Finite Group Databasebeta

← C31×#14409 #21471168

Subgroups — C31×#14409 #21471168

Order 7936.

1606 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
1C2×C31×#387C212yesmaximal, complemented
2C2×C31×#385C211yesmaximal, characteristic
3C2×C31×#380C212yesmaximal
4C31×#1442C212yesmaximal, complemented
5C31×#1441C212yesmaximal, complemented
6C31×#1440C212yesmaximal
7C31×#1437C211yesmaximal, characteristic
8C31×#1437C211yesmaximal, characteristic
9C31×#1436C212yesmaximal, complemented
10C24×C4×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yes—
12C22×C4⋊C4×C31C2212yes—
13C22×C4⋊C4×C31C2212yes—
14C22×C22⋊C4×C31C2212yes—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2211yescharacteristic
20C31×#387—28no—
21C31×#385C418yescomplemented
22C31×#380—28no—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C25×C31C2311yescharacteristic
35C23×C4×C31—24no—
36C23×C4×C31—24no—
37C23×C4×C31—41no—
38C23×C4×C31—41no—
39C23×C4×C31C2×C414yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2312yes—
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C2×C4⋊C4×C31—24no—
49C2×C4⋊C4×C31—24no—
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—42no—
55C2×C4⋊C4×C31—42no—
56C2×C4⋊C4×C31C2×C418yes—
57C2×C22⋊C4×C31—24no—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—24no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—41no—
63C2×C22⋊C4×C31—41no—
64C2×C22⋊C4×C31—42no—
65C2×C22⋊C4×C31—42no—
66C2×C22⋊C4×C31C2×C414yes—
67C2×C22⋊C4×C31C2×C414yes—
68C2×C42×C31—24no—
69C2×C42×C31—41no—
70C2×C42×C31—42no—
71C2×C42×C31—41no—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—24no—
75C31×#95—24no—
76C31×#95—42no—
77C31×#95—42no—
78C31×#95—42no—
79C31×#95—41no—
80C31×#95—41no—
81C31×#95C2×C418yes—
82C31×#95D418yes—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31—22no—
86C24×C31—21no—
87C24×C31—21no—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31C22×C412yes—
91C24×C31#4114yes—
92C24×C31C2411yescharacteristic
93C22×C4×C31—22no—
94C22×C4×C31—22no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—21no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—216no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—44no—
139C22×C4×C31—44no—
140C22×C4×C31—48no—
141C22×C4×C31—44no—
142C22×C4×C31C22×C412yes—
143C22×C4×C31C22×C414yes—
144C22×C4×C31C22×C412yes—
145C22×C4×C31C22×C414yes—
146C22×C4×C31C2×D414yes—
147C22×C4×C31C2×D414yes—
148C22×C4×C31C2×D414yes—
149C22×C4×C31#4114yes—
150C4⋊C4×C31—216no—
151C4⋊C4×C31—48no—
152C4⋊C4×C31—48no—
153C22⋊C4×C31—28no—
154C22⋊C4×C31—44no—
155C22⋊C4×C31—48no—
156C22⋊C4×C31—48no—
157C42×C31—44no—
158C42×C31—44no—
159#14409C3111yesmaximal, characteristic, direct product factor, Sylow
160C23×C31—24no—
161C23×C31—22no—
162C23×C31—22no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—24no—
166C23×C31—24no—
167C23×C31—24no—
168C23×C31—24no—
169C23×C31—24no—
170C23×C31—42no—
171C23×C31—42no—
172C23×C31—42no—
173C23×C31—42no—
174C23×C31—41no—
175C23×C31—42no—
176C23×C31—41no—
177C23×C31—41no—
178C23×C31—42no—
179C23×C31—41no—
180C23×C31#11714yes—
181C23×C31C23×C411yescharacteristic
182C23×C31C22×D412yes—
183C23×C31C2×#4112yes—
184C23×C31C2×#4112yes—
185C23×C31H(5,𝔽2)11yescharacteristic
186C23×C31H(5,𝔽2)11yescharacteristic
187C23×C31H(5,𝔽2)12yes—
188C23×C312−1+412yes—
189C23×C312−1+412yes—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
198C2×C4×C31—24no—
199C2×C4×C31—22no—
200C2×C4×C31—22no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—24no—
205C2×C4×C31—24no—
206C2×C4×C31—24no—
207C2×C4×C31—24no—
208C2×C4×C31—24no—
209C2×C4×C31—416no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—41no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—42no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—41no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—41no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31C4×D418yes—
243C2×#387C2×C3112yescomplemented
244C2×#385C2×C3111yescharacteristic
245C2×#380C2×C3112yes—
246#1442C2×C3112yescomplemented
247#1441C2×C3112yescomplemented
248#1440C2×C3112yes—
249#1437C2×C3111yescharacteristic
250#1437C2×C3111yescharacteristic
251#1436C2×C3112yescomplemented
252C22×C31—24no—
253C22×C31—28no—
254C22×C31—44no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—44no—
258C22×C31—44no—
259C22×C31—44no—
260C22×C31—44no—
261C22×C31C2×#11711yescharacteristic
262C22×C31C2×C4×D412yes—
263C22×C31#51811yescharacteristic
264C22×C31#51911yescharacteristic
265C22×C31#52012yes—
266C22×C31#53612yes—
267C22×C31#53712yes—
268C22×C31#53912yes—
269C22×C31#53912yes—
270C22×C31#54112yes—
271C22×C31#54212yes—
272C22×C31D4211yescharacteristic
273C22×C31#54612yes—
274C22×C31#54612yes—
275C22×C31#54812yes—
276C22×C31#55111yescharacteristic
277C22×C31#55212yes—
278C22×C31#55312yes—
279C22×C31#56011yescharacteristic
280C22×C31#56212yes—
281C22×C31#56311yescharacteristic
282C4×C31—28no—
283C4×C31—44no—
284C4×C31—42no—
285C4×C31—42no—
286C4×C31—44no—
287C4×C31—44no—
288C4×C31—82no—
289C4×C31—82no—
290C24×C4C22×C3111yescharacteristic
291C22×C4⋊C4C22×C3112yes—
292C22×C4⋊C4C22×C3112yes—
293C22×C4⋊C4C22×C3112yes—
294C22×C22⋊C4C22×C3112yes—
295C22×C22⋊C4C22×C3112yes—
296C22×C22⋊C4C22×C3111yescharacteristic
297C22×C22⋊C4C22×C3111yescharacteristic
298C22×C42C22×C3111yescharacteristic
299C22×C42C22×C3111yescharacteristic
300#387—28no—
301#385C4×C3118yescomplemented
302#380—28no—
303C2×#95C22×C3112yes—
304C2×#95C22×C3112yes—
305C2×#95C22×C3112yes—
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×#95C22×C3112yes—
309C2×#95C22×C3111yescharacteristic
310C2×#95C22×C3111yescharacteristic
311C2×#95C22×C3112yes—
312C2×#95C22×C3112yes—
313C2×#95C22×C3112yes—
314C2×C31—44no—
315C2×C31#231311yescharacteristic
316C2×C31#232312yes—
317C2×C31#235212yes—
318C2×C31#235811yescharacteristic
319C2×C31#237611yescharacteristic
320C2×C31#268112yes—
321C2×C31#269012yes—
322C2×C31#269112yes—
323C2×C31#274712yes—
324C25C23×C3111yescharacteristic
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—41no—
328C23×C4—41no—
329C23×C4C2×C4×C3114yes—
330C23×C4C23×C3112yes—
331C23×C4C23×C3112yes—
332C23×C4C23×C3111yescharacteristic
333C23×C4C23×C3112yes—
334C23×C4C23×C3111yescharacteristic
335C23×C4C23×C3112yes—
336C23×C4C23×C3112yes—
337C23×C4C23×C3112yes—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4C2×C4×C3118yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4C2×C4×C3114yes—
357C2×C22⋊C4C2×C4×C3114yes—
358C2×C42—24no—
359C2×C42—41no—
360C2×C42—42no—
361C2×C42—41no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—41no—
370#95—41no—
371#95C2×C4×C3118yes—
372#95D4×C3118yes—
373C31#1440911yescharacteristic, direct product factor, Sylow
374C24—22no—
375C24—22no—
376C24—22no—
377C24—21no—
378C24—21no—
379C24—22no—
380C24—22no—
381C24C22×C4×C3112yes—
382C24#41×C3114yes—
383C24C24×C3111yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—216no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4C22×C4×C3112yes—
434C22×C4C22×C4×C3114yes—
435C22×C4C22×C4×C3112yes—
436C22×C4C22×C4×C3114yes—
437C22×C4C2×D4×C3114yes—
438C22×C4C2×D4×C3114yes—
439C22×C4C2×D4×C3114yes—
440C22×C4#41×C3114yes—
441C4⋊C4—216no—
442C4⋊C4—48no—
443C4⋊C4—48no—
444C22⋊C4—28no—
445C22⋊C4—44no—
446C22⋊C4—48no—
447C22⋊C4—48no—
448C42—44no—
449C42—44no—
450C23—24no—
451C23—22no—
452C23—22no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23—42no—
469C23—41no—
470C23C31×#11714yes—
471C23C23×C4×C3111yescharacteristic
472C23C22×D4×C3112yes—
473C23C2×#41×C3112yes—
474C23C2×#41×C3112yes—
475C23C31×H(5,𝔽2)11yescharacteristic
476C23C31×H(5,𝔽2)11yescharacteristic
477C23C31×H(5,𝔽2)12yes—
478C23C31×2−1+412yes—
479C23C31×2−1+412yes—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4C4×D4×C3118yes—
533C22—24no—
534C22—28no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22C2×C31×#11711yescharacteristic
543C22C2×C4×D4×C3112yes—
544C22C31×#51811yescharacteristic
545C22C31×#51911yescharacteristic
546C22C31×#52012yes—
547C22C31×#53612yes—
548C22C31×#53712yes—
549C22C31×#53912yes—
550C22C31×#53912yes—
551C22C31×#54112yes—
552C22C31×#54212yes—
553C22D42×C3111yescharacteristic
554C22C31×#54612yes—
555C22C31×#54612yes—
556C22C31×#54812yes—
557C22C31×#55111yescharacteristic
558C22C31×#55212yes—
559C22C31×#55312yes—
560C22C31×#56011yescharacteristic
561C22C31×#56212yes—
562C22C31×#56311yescharacteristic
563C4—28no—
564C4—44no—
565C4—42no—
566C4—42no—
567C4—44no—
568C4—44no—
569C4—82no—
570C4—82no—
571C2—44no—
572C2C31×#231311yescharacteristic
573C2C31×#232312yes—
574C2C31×#235212yes—
575C2C31×#235811yescharacteristic
576C2C31×#237611yescharacteristic
577C2C31×#268112yes—
578C2C31×#269012yes—
579C2C31×#269112yes—
580C2C31×#274712yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#387C2semidirect
4. C31×#1442C2semidirect
5. C31×#1441C2semidirect
9. C31×#1436C2semidirect
21. C31×#385C4semidirect
159. #14409C31direct (N × H)
243. C2×#387C2×C31semidirect
246. #1442C2×C31semidirect
247. #1441C2×C31semidirect
251. #1436C2×C31semidirect
301. #385C4×C31semidirect
373. C31#14409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C2×C31×#3852
C2×C31×#3802
C31×#14422
C31×#14412
C31×#14402
C31×#14372
C31×#14362
#1440931