Finite Group Databasebeta

← C31×#21334 #21478093

Subgroups — C31×#21334 #21478093

Order 7936.

1142 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic
2C31×#2316C211yesmaximal, characteristic
3C31×#2274C211yesmaximal, characteristic
4C31×#1996C218yesmaximal
5C31×#1740C214yesmaximal
6C31×#544—24no—
7C31×#544—24no—
8C2×C31×C4⋊Q8C414yescomplemented
9C2×C31×#125C414yescomplemented
10C2×C31×C22⋊Q8C2214yes—
11C2×C31×#117C2212yes—
12C2×C31×#117C2212yes—
13C2×C31×#117C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C31×#389—24no—
16C31×#380C2214yes—
17C4×C4⋊C4×C31—24no—
18C4×C22⋊C4×C31C2214yes—
19C31×#342C22116yes—
20C22×Q8×C31C2×C414yes—
21C23×C4×C31C2312yes—
22C23×C4×C31C2311yescharacteristic
23C31×C4⋊Q8—216no—
24C31×#125—216no—
25C31×C22⋊Q8—28no—
26C31×C22⋊Q8—28no—
27C31×#117—24no—
28C31×#117—24no—
29C31×#117—24no—
30C31×#117—28no—
31C31×#117Q818yescomplemented
32C2×C4⋊C4×C31—22no—
33C2×C4⋊C4×C31—22no—
34C2×C4⋊C4×C31—24no—
35C2×C4⋊C4×C31C2×C412yes—
36C2×C4⋊C4×C31C2×C412yes—
37C2×C4⋊C4×C31C2×C414yes—
38C2×C4⋊C4×C31C2×C418yes—
39C2×C4⋊C4×C31C2×C414yes—
40C2×C4⋊C4×C31D414yes—
41C2×C4⋊C4×C31D414yes—
42C2×C22⋊C4×C31C2314yes—
43C2×C22⋊C4×C31C2314yes—
44C2×C22⋊C4×C31C2314yes—
45C2×C42×C31—22no—
46C2×C42×C31—22no—
47C2×C42×C31—24no—
48C2×C42×C31C2×C414yes—
49C31×#95—24no—
50C31×#95—24no—
51C24×C31C2411yescharacteristic
52C2×Q8×C31—28no—
53C2×Q8×C31—84no—
54C22×C4×C31—24no—
55C22×C4×C31—24no—
56C22×C4×C31—82no—
57C22×C4×C31C22×C414yes—
58C22×C4×C31C22×C414yes—
59C22×C4×C31C22×C414yes—
60C22×C4×C31C22×C412yes—
61C22×C4×C31C2×D414yes—
62C22×C4×C31C2×D414yes—
63C22×C4×C31C2×D412yes—
64C22×C4×C31C2×D412yes—
65C22×C4×C31C2×Q814yes—
66C22×C4×C31#4114yes—
67C4⋊C4×C31—24no—
68C4⋊C4×C31—24no—
69C4⋊C4×C31—28no—
70C4⋊C4×C31—216no—
71C4⋊C4×C31—28no—
72C4⋊C4×C31—44no—
73C4⋊C4×C31—84no—
74C4⋊C4×C31C22⋊C4116yes—
75C22⋊C4×C31—24no—
76C22⋊C4×C31—24no—
77C22⋊C4×C31—24no—
78C22⋊C4×C31—28no—
79C22⋊C4×C31C2×Q818yes—
80C42×C31—28no—
81C42×C31—28no—
82C42×C31—44no—
83C42×C31—84no—
84#21334C3111yesmaximal, characteristic, direct product factor, Sylow
85C23×C31—41no—
86C23×C31—41no—
87C23×C31C23×C411yescharacteristic
88C23×C31C22×D411yescharacteristic
89C23×C31C22×D411yescharacteristic
90C23×C31C22×Q812yes—
91C23×C31C2×#4112yes—
92Q8×C31—88no—
93C2×C4×C31—24no—
94C2×C4×C31—24no—
95C2×C4×C31—28no—
96C2×C4×C31—44no—
97C2×C4×C31—44no—
98C2×C4×C31—44no—
99C2×C4×C31—44no—
100C2×C4×C31—44no—
101C2×C4×C31—44no—
102C2×C4×C31—44no—
103C2×C4×C31—44no—
104C2×C4×C31—44no—
105C2×C4×C31—44no—
106C2×C4×C31C2×C22⋊C418yes—
107C2×C4×C31C2×C22⋊C414yes—
108C2×C4×C31C4×Q818yes—
109C2×C4×C31C22⋊Q814yes—
110C2×C4×C31C22⋊Q814yes—
111C2×C4×C31#12414yes—
112C2×C4×C31C4⋊Q814yes—
113C2×#544C2×C3111yescharacteristic
114#2316C2×C3111yescharacteristic
115#2274C2×C3111yescharacteristic
116#1996C2×C3118yes—
117#1740C2×C3114yes—
118C22×C31—21no—
119C22×C31—21no—
120C22×C31—21no—
121C22×C31—21no—
122C22×C31—21no—
123C22×C31—21no—
124C22×C31—42no—
125C22×C31—42no—
126C22×C31C22×C22⋊C411yescharacteristic
127C22×C31C2×C4×Q812yes—
128C22×C31C2×C22⋊Q812yes—
129C22×C31C2×#12411yescharacteristic
130C22×C31C2×C4⋊Q811yescharacteristic
131C4×C31—28no—
132C4×C31—48no—
133C4×C31—44no—
134C4×C31—44no—
135C4×C31—84no—
136C4×C31#39118yes—
137#544—24no—
138#544—24no—
139C2×C4⋊Q8C4×C3114yescomplemented
140C2×#125C4×C3114yescomplemented
141C2×C22⋊Q8C22×C3114yes—
142C2×#117C22×C3112yes—
143C2×#117C22×C3112yes—
144C2×#117C22×C3112yes—
145C22×C4⋊C4C22×C3111yescharacteristic
146#389—24no—
147#380C22×C3114yes—
148C4×C4⋊C4—24no—
149C4×C22⋊C4C22×C3114yes—
150#342C22×C31116yes—
151C2×C31—22no—
152C2×C31—21no—
153C2×C31—22no—
154C2×C31—21no—
155C2×C31C2×#39111yescharacteristic
156C2×C31#288311yescharacteristic
157C2×C31#288411yescharacteristic
158C22×Q8C2×C4×C3114yes—
159C23×C4C23×C3112yes—
160C23×C4C23×C3111yescharacteristic
161C4⋊Q8—216no—
162#125—216no—
163C22⋊Q8—28no—
164C22⋊Q8—28no—
165#117—24no—
166#117—24no—
167#117—24no—
168#117—28no—
169#117Q8×C3118yescomplemented
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4C2×C4×C3112yes—
174C2×C4⋊C4C2×C4×C3112yes—
175C2×C4⋊C4C2×C4×C3114yes—
176C2×C4⋊C4C2×C4×C3118yes—
177C2×C4⋊C4C2×C4×C3114yes—
178C2×C4⋊C4D4×C3114yes—
179C2×C4⋊C4D4×C3114yes—
180C2×C22⋊C4C23×C3114yes—
181C2×C22⋊C4C23×C3114yes—
182C2×C22⋊C4C23×C3114yes—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—24no—
186C2×C42C2×C4×C3114yes—
187#95—24no—
188#95—24no—
189C31#2133411yescharacteristic, direct product factor, Sylow
190C24C24×C3111yescharacteristic
191C2×Q8—28no—
192C2×Q8—84no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—82no—
196C22×C4C22×C4×C3114yes—
197C22×C4C22×C4×C3114yes—
198C22×C4C22×C4×C3114yes—
199C22×C4C22×C4×C3112yes—
200C22×C4C2×D4×C3114yes—
201C22×C4C2×D4×C3114yes—
202C22×C4C2×D4×C3112yes—
203C22×C4C2×D4×C3112yes—
204C22×C4C2×Q8×C3114yes—
205C22×C4#41×C3114yes—
206C4⋊C4—24no—
207C4⋊C4—24no—
208C4⋊C4—28no—
209C4⋊C4—216no—
210C4⋊C4—28no—
211C4⋊C4—44no—
212C4⋊C4—84no—
213C4⋊C4C22⋊C4×C31116yes—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—28no—
218C22⋊C4C2×Q8×C3118yes—
219C42—28no—
220C42—28no—
221C42—44no—
222C42—84no—
223C23—41no—
224C23—41no—
225C23C23×C4×C3111yescharacteristic
226C23C22×D4×C3111yescharacteristic
227C23C22×D4×C3111yescharacteristic
228C23C22×Q8×C3112yes—
229C23C2×#41×C3112yes—
230Q8—88no—
231C2×C4—24no—
232C2×C4—24no—
233C2×C4—28no—
234C2×C4—44no—
235C2×C4—44no—
236C2×C4—44no—
237C2×C4—44no—
238C2×C4—44no—
239C2×C4—44no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4C2×C22⋊C4×C3118yes—
245C2×C4C2×C22⋊C4×C3114yes—
246C2×C4C4×Q8×C3118yes—
247C2×C4C31×C22⋊Q814yes—
248C2×C4C31×C22⋊Q814yes—
249C2×C4C31×#12414yes—
250C2×C4C31×C4⋊Q814yes—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—42no—
258C22—42no—
259C22C22×C22⋊C4×C3111yescharacteristic
260C22C2×C4×Q8×C3112yes—
261C22C2×C31×C22⋊Q812yes—
262C22C2×C31×#12411yescharacteristic
263C22C2×C31×C4⋊Q811yescharacteristic
264C4—28no—
265C4—48no—
266C4—44no—
267C4—44no—
268C4—84no—
269C4C31×#39118yes—
270C2—22no—
271C2—21no—
272C2—22no—
273C2—21no—
274C2C2×C31×#39111yescharacteristic
275C2C31×#288311yescharacteristic
276C2C31×#288411yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC24×C31C24
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
8. C2×C31×C4⋊Q8C4semidirect
9. C2×C31×#125C4semidirect
31. C31×#117Q8semidirect
84. #21334C31direct (N × H)
139. C2×C4⋊Q8C4×C31semidirect
140. C2×#125C4×C31semidirect
169. #117Q8×C31semidirect
189. C31#21334direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C31×#23162
C31×#22742
C31×#19962
C31×#17402
#2133431