Finite Group Databasebeta

← C31×#8719 #21465478

Subgroups — C31×#8719 #21465478

Order 7936.

554 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×C31×#382C211yesmaximal, characteristic
2C31×#1749C212yesmaximal
3C31×#1295C214yesmaximal, complemented
4C22×C4⋊C4×C31C412yes—
5C22×C42×C31C2211yescharacteristic
6C2×C31×C22⋊C8—22no—
7C2×C31×#97C2214yes—
8C31×#382—22no—
9C31×#382C412yes—
10C31×#382C2212yes—
11C2×C31×#95—22no—
12C31×#336—22no—
13C23×C4×C31—22no—
14C23×C4×C31C2×C411yescharacteristic
15C23×C4×C31D412yes—
16C22×C8×C31—24no—
17C2×C4⋊C4×C31—22no—
18C2×C4⋊C4×C31—44no—
19C2×C4⋊C4×C31C2×C414yes—
20C2×C42×C31—24no—
21C2×C42×C31C2×C411yescharacteristic
22C2×C42×C31D412yes—
23C2×C42×C31C2311yescharacteristic
24C31×C22⋊C8—28no—
25C31×#97—28no—
26C31×#95—24no—
27C31×#95—24no—
28C24×C31C22⋊C411yescharacteristic
29C22×C4×C31—22no—
30C22×C4×C31—22no—
31C22×C4×C31—22no—
32C22×C4×C31—24no—
33C22×C4×C31—24no—
34C22×C4×C31—24no—
35C22×C4×C31—42no—
36C22×C4×C31—44no—
37C22×C4×C31—44no—
38C22×C4×C31—44no—
39C22×C4×C31C22⋊C412yes—
40C22×C4×C31C22⋊C411yescharacteristic
41C22×C4×C31C22×C411yescharacteristic
42C22×C4×C31C2×D412yes—
43C2×C8×C31—28no—
44C2×C8×C31—44no—
45C2×C8×C31—44no—
46C4⋊C4×C31—44no—
47C4⋊C4×C31—44no—
48C42×C31—22no—
49C42×C31—24no—
50C42×C31#4114yes—
51#8719C3111yesmaximal, characteristic, direct product factor, Sylow
52C23×C31—21no—
53C23×C31—21no—
54C23×C31—22no—
55C23×C31#10112yes—
56C23×C31#10414yes—
57C23×C31C2×C22⋊C411yescharacteristic
58C2×C4×C31—28no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—21no—
63C2×C4×C31—22no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—48no—
69C2×C4×C31—44no—
70C2×C4×C31—44no—
71C2×C4×C31—44no—
72C2×C4×C31—88no—
73C2×C4×C31#10012yes—
74C2×C4×C31#11712yes—
75C2×C4×C31#12314yes—
76C8×C31—48no—
77C2×#382C2×C3111yescharacteristic
78#1749C2×C3112yes—
79#1295C2×C3114yescomplemented
80C22×C31—22no—
81C22×C31—24no—
82C22×C31—24no—
83C22×C31—22no—
84C22×C31#33014yes—
85C22×C31#38111yescharacteristic
86C22×C31C2×#10011yescharacteristic
87C22×C31C2×#10111yescharacteristic
88C22×C31C2×#10412yes—
89C22×C31#42112yes—
90C4×C31—22no—
91C4×C31—22no—
92C4×C31—24no—
93C4×C31—42no—
94C4×C31—84no—
95C22×C4⋊C4C4×C3112yes—
96C22×C42C22×C3111yescharacteristic
97C2×C22⋊C8—22no—
98C2×#97C22×C3114yes—
99#382—22no—
100#382C4×C3112yes—
101#382C22×C3112yes—
102C2×#95—22no—
103#336—22no—
104C2×C31—24no—
105C2×C31C2×#33011yescharacteristic
106C2×C31#152712yes—
107C2×C31#153411yescharacteristic
108C2×C31#182111yescharacteristic
109C2×C31#182612yes—
110C23×C4—22no—
111C23×C4C2×C4×C3111yescharacteristic
112C23×C4D4×C3112yes—
113C22×C8—24no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—44no—
116C2×C4⋊C4C2×C4×C3114yes—
117C2×C42—24no—
118C2×C42C2×C4×C3111yescharacteristic
119C2×C42D4×C3112yes—
120C2×C42C23×C3111yescharacteristic
121C22⋊C8—28no—
122#97—28no—
123#95—24no—
124#95—24no—
125C31#871911yescharacteristic, direct product factor, Sylow
126C24C22⋊C4×C3111yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—24no—
131C22×C4—24no—
132C22×C4—24no—
133C22×C4—42no—
134C22×C4—44no—
135C22×C4—44no—
136C22×C4—44no—
137C22×C4C22⋊C4×C3112yes—
138C22×C4C22⋊C4×C3111yescharacteristic
139C22×C4C22×C4×C3111yescharacteristic
140C22×C4C2×D4×C3112yes—
141C2×C8—28no—
142C2×C8—44no—
143C2×C8—44no—
144C4⋊C4—44no—
145C4⋊C4—44no—
146C42—22no—
147C42—24no—
148C42#41×C3114yes—
149C23—21no—
150C23—22no—
151C23—21no—
152C23C31×#10112yes—
153C23C31×#10414yes—
154C23C2×C22⋊C4×C3111yescharacteristic
155C2×C4—28no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—48no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4—88no—
170C2×C4C31×#10012yes—
171C2×C4C31×#11712yes—
172C2×C4C31×#12314yes—
173C8—48no—
174C22—22no—
175C22—24no—
176C22—24no—
177C22—22no—
178C22C31×#33014yes—
179C22C31×#38111yescharacteristic
180C22C2×C31×#10011yescharacteristic
181C22C2×C31×#10111yescharacteristic
182C22C2×C31×#10412yes—
183C22C31×#42112yes—
184C4—22no—
185C4—22no—
186C4—24no—
187C4—42no—
188C4—84no—
189C2—24no—
190C2C2×C31×#33011yescharacteristic
191C2C31×#152712yes—
192C2C31×#153411yescharacteristic
193C2C31×#182111yescharacteristic
194C2C31×#182612yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC24×C31C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C31×#1295C2semidirect
51. #8719C31direct (N × H)
79. #1295C2×C31semidirect
125. C31#8719direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3822
C31×#17492
C31×#12952
#871931