Finite Group Databasebeta

← C31×#23388 #21480147

Subgroups — C31×#23388 #21480147

Order 7936.

2142 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C31C211yesmaximal, characteristic, complemented
2C2×C31×#536C211yesmaximal, characteristic, complemented
3C2×C31×#535C211yesmaximal, characteristic
4C2×C31×#419C211yesmaximal, characteristic, complemented
5C2×C31×#418C211yesmaximal, characteristic, complemented
6C2×C31×#408C211yesmaximal, characteristic, complemented
7C31×#2000C218yesmaximal, complemented
8C31×#1735C211yesmaximal, characteristic, complemented
9C22×#41×C31C2211yescharacteristic
10C23×Q8×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C22×SD16×C31—24no—
13C22×SD16×C31—24no—
14C22×SD16×C31—24no—
15C22×SD16×C31C2214yes—
16C22×M16×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C31×#536—24no—
19C31×#536—24no—
20C31×#535—24no—
21C31×#535—24no—
22C2×C31×C4⋊Q8—21no—
23C2×C31×#127—21no—
24C2×C31×#124—21no—
25C2×C31×#124—21no—
26C2×C31×#123—22no—
27C2×C31×C22⋊Q8C2214yescomplemented
28C2×C31×#121C2214yes—
29C2×C31×#120—22no—
30C2×C31×#117C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C31×#419—24no—
33C31×#418—24no—
34C2×C31×#103C2214yescomplemented
35C2×C31×#102C2214yes—
36C31×#408—24no—
37C2×C31×C22⋊C8C2214yescomplemented
38C31×#340C2214yescomplemented
39C25×C31—21no—
40C2×#41×C31—22no—
41C2×#41×C31—22no—
42C2×#41×C31—22no—
43C2×#41×C31—22no—
44C2×#41×C31—22no—
45C2×#41×C31—22no—
46C22×Q8×C31—21no—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31—22no—
51C22×Q8×C31—22no—
52C22×Q8×C31D411yescharacteristic
53C22×Q8×C31D414yescomplemented
54C22×Q8×C31C2312yes—
55C22×D4×C31—24no—
56C22×D4×C31—22no—
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—21no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31D412yes—
63C22×D4×C31D411yescharacteristic
64C22×D4×C31D414yes—
65C22×D4×C31C2312yes—
66C23×C4×C31—21no—
67C23×C4×C31C2312yes—
68C23×C4×C31C2311yescharacteristic
69C2×SD16×C31—232no—
70C2×SD16×C31—28no—
71C2×SD16×C31—28no—
72C2×SD16×C31—28no—
73C2×M16×C31—22no—
74C2×M16×C31—22no—
75C2×M16×C31—22no—
76C22×C8×C31—22no—
77C22×C8×C31—22no—
78C22×C8×C31D414yescomplemented
79C22×C8×C31C2312yes—
80C22×C8×C31C2312yes—
81C31×C4⋊Q8—28no—
82C31×#127—28no—
83C31×#124—28no—
84C31×#124—28no—
85C31×#123—216no—
86C31×C22⋊Q8—28no—
87C31×C22⋊Q8—28no—
88C31×#121—28no—
89C31×#121—28no—
90C31×#120—216no—
91C31×#117—22no—
92C31×#117—22no—
93C31×#117D414yes—
94C31×#117D414yescomplemented
95C2×C4⋊C4×C31—24no—
96C2×C4⋊C4×C31C2312yes—
97C2×C4⋊C4×C31C2312yes—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—24no—
101C2×C22⋊C4×C31—24no—
102C2×C42×C31—21no—
103C2×C42×C31—21no—
104C31×#103—28no—
105C31×#102—28no—
106C31×C22⋊C8—28no—
107C24×C31—22no—
108C24×C31—24no—
109C24×C31—42no—
110C24×C31—42no—
111C24×C31—84no—
112C24×C31C2×D412yes—
113C24×C31C2×D411yescharacteristic
114#41×C31—44no—
115#41×C31—44no—
116#41×C31—44no—
117#41×C31—44no—
118C2×Q8×C31—22no—
119C2×Q8×C31—24no—
120C2×Q8×C31—22no—
121C2×Q8×C31—22no—
122C2×Q8×C31—22no—
123C2×Q8×C31—28no—
124C2×Q8×C31—28no—
125C2×Q8×C31—22no—
126C2×Q8×C31—22no—
127C2×Q8×C31—22no—
128C2×Q8×C31—22no—
129C2×Q8×C31—42no—
130C2×Q8×C31—42no—
131C2×Q8×C31—44no—
132C2×Q8×C31—44no—
133C2×Q8×C31C2×D414yes—
134C2×D4×C31—24no—
135C2×D4×C31—24no—
136C2×D4×C31—24no—
137C2×D4×C31—216no—
138C2×D4×C31—28no—
139C2×D4×C31—22no—
140C2×D4×C31—24no—
141C2×D4×C31—22no—
142C2×D4×C31—28no—
143C2×D4×C31—22no—
144C2×D4×C31—22no—
145C2×D4×C31—22no—
146C2×D4×C31—22no—
147C2×D4×C31—22no—
148C2×D4×C31—22no—
149C2×D4×C31—42no—
150C2×D4×C31—44no—
151C2×D4×C31—42no—
152C2×D4×C31—44no—
153C2×D4×C31—88no—
154C2×D4×C31C2×D414yes—
155C22×C4×C31—24no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—42no—
166C22×C4×C31—42no—
167C22×C4×C31C2×D412yes—
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D412yes—
170C22×C4×C31C2×D412yes—
171C22×C4×C31C2×D412yes—
172C22×C4×C31C2×D412yes—
173C22×C4×C31C2×D412yes—
174C22×C4×C31#4112yes—
175C22×C4×C31C2411yescharacteristic
176SD16×C31—232no—
177M16×C31—44no—
178C2×C8×C31—28no—
179C2×C8×C31—22no—
180C2×C8×C31—22no—
181C2×C8×C31—22no—
182C2×C8×C31—22no—
183C2×C8×C31—22no—
184C2×C8×C31C2×D414yes—
185C4⋊C4×C31—216no—
186C4⋊C4×C31—22no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31C2×D414yes—
189C4⋊C4×C31C2×D414yes—
190C22⋊C4×C31—216no—
191C22⋊C4×C31—216no—
192C22⋊C4×C31—24no—
193C22⋊C4×C31—24no—
194C42×C31—24no—
195C42×C31—24no—
196#23388C3111yesmaximal, characteristic, direct product factor, Sylow
197C23×C31—24no—
198C23×C31—22no—
199C23×C31—24no—
200C23×C31—22no—
201C23×C31—22no—
202C23×C31—28no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—48no—
206C23×C31—48no—
207C23×C31—88no—
208C23×C31—88no—
209C23×C31—88no—
210C23×C31#12012yes—
211C23×C31#12012yes—
212C23×C31#12112yes—
213C23×C31C22×D411yescharacteristic
214Q8×C31—24no—
215Q8×C31—24no—
216Q8×C31—42no—
217Q8×C31—42no—
218Q8×C31—48no—
219Q8×C31—44no—
220D4×C31—24no—
221D4×C31—24no—
222D4×C31—48no—
223D4×C31—42no—
224D4×C31—42no—
225D4×C31—48no—
226D4×C31—44no—
227D4×C31—816no—
228C2×C4×C31—24no—
229C2×C4×C31—24no—
230C2×C4×C31—22no—
231C2×C4×C31—24no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—44no—
237C2×C4×C31—44no—
238C2×C4×C31—48no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31#12014yes—
244C2×C4×C31#12012yes—
245C2×C4×C31#12012yes—
246C2×C4×C31#12114yes—
247C2×C4×C31#12114yes—
248C2×C4×C31#12112yes—
249C2×C4×C31#12714yes—
250C2×C4×C31C22×D411yescharacteristic
251C2×C4×C31C22×D411yescharacteristic
252C2×C4×C31C22×D411yescharacteristic
253C2×C4×C31C22×D411yescharacteristic
254C2×C4×C31C22×D411yescharacteristic
255C2×C4×C31C2×#4111yescharacteristic
256C8×C31—24no—
257C8×C31—42no—
258C23×SD16C2×C3111yescharacteristic, complemented
259C2×#536C2×C3111yescharacteristic, complemented
260C2×#535C2×C3111yescharacteristic
261C2×#419C2×C3111yescharacteristic, complemented
262C2×#418C2×C3111yescharacteristic, complemented
263C2×#408C2×C3111yescharacteristic, complemented
264#2000C2×C3118yescomplemented
265#1735C2×C3111yescharacteristic, complemented
266C22×C31—24no—
267C22×C31—24no—
268C22×C31—24no—
269C22×C31—42no—
270C22×C31—44no—
271C22×C31—44no—
272C22×C31—48no—
273C22×C31—44no—
274C22×C31—44no—
275C22×C31—816no—
276C22×C31—84no—
277C22×C31—84no—
278C22×C31#39214yes—
279C22×C31C2×#12011yescharacteristic
280C22×C31C2×#12011yescharacteristic
281C22×C31C2×#12111yescharacteristic
282C22×C31#57714yes—
283C4×C31—42no—
284C4×C31—44no—
285C4×C31—44no—
286C4×C31—44no—
287C4×C31#39214yes—
288C4×C31C2×#12011yescharacteristic
289C4×C31C2×#12111yescharacteristic
290C4×C31C2×#12111yescharacteristic
291C4×C31C2×#12711yescharacteristic
292C22×#41C22×C3111yescharacteristic
293C23×Q8C22×C3111yescharacteristic
294C23×D4C22×C3111yescharacteristic
295C22×SD16—24no—
296C22×SD16—24no—
297C22×SD16—24no—
298C22×SD16C22×C3114yes—
299C22×M16C22×C3111yescharacteristic
300C23×C8C22×C3111yescharacteristic
301#536—24no—
302#536—24no—
303#535—24no—
304#535—24no—
305C2×C4⋊Q8—21no—
306C2×#127—21no—
307C2×#124—21no—
308C2×#124—21no—
309C2×#123—22no—
310C2×C22⋊Q8C22×C3114yescomplemented
311C2×#121C22×C3114yes—
312C2×#120—22no—
313C2×#117C22×C3111yescharacteristic
314C2×#117C22×C3111yescharacteristic
315#419—24no—
316#418—24no—
317C2×#103C22×C3114yescomplemented
318C2×#102C22×C3114yes—
319#408—24no—
320C2×C22⋊C8C22×C3114yescomplemented
321#340C22×C3114yescomplemented
322C2×C31—24no—
323C2×C31—82no—
324C2×C31—84no—
325C2×C31C2×#39211yescharacteristic
326C2×C31#300912yes—
327C2×C31#301012yes—
328C2×C31#305712yes—
329C25—21no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—22no—
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8D4×C3111yescharacteristic
343C22×Q8D4×C3114yescomplemented
344C22×Q8C23×C3112yes—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—21no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4D4×C3112yes—
353C22×D4D4×C3111yescharacteristic
354C22×D4D4×C3114yes—
355C22×D4C23×C3112yes—
356C23×C4—21no—
357C23×C4C23×C3112yes—
358C23×C4C23×C3111yescharacteristic
359C2×SD16—232no—
360C2×SD16—28no—
361C2×SD16—28no—
362C2×SD16—28no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16—22no—
366C22×C8—22no—
367C22×C8—22no—
368C22×C8D4×C3114yescomplemented
369C22×C8C23×C3112yes—
370C22×C8C23×C3112yes—
371C4⋊Q8—28no—
372#127—28no—
373#124—28no—
374#124—28no—
375#123—216no—
376C22⋊Q8—28no—
377C22⋊Q8—28no—
378#121—28no—
379#121—28no—
380#120—216no—
381#117—22no—
382#117—22no—
383#117D4×C3114yes—
384#117D4×C3114yescomplemented
385C2×C4⋊C4—24no—
386C2×C4⋊C4C23×C3112yes—
387C2×C4⋊C4C23×C3112yes—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C42—21no—
393C2×C42—21no—
394#103—28no—
395#102—28no—
396C22⋊C8—28no—
397C31#2338811yescharacteristic, direct product factor, Sylow
398C24—22no—
399C24—24no—
400C24—42no—
401C24—42no—
402C24—84no—
403C24C2×D4×C3112yes—
404C24C2×D4×C3111yescharacteristic
405#41—44no—
406#41—44no—
407#41—44no—
408#41—44no—
409C2×Q8—22no—
410C2×Q8—24no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—28no—
415C2×Q8—28no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—42no—
421C2×Q8—42no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8C2×D4×C3114yes—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—216no—
429C2×D4—28no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—22no—
433C2×D4—28no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—42no—
443C2×D4—44no—
444C2×D4—88no—
445C2×D4C2×D4×C3114yes—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4C2×D4×C3112yes—
459C22×C4C2×D4×C3111yescharacteristic
460C22×C4C2×D4×C3112yes—
461C22×C4C2×D4×C3112yes—
462C22×C4C2×D4×C3112yes—
463C22×C4C2×D4×C3112yes—
464C22×C4C2×D4×C3112yes—
465C22×C4#41×C3112yes—
466C22×C4C24×C3111yescharacteristic
467SD16—232no—
468M16—44no—
469C2×C8—28no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8C2×D4×C3114yes—
476C4⋊C4—216no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4C2×D4×C3114yes—
480C4⋊C4C2×D4×C3114yes—
481C22⋊C4—216no—
482C22⋊C4—216no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C42—24no—
486C42—24no—
487C23—24no—
488C23—22no—
489C23—24no—
490C23—22no—
491C23—22no—
492C23—28no—
493C23—42no—
494C23—42no—
495C23—48no—
496C23—48no—
497C23—88no—
498C23—88no—
499C23—88no—
500C23C31×#12012yes—
501C23C31×#12012yes—
502C23C31×#12112yes—
503C23C22×D4×C3111yescharacteristic
504Q8—24no—
505Q8—24no—
506Q8—42no—
507Q8—42no—
508Q8—48no—
509Q8—44no—
510D4—24no—
511D4—24no—
512D4—48no—
513D4—42no—
514D4—42no—
515D4—48no—
516D4—44no—
517D4—816no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—48no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4C31×#12014yes—
534C2×C4C31×#12012yes—
535C2×C4C31×#12012yes—
536C2×C4C31×#12114yes—
537C2×C4C31×#12114yes—
538C2×C4C31×#12112yes—
539C2×C4C31×#12714yes—
540C2×C4C22×D4×C3111yescharacteristic
541C2×C4C22×D4×C3111yescharacteristic
542C2×C4C22×D4×C3111yescharacteristic
543C2×C4C22×D4×C3111yescharacteristic
544C2×C4C22×D4×C3111yescharacteristic
545C2×C4C2×#41×C3111yescharacteristic
546C8—24no—
547C8—42no—
548C22—24no—
549C22—24no—
550C22—24no—
551C22—42no—
552C22—44no—
553C22—44no—
554C22—48no—
555C22—44no—
556C22—44no—
557C22—816no—
558C22—84no—
559C22—84no—
560C22C31×#39214yes—
561C22C2×C31×#12011yescharacteristic
562C22C2×C31×#12011yescharacteristic
563C22C2×C31×#12111yescharacteristic
564C22C31×#57714yes—
565C4—42no—
566C4—44no—
567C4—44no—
568C4—44no—
569C4C31×#39214yes—
570C4C2×C31×#12011yescharacteristic
571C4C2×C31×#12111yescharacteristic
572C4C2×C31×#12111yescharacteristic
573C4C2×C31×#12711yescharacteristic
574C2—24no—
575C2—82no—
576C2—84no—
577C2C2×C31×#39211yescharacteristic
578C2C31×#300912yes—
579C2C31×#301012yes—
580C2C31×#305712yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×SD16×C31C2semidirect
2. C2×C31×#536C2semidirect
4. C2×C31×#419C2semidirect
5. C2×C31×#418C2semidirect
6. C2×C31×#408C2semidirect
7. C31×#2000C2semidirect
8. C31×#1735C2semidirect
27. C2×C31×C22⋊Q8C22semidirect
34. C2×C31×#103C22semidirect
37. C2×C31×C22⋊C8C22semidirect
38. C31×#340C22semidirect
53. C22×Q8×C31D4semidirect
78. C22×C8×C31D4semidirect
94. C31×#117D4semidirect
196. #23388C31direct (N × H)
258. C23×SD16C2×C31semidirect
259. C2×#536C2×C31semidirect
261. C2×#419C2×C31semidirect
262. C2×#418C2×C31semidirect
263. C2×#408C2×C31semidirect
264. #2000C2×C31semidirect
265. #1735C2×C31semidirect
310. C2×C22⋊Q8C22×C31semidirect
317. C2×#103C22×C31semidirect
320. C2×C22⋊C8C22×C31semidirect
321. #340C22×C31semidirect
343. C22×Q8D4×C31semidirect
368. C22×C8D4×C31semidirect
384. #117D4×C31semidirect
397. C31#23388direct (N × H)

Maximal subgroups

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

subgroupindex
C23×SD16×C312
C2×C31×#5362
C2×C31×#5352
C2×C31×#4192
C2×C31×#4182
C2×C31×#4082
C31×#20002
C31×#17352
#2338831