Finite Group Databasebeta

← C31×#9392 #21466151

Subgroups — C31×#9392 #21466151

Order 7936.

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

normal subgroups only

This group has 486 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×#2982C211yesmaximal, characteristic
2C31×#2567C211yesmaximal, characteristic
3C31×#1801C211yesmaximal, characteristic
4C31×#1548C212yesmaximal
5C31×#1303C212yesmaximal
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C4×Q8×C31C2211yescharacteristic
8C8×Q8×C31—24no—
9C31×#431—22no—
10C31×#431C2212yes—
11C31×#423C2212yes—
12C2×C31×#101—21no—
13C31×#395C414yes—
14C31×#391—21no—
15C31×#389—22no—
16C31×#384—21no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#343—21no—
19C31×#333—24no—
20C22×Q8×C31C2×C412yes—
21C22×Q8×C31D411yescharacteristic
22C2×M16×C31—22no—
23C31×C4⋊Q8—22no—
24C31×C4⋊Q8—22no—
25C4×Q8×C31—22no—
26C4×Q8×C31—22no—
27C2×C4⋊C4×C31—21no—
28C2×C4⋊C4×C31—21no—
29C2×C4⋊C4×C31—21no—
30C2×C4⋊C4×C31—24no—
31C2×C4⋊C4×C31C2×C412yes—
32C2×C4⋊C4×C31D411yescharacteristic
33C2×C42×C31—21no—
34C2×C42×C31D412yes—
35C2×C42×C31C2311yescharacteristic
36C31×C4⋊C8—24no—
37C31×C4⋊C8—22no—
38C31×C4⋊C8—22no—
39C31×C4⋊C8D414yes—
40C31×#101—42no—
41C31×C22⋊C8—22no—
42C4×C8×C31—24no—
43C4×C8×C31—22no—
44C31×#95—24no—
45C31×#95C2×C412yes—
46C2×Q8×C31—22no—
47C2×Q8×C31—22no—
48C2×Q8×C31—24no—
49C2×Q8×C31—82no—
50C2×Q8×C31SD1612yes—
51C2×Q8×C31Q1612yes—
52C22×C4×C31—22no—
53C22×C4×C31—22no—
54C22×C4×C31C22⋊C412yes—
55C22×C4×C31C22⋊C412yes—
56C22×C4×C31C22×C411yescharacteristic
57C22×C4×C31C2×D411yescharacteristic
58C22×C4×C31C2×D411yescharacteristic
59M16×C31—42no—
60M16×C31—42no—
61C2×C8×C31—24no—
62C2×C8×C31—42no—
63C4⋊C4×C31—24no—
64C4⋊C4×C31—24no—
65C4⋊C4×C31—22no—
66C4⋊C4×C31—41no—
67C4⋊C4×C31—42no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—84no—
70C42×C31—22no—
71C42×C31—22no—
72C42×C31—42no—
73C42×C31C2×D412yes—
74C42×C31#4112yes—
75#9392C3111yesmaximal, characteristic, direct product factor, Sylow
76C23×C31C2×C22⋊C411yescharacteristic
77Q8×C31—24no—
78Q8×C31—24no—
79Q8×C31—84no—
80C2×C4×C31—22no—
81C2×C4×C31—22no—
82C2×C4×C31—22no—
83C2×C4×C31—24no—
84C2×C4×C31—22no—
85C2×C4×C31—41no—
86C2×C4×C31—42no—
87C2×C4×C31—42no—
88C2×C4×C31—42no—
89C2×C4×C31—44no—
90C2×C4×C31—42no—
91C2×C4×C31#10314yes—
92C2×C4×C31C4×D412yes—
93C2×C4×C31#12011yescharacteristic
94C2×C4×C31#12112yes—
95C2×C4×C31#12311yescharacteristic
96C2×C4×C31C2×SD1611yescharacteristic
97C2×C4×C31C2×Q1611yescharacteristic
98C2×C4×C31#13512yes—
99C8×C31—44no—
100C8×C31—82no—
101#2982C2×C3111yescharacteristic
102#2567C2×C3111yescharacteristic
103#1801C2×C3111yescharacteristic
104#1548C2×C3112yes—
105#1303C2×C3112yes—
106C22×C31—21no—
107C22×C31—21no—
108C22×C31#38611yescharacteristic
109C22×C31C2×#10311yescharacteristic
110C22×C31#41611yescharacteristic
111C4×C31—21no—
112C4×C31—24no—
113C4×C31—22no—
114C4×C31—44no—
115C4×C31—42no—
116C4×C31—82no—
117C4×C31#45612yes—
118C4×C31#46512yes—
119C4×C31#46712yes—
120C2×C4⋊Q8C22×C3111yescharacteristic
121C2×C4×Q8C22×C3111yescharacteristic
122C8×Q8—24no—
123#431—22no—
124#431C22×C3112yes—
125#423C22×C3112yes—
126C2×#101—21no—
127#395C4×C3114yes—
128#391—21no—
129#389—22no—
130#384—21no—
131C4×C4⋊C4C22×C3111yescharacteristic
132#343—21no—
133#333—24no—
134C2×C31—21no—
135C2×C31—21no—
136C2×C31#188611yescharacteristic
137C2×C31#189211yescharacteristic
138C2×C31#191411yescharacteristic
139C22×Q8C2×C4×C3112yes—
140C22×Q8D4×C3111yescharacteristic
141C2×M16—22no—
142C4⋊Q8—22no—
143C4⋊Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—24no—
150C2×C4⋊C4C2×C4×C3112yes—
151C2×C4⋊C4D4×C3111yescharacteristic
152C2×C42—21no—
153C2×C42D4×C3112yes—
154C2×C42C23×C3111yescharacteristic
155C4⋊C8—24no—
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8D4×C3114yes—
159#101—42no—
160C22⋊C8—22no—
161C4×C8—24no—
162C4×C8—22no—
163#95—24no—
164#95C2×C4×C3112yes—
165C31#939211yescharacteristic, direct product factor, Sylow
166C2×Q8—22no—
167C2×Q8—22no—
168C2×Q8—24no—
169C2×Q8—82no—
170C2×Q8SD16×C3112yes—
171C2×Q8Q16×C3112yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4C22⋊C4×C3112yes—
175C22×C4C22⋊C4×C3112yes—
176C22×C4C22×C4×C3111yescharacteristic
177C22×C4C2×D4×C3111yescharacteristic
178C22×C4C2×D4×C3111yescharacteristic
179M16—42no—
180M16—42no—
181C2×C8—24no—
182C2×C8—42no—
183C4⋊C4—24no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—41no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—84no—
190C42—22no—
191C42—22no—
192C42—42no—
193C42C2×D4×C3112yes—
194C42#41×C3112yes—
195C23C2×C22⋊C4×C3111yescharacteristic
196Q8—24no—
197Q8—24no—
198Q8—84no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4C31×#10314yes—
211C2×C4C4×D4×C3112yes—
212C2×C4C31×#12011yescharacteristic
213C2×C4C31×#12112yes—
214C2×C4C31×#12311yescharacteristic
215C2×C4C2×SD16×C3111yescharacteristic
216C2×C4C2×Q16×C3111yescharacteristic
217C2×C4C31×#13512yes—
218C8—44no—
219C8—82no—
220C22—21no—
221C22—21no—
222C22C31×#38611yescharacteristic
223C22C2×C31×#10311yescharacteristic
224C22C31×#41611yescharacteristic
225C4—21no—
226C4—24no—
227C4—22no—
228C4—44no—
229C4—42no—
230C4—82no—
231C4C31×#45612yes—
232C4C31×#46512yes—
233C4C31×#46712yes—
234C2—21no—
235C2—21no—
236C2C31×#188611yescharacteristic
237C2C31×#189211yescharacteristic
238C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC23×C31C2×C22⋊C4
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
75. #9392C31direct (N × H)
165. C31#9392direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29822
C31×#25672
C31×#18012
C31×#15482
C31×#13032
#939231