Finite Group Databasebeta

← C31×#8440 #21465199

Subgroups — C31×#8440 #21465199

Order 7936.

884 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3481C211yesmaximal, characteristic
2C31×#1962C211yesmaximal, characteristic, complemented
3C4×C31×#104C212yesmaximal, complemented
4C31×#1525C211yesmaximal, characteristic, complemented
5C31×#1489C212yesmaximal, complemented
6C31×#559C411yescharacteristic, complemented
7C31×#554C412yescomplemented
8C31×#553—22no—
9C31×#551—22no—
10C31×#546—22no—
11D42×C31C411yescharacteristic, complemented
12C31×#532C2211yescharacteristic
13C31×#529—22no—
14C31×#525—22no—
15C4×#41×C31C2212yes—
16C2×C4×D4×C31—22no—
17C31×#423C2211yescharacteristic, complemented
18C2×C31×#104—22no—
19C2×C31×#104—22no—
20C4×M16×C31C2212yescomplemented
21C43×C31C2211yescharacteristic, complemented
22C31×#339—22no—
23C31×#329—22no—
24C31×Q8⋊C8—22no—
25C31×D4⋊C8—22no—
26C2×#41×C31D412yes—
27C2×#41×C31D412yes—
28C22×D4×C31—22no—
29C23×C4×C31—22no—
30C2×M16×C31—22no—
31C2×M16×C31—21no—
32C31×C4⋊Q8C2×C411yescharacteristic
33C31×#127C2×C411yescharacteristic
34C31×#126—24no—
35C31×#125—22no—
36C31×#124—22no—
37C31×#124D412yes—
38C31×#123—22no—
39C31×#123—24no—
40C31×#123—22no—
41C31×C22⋊Q8—24no—
42C31×C22⋊Q8—22no—
43C31×#121—24no—
44C31×#121—22no—
45C31×#121—22no—
46C31×#120—22no—
47C31×#120—22no—
48C4×Q8×C31C2×C412yes—
49C4×Q8×C31D412yes—
50C4×D4×C31—24no—
51C4×D4×C31—24no—
52C4×D4×C31—22no—
53C4×D4×C31—22no—
54C4×D4×C31—22no—
55C4×D4×C31—22no—
56C4×D4×C31—22no—
57C4×D4×C31C2×C412yes—
58C4×D4×C31D412yes—
59C31×#117—22no—
60C31×#117—22no—
61C31×#117D412yes—
62C2×C4⋊C4×C31—22no—
63C2×C22⋊C4×C31—24no—
64C2×C42×C31—22no—
65C2×C42×C31—21no—
66C2×C42×C31—22no—
67C2×C42×C31C2311yescharacteristic
68C31×C4⋊C8—22no—
69C31×#104—28no—
70C31×#104—44no—
71C31×#97—22no—
72C4×C8×C31—22no—
73C24×C31—22no—
74#41×C31—24no—
75#41×C31—42no—
76#41×C31—42no—
77#41×C31—42no—
78C2×Q8×C31C22⋊C412yes—
79C2×Q8×C31C22⋊C412yes—
80C2×D4×C31—24no—
81C2×D4×C31—22no—
82C2×D4×C31—22no—
83C2×D4×C31—22no—
84C2×D4×C31—44no—
85C2×D4×C31—44no—
86C2×D4×C31C22⋊C412yes—
87C2×D4×C31C22⋊C412yes—
88C22×C4×C31—24no—
89C22×C4×C31—22no—
90C22×C4×C31—22no—
91C22×C4×C31—22no—
92C22×C4×C31—22no—
93C22×C4×C31—22no—
94C22×C4×C31—41no—
95C22×C4×C31—82no—
96C22×C4×C31—82no—
97C22×C4×C31C2×D412yes—
98C22×C4×C31C2×D411yescharacteristic
99M16×C31—24no—
100M16×C31—42no—
101M16×C31—42no—
102C2×C8×C31—42no—
103C2×C8×C31—41no—
104C4⋊C4×C31—24no—
105C4⋊C4×C31—24no—
106C4⋊C4×C31—22no—
107C4⋊C4×C31—22no—
108C4⋊C4×C31—22no—
109C4⋊C4×C31C22⋊C412yes—
110C4⋊C4×C31C22⋊C412yes—
111C22⋊C4×C31—24no—
112C22⋊C4×C31—24no—
113C22⋊C4×C31—22no—
114C22⋊C4×C31—22no—
115C22⋊C4×C31—22no—
116C22⋊C4×C31—22no—
117C22⋊C4×C31—22no—
118C22⋊C4×C31—24no—
119C42×C31—22no—
120C42×C31—22no—
121C42×C31—22no—
122C42×C31—24no—
123C42×C31—22no—
124C42×C31—42no—
125C42×C31—41no—
126C42×C31C22×C411yescharacteristic
127C42×C31C2×D411yescharacteristic
128C42×C31C2×D412yes—
129#8440C3111yesmaximal, characteristic, direct product factor, Sylow
130C23×C31—22no—
131C23×C31—22no—
132C23×C31—48no—
133C23×C31—82no—
134C23×C31#12011yescharacteristic
135Q8×C31—22no—
136Q8×C31—22no—
137Q8×C31—42no—
138D4×C31—22no—
139D4×C31—42no—
140D4×C31—44no—
141D4×C31—48no—
142D4×C31—42no—
143D4×C31—42no—
144D4×C31—82no—
145D4×C31#10414yescomplemented
146C2×C4×C31—22no—
147C2×C4×C31—22no—
148C2×C4×C31—21no—
149C2×C4×C31—21no—
150C2×C4×C31—22no—
151C2×C4×C31—22no—
152C2×C4×C31—22no—
153C2×C4×C31—22no—
154C2×C4×C31—44no—
155C2×C4×C31—42no—
156C2×C4×C31—44no—
157C2×C4×C31—42no—
158C2×C4×C31—42no—
159C2×C4×C31—42no—
160C2×C4×C31—42no—
161C2×C4×C31—42no—
162C2×C4×C31—42no—
163C2×C4×C31—82no—
164C2×C4×C31—84no—
165C2×C4×C31C2×C22⋊C411yescharacteristic
166C2×C4×C31C2×C22⋊C412yes—
167C2×C4×C31#12012yes—
168C2×C4×C31#12011yescharacteristic
169C8×C31—44no—
170C8×C31—81no—
171#3481C2×C3111yescharacteristic
172#1962C2×C3111yescharacteristic, complemented
173C4×#104C2×C3112yescomplemented
174#1525C2×C3111yescharacteristic, complemented
175#1489C2×C3112yescomplemented
176C22×C31—21no—
177C22×C31—22no—
178C22×C31—24no—
179C22×C31—42no—
180C22×C31—42no—
181C22×C31—42no—
182C22×C31—44no—
183C22×C31—88no—
184C22×C31#37911yescharacteristic
185C4×C31—21no—
186C4×C31—22no—
187C4×C31—44no—
188C4×C31—42no—
189C4×C31—42no—
190C4×C31—42no—
191C4×C31—42no—
192C4×C31C2×#10412yes—
193C4×C31#42112yes—
194C4×C31#45311yescharacteristic
195C4×C31#45511yescharacteristic
196#559C4×C3111yescharacteristic, complemented
197#554C4×C3112yescomplemented
198#553—22no—
199#551—22no—
200#546—22no—
201D42C4×C3111yescharacteristic, complemented
202#532C22×C3111yescharacteristic
203#529—22no—
204#525—22no—
205C4×#41C22×C3112yes—
206C2×C4×D4—22no—
207#423C22×C3111yescharacteristic, complemented
208C2×#104—22no—
209C2×#104—22no—
210C4×M16C22×C3112yescomplemented
211C43C22×C3111yescharacteristic, complemented
212#339—22no—
213#329—22no—
214Q8⋊C8—22no—
215D4⋊C8—22no—
216C2×C31—41no—
217C2×C31—44no—
218C2×C31—82no—
219C2×C31#178912yes—
220C2×C31#179211yescharacteristic
221C2×#41D4×C3112yes—
222C2×#41D4×C3112yes—
223C22×D4—22no—
224C23×C4—22no—
225C2×M16—22no—
226C2×M16—21no—
227C4⋊Q8C2×C4×C3111yescharacteristic
228#127C2×C4×C3111yescharacteristic
229#126—24no—
230#125—22no—
231#124—22no—
232#124D4×C3112yes—
233#123—22no—
234#123—24no—
235#123—22no—
236C22⋊Q8—24no—
237C22⋊Q8—22no—
238#121—24no—
239#121—22no—
240#121—22no—
241#120—22no—
242#120—22no—
243C4×Q8C2×C4×C3112yes—
244C4×Q8D4×C3112yes—
245C4×D4—24no—
246C4×D4—24no—
247C4×D4—22no—
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4C2×C4×C3112yes—
253C4×D4D4×C3112yes—
254#117—22no—
255#117—22no—
256#117D4×C3112yes—
257C2×C4⋊C4—22no—
258C2×C22⋊C4—24no—
259C2×C42—22no—
260C2×C42—22no—
261C2×C42—21no—
262C2×C42C23×C3111yescharacteristic
263C4⋊C8—22no—
264#104—28no—
265#104—44no—
266#97—22no—
267C4×C8—22no—
268C31#844011yescharacteristic, direct product factor, Sylow
269C24—22no—
270#41—24no—
271#41—42no—
272#41—42no—
273#41—42no—
274C2×Q8C22⋊C4×C3112yes—
275C2×Q8C22⋊C4×C3112yes—
276C2×D4—24no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4C22⋊C4×C3112yes—
283C2×D4C22⋊C4×C3112yes—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—41no—
291C22×C4—82no—
292C22×C4—82no—
293C22×C4C2×D4×C3112yes—
294C22×C4C2×D4×C3111yescharacteristic
295M16—24no—
296M16—42no—
297M16—42no—
298C2×C8—42no—
299C2×C8—41no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4C22⋊C4×C3112yes—
306C4⋊C4C22⋊C4×C3112yes—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—24no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—24no—
319C42—22no—
320C42—42no—
321C42—41no—
322C42C22×C4×C3111yescharacteristic
323C42C2×D4×C3112yes—
324C42C2×D4×C3111yescharacteristic
325C23—22no—
326C23—22no—
327C23—48no—
328C23—82no—
329C23C31×#12011yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—42no—
333D4—22no—
334D4—42no—
335D4—44no—
336D4—48no—
337D4—42no—
338D4—42no—
339D4—82no—
340D4C31×#10414yescomplemented
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—84no—
360C2×C4C2×C22⋊C4×C3111yescharacteristic
361C2×C4C2×C22⋊C4×C3112yes—
362C2×C4C31×#12012yes—
363C2×C4C31×#12011yescharacteristic
364C8—44no—
365C8—81no—
366C22—22no—
367C22—24no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—44no—
372C22—42no—
373C22—88no—
374C22C31×#37911yescharacteristic
375C4—22no—
376C4—21no—
377C4—44no—
378C4—42no—
379C4—42no—
380C4—42no—
381C4—42no—
382C4C2×C31×#10412yes—
383C4C31×#42112yes—
384C4C31×#45311yescharacteristic
385C4C31×#45511yescharacteristic
386C2—41no—
387C2—44no—
388C2—82no—
389C2C31×#178912yes—
390C2C31×#179211yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutatorC42C22×C4×C31
Frattini, cosocleC2×C42C23×C31
socleC22×C31#379
prime radicalC31×#3481C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1962C2semidirect
3. C4×C31×#104C2semidirect
4. C31×#1525C2semidirect
5. C31×#1489C2semidirect
6. C31×#559C4semidirect
7. C31×#554C4semidirect
11. D42×C31C4semidirect
17. C31×#423C22semidirect
20. C4×M16×C31C22semidirect
21. C43×C31C22semidirect
129. #8440C31direct (N × H)
145. D4×C31#104semidirect
172. #1962C2×C31semidirect
173. C4×#104C2×C31semidirect
174. #1525C2×C31semidirect
175. #1489C2×C31semidirect
196. #559C4×C31semidirect
197. #554C4×C31semidirect
201. D42C4×C31semidirect
207. #423C22×C31semidirect
210. C4×M16C22×C31semidirect
211. C43C22×C31semidirect
268. C31#8440direct (N × H)
340. D4C31×#104semidirect

Maximal subgroups

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

subgroupindex
C31×#34812
C31×#19622
C4×C31×#1042
C31×#15252
C31×#14892
#844031