Finite Group Databasebeta

← C31×#11069 #21467828

Subgroups — C31×#11069 #21467828

Order 7936.

2538 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2315C211yesmaximal, characteristic, complemented
2C2×C31×#379C212yesmaximal
3C2×C31×#379C211yesmaximal, characteristic
4C2×C31×#342C212yesmaximal, complemented
5C2×C31×#342C211yesmaximal, characteristic, complemented
6C26×C31C2211yescharacteristic
7C22×C22⋊C4×C31—24no—
8C22×C22⋊C4×C31—22no—
9C22×C22⋊C4×C31C2212yes—
10C22×C22⋊C4×C31C2211yescharacteristic
11C22×C22⋊C4×C31C2212yes—
12C22×C22⋊C4×C31C2211yescharacteristic
13C31×#385—24no—
14C31×#380—22no—
15C31×#379—24no—
16C31×#379—24no—
17C31×#379—22no—
18C31×#379C414yescomplemented
19C31×#342—22no—
20C31×#342—24no—
21C25×C31—21no—
22C25×C31—22no—
23C25×C31—21no—
24C25×C31—22no—
25C25×C31—22no—
26C25×C31—21no—
27C25×C31—21no—
28C25×C31—22no—
29C25×C31—48no—
30C25×C31C2×C412yes—
31C25×C31D412yes—
32C25×C31Q812yes—
33C25×C31C2311yescharacteristic
34C23×C4×C31—21no—
35C23×C4×C31—22no—
36C23×C4×C31D414yes—
37C23×C4×C31D412yes—
38C2×C4⋊C4×C31—24no—
39C2×C22⋊C4×C31—22no—
40C2×C22⋊C4×C31—22no—
41C2×C22⋊C4×C31—22no—
42C2×C22⋊C4×C31—22no—
43C2×C22⋊C4×C31—22no—
44C2×C22⋊C4×C31—22no—
45C2×C22⋊C4×C31—22no—
46C2×C22⋊C4×C31—22no—
47C2×C22⋊C4×C31—216no—
48C2×C22⋊C4×C31—22no—
49C2×C22⋊C4×C31—22no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31—22no—
56C2×C22⋊C4×C31—28no—
57C2×C22⋊C4×C31—48no—
58C2×C22⋊C4×C31—416no—
59C2×C22⋊C4×C31C2×C412yes—
60C2×C22⋊C4×C31C2×C412yes—
61C2×C22⋊C4×C31D414yes—
62C2×C22⋊C4×C31D412yes—
63C31×#95—24no—
64C24×C31—28no—
65C24×C31—216no—
66C24×C31—22no—
67C24×C31—24no—
68C24×C31—24no—
69C24×C31—22no—
70C24×C31—22no—
71C24×C31—24no—
72C24×C31—22no—
73C24×C31—24no—
74C24×C31—22no—
75C24×C31—22no—
76C24×C31—24no—
77C24×C31—24no—
78C24×C31—48no—
79C24×C31—48no—
80C24×C31—48no—
81C24×C31—44no—
82C24×C31—44no—
83C24×C31—48no—
84C24×C31—48no—
85C24×C31—416no—
86C24×C31—416no—
87C24×C31—48no—
88C24×C31—48no—
89C24×C31—416no—
90C24×C31—41no—
91C24×C31—42no—
92C24×C31—42no—
93C24×C31—42no—
94C24×C31—41no—
95C24×C31—42no—
96C24×C31—42no—
97C24×C31—41no—
98C24×C31—42no—
99C24×C31—41no—
100C24×C31C4⋊C414yescomplemented
101C24×C31C22×C411yescharacteristic
102C24×C31C2×D411yescharacteristic
103C24×C31C2×D412yes—
104C24×C31C2×D411yescharacteristic
105C24×C31C2×D411yescharacteristic
106C24×C31C2×D412yes—
107C24×C31C2×Q811yescharacteristic
108C24×C31#4111yescharacteristic
109C24×C31#4111yescharacteristic
110C24×C31#4112yes—
111C24×C31#4112yes—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—24no—
116C22×C4×C31—24no—
117C22×C4×C31—24no—
118C22×C4×C31—24no—
119C22×C4×C31—44no—
120C22×C4×C31—48no—
121C22×C4×C31—44no—
122C22×C4×C31—48no—
123C22×C4×C31—42no—
124C22×C4×C31—41no—
125C22×C4×C31—42no—
126C22×C4×C31—41no—
127C22×C4×C31C22⋊C414yescomplemented
128C4⋊C4×C31—84no—
129C22⋊C4×C31—24no—
130C22⋊C4×C31—24no—
131C22⋊C4×C31—24no—
132C22⋊C4×C31—24no—
133C22⋊C4×C31—24no—
134C22⋊C4×C31—416no—
135C22⋊C4×C31—432no—
136C22⋊C4×C31—42no—
137C22⋊C4×C31—42no—
138C22⋊C4×C31—42no—
139C22⋊C4×C31—42no—
140C22⋊C4×C31—42no—
141C22⋊C4×C31—42no—
142C22⋊C4×C31—42no—
143#11069C3111yesmaximal, characteristic, direct product factor, Sylow
144C23×C31—24no—
145C23×C31—28no—
146C23×C31—28no—
147C23×C31—216no—
148C23×C31—216no—
149C23×C31—28no—
150C23×C31—28no—
151C23×C31—216no—
152C23×C31—24no—
153C23×C31—28no—
154C23×C31—48no—
155C23×C31—42no—
156C23×C31—42no—
157C23×C31—42no—
158C23×C31—44no—
159C23×C31—42no—
160C23×C31—44no—
161C23×C31—42no—
162C23×C31—42no—
163C23×C31—44no—
164C23×C31—44no—
165C23×C31—416no—
166C23×C31—48no—
167C23×C31—48no—
168C23×C31—48no—
169C23×C31—416no—
170C23×C31—48no—
171C23×C31—44no—
172C23×C31—48no—
173C23×C31—416no—
174C23×C31—44no—
175C23×C31—48no—
176C23×C31—48no—
177C23×C31—416no—
178C23×C31—48no—
179C23×C31—48no—
180C23×C31—416no—
181C23×C31—416no—
182C23×C31—416no—
183C23×C31—416no—
184C23×C31—416no—
185C23×C31—42no—
186C23×C31—44no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—44no—
191C23×C31—44no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—48no—
195C23×C31C2×C22⋊C411yescharacteristic
196C23×C31C2×C4⋊C411yescharacteristic
197C23×C31#11711yescharacteristic
198C23×C31C4×D412yes—
199C23×C31C4×D412yes—
200C23×C31#12012yes—
201C23×C31#12011yescharacteristic
202C23×C31#12111yescharacteristic
203C23×C31#12112yes—
204C23×C31#12112yes—
205C23×C31#12111yescharacteristic
206C23×C31#12112yes—
207C23×C31C22⋊Q811yescharacteristic
208C23×C31C22⋊Q812yes—
209C23×C31C22⋊Q811yescharacteristic
210C23×C31C22⋊Q812yes—
211C23×C31#12311yescharacteristic
212C23×C31#12312yes—
213C23×C31#12312yes—
214C23×C31#12412yes—
215C23×C31#12411yescharacteristic
216C23×C31#12612yes—
217C23×C31#12711yescharacteristic
218C2×C4×C31—24no—
219C2×C4×C31—44no—
220C2×C4×C31—44no—
221C2×C4×C31—44no—
222C2×C4×C31—48no—
223C2×C4×C31—48no—
224C2×C4×C31—42no—
225C2×C4×C31—44no—
226C2×C4×C31—44no—
227C2×C4×C31—48no—
228C2×C4×C31—82no—
229C2×C4×C31—84no—
230C2×C4×C31—82no—
231C2×C4×C31—82no—
232C2×C4×C31—84no—
233C2×C4×C31—84no—
234#2315C2×C3111yescharacteristic, complemented
235C2×#379C2×C3112yes—
236C2×#379C2×C3111yescharacteristic
237C2×#342C2×C3112yescomplemented
238C2×#342C2×C3111yescharacteristic, complemented
239C22×C31—22no—
240C22×C31—24no—
241C22×C31—22no—
242C22×C31—24no—
243C22×C31—24no—
244C22×C31—24no—
245C22×C31—22no—
246C22×C31—22no—
247C22×C31—22no—
248C22×C31—24no—
249C22×C31—22no—
250C22×C31—24no—
251C22×C31—28no—
252C22×C31—216no—
253C22×C31—41no—
254C22×C31—41no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—41no—
258C22×C31—41no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—48no—
264C22×C31—416no—
265C22×C31—44no—
266C22×C31—48no—
267C22×C31—416no—
268C22×C31—416no—
269C22×C31—48no—
270C22×C31—48no—
271C22×C31—48no—
272C22×C31—44no—
273C22×C31—48no—
274C22×C31—48no—
275C22×C31#38011yescharacteristic
276C22×C31#38512yes—
277C22×C31#38611yescharacteristic
278C22×C31#38812yes—
279C22×C31#39011yescharacteristic
280C22×C31#39211yescharacteristic
281C22×C31#39311yescharacteristic
282C22×C31#39412yes—
283C22×C31#39612yes—
284C22×C31#39711yescharacteristic
285C22×C31#39911yescharacteristic
286C22×C31B(4,𝔽2)14yes—
287C4×C31—44no—
288C4×C31—82no—
289C4×C31—84no—
290C4×C31—84no—
291C26C22×C3111yescharacteristic
292C22×C22⋊C4—24no—
293C22×C22⋊C4—22no—
294C22×C22⋊C4C22×C3112yes—
295C22×C22⋊C4C22×C3111yescharacteristic
296C22×C22⋊C4C22×C3112yes—
297C22×C22⋊C4C22×C3111yescharacteristic
298#385—24no—
299#380—22no—
300#379—24no—
301#379—24no—
302#379—22no—
303#379C4×C3114yescomplemented
304#342—22no—
305#342—24no—
306C2×C31—21no—
307C2×C31—22no—
308C2×C31—21no—
309C2×C31—22no—
310C2×C31—22no—
311C2×C31—22no—
312C2×C31—21no—
313C2×C31—21no—
314C2×C31—48no—
315C2×C31#143911yescharacteristic
316C2×C31#188912yes—
317C2×C31#202112yes—
318C2×C31#202912yes—
319C25—21no—
320C25—22no—
321C25—21no—
322C25—22no—
323C25—22no—
324C25—21no—
325C25—21no—
326C25—22no—
327C25—48no—
328C25C2×C4×C3112yes—
329C25D4×C3112yes—
330C25Q8×C3112yes—
331C25C23×C3111yescharacteristic
332C23×C4—21no—
333C23×C4—22no—
334C23×C4D4×C3114yes—
335C23×C4D4×C3112yes—
336C2×C4⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—216no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—48no—
356C2×C22⋊C4—416no—
357C2×C22⋊C4C2×C4×C3112yes—
358C2×C22⋊C4C2×C4×C3112yes—
359C2×C22⋊C4D4×C3114yes—
360C2×C22⋊C4D4×C3112yes—
361#95—24no—
362C31#1106911yescharacteristic, direct product factor, Sylow
363C24—28no—
364C24—216no—
365C24—22no—
366C24—24no—
367C24—24no—
368C24—22no—
369C24—22no—
370C24—24no—
371C24—22no—
372C24—24no—
373C24—22no—
374C24—22no—
375C24—24no—
376C24—24no—
377C24—48no—
378C24—48no—
379C24—48no—
380C24—44no—
381C24—44no—
382C24—48no—
383C24—48no—
384C24—416no—
385C24—416no—
386C24—48no—
387C24—48no—
388C24—416no—
389C24—41no—
390C24—42no—
391C24—42no—
392C24—42no—
393C24—41no—
394C24—42no—
395C24—41no—
396C24—42no—
397C24—42no—
398C24—41no—
399C24C4⋊C4×C3114yescomplemented
400C24C22×C4×C3111yescharacteristic
401C24C2×D4×C3111yescharacteristic
402C24C2×D4×C3112yes—
403C24C2×D4×C3111yescharacteristic
404C24C2×D4×C3111yescharacteristic
405C24C2×D4×C3112yes—
406C24C2×Q8×C3111yescharacteristic
407C24#41×C3111yescharacteristic
408C24#41×C3111yescharacteristic
409C24#41×C3112yes—
410C24#41×C3112yes—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—44no—
419C22×C4—48no—
420C22×C4—44no—
421C22×C4—48no—
422C22×C4—42no—
423C22×C4—41no—
424C22×C4—42no—
425C22×C4—41no—
426C22×C4C22⋊C4×C3114yescomplemented
427C4⋊C4—84no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—416no—
434C22⋊C4—432no—
435C22⋊C4—42no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—42no—
441C22⋊C4—42no—
442C23—24no—
443C23—28no—
444C23—28no—
445C23—216no—
446C23—216no—
447C23—28no—
448C23—28no—
449C23—216no—
450C23—24no—
451C23—28no—
452C23—48no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—44no—
457C23—42no—
458C23—44no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—44no—
463C23—416no—
464C23—48no—
465C23—48no—
466C23—48no—
467C23—416no—
468C23—48no—
469C23—44no—
470C23—48no—
471C23—416no—
472C23—44no—
473C23—48no—
474C23—48no—
475C23—416no—
476C23—48no—
477C23—48no—
478C23—416no—
479C23—416no—
480C23—416no—
481C23—416no—
482C23—416no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—48no—
487C23—42no—
488C23—44no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—44no—
493C23C2×C22⋊C4×C3111yescharacteristic
494C23C2×C4⋊C4×C3111yescharacteristic
495C23C31×#11711yescharacteristic
496C23C4×D4×C3112yes—
497C23C4×D4×C3112yes—
498C23C31×#12012yes—
499C23C31×#12011yescharacteristic
500C23C31×#12112yes—
501C23C31×#12112yes—
502C23C31×#12111yescharacteristic
503C23C31×#12112yes—
504C23C31×#12111yescharacteristic
505C23C31×C22⋊Q812yes—
506C23C31×C22⋊Q811yescharacteristic
507C23C31×C22⋊Q811yescharacteristic
508C23C31×C22⋊Q812yes—
509C23C31×#12311yescharacteristic
510C23C31×#12312yes—
511C23C31×#12312yes—
512C23C31×#12411yescharacteristic
513C23C31×#12412yes—
514C23C31×#12612yes—
515C23C31×#12711yescharacteristic
516C2×C4—24no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—48no—
522C2×C4—48no—
523C2×C4—42no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—82no—
527C2×C4—84no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C22—22no—
533C22—24no—
534C22—22no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—24no—
542C22—22no—
543C22—24no—
544C22—28no—
545C22—216no—
546C22—41no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—41no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—48no—
557C22—416no—
558C22—44no—
559C22—48no—
560C22—416no—
561C22—48no—
562C22—48no—
563C22—416no—
564C22—48no—
565C22—44no—
566C22—48no—
567C22—48no—
568C22C31×#38011yescharacteristic
569C22C31×#38512yes—
570C22C31×#38611yescharacteristic
571C22C31×#38812yes—
572C22C31×#39011yescharacteristic
573C22C31×#39211yescharacteristic
574C22C31×#39311yescharacteristic
575C22C31×#39412yes—
576C22C31×#39612yes—
577C22C31×#39711yescharacteristic
578C22C31×#39911yescharacteristic
579C22C31×B(4,𝔽2)14yes—
580C4—44no—
581C4—82no—
582C4—84no—
583C4—84no—
584C2—21no—
585C2—22no—
586C2—21no—
587C2—22no—
588C2—22no—
589C2—21no—
590C2—21no—
591C2—22no—
592C2—48no—
593C2C31×#143911yescharacteristic
594C2C31×#188912yes—
595C2C31×#202112yes—
596C2C31×#202912yes—
subgroupG/H
center, socleC23×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#2315C2semidirect
4. C2×C31×#342C2semidirect
5. C2×C31×#342C2semidirect
18. C31×#379C4semidirect
100. C24×C31C4⋊C4semidirect
127. C22×C4×C31C22⋊C4semidirect
143. #11069C31direct (N × H)
234. #2315C2×C31semidirect
237. C2×#342C2×C31semidirect
238. C2×#342C2×C31semidirect
303. #379C4×C31semidirect
362. C31#11069direct (N × H)
399. C24C4⋊C4×C31semidirect
426. C22×C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#23152
C2×C31×#3792
C2×C31×#3422
#1106931