Finite Group Databasebeta

← C31×#11381 #21468140

Subgroups — C31×#11381 #21468140

Order 7936.

1426 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#342C214yesmaximal
3C31×C22⋊#95C212yesmaximal
4C23×Q8×C31C411yescharacteristic, complemented
5C24×C4×C31C2211yescharacteristic
6C2×C31×C22⋊Q8—24no—
7C2×C31×C22⋊Q8—28no—
8C22×C4⋊C4×C31C411yescharacteristic, complemented
9C22×C4⋊C4×C31C412yescomplemented
10C22×C22⋊C4×C31C2214yes—
11C22×C22⋊C4×C31C2212yes—
12C2×C31×#95—24no—
13C31×#342—28no—
14C25×C31C2311yescharacteristic
15C22×Q8×C31—24no—
16C22×Q8×C31—22no—
17C22×Q8×C31—44no—
18C23×C4×C31—24no—
19C23×C4×C31—24no—
20C23×C4×C31—44no—
21C23×C4×C31C2×C411yescharacteristic
22C23×C4×C31C2×C412yes—
23C23×C4×C31C2×C412yes—
24C23×C4×C31C2×C411yescharacteristic
25C23×C4×C31D414yes—
26C31×C22⋊Q8—232no—
27C2×C4⋊C4×C31—24no—
28C2×C4⋊C4×C31—24no—
29C2×C4⋊C4×C31—24no—
30C2×C4⋊C4×C31—22no—
31C2×C4⋊C4×C31—24no—
32C2×C22⋊C4×C31—24no—
33C2×C22⋊C4×C31—24no—
34C2×C22⋊C4×C31—28no—
35C2×C22⋊C4×C31—28no—
36C2×C22⋊C4×C31—24no—
37C2×C22⋊C4×C31D418yes—
38C2×C22⋊C4×C31Q818yescomplemented
39C31×#95—48no—
40C24×C31—42no—
41C24×C31—42no—
42C24×C31C22×C411yescharacteristic
43C24×C31C2×D412yes—
44C24×C31C2×D414yes—
45C24×C31C2×Q814yes—
46C24×C31#4114yes—
47C2×Q8×C31—28no—
48C2×Q8×C31—416no—
49C2×Q8×C31—44no—
50C2×Q8×C31—44no—
51C22×C4×C31—22no—
52C22×C4×C31—24no—
53C22×C4×C31—22no—
54C22×C4×C31—22no—
55C22×C4×C31—22no—
56C22×C4×C31—22no—
57C22×C4×C31—22no—
58C22×C4×C31—28no—
59C22×C4×C31—28no—
60C22×C4×C31—28no—
61C22×C4×C31—42no—
62C22×C4×C31—44no—
63C22×C4×C31—416no—
64C22×C4×C31—44no—
65C22×C4×C31—44no—
66C22×C4×C31—48no—
67C22×C4×C31—48no—
68C22×C4×C31—44no—
69C22×C4×C31—44no—
70C22×C4×C31C22⋊C412yes—
71C22×C4×C31C22⋊C412yes—
72C22×C4×C31C22⋊C414yes—
73C22×C4×C31C22⋊C414yes—
74C4⋊C4×C31—28no—
75C4⋊C4×C31—216no—
76C22⋊C4×C31—216no—
77C22⋊C4×C31—216no—
78C22⋊C4×C31—48no—
79#11381C3111yesmaximal, characteristic, direct product factor, Sylow
80C23×C31—22no—
81C23×C31—24no—
82C23×C31—22no—
83C23×C31—24no—
84C23×C31—44no—
85C23×C31—44no—
86C23×C31—48no—
87C23×C31—48no—
88C23×C31C2×C22⋊C412yes—
89C23×C31C2×C22⋊C411yescharacteristic
90C23×C31C4×Q814yes—
91C23×C31#12014yes—
92C23×C31C22⋊Q814yes—
93C23×C31C22⋊Q818yes—
94C23×C31#12412yes—
95C23×C31#12414yes—
96C23×C31C4⋊Q812yes—
97C23×C31C4⋊Q814yes—
98Q8×C31—416no—
99C2×C4×C31—28no—
100C2×C4×C31—22no—
101C2×C4×C31—22no—
102C2×C4×C31—24no—
103C2×C4×C31—24no—
104C2×C4×C31—22no—
105C2×C4×C31—24no—
106C2×C4×C31—416no—
107C2×C4×C31—44no—
108C2×C4×C31—44no—
109C2×C4×C31—44no—
110C2×C4×C31—44no—
111C2×C4×C31—44no—
112C2×C4×C31—44no—
113C2×C4×C31—44no—
114C2×C4×C31—416no—
115C2×C4×C31—48no—
116C2×C4×C31—88no—
117C2×C4×C31—84no—
118C2×C4×C31—84no—
119C2×C4×C31#9914yes—
120C22×C22⋊Q8C2×C3111yescharacteristic
121C2×#342C2×C3114yes—
122C22⋊#95C2×C3112yes—
123C22×C31—28no—
124C22×C31—24no—
125C22×C31—28no—
126C22×C31—24no—
127C22×C31—22no—
128C22×C31—24no—
129C22×C31—22no—
130C22×C31—24no—
131C22×C31—48no—
132C22×C31—44no—
133C22×C31—44no—
134C22×C31#37911yescharacteristic
135C22×C31#39114yes—
136C22×C31#39112yes—
137C22×C31#39314yes—
138C22×C31#39514yes—
139C22×C31C2×#9912yes—
140C22×C31#41012yes—
141C4×C31—24no—
142C4×C31—42no—
143C4×C31—44no—
144C4×C31—44no—
145C4×C31—88no—
146C23×Q8C4×C3111yescharacteristic, complemented
147C24×C4C22×C3111yescharacteristic
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—28no—
150C22×C4⋊C4C4×C3111yescharacteristic, complemented
151C22×C4⋊C4C4×C3112yescomplemented
152C22×C22⋊C4C22×C3114yes—
153C22×C22⋊C4C22×C3112yes—
154C2×#95—24no—
155#342—28no—
156C2×C31—24no—
157C2×C31—24no—
158C2×C31—24no—
159C2×C31#144611yescharacteristic
160C2×C31#178111yescharacteristic
161C2×C31#178211yescharacteristic
162C2×C31#199614yes—
163C25C23×C3111yescharacteristic
164C22×Q8—24no—
165C22×Q8—22no—
166C22×Q8—44no—
167C23×C4—24no—
168C23×C4—24no—
169C23×C4—44no—
170C23×C4C2×C4×C3111yescharacteristic
171C23×C4C2×C4×C3112yes—
172C23×C4C2×C4×C3112yes—
173C23×C4C2×C4×C3111yescharacteristic
174C23×C4D4×C3114yes—
175C22⋊Q8—232no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—28no—
184C2×C22⋊C4—28no—
185C2×C22⋊C4—24no—
186C2×C22⋊C4D4×C3118yes—
187C2×C22⋊C4Q8×C3118yescomplemented
188#95—48no—
189C31#1138111yescharacteristic, direct product factor, Sylow
190C24—42no—
191C24—42no—
192C24C22×C4×C3111yescharacteristic
193C24C2×D4×C3112yes—
194C24C2×D4×C3114yes—
195C24C2×Q8×C3114yes—
196C24#41×C3114yes—
197C2×Q8—28no—
198C2×Q8—416no—
199C2×Q8—44no—
200C2×Q8—44no—
201C22×C4—22no—
202C22×C4—24no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—28no—
209C22×C4—28no—
210C22×C4—28no—
211C22×C4—42no—
212C22×C4—44no—
213C22×C4—416no—
214C22×C4—44no—
215C22×C4—44no—
216C22×C4—48no—
217C22×C4—48no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4C22⋊C4×C3112yes—
221C22×C4C22⋊C4×C3112yes—
222C22×C4C22⋊C4×C3114yes—
223C22×C4C22⋊C4×C3114yes—
224C4⋊C4—28no—
225C4⋊C4—216no—
226C22⋊C4—216no—
227C22⋊C4—216no—
228C22⋊C4—48no—
229C23—22no—
230C23—24no—
231C23—22no—
232C23—24no—
233C23—44no—
234C23—44no—
235C23—48no—
236C23—48no—
237C23C2×C22⋊C4×C3112yes—
238C23C2×C22⋊C4×C3111yescharacteristic
239C23C4×Q8×C3114yes—
240C23C31×#12014yes—
241C23C31×C22⋊Q814yes—
242C23C31×C22⋊Q818yes—
243C23C31×#12412yes—
244C23C31×#12414yes—
245C23C31×C4⋊Q812yes—
246C23C31×C4⋊Q814yes—
247Q8—416no—
248C2×C4—28no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—416no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—416no—
264C2×C4—48no—
265C2×C4—88no—
266C2×C4—84no—
267C2×C4—84no—
268C2×C4C31×#9914yes—
269C22—28no—
270C22—24no—
271C22—28no—
272C22—24no—
273C22—22no—
274C22—24no—
275C22—22no—
276C22—24no—
277C22—48no—
278C22—44no—
279C22—44no—
280C22C31×#37911yescharacteristic
281C22C31×#39114yes—
282C22C31×#39112yes—
283C22C31×#39314yes—
284C22C31×#39514yes—
285C22C2×C31×#9912yes—
286C22C31×#41012yes—
287C4—24no—
288C4—42no—
289C4—44no—
290C4—44no—
291C4—88no—
292C2—24no—
293C2—24no—
294C2—24no—
295C2C31×#144611yescharacteristic
296C2C31×#178111yescharacteristic
297C2C31×#178211yescharacteristic
298C2C31×#199614yes—
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C23×Q8×C31C4semidirect
8. C22×C4⋊C4×C31C4semidirect
9. C22×C4⋊C4×C31C4semidirect
38. C2×C22⋊C4×C31Q8semidirect
79. #11381C31direct (N × H)
146. C23×Q8C4×C31semidirect
150. C22×C4⋊C4C4×C31semidirect
151. C22×C4⋊C4C4×C31semidirect
187. C2×C22⋊C4Q8×C31semidirect
189. C31#11381direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3422
C31×C22⋊#952
#1138131