Finite Group Databasebeta

← C31×#14339 #21471098

Subgroups — C31×#14339 #21471098

Order 7936.

2142 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C31C211yesmaximal, characteristic
2C2×C31×#381C212yesmaximal
3C2×C31×#380C212yesmaximal
4C31×#1441C218yesmaximal, complemented
5C31×C22⋊#95C212yesmaximal
6C24×C4×C31C2211yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C24×C4×C31C2211yescharacteristic
9C22×C4⋊C4×C31—28no—
10C22×C4⋊C4×C31C418yescomplemented
11C22×C4⋊C4×C31C2214yes—
12C22×C4⋊C4×C31C2214yes—
13C22×C22⋊C4×C31C2214yes—
14C31×#381—28no—
15C31×#380—28no—
16C2×C31×#95C2214yes—
17C2×C31×#95C2218yes—
18C2×C31×#95C2218yes—
19C25×C31C2311yescharacteristic
20C23×C4×C31—24no—
21C23×C4×C31—24no—
22C23×C4×C31—24no—
23C23×C4×C31—44no—
24C23×C4×C31—44no—
25C23×C4×C31C2×C414yes—
26C23×C4×C31C2×C414yes—
27C23×C4×C31C2×C414yes—
28C23×C4×C31D414yes—
29C23×C4×C31D418yes—
30C23×C4×C31Q814yes—
31C23×C4×C31C2318yes—
32C23×C4×C31C2312yes—
33C23×C4×C31C2312yes—
34C23×C4×C31C2312yes—
35C2×C4⋊C4×C31—232no—
36C2×C4⋊C4×C31—28no—
37C2×C4⋊C4×C31—28no—
38C2×C4⋊C4×C31—28no—
39C2×C4⋊C4×C31—48no—
40C2×C4⋊C4×C31C2×C4116yes—
41C2×C22⋊C4×C31—28no—
42C2×C22⋊C4×C31—28no—
43C2×C22⋊C4×C31—28no—
44C31×#95—28no—
45C31×#95—216no—
46C31×#95—48no—
47C24×C31—24no—
48C24×C31—24no—
49C24×C31C22×C412yes—
50C24×C31C2×D414yes—
51C24×C31C2×D412yes—
52C24×C31C2×Q812yes—
53C24×C31#4114yes—
54C24×C31C2411yescharacteristic
55C22×C4×C31—28no—
56C22×C4×C31—28no—
57C22×C4×C31—216no—
58C22×C4×C31—216no—
59C22×C4×C31—24no—
60C22×C4×C31—24no—
61C22×C4×C31—28no—
62C22×C4×C31—28no—
63C22×C4×C31—24no—
64C22×C4×C31—28no—
65C22×C4×C31—28no—
66C22×C4×C31—28no—
67C22×C4×C31—28no—
68C22×C4×C31—216no—
69C22×C4×C31—216no—
70C22×C4×C31—48no—
71C22×C4×C31—48no—
72C22×C4×C31—416no—
73C22×C4×C31—416no—
74C22×C4×C31C22⋊C4116yes—
75C22×C4×C31C4⋊C4116yescomplemented
76C22×C4×C31C22×C414yes—
77C22×C4×C31C22×C414yes—
78C22×C4×C31C22×C414yes—
79C22×C4×C31C2×D414yes—
80C22×C4×C31C2×D414yes—
81C22×C4×C31C2×D414yes—
82C22×C4×C31C2×Q814yes—
83C4⋊C4×C31—232no—
84C4⋊C4×C31—416no—
85C22⋊C4×C31—416no—
86#14339C3111yesmaximal, characteristic, direct product factor, Sylow
87C23×C31—24no—
88C23×C31—24no—
89C23×C31—28no—
90C23×C31—28no—
91C23×C31—28no—
92C23×C31—216no—
93C23×C31—28no—
94C23×C31C2×C22⋊C414yes—
95C23×C31C2×C4⋊C414yes—
96C23×C31#11714yes—
97C23×C31#12118yes—
98C23×C31C22⋊Q818yes—
99C23×C31C23×C411yescharacteristic
100C23×C31C22×D412yes—
101C23×C31C22×D411yescharacteristic
102C23×C31C22×Q811yescharacteristic
103C23×C31C2×#4112yes—
104C23×C31H(5,𝔽2)14yes—
105C23×C312−1+414yes—
106C2×C4×C31—24no—
107C2×C4×C31—24no—
108C2×C4×C31—28no—
109C2×C4×C31—28no—
110C2×C4×C31—28no—
111C2×C4×C31—28no—
112C2×C4×C31—28no—
113C2×C4×C31—232no—
114C2×C4×C31—24no—
115C2×C4×C31—28no—
116C2×C4×C31—416no—
117C2×C4×C31—416no—
118C2×C4×C31—48no—
119C2×C4×C31—48no—
120C2×C4×C31—48no—
121C2×C4×C31—48no—
122C2×C4×C31—416no—
123C2×C4×C31—416no—
124C2×C4×C31C2×C22⋊C418yes—
125C2×C4×C31C2×C4⋊C418yes—
126C23×C4⋊C4C2×C3111yescharacteristic
127C2×#381C2×C3112yes—
128C2×#380C2×C3112yes—
129#1441C2×C3118yescomplemented
130C22⋊#95C2×C3112yes—
131C22×C31—24no—
132C22×C31—24no—
133C22×C31—28no—
134C22×C31—28no—
135C22×C31—216no—
136C22×C31—216no—
137C22×C31#38018yes—
138C22×C31C22×C22⋊C411yescharacteristic
139C22×C31C22×C4⋊C411yescharacteristic
140C22×C31C2×#11711yescharacteristic
141C22×C31#51812yes—
142C22×C31#51912yes—
143C22×C31C2×#12112yes—
144C22×C31C2×C22⋊Q812yes—
145C22×C31#53414yes—
146C22×C31#53614yes—
147C22×C31#53714yes—
148C22×C31#53918yes—
149C22×C31#54414yes—
150C4×C31—28no—
151C4×C31—28no—
152C4×C31—44no—
153C4×C31—88no—
154C24×C4C22×C3111yescharacteristic
155C24×C4C22×C3111yescharacteristic
156C24×C4C22×C3111yescharacteristic
157C22×C4⋊C4—28no—
158C22×C4⋊C4C4×C3118yescomplemented
159C22×C4⋊C4C22×C3114yes—
160C22×C4⋊C4C22×C3114yes—
161C22×C22⋊C4C22×C3114yes—
162#381—28no—
163#380—28no—
164C2×#95C22×C3114yes—
165C2×#95C22×C3118yes—
166C2×#95C22×C3118yes—
167C2×C31—28no—
168C2×C31C2×#38011yescharacteristic
169C2×C31#230811yescharacteristic
170C2×C31#231011yescharacteristic
171C2×C31#231312yes—
172C2×C31#231612yes—
173C2×C31#261814yes—
174C2×C31#262714yes—
175C25C23×C3111yescharacteristic
176C23×C4—24no—
177C23×C4—24no—
178C23×C4—24no—
179C23×C4—44no—
180C23×C4—44no—
181C23×C4C2×C4×C3114yes—
182C23×C4C2×C4×C3114yes—
183C23×C4C2×C4×C3114yes—
184C23×C4D4×C3114yes—
185C23×C4D4×C3118yes—
186C23×C4Q8×C3114yes—
187C23×C4C23×C3118yes—
188C23×C4C23×C3112yes—
189C23×C4C23×C3112yes—
190C23×C4C23×C3112yes—
191C2×C4⋊C4—232no—
192C2×C4⋊C4—28no—
193C2×C4⋊C4—28no—
194C2×C4⋊C4—28no—
195C2×C4⋊C4—48no—
196C2×C4⋊C4C2×C4×C31116yes—
197C2×C22⋊C4—28no—
198C2×C22⋊C4—28no—
199C2×C22⋊C4—28no—
200#95—28no—
201#95—216no—
202#95—48no—
203C31#1433911yescharacteristic, direct product factor, Sylow
204C24—24no—
205C24—24no—
206C24C22×C4×C3112yes—
207C24C2×D4×C3114yes—
208C24C2×D4×C3112yes—
209C24C2×Q8×C3112yes—
210C24#41×C3114yes—
211C24C24×C3111yescharacteristic
212C22×C4—28no—
213C22×C4—28no—
214C22×C4—216no—
215C22×C4—216no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—28no—
219C22×C4—28no—
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—28no—
223C22×C4—28no—
224C22×C4—28no—
225C22×C4—216no—
226C22×C4—216no—
227C22×C4—48no—
228C22×C4—48no—
229C22×C4—416no—
230C22×C4—416no—
231C22×C4C22⋊C4×C31116yes—
232C22×C4C4⋊C4×C31116yescomplemented
233C22×C4C22×C4×C3114yes—
234C22×C4C22×C4×C3114yes—
235C22×C4C22×C4×C3114yes—
236C22×C4C2×D4×C3114yes—
237C22×C4C2×D4×C3114yes—
238C22×C4C2×D4×C3114yes—
239C22×C4C2×Q8×C3114yes—
240C4⋊C4—232no—
241C4⋊C4—416no—
242C22⋊C4—416no—
243C23—24no—
244C23—24no—
245C23—28no—
246C23—28no—
247C23—28no—
248C23—216no—
249C23—28no—
250C23C2×C22⋊C4×C3114yes—
251C23C2×C4⋊C4×C3114yes—
252C23C31×#11714yes—
253C23C31×#12118yes—
254C23C31×C22⋊Q818yes—
255C23C23×C4×C3111yescharacteristic
256C23C22×D4×C3112yes—
257C23C22×D4×C3111yescharacteristic
258C23C22×Q8×C3111yescharacteristic
259C23C2×#41×C3112yes—
260C23C31×H(5,𝔽2)14yes—
261C23C31×2−1+414yes—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—28no—
265C2×C4—28no—
266C2×C4—28no—
267C2×C4—28no—
268C2×C4—28no—
269C2×C4—232no—
270C2×C4—24no—
271C2×C4—28no—
272C2×C4—416no—
273C2×C4—416no—
274C2×C4—48no—
275C2×C4—48no—
276C2×C4—48no—
277C2×C4—48no—
278C2×C4—416no—
279C2×C4—416no—
280C2×C4C2×C22⋊C4×C3118yes—
281C2×C4C2×C4⋊C4×C3118yes—
282C22—24no—
283C22—24no—
284C22—28no—
285C22—28no—
286C22—216no—
287C22—216no—
288C22C31×#38018yes—
289C22C22×C22⋊C4×C3111yescharacteristic
290C22C22×C4⋊C4×C3111yescharacteristic
291C22C2×C31×#11711yescharacteristic
292C22C31×#51812yes—
293C22C31×#51912yes—
294C22C2×C31×#12112yes—
295C22C2×C31×C22⋊Q812yes—
296C22C31×#53414yes—
297C22C31×#53614yes—
298C22C31×#53714yes—
299C22C31×#53918yes—
300C22C31×#54414yes—
301C4—28no—
302C4—28no—
303C4—44no—
304C4—88no—
305C2—28no—
306C2C2×C31×#38011yescharacteristic
307C2C31×#230811yescharacteristic
308C2C31×#231011yescharacteristic
309C2C31×#231312yes—
310C2C31×#231612yes—
311C2C31×#261814yes—
312C2C31×#262714yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1441C2semidirect
10. C22×C4⋊C4×C31C4semidirect
75. C22×C4×C31C4⋊C4semidirect
86. #14339C31direct (N × H)
129. #1441C2×C31semidirect
158. C22×C4⋊C4C4×C31semidirect
203. C31#14339direct (N × H)
232. C22×C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C312
C2×C31×#3812
C2×C31×#3802
C31×#14412
C31×C22⋊#952
#1433931