Finite Group Databasebeta

← C31×#24183 #21480942

Subgroups — C31×#24183 #21480942

Order 7936.

1002 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3507C211yesmaximal, characteristic
2C31×#3078C211yesmaximal, characteristic, complemented
3C31×#3037C211yesmaximal, characteristic
4C31×#2327C211yesmaximal, characteristic, complemented
5C31×#2038C212yesmaximal, complemented
6C31×#2005C212yesmaximal, complemented
7C31×#1995C211yesmaximal, characteristic, complemented
8C31×#1963C211yesmaximal, characteristic
9C31×#1882C212yesmaximal, complemented
10C31×#1860C212yesmaximal, complemented
11C31×#1801C211yesmaximal, characteristic, complemented
12C2×C31×#137C2212yes—
13C31×#559—21no—
14C31×#557—21no—
15C31×#556—21no—
16C31×#556—22no—
17C31×#554—21no—
18C31×#552—22no—
19C31×#539—22no—
20C31×#536C2212yes—
21C31×#533C2211yescharacteristic
22C31×#532C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#529—22no—
25C31×#520C2212yes—
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C31×#479—22no—
29C31×#477—21no—
30C31×#475—21no—
31C31×#464—22no—
32C31×#462—21no—
33C31×#460—21no—
34C31×#428C2212yes—
35C31×#423C2211yescharacteristic
36C31×#423C2211yescharacteristic
37C2×C31×#104C2212yes—
38C2×C31×#104C2212yes—
39C31×#419C2212yes—
40C31×#417C2212yes—
41C2×C31×#101C2212yes—
42C31×#391C2211yescharacteristic
43C31×#391C2211yescharacteristic
44C31×#387—22no—
45C31×#387—22no—
46C31×#382C2211yescharacteristic
47C31×#376C2211yescharacteristic
48C31×#343C2212yes—
49C31×#339C2212yes—
50C31×#339C2212yes—
51C2×#41×C31C2312yes—
52C22×Q8×C31C2311yescharacteristic
53C22×Q8×C31C2311yescharacteristic
54C31×#137—24no—
55C31×#137—42no—
56C2×Q16×C31—22no—
57C2×SD16×C31—22no—
58C2×M16×C31C2312yes—
59C2×M16×C31C2312yes—
60C31×C4⋊Q8—22no—
61C31×C4⋊Q8—22no—
62C31×C4⋊Q8—22no—
63C31×C4⋊Q8D411yescharacteristic
64C31×C4⋊Q8D411yescharacteristic
65C31×C4⋊Q8D411yescharacteristic
66C31×#127D411yescharacteristic
67C31×#126—24no—
68C31×#126—24no—
69C31×#125—22no—
70C31×#125—24no—
71C31×#125D412yes—
72C31×#124—22no—
73C31×#124—22no—
74C31×#124D412yes—
75C31×#123—24no—
76C31×#123—24no—
77C31×C22⋊Q8—24no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—22no—
82C31×#121—21no—
83C31×#121—21no—
84C4×Q8×C31—22no—
85C4×Q8×C31—22no—
86C4×Q8×C31—21no—
87C4×Q8×C31—21no—
88C4×Q8×C31—21no—
89C4×Q8×C31—21no—
90C4×Q8×C31—21no—
91C4×Q8×C31—21no—
92C4×Q8×C31—21no—
93C4×Q8×C31—21no—
94C4×Q8×C31—21no—
95C4×Q8×C31—21no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—24no—
99C4×D4×C31—21no—
100C4×D4×C31—21no—
101C31×#117—24no—
102C31×#117—22no—
103C31×#117C2312yes—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31D412yes—
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C42×C31—21no—
111C2×C42×C31D412yes—
112C2×C42×C31C2311yescharacteristic
113C2×C42×C31C2311yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C31×#107—22no—
116C31×#106—22no—
117C31×C4⋊C8—21no—
118C31×C4⋊C8—21no—
119C31×C4⋊C8—21no—
120C31×C4⋊C8—21no—
121C31×#104—24no—
122C31×#104—42no—
123C31×#103—22no—
124C31×#103—22no—
125C31×#103—22no—
126C31×#102—22no—
127C31×#101—42no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—22no—
133#41×C31—22no—
134#41×C31—22no—
135#41×C31—22no—
136#41×C31—22no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31—21no—
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31C2×D412yes—
151C2×Q8×C31#4112yes—
152C2×D4×C31—22no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31C2×D412yes—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—24no—
159C22×C4×C31—22no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31C2×D412yes—
163C22×C4×C31C2×D412yes—
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2411yescharacteristic
167Q16×C31—44no—
168SD16×C31—44no—
169M16×C31—22no—
170M16×C31—22no—
171M16×C31—22no—
172M16×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C4⋊C4×C31—24no—
176C4⋊C4×C31—28no—
177C4⋊C4×C31—24no—
178C4⋊C4×C31—24no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—22no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—41no—
192C4⋊C4×C31—41no—
193C4⋊C4×C31C2×D412yes—
194C4⋊C4×C31C2×D412yes—
195C22⋊C4×C31—24no—
196C22⋊C4×C31—24no—
197C22⋊C4×C31—24no—
198C22⋊C4×C31—22no—
199C22⋊C4×C31—22no—
200C22⋊C4×C31—22no—
201C42×C31—24no—
202C42×C31—22no—
203C42×C31—22no—
204C42×C31—22no—
205C42×C31—21no—
206C42×C31—21no—
207C42×C31—21no—
208C42×C31—41no—
209C42×C31—41no—
210C42×C31C2×D411yescharacteristic
211C42×C31C2×D411yescharacteristic
212C42×C31C2×D411yescharacteristic
213C42×C31C2×D411yescharacteristic
214C42×C31#4112yes—
215#24183C3111yesmaximal, characteristic, direct product factor, Sylow
216C23×C31—22no—
217C23×C31C22×D411yescharacteristic
218Q8×C31—22no—
219Q8×C31—22no—
220Q8×C31—22no—
221Q8×C31—22no—
222Q8×C31—42no—
223Q8×C31—41no—
224Q8×C31—41no—
225Q8×C31—41no—
226Q8×C31—41no—
227Q8×C31—41no—
228Q8×C31—41no—
229Q8×C31—81no—
230D4×C31—22no—
231D4×C31—22no—
232D4×C31—42no—
233D4×C31—42no—
234D4×C31—42no—
235D4×C31—81no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—41no—
246C2×C4×C31—41no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—42no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—84no—
260C2×C4×C31#12011yescharacteristic
261C2×C4×C31#12011yescharacteristic
262C2×C4×C31#12011yescharacteristic
263C2×C4×C31#12011yescharacteristic
264C2×C4×C31C22×D411yescharacteristic
265C2×C4×C31C22×D411yescharacteristic
266C2×C4×C31C2×#4111yescharacteristic
267C2×C4×C31C2×#4111yescharacteristic
268C2×C4×C31H(5,𝔽2)11yescharacteristic
269C2×C4×C312−1+411yescharacteristic
270C8×C31—42no—
271C8×C31—42no—
272#3507C2×C3111yescharacteristic
273#3078C2×C3111yescharacteristic, complemented
274#3037C2×C3111yescharacteristic
275#2327C2×C3111yescharacteristic, complemented
276#2038C2×C3112yescomplemented
277#2005C2×C3112yescomplemented
278#1995C2×C3111yescharacteristic, complemented
279#1963C2×C3111yescharacteristic
280#1882C2×C3112yescomplemented
281#1860C2×C3112yescomplemented
282#1801C2×C3111yescharacteristic, complemented
283C22×C31—21no—
284C22×C31—21no—
285C22×C31—42no—
286C22×C31—42no—
287C22×C31—42no—
288C22×C31C2×#12011yescharacteristic
289C22×C31#52511yescharacteristic
290C22×C31#53711yescharacteristic
291C4×C31—21no—
292C4×C31—21no—
293C4×C31—21no—
294C4×C31—21no—
295C4×C31—42no—
296C4×C31—42no—
297C4×C31—42no—
298C4×C31—42no—
299C4×C31—42no—
300C4×C31—42no—
301C4×C31—42no—
302C4×C31—81no—
303C4×C31—81no—
304C4×C31#54611yescharacteristic
305C4×C31#54711yescharacteristic
306C4×C31#54811yescharacteristic
307C4×C31#55011yescharacteristic
308C2×#137C22×C3112yes—
309#559—21no—
310#557—21no—
311#556—21no—
312#556—22no—
313#554—21no—
314#552—22no—
315#539—22no—
316#536C22×C3112yes—
317#533C22×C3111yescharacteristic
318#532C22×C3111yescharacteristic
319C2×C4⋊Q8C22×C3111yescharacteristic
320#529—22no—
321#520C22×C3112yes—
322C2×C4×Q8C22×C3111yescharacteristic
323C2×C4×Q8C22×C3111yescharacteristic
324#479—22no—
325#477—21no—
326#475—21no—
327#464—22no—
328#462—21no—
329#460—21no—
330#428C22×C3112yes—
331#423C22×C3111yescharacteristic
332#423C22×C3111yescharacteristic
333C2×#104C22×C3112yes—
334C2×#104C22×C3112yes—
335#419C22×C3112yes—
336#417C22×C3112yes—
337C2×#101C22×C3112yes—
338#391C22×C3111yescharacteristic
339#391C22×C3111yescharacteristic
340#387—22no—
341#387—22no—
342#382C22×C3111yescharacteristic
343#376C22×C3111yescharacteristic
344#343C22×C3112yes—
345#339C22×C3112yes—
346#339C22×C3112yes—
347C2×C31—21no—
348C2×C31—21no—
349C2×C31—82no—
350C2×C31#240711yescharacteristic
351C2×C31#302011yescharacteristic
352C2×C31#302211yescharacteristic
353C2×#41C23×C3112yes—
354C22×Q8C23×C3111yescharacteristic
355C22×Q8C23×C3111yescharacteristic
356#137—24no—
357#137—42no—
358C2×Q16—22no—
359C2×SD16—22no—
360C2×M16C23×C3112yes—
361C2×M16C23×C3112yes—
362C4⋊Q8—22no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8D4×C3111yescharacteristic
366C4⋊Q8D4×C3111yescharacteristic
367C4⋊Q8D4×C3111yescharacteristic
368#127D4×C3111yescharacteristic
369#126—24no—
370#126—24no—
371#125—22no—
372#125—24no—
373#125D4×C3112yes—
374#124—22no—
375#124—22no—
376#124D4×C3112yes—
377#123—24no—
378#123—24no—
379C22⋊Q8—24no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384#121—21no—
385#121—21no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—24no—
401C4×D4—21no—
402C4×D4—21no—
403#117—24no—
404#117—22no—
405#117C23×C3112yes—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4D4×C3112yes—
410C2×C4⋊C4C23×C3111yescharacteristic
411C2×C4⋊C4C23×C3111yescharacteristic
412C2×C42—21no—
413C2×C42D4×C3112yes—
414C2×C42C23×C3111yescharacteristic
415C2×C42C23×C3111yescharacteristic
416C2×C42C23×C3111yescharacteristic
417#107—22no—
418#106—22no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423#104—24no—
424#104—42no—
425#103—22no—
426#103—22no—
427#103—22no—
428#102—22no—
429#101—42no—
430#95—21no—
431#95—21no—
432#95—22no—
433#95—22no—
434#95—22no—
435C31#2418311yescharacteristic, direct product factor, Sylow
436#41—22no—
437#41—22no—
438#41—22no—
439#41—22no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×D4×C3112yes—
454C2×Q8#41×C3112yes—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4C2×D4×C3112yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4C2×D4×C3112yes—
466C22×C4C2×D4×C3112yes—
467C22×C4C2×D4×C3111yescharacteristic
468C22×C4C2×D4×C3111yescharacteristic
469C22×C4C24×C3111yescharacteristic
470Q16—44no—
471SD16—44no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476C2×C8—22no—
477C2×C8—22no—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—24no—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4C2×D4×C3112yes—
497C4⋊C4C2×D4×C3112yes—
498C22⋊C4—24no—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C42—24no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—41no—
512C42—41no—
513C42C2×D4×C3111yescharacteristic
514C42C2×D4×C3111yescharacteristic
515C42C2×D4×C3111yescharacteristic
516C42C2×D4×C3111yescharacteristic
517C42#41×C3112yes—
518C23—22no—
519C23C22×D4×C3111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8—22no—
524Q8—42no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—81no—
532D4—22no—
533D4—22no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—81no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—84no—
562C2×C4C31×#12011yescharacteristic
563C2×C4C31×#12011yescharacteristic
564C2×C4C31×#12011yescharacteristic
565C2×C4C31×#12011yescharacteristic
566C2×C4C22×D4×C3111yescharacteristic
567C2×C4C22×D4×C3111yescharacteristic
568C2×C4C2×#41×C3111yescharacteristic
569C2×C4C2×#41×C3111yescharacteristic
570C2×C4C31×H(5,𝔽2)11yescharacteristic
571C2×C4C31×2−1+411yescharacteristic
572C8—42no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×C31×#12011yescharacteristic
580C22C31×#52511yescharacteristic
581C22C31×#53711yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—81no—
595C4C31×#54611yescharacteristic
596C4C31×#54711yescharacteristic
597C4C31×#54811yescharacteristic
598C4C31×#55011yescharacteristic
599C2—21no—
600C2—21no—
601C2—82no—
602C2C31×#240711yescharacteristic
603C2C31×#302011yescharacteristic
604C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3078C2semidirect
4. C31×#2327C2semidirect
5. C31×#2038C2semidirect
6. C31×#2005C2semidirect
7. C31×#1995C2semidirect
9. C31×#1882C2semidirect
10. C31×#1860C2semidirect
11. C31×#1801C2semidirect
215. #24183C31direct (N × H)
273. #3078C2×C31semidirect
275. #2327C2×C31semidirect
276. #2038C2×C31semidirect
277. #2005C2×C31semidirect
278. #1995C2×C31semidirect
280. #1882C2×C31semidirect
281. #1860C2×C31semidirect
282. #1801C2×C31semidirect
435. C31#24183direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35072
C31×#30782
C31×#30372
C31×#23272
C31×#20382
C31×#20052
C31×#19952
C31×#19632
C31×#18822
C31×#18602
C31×#18012
#2418331