Finite Group Databasebeta

← C31×#13583 #21470342

Subgroups — C31×#13583 #21470342

Order 7936.

416 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3147C211yesmaximal, characteristic
2C31×#2126C212yesmaximal, complemented
3C31×#1409C212yesmaximal, complemented
4C31×#1408C212yesmaximal, complemented
5C2×C31×#135—22no—
6C31×#532C411yescharacteristic, complemented
7C31×#532C2211yescharacteristic
8C31×#495—22no—
9C31×#494C411yescharacteristic, complemented
10C31×#493C2211yescharacteristic
11C31×#492C411yescharacteristic, complemented
12C31×#492C2211yescharacteristic
13C31×#410—22no—
14C2×C4×C8×C31C411yescharacteristic, complemented
15C31×#354—22no—
16C31×#353C2214yes—
17C2×#41×C31—21no—
18C2×#41×C31D412yes—
19C31×#135—44no—
20C31×#135—44no—
21C2×Q16×C31—22no—
22C2×SD16×C31—22no—
23C2×SD16×C31—22no—
24C2×D8×C31—22no—
25C22×C8×C31—21no—
26C31×C4⋊Q8C2×C411yescharacteristic
27C31×C4⋊Q8C2×C411yescharacteristic
28C31×#127C2×C411yescharacteristic
29C31×#127C2311yescharacteristic
30C31×#124—21no—
31C31×#124D412yes—
32C31×#121—41no—
33C31×#121—41no—
34C4×D4×C31—41no—
35C4×D4×C31—41no—
36C31×#117—42no—
37C2×C42×C31C2×C411yescharacteristic
38C31×#99—24no—
39C31×#99—42no—
40C4×C8×C31—21no—
41C4×C8×C31C2×C411yescharacteristic
42C4×C8×C31C2×C411yescharacteristic
43#41×C31—42no—
44#41×C31—42no—
45#41×C31—42no—
46#41×C31—42no—
47C2×Q8×C31—21no—
48C2×Q8×C31C22⋊C412yes—
49C2×D4×C31—22no—
50C2×D4×C31—21no—
51C2×D4×C31—41no—
52C2×D4×C31—41no—
53C2×D4×C31—41no—
54C2×D4×C31C2×D412yes—
55C22×C4×C31—21no—
56C22×C4×C31—22no—
57C22×C4×C31—41no—
58C22×C4×C31C22⋊C411yescharacteristic
59Q16×C31—44no—
60SD16×C31—44no—
61SD16×C31—44no—
62D8×C31—44no—
63C2×C8×C31—22no—
64C2×C8×C31—22no—
65C2×C8×C31—21no—
66C2×C8×C31—21no—
67C4⋊C4×C31—41no—
68C4⋊C4×C31—41no—
69C4⋊C4×C31—82no—
70C22⋊C4×C31—42no—
71C22⋊C4×C31—42no—
72C22⋊C4×C31—44no—
73C42×C31—21no—
74C42×C31—82no—
75C42×C31C22⋊C411yescharacteristic
76C42×C31C22×C411yescharacteristic
77#13583C3111yesmaximal, characteristic, direct product factor, Sylow
78C23×C31—22no—
79C23×C31—41no—
80C23×C31#9911yescharacteristic
81Q8×C31—42no—
82Q8×C31—42no—
83D4×C31—42no—
84D4×C31—42no—
85D4×C31—82no—
86D4×C31—82no—
87D4×C31—82no—
88D4×C31—82no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31—21no—
92C2×C4×C31—21no—
93C2×C4×C31—22no—
94C2×C4×C31—42no—
95C2×C4×C31—42no—
96C2×C4×C31—42no—
97C2×C4×C31—41no—
98C2×C4×C31—81no—
99C2×C4×C31—81no—
100C2×C4×C31—84no—
101C2×C4×C31#9911yescharacteristic
102C2×C4×C31C2×C22⋊C411yescharacteristic
103C8×C31—22no—
104C8×C31—22no—
105#3147C2×C3111yescharacteristic
106#2126C2×C3112yescomplemented
107#1409C2×C3112yescomplemented
108#1408C2×C3112yescomplemented
109C22×C31—21no—
110C22×C31—41no—
111C22×C31—42no—
112C22×C31—82no—
113C22×C31—82no—
114C22×C31—81no—
115C22×C31C2×#9911yescharacteristic
116C4×C31—22no—
117C4×C31—21no—
118C4×C31—41no—
119C4×C31—42no—
120C4×C31—81no—
121C4×C31—164no—
122C4×C31#35311yescharacteristic
123C4×C31#35311yescharacteristic
124C2×#135—22no—
125#532C4×C3111yescharacteristic, complemented
126#532C22×C3111yescharacteristic
127#495—22no—
128#494C4×C3111yescharacteristic, complemented
129#493C22×C3111yescharacteristic
130#492C4×C3111yescharacteristic, complemented
131#492C22×C3111yescharacteristic
132#410—22no—
133C2×C4×C8C4×C3111yescharacteristic, complemented
134#354—22no—
135#353C22×C3114yes—
136C2×C31—21no—
137C2×C31—41no—
138C2×C31—82no—
139C2×C31—161no—
140C2×C31C2×#35311yescharacteristic
141C2×#41—21no—
142C2×#41D4×C3112yes—
143#135—44no—
144#135—44no—
145C2×Q16—22no—
146C2×SD16—22no—
147C2×SD16—22no—
148C2×D8—22no—
149C22×C8—21no—
150C4⋊Q8C2×C4×C3111yescharacteristic
151C4⋊Q8C2×C4×C3111yescharacteristic
152#127C2×C4×C3111yescharacteristic
153#127C23×C3111yescharacteristic
154#124—21no—
155#124D4×C3112yes—
156#121—41no—
157#121—41no—
158C4×D4—41no—
159C4×D4—41no—
160#117—42no—
161C2×C42C2×C4×C3111yescharacteristic
162#99—24no—
163#99—42no—
164C4×C8—21no—
165C4×C8C2×C4×C3111yescharacteristic
166C4×C8C2×C4×C3111yescharacteristic
167C31#1358311yescharacteristic, direct product factor, Sylow
168#41—42no—
169#41—42no—
170#41—42no—
171#41—42no—
172C2×Q8—21no—
173C2×Q8C22⋊C4×C3112yes—
174C2×D4—22no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4C2×D4×C3112yes—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4C22⋊C4×C3111yescharacteristic
184Q16—44no—
185SD16—44no—
186SD16—44no—
187D8—44no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—82no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—44no—
198C42—21no—
199C42—82no—
200C42C22⋊C4×C3111yescharacteristic
201C42C22×C4×C3111yescharacteristic
202C23—22no—
203C23—41no—
204C23C31×#9911yescharacteristic
205Q8—42no—
206Q8—42no—
207D4—42no—
208D4—42no—
209D4—82no—
210D4—82no—
211D4—82no—
212D4—82no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—84no—
225C2×C4C31×#9911yescharacteristic
226C2×C4C2×C22⋊C4×C3111yescharacteristic
227C8—22no—
228C8—22no—
229C22—21no—
230C22—41no—
231C22—42no—
232C22—82no—
233C22—82no—
234C22—81no—
235C22C2×C31×#9911yescharacteristic
236C4—22no—
237C4—21no—
238C4—41no—
239C4—42no—
240C4—81no—
241C4—164no—
242C4C31×#35311yescharacteristic
243C4C31×#35311yescharacteristic
244C2—21no—
245C2—41no—
246C2—82no—
247C2—161no—
248C2C2×C31×#35311yescharacteristic
subgroupG/H
centerC4×C31#353
commutatorC42C22×C4×C31
Frattini, cosocle#127C23×C31
socleC2×C31C2×#353
prime radicalC31×#3147C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C22×C4×C31 ◁ C31×#532 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2126C2semidirect
3. C31×#1409C2semidirect
4. C31×#1408C2semidirect
6. C31×#532C4semidirect
9. C31×#494C4semidirect
11. C31×#492C4semidirect
14. C2×C4×C8×C31C4semidirect
77. #13583C31direct (N × H)
106. #2126C2×C31semidirect
107. #1409C2×C31semidirect
108. #1408C2×C31semidirect
125. #532C4×C31semidirect
128. #494C4×C31semidirect
130. #492C4×C31semidirect
133. C2×C4×C8C4×C31semidirect
167. C31#13583direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31472
C31×#21262
C31×#14092
C31×#14082
#1358331