Finite Group Databasebeta

← C31×#21333 #21478092

Subgroups — C31×#21333 #21478092

Order 7936.

1338 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#543C211yesmaximal, characteristic
2C31×#2315C211yesmaximal, characteristic
3C31×#2273C211yesmaximal, characteristic
4C31×#1996C218yesmaximal, complemented
5C2×C31×#342C214yesmaximal
6C31×#543—24no—
7C31×#543—24no—
8C2×C31×C22⋊Q8C418yescomplemented
9C2×C31×C22⋊Q8C2214yes—
10C22×C22⋊C4×C31C2212yes—
11C22×C22⋊C4×C31C2212yes—
12C22×C22⋊C4×C31C2212yes—
13C22×C22⋊C4×C31C2211yescharacteristic
14C31×#385—24no—
15C31×#380C2214yes—
16C4×C22⋊C4×C31—24no—
17C4×C22⋊C4×C31C2214yes—
18C31×#342C22116yes—
19C25×C31C2311yescharacteristic
20C22×Q8×C31C2×C414yescomplemented
21C23×C4×C31—22no—
22C23×C4×C31—22no—
23C23×C4×C31C2×C414yes—
24C23×C4×C31C2312yes—
25C31×C22⋊Q8—28no—
26C31×C22⋊Q8—28no—
27C31×C22⋊Q8—232no—
28C2×C4⋊C4×C31—24no—
29C2×C4⋊C4×C31C2×C4112yescomplemented
30C2×C22⋊C4×C31—24no—
31C2×C22⋊C4×C31—24no—
32C2×C22⋊C4×C31—22no—
33C2×C22⋊C4×C31—24no—
34C2×C22⋊C4×C31—28no—
35C2×C22⋊C4×C31—22no—
36C2×C22⋊C4×C31C2×C414yes—
37C2×C22⋊C4×C31C2×C414yes—
38C2×C22⋊C4×C31D414yes—
39C2×C22⋊C4×C31D414yes—
40C2×C22⋊C4×C31Q818yescomplemented
41C2×C22⋊C4×C31C2314yes—
42C2×C22⋊C4×C31C2314yes—
43C2×C22⋊C4×C31C2314yes—
44C2×C42×C31—24no—
45C31×#95—24no—
46C31×#95—24no—
47C24×C31—82no—
48C24×C31C22×C412yes—
49C24×C31C2×D412yes—
50C24×C31C2×D412yes—
51C24×C31C2×Q814yes—
52C24×C31#4114yes—
53C24×C31C2411yescharacteristic
54C2×Q8×C31—28no—
55C2×Q8×C31—84no—
56C22×C4×C31—24no—
57C22×C4×C31—28no—
58C22×C4×C31—28no—
59C22×C4×C31—24no—
60C22×C4×C31—44no—
61C22×C4×C31—82no—
62C22×C4×C31—84no—
63C22×C4×C31—84no—
64C22×C4×C31—84no—
65C22×C4×C31C22×C418yes—
66C22×C4×C31C22×C414yes—
67C22×C4×C31C2×D414yes—
68C22×C4×C31C2×D414yes—
69C4⋊C4×C31—224no—
70C4⋊C4×C31—84no—
71C22⋊C4×C31—28no—
72C22⋊C4×C31—28no—
73C22⋊C4×C31—24no—
74C22⋊C4×C31—24no—
75C22⋊C4×C31—24no—
76C22⋊C4×C31—28no—
77C22⋊C4×C31—44no—
78C22⋊C4×C31C22⋊C4116yes—
79C22⋊C4×C31C2×Q818yes—
80C42×C31—84no—
81#21333C3111yesmaximal, characteristic, direct product factor, Sylow
82C23×C31—44no—
83C23×C31—44no—
84C23×C31—44no—
85C23×C31—42no—
86C23×C31—84no—
87C23×C31—84no—
88C23×C31C2×C22⋊C414yes—
89C23×C31C4×Q818yes—
90C23×C31C22⋊Q814yes—
91C23×C31C22⋊Q814yes—
92C23×C31#12414yes—
93C23×C31C4⋊Q814yes—
94C23×C31C23×C411yescharacteristic
95C23×C31C22×D411yescharacteristic
96C23×C31C22×D411yescharacteristic
97C23×C31C22×Q812yes—
98C23×C31C2×#4112yes—
99Q8×C31—88no—
100C2×C4×C31—28no—
101C2×C4×C31—28no—
102C2×C4×C31—44no—
103C2×C4×C31—44no—
104C2×C4×C31—44no—
105C2×C4×C31—48no—
106C2×C4×C31—48no—
107C2×C4×C31—48no—
108C2×C4×C31—44no—
109C2×C4×C31—88no—
110C2×C4×C31—88no—
111C2×C4×C31—88no—
112C2×C4×C31C2×C22⋊C418yes—
113C2×#543C2×C3111yescharacteristic
114#2315C2×C3111yescharacteristic
115#2273C2×C3111yescharacteristic
116#1996C2×C3118yescomplemented
117C2×#342C2×C3114yes—
118C22×C31—22no—
119C22×C31—22no—
120C22×C31—22no—
121C22×C31—28no—
122C22×C31—44no—
123C22×C31—44no—
124C22×C31—48no—
125C22×C31—44no—
126C22×C31—44no—
127C22×C31—42no—
128C22×C31—42no—
129C22×C31#39118yes—
130C22×C31C22×C22⋊C411yescharacteristic
131C22×C31C2×C4×Q812yes—
132C22×C31C2×C22⋊Q812yes—
133C22×C31C2×#12411yescharacteristic
134C22×C31C2×C4⋊Q811yescharacteristic
135C4×C31—28no—
136C4×C31—48no—
137C4×C31—48no—
138C4×C31—84no—
139#543—24no—
140#543—24no—
141C2×C22⋊Q8C4×C3118yescomplemented
142C2×C22⋊Q8C22×C3114yes—
143C22×C22⋊C4C22×C3112yes—
144C22×C22⋊C4C22×C3112yes—
145C22×C22⋊C4C22×C3112yes—
146C22×C22⋊C4C22×C3111yescharacteristic
147#385—24no—
148#380C22×C3114yes—
149C4×C22⋊C4—24no—
150C4×C22⋊C4C22×C3114yes—
151#342C22×C31116yes—
152C2×C31—22no—
153C2×C31—21no—
154C2×C31—22no—
155C2×C31—21no—
156C2×C31—28no—
157C2×C31C2×#39111yescharacteristic
158C2×C31#288312yes—
159C25C23×C3111yescharacteristic
160C22×Q8C2×C4×C3114yescomplemented
161C23×C4—22no—
162C23×C4—22no—
163C23×C4C2×C4×C3114yes—
164C23×C4C23×C3112yes—
165C22⋊Q8—28no—
166C22⋊Q8—28no—
167C22⋊Q8—232no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4C2×C4×C31112yescomplemented
170C2×C22⋊C4—24no—
171C2×C22⋊C4—24no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—24no—
174C2×C22⋊C4—28no—
175C2×C22⋊C4—22no—
176C2×C22⋊C4C2×C4×C3114yes—
177C2×C22⋊C4C2×C4×C3114yes—
178C2×C22⋊C4D4×C3114yes—
179C2×C22⋊C4D4×C3114yes—
180C2×C22⋊C4Q8×C3118yescomplemented
181C2×C22⋊C4C23×C3114yes—
182C2×C22⋊C4C23×C3114yes—
183C2×C22⋊C4C23×C3114yes—
184C2×C42—24no—
185#95—24no—
186#95—24no—
187C31#2133311yescharacteristic, direct product factor, Sylow
188C24—82no—
189C24C22×C4×C3112yes—
190C24C2×D4×C3112yes—
191C24C2×D4×C3112yes—
192C24C2×Q8×C3114yes—
193C24#41×C3114yes—
194C24C24×C3111yescharacteristic
195C2×Q8—28no—
196C2×Q8—84no—
197C22×C4—24no—
198C22×C4—28no—
199C22×C4—28no—
200C22×C4—24no—
201C22×C4—44no—
202C22×C4—82no—
203C22×C4—84no—
204C22×C4—84no—
205C22×C4—84no—
206C22×C4C22×C4×C3118yes—
207C22×C4C22×C4×C3114yes—
208C22×C4C2×D4×C3114yes—
209C22×C4C2×D4×C3114yes—
210C4⋊C4—224no—
211C4⋊C4—84no—
212C22⋊C4—28no—
213C22⋊C4—28no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—28no—
218C22⋊C4—44no—
219C22⋊C4C22⋊C4×C31116yes—
220C22⋊C4C2×Q8×C3118yes—
221C42—84no—
222C23—44no—
223C23—44no—
224C23—44no—
225C23—42no—
226C23—84no—
227C23—84no—
228C23C2×C22⋊C4×C3114yes—
229C23C4×Q8×C3118yes—
230C23C31×C22⋊Q814yes—
231C23C31×C22⋊Q814yes—
232C23C31×#12414yes—
233C23C31×C4⋊Q814yes—
234C23C23×C4×C3111yescharacteristic
235C23C22×D4×C3111yescharacteristic
236C23C22×D4×C3111yescharacteristic
237C23C22×Q8×C3112yes—
238C23C2×#41×C3112yes—
239Q8—88no—
240C2×C4—28no—
241C2×C4—28no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—48no—
246C2×C4—48no—
247C2×C4—48no—
248C2×C4—44no—
249C2×C4—88no—
250C2×C4—88no—
251C2×C4—88no—
252C2×C4C2×C22⋊C4×C3118yes—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—28no—
257C22—44no—
258C22—44no—
259C22—48no—
260C22—44no—
261C22—44no—
262C22—42no—
263C22—42no—
264C22C31×#39118yes—
265C22C22×C22⋊C4×C3111yescharacteristic
266C22C2×C4×Q8×C3112yes—
267C22C2×C31×C22⋊Q812yes—
268C22C2×C31×#12411yescharacteristic
269C22C2×C31×C4⋊Q811yescharacteristic
270C4—28no—
271C4—48no—
272C4—48no—
273C4—84no—
274C2—22no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2—28no—
279C2C2×C31×#39111yescharacteristic
280C2C31×#288312yes—
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1996C2semidirect
8. C2×C31×C22⋊Q8C4semidirect
20. C22×Q8×C31C2×C4semidirect
29. C2×C4⋊C4×C31C2×C4semidirect
40. C2×C22⋊C4×C31Q8semidirect
81. #21333C31direct (N × H)
116. #1996C2×C31semidirect
141. C2×C22⋊Q8C4×C31semidirect
160. C22×Q8C2×C4×C31semidirect
169. C2×C4⋊C4C2×C4×C31semidirect
180. C2×C22⋊C4Q8×C31semidirect
187. C31#21333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5432
C31×#23152
C31×#22732
C31×#19962
C2×C31×#3422
#2133331