Finite Group Databasebeta

← C31×#7983 #21464742

Subgroups — C31×#7983 #21464742

Order 7936.

1026 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#407C211yesmaximal, characteristic
2C31×#2280C211yesmaximal, characteristic
3C2×C31×#380C211yesmaximal, characteristic
4C31×#1289C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×M16×C31C412yescomplemented
7C2×C31×#117—21no—
8C22×C4⋊C4×C31—21no—
9C22×C22⋊C4×C31—21no—
10C31×#407—21no—
11C31×#407—21no—
12C31×#407—21no—
13C31×#407—21no—
14C2×C31×C22⋊C8C412yescomplemented
15C2×C31×C22⋊C8C2212yes—
16C31×#381C412yescomplemented
17C31×#380—21no—
18C31×#380—21no—
19C31×#380—21no—
20C31×#380C412yescomplemented
21C31×#380C2212yes—
22C31×#380C2212yes—
23C31×#379—21no—
24C4×C22⋊C4×C31—21no—
25C4×C22⋊C4×C31C412yescomplemented
26C2×C31×#95C412yescomplemented
27C25×C31D411yescharacteristic
28C23×C4×C31—22no—
29C23×C4×C31—44no—
30C23×C4×C31C2×C411yescharacteristic
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31C2×C411yescharacteristic
35C23×C4×C31C2×C411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31D411yescharacteristic
39C23×C4×C31D411yescharacteristic
40C23×C4×C31D411yescharacteristic
41C23×C4×C31Q811yescharacteristic
42C23×C4×C31Q811yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C2×M16×C31—22no—
45C2×M16×C31—22no—
46C2×M16×C31—44no—
47C22×C8×C31C2×C414yescomplemented
48C31×#117—44no—
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—44no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31—22no—
56C2×C22⋊C4×C31—22no—
57C2×C22⋊C4×C31—22no—
58C2×C22⋊C4×C31—44no—
59C2×C42×C31—22no—
60C31×C22⋊C8—22no—
61C31×C22⋊C8—22no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—22no—
64C31×#95—22no—
65C31×#95—22no—
66C31×#95C2×C414yes—
67C31×#95C2×C414yescomplemented
68C24×C31—22no—
69C24×C31—22no—
70C24×C31—42no—
71C24×C31—42no—
72C24×C31C22⋊C411yescharacteristic
73C24×C31C22⋊C411yescharacteristic
74C24×C31C22⋊C411yescharacteristic
75C24×C31C22⋊C411yescharacteristic
76C24×C31C4⋊C411yescharacteristic
77C24×C31C4⋊C411yescharacteristic
78C24×C31C2×D411yescharacteristic
79C22×C4×C31—24no—
80C22×C4×C31—24no—
81C22×C4×C31—24no—
82C22×C4×C31—24no—
83C22×C4×C31—24no—
84C22×C4×C31—42no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31—44no—
96C22×C4×C31—44no—
97C22×C4×C31—44no—
98C22×C4×C31C4211yescharacteristic
99C22×C4×C31C4211yescharacteristic
100C22×C4×C31C4211yescharacteristic
101C22×C4×C31C4211yescharacteristic
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22⋊C411yescharacteristic
105C22×C4×C31C22⋊C411yescharacteristic
106C22×C4×C31C22⋊C411yescharacteristic
107C22×C4×C31C22⋊C411yescharacteristic
108C22×C4×C31C22⋊C411yescharacteristic
109C22×C4×C31C22⋊C411yescharacteristic
110C22×C4×C31C4⋊C411yescharacteristic
111C22×C4×C31C4⋊C411yescharacteristic
112C22×C4×C31C4⋊C411yescharacteristic
113C22×C4×C31C4⋊C411yescharacteristic
114C22×C4×C31C4⋊C411yescharacteristic
115C22×C4×C31C4⋊C411yescharacteristic
116C22×C4×C31C4⋊C411yescharacteristic
117C22×C4×C31C4⋊C411yescharacteristic
118C22×C4×C31C4⋊C411yescharacteristic
119C22×C4×C31C4⋊C411yescharacteristic
120C22×C4×C31C22×C411yescharacteristic
121C22×C4×C31C22×C411yescharacteristic
122C22×C4×C31C22×C411yescharacteristic
123C22×C4×C31C2×D411yescharacteristic
124C22×C4×C31C2×D411yescharacteristic
125C22×C4×C31C2×Q811yescharacteristic
126M16×C31—44no—
127M16×C31—44no—
128C2×C8×C31—24no—
129C2×C8×C31—44no—
130C4⋊C4×C31—44no—
131C4⋊C4×C31—44no—
132C4⋊C4×C31—44no—
133C22⋊C4×C31—44no—
134C22⋊C4×C31—44no—
135C22⋊C4×C31—44no—
136C22⋊C4×C31—42no—
137C22⋊C4×C31—44no—
138C22⋊C4×C31—42no—
139C42×C31—44no—
140#7983C3111yesmaximal, characteristic, direct product factor, Sylow
141C23×C31—22no—
142C23×C31—22no—
143C23×C31—21no—
144C23×C31—21no—
145C23×C31—22no—
146C23×C31—22no—
147C23×C31—22no—
148C23×C31—22no—
149C23×C31—22no—
150C23×C31—22no—
151C23×C31—21no—
152C23×C31—21no—
153C23×C31—22no—
154C23×C31—22no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—41no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31—41no—
161C23×C31—41no—
162C23×C31—41no—
163C23×C31—48no—
164C23×C31—48no—
165C23×C31#9511yescharacteristic
166C23×C31#9511yescharacteristic
167C23×C31#9511yescharacteristic
168C23×C31#9511yescharacteristic
169C23×C31C2×C22⋊C411yescharacteristic
170C23×C31C2×C22⋊C411yescharacteristic
171C23×C31C2×C4⋊C411yescharacteristic
172C23×C31AGL(1,ℤ/8)12yes—
173C23×C31#13712yes—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—44no—
202C2×C4×C31—44no—
203C2×C4×C31—44no—
204C2×C4×C31—44no—
205C2×C4×C31—44no—
206C2×C4×C31—44no—
207C2×C4×C31—88no—
208C2×C4×C31#9511yescharacteristic
209C2×C4×C31#9511yescharacteristic
210C2×C4×C31#9511yescharacteristic
211C2×C4×C31#9511yescharacteristic
212C2×C4×C31#9914yes—
213C2×C4×C31C2×C4211yescharacteristic
214C2×C4×C31C2×C22⋊C411yescharacteristic
215C2×C4×C31C2×C4⋊C411yescharacteristic
216C2×C4×C31C2×C4⋊C411yescharacteristic
217C8×C31—44no—
218C2×#407C2×C3111yescharacteristic
219#2280C2×C3111yescharacteristic
220C2×#380C2×C3111yescharacteristic
221#1289C2×C3114yescomplemented
222C22×C31—24no—
223C22×C31—24no—
224C22×C31—21no—
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—21no—
236C22×C31—21no—
237C22×C31—21no—
238C22×C31—21no—
239C22×C31—21no—
240C22×C31—42no—
241C22×C31—42no—
242C22×C31—44no—
243C22×C31—44no—
244C22×C31—44no—
245C22×C31—44no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31H(3,ℤ/4)12yes—
249C22×C31#34212yes—
250C22×C31C2×#9511yescharacteristic
251C22×C31#41712yes—
252C22×C31#41811yescharacteristic
253C22×C31#41911yescharacteristic
254C22×C31#42812yes—
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—21no—
258C4×C31—21no—
259C4×C31—21no—
260C4×C31—21no—
261C4×C31—84no—
262C4×C31—84no—
263C4×C31#34212yes—
264C4×C31C2×#9912yes—
265C24×C4C22×C3111yescharacteristic
266C22×M16C4×C3112yescomplemented
267C2×#117—21no—
268C22×C4⋊C4—21no—
269C22×C22⋊C4—21no—
270#407—21no—
271#407—21no—
272#407—21no—
273#407—21no—
274C2×C22⋊C8C4×C3112yescomplemented
275C2×C22⋊C8C22×C3112yes—
276#381C4×C3112yescomplemented
277#380—21no—
278#380—21no—
279#380—21no—
280#380C4×C3112yescomplemented
281#380C22×C3112yes—
282#380C22×C3112yes—
283#379—21no—
284C4×C22⋊C4—21no—
285C4×C22⋊C4C4×C3112yescomplemented
286C2×#95C4×C3112yescomplemented
287C2×C31—21no—
288C2×C31—22no—
289C2×C31—22no—
290C2×C31—22no—
291C2×C31—21no—
292C2×C31—22no—
293C2×C31—41no—
294C2×C31—41no—
295C2×C31C2×H(3,ℤ/4)11yescharacteristic
296C2×C31#173611yescharacteristic
297C2×C31C2×#34211yescharacteristic
298C25D4×C3111yescharacteristic
299C23×C4—22no—
300C23×C4—44no—
301C23×C4C2×C4×C3111yescharacteristic
302C23×C4C2×C4×C3111yescharacteristic
303C23×C4C2×C4×C3111yescharacteristic
304C23×C4C2×C4×C3111yescharacteristic
305C23×C4C2×C4×C3111yescharacteristic
306C23×C4C2×C4×C3111yescharacteristic
307C23×C4D4×C3111yescharacteristic
308C23×C4D4×C3111yescharacteristic
309C23×C4D4×C3111yescharacteristic
310C23×C4D4×C3111yescharacteristic
311C23×C4D4×C3111yescharacteristic
312C23×C4Q8×C3111yescharacteristic
313C23×C4Q8×C3111yescharacteristic
314C23×C4C23×C3111yescharacteristic
315C2×M16—22no—
316C2×M16—22no—
317C2×M16—44no—
318C22×C8C2×C4×C3114yescomplemented
319#117—44no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—44no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—44no—
330C2×C42—22no—
331C22⋊C8—22no—
332C22⋊C8—22no—
333C22⋊C8—22no—
334C22⋊C8—22no—
335#95—22no—
336#95—22no—
337#95C2×C4×C3114yes—
338#95C2×C4×C3114yescomplemented
339C31#798311yescharacteristic, direct product factor, Sylow
340C24—22no—
341C24—22no—
342C24—42no—
343C24—42no—
344C24C22⋊C4×C3111yescharacteristic
345C24C22⋊C4×C3111yescharacteristic
346C24C22⋊C4×C3111yescharacteristic
347C24C22⋊C4×C3111yescharacteristic
348C24C4⋊C4×C3111yescharacteristic
349C24C4⋊C4×C3111yescharacteristic
350C24C2×D4×C3111yescharacteristic
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—44no—
368C22×C4—44no—
369C22×C4—44no—
370C22×C4C42×C3111yescharacteristic
371C22×C4C42×C3111yescharacteristic
372C22×C4C42×C3111yescharacteristic
373C22×C4C42×C3111yescharacteristic
374C22×C4C22⋊C4×C3111yescharacteristic
375C22×C4C22⋊C4×C3111yescharacteristic
376C22×C4C22⋊C4×C3111yescharacteristic
377C22×C4C22⋊C4×C3111yescharacteristic
378C22×C4C22⋊C4×C3111yescharacteristic
379C22×C4C22⋊C4×C3111yescharacteristic
380C22×C4C22⋊C4×C3111yescharacteristic
381C22×C4C22⋊C4×C3111yescharacteristic
382C22×C4C4⋊C4×C3111yescharacteristic
383C22×C4C4⋊C4×C3111yescharacteristic
384C22×C4C4⋊C4×C3111yescharacteristic
385C22×C4C4⋊C4×C3111yescharacteristic
386C22×C4C4⋊C4×C3111yescharacteristic
387C22×C4C4⋊C4×C3111yescharacteristic
388C22×C4C4⋊C4×C3111yescharacteristic
389C22×C4C4⋊C4×C3111yescharacteristic
390C22×C4C4⋊C4×C3111yescharacteristic
391C22×C4C4⋊C4×C3111yescharacteristic
392C22×C4C22×C4×C3111yescharacteristic
393C22×C4C22×C4×C3111yescharacteristic
394C22×C4C22×C4×C3111yescharacteristic
395C22×C4C2×D4×C3111yescharacteristic
396C22×C4C2×D4×C3111yescharacteristic
397C22×C4C2×Q8×C3111yescharacteristic
398M16—44no—
399M16—44no—
400C2×C8—24no—
401C2×C8—44no—
402C4⋊C4—44no—
403C4⋊C4—44no—
404C4⋊C4—44no—
405C22⋊C4—44no—
406C22⋊C4—44no—
407C22⋊C4—44no—
408C22⋊C4—42no—
409C22⋊C4—44no—
410C22⋊C4—42no—
411C42—44no—
412C23—21no—
413C23—21no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—48no—
435C23—48no—
436C23C31×#9511yescharacteristic
437C23C31×#9511yescharacteristic
438C23C31×#9511yescharacteristic
439C23C31×#9511yescharacteristic
440C23C2×C22⋊C4×C3111yescharacteristic
441C23C2×C22⋊C4×C3111yescharacteristic
442C23C2×C4⋊C4×C3111yescharacteristic
443C23C31×AGL(1,ℤ/8)12yes—
444C23C31×#13712yes—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—44no—
474C2×C4—44no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—88no—
479C2×C4C31×#9511yescharacteristic
480C2×C4C31×#9511yescharacteristic
481C2×C4C31×#9511yescharacteristic
482C2×C4C31×#9511yescharacteristic
483C2×C4C31×#9914yes—
484C2×C4C2×C42×C3111yescharacteristic
485C2×C4C2×C22⋊C4×C3111yescharacteristic
486C2×C4C2×C4⋊C4×C3111yescharacteristic
487C2×C4C2×C4⋊C4×C3111yescharacteristic
488C8—44no—
489C22—24no—
490C22—24no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—44no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—42no—
514C22—42no—
515C22C31×H(3,ℤ/4)12yes—
516C22C31×#34212yes—
517C22C2×C31×#9511yescharacteristic
518C22C31×#41712yes—
519C22C31×#41811yescharacteristic
520C22C31×#41911yescharacteristic
521C22C31×#42812yes—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—84no—
529C4—84no—
530C4C31×#34212yes—
531C4C2×C31×#9912yes—
532C2—21no—
533C2—22no—
534C2—21no—
535C2—22no—
536C2—22no—
537C2—22no—
538C2—41no—
539C2—41no—
540C2C2×C31×H(3,ℤ/4)11yescharacteristic
541C2C31×#173611yescharacteristic
542C2C2×C31×#34211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#95
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1289C2semidirect
6. C22×M16×C31C4semidirect
14. C2×C31×C22⋊C8C4semidirect
16. C31×#381C4semidirect
20. C31×#380C4semidirect
25. C4×C22⋊C4×C31C4semidirect
26. C2×C31×#95C4semidirect
47. C22×C8×C31C2×C4semidirect
67. C31×#95C2×C4semidirect
140. #7983C31direct (N × H)
221. #1289C2×C31semidirect
266. C22×M16C4×C31semidirect
274. C2×C22⋊C8C4×C31semidirect
276. #381C4×C31semidirect
280. #380C4×C31semidirect
285. C4×C22⋊C4C4×C31semidirect
286. C2×#95C4×C31semidirect
318. C22×C8C2×C4×C31semidirect
338. #95C2×C4×C31semidirect
339. C31#7983direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4072
C31×#22802
C2×C31×#3802
C31×#12892
#798331