Finite Group Databasebeta

← C31×#34177 #21490936

Subgroups — C31×#34177 #21490936

Order 7936.

2446 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C31×#2343C2116yesmaximal, complemented
3C31×#2315C212yesmaximal
4C31×#2313C214yesmaximal, complemented
5C31×#2283C214yesmaximal, complemented
6C2×C31×#381C212yesmaximal
7C31×#2273C212yesmaximal
8C24×C4×C31C2211yescharacteristic
9C2×C31×#117C4116yescomplemented
10C2×C31×#117C2218yes—
11C22×C4⋊C4×C31C2212yes—
12C22×C22⋊C4×C31C2214yes—
13C22×C22⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C42×C31C2212yes—
16C31×#387C22132yescomplemented
17C31×#385C22116yes—
18C31×#383C2218yescomplemented
19C31×#382C2218yescomplemented
20C31×#381C2214yes—
21C31×#381C2218yes—
22C31×#381C2214yes—
23C31×#380C2218yes—
24C4×C4⋊C4×C31C2218yescomplemented
25C4×C22⋊C4×C31C2218yes—
26C4×C22⋊C4×C31C22116yes—
27C31×#376C2218yescomplemented
28C2×C31×#95C2218yes—
29C25×C31C2311yescharacteristic
30C23×C4×C31—28no—
31C23×C4×C31C2×C418yes—
32C23×C4×C31C2311yescharacteristic
33C23×C4×C31C2311yescharacteristic
34C23×C4×C31C2314yes—
35C23×C4×C31C2318yes—
36C23×C4×C31C2312yes—
37C23×C4×C31C2312yes—
38C31×#117C2×C4164yescomplemented
39C2×C4⋊C4×C31C2×C4116yescomplemented
40C2×C4⋊C4×C31C23116yes—
41C2×C4⋊C4×C31C2318yes—
42C2×C22⋊C4×C31—216no—
43C2×C22⋊C4×C31C2×C418yes—
44C2×C22⋊C4×C31C2×C418yes—
45C2×C22⋊C4×C31C2318yes—
46C2×C22⋊C4×C31C2318yes—
47C2×C22⋊C4×C31C2314yes—
48C2×C22⋊C4×C31C2314yes—
49C2×C42×C31C2×C4116yescomplemented
50C2×C42×C31C23116yes—
51C2×C42×C31C2314yes—
52C2×C42×C31C2314yes—
53C31×#95C23116yes—
54C31×#95C23116yes—
55C31×#95C23116yes—
56C31×#95C23116yes—
57C24×C31—44no—
58C24×C31C22×C414yes—
59C24×C31#4118yes—
60C24×C31C2412yes—
61C24×C31C2411yescharacteristic
62C22×C4×C31—232no—
63C22×C4×C31—24no—
64C22×C4×C31—24no—
65C22×C4×C31—216no—
66C22×C4×C31—216no—
67C22×C4×C31—44no—
68C22×C4×C31—44no—
69C22×C4×C31—416no—
70C22×C4×C31C22×C414yes—
71C22×C4×C31C22×C414yes—
72C22×C4×C31C22×C4116yes—
73C22×C4×C31C22×C418yes—
74C22×C4×C31C22×C418yes—
75C22×C4×C31C24116yes—
76C22×C4×C31C2412yes—
77C22×C4×C31C2412yes—
78C22×C4×C31C2414yes—
79C22×C4×C31C2414yes—
80C4⋊C4×C31—416no—
81C4⋊C4×C31C22×C4132yes—
82C22⋊C4×C31—216no—
83C22⋊C4×C31—216no—
84C22⋊C4×C31C22×C4116yes—
85C22⋊C4×C31C22×C4116yes—
86C42×C31—416no—
87C42×C31C22×C4116yes—
88C42×C31C22×C4116yes—
89#34177C3111yesmaximal, characteristic, direct product factor, Sylow
90C23×C31—24no—
91C23×C31—28no—
92C23×C31—48no—
93C23×C31—416no—
94C23×C31#117116yes—
95C23×C31C23×C414yes—
96C23×C31C23×C412yes—
97C23×C31C2×#4114yes—
98C23×C31C2×#4118yes—
99C23×C31C2511yescharacteristic
100C2×C4×C31—28no—
101C2×C4×C31—28no—
102C2×C4×C31—232no—
103C2×C4×C31—24no—
104C2×C4×C31—24no—
105C2×C4×C31—28no—
106C2×C4×C31—28no—
107C2×C4×C31—216no—
108C2×C4×C31—232no—
109C2×C4×C31—48no—
110C2×C4×C31—48no—
111C2×C4×C31—816no—
112C2×C4×C31C23×C414yes—
113C2×C4×C31C23×C418yes—
114C2×C4×C31C23×C418yes—
115C2×C4×C31C23×C414yes—
116C22×#117C2×C3111yescharacteristic
117#2343C2×C31116yescomplemented
118#2315C2×C3112yes—
119#2313C2×C3114yescomplemented
120#2283C2×C3114yescomplemented
121C2×#381C2×C3112yes—
122#2273C2×C3112yes—
123C22×C31—24no—
124C22×C31—28no—
125C22×C31—216no—
126C22×C31—28no—
127C22×C31—416no—
128C22×C31C2×#11718yes—
129C22×C31C2×#11714yes—
130C22×C31C24×C411yescharacteristic
131C22×C31C22×#4112yes—
132C22×C31#58514yes—
133C4×C31—24no—
134C4×C31—24no—
135C4×C31—28no—
136C4×C31—28no—
137C4×C31—416no—
138C24×C4C22×C3111yescharacteristic
139C2×#117C4×C31116yescomplemented
140C2×#117C22×C3118yes—
141C22×C4⋊C4C22×C3112yes—
142C22×C22⋊C4C22×C3114yes—
143C22×C22⋊C4C22×C3111yescharacteristic
144C22×C22⋊C4C22×C3111yescharacteristic
145C22×C42C22×C3112yes—
146#387C22×C31132yescomplemented
147#385C22×C31116yes—
148#383C22×C3118yescomplemented
149#382C22×C3118yescomplemented
150#381C22×C3114yes—
151#381C22×C3118yes—
152#381C22×C3114yes—
153#380C22×C3118yes—
154C4×C4⋊C4C22×C3118yescomplemented
155C4×C22⋊C4C22×C3118yes—
156C4×C22⋊C4C22×C31116yes—
157#376C22×C3118yescomplemented
158C2×#95C22×C3118yes—
159C2×C31—24no—
160C2×C31—28no—
161C2×C31C22×#11711yescharacteristic
162C2×C31#342812yes—
163C2×C31#349114yes—
164C25C23×C3111yescharacteristic
165C23×C4—28no—
166C23×C4C2×C4×C3118yes—
167C23×C4C23×C3111yescharacteristic
168C23×C4C23×C3114yes—
169C23×C4C23×C3111yescharacteristic
170C23×C4C23×C3118yes—
171C23×C4C23×C3112yes—
172C23×C4C23×C3112yes—
173#117C2×C4×C31164yescomplemented
174C2×C4⋊C4C2×C4×C31116yescomplemented
175C2×C4⋊C4C23×C31116yes—
176C2×C4⋊C4C23×C3118yes—
177C2×C22⋊C4—216no—
178C2×C22⋊C4C2×C4×C3118yes—
179C2×C22⋊C4C2×C4×C3118yes—
180C2×C22⋊C4C23×C3118yes—
181C2×C22⋊C4C23×C3118yes—
182C2×C22⋊C4C23×C3114yes—
183C2×C22⋊C4C23×C3114yes—
184C2×C42C2×C4×C31116yescomplemented
185C2×C42C23×C31116yes—
186C2×C42C23×C3114yes—
187C2×C42C23×C3114yes—
188#95C23×C31116yes—
189#95C23×C31116yes—
190#95C23×C31116yes—
191#95C23×C31116yes—
192C31#3417711yescharacteristic, direct product factor, Sylow
193C24—44no—
194C24C22×C4×C3114yes—
195C24#41×C3118yes—
196C24C24×C3112yes—
197C24C24×C3111yescharacteristic
198C22×C4—232no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—216no—
202C22×C4—216no—
203C22×C4—44no—
204C22×C4—44no—
205C22×C4—416no—
206C22×C4C22×C4×C3114yes—
207C22×C4C22×C4×C3114yes—
208C22×C4C22×C4×C31116yes—
209C22×C4C22×C4×C3118yes—
210C22×C4C22×C4×C3118yes—
211C22×C4C24×C31116yes—
212C22×C4C24×C3112yes—
213C22×C4C24×C3112yes—
214C22×C4C24×C3114yes—
215C22×C4C24×C3114yes—
216C4⋊C4—416no—
217C4⋊C4C22×C4×C31132yes—
218C22⋊C4—216no—
219C22⋊C4—216no—
220C22⋊C4C22×C4×C31116yes—
221C22⋊C4C22×C4×C31116yes—
222C42—416no—
223C42C22×C4×C31116yes—
224C42C22×C4×C31116yes—
225C23—24no—
226C23—28no—
227C23—48no—
228C23—416no—
229C23C31×#117116yes—
230C23C23×C4×C3114yes—
231C23C23×C4×C3112yes—
232C23C2×#41×C3114yes—
233C23C2×#41×C3118yes—
234C23C25×C3111yescharacteristic
235C2×C4—28no—
236C2×C4—28no—
237C2×C4—232no—
238C2×C4—24no—
239C2×C4—24no—
240C2×C4—28no—
241C2×C4—28no—
242C2×C4—216no—
243C2×C4—232no—
244C2×C4—48no—
245C2×C4—48no—
246C2×C4—816no—
247C2×C4C23×C4×C3114yes—
248C2×C4C23×C4×C3118yes—
249C2×C4C23×C4×C3118yes—
250C2×C4C23×C4×C3114yes—
251C22—24no—
252C22—28no—
253C22—216no—
254C22—28no—
255C22—416no—
256C22C2×C31×#11718yes—
257C22C2×C31×#11714yes—
258C22C24×C4×C3111yescharacteristic
259C22C22×#41×C3112yes—
260C22C31×#58514yes—
261C4—24no—
262C4—24no—
263C4—28no—
264C4—28no—
265C4—416no—
266C2—24no—
267C2—28no—
268C2C22×C31×#11711yescharacteristic
269C2C31×#342812yes—
270C2C31×#349114yes—
subgroupG/H
center, socleC23×C31C25
commutatorC22C24×C4×C31
Frattini, cosocleC23C25×C31
prime radicalC25×C31C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2343C2semidirect
4. C31×#2313C2semidirect
5. C31×#2283C2semidirect
9. C2×C31×#117C4semidirect
16. C31×#387C22semidirect
18. C31×#383C22semidirect
19. C31×#382C22semidirect
24. C4×C4⋊C4×C31C22semidirect
27. C31×#376C22semidirect
38. C31×#117C2×C4semidirect
39. C2×C4⋊C4×C31C2×C4semidirect
49. C2×C42×C31C2×C4semidirect
89. #34177C31direct (N × H)
117. #2343C2×C31semidirect
119. #2313C2×C31semidirect
120. #2283C2×C31semidirect
139. C2×#117C4×C31semidirect
146. #387C22×C31semidirect
148. #383C22×C31semidirect
149. #382C22×C31semidirect
154. C4×C4⋊C4C22×C31semidirect
157. #376C22×C31semidirect
173. #117C2×C4×C31semidirect
174. C2×C4⋊C4C2×C4×C31semidirect
184. C2×C42C2×C4×C31semidirect
192. C31#34177direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C31×#23432
C31×#23152
C31×#23132
C31×#22832
C2×C31×#3812
C31×#22732
#3417731