Finite Group Databasebeta

← C31×#23480 #21480239

Subgroups — C31×#23480 #21480239

Order 7936.

1902 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#428C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C2×C31×#407C211yesmaximal, characteristic, complemented
6C31×#2280C211yesmaximal, characteristic, complemented
7C31×#2034C214yesmaximal, complemented
8C31×#2033C214yesmaximal, complemented
9C31×#1736C211yesmaximal, characteristic, complemented
10C23×D4×C31—21no—
11C23×D4×C31C2211yescharacteristic
12C24×C4×C31C2211yescharacteristic
13C22×M16×C31C2211yescharacteristic
14C22×M16×C31C2211yescharacteristic
15C2×C31×#121—24no—
16C2×C31×#121—22no—
17C2×C31×#121—24no—
18C2×C31×#121C2214yes—
19C2×C31×#117C2211yescharacteristic
20C2×C31×#117C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31—21no—
23C31×#428—24no—
24C2×C31×#107C2212yescomplemented
25C2×C31×#106C2212yescomplemented
26C31×#418—24no—
27C31×#418—24no—
28C2×C31×#102C2212yescomplemented
29C2×C31×#102C2214yescomplemented
30C2×C31×#102C2212yescomplemented
31C31×#407—24no—
32C2×C31×C22⋊C8C2214yescomplemented
33C31×#381—21no—
34C31×#380C2212yescomplemented
35C31×#380C2212yescomplemented
36C31×#379—21no—
37C4×C22⋊C4×C31—22no—
38C31×#340C2214yescomplemented
39C25×C31—21no—
40C25×C31D411yescharacteristic
41C22×D4×C31—28no—
42C22×D4×C31—24no—
43C22×D4×C31—22no—
44C22×D4×C31—21no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—48no—
50C22×D4×C31D414yes—
51C22×D4×C31C2312yes—
52C23×C4×C31—21no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31D411yescharacteristic
60C23×C4×C31D412yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C2×M16×C31—22no—
64C2×M16×C31—22no—
65C2×M16×C31—22no—
66C2×M16×C31—22no—
67C2×M16×C31—22no—
68C2×M16×C31D414yescomplemented
69C22×C8×C31C2312yes—
70C22×C8×C31C2312yes—
71C31×#121—216no—
72C31×#121—28no—
73C31×#121—28no—
74C31×#117—22no—
75C31×#117—22no—
76C31×#117—22no—
77C31×#117—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31D414yes—
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2312yes—
84C2×C4⋊C4×C31C2312yes—
85C2×C22⋊C4×C31—28no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C42×C31—21no—
92C2×C42×C31—21no—
93C31×#107—24no—
94C31×#106—24no—
95C31×#102—24no—
96C31×#102—24no—
97C31×#102—28no—
98C31×C22⋊C8—28no—
99C31×#95—22no—
100C31×#95—22no—
101C24×C31—22no—
102C24×C31—24no—
103C24×C31—24no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31—22no—
107C24×C31—42no—
108C24×C31—44no—
109C24×C31—44no—
110C24×C31—42no—
111C24×C31—42no—
112C24×C31C2×D412yes—
113C24×C31C2×D411yescharacteristic
114C2×D4×C31—216no—
115C2×D4×C31—24no—
116C2×D4×C31—28no—
117C2×D4×C31—28no—
118C2×D4×C31—22no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—432no—
124C2×D4×C31—48no—
125C2×D4×C31—48no—
126C2×D4×C31—44no—
127C2×D4×C31—42no—
128C2×D4×C31—42no—
129C2×D4×C31—44no—
130C2×D4×C31C2×D414yes—
131C22×C4×C31—22no—
132C22×C4×C31—24no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—24no—
137C22×C4×C31—24no—
138C22×C4×C31—24no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—44no—
149C22×C4×C31—44no—
150C22×C4×C31—44no—
151C22×C4×C31—44no—
152C22×C4×C31—44no—
153C22×C4×C31C2×D412yes—
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D412yes—
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31#4112yes—
159C22×C4×C31#4112yes—
160C22×C4×C31#4112yes—
161C22×C4×C31C2411yescharacteristic
162M16×C31—28no—
163M16×C31—44no—
164C2×C8×C31—22no—
165C2×C8×C31—22no—
166C2×C8×C31—22no—
167C2×C8×C31—22no—
168C2×C8×C31—22no—
169C2×C8×C31C2×D414yescomplemented
170C4⋊C4×C31—24no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—21no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31C2×D414yes—
179C22⋊C4×C31—216no—
180C22⋊C4×C31—44no—
181C22⋊C4×C31—42no—
182C22⋊C4×C31—42no—
183C22⋊C4×C31—44no—
184C42×C31—42no—
185C42×C31—42no—
186#23480C3111yesmaximal, characteristic, direct product factor, Sylow
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—28no—
190C23×C31—22no—
191C23×C31—22no—
192C23×C31—22no—
193C23×C31—22no—
194C23×C31—22no—
195C23×C31—22no—
196C23×C31—24no—
197C23×C31—48no—
198C23×C31—48no—
199C23×C31—44no—
200C23×C31—48no—
201C23×C31—48no—
202C23×C31—44no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—44no—
206C23×C31—44no—
207C23×C31—48no—
208C23×C31—88no—
209C23×C31—88no—
210C23×C31#12012yes—
211C23×C31#12112yes—
212C23×C31#12312yes—
213C23×C31AGL(1,ℤ/8)14yes—
214C23×C31C22×D411yescharacteristic
215D4×C31—24no—
216D4×C31—24no—
217D4×C31—432no—
218D4×C31—42no—
219D4×C31—42no—
220D4×C31—48no—
221C2×C4×C31—22no—
222C2×C4×C31—24no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—48no—
226C2×C4×C31—44no—
227C2×C4×C31—44no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—48no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31#12012yes—
241C2×C4×C31#12114yes—
242C2×C4×C31#12114yes—
243C2×C4×C31#12112yes—
244C2×C4×C31#12314yes—
245C2×C4×C31#12312yes—
246C2×C4×C31#12414yes—
247C2×C4×C31C22×D411yescharacteristic
248C2×C4×C31C22×D411yescharacteristic
249C2×C4×C31C22×D411yescharacteristic
250C2×C4×C31C2×#4111yescharacteristic
251C2×C4×C31C2×#4111yescharacteristic
252C2×C4×C31C2×#4111yescharacteristic
253C8×C31—24no—
254C8×C31—42no—
255C22×#121C2×C3111yescharacteristic
256C2×#428C2×C3111yescharacteristic, complemented
257C2×#418C2×C3111yescharacteristic, complemented
258C2×#418C2×C3111yescharacteristic, complemented
259C2×#407C2×C3111yescharacteristic, complemented
260#2280C2×C3111yescharacteristic, complemented
261#2034C2×C3114yescomplemented
262#2033C2×C3114yescomplemented
263#1736C2×C3111yescharacteristic, complemented
264C22×C31—24no—
265C22×C31—22no—
266C22×C31—22no—
267C22×C31—24no—
268C22×C31—24no—
269C22×C31—24no—
270C22×C31—24no—
271C22×C31—416no—
272C22×C31—42no—
273C22×C31—42no—
274C22×C31—42no—
275C22×C31—42no—
276C22×C31—44no—
277C22×C31—44no—
278C22×C31—44no—
279C22×C31—816no—
280C22×C31—84no—
281C22×C31—84no—
282C22×C31#39414yes—
283C22×C31C2×#12011yescharacteristic
284C22×C31C2×#12111yescharacteristic
285C22×C31C2×#12311yescharacteristic
286C22×C31C2×AGL(1,ℤ/8)12yes—
287C22×C31#57512yes—
288C4×C31—42no—
289C4×C31—44no—
290C4×C31—81no—
291C4×C31—81no—
292C4×C31—82no—
293C4×C31#39414yes—
294C4×C31C2×#12111yescharacteristic
295C4×C31C2×#12111yescharacteristic
296C4×C31C2×#12311yescharacteristic
297C4×C31C2×#12411yescharacteristic
298C23×D4—21no—
299C23×D4C22×C3111yescharacteristic
300C24×C4C22×C3111yescharacteristic
301C22×M16C22×C3111yescharacteristic
302C22×M16C22×C3111yescharacteristic
303C2×#121—24no—
304C2×#121—22no—
305C2×#121—24no—
306C2×#121C22×C3114yes—
307C2×#117C22×C3111yescharacteristic
308C2×#117C22×C3111yescharacteristic
309C22×C4⋊C4C22×C3111yescharacteristic
310C22×C22⋊C4—21no—
311#428—24no—
312C2×#107C22×C3112yescomplemented
313C2×#106C22×C3112yescomplemented
314#418—24no—
315#418—24no—
316C2×#102C22×C3112yescomplemented
317C2×#102C22×C3114yescomplemented
318C2×#102C22×C3112yescomplemented
319#407—24no—
320C2×C22⋊C8C22×C3114yescomplemented
321#381—21no—
322#380C22×C3112yescomplemented
323#380C22×C3112yescomplemented
324#379—21no—
325C4×C22⋊C4—22no—
326#340C22×C3114yescomplemented
327C2×C31—24no—
328C2×C31—44no—
329C2×C31—84no—
330C2×C31C2×#39411yescharacteristic
331C2×C31#300311yescharacteristic
332C2×C31#300511yescharacteristic
333C2×C31#305512yes—
334C2×C31#309412yes—
335C25—21no—
336C25D4×C3111yescharacteristic
337C22×D4—28no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—48no—
346C22×D4D4×C3114yes—
347C22×D4C23×C3112yes—
348C23×C4—21no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4D4×C3111yescharacteristic
356C23×C4D4×C3112yes—
357C23×C4C23×C3112yes—
358C23×C4C23×C3111yescharacteristic
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16D4×C3114yescomplemented
365C22×C8C23×C3112yes—
366C22×C8C23×C3112yes—
367#121—216no—
368#121—28no—
369#121—28no—
370#117—22no—
371#117—22no—
372#117—22no—
373#117—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4D4×C3114yes—
377C2×C4⋊C4C23×C3112yes—
378C2×C4⋊C4C23×C3111yescharacteristic
379C2×C4⋊C4C23×C3111yescharacteristic
380C2×C4⋊C4C23×C3112yes—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C42—21no—
388C2×C42—21no—
389#107—24no—
390#106—24no—
391#102—24no—
392#102—24no—
393#102—28no—
394C22⋊C8—28no—
395#95—22no—
396#95—22no—
397C31#2348011yescharacteristic, direct product factor, Sylow
398C24—22no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—42no—
405C24—44no—
406C24—44no—
407C24—42no—
408C24—42no—
409C24C2×D4×C3112yes—
410C24C2×D4×C3111yescharacteristic
411C2×D4—216no—
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—432no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—44no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—44no—
427C2×D4C2×D4×C3114yes—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4C2×D4×C3112yes—
451C22×C4C2×D4×C3111yescharacteristic
452C22×C4C2×D4×C3112yes—
453C22×C4C2×D4×C3112yes—
454C22×C4C2×D4×C3112yes—
455C22×C4#41×C3112yes—
456C22×C4#41×C3112yes—
457C22×C4#41×C3112yes—
458C22×C4C24×C3111yescharacteristic
459M16—28no—
460M16—44no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8C2×D4×C3114yescomplemented
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4C2×D4×C3114yes—
476C22⋊C4—216no—
477C22⋊C4—44no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—44no—
481C42—42no—
482C42—42no—
483C23—22no—
484C23—22no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—48no—
494C23—48no—
495C23—44no—
496C23—48no—
497C23—48no—
498C23—44no—
499C23—42no—
500C23—42no—
501C23—44no—
502C23—44no—
503C23—48no—
504C23—88no—
505C23—88no—
506C23C31×#12012yes—
507C23C31×#12112yes—
508C23C31×#12312yes—
509C23C31×AGL(1,ℤ/8)14yes—
510C23C22×D4×C3111yescharacteristic
511D4—24no—
512D4—24no—
513D4—432no—
514D4—42no—
515D4—42no—
516D4—48no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—48no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4C31×#12012yes—
537C2×C4C31×#12114yes—
538C2×C4C31×#12114yes—
539C2×C4C31×#12112yes—
540C2×C4C31×#12314yes—
541C2×C4C31×#12312yes—
542C2×C4C31×#12414yes—
543C2×C4C22×D4×C3111yescharacteristic
544C2×C4C22×D4×C3111yescharacteristic
545C2×C4C22×D4×C3111yescharacteristic
546C2×C4C2×#41×C3111yescharacteristic
547C2×C4C2×#41×C3111yescharacteristic
548C2×C4C2×#41×C3111yescharacteristic
549C8—24no—
550C8—42no—
551C22—24no—
552C22—22no—
553C22—22no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—416no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—816no—
567C22—84no—
568C22—84no—
569C22C31×#39414yes—
570C22C2×C31×#12011yescharacteristic
571C22C2×C31×#12111yescharacteristic
572C22C2×C31×#12311yescharacteristic
573C22C2×C31×AGL(1,ℤ/8)12yes—
574C22C31×#57512yes—
575C4—42no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—82no—
580C4C31×#39414yes—
581C4C2×C31×#12111yescharacteristic
582C4C2×C31×#12111yescharacteristic
583C4C2×C31×#12311yescharacteristic
584C4C2×C31×#12411yescharacteristic
585C2—24no—
586C2—44no—
587C2—84no—
588C2C2×C31×#39411yescharacteristic
589C2C31×#300311yescharacteristic
590C2C31×#300511yescharacteristic
591C2C31×#305512yes—
592C2C31×#309412yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#428C2semidirect
3. C2×C31×#418C2semidirect
4. C2×C31×#418C2semidirect
5. C2×C31×#407C2semidirect
6. C31×#2280C2semidirect
7. C31×#2034C2semidirect
8. C31×#2033C2semidirect
9. C31×#1736C2semidirect
24. C2×C31×#107C22semidirect
25. C2×C31×#106C22semidirect
28. C2×C31×#102C22semidirect
29. C2×C31×#102C22semidirect
30. C2×C31×#102C22semidirect
32. C2×C31×C22⋊C8C22semidirect
34. C31×#380C22semidirect
35. C31×#380C22semidirect
38. C31×#340C22semidirect
68. C2×M16×C31D4semidirect
169. C2×C8×C31C2×D4semidirect
186. #23480C31direct (N × H)
256. C2×#428C2×C31semidirect
257. C2×#418C2×C31semidirect
258. C2×#418C2×C31semidirect
259. C2×#407C2×C31semidirect
260. #2280C2×C31semidirect
261. #2034C2×C31semidirect
262. #2033C2×C31semidirect
263. #1736C2×C31semidirect
312. C2×#107C22×C31semidirect
313. C2×#106C22×C31semidirect
316. C2×#102C22×C31semidirect
317. C2×#102C22×C31semidirect
318. C2×#102C22×C31semidirect
320. C2×C22⋊C8C22×C31semidirect
322. #380C22×C31semidirect
323. #380C22×C31semidirect
326. #340C22×C31semidirect
364. C2×M16D4×C31semidirect
397. C31#23480direct (N × H)
466. C2×C8C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#4282
C2×C31×#4182
C2×C31×#4072
C31×#22802
C31×#20342
C31×#20332
C31×#17362
#2348031