Finite Group Databasebeta

← C31×#20959 #21477718

Subgroups — C31×#20959 #21477718

Order 7936.

1974 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C31×#3428C211yesmaximal, characteristic, complemented
3C2×C31×#410C211yesmaximal, characteristic, complemented
4C31×#2280C212yesmaximal, complemented
5C31×#1890C214yesmaximal, complemented
6C31×#1889C214yesmaximal, complemented
7C31×#1740C212yesmaximal, complemented
8C22×#41×C31C2211yescharacteristic
9C24×C4×C31C2211yescharacteristic
10C31×#525—24no—
11C31×#525C418yescomplemented
12C2×C31×#123C2212yes—
13C2×C31×C22⋊Q8—21no—
14C2×C31×#121—21no—
15C2×C31×#120C2212yes—
16C31×#520—24no—
17C31×#519—21no—
18C31×#518—21no—
19C31×#518C2214yes—
20C4×#41×C31—24no—
21C2×C4×D4×C31—22no—
22C2×C31×#117—22no—
23C2×C31×#117C2212yes—
24C2×C31×#117C2211yescharacteristic
25C2×C31×#117C2212yes—
26C31×#410—24no—
27C2×C31×#99C2214yes—
28C31×#381C2214yes—
29C31×#380—24no—
30C31×#379C2214yes—
31C4×C22⋊C4×C31—24no—
32C31×#342C2218yes—
33C25×C31C2311yescharacteristic
34C2×#41×C31—22no—
35C2×#41×C31—22no—
36C2×#41×C31—24no—
37C2×#41×C31C2×C414yes—
38C2×#41×C31D414yes—
39C22×Q8×C31D411yescharacteristic
40C22×D4×C31—22no—
41C22×D4×C31D411yescharacteristic
42C22×D4×C31C2312yes—
43C23×C4×C31—21no—
44C23×C4×C31—21no—
45C23×C4×C31—22no—
46C23×C4×C31—22no—
47C23×C4×C31—22no—
48C23×C4×C31—24no—
49C23×C4×C31C2×C414yescomplemented
50C23×C4×C31D412yes—
51C23×C4×C31C2311yescharacteristic
52C23×C4×C31C2311yescharacteristic
53C31×#123—24no—
54C31×#123C2×C418yescomplemented
55C31×C22⋊Q8—28no—
56C31×#121—28no—
57C31×#120—24no—
58C31×#120C2×C418yescomplemented
59C4×Q8×C31—28no—
60C4×D4×C31—28no—
61C4×D4×C31—216no—
62C4×D4×C31—216no—
63C31×#117—24no—
64C31×#117—24no—
65C31×#117—22no—
66C31×#117—24no—
67C31×#117—22no—
68C31×#117—22no—
69C31×#117—22no—
70C31×#117—22no—
71C31×#117—24no—
72C31×#117—24no—
73C31×#117C2×C414yescomplemented
74C2×C4⋊C4×C31—24no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31D414yescomplemented
79C2×C22⋊C4×C31—24no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—28no—
83C2×C22⋊C4×C31C2314yes—
84C2×C22⋊C4×C31C2314yes—
85C2×C22⋊C4×C31C2312yes—
86C2×C42×C31—24no—
87C2×C42×C31—21no—
88C2×C42×C31—22no—
89C2×C42×C31D414yescomplemented
90C31×#99—28no—
91C31×#95—28no—
92C24×C31—22no—
93C24×C31—21no—
94C24×C31—21no—
95C24×C31—22no—
96C24×C31—44no—
97C24×C31C22×C412yes—
98C24×C31C2×D412yes—
99C24×C31C2411yescharacteristic
100#41×C31—28no—
101#41×C31—28no—
102#41×C31—28no—
103#41×C31—28no—
104C2×Q8×C31—22no—
105C2×Q8×C31—22no—
106C2×Q8×C31C22⋊C414yescomplemented
107C2×D4×C31—24no—
108C2×D4×C31—24no—
109C2×D4×C31—28no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—48no—
113C2×D4×C31C22⋊C414yescomplemented
114C2×D4×C31C22×C414yes—
115C2×D4×C31C2×D414yes—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—24no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—22no—
124C22×C4×C31—28no—
125C22×C4×C31—24no—
126C22×C4×C31—24no—
127C22×C4×C31—28no—
128C22×C4×C31—28no—
129C22×C4×C31—24no—
130C22×C4×C31—42no—
131C22×C4×C31—41no—
132C22×C4×C31—41no—
133C22×C4×C31—44no—
134C22×C4×C31—44no—
135C22×C4×C31—42no—
136C22×C4×C31—42no—
137C22×C4×C31C22⋊C418yescomplemented
138C22×C4×C31C22×C412yes—
139C22×C4×C31C22×C412yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D418yes—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31#4114yes—
148C4⋊C4×C31—28no—
149C4⋊C4×C31—24no—
150C4⋊C4×C31—28no—
151C4⋊C4×C31—24no—
152C4⋊C4×C31—24no—
153C4⋊C4×C31—44no—
154C22⋊C4×C31—28no—
155C22⋊C4×C31—28no—
156C22⋊C4×C31—24no—
157C22⋊C4×C31—24no—
158C22⋊C4×C31—22no—
159C22⋊C4×C31—28no—
160C22⋊C4×C31—24no—
161C22⋊C4×C31—24no—
162C22⋊C4×C31—416no—
163C22⋊C4×C31C22×C414yes—
164C42×C31—28no—
165C42×C31—24no—
166C42×C31—24no—
167C42×C31—24no—
168C42×C31—44no—
169#20959C3111yesmaximal, characteristic, direct product factor, Sylow
170C23×C31—28no—
171C23×C31—24no—
172C23×C31—22no—
173C23×C31—24no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—44no—
177C23×C31—42no—
178C23×C31—44no—
179C23×C31—42no—
180C23×C31—44no—
181C23×C31—48no—
182C23×C31—44no—
183C23×C31—41no—
184C23×C31—42no—
185C23×C31—41no—
186C23×C31C2×C22⋊C414yes—
187C23×C31C23×C411yescharacteristic
188C23×C31C22×D411yescharacteristic
189C23×C31C22×D412yes—
190C23×C31C22×D411yescharacteristic
191C23×C31C2×#4112yes—
192Q8×C31—28no—
193D4×C31—28no—
194D4×C31—28no—
195D4×C31—28no—
196D4×C31—416no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—28no—
200C2×C4×C31—28no—
201C2×C4×C31—24no—
202C2×C4×C31—22no—
203C2×C4×C31—24no—
204C2×C4×C31—28no—
205C2×C4×C31—44no—
206C2×C4×C31—41no—
207C2×C4×C31—42no—
208C2×C4×C31—41no—
209C2×C4×C31—44no—
210C2×C4×C31—44no—
211C2×C4×C31—48no—
212C2×C4×C31—48no—
213C2×C4×C31—48no—
214C2×C4×C31—44no—
215C2×C4×C31—88no—
216C2×C4×C31C2×C22⋊C414yes—
217C2×C4×C31C2×C22⋊C412yes—
218C2×C4×C31C2×C22⋊C412yes—
219C2×C4×C31C4×D414yes—
220C2×C4×C31C4×D414yes—
221C2×C4×C31#12012yes—
222C2×C4×C31#12011yescharacteristic
223C2×C4×C31#12011yescharacteristic
224C2×C4×C31#12114yes—
225C2×C4×C31#12114yes—
226C2×C4×C31#12312yes—
227C2×C4×C31#12312yes—
228C2×#525C2×C3111yescharacteristic
229#3428C2×C3111yescharacteristic, complemented
230C2×#410C2×C3111yescharacteristic, complemented
231#2280C2×C3112yescomplemented
232#1890C2×C3114yescomplemented
233#1889C2×C3114yescomplemented
234#1740C2×C3112yescomplemented
235C22×C31—24no—
236C22×C31—22no—
237C22×C31—24no—
238C22×C31—28no—
239C22×C31—24no—
240C22×C31—41no—
241C22×C31—41no—
242C22×C31—42no—
243C22×C31—44no—
244C22×C31—42no—
245C22×C31—48no—
246C22×C31—44no—
247C22×C31—44no—
248C22×C31—44no—
249C22×C31—44no—
250C22×C31—42no—
251C22×C31—82no—
252C22×C31C22×C22⋊C411yescharacteristic
253C22×C31C2×C4×D412yes—
254C22×C31C2×#12011yescharacteristic
255C22×C31C2×#12112yes—
256C22×C31C2×#12311yescharacteristic
257C4×C31—24no—
258C4×C31—44no—
259C4×C31—48no—
260C4×C31—42no—
261C4×C31—84no—
262C4×C31#38612yes—
263C4×C31#38612yes—
264C4×C31#38614yes—
265C22×#41C22×C3111yescharacteristic
266C24×C4C22×C3111yescharacteristic
267#525—24no—
268#525C4×C3118yescomplemented
269C2×#123C22×C3112yes—
270C2×C22⋊Q8—21no—
271C2×#121—21no—
272C2×#120C22×C3112yes—
273#520—24no—
274#519—21no—
275#518—21no—
276#518C22×C3114yes—
277C4×#41—24no—
278C2×C4×D4—22no—
279C2×#117—22no—
280C2×#117C22×C3112yes—
281C2×#117C22×C3111yescharacteristic
282C2×#117C22×C3112yes—
283#410—24no—
284C2×#99C22×C3114yes—
285#381C22×C3114yes—
286#380—24no—
287#379C22×C3114yes—
288C4×C22⋊C4—24no—
289#342C22×C3118yes—
290C2×C31—21no—
291C2×C31—22no—
292C2×C31—22no—
293C2×C31—21no—
294C2×C31—44no—
295C2×C31—44no—
296C2×C31C2×#38611yescharacteristic
297C2×C31#302512yes—
298C25C23×C3111yescharacteristic
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—24no—
302C2×#41C2×C4×C3114yes—
303C2×#41D4×C3114yes—
304C22×Q8D4×C3111yescharacteristic
305C22×D4—22no—
306C22×D4D4×C3111yescharacteristic
307C22×D4C23×C3112yes—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—24no—
314C23×C4C2×C4×C3114yescomplemented
315C23×C4D4×C3112yes—
316C23×C4C23×C3111yescharacteristic
317C23×C4C23×C3111yescharacteristic
318#123—24no—
319#123C2×C4×C3118yescomplemented
320C22⋊Q8—28no—
321#121—28no—
322#120—24no—
323#120C2×C4×C3118yescomplemented
324C4×Q8—28no—
325C4×D4—28no—
326C4×D4—216no—
327C4×D4—216no—
328#117—24no—
329#117—24no—
330#117—22no—
331#117—24no—
332#117—22no—
333#117—22no—
334#117—22no—
335#117—22no—
336#117—24no—
337#117—24no—
338#117C2×C4×C3114yescomplemented
339C2×C4⋊C4—24no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4D4×C3114yescomplemented
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4C23×C3114yes—
349C2×C22⋊C4C23×C3114yes—
350C2×C22⋊C4C23×C3112yes—
351C2×C42—24no—
352C2×C42—21no—
353C2×C42—22no—
354C2×C42D4×C3114yescomplemented
355#99—28no—
356#95—28no—
357C31#2095911yescharacteristic, direct product factor, Sylow
358C24—22no—
359C24—21no—
360C24—21no—
361C24—22no—
362C24—44no—
363C24C22×C4×C3112yes—
364C24C2×D4×C3112yes—
365C24C24×C3111yescharacteristic
366#41—28no—
367#41—28no—
368#41—28no—
369#41—28no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8C22⋊C4×C3114yescomplemented
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—28no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—48no—
379C2×D4C22⋊C4×C3114yescomplemented
380C2×D4C22×C4×C3114yes—
381C2×D4C2×D4×C3114yes—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—28no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—28no—
394C22×C4—28no—
395C22×C4—24no—
396C22×C4—42no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—44no—
400C22×C4—44no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4C22⋊C4×C3118yescomplemented
404C22×C4C22×C4×C3112yes—
405C22×C4C22×C4×C3112yes—
406C22×C4C2×D4×C3112yes—
407C22×C4C2×D4×C3118yes—
408C22×C4C2×D4×C3111yescharacteristic
409C22×C4C2×D4×C3111yescharacteristic
410C22×C4C2×D4×C3112yes—
411C22×C4C2×D4×C3112yes—
412C22×C4C2×D4×C3112yes—
413C22×C4#41×C3114yes—
414C4⋊C4—28no—
415C4⋊C4—24no—
416C4⋊C4—28no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—44no—
420C22⋊C4—28no—
421C22⋊C4—28no—
422C22⋊C4—24no—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—28no—
426C22⋊C4—24no—
427C22⋊C4—24no—
428C22⋊C4—416no—
429C22⋊C4C22×C4×C3114yes—
430C42—28no—
431C42—24no—
432C42—24no—
433C42—24no—
434C42—44no—
435C23—28no—
436C23—24no—
437C23—22no—
438C23—24no—
439C23—22no—
440C23—22no—
441C23—44no—
442C23—42no—
443C23—44no—
444C23—42no—
445C23—44no—
446C23—48no—
447C23—44no—
448C23—41no—
449C23—42no—
450C23—41no—
451C23C2×C22⋊C4×C3114yes—
452C23C23×C4×C3111yescharacteristic
453C23C22×D4×C3111yescharacteristic
454C23C22×D4×C3112yes—
455C23C22×D4×C3111yescharacteristic
456C23C2×#41×C3112yes—
457Q8—28no—
458D4—28no—
459D4—28no—
460D4—28no—
461D4—416no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—28no—
465C2×C4—28no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—28no—
470C2×C4—44no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—48no—
477C2×C4—48no—
478C2×C4—48no—
479C2×C4—44no—
480C2×C4—88no—
481C2×C4C2×C22⋊C4×C3114yes—
482C2×C4C2×C22⋊C4×C3112yes—
483C2×C4C2×C22⋊C4×C3112yes—
484C2×C4C4×D4×C3114yes—
485C2×C4C4×D4×C3114yes—
486C2×C4C31×#12012yes—
487C2×C4C31×#12011yescharacteristic
488C2×C4C31×#12011yescharacteristic
489C2×C4C31×#12114yes—
490C2×C4C31×#12114yes—
491C2×C4C31×#12312yes—
492C2×C4C31×#12312yes—
493C22—24no—
494C22—22no—
495C22—24no—
496C22—28no—
497C22—24no—
498C22—41no—
499C22—41no—
500C22—42no—
501C22—44no—
502C22—42no—
503C22—48no—
504C22—44no—
505C22—44no—
506C22—44no—
507C22—44no—
508C22—42no—
509C22—82no—
510C22C22×C22⋊C4×C3111yescharacteristic
511C22C2×C4×D4×C3112yes—
512C22C2×C31×#12011yescharacteristic
513C22C2×C31×#12112yes—
514C22C2×C31×#12311yescharacteristic
515C4—24no—
516C4—44no—
517C4—48no—
518C4—42no—
519C4—84no—
520C4C31×#38612yes—
521C4C31×#38612yes—
522C4C31×#38614yes—
523C2—21no—
524C2—22no—
525C2—22no—
526C2—21no—
527C2—44no—
528C2—44no—
529C2C2×C31×#38611yescharacteristic
530C2C31×#302512yes—
subgroupG/H
centerC2×C4×C31#120
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
socleC22×C31C2×#120
prime radicalC2×C31×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3428C2semidirect
3. C2×C31×#410C2semidirect
4. C31×#2280C2semidirect
5. C31×#1890C2semidirect
6. C31×#1889C2semidirect
7. C31×#1740C2semidirect
11. C31×#525C4semidirect
49. C23×C4×C31C2×C4semidirect
54. C31×#123C2×C4semidirect
58. C31×#120C2×C4semidirect
73. C31×#117C2×C4semidirect
78. C2×C4⋊C4×C31D4semidirect
89. C2×C42×C31D4semidirect
106. C2×Q8×C31C22⋊C4semidirect
113. C2×D4×C31C22⋊C4semidirect
137. C22×C4×C31C22⋊C4semidirect
169. #20959C31direct (N × H)
229. #3428C2×C31semidirect
230. C2×#410C2×C31semidirect
231. #2280C2×C31semidirect
232. #1890C2×C31semidirect
233. #1889C2×C31semidirect
234. #1740C2×C31semidirect
268. #525C4×C31semidirect
314. C23×C4C2×C4×C31semidirect
319. #123C2×C4×C31semidirect
323. #120C2×C4×C31semidirect
338. #117C2×C4×C31semidirect
343. C2×C4⋊C4D4×C31semidirect
354. C2×C42D4×C31semidirect
357. C31#20959direct (N × H)
372. C2×Q8C22⋊C4×C31semidirect
379. C2×D4C22⋊C4×C31semidirect
403. C22×C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C31×#34282
C2×C31×#4102
C31×#22802
C31×#18902
C31×#18892
C31×#17402
#2095931