Finite Group Databasebeta

← C31×#33014 #21489773

Subgroups — C31×#33014 #21489773

Order 7936.

1474 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#518C211yesmaximal, characteristic, complemented
2C2×C31×#482C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic
4C31×#2624C211yesmaximal, characteristic, complemented
5C31×#1879C212yesmaximal, complemented
6C31×#1879C212yesmaximal, complemented
7C31×#1864C212yesmaximal, complemented
8C31×#1862C212yesmaximal, complemented
9C31×#1825C211yesmaximal, characteristic, complemented
10C31×#1818C211yesmaximal, characteristic, complemented
11C31×#1786C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C22×D8×C31C2212yes—
14C2×C31×#121C2211yescharacteristic
15C31×#518—24no—
16C31×#518—24no—
17C2×C4×D4×C31—21no—
18C2×C4×D4×C31—21no—
19C2×C4×D4×C31C2212yes—
20C2×C4×D4×C31C2212yes—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C22⋊C4×C31—22no—
24C31×#482—24no—
25C31×#447—24no—
26C2×C31×#107C2211yescharacteristic, complemented
27C2×C31×#106C2211yescharacteristic, complemented
28C2×C31×#102C2212yes—
29C2×C31×#102C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×#102C2211yescharacteristic, complemented
32C2×C31×#102C2211yescharacteristic, complemented
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×C22⋊C8C2211yescharacteristic
35C31×#399—21no—
36C31×#397—21no—
37C31×#394—22no—
38C31×#390C2212yescomplemented
39C31×#389C2212yescomplemented
40C31×#380C2211yescharacteristic
41C31×#340C2212yescomplemented
42C31×#340C2212yescomplemented
43C31×#336C2212yescomplemented
44C31×#336C2212yescomplemented
45C25×C31—21no—
46C22×D4×C31—24no—
47C22×D4×C31—24no—
48C22×D4×C31—21no—
49C22×D4×C31—21no—
50C22×D4×C31—22no—
51C22×D4×C31D414yes—
52C22×D4×C31C2311yescharacteristic
53C22×D4×C31C2312yes—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31C2311yescharacteristic
57C2×D8×C31—24no—
58C2×D8×C31—24no—
59C2×D8×C31—24no—
60C22×C8×C31C2311yescharacteristic
61C22×C8×C31C2311yescharacteristic
62C22×C8×C31C2312yes—
63C31×#121—22no—
64C31×#121—22no—
65C4×D4×C31—28no—
66C4×D4×C31—28no—
67C4×D4×C31—24no—
68C4×D4×C31—24no—
69C4×D4×C31—24no—
70C4×D4×C31—24no—
71C31×#117—22no—
72C31×#117—22no—
73C31×#117—22no—
74C31×#117D414yes—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31D411yescharacteristic
77C2×C4⋊C4×C31D411yescharacteristic
78C2×C4⋊C4×C31C2311yescharacteristic
79C2×C4⋊C4×C31C2312yes—
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C22⋊C4×C31—216no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31D412yes—
91C2×C42×C31—21no—
92C2×C42×C31C2312yes—
93C31×#107—22no—
94C31×#106—22no—
95C31×#102—24no—
96C31×#102—24no—
97C31×#102—24no—
98C31×#102—22no—
99C31×#102—22no—
100C31×C22⋊C8—22no—
101C31×C22⋊C8—22no—
102C31×#95—21no—
103C31×#95—22no—
104C24×C31—28no—
105C24×C31—22no—
106C24×C31—24no—
107C24×C31—21no—
108C24×C31—81no—
109C24×C31—82no—
110C24×C31—81no—
111C24×C31C2×D411yescharacteristic
112C2×D4×C31—28no—
113C2×D4×C31—28no—
114C2×D4×C31—28no—
115C2×D4×C31—216no—
116C2×D4×C31—24no—
117C2×D4×C31—22no—
118C2×D4×C31—21no—
119C2×D4×C31—21no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—42no—
125C2×D4×C31—82no—
126C2×D4×C31C2×D414yes—
127C2×D4×C31#4114yes—
128C2×D4×C31#4114yes—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—28no—
134C22×C4×C31—28no—
135C22×C4×C31—22no—
136C22×C4×C31—21no—
137C22×C4×C31—82no—
138C22×C4×C31—82no—
139C22×C4×C31—82no—
140C22×C4×C31—82no—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2411yescharacteristic
147D8×C31—48no—
148C2×C8×C31—21no—
149C2×C8×C31—21no—
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—21no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—82no—
164C4⋊C4×C31C2×D412yes—
165C4⋊C4×C31C2×D412yes—
166C22⋊C4×C31—28no—
167C22⋊C4×C31—28no—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—42no—
171C22⋊C4×C31—82no—
172C22⋊C4×C31—82no—
173C22⋊C4×C31—81no—
174C42×C31—24no—
175C42×C31—22no—
176C42×C31—22no—
177#33014C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—216no—
179C23×C31—24no—
180C23×C31—22no—
181C23×C31—24no—
182C23×C31—24no—
183C23×C31—21no—
184C23×C31—22no—
185C23×C31—21no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—42no—
192C23×C31—41no—
193C23×C31—42no—
194C23×C31—41no—
195C23×C31—84no—
196C23×C31—84no—
197C23×C31—88no—
198C23×C31—88no—
199C23×C31#12012yes—
200C23×C31C22×D411yescharacteristic
201D4×C31—216no—
202D4×C31—24no—
203D4×C31—24no—
204D4×C31—24no—
205D4×C31—42no—
206D4×C31—41no—
207D4×C31—41no—
208D4×C31—84no—
209D4×C31#12318yes—
210C2×C4×C31—22no—
211C2×C4×C31—24no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—42no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—88no—
231C2×C4×C31—88no—
232C2×C4×C31#12012yes—
233C2×C4×C31C22×D411yescharacteristic
234C2×C4×C31C22×D411yescharacteristic
235C2×C4×C31C2×#4112yes—
236C2×C4×C31C2×#4112yes—
237C8×C31—42no—
238C8×C31—41no—
239C8×C31—41no—
240C2×#518C2×C3111yescharacteristic, complemented
241C2×#482C2×C3111yescharacteristic, complemented
242C2×#447C2×C3111yescharacteristic
243#2624C2×C3111yescharacteristic, complemented
244#1879C2×C3112yescomplemented
245#1879C2×C3112yescomplemented
246#1864C2×C3112yescomplemented
247#1862C2×C3112yescomplemented
248#1825C2×C3111yescharacteristic, complemented
249#1818C2×C3111yescharacteristic, complemented
250#1786C2×C3111yescharacteristic, complemented
251C22×C31—22no—
252C22×C31—28no—
253C22×C31—22no—
254C22×C31—22no—
255C22×C31—42no—
256C22×C31—44no—
257C22×C31—44no—
258C22×C31—42no—
259C22×C31—44no—
260C22×C31—44no—
261C22×C31—44no—
262C22×C31—44no—
263C22×C31—816no—
264C22×C31—81no—
265C22×C31—82no—
266C22×C31—82no—
267C22×C31—81no—
268C22×C31—81no—
269C22×C31C2×#12011yescharacteristic
270C22×C31#52512yes—
271C22×C31#57612yes—
272C22×C31#57611yescharacteristic
273C22×C31#57711yescharacteristic
274C4×C31—22no—
275C4×C31—42no—
276C4×C31—42no—
277C4×C31—42no—
278C4×C31—42no—
279C4×C31—82no—
280C4×C31—81no—
281C4×C31C2×#12312yes—
282C4×C31#52511yescharacteristic
283C4×C31#52511yescharacteristic
284C23×D4C22×C3111yescharacteristic
285C22×D8C22×C3112yes—
286C2×#121C22×C3111yescharacteristic
287#518—24no—
288#518—24no—
289C2×C4×D4—21no—
290C2×C4×D4—21no—
291C2×C4×D4C22×C3112yes—
292C2×C4×D4C22×C3112yes—
293C2×#117C22×C3111yescharacteristic
294C2×#117C22×C3111yescharacteristic
295C22×C22⋊C4—22no—
296#482—24no—
297#447—24no—
298C2×#107C22×C3111yescharacteristic, complemented
299C2×#106C22×C3111yescharacteristic, complemented
300C2×#102C22×C3112yes—
301C2×#102C22×C3112yes—
302C2×#102C22×C3112yes—
303C2×#102C22×C3111yescharacteristic, complemented
304C2×#102C22×C3111yescharacteristic, complemented
305C2×C22⋊C8C22×C3111yescharacteristic
306C2×C22⋊C8C22×C3111yescharacteristic
307#399—21no—
308#397—21no—
309#394—22no—
310#390C22×C3112yescomplemented
311#389C22×C3112yescomplemented
312#380C22×C3111yescharacteristic
313#340C22×C3112yescomplemented
314#340C22×C3112yescomplemented
315#336C22×C3112yescomplemented
316#336C22×C3112yescomplemented
317C2×C31—42no—
318C2×C31—48no—
319C2×C31—161no—
320C2×C31#284911yescharacteristic
321C2×C31#300811yescharacteristic
322C2×C31#301211yescharacteristic
323C2×C31#311812yes—
324C2×C31#312212yes—
325C25—21no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4D4×C3114yes—
332C22×D4C23×C3111yescharacteristic
333C22×D4C23×C3112yes—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4C23×C3111yescharacteristic
337C2×D8—24no—
338C2×D8—24no—
339C2×D8—24no—
340C22×C8C23×C3112yes—
341C22×C8C23×C3111yescharacteristic
342C22×C8C23×C3111yescharacteristic
343#121—22no—
344#121—22no—
345C4×D4—28no—
346C4×D4—28no—
347C4×D4—24no—
348C4×D4—24no—
349C4×D4—24no—
350C4×D4—24no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117D4×C3114yes—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C3111yescharacteristic
357C2×C4⋊C4D4×C3111yescharacteristic
358C2×C4⋊C4C23×C3111yescharacteristic
359C2×C4⋊C4C23×C3112yes—
360C2×C4⋊C4C23×C3111yescharacteristic
361C2×C4⋊C4C23×C3111yescharacteristic
362C2×C22⋊C4—216no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4D4×C3112yes—
371C2×C42—21no—
372C2×C42C23×C3112yes—
373#107—22no—
374#106—22no—
375#102—24no—
376#102—24no—
377#102—24no—
378#102—22no—
379#102—22no—
380C22⋊C8—22no—
381C22⋊C8—22no—
382#95—21no—
383#95—22no—
384C31#3301411yescharacteristic, direct product factor, Sylow
385C24—28no—
386C24—22no—
387C24—24no—
388C24—21no—
389C24—81no—
390C24—82no—
391C24—81no—
392C24C2×D4×C3111yescharacteristic
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—28no—
396C2×D4—216no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—42no—
406C2×D4—82no—
407C2×D4C2×D4×C3114yes—
408C2×D4#41×C3114yes—
409C2×D4#41×C3114yes—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4—82no—
422C22×C4C2×D4×C3112yes—
423C22×C4C2×D4×C3112yes—
424C22×C4C2×D4×C3111yescharacteristic
425C22×C4C2×D4×C3112yes—
426C22×C4C2×D4×C3112yes—
427C22×C4C24×C3111yescharacteristic
428D8—48no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—82no—
445C4⋊C4C2×D4×C3112yes—
446C4⋊C4C2×D4×C3112yes—
447C22⋊C4—28no—
448C22⋊C4—28no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—42no—
452C22⋊C4—82no—
453C22⋊C4—82no—
454C22⋊C4—81no—
455C42—24no—
456C42—22no—
457C42—22no—
458C23—216no—
459C23—24no—
460C23—22no—
461C23—24no—
462C23—24no—
463C23—21no—
464C23—22no—
465C23—21no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—41no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—84no—
476C23—84no—
477C23—88no—
478C23—88no—
479C23C31×#12012yes—
480C23C22×D4×C3111yescharacteristic
481D4—216no—
482D4—24no—
483D4—24no—
484D4—24no—
485D4—42no—
486D4—41no—
487D4—41no—
488D4—84no—
489D4C31×#12318yes—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—88no—
511C2×C4—88no—
512C2×C4C31×#12012yes—
513C2×C4C22×D4×C3111yescharacteristic
514C2×C4C22×D4×C3111yescharacteristic
515C2×C4C2×#41×C3112yes—
516C2×C4C2×#41×C3112yes—
517C8—42no—
518C8—41no—
519C8—41no—
520C22—22no—
521C22—28no—
522C22—22no—
523C22—22no—
524C22—42no—
525C22—44no—
526C22—44no—
527C22—42no—
528C22—44no—
529C22—44no—
530C22—44no—
531C22—44no—
532C22—816no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22C2×C31×#12011yescharacteristic
539C22C31×#52512yes—
540C22C31×#57612yes—
541C22C31×#57611yescharacteristic
542C22C31×#57711yescharacteristic
543C4—22no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—82no—
549C4—81no—
550C4C2×C31×#12312yes—
551C4C31×#52511yescharacteristic
552C4C31×#52511yescharacteristic
553C2—42no—
554C2—48no—
555C2—161no—
556C2C31×#284911yescharacteristic
557C2C31×#300811yescharacteristic
558C2C31×#301211yescharacteristic
559C2C31×#311812yes—
560C2C31×#312212yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#518C2semidirect
2. C2×C31×#482C2semidirect
4. C31×#2624C2semidirect
5. C31×#1879C2semidirect
6. C31×#1879C2semidirect
7. C31×#1864C2semidirect
8. C31×#1862C2semidirect
9. C31×#1825C2semidirect
10. C31×#1818C2semidirect
11. C31×#1786C2semidirect
26. C2×C31×#107C22semidirect
27. C2×C31×#106C22semidirect
31. C2×C31×#102C22semidirect
32. C2×C31×#102C22semidirect
38. C31×#390C22semidirect
39. C31×#389C22semidirect
41. C31×#340C22semidirect
42. C31×#340C22semidirect
43. C31×#336C22semidirect
44. C31×#336C22semidirect
177. #33014C31direct (N × H)
240. C2×#518C2×C31semidirect
241. C2×#482C2×C31semidirect
243. #2624C2×C31semidirect
244. #1879C2×C31semidirect
245. #1879C2×C31semidirect
246. #1864C2×C31semidirect
247. #1862C2×C31semidirect
248. #1825C2×C31semidirect
249. #1818C2×C31semidirect
250. #1786C2×C31semidirect
298. C2×#107C22×C31semidirect
299. C2×#106C22×C31semidirect
303. C2×#102C22×C31semidirect
304. C2×#102C22×C31semidirect
310. #390C22×C31semidirect
311. #389C22×C31semidirect
313. #340C22×C31semidirect
314. #340C22×C31semidirect
315. #336C22×C31semidirect
316. #336C22×C31semidirect
384. C31#33014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5182
C2×C31×#4822
C2×C31×#4472
C31×#26242
C31×#18792
C31×#18642
C31×#18622
C31×#18252
C31×#18182
C31×#17862
#3301431