Finite Group Databasebeta

← C31×#13852 #21470611

Subgroups — C31×#13852 #21470611

Order 7936.

2118 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C31C212yesmaximal, complemented
3C2×C4×C22⋊C4×C31C212yesmaximal
4C31×#1441C214yesmaximal, complemented
5C31×#1439C214yesmaximal
6C4×C31×#95C212yesmaximal, complemented
7C24×C4×C31C2211yescharacteristic
8C2×C31×#117—28no—
9C2×C31×#117C418yescomplemented
10C22×C4⋊C4×C31C2214yes—
11C22×C4⋊C4×C31C2212yes—
12C22×C22⋊C4×C31C2214yes—
13C22×C22⋊C4×C31C2212yes—
14C22×C42×C31C2214yes—
15C22×C42×C31C2211yescharacteristic
16C22×C42×C31C2211yescharacteristic
17C4×C4⋊C4×C31—28no—
18C4×C22⋊C4×C31—28no—
19C2×C31×#95C2218yes—
20C2×C31×#95C2214yes—
21C2×C31×#95C2214yes—
22C25×C31C2311yescharacteristic
23C23×C4×C31—24no—
24C23×C4×C31—24no—
25C23×C4×C31C2×C414yes—
26C23×C4×C31D414yes—
27C23×C4×C31Q814yes—
28C23×C4×C31C2312yes—
29C23×C4×C31C2318yes—
30C23×C4×C31C2312yes—
31C23×C4×C31C2311yescharacteristic
32C23×C4×C31C2311yescharacteristic
33C31×#117—232no—
34C2×C4⋊C4×C31—24no—
35C2×C4⋊C4×C31—24no—
36C2×C4⋊C4×C31—28no—
37C2×C4⋊C4×C31—216no—
38C2×C4⋊C4×C31C2×C418yes—
39C2×C22⋊C4×C31—28no—
40C2×C22⋊C4×C31—24no—
41C2×C22⋊C4×C31—24no—
42C2×C22⋊C4×C31—216no—
43C2×C22⋊C4×C31C2×C418yes—
44C2×C42×C31—24no—
45C2×C42×C31—28no—
46C2×C42×C31—28no—
47C2×C42×C31—28no—
48C2×C42×C31C2×C414yes—
49C2×C42×C31C2×C414yes—
50C2×C42×C31D418yes—
51C31×#95—28no—
52C31×#95—28no—
53C31×#95—216no—
54C24×C31—22no—
55C24×C31—28no—
56C24×C31—22no—
57C24×C31C22×C412yes—
58C24×C31C2×D412yes—
59C24×C31C2×Q812yes—
60C24×C31C2411yescharacteristic
61C22×C4×C31—22no—
62C22×C4×C31—28no—
63C22×C4×C31—22no—
64C22×C4×C31—28no—
65C22×C4×C31—28no—
66C22×C4×C31—216no—
67C22×C4×C31—216no—
68C22×C4×C31—28no—
69C22×C4×C31—28no—
70C22×C4×C31—22no—
71C22×C4×C31—22no—
72C22×C4×C31—28no—
73C22×C4×C31—28no—
74C22×C4×C31—28no—
75C22×C4×C31—28no—
76C22×C4×C31—28no—
77C22×C4×C31C4⋊C4116yescomplemented
78C22×C4×C31C22×C414yes—
79C22×C4×C31C22×C414yes—
80C22×C4×C31C22×C412yes—
81C22×C4×C31C22×C412yes—
82C22×C4×C31C2×D414yes—
83C22×C4×C31C2×D414yes—
84C22×C4×C31C2×D412yes—
85C22×C4×C31C2×D414yes—
86C22×C4×C31C2×D412yes—
87C22×C4×C31C2×Q812yes—
88C22×C4×C31C2×Q812yes—
89C22×C4×C31#41116yes—
90C22×C4×C31#4114yes—
91C4⋊C4×C31—232no—
92C4⋊C4×C31—216no—
93C22⋊C4×C31—232no—
94C22⋊C4×C31—216no—
95C42×C31—28no—
96C42×C31—416no—
97C42×C31C22⋊C4116yescomplemented
98#13852C3111yesmaximal, characteristic, direct product factor, Sylow
99C23×C31—22no—
100C23×C31—22no—
101C23×C31—28no—
102C23×C31—24no—
103C23×C31—24no—
104C23×C31—28no—
105C23×C31—28no—
106C23×C31—44no—
107C23×C31—48no—
108C23×C31—44no—
109C23×C31C2×C4⋊C414yes—
110C23×C31C23×C411yescharacteristic
111C23×C31C22×D412yes—
112C23×C31C22×D411yescharacteristic
113C23×C31C22×Q811yescharacteristic
114C23×C31C2×#4112yes—
115C23×C31C2×#4118yes—
116C2×C4×C31—22no—
117C2×C4×C31—22no—
118C2×C4×C31—28no—
119C2×C4×C31—24no—
120C2×C4×C31—24no—
121C2×C4×C31—28no—
122C2×C4×C31—28no—
123C2×C4×C31—232no—
124C2×C4×C31—24no—
125C2×C4×C31—28no—
126C2×C4×C31—216no—
127C2×C4×C31—216no—
128C2×C4×C31—216no—
129C2×C4×C31—48no—
130C2×C4×C31—48no—
131C2×C4×C31—44no—
132C2×C4×C31—48no—
133C2×C4×C31—48no—
134C2×C4×C31—44no—
135C2×C4×C31C2×C22⋊C418yes—
136C2×C4×C31C2×C22⋊C414yes—
137C2×C4×C31C2×C4⋊C414yes—
138C2×C4×C31C2×C4⋊C414yes—
139C2×C4×C31#11714yes—
140C2×C4×C31#12118yes—
141C2×C4×C31C22⋊Q818yes—
142C22×#117C2×C3111yescharacteristic
143C2×C4×C4⋊C4C2×C3112yescomplemented
144C2×C4×C22⋊C4C2×C3112yes—
145#1441C2×C3114yescomplemented
146#1439C2×C3114yes—
147C4×#95C2×C3112yescomplemented
148C22×C31—24no—
149C22×C31—28no—
150C22×C31—48no—
151C22×C31—48no—
152C22×C31—44no—
153C22×C31—44no—
154C22×C31C22×C22⋊C411yescharacteristic
155C22×C31C22×C4⋊C411yescharacteristic
156C22×C31C2×#11711yescharacteristic
157C22×C31C4×#4114yes—
158C22×C31C2×#12112yes—
159C22×C31C2×C22⋊Q812yes—
160C22×C31#52514yes—
161C22×C31#52514yes—
162C22×C31#52918yes—
163C22×C31#53214yes—
164C22×C31#53314yes—
165C4×C31—24no—
166C4×C31—28no—
167C4×C31—416no—
168C4×C31—44no—
169C4×C31#38018yes—
170C24×C4C22×C3111yescharacteristic
171C2×#117—28no—
172C2×#117C4×C3118yescomplemented
173C22×C4⋊C4C22×C3114yes—
174C22×C4⋊C4C22×C3112yes—
175C22×C22⋊C4C22×C3114yes—
176C22×C22⋊C4C22×C3112yes—
177C22×C42C22×C3114yes—
178C22×C42C22×C3111yescharacteristic
179C22×C42C22×C3111yescharacteristic
180C4×C4⋊C4—28no—
181C4×C22⋊C4—28no—
182C2×#95C22×C3118yes—
183C2×#95C22×C3114yes—
184C2×#95C22×C3114yes—
185C2×C31—44no—
186C2×C31C2×#38011yescharacteristic
187C2×C31#229612yes—
188C2×C31#229712yes—
189C2×C31#229812yes—
190C2×C31#239214yes—
191C2×C31#239614yes—
192C25C23×C3111yescharacteristic
193C23×C4—24no—
194C23×C4—24no—
195C23×C4C2×C4×C3114yes—
196C23×C4D4×C3114yes—
197C23×C4Q8×C3114yes—
198C23×C4C23×C3112yes—
199C23×C4C23×C3118yes—
200C23×C4C23×C3112yes—
201C23×C4C23×C3111yescharacteristic
202C23×C4C23×C3111yescharacteristic
203#117—232no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—24no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—216no—
208C2×C4⋊C4C2×C4×C3118yes—
209C2×C22⋊C4—28no—
210C2×C22⋊C4—24no—
211C2×C22⋊C4—24no—
212C2×C22⋊C4—216no—
213C2×C22⋊C4C2×C4×C3118yes—
214C2×C42—24no—
215C2×C42—28no—
216C2×C42—28no—
217C2×C42—28no—
218C2×C42C2×C4×C3114yes—
219C2×C42C2×C4×C3114yes—
220C2×C42D4×C3118yes—
221#95—28no—
222#95—28no—
223#95—216no—
224C31#1385211yescharacteristic, direct product factor, Sylow
225C24—22no—
226C24—28no—
227C24—22no—
228C24C22×C4×C3112yes—
229C24C2×D4×C3112yes—
230C24C2×Q8×C3112yes—
231C24C24×C3111yescharacteristic
232C22×C4—22no—
233C22×C4—28no—
234C22×C4—22no—
235C22×C4—28no—
236C22×C4—28no—
237C22×C4—216no—
238C22×C4—216no—
239C22×C4—28no—
240C22×C4—28no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—28no—
244C22×C4—28no—
245C22×C4—28no—
246C22×C4—28no—
247C22×C4—28no—
248C22×C4C4⋊C4×C31116yescomplemented
249C22×C4C22×C4×C3114yes—
250C22×C4C22×C4×C3114yes—
251C22×C4C22×C4×C3112yes—
252C22×C4C22×C4×C3112yes—
253C22×C4C2×D4×C3114yes—
254C22×C4C2×D4×C3114yes—
255C22×C4C2×D4×C3112yes—
256C22×C4C2×D4×C3114yes—
257C22×C4C2×D4×C3112yes—
258C22×C4C2×Q8×C3112yes—
259C22×C4C2×Q8×C3112yes—
260C22×C4#41×C31116yes—
261C22×C4#41×C3114yes—
262C4⋊C4—232no—
263C4⋊C4—216no—
264C22⋊C4—232no—
265C22⋊C4—216no—
266C42—28no—
267C42—416no—
268C42C22⋊C4×C31116yescomplemented
269C23—22no—
270C23—22no—
271C23—28no—
272C23—24no—
273C23—24no—
274C23—28no—
275C23—28no—
276C23—44no—
277C23—48no—
278C23—44no—
279C23C2×C4⋊C4×C3114yes—
280C23C23×C4×C3111yescharacteristic
281C23C22×D4×C3112yes—
282C23C22×D4×C3111yescharacteristic
283C23C22×Q8×C3111yescharacteristic
284C23C2×#41×C3112yes—
285C23C2×#41×C3118yes—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—28no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—28no—
292C2×C4—28no—
293C2×C4—232no—
294C2×C4—24no—
295C2×C4—28no—
296C2×C4—216no—
297C2×C4—216no—
298C2×C4—216no—
299C2×C4—48no—
300C2×C4—48no—
301C2×C4—44no—
302C2×C4—48no—
303C2×C4—48no—
304C2×C4—44no—
305C2×C4C2×C22⋊C4×C3118yes—
306C2×C4C2×C22⋊C4×C3114yes—
307C2×C4C2×C4⋊C4×C3114yes—
308C2×C4C2×C4⋊C4×C3114yes—
309C2×C4C31×#11714yes—
310C2×C4C31×#12118yes—
311C2×C4C31×C22⋊Q818yes—
312C22—24no—
313C22—28no—
314C22—48no—
315C22—48no—
316C22—44no—
317C22—44no—
318C22C22×C22⋊C4×C3111yescharacteristic
319C22C22×C4⋊C4×C3111yescharacteristic
320C22C2×C31×#11711yescharacteristic
321C22C4×#41×C3114yes—
322C22C2×C31×#12112yes—
323C22C2×C31×C22⋊Q812yes—
324C22C31×#52514yes—
325C22C31×#52514yes—
326C22C31×#52918yes—
327C22C31×#53214yes—
328C22C31×#53314yes—
329C4—24no—
330C4—28no—
331C4—416no—
332C4—44no—
333C4C31×#38018yes—
334C2—44no—
335C2C2×C31×#38011yescharacteristic
336C2C31×#229612yes—
337C2C31×#229712yes—
338C2C31×#229812yes—
339C2C31×#239214yes—
340C2C31×#239614yes—
subgroupG/H
centerC23×C4×C31C23
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
socleC24×C31C24
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊C4×C31C2semidirect
4. C31×#1441C2semidirect
6. C4×C31×#95C2semidirect
9. C2×C31×#117C4semidirect
77. C22×C4×C31C4⋊C4semidirect
97. C42×C31C22⋊C4semidirect
98. #13852C31direct (N × H)
143. C2×C4×C4⋊C4C2×C31semidirect
145. #1441C2×C31semidirect
147. C4×#95C2×C31semidirect
172. C2×#117C4×C31semidirect
224. C31#13852direct (N × H)
248. C22×C4C4⋊C4×C31semidirect
268. C42C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C31×#14412
C31×#14392
C4×C31×#952
#1385231