Finite Group Databasebeta

← C2×C31×#2015 #21480177

Subgroups — C2×C31×#2015 #21480177

Order 7936.

2166 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q16×C31C211yesmaximal, characteristic, complemented
2C23×SD16×C31C211yesmaximal, characteristic
3C22×C31×#124C211yesmaximal, characteristic
4C22×C31×#103C211yesmaximal, characteristic, complemented
5C22×C31×#102C211yesmaximal, characteristic
6C2×C31×#391C211yesmaximal, characteristic, complemented
7C31×#2015C218yesmaximal, direct product factor
8C2×C31×#336C211yesmaximal, characteristic, complemented
9C23×Q8×C31C2211yescharacteristic
10C23×Q8×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C22×Q16×C31—24no—
13C22×Q16×C31—24no—
14C22×Q16×C31—24no—
15C22×Q16×C31C2214yescomplemented
16C22×SD16×C31—24no—
17C22×SD16×C31—24no—
18C22×SD16×C31—24no—
19C22×SD16×C31C2214yes—
20C23×C8×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C2×C31×#124—24no—
23C2×C31×#124—24no—
24C2×C31×#124—22no—
25C2×C31×#124C2214yes—
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31—22no—
28C22×C42×C31C2211yescharacteristic
29C2×C31×#103—24no—
30C2×C31×#103C2214yescomplemented
31C2×C31×#102—24no—
32C2×C31×#102C2214yes—
33C31×#391—22no—
34C31×#391C2214yescomplemented
35C2×C31×#95—22no—
36C31×#336C2214yescomplemented
37C25×C31—21no—
38C22×Q8×C31—22no—
39C22×Q8×C31—21no—
40C22×Q8×C31—21no—
41C22×Q8×C31—22no—
42C22×Q8×C31—22no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31D414yes—
51C22×Q8×C31D414yes—
52C22×Q8×C31C2312yes—
53C22×Q8×C31C2312yes—
54C22×D4×C31—22no—
55C22×D4×C31—22no—
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31D414yes—
61C22×D4×C31C2312yes—
62C23×C4×C31—21no—
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31D412yes—
66C23×C4×C31C2311yescharacteristic
67C2×Q16×C31—232no—
68C2×Q16×C31—28no—
69C2×Q16×C31—28no—
70C2×Q16×C31—28no—
71C2×SD16×C31—232no—
72C2×SD16×C31—28no—
73C2×SD16×C31—28no—
74C2×SD16×C31—28no—
75C22×C8×C31—22no—
76C22×C8×C31—22no—
77C22×C8×C31—22no—
78C22×C8×C31—22no—
79C22×C8×C31D414yes—
80C22×C8×C31D414yes—
81C22×C8×C31C2312yes—
82C22×C8×C31C2312yes—
83C31×#124—216no—
84C31×#124—28no—
85C31×#124—28no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31C2312yes—
90C2×C22⋊C4×C31—216no—
91C2×C22⋊C4×C31—28no—
92C2×C42×C31—22no—
93C2×C42×C31—22no—
94C2×C42×C31D412yes—
95C2×C42×C31C2312yes—
96C31×#103—28no—
97C31×#102—28no—
98C31×#95—28no—
99C24×C31—24no—
100C24×C31—22no—
101C24×C31—42no—
102C24×C31—42no—
103C24×C31—44no—
104C24×C31—44no—
105C24×C31C2×D411yescharacteristic
106C2×Q8×C31—24no—
107C2×Q8×C31—24no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—28no—
111C2×Q8×C31—28no—
112C2×Q8×C31—28no—
113C2×Q8×C31—28no—
114C2×Q8×C31—22no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31—22no—
121C2×Q8×C31—22no—
122C2×Q8×C31—42no—
123C2×Q8×C31—44no—
124C2×Q8×C31—42no—
125C2×Q8×C31—44no—
126C2×Q8×C31—44no—
127C2×Q8×C31—44no—
128C2×Q8×C31—42no—
129C2×Q8×C31—42no—
130C2×Q8×C31C2×D414yes—
131C2×Q8×C31C2×D414yes—
132C2×D4×C31—28no—
133C2×D4×C31—24no—
134C2×D4×C31—28no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—22no—
140C2×D4×C31—44no—
141C2×D4×C31—44no—
142C2×D4×C31—42no—
143C2×D4×C31—42no—
144C2×D4×C31C2×D414yes—
145C22×C4×C31—24no—
146C22×C4×C31—24no—
147C22×C4×C31—24no—
148C22×C4×C31—24no—
149C22×C4×C31—24no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—42no—
154C22×C4×C31—42no—
155C22×C4×C31—42no—
156C22×C4×C31—42no—
157C22×C4×C31—42no—
158C22×C4×C31—44no—
159C22×C4×C31C2×D414yes—
160C22×C4×C31C2×D412yes—
161C22×C4×C31C2×D412yes—
162C22×C4×C31C2×D412yes—
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31C2×D412yes—
165C22×C4×C31C2×D412yes—
166C22×C4×C31#4112yes—
167C22×C4×C31C2411yescharacteristic
168Q16×C31—232no—
169SD16×C31—232no—
170C2×C8×C31—28no—
171C2×C8×C31—28no—
172C2×C8×C31—22no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—22no—
176C2×C8×C31C2×D414yes—
177C2×C8×C31C2×D414yes—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—42no—
181C22⋊C4×C31—232no—
182C42×C31—24no—
183C42×C31—22no—
184C42×C31—22no—
185C2×#2015C3111yesmaximal, characteristic, direct product factor, Sylow
186C23×C31—24no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—44no—
190C23×C31—44no—
191C23×C31—48no—
192C23×C31—416no—
193C23×C31—88no—
194C23×C31—84no—
195C23×C31—84no—
196C23×C31#12012yes—
197C23×C31#12112yes—
198C23×C31#12712yes—
199C23×C31#13514yes—
200C23×C31#13714yes—
201C23×C31C22×D411yescharacteristic
202Q8×C31—24no—
203Q8×C31—24no—
204Q8×C31—24no—
205Q8×C31—24no—
206Q8×C31—42no—
207Q8×C31—42no—
208Q8×C31—42no—
209Q8×C31—42no—
210Q8×C31—48no—
211Q8×C31—48no—
212D4×C31—24no—
213D4×C31—24no—
214D4×C31—42no—
215D4×C31—42no—
216D4×C31—48no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—24no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—48no—
227C2×C4×C31—48no—
228C2×C4×C31—48no—
229C2×C4×C31—42no—
230C2×C4×C31—44no—
231C2×C4×C31—84no—
232C2×C4×C31#12014yes—
233C2×C4×C31#12014yes—
234C2×C4×C31#12012yes—
235C2×C4×C31#12114yes—
236C2×C4×C31#12114yes—
237C2×C4×C31#12112yes—
238C2×C4×C31#12712yes—
239C2×C4×C31C22×D411yescharacteristic
240C2×C4×C31C22×D411yescharacteristic
241C2×C4×C31C22×D411yescharacteristic
242C2×C4×C31C22×D411yescharacteristic
243C2×C4×C31C22×D411yescharacteristic
244C2×C4×C31C2×#4111yescharacteristic
245C8×C31—24no—
246C8×C31—24no—
247C23×Q16C2×C3111yescharacteristic, complemented
248C23×SD16C2×C3111yescharacteristic
249C22×#124C2×C3111yescharacteristic
250C22×#103C2×C3111yescharacteristic, complemented
251C22×#102C2×C3111yescharacteristic
252C2×#391C2×C3111yescharacteristic, complemented
253#2015C2×C3118yesdirect product factor
254C2×#336C2×C3111yescharacteristic, complemented
255C22×C31—44no—
256C22×C31—48no—
257C22×C31—82no—
258C22×C31—82no—
259C22×C31—84no—
260C22×C31—816no—
261C22×C31#39214yes—
262C22×C31#45218yes—
263C22×C31#46418yes—
264C22×C31#49514yes—
265C22×C31#49714yes—
266C22×C31C2×#12011yescharacteristic
267C22×C31C2×#12111yescharacteristic
268C22×C31C2×#12711yescharacteristic
269C22×C31C2×#13512yes—
270C22×C31C2×#13712yes—
271C4×C31—44no—
272C4×C31—44no—
273C4×C31—44no—
274C4×C31—82no—
275C4×C31#39214yes—
276C4×C31C2×#12011yescharacteristic
277C4×C31C2×#12011yescharacteristic
278C4×C31C2×#12111yescharacteristic
279C4×C31C2×#12111yescharacteristic
280C23×Q8C22×C3111yescharacteristic
281C23×Q8C22×C3111yescharacteristic
282C23×D4C22×C3111yescharacteristic
283C22×Q16—24no—
284C22×Q16—24no—
285C22×Q16—24no—
286C22×Q16C22×C3114yescomplemented
287C22×SD16—24no—
288C22×SD16—24no—
289C22×SD16—24no—
290C22×SD16C22×C3114yes—
291C23×C8C22×C3111yescharacteristic
292C23×C8C22×C3111yescharacteristic
293C2×#124—24no—
294C2×#124—24no—
295C2×#124—22no—
296C2×#124C22×C3114yes—
297C22×C4⋊C4C22×C3111yescharacteristic
298C22×C22⋊C4—22no—
299C22×C42C22×C3111yescharacteristic
300C2×#103—24no—
301C2×#103C22×C3114yescomplemented
302C2×#102—24no—
303C2×#102C22×C3114yes—
304#391—22no—
305#391C22×C3114yescomplemented
306C2×#95—22no—
307#336C22×C3114yescomplemented
308C2×C31—84no—
309C2×C31#201518yesdirect product factor
310C2×C31C2×#39211yescharacteristic
311C2×C31C2×#45212yes—
312C2×C31C2×#46412yes—
313C2×C31C2×#49511yescharacteristic
314C2×C31C2×#49711yescharacteristic
315C25—21no—
316C22×Q8—22no—
317C22×Q8—21no—
318C22×Q8—21no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8D4×C3114yes—
329C22×Q8D4×C3114yes—
330C22×Q8C23×C3112yes—
331C22×Q8C23×C3112yes—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—21no—
337C22×D4—22no—
338C22×D4D4×C3114yes—
339C22×D4C23×C3112yes—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4D4×C3112yes—
344C23×C4C23×C3111yescharacteristic
345C2×Q16—232no—
346C2×Q16—28no—
347C2×Q16—28no—
348C2×Q16—28no—
349C2×SD16—232no—
350C2×SD16—28no—
351C2×SD16—28no—
352C2×SD16—28no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8D4×C3114yes—
358C22×C8D4×C3114yes—
359C22×C8C23×C3112yes—
360C22×C8C23×C3112yes—
361#124—216no—
362#124—28no—
363#124—28no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C3112yes—
368C2×C22⋊C4—216no—
369C2×C22⋊C4—28no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42D4×C3112yes—
373C2×C42C23×C3112yes—
374#103—28no—
375#102—28no—
376#95—28no—
377C31C2×#201511yescharacteristic, direct product factor, Sylow
378C24—24no—
379C24—22no—
380C24—42no—
381C24—42no—
382C24—44no—
383C24—44no—
384C24C2×D4×C3111yescharacteristic
385C2×Q8—24no—
386C2×Q8—24no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—28no—
390C2×Q8—28no—
391C2×Q8—28no—
392C2×Q8—28no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—42no—
402C2×Q8—44no—
403C2×Q8—42no—
404C2×Q8—44no—
405C2×Q8—44no—
406C2×Q8—44no—
407C2×Q8—42no—
408C2×Q8—42no—
409C2×Q8C2×D4×C3114yes—
410C2×Q8C2×D4×C3114yes—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4C2×D4×C3114yes—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4C2×D4×C3114yes—
439C22×C4C2×D4×C3112yes—
440C22×C4C2×D4×C3112yes—
441C22×C4C2×D4×C3112yes—
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4C2×D4×C3112yes—
444C22×C4C2×D4×C3112yes—
445C22×C4#41×C3112yes—
446C22×C4C24×C3111yescharacteristic
447Q16—232no—
448SD16—232no—
449C2×C8—28no—
450C2×C8—28no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8C2×D4×C3114yes—
456C2×C8C2×D4×C3114yes—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—42no—
460C22⋊C4—232no—
461C42—24no—
462C42—22no—
463C42—22no—
464C23—24no—
465C23—416no—
466C23—42no—
467C23—42no—
468C23—44no—
469C23—44no—
470C23—48no—
471C23—88no—
472C23—84no—
473C23—84no—
474C23C31×#12012yes—
475C23C31×#12112yes—
476C23C31×#12712yes—
477C23C31×#13514yes—
478C23C31×#13714yes—
479C23C22×D4×C3111yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—24no—
483Q8—24no—
484Q8—42no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488Q8—48no—
489Q8—48no—
490D4—24no—
491D4—24no—
492D4—42no—
493D4—42no—
494D4—48no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—48no—
506C2×C4—48no—
507C2×C4—42no—
508C2×C4—44no—
509C2×C4—84no—
510C2×C4C31×#12014yes—
511C2×C4C31×#12014yes—
512C2×C4C31×#12012yes—
513C2×C4C31×#12114yes—
514C2×C4C31×#12114yes—
515C2×C4C31×#12112yes—
516C2×C4C31×#12712yes—
517C2×C4C22×D4×C3111yescharacteristic
518C2×C4C22×D4×C3111yescharacteristic
519C2×C4C22×D4×C3111yescharacteristic
520C2×C4C22×D4×C3111yescharacteristic
521C2×C4C22×D4×C3111yescharacteristic
522C2×C4C2×#41×C3111yescharacteristic
523C8—24no—
524C8—24no—
525C22—44no—
526C22—48no—
527C22—82no—
528C22—82no—
529C22—84no—
530C22—816no—
531C22C31×#39214yes—
532C22C31×#45218yes—
533C22C31×#46418yes—
534C22C31×#49514yes—
535C22C31×#49714yes—
536C22C2×C31×#12011yescharacteristic
537C22C2×C31×#12111yescharacteristic
538C22C2×C31×#12711yescharacteristic
539C22C2×C31×#13512yes—
540C22C2×C31×#13712yes—
541C4—44no—
542C4—44no—
543C4—44no—
544C4—82no—
545C4C31×#39214yes—
546C4C2×C31×#12011yescharacteristic
547C4C2×C31×#12011yescharacteristic
548C4C2×C31×#12111yescharacteristic
549C4C2×C31×#12111yescharacteristic
550C2—84no—
551C2C31×#201518yesdirect product factor
552C2C2×C31×#39211yescharacteristic
553C2C2×C31×#45212yes—
554C2C2×C31×#46412yes—
555C2C2×C31×#49511yescharacteristic
556C2C2×C31×#49711yescharacteristic
subgroupG/H
center, socleC24×C31C2×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×Q16×C31C2semidirect
4. C22×C31×#103C2semidirect
6. C2×C31×#391C2semidirect
7. C31×#2015C2direct (N × H)
8. C2×C31×#336C2semidirect
15. C22×Q16×C31C22semidirect
30. C2×C31×#103C22semidirect
34. C31×#391C22semidirect
36. C31×#336C22semidirect
185. C2×#2015C31direct (N × H)
247. C23×Q16C2×C31semidirect
250. C22×#103C2×C31semidirect
252. C2×#391C2×C31semidirect
253. #2015C2×C31direct (N × H)
254. C2×#336C2×C31semidirect
286. C22×Q16C22×C31semidirect
301. C2×#103C22×C31semidirect
305. #391C22×C31semidirect
307. #336C22×C31semidirect
309. C2×C31#2015direct (N × H)
377. C31C2×#2015direct (N × H)
551. C2C31×#2015direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q16×C312
C23×SD16×C312
C22×C31×#1242
C22×C31×#1032
C22×C31×#1022
C2×C31×#3912
C31×#20152
C2×C31×#3362
C2×#201531