Finite Group Databasebeta

← C31×#19088 #21475847

Subgroups — C31×#19088 #21475847

Order 7936.

884 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3559C211yesmaximal, characteristic, complemented
2C31×#3234C211yesmaximal, characteristic, complemented
3C31×#3219C211yesmaximal, characteristic, complemented
4C31×#3214C211yesmaximal, characteristic, complemented
5C31×#1664C212yesmaximal, complemented
6C31×#1661C212yesmaximal, complemented
7C31×#1657C212yesmaximal, complemented
8C31×#1656C212yesmaximal, complemented
9C31×#1536C211yesmaximal, characteristic, complemented
10C31×#1535C211yesmaximal, characteristic, complemented
11C31×#1534C211yesmaximal, characteristic, complemented
12C31×#563C2212yes—
13C31×#562C2212yes—
14C31×#554—21no—
15C31×#553—21no—
16C31×#553—21no—
17C31×#547—22no—
18C31×#547—21no—
19C31×#544—21no—
20C31×#540—21no—
21C31×#539—22no—
22C31×#539—21no—
23C31×#537—21no—
24C31×#532C2211yescharacteristic
25C31×#532C2211yescharacteristic
26C31×#529C2211yescharacteristic
27C2×C31×#125C2211yescharacteristic
28C31×#501C2212yes—
29C31×#497C2211yescharacteristic
30C31×#496C2211yescharacteristic
31C31×#496C2212yes—
32C31×#491C2211yescharacteristic
33C31×#490C2212yes—
34C31×#490C2211yescharacteristic
35C31×#489C2212yes—
36C31×#481—21no—
37C31×#480—21no—
38C31×#478—22no—
39C31×#464—21no—
40C31×#463—21no—
41C31×#461—21no—
42C31×#459—21no—
43C31×#452—21no—
44C31×#449—22no—
45C31×#449—21no—
46C31×#432C2211yescharacteristic
47C31×#432C2211yescharacteristic
48C31×#432C2211yescharacteristic
49C31×#330C2212yes—
50C31×#330C2212yes—
51C31×#330C2212yes—
52C31×#329C2212yes—
53C31×#329C2212yes—
54C31×#329C2212yes—
55C2×#41×C31—22no—
56C2×#41×C31—21no—
57C2×#41×C31D412yes—
58C2×Q16×C31—21no—
59C2×SD16×C31—22no—
60C2×SD16×C31—21no—
61C2×SD16×C31—21no—
62C2×D8×C31—22no—
63C2×D8×C31—21no—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—22no—
66C31×C4⋊Q8D411yescharacteristic
67C31×C4⋊Q8C2311yescharacteristic
68C31×#127D411yescharacteristic
69C31×#127C2311yescharacteristic
70C31×#126—22no—
71C31×#126—22no—
72C31×#126—21no—
73C31×#125—22no—
74C31×#125—21no—
75C31×#125—21no—
76C31×#125—21no—
77C31×#125D412yes—
78C31×#125C2311yescharacteristic
79C31×#125C2312yes—
80C31×#124—21no—
81C31×#124C2312yes—
82C31×#124C2311yescharacteristic
83C31×#123—22no—
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—22no—
87C31×#123—21no—
88C31×#123—22no—
89C31×#123—22no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8D411yescharacteristic
97C31×#121—22no—
98C31×#121—22no—
99C31×#121—21no—
100C31×#121—21no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—21no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—21no—
107C31×#121D411yescharacteristic
108C4×Q8×C31D411yescharacteristic
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31D411yescharacteristic
119C31×#117—21no—
120C31×#117—21no—
121C2×C4⋊C4×C31—22no—
122C2×C4⋊C4×C31—21no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31D411yescharacteristic
126C2×C4⋊C4×C31D411yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C31×#107—22no—
129C31×#106—22no—
130C31×C4⋊C8—21no—
131C31×C4⋊C8—21no—
132C31×C4⋊C8—21no—
133C31×#103—22no—
134C31×#103—21no—
135C31×#103—21no—
136C31×#102—22no—
137C31×#102—21no—
138C31×#102—21no—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—21no—
142C31×C22⋊C8—21no—
143C31×C22⋊C8—21no—
144C31×#97C2312yes—
145C31×#97C2311yescharacteristic
146C31×#97C2312yes—
147C31×#97C2311yescharacteristic
148#41×C31—84no—
149#41×C31—81no—
150#41×C31—81no—
151#41×C31—82no—
152C2×Q8×C31—22no—
153C2×Q8×C31—21no—
154C2×Q8×C31C2×D412yes—
155C2×Q8×C31C2×D411yescharacteristic
156C2×D4×C31—22no—
157C2×D4×C31—21no—
158C2×D4×C31—22no—
159C2×D4×C31—22no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—41no—
166C2×D4×C31C2×D412yes—
167C2×D4×C31C2×D411yescharacteristic
168C22×C4×C31—21no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—22no—
175C22×C4×C31—41no—
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179Q16×C31—81no—
180SD16×C31—82no—
181SD16×C31—81no—
182SD16×C31—81no—
183D8×C31—81no—
184D8×C31—82no—
185C2×C8×C31—22no—
186C2×C8×C31—21no—
187C2×C8×C31—22no—
188C2×C8×C31—21no—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31C2×D411yescharacteristic
208C4⋊C4×C31C2×D411yescharacteristic
209C4⋊C4×C31C2×D412yes—
210C4⋊C4×C31C2×D412yes—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—21no—
217C22⋊C4×C31—21no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—21no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—21no—
223C22⋊C4×C31—41no—
224C22⋊C4×C31—41no—
225C42×C31—22no—
226C42×C31—21no—
227C42×C31C2×D411yescharacteristic
228C42×C31C2×D411yescharacteristic
229C42×C31C2×D411yescharacteristic
230C42×C31C2411yescharacteristic
231#19088C3111yesmaximal, characteristic, direct product factor, Sylow
232C23×C31—22no—
233C23×C31—21no—
234C23×C31—41no—
235C23×C31#12011yescharacteristic
236Q8×C31—41no—
237Q8×C31—42no—
238Q8×C31—41no—
239Q8×C31—41no—
240Q8×C31—82no—
241D4×C31—41no—
242D4×C31—42no—
243D4×C31—42no—
244D4×C31—41no—
245D4×C31—41no—
246D4×C31—41no—
247D4×C31—41no—
248D4×C31—42no—
249D4×C31—44no—
250D4×C31—42no—
251D4×C31—81no—
252D4×C31—82no—
253D4×C31—82no—
254D4×C31—82no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—21no—
260C2×C4×C31—22no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—41no—
267C2×C4×C31—82no—
268C2×C4×C31—82no—
269C2×C4×C31—81no—
270C2×C4×C31—82no—
271C2×C4×C31—82no—
272C2×C4×C31—82no—
273C2×C4×C31#12011yescharacteristic
274C2×C4×C31#12011yescharacteristic
275C2×C4×C31#12011yescharacteristic
276C2×C4×C31C22×D411yescharacteristic
277C2×C4×C31C22×D411yescharacteristic
278C2×C4×C31C22×D411yescharacteristic
279C8×C31—42no—
280C8×C31—42no—
281C8×C31—41no—
282C8×C31—41no—
283#3559C2×C3111yescharacteristic, complemented
284#3234C2×C3111yescharacteristic, complemented
285#3219C2×C3111yescharacteristic, complemented
286#3214C2×C3111yescharacteristic, complemented
287#1664C2×C3112yescomplemented
288#1661C2×C3112yescomplemented
289#1657C2×C3112yescomplemented
290#1656C2×C3112yescomplemented
291#1536C2×C3111yescharacteristic, complemented
292#1535C2×C3111yescharacteristic, complemented
293#1534C2×C3111yescharacteristic, complemented
294C22×C31—21no—
295C22×C31—21no—
296C22×C31—21no—
297C22×C31—42no—
298C22×C31—41no—
299C22×C31—41no—
300C22×C31—42no—
301C22×C31—42no—
302C22×C31—41no—
303C22×C31—81no—
304C22×C31—81no—
305C22×C31—81no—
306C22×C31C2×#12011yescharacteristic
307C4×C31—21no—
308C4×C31—21no—
309C4×C31—21no—
310C4×C31—21no—
311C4×C31—21no—
312C4×C31—21no—
313C4×C31—42no—
314C4×C31—42no—
315C4×C31—41no—
316C4×C31—41no—
317C4×C31—42no—
318C4×C31—41no—
319C4×C31—81no—
320#563C22×C3112yes—
321#562C22×C3112yes—
322#554—21no—
323#553—21no—
324#553—21no—
325#547—22no—
326#547—21no—
327#544—21no—
328#540—21no—
329#539—22no—
330#539—21no—
331#537—21no—
332#532C22×C3111yescharacteristic
333#532C22×C3111yescharacteristic
334#529C22×C3111yescharacteristic
335C2×#125C22×C3111yescharacteristic
336#501C22×C3112yes—
337#497C22×C3111yescharacteristic
338#496C22×C3111yescharacteristic
339#496C22×C3112yes—
340#491C22×C3111yescharacteristic
341#490C22×C3112yes—
342#490C22×C3111yescharacteristic
343#489C22×C3112yes—
344#481—21no—
345#480—21no—
346#478—22no—
347#464—21no—
348#463—21no—
349#461—21no—
350#459—21no—
351#452—21no—
352#449—22no—
353#449—21no—
354#432C22×C3111yescharacteristic
355#432C22×C3111yescharacteristic
356#432C22×C3111yescharacteristic
357#330C22×C3112yes—
358#330C22×C3112yes—
359#330C22×C3112yes—
360#329C22×C3112yes—
361#329C22×C3112yes—
362#329C22×C3112yes—
363C2×C31—41no—
364C2×C31—82no—
365C2×C31—81no—
366C2×C31—161no—
367C2×C31#301911yescharacteristic
368C2×C31#302011yescharacteristic
369C2×C31#302111yescharacteristic
370C2×#41—22no—
371C2×#41—21no—
372C2×#41D4×C3112yes—
373C2×Q16—21no—
374C2×SD16—22no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×D8—22no—
378C2×D8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—22no—
381C4⋊Q8D4×C3111yescharacteristic
382C4⋊Q8C23×C3111yescharacteristic
383#127D4×C3111yescharacteristic
384#127C23×C3111yescharacteristic
385#126—22no—
386#126—22no—
387#126—21no—
388#125—22no—
389#125—21no—
390#125—21no—
391#125—21no—
392#125D4×C3112yes—
393#125C23×C3112yes—
394#125C23×C3111yescharacteristic
395#124—21no—
396#124C23×C3111yescharacteristic
397#124C23×C3112yes—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—21no—
403#123—22no—
404#123—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8D4×C3111yescharacteristic
412#121—22no—
413#121—22no—
414#121—21no—
415#121—21no—
416#121—22no—
417#121—22no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121D4×C3111yescharacteristic
423C4×Q8D4×C3111yescharacteristic
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4D4×C3111yescharacteristic
434#117—21no—
435#117—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4D4×C3111yescharacteristic
441C2×C4⋊C4D4×C3111yescharacteristic
442C2×C42C23×C3111yescharacteristic
443#107—22no—
444#106—22no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448#103—22no—
449#103—21no—
450#103—21no—
451#102—22no—
452#102—21no—
453#102—21no—
454#102—22no—
455#102—22no—
456C22⋊C8—21no—
457C22⋊C8—21no—
458C22⋊C8—21no—
459#97C23×C3112yes—
460#97C23×C3111yescharacteristic
461#97C23×C3111yescharacteristic
462#97C23×C3112yes—
463C31#1908811yescharacteristic, direct product factor, Sylow
464#41—84no—
465#41—81no—
466#41—81no—
467#41—82no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8C2×D4×C3112yes—
471C2×Q8C2×D4×C3111yescharacteristic
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—41no—
482C2×D4C2×D4×C3112yes—
483C2×D4C2×D4×C3111yescharacteristic
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4C2×D4×C3111yescharacteristic
493C22×C4C2×D4×C3111yescharacteristic
494C22×C4C2×D4×C3111yescharacteristic
495Q16—81no—
496SD16—82no—
497SD16—81no—
498SD16—81no—
499D8—81no—
500D8—82no—
501C2×C8—22no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4C2×D4×C3111yescharacteristic
524C4⋊C4C2×D4×C3111yescharacteristic
525C4⋊C4C2×D4×C3112yes—
526C4⋊C4C2×D4×C3112yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C42—22no—
542C42—21no—
543C42C2×D4×C3111yescharacteristic
544C42C2×D4×C3111yescharacteristic
545C42C2×D4×C3111yescharacteristic
546C42C24×C3111yescharacteristic
547C23—22no—
548C23—21no—
549C23—41no—
550C23C31×#12011yescharacteristic
551Q8—41no—
552Q8—42no—
553Q8—41no—
554Q8—41no—
555Q8—82no—
556D4—41no—
557D4—42no—
558D4—42no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—81no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4C31×#12011yescharacteristic
589C2×C4C31×#12011yescharacteristic
590C2×C4C31×#12011yescharacteristic
591C2×C4C22×D4×C3111yescharacteristic
592C2×C4C22×D4×C3111yescharacteristic
593C2×C4C22×D4×C3111yescharacteristic
594C8—42no—
595C8—42no—
596C8—41no—
597C8—41no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22C2×C31×#12011yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—81no—
624C2—41no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C31×#301911yescharacteristic
629C2C31×#302011yescharacteristic
630C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3559C2semidirect
2. C31×#3234C2semidirect
3. C31×#3219C2semidirect
4. C31×#3214C2semidirect
5. C31×#1664C2semidirect
6. C31×#1661C2semidirect
7. C31×#1657C2semidirect
8. C31×#1656C2semidirect
9. C31×#1536C2semidirect
10. C31×#1535C2semidirect
11. C31×#1534C2semidirect
231. #19088C31direct (N × H)
283. #3559C2×C31semidirect
284. #3234C2×C31semidirect
285. #3219C2×C31semidirect
286. #3214C2×C31semidirect
287. #1664C2×C31semidirect
288. #1661C2×C31semidirect
289. #1657C2×C31semidirect
290. #1656C2×C31semidirect
291. #1536C2×C31semidirect
292. #1535C2×C31semidirect
293. #1534C2×C31semidirect
463. C31#19088direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35592
C31×#32342
C31×#32192
C31×#32142
C31×#16642
C31×#16612
C31×#16572
C31×#16562
C31×#15362
C31×#15352
C31×#15342
#1908831