Finite Group Databasebeta

← C31×#9403 #21466162

Subgroups — C31×#9403 #21466162

Order 7936.

570 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2975C211yesmaximal, characteristic
2C31×#2542C211yesmaximal, characteristic
3C31×#1800C211yesmaximal, characteristic
4C31×#1549C212yesmaximal, complemented
5C31×#1303C212yesmaximal, complemented
6C2×C31×C4⋊Q8C2211yescharacteristic
7C2×C31×C22⋊Q8—22no—
8C2×C4×D4×C31C2211yescharacteristic
9C31×#436—24no—
10C31×#431C2212yes—
11C31×#423C2212yes—
12C2×C31×#100—21no—
13C31×#407—22no—
14C31×#399C414yes—
15C31×#390—21no—
16C31×#384—21no—
17C4×C4⋊C4×C31C2211yescharacteristic
18C31×#343—21no—
19C31×#332—24no—
20C22×Q8×C31—21no—
21C22×D4×C31D411yescharacteristic
22C23×C4×C31D412yes—
23C2×M16×C31—24no—
24C2×M16×C31—22no—
25C31×C4⋊Q8—22no—
26C31×C4⋊Q8—22no—
27C31×C22⋊Q8—48no—
28C4×D4×C31—22no—
29C4×D4×C31—22no—
30C2×C4⋊C4×C31—21no—
31C2×C4⋊C4×C31—24no—
32C2×C4⋊C4×C31—21no—
33C2×C4⋊C4×C31C2×C412yes—
34C2×C4⋊C4×C31D411yescharacteristic
35C2×C22⋊C4×C31—24no—
36C2×C22⋊C4×C31C2×C412yes—
37C2×C42×C31—21no—
38C2×C42×C31C2311yescharacteristic
39C31×C4⋊C8—22no—
40C31×C4⋊C8—22no—
41C31×C4⋊C8D414yes—
42C31×#100—42no—
43C31×C22⋊C8—24no—
44C31×C22⋊C8—22no—
45C4×C8×C31—22no—
46C31×#95C2×C412yes—
47C24×C31C22⋊C412yes—
48C2×Q8×C31—44no—
49C2×Q8×C31—41no—
50C2×Q8×C31—41no—
51C2×D4×C31—22no—
52C2×D4×C31—21no—
53C2×D4×C31—22no—
54C2×D4×C31—21no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—22no—
59C22×C4×C31—44no—
60C22×C4×C31C22⋊C412yes—
61C22×C4×C31C22×C411yescharacteristic
62C22×C4×C31C2×D411yescharacteristic
63C22×C4×C31C2×D411yescharacteristic
64M16×C31—42no—
65M16×C31—42no—
66M16×C31—84no—
67C2×C8×C31—24no—
68C2×C8×C31—42no—
69C4⋊C4×C31—24no—
70C4⋊C4×C31—22no—
71C4⋊C4×C31—24no—
72C4⋊C4×C31—48no—
73C4⋊C4×C31—42no—
74C22⋊C4×C31—24no—
75C22⋊C4×C31—48no—
76C42×C31—41no—
77C42×C31—41no—
78C42×C31C2×D412yes—
79C42×C31#4112yes—
80#9403C3111yesmaximal, characteristic, direct product factor, Sylow
81C23×C31—22no—
82C23×C31—22no—
83C23×C31—22no—
84C23×C31—42no—
85C23×C31—42no—
86C23×C31C2×C22⋊C411yescharacteristic
87Q8×C31—82no—
88Q8×C31—82no—
89D4×C31—42no—
90D4×C31—42no—
91C2×C4×C31—22no—
92C2×C4×C31—24no—
93C2×C4×C31—22no—
94C2×C4×C31—41no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—44no—
98C2×C4×C31—42no—
99C2×C4×C31—44no—
100C2×C4×C31—42no—
101C2×C4×C31—82no—
102C2×C4×C31C4×D412yes—
103C2×C4×C31#12011yescharacteristic
104C2×C4×C31#12112yes—
105C2×C4×C31#12311yescharacteristic
106C2×C4×C31AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C31#13712yes—
108C2×C4×C31#13711yescharacteristic
109C8×C31—44no—
110C8×C31—82no—
111#2975C2×C3111yescharacteristic
112#2542C2×C3111yescharacteristic
113#1800C2×C3111yescharacteristic
114#1549C2×C3112yescomplemented
115#1303C2×C3112yescomplemented
116C22×C31—21no—
117C22×C31—21no—
118C22×C31—44no—
119C22×C31—42no—
120C22×C31—42no—
121C22×C31—42no—
122C22×C31—82no—
123C22×C31#38611yescharacteristic
124C22×C31#41711yescharacteristic
125C22×C31#41911yescharacteristic
126C4×C31—21no—
127C4×C31—22no—
128C4×C31—44no—
129C4×C31—42no—
130C4×C31—82no—
131C4×C31#45312yes—
132C4×C31#46812yes—
133C4×C31#47012yes—
134C2×C4⋊Q8C22×C3111yescharacteristic
135C2×C22⋊Q8—22no—
136C2×C4×D4C22×C3111yescharacteristic
137#436—24no—
138#431C22×C3112yes—
139#423C22×C3112yes—
140C2×#100—21no—
141#407—22no—
142#399C4×C3114yes—
143#390—21no—
144#384—21no—
145C4×C4⋊C4C22×C3111yescharacteristic
146#343—21no—
147#332—24no—
148C2×C31—21no—
149C2×C31—21no—
150C2×C31—82no—
151C2×C31#188711yescharacteristic
152C2×C31#189411yescharacteristic
153C2×C31#191511yescharacteristic
154C22×Q8—21no—
155C22×D4D4×C3111yescharacteristic
156C23×C4D4×C3112yes—
157C2×M16—24no—
158C2×M16—22no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C22⋊Q8—48no—
162C4×D4—22no—
163C4×D4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×C4×C3112yes—
168C2×C4⋊C4D4×C3111yescharacteristic
169C2×C22⋊C4—24no—
170C2×C22⋊C4C2×C4×C3112yes—
171C2×C42—21no—
172C2×C42C23×C3111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8D4×C3114yes—
176#100—42no—
177C22⋊C8—24no—
178C22⋊C8—22no—
179C4×C8—22no—
180#95C2×C4×C3112yes—
181C31#940311yescharacteristic, direct product factor, Sylow
182C24C22⋊C4×C3112yes—
183C2×Q8—44no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4C22⋊C4×C3112yes—
196C22×C4C22×C4×C3111yescharacteristic
197C22×C4C2×D4×C3111yescharacteristic
198C22×C4C2×D4×C3111yescharacteristic
199M16—42no—
200M16—42no—
201M16—84no—
202C2×C8—24no—
203C2×C8—42no—
204C4⋊C4—24no—
205C4⋊C4—22no—
206C4⋊C4—24no—
207C4⋊C4—48no—
208C4⋊C4—42no—
209C22⋊C4—24no—
210C22⋊C4—48no—
211C42—41no—
212C42—41no—
213C42C2×D4×C3112yes—
214C42#41×C3112yes—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—42no—
219C23—42no—
220C23C2×C22⋊C4×C3111yescharacteristic
221Q8—82no—
222Q8—82no—
223D4—42no—
224D4—42no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4C4×D4×C3112yes—
237C2×C4C31×#12011yescharacteristic
238C2×C4C31×#12112yes—
239C2×C4C31×#12311yescharacteristic
240C2×C4C31×AGL(1,ℤ/8)11yescharacteristic
241C2×C4C31×#13712yes—
242C2×C4C31×#13711yescharacteristic
243C8—44no—
244C8—82no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22C31×#38611yescharacteristic
253C22C31×#41711yescharacteristic
254C22C31×#41911yescharacteristic
255C4—21no—
256C4—22no—
257C4—44no—
258C4—42no—
259C4—82no—
260C4C31×#45312yes—
261C4C31×#46812yes—
262C4C31×#47012yes—
263C2—21no—
264C2—21no—
265C2—82no—
266C2C31×#188711yescharacteristic
267C2C31×#189411yescharacteristic
268C2C31×#191511yescharacteristic
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×#1549C2semidirect
5. C31×#1303C2semidirect
80. #9403C31direct (N × H)
114. #1549C2×C31semidirect
115. #1303C2×C31semidirect
181. C31#9403direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#29752
C31×#25422
C31×#18002
C31×#15492
C31×#13032
#940331