×#95—42no—
26C24×C31C22⋊C412yes—
27C2×D4×C31—24no—
28C2×D4×C31—41no—
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31—42no—
32C22×C4×C31—42no—
33C22×C4×C31—44no—
34C22×C4×C31C4211yescharacteristic
35C22×C4×C31C22⋊C411yescharacteristic
36C22×C4×C31C4⋊C411yescharacteristic
37C22×C4×C31C4⋊C412yes—
38C2×C8×C31—22no—
39C2×C8×C31—41no—
40C2×C8×C31—41no—
41C2×C8×C31—42no—
42C2×C8×C31—41no—
43C4⋊C4×C31—41no—
44C22⋊C4×C31—28no—
45C22⋊C4×C31—42no—
46C22⋊C4×C31—44no—
47C42×C31—21no—
48C42×C31—21no—
49C42×C31—82no—
50C42×C31—82no—
51#7283C3111yesmaximal, characteristic, direct product factor, Sylow
52C23×C31—22no—
53C23×C31—22no—
54C23×C31—42no—
55C23×C31—42no—
56C23×C31#9511yescharacteristic
57C23×C31#10414yes—
58D4×C31—44no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—22no—
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—22no—
65C2×C4×C31—42no—
66C2×C4×C31—42no—
67C2×C4×C31—42no—
68C2×C4×C31—41no—
69C2×C4×C31—48no—
70C2×C4×C31—82no—
71C2×C4×C31—84no—
72C2×C4×C31—84no—
73C2×C4×C31#9911yescharacteristic
74C2×C4×C31#9911yescharacteristic
75C8×C31—42no—
76C8×C31—81no—
77#1955C2×C3111yescharacteristic
78C4×#99C2×C3112yes—
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—24no—
82C22×C31—44no—
83C22×C31—42no—
84C22×C31—42no—
85C22×C31—82no—
86C22×C31#33912yes—
87C22×C31#34211yescharacteristic
88C4×C31—21no—
89C4×C31—41no—
90C4×C31—41no—
91C4×C31—42no—
92C4×C31—88no—
93C4×C31#35311yescharacteristic
94C4×C31#35411yescharacteristic
95C2×C4×D4C22×C3111yescharacteristic
96C2×C4⋊C8C4×C3111yescharacteristic, complemented
97C2×#99—22no—
98C2×C22⋊C8—22no—
99C2×#97C4×C3111yescharacteristic, complemented
100C4×C22⋊C4—22no—
101#342C4×C3114yescomplemented
102C2×C31—22no—
103C2×C31—44no—
104C2×C31#129711yescharacteristic
105C2×C31#139111yescharacteristic
106C2×C31#139311yescharacteristic
107C22×D4D4×C3111yescharacteristic
108C23×C4D4×C3112yes—
109C22×C8—21no—
110C22×C8—21no—
111C4×D4—41no—
112C4×D4—41no—
113C2×C4⋊C4Q8×C3111yescharacteristic
114C2×C22⋊C4—24no—
115C2×C22⋊C4C2×C4×C3112yes—
116C2×C42—42no—
117C2×C42C2×C4×C3111yescharacteristic
118C4⋊C8—41no—
119#99—28no—
120C22⋊C8—44no—
121#97—41no—
122#95—42no—
123C31#728311yescharacteristic, direct product factor, Sylow
124C24C22⋊C4×C3112yes—
125C2×D4—24no—
126C2×D4—41no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4—44no—
132C22×C4C42×C3111yescharacteristic
133C22×C4C22⋊C4×C3111yescharacteristic
134C22×C4C4⋊C4×C3111yescharacteristic
135C22×C4C4⋊C4×C3112yes—
136C2×C8—22no—
137C2×C8—41no—
138C2×C8—41no—
139C2×C8—42no—
140C2×C8—41no—
141C4⋊C4—41no—
142C22⋊C4—28no—
143C22⋊C4—42no—
144C22⋊C4—44no—
145C42—21no—
146C42—21no—
147C42—82no—
148C42—82no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—42no—
153C23C31×#9511yescharacteristic
154C23C31×#10414yes—
155D4—44no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—48no—
167C2×C4—82no—
168C2×C4—84no—
169C2×C4—84no—
170C2×C4C31×#9911yescharacteristic
171C2×C4C31×#9911yescharacteristic
172C8—42no—
173C8—81no—
174C22—21no—
175C22—21no—
176C22—24no—
177C22—44no—
178C22—42no—
179C22—42no—
180C22—82no—
181C22C31×#33912yes—
182C22C31×#34211yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—42no—
187C4—88no—
188C4C31×#35311yescharacteristic
189C4C31×#35411yescharacteristic
190C2—22no—
191C2—44no—
192C2C31×#129711yescharacteristic
193C2C31×#139111yescharacteristic
194C2C31×#139311yescharacteristic
subgroupG/H
centerC2×C4×C31#99
commutatorC22×C4C42×C31
Frattini, cosocleC2×C4×D4C22×C31
socleC22×C31#342
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×C4⋊C8C4semidirect
7. C2×C31×#97C4semidirect
9. C31×#342C4semidirect
51. #7283C31direct (N × H)
96. C2×C4⋊C8C4×C31semidirect
99. C2×#97C4×C31semidirect
101. #342C4×C31semidirect
123. C31#7283direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#19552
C4×C31×#992
#728331