Finite Group Databasebeta

← C31×#21263 #21478022

Subgroups — C31×#21263 #21478022

Order 7936.

1726 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#535C211yesmaximal, characteristic
2C2×C31×#424C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C2×C31×#416C211yesmaximal, characteristic, complemented
6C22×C31×#102C211yesmaximal, characteristic, complemented
7C31×#2274C211yesmaximal, characteristic, complemented
8C31×#1983C214yesmaximal, complemented
9C31×#1982C214yesmaximal, complemented
10C22×#41×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C22×M16×C31C2211yescharacteristic
13C23×C8×C31C2211yescharacteristic
14C31×#535—24no—
15C31×#535C418yescomplemented
16C2×C31×#127C2212yes—
17C2×C31×#124C2212yes—
18C2×C31×#121—22no—
19C2×C31×#120—22no—
20C2×C31×#117C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#424—24no—
24C2×C31×C4⋊C8C2214yescomplemented
25C31×#418—24no—
26C31×#417—24no—
27C31×#416—24no—
28C2×C31×#103C2212yescomplemented
29C2×C31×#103C2212yescomplemented
30C2×C31×#102—24no—
31C2×C31×#102C2214yes—
32C2×C31×#102C2214yes—
33C2×C31×#102C2212yescomplemented
34C2×C31×#102C2212yescomplemented
35C4×C4⋊C4×C31—22no—
36C4×C4⋊C4×C31C2214yescomplemented
37C4×C22⋊C4×C31—22no—
38C25×C31—21no—
39C2×#41×C31—22no—
40C2×#41×C31—22no—
41C2×#41×C31—22no—
42C2×#41×C31—22no—
43C2×#41×C31—22no—
44C2×#41×C31C2×C414yes—
45C22×Q8×C31C2311yescharacteristic
46C22×D4×C31—21no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—21no—
50C22×D4×C31—22no—
51C22×D4×C31—24no—
52C22×D4×C31—22no—
53C22×D4×C31—22no—
54C22×D4×C31C2×C414yes—
55C22×D4×C31C2312yes—
56C22×D4×C31C2311yescharacteristic
57C23×C4×C31—21no—
58C23×C4×C31—21no—
59C23×C4×C31C2311yescharacteristic
60C2×M16×C31—22no—
61C2×M16×C31—22no—
62C2×M16×C31—22no—
63C22×C8×C31—22no—
64C22×C8×C31—22no—
65C22×C8×C31—22no—
66C22×C8×C31C2312yes—
67C22×C8×C31C2312yes—
68C31×#127—24no—
69C31×#127C2×C418yescomplemented
70C31×#124—24no—
71C31×#124C2×C418yescomplemented
72C31×#121—216no—
73C31×#120—216no—
74C31×#117—22no—
75C31×#117C2×C414yes—
76C31×#117D414yes—
77C31×#117D414yescomplemented
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31D412yes—
81C2×C4⋊C4×C31D414yescomplemented
82C2×C4⋊C4×C31C2312yes—
83C2×C4⋊C4×C31C2312yes—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—24no—
86C2×C22⋊C4×C31D412yes—
87C2×C42×C31—21no—
88C2×C42×C31—24no—
89C2×C42×C31C2312yes—
90C31×C4⋊C8—28no—
91C31×#103—24no—
92C31×#103—24no—
93C31×#102—28no—
94C31×#102—28no—
95C31×#102—24no—
96C31×#102—24no—
97C31×#95—24no—
98C24×C31—22no—
99C24×C31—21no—
100C24×C31—24no—
101C24×C31—42no—
102C24×C31—42no—
103C24×C31—82no—
104C24×C31—82no—
105C24×C31C2×D411yescharacteristic
106#41×C31—28no—
107#41×C31—28no—
108#41×C31—44no—
109#41×C31—44no—
110C2×Q8×C31—21no—
111C2×Q8×C31—21no—
112C2×Q8×C31—21no—
113C2×Q8×C31—21no—
114C2×Q8×C31—21no—
115C2×Q8×C31C22×C412yes—
116C2×D4×C31—24no—
117C2×D4×C31—24no—
118C2×D4×C31—216no—
119C2×D4×C31—28no—
120C2×D4×C31—28no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C2×D4×C31—22no—
126C2×D4×C31—21no—
127C2×D4×C31—22no—
128C2×D4×C31—22no—
129C2×D4×C31—21no—
130C2×D4×C31—21no—
131C2×D4×C31—42no—
132C2×D4×C31—42no—
133C2×D4×C31—42no—
134C2×D4×C31—42no—
135C2×D4×C31—44no—
136C2×D4×C31—44no—
137C2×D4×C31—84no—
138C2×D4×C31—84no—
139C2×D4×C31C22×C414yes—
140C2×D4×C31C22×C412yes—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—21no—
144C22×C4×C31—24no—
145C22×C4×C31—24no—
146C22×C4×C31—42no—
147C22×C4×C31—42no—
148C22×C4×C31—82no—
149C22×C4×C31C22×C412yes—
150C22×C4×C31C2×D414yes—
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D412yes—
153C22×C4×C31C2×D412yes—
154C22×C4×C31C2×D412yes—
155C22×C4×C31#4112yes—
156C22×C4×C31#4112yes—
157C22×C4×C31C2411yescharacteristic
158M16×C31—44no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31—22no—
164C2×C8×C31—22no—
165C2×C8×C31—44no—
166C4⋊C4×C31—24no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31C22⋊C418yes—
170C4⋊C4×C31C2×D414yes—
171C4⋊C4×C31C2×D414yes—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—216no—
174C22⋊C4×C31C22⋊C418yes—
175C42×C31—24no—
176C42×C31—84no—
177C42×C31C22×C414yes—
178C42×C31C2×D414yes—
179#21263C3111yesmaximal, characteristic, direct product factor, Sylow
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—24no—
183C23×C31—22no—
184C23×C31—41no—
185C23×C31—41no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—44no—
190C23×C31—42no—
191C23×C31—44no—
192C23×C31—48no—
193C23×C31—88no—
194C23×C31—84no—
195C23×C31—84no—
196C23×C31—88no—
197C23×C31C2×C22⋊C412yes—
198C23×C31#12112yes—
199C23×C31#12112yes—
200C23×C31C22×D411yescharacteristic
201Q8×C31—22no—
202Q8×C31—22no—
203Q8×C31—41no—
204Q8×C31—41no—
205D4×C31—24no—
206D4×C31—24no—
207D4×C31—22no—
208D4×C31—22no—
209D4×C31—48no—
210D4×C31—42no—
211D4×C31—41no—
212D4×C31—42no—
213D4×C31—41no—
214D4×C31—48no—
215D4×C31—816no—
216C2×C4×C31—24no—
217C2×C4×C31—24no—
218C2×C4×C31—22no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—44no—
225C2×C4×C31—42no—
226C2×C4×C31—48no—
227C2×C4×C31—84no—
228C2×C4×C31C2×C22⋊C418yes—
229C2×C4×C31C2×C22⋊C412yes—
230C2×C4×C31C4×D414yes—
231C2×C4×C31C4×D414yes—
232C2×C4×C31#12112yes—
233C2×C4×C31#12112yes—
234C2×C4×C31#12414yes—
235C2×C4×C31#12714yes—
236C2×C4×C31C23×C411yescharacteristic
237C2×C4×C31C22×D411yescharacteristic
238C2×C4×C31C22×D411yescharacteristic
239C2×C4×C31C22×D411yescharacteristic
240C2×C4×C31C2×#4111yescharacteristic
241C2×C4×C31C2×#4111yescharacteristic
242C8×C31—42no—
243C8×C31—42no—
244C2×#535C2×C3111yescharacteristic
245C2×#424C2×C3111yescharacteristic, complemented
246C2×#417C2×C3111yescharacteristic, complemented
247C2×#418C2×C3111yescharacteristic, complemented
248C2×#416C2×C3111yescharacteristic, complemented
249C22×#102C2×C3111yescharacteristic, complemented
250#2274C2×C3111yescharacteristic, complemented
251#1983C2×C3114yescomplemented
252#1982C2×C3114yescomplemented
253C22×C31—24no—
254C22×C31—22no—
255C22×C31—22no—
256C22×C31—24no—
257C22×C31—44no—
258C22×C31—48no—
259C22×C31—42no—
260C22×C31—44no—
261C22×C31—816no—
262C22×C31—81no—
263C22×C31—82no—
264C22×C31—81no—
265C22×C31—82no—
266C22×C31—82no—
267C22×C31—84no—
268C22×C31#39014yes—
269C22×C31C22×C22⋊C411yescharacteristic
270C22×C31C2×#12111yescharacteristic
271C22×C31C2×#12111yescharacteristic
272C22×C31#57612yes—
273C22×C31#57712yes—
274C4×C31—28no—
275C4×C31—44no—
276C4×C31—44no—
277C4×C31—42no—
278C4×C31#39014yes—
279C4×C31C2×C4×D411yescharacteristic
280C4×C31C2×C4×D411yescharacteristic
281C4×C31C2×#12411yescharacteristic
282C4×C31C2×#12711yescharacteristic
283C22×#41C22×C3111yescharacteristic
284C23×D4C22×C3111yescharacteristic
285C22×M16C22×C3111yescharacteristic
286C23×C8C22×C3111yescharacteristic
287#535—24no—
288#535C4×C3118yescomplemented
289C2×#127C22×C3112yes—
290C2×#124C22×C3112yes—
291C2×#121—22no—
292C2×#120—22no—
293C2×#117C22×C3111yescharacteristic
294C2×#117C22×C3111yescharacteristic
295C22×C4⋊C4C22×C3111yescharacteristic
296#424—24no—
297C2×C4⋊C8C22×C3114yescomplemented
298#418—24no—
299#417—24no—
300#416—24no—
301C2×#103C22×C3112yescomplemented
302C2×#103C22×C3112yescomplemented
303C2×#102—24no—
304C2×#102C22×C3114yes—
305C2×#102C22×C3114yes—
306C2×#102C22×C3112yescomplemented
307C2×#102C22×C3112yescomplemented
308C4×C4⋊C4—22no—
309C4×C4⋊C4C22×C3114yescomplemented
310C4×C22⋊C4—22no—
311C2×C31—24no—
312C2×C31—82no—
313C2×C31—84no—
314C2×C31C2×#39011yescharacteristic
315C2×C31#289712yes—
316C2×C31#304111yescharacteristic
317C2×C31#304311yescharacteristic
318C2×C31#304512yes—
319C25—21no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41C2×C4×C3114yes—
326C22×Q8C23×C3111yescharacteristic
327C22×D4—21no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—21no—
331C22×D4—22no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4C2×C4×C3114yes—
336C22×D4C23×C3112yes—
337C22×D4C23×C3111yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4C23×C3111yescharacteristic
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8C23×C3112yes—
348C22×C8C23×C3112yes—
349#127—24no—
350#127C2×C4×C3118yescomplemented
351#124—24no—
352#124C2×C4×C3118yescomplemented
353#121—216no—
354#120—216no—
355#117—22no—
356#117C2×C4×C3114yes—
357#117D4×C3114yes—
358#117D4×C3114yescomplemented
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C3112yes—
362C2×C4⋊C4D4×C3114yescomplemented
363C2×C4⋊C4C23×C3112yes—
364C2×C4⋊C4C23×C3112yes—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4D4×C3112yes—
368C2×C42—21no—
369C2×C42—24no—
370C2×C42C23×C3112yes—
371C4⋊C8—28no—
372#103—24no—
373#103—24no—
374#102—28no—
375#102—28no—
376#102—24no—
377#102—24no—
378#95—24no—
379C31#2126311yescharacteristic, direct product factor, Sylow
380C24—22no—
381C24—21no—
382C24—24no—
383C24—42no—
384C24—42no—
385C24—82no—
386C24—82no—
387C24C2×D4×C3111yescharacteristic
388#41—28no—
389#41—28no—
390#41—44no—
391#41—44no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8C22×C4×C3112yes—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—216no—
401C2×D4—28no—
402C2×D4—28no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—84no—
420C2×D4—84no—
421C2×D4C22×C4×C3114yes—
422C2×D4C22×C4×C3112yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—82no—
431C22×C4C22×C4×C3112yes—
432C22×C4C2×D4×C3114yes—
433C22×C4C2×D4×C3111yescharacteristic
434C22×C4C2×D4×C3112yes—
435C22×C4C2×D4×C3112yes—
436C22×C4C2×D4×C3112yes—
437C22×C4#41×C3112yes—
438C22×C4#41×C3112yes—
439C22×C4C24×C3111yescharacteristic
440M16—44no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—44no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4C22⋊C4×C3118yes—
452C4⋊C4C2×D4×C3114yes—
453C4⋊C4C2×D4×C3114yes—
454C22⋊C4—24no—
455C22⋊C4—216no—
456C22⋊C4C22⋊C4×C3118yes—
457C42—24no—
458C42—84no—
459C42C22×C4×C3114yes—
460C42C2×D4×C3114yes—
461C23—22no—
462C23—22no—
463C23—24no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—44no—
471C23—42no—
472C23—44no—
473C23—48no—
474C23—88no—
475C23—84no—
476C23—84no—
477C23—88no—
478C23C2×C22⋊C4×C3112yes—
479C23C31×#12112yes—
480C23C31×#12112yes—
481C23C22×D4×C3111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486D4—24no—
487D4—24no—
488D4—22no—
489D4—22no—
490D4—48no—
491D4—42no—
492D4—41no—
493D4—42no—
494D4—41no—
495D4—48no—
496D4—816no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—48no—
508C2×C4—84no—
509C2×C4C2×C22⋊C4×C3118yes—
510C2×C4C2×C22⋊C4×C3112yes—
511C2×C4C4×D4×C3114yes—
512C2×C4C4×D4×C3114yes—
513C2×C4C31×#12112yes—
514C2×C4C31×#12112yes—
515C2×C4C31×#12414yes—
516C2×C4C31×#12714yes—
517C2×C4C23×C4×C3111yescharacteristic
518C2×C4C22×D4×C3111yescharacteristic
519C2×C4C22×D4×C3111yescharacteristic
520C2×C4C22×D4×C3111yescharacteristic
521C2×C4C2×#41×C3111yescharacteristic
522C2×C4C2×#41×C3111yescharacteristic
523C8—42no—
524C8—42no—
525C22—24no—
526C22—22no—
527C22—22no—
528C22—24no—
529C22—44no—
530C22—48no—
531C22—42no—
532C22—44no—
533C22—816no—
534C22—82no—
535C22—81no—
536C22—82no—
537C22—81no—
538C22—84no—
539C22—82no—
540C22C31×#39014yes—
541C22C22×C22⋊C4×C3111yescharacteristic
542C22C2×C31×#12111yescharacteristic
543C22C2×C31×#12111yescharacteristic
544C22C31×#57612yes—
545C22C31×#57712yes—
546C4—28no—
547C4—44no—
548C4—44no—
549C4—42no—
550C4C31×#39014yes—
551C4C2×C4×D4×C3111yescharacteristic
552C4C2×C4×D4×C3111yescharacteristic
553C4C2×C31×#12411yescharacteristic
554C4C2×C31×#12711yescharacteristic
555C2—24no—
556C2—84no—
557C2—82no—
558C2C2×C31×#39011yescharacteristic
559C2C31×#289712yes—
560C2C31×#304111yescharacteristic
561C2C31×#304311yescharacteristic
562C2C31×#304512yes—
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#535C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#424C2semidirect
3. C2×C31×#417C2semidirect
4. C2×C31×#418C2semidirect
5. C2×C31×#416C2semidirect
6. C22×C31×#102C2semidirect
7. C31×#2274C2semidirect
8. C31×#1983C2semidirect
9. C31×#1982C2semidirect
15. C31×#535C4semidirect
24. C2×C31×C4⋊C8C22semidirect
28. C2×C31×#103C22semidirect
29. C2×C31×#103C22semidirect
33. C2×C31×#102C22semidirect
34. C2×C31×#102C22semidirect
36. C4×C4⋊C4×C31C22semidirect
69. C31×#127C2×C4semidirect
71. C31×#124C2×C4semidirect
77. C31×#117D4semidirect
81. C2×C4⋊C4×C31D4semidirect
179. #21263C31direct (N × H)
245. C2×#424C2×C31semidirect
246. C2×#417C2×C31semidirect
247. C2×#418C2×C31semidirect
248. C2×#416C2×C31semidirect
249. C22×#102C2×C31semidirect
250. #2274C2×C31semidirect
251. #1983C2×C31semidirect
252. #1982C2×C31semidirect
288. #535C4×C31semidirect
297. C2×C4⋊C8C22×C31semidirect
301. C2×#103C22×C31semidirect
302. C2×#103C22×C31semidirect
306. C2×#102C22×C31semidirect
307. C2×#102C22×C31semidirect
309. C4×C4⋊C4C22×C31semidirect
350. #127C2×C4×C31semidirect
352. #124C2×C4×C31semidirect
358. #117D4×C31semidirect
362. C2×C4⋊C4D4×C31semidirect
379. C31#21263direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5352
C2×C31×#4242
C2×C31×#4172
C2×C31×#4182
C2×C31×#4162
C22×C31×#1022
C31×#22742
C31×#19832
C31×#19822
#2126331