Finite Group Databasebeta

← C31×#9391 #21466150

Subgroups — C31×#9391 #21466150

Order 7936.

538 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 154 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×#2972C211yesmaximal, characteristic
2C31×#2563C211yesmaximal, characteristic
3C31×#1800C211yesmaximal, characteristic
4C31×#1548C212yesmaximal, complemented
5C31×#1303C212yesmaximal, complemented
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C4×D4×C31C2211yescharacteristic
8C8×D4×C31—24no—
9C31×#431C2212yes—
10C31×#423C2212yes—
11C2×C31×#100—21no—
12C2×C31×C22⋊C8—22no—
13C31×#393C414yes—
14C31×#390—21no—
15C31×#382—21no—
16C31×#380—22no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#343—21no—
19C31×#333—24no—
20C22×Q8×C31C2×C412yes—
21C22×D4×C31D411yescharacteristic
22C23×C4×C31D412yes—
23C2×M16×C31—22no—
24C22×C8×C31—24no—
25C31×C4⋊Q8—22no—
26C31×C4⋊Q8—22no—
27C4×D4×C31—22no—
28C4×D4×C31—22no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—21no—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C22⋊C4×C31—24no—
34C2×C22⋊C4×C31C2×C412yes—
35C2×C42×C31—21no—
36C2×C42×C31C2311yescharacteristic
37C31×C4⋊C8—22no—
38C31×C4⋊C8—22no—
39C31×C4⋊C8D414yes—
40C31×#100—42no—
41C31×C22⋊C8—24no—
42C31×C22⋊C8—22no—
43C4×C8×C31—22no—
44C31×#95—24no—
45C31×#95C2×C412yes—
46C24×C31C22⋊C412yes—
47C2×Q8×C31—24no—
48C2×Q8×C31—82no—
49C2×D4×C31—22no—
50C2×D4×C31—22no—
51C2×D4×C31SD1612yes—
52C2×D4×C31Q1612yes—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—44no—
58C22×C4×C31C22⋊C412yes—
59C22×C4×C31C22×C411yescharacteristic
60C22×C4×C31C2×D411yescharacteristic
61C22×C4×C31C2×D411yescharacteristic
62M16×C31—42no—
63M16×C31—42no—
64C2×C8×C31—24no—
65C2×C8×C31—42no—
66C2×C8×C31—84no—
67C4⋊C4×C31—22no—
68C4⋊C4×C31—42no—
69C4⋊C4×C31—41no—
70C4⋊C4×C31—42no—
71C4⋊C4×C31—41no—
72C22⋊C4×C31—24no—
73C22⋊C4×C31—84no—
74C42×C31—42no—
75C42×C31C2×D412yes—
76C42×C31#4112yes—
77#9391C3111yesmaximal, characteristic, direct product factor, Sylow
78C23×C31—22no—
79C23×C31—22no—
80C23×C31—42no—
81C23×C31—42no—
82C23×C31#10314yes—
83C23×C31C2×C22⋊C411yescharacteristic
84Q8×C31—84no—
85D4×C31—24no—
86D4×C31—24no—
87C2×C4×C31—22no—
88C2×C4×C31—22no—
89C2×C4×C31—41no—
90C2×C4×C31—44no—
91C2×C4×C31—42no—
92C2×C4×C31—42no—
93C2×C4×C31—44no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—82no—
98C2×C4×C31C4×D412yes—
99C2×C4×C31#12011yescharacteristic
100C2×C4×C31#12112yes—
101C2×C4×C31#12311yescharacteristic
102C2×C4×C31C2×SD1611yescharacteristic
103C2×C4×C31C2×Q1611yescharacteristic
104C2×C4×C31#13512yes—
105C8×C31—44no—
106C8×C31—82no—
107#2972C2×C3111yescharacteristic
108#2563C2×C3111yescharacteristic
109#1800C2×C3111yescharacteristic
110#1548C2×C3112yescomplemented
111#1303C2×C3112yescomplemented
112C22×C31—21no—
113C22×C31—21no—
114C22×C31—24no—
115C22×C31—44no—
116C22×C31—42no—
117C22×C31—42no—
118C22×C31—82no—
119C22×C31#38611yescharacteristic
120C22×C31C2×#10311yescharacteristic
121C22×C31#41611yescharacteristic
122C4×C31—21no—
123C4×C31—22no—
124C4×C31—42no—
125C4×C31—82no—
126C4×C31—82no—
127C4×C31#45512yes—
128C4×C31#46512yes—
129C4×C31#46712yes—
130C2×C4⋊Q8C22×C3111yescharacteristic
131C2×C4×D4C22×C3111yescharacteristic
132C8×D4—24no—
133#431C22×C3112yes—
134#423C22×C3112yes—
135C2×#100—21no—
136C2×C22⋊C8—22no—
137#393C4×C3114yes—
138#390—21no—
139#382—21no—
140#380—22no—
141C4×C4⋊C4C22×C3111yescharacteristic
142#343—21no—
143#333—24no—
144C2×C31—21no—
145C2×C31—21no—
146C2×C31—44no—
147C2×C31#188511yescharacteristic
148C2×C31#189211yescharacteristic
149C2×C31#191411yescharacteristic
150C22×Q8C2×C4×C3112yes—
151C22×D4D4×C3111yescharacteristic
152C23×C4D4×C3112yes—
153C2×M16—22no—
154C22×C8—24no—
155C4⋊Q8—22no—
156C4⋊Q8—22no—
157C4×D4—22no—
158C4×D4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4D4×C3111yescharacteristic
163C2×C22⋊C4—24no—
164C2×C22⋊C4C2×C4×C3112yes—
165C2×C42—21no—
166C2×C42C23×C3111yescharacteristic
167C4⋊C8—22no—
168C4⋊C8—22no—
169C4⋊C8D4×C3114yes—
170#100—42no—
171C22⋊C8—24no—
172C22⋊C8—22no—
173C4×C8—22no—
174#95—24no—
175#95C2×C4×C3112yes—
176C31#939111yescharacteristic, direct product factor, Sylow
177C24C22⋊C4×C3112yes—
178C2×Q8—24no—
179C2×Q8—82no—
180C2×D4—22no—
181C2×D4—22no—
182C2×D4SD16×C3112yes—
183C2×D4Q16×C3112yes—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—44no—
189C22×C4C22⋊C4×C3112yes—
190C22×C4C22×C4×C3111yescharacteristic
191C22×C4C2×D4×C3111yescharacteristic
192C22×C4C2×D4×C3111yescharacteristic
193M16—42no—
194M16—42no—
195C2×C8—24no—
196C2×C8—42no—
197C2×C8—84no—
198C4⋊C4—22no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C22⋊C4—24no—
204C22⋊C4—84no—
205C42—42no—
206C42C2×D4×C3112yes—
207C42#41×C3112yes—
208C23—22no—
209C23—22no—
210C23—42no—
211C23—42no—
212C23C31×#10314yes—
213C23C2×C22⋊C4×C3111yescharacteristic
214Q8—84no—
215D4—24no—
216D4—24no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—44no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—44no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—82no—
228C2×C4C4×D4×C3112yes—
229C2×C4C31×#12011yescharacteristic
230C2×C4C31×#12112yes—
231C2×C4C31×#12311yescharacteristic
232C2×C4C2×SD16×C3111yescharacteristic
233C2×C4C2×Q16×C3111yescharacteristic
234C2×C4C31×#13512yes—
235C8—44no—
236C8—82no—
237C22—21no—
238C22—21no—
239C22—24no—
240C22—44no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22C31×#38611yescharacteristic
245C22C2×C31×#10311yescharacteristic
246C22C31×#41611yescharacteristic
247C4—21no—
248C4—22no—
249C4—42no—
250C4—82no—
251C4—82no—
252C4C31×#45512yes—
253C4C31×#46512yes—
254C4C31×#46712yes—
255C2—21no—
256C2—21no—
257C2—44no—
258C2C31×#188511yescharacteristic
259C2C31×#189211yescharacteristic
260C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1548C2semidirect
5. C31×#1303C2semidirect
77. #9391C31direct (N × H)
110. #1548C2×C31semidirect
111. #1303C2×C31semidirect
176. C31#9391direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29722
C31×#25632
C31×#18002
C31×#15482
C31×#13032
#939131