Finite Group Databasebeta

← C31×#24731 #21481490

Subgroups — C31×#24731 #21481490

Order 7936.

1086 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#463C212yesmaximal, complemented
2C2×C31×#459C211yesmaximal, characteristic
3C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
4C31×#2548C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#2065C212yesmaximal, complemented
7C31×#2042C212yesmaximal, complemented
8C31×#1957C211yesmaximal, characteristic, complemented
9C31×#1939C211yesmaximal, characteristic, complemented
10C31×#1879C212yesmaximal, complemented
11C31×#1803C211yesmaximal, characteristic, complemented
12C22×SD16×C31C2211yescharacteristic
13C22×D8×C31C2212yes—
14C2×C31×#127C2211yescharacteristic
15C2×C31×#124C2212yes—
16C2×C4×Q8×C31C2211yescharacteristic
17C2×C4×D4×C31C2212yes—
18C2×C4×D4×C31C2211yescharacteristic
19C22×C4⋊C4×C31—21no—
20C31×#463—28no—
21C31×#459—24no—
22C4×SD16×C31—24no—
23C2×C31×#106C2211yescharacteristic
24C2×C31×C4⋊C8C2211yescharacteristic
25C2×C31×C4⋊C8C2212yes—
26C2×C31×#103C2212yes—
27C2×C31×#103C2211yescharacteristic
28C2×C31×#102C2212yes—
29C2×C31×#102C2212yes—
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2212yes—
32C2×C4×C8×C31C2211yescharacteristic
33C31×#394—22no—
34C31×#390—21no—
35C31×#390—21no—
36C31×#390C2212yes—
37C31×#389C2212yes—
38C31×#385—22no—
39C31×#384C2211yescharacteristic
40C31×#380—21no—
41C4×C4⋊C4×C31C2211yescharacteristic
42C31×#340C2212yes—
43C31×#336C2212yes—
44C22×Q8×C31C2311yescharacteristic
45C22×D4×C31—21no—
46C22×D4×C31—21no—
47C22×D4×C31C2312yes—
48C22×D4×C31C2311yescharacteristic
49C23×C4×C31—21no—
50C23×C4×C31—22no—
51C2×SD16×C31—22no—
52C2×SD16×C31—22no—
53C2×SD16×C31D414yescomplemented
54C2×D8×C31—24no—
55C2×D8×C31—24no—
56C2×D8×C31—24no—
57C22×C8×C31C2311yescharacteristic
58C22×C8×C31C2312yes—
59C22×C8×C31C2311yescharacteristic
60C31×#127—22no—
61C31×#127—22no—
62C31×#124—24no—
63C31×#124—42no—
64C4×Q8×C31—22no—
65C4×Q8×C31—22no—
66C4×D4×C31—24no—
67C4×D4×C31—22no—
68C4×D4×C31—42no—
69C4×D4×C31D414yes—
70C2×C4⋊C4×C31—21no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—44no—
75C2×C4⋊C4×C31D411yescharacteristic
76C2×C4⋊C4×C31D411yescharacteristic
77C2×C4⋊C4×C31C2312yes—
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C22⋊C4×C31—21no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C42×C31—21no—
87C2×C42×C31C2312yes—
88C2×C42×C31C2311yescharacteristic
89C31×#106—22no—
90C31×C4⋊C8—24no—
91C31×C4⋊C8—22no—
92C31×#103—24no—
93C31×#103—22no—
94C31×#102—22no—
95C31×#102—24no—
96C31×#102—24no—
97C31×#102—42no—
98C4×C8×C31—22no—
99C31×#95—22no—
100C31×#95D412yes—
101C24×C31—21no—
102C24×C31—22no—
103C2×Q8×C31—21no—
104C2×Q8×C31—21no—
105C2×Q8×C31—21no—
106C2×Q8×C31—21no—
107C2×Q8×C31—21no—
108C2×Q8×C31C2×D412yes—
109C2×D4×C31—22no—
110C2×D4×C31—22no—
111C2×D4×C31—21no—
112C2×D4×C31—22no—
113C2×D4×C31—22no—
114C2×D4×C31—21no—
115C2×D4×C31—22no—
116C2×D4×C31—21no—
117C2×D4×C31—22no—
118C2×D4×C31—42no—
119C2×D4×C31—42no—
120C2×D4×C31—42no—
121C2×D4×C31—42no—
122C2×D4×C31—81no—
123C2×D4×C31—81no—
124C2×D4×C31C2×D412yes—
125C2×D4×C31C2×D412yes—
126C2×D4×C31#4112yes—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—44no—
133C22×C4×C31—44no—
134C22×C4×C31—42no—
135C22×C4×C31—42no—
136C22×C4×C31—82no—
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2411yescharacteristic
142SD16×C31—28no—
143D8×C31—48no—
144C2×C8×C31—21no—
145C2×C8×C31—21no—
146C2×C8×C31—21no—
147C2×C8×C31—22no—
148C2×C8×C31—22no—
149C2×C8×C31—22no—
150C2×C8×C31—21no—
151C2×C8×C31—21no—
152C2×C8×C31C2×D412yes—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—44no—
161C4⋊C4×C31—42no—
162C4⋊C4×C31—42no—
163C4⋊C4×C31—81no—
164C4⋊C4×C31C2×D412yes—
165C22⋊C4×C31—24no—
166C22⋊C4×C31—44no—
167C22⋊C4×C31—44no—
168C22⋊C4×C31—44no—
169C22⋊C4×C31—82no—
170C22⋊C4×C31—82no—
171C42×C31—22no—
172C42×C31—22no—
173C42×C31—42no—
174C42×C31C2×D412yes—
175C42×C31#4112yes—
176#24731C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—41no—
181C23×C31—41no—
182C23×C31—41no—
183C23×C31—41no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31C22×D411yescharacteristic
192Q8×C31—22no—
193Q8×C31—22no—
194Q8×C31—41no—
195Q8×C31—41no—
196D4×C31—22no—
197D4×C31—22no—
198D4×C31—22no—
199D4×C31—42no—
200D4×C31—42no—
201D4×C31—42no—
202D4×C31—42no—
203D4×C31—84no—
204D4×C31—84no—
205D4×C31#12114yes—
206C2×C4×C31—21no—
207C2×C4×C31—21no—
208C2×C4×C31—22no—
209C2×C4×C31—22no—
210C2×C4×C31—22no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—48no—
221C2×C4×C31—41no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—41no—
225C2×C4×C31—42no—
226C2×C4×C31—41no—
227C2×C4×C31—88no—
228C2×C4×C31#12112yes—
229C2×C4×C31#12112yes—
230C2×C4×C31#13512yes—
231C2×C4×C31AGL(1,ℤ/8)12yes—
232C2×C4×C31C22×D411yescharacteristic
233C2×C4×C31C22×D411yescharacteristic
234C2×C4×C31C2×#4111yescharacteristic
235C2×C4×C31C2×#4111yescharacteristic
236C2×C4×C31H(5,𝔽2)11yescharacteristic
237C2×C4×C312−1+411yescharacteristic
238C8×C31—22no—
239C8×C31—42no—
240C8×C31—41no—
241C2×#463C2×C3112yescomplemented
242C2×#459C2×C3111yescharacteristic
243C2×C4×SD16C2×C3111yescharacteristic, complemented
244#2548C2×C3111yescharacteristic, complemented
245D4×C4⋊C4C2×C3111yescharacteristic, complemented
246#2065C2×C3112yescomplemented
247#2042C2×C3112yescomplemented
248#1957C2×C3111yescharacteristic, complemented
249#1939C2×C3111yescharacteristic, complemented
250#1879C2×C3112yescomplemented
251#1803C2×C3111yescharacteristic, complemented
252C22×C31—24no—
253C22×C31—42no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—82no—
260C22×C31—82no—
261C22×C31—82no—
262C22×C31—82no—
263C22×C31—82no—
264C22×C31—82no—
265C22×C31—82no—
266C22×C31C2×#12111yescharacteristic
267C22×C31D4211yescharacteristic
268C22×C31#54811yescharacteristic
269C22×C31C2×#13511yescharacteristic
270C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C31#57611yescharacteristic
272C22×C31#57711yescharacteristic
273C4×C31—22no—
274C4×C31—42no—
275C4×C31—42no—
276C4×C31—42no—
277C4×C31—42no—
278C4×C31—82no—
279C4×C31—81no—
280C4×C31#46314yescomplemented
281C4×C31C2×#12111yescharacteristic
282C4×C31#53711yescharacteristic
283C4×C31#54711yescharacteristic
284C4×C31#55311yescharacteristic
285C22×SD16C22×C3111yescharacteristic
286C22×D8C22×C3112yes—
287C2×#127C22×C3111yescharacteristic
288C2×#124C22×C3112yes—
289C2×C4×Q8C22×C3111yescharacteristic
290C2×C4×D4C22×C3112yes—
291C2×C4×D4C22×C3111yescharacteristic
292C22×C4⋊C4—21no—
293#463—28no—
294#459—24no—
295C4×SD16—24no—
296C2×#106C22×C3111yescharacteristic
297C2×C4⋊C8C22×C3111yescharacteristic
298C2×C4⋊C8C22×C3112yes—
299C2×#103C22×C3112yes—
300C2×#103C22×C3111yescharacteristic
301C2×#102C22×C3112yes—
302C2×#102C22×C3112yes—
303C2×#102C22×C3111yescharacteristic
304C2×#102C22×C3112yes—
305C2×C4×C8C22×C3111yescharacteristic
306#394—22no—
307#390—21no—
308#390—21no—
309#390C22×C3112yes—
310#389C22×C3112yes—
311#385—22no—
312#384C22×C3111yescharacteristic
313#380—21no—
314C4×C4⋊C4C22×C3111yescharacteristic
315#340C22×C3112yes—
316#336C22×C3112yes—
317C2×C31—44no—
318C2×C31—162no—
319C2×C31#241611yescharacteristic
320C2×C31C2×#46311yescharacteristic
321C2×C31#304511yescharacteristic
322C2×C31#327411yescharacteristic
323C2×C31#328411yescharacteristic
324C2×C31#336111yescharacteristic
325C2×C31#337311yescharacteristic
326C22×Q8C23×C3111yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4C23×C3112yes—
330C22×D4C23×C3111yescharacteristic
331C23×C4—21no—
332C23×C4—22no—
333C2×SD16—22no—
334C2×SD16—22no—
335C2×SD16D4×C3114yescomplemented
336C2×D8—24no—
337C2×D8—24no—
338C2×D8—24no—
339C22×C8C23×C3112yes—
340C22×C8C23×C3111yescharacteristic
341C22×C8C23×C3111yescharacteristic
342#127—22no—
343#127—22no—
344#124—24no—
345#124—42no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×D4—24no—
349C4×D4—22no—
350C4×D4—42no—
351C4×D4D4×C3114yes—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4D4×C3111yescharacteristic
358C2×C4⋊C4D4×C3111yescharacteristic
359C2×C4⋊C4C23×C3112yes—
360C2×C4⋊C4C23×C3111yescharacteristic
361C2×C4⋊C4C23×C3111yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C42—21no—
369C2×C42C23×C3112yes—
370C2×C42C23×C3111yescharacteristic
371#106—22no—
372C4⋊C8—24no—
373C4⋊C8—22no—
374#103—24no—
375#103—22no—
376#102—22no—
377#102—24no—
378#102—24no—
379#102—42no—
380C4×C8—22no—
381#95—22no—
382#95D4×C3112yes—
383C31#2473111yescharacteristic, direct product factor, Sylow
384C24—21no—
385C24—22no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8C2×D4×C3112yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—81no—
406C2×D4—81no—
407C2×D4C2×D4×C3112yes—
408C2×D4C2×D4×C3112yes—
409C2×D4#41×C3112yes—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—44no—
416C22×C4—44no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—82no—
420C22×C4C2×D4×C3112yes—
421C22×C4C2×D4×C3112yes—
422C22×C4C2×D4×C3111yescharacteristic
423C22×C4C2×D4×C3111yescharacteristic
424C22×C4C24×C3111yescharacteristic
425SD16—28no—
426D8—48no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8C2×D4×C3112yes—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—44no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—81no—
447C4⋊C4C2×D4×C3112yes—
448C22⋊C4—24no—
449C22⋊C4—44no—
450C22⋊C4—44no—
451C22⋊C4—44no—
452C22⋊C4—82no—
453C22⋊C4—82no—
454C42—22no—
455C42—22no—
456C42—42no—
457C42C2×D4×C3112yes—
458C42#41×C3112yes—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23C22×D4×C3111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—41no—
477Q8—41no—
478D4—22no—
479D4—22no—
480D4—22no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—84no—
486D4—84no—
487D4C31×#12114yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—48no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—88no—
510C2×C4C31×#12112yes—
511C2×C4C31×#12112yes—
512C2×C4C31×#13512yes—
513C2×C4C31×AGL(1,ℤ/8)12yes—
514C2×C4C22×D4×C3111yescharacteristic
515C2×C4C22×D4×C3111yescharacteristic
516C2×C4C2×#41×C3111yescharacteristic
517C2×C4C2×#41×C3111yescharacteristic
518C2×C4C31×H(5,𝔽2)11yescharacteristic
519C2×C4C31×2−1+411yescharacteristic
520C8—22no—
521C8—42no—
522C8—41no—
523C22—24no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—82no—
536C22—82no—
537C22C2×C31×#12111yescharacteristic
538C22D42×C3111yescharacteristic
539C22C31×#54811yescharacteristic
540C22C2×C31×#13511yescharacteristic
541C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
542C22C31×#57611yescharacteristic
543C22C31×#57711yescharacteristic
544C4—22no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—82no—
550C4—81no—
551C4C31×#46314yescomplemented
552C4C2×C31×#12111yescharacteristic
553C4C31×#53711yescharacteristic
554C4C31×#54711yescharacteristic
555C4C31×#55311yescharacteristic
556C2—44no—
557C2—162no—
558C2C31×#241611yescharacteristic
559C2C2×C31×#46311yescharacteristic
560C2C31×#304511yescharacteristic
561C2C31×#327411yescharacteristic
562C2C31×#328411yescharacteristic
563C2C31×#336111yescharacteristic
564C2C31×#337311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#463C2semidirect
3. C2×C4×SD16×C31C2semidirect
4. C31×#2548C2semidirect
5. D4×C4⋊C4×C31C2semidirect
6. C31×#2065C2semidirect
7. C31×#2042C2semidirect
8. C31×#1957C2semidirect
9. C31×#1939C2semidirect
10. C31×#1879C2semidirect
11. C31×#1803C2semidirect
53. C2×SD16×C31D4semidirect
176. #24731C31direct (N × H)
241. C2×#463C2×C31semidirect
243. C2×C4×SD16C2×C31semidirect
244. #2548C2×C31semidirect
245. D4×C4⋊C4C2×C31semidirect
246. #2065C2×C31semidirect
247. #2042C2×C31semidirect
248. #1957C2×C31semidirect
249. #1939C2×C31semidirect
250. #1879C2×C31semidirect
251. #1803C2×C31semidirect
280. C4×C31#463semidirect
335. C2×SD16D4×C31semidirect
383. C31#24731direct (N × H)
551. C4C31×#463semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4632
C2×C31×#4592
C2×C4×SD16×C312
C31×#25482
D4×C4⋊C4×C312
C31×#20652
C31×#20422
C31×#19572
C31×#19392
C31×#18792
C31×#18032
#2473131