Finite Group Databasebeta

← C31×#19090 #21475849

Subgroups — C31×#19090 #21475849

Order 7936.

888 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3561C211yesmaximal, characteristic, complemented
2C31×#3235C211yesmaximal, characteristic, complemented
3C31×#3219C211yesmaximal, characteristic, complemented
4C31×#3213C211yesmaximal, characteristic, complemented
5C31×#1664C212yesmaximal, complemented
6C31×#1661C212yesmaximal, complemented
7C31×#1657C212yesmaximal, complemented
8C31×#1656C212yesmaximal, complemented
9C31×#1537C211yesmaximal, characteristic, complemented
10C31×#1535C211yesmaximal, characteristic, complemented
11C31×#1533C211yesmaximal, characteristic, complemented
12C31×#563C2212yes—
13C31×#562C2212yes—
14C31×#556—21no—
15C31×#551—22no—
16D4×Q8×C31—21no—
17C31×#548—21no—
18C31×#546—21no—
19C31×#543—21no—
20C31×#542—21no—
21C31×#542—22no—
22C31×#538—21no—
23C31×#536—21no—
24C31×#533C2211yescharacteristic
25C31×#532C2211yescharacteristic
26C31×#529C2211yescharacteristic
27C2×C31×#124C2211yescharacteristic
28C31×#501C2212yescomplemented
29C31×#497C2211yescharacteristic, complemented
30C31×#496C2212yes—
31C31×#496C2211yescharacteristic, complemented
32C31×#491C2211yescharacteristic, complemented
33C31×#490C2212yescomplemented
34C31×#490C2211yescharacteristic, complemented
35C31×#489C2212yes—
36C31×#482—22no—
37C31×#476—21no—
38C31×#474—21no—
39C31×#464—21no—
40C31×#463—22no—
41C31×#463—21no—
42C31×#452—21no—
43C31×#449—21no—
44C31×#448—21no—
45C31×#447—21no—
46C31×#432C2211yescharacteristic
47C31×#432C2211yescharacteristic
48C31×#432C2211yescharacteristic
49C31×#330C2212yescomplemented
50C31×#330C2212yescomplemented
51C31×#330C2212yescomplemented
52C31×#329C2212yes—
53C31×#329C2212yes—
54C31×#329C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C22×Q8×C31—21no—
58C22×Q8×C31D411yescharacteristic
59C22×D4×C31D411yescharacteristic
60C2×Q16×C31—21no—
61C2×SD16×C31—22no—
62C2×SD16×C31—21no—
63C2×SD16×C31—21no—
64C2×D8×C31—22no—
65C2×D8×C31—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8—22no—
68C31×C4⋊Q8D411yescharacteristic
69C31×C4⋊Q8D411yescharacteristic
70C31×C4⋊Q8C2311yescharacteristic
71C31×#127C2311yescharacteristic
72C31×#126—22no—
73C31×#126—22no—
74C31×#126—22no—
75C31×#126—21no—
76C31×#125C2311yescharacteristic
77C31×#125C2312yes—
78C31×#124—21no—
79C31×#124—22no—
80C31×#124—22no—
81C31×#124—21no—
82C31×#124—21no—
83C31×#124—21no—
84C31×#124D412yes—
85C31×#124C2312yes—
86C31×#124C2311yescharacteristic
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—21no—
90C31×#123—22no—
91C31×#123—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—22no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8D411yescharacteristic
103C31×#121—21no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121D411yescharacteristic
109C31×#120—22no—
110C4×Q8×C31—21no—
111C4×Q8×C31—21no—
112C4×Q8×C31—21no—
113C4×Q8×C31D411yescharacteristic
114C4×D4×C31—22no—
115C4×D4×C31—21no—
116C4×D4×C31—22no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31D411yescharacteristic
121C31×#117—22no—
122C31×#117—21no—
123C31×#117D412yes—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
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
148C24×C31—21no—
149#41×C31—81no—
150#41×C31—81no—
151#41×C31—82no—
152C2×Q8×C31—22no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—82no—
158C2×Q8×C31—81no—
159C2×Q8×C31C2×D412yes—
160C2×Q8×C31C2×D411yescharacteristic
161C2×D4×C31—21no—
162C2×D4×C31—22no—
163C2×D4×C31—22no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—41no—
169C2×D4×C31—81no—
170C2×D4×C31C2×D412yes—
171C2×D4×C31C2×D411yescharacteristic
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—41no—
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181Q16×C31—81no—
182SD16×C31—82no—
183SD16×C31—81no—
184SD16×C31—81no—
185D8×C31—81no—
186D8×C31—82no—
187C2×C8×C31—22no—
188C2×C8×C31—21no—
189C2×C8×C31—22no—
190C2×C8×C31—21no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—22no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
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×C31C2×D411yescharacteristic
206C4⋊C4×C31C2×D411yescharacteristic
207C4⋊C4×C31C2×D412yes—
208C4⋊C4×C31C2×D412yes—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—21no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—21no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—22no—
222C22⋊C4×C31—21no—
223C22⋊C4×C31—21no—
224C22⋊C4×C31—41no—
225C22⋊C4×C31—41no—
226C42×C31—22no—
227C42×C31—22no—
228C42×C31—21no—
229C42×C31C2×D411yescharacteristic
230C42×C31C2×D411yescharacteristic
231C42×C31C2×D411yescharacteristic
232C42×C31C2411yescharacteristic
233#19090C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—22no—
235C23×C31—21no—
236C23×C31—42no—
237C23×C31—41no—
238C23×C31—81no—
239C23×C31—81no—
240C23×C31#12011yescharacteristic
241Q8×C31—41no—
242Q8×C31—42no—
243Q8×C31—42no—
244Q8×C31—42no—
245Q8×C31—41no—
246Q8×C31—41no—
247Q8×C31—81no—
248Q8×C31—82no—
249D4×C31—41no—
250D4×C31—42no—
251D4×C31—42no—
252D4×C31—42no—
253D4×C31—41no—
254D4×C31—41no—
255D4×C31—42no—
256D4×C31—42no—
257D4×C31—82no—
258D4×C31—82no—
259D4×C31—82no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—21no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—21no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—42no—
270C2×C4×C31—41no—
271C2×C4×C31—82no—
272C2×C4×C31—81no—
273C2×C4×C31—82no—
274C2×C4×C31—82no—
275C2×C4×C31—82no—
276C2×C4×C31#12011yescharacteristic
277C2×C4×C31#12011yescharacteristic
278C2×C4×C31#12011yescharacteristic
279C2×C4×C31C22×D411yescharacteristic
280C2×C4×C31C22×D411yescharacteristic
281C2×C4×C31C22×D411yescharacteristic
282C8×C31—42no—
283C8×C31—42no—
284C8×C31—41no—
285C8×C31—41no—
286#3561C2×C3111yescharacteristic, complemented
287#3235C2×C3111yescharacteristic, complemented
288#3219C2×C3111yescharacteristic, complemented
289#3213C2×C3111yescharacteristic, complemented
290#1664C2×C3112yescomplemented
291#1661C2×C3112yescomplemented
292#1657C2×C3112yescomplemented
293#1656C2×C3112yescomplemented
294#1537C2×C3111yescharacteristic, complemented
295#1535C2×C3111yescharacteristic, complemented
296#1533C2×C3111yescharacteristic, complemented
297C22×C31—21no—
298C22×C31—21no—
299C22×C31—21no—
300C22×C31—41no—
301C22×C31—42no—
302C22×C31—41no—
303C22×C31—42no—
304C22×C31—42no—
305C22×C31—41no—
306C22×C31—81no—
307C22×C31—81no—
308C22×C31—81no—
309C22×C31—162no—
310C22×C31C2×#12011yescharacteristic
311C4×C31—21no—
312C4×C31—21no—
313C4×C31—21no—
314C4×C31—21no—
315C4×C31—21no—
316C4×C31—21no—
317C4×C31—41no—
318C4×C31—42no—
319C4×C31—42no—
320C4×C31—41no—
321C4×C31—41no—
322C4×C31—42no—
323C4×C31—81no—
324#563C22×C3112yes—
325#562C22×C3112yes—
326#556—21no—
327#551—22no—
328D4×Q8—21no—
329#548—21no—
330#546—21no—
331#543—21no—
332#542—21no—
333#542—22no—
334#538—21no—
335#536—21no—
336#533C22×C3111yescharacteristic
337#532C22×C3111yescharacteristic
338#529C22×C3111yescharacteristic
339C2×#124C22×C3111yescharacteristic
340#501C22×C3112yescomplemented
341#497C22×C3111yescharacteristic, complemented
342#496C22×C3112yes—
343#496C22×C3111yescharacteristic, complemented
344#491C22×C3111yescharacteristic, complemented
345#490C22×C3112yescomplemented
346#490C22×C3111yescharacteristic, complemented
347#489C22×C3112yes—
348#482—22no—
349#476—21no—
350#474—21no—
351#464—21no—
352#463—22no—
353#463—21no—
354#452—21no—
355#449—21no—
356#448—21no—
357#447—21no—
358#432C22×C3111yescharacteristic
359#432C22×C3111yescharacteristic
360#432C22×C3111yescharacteristic
361#330C22×C3112yescomplemented
362#330C22×C3112yescomplemented
363#330C22×C3112yescomplemented
364#329C22×C3112yes—
365#329C22×C3112yes—
366#329C22×C3112yescomplemented
367C2×C31—41no—
368C2×C31—81no—
369C2×C31—82no—
370C2×C31—161no—
371C2×C31#301911yescharacteristic
372C2×C31#302011yescharacteristic
373C2×C31#302111yescharacteristic
374C2×#41—21no—
375C2×#41—21no—
376C22×Q8—21no—
377C22×Q8D4×C3111yescharacteristic
378C22×D4D4×C3111yescharacteristic
379C2×Q16—21no—
380C2×SD16—22no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×D8—22no—
384C2×D8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—22no—
387C4⋊Q8D4×C3111yescharacteristic
388C4⋊Q8D4×C3111yescharacteristic
389C4⋊Q8C23×C3111yescharacteristic
390#127C23×C3111yescharacteristic
391#126—22no—
392#126—22no—
393#126—22no—
394#126—21no—
395#125C23×C3111yescharacteristic
396#125C23×C3112yes—
397#124—21no—
398#124—22no—
399#124—22no—
400#124—21no—
401#124—21no—
402#124—21no—
403#124D4×C3112yes—
404#124C23×C3112yes—
405#124C23×C3111yescharacteristic
406#123—22no—
407#123—22no—
408#123—21no—
409#123—22no—
410#123—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8D4×C3111yescharacteristic
422#121—21no—
423#121—22no—
424#121—22no—
425#121—21no—
426#121—21no—
427#121D4×C3111yescharacteristic
428#120—22no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8D4×C3111yescharacteristic
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4D4×C3111yescharacteristic
440#117—22no—
441#117—21no—
442#117D4×C3112yes—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42C23×C3111yescharacteristic
447#107—22no—
448#106—22no—
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452#103—22no—
453#103—21no—
454#103—21no—
455#102—22no—
456#102—21no—
457#102—21no—
458#102—22no—
459#102—22no—
460C22⋊C8—21no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463#97C23×C3112yes—
464#97C23×C3111yescharacteristic
465#97C23×C3111yescharacteristic
466#97C23×C3112yes—
467C31#1909011yescharacteristic, direct product factor, Sylow
468C24—21no—
469#41—81no—
470#41—81no—
471#41—82no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—82no—
478C2×Q8—81no—
479C2×Q8C2×D4×C3112yes—
480C2×Q8C2×D4×C3111yescharacteristic
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—41no—
489C2×D4—81no—
490C2×D4C2×D4×C3112yes—
491C2×D4C2×D4×C3111yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—41no—
498C22×C4C2×D4×C3111yescharacteristic
499C22×C4C2×D4×C3111yescharacteristic
500C22×C4C2×D4×C3111yescharacteristic
501Q16—81no—
502SD16—82no—
503SD16—81no—
504SD16—81no—
505D8—81no—
506D8—82no—
507C2×C8—22no—
508C2×C8—21no—
509C2×C8—22no—
510C2×C8—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4C2×D4×C3111yescharacteristic
526C4⋊C4C2×D4×C3111yescharacteristic
527C4⋊C4C2×D4×C3112yes—
528C4⋊C4C2×D4×C3112yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C42—22no—
547C42—22no—
548C42—21no—
549C42C2×D4×C3111yescharacteristic
550C42C2×D4×C3111yescharacteristic
551C42C2×D4×C3111yescharacteristic
552C42C24×C3111yescharacteristic
553C23—22no—
554C23—21no—
555C23—42no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23C31×#12011yescharacteristic
560Q8—41no—
561Q8—42no—
562Q8—42no—
563Q8—42no—
564Q8—41no—
565Q8—41no—
566Q8—81no—
567Q8—82no—
568D4—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—42no—
575D4—42no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—82no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4C31×#12011yescharacteristic
596C2×C4C31×#12011yescharacteristic
597C2×C4C31×#12011yescharacteristic
598C2×C4C22×D4×C3111yescharacteristic
599C2×C4C22×D4×C3111yescharacteristic
600C2×C4C22×D4×C3111yescharacteristic
601C8—42no—
602C8—42no—
603C8—41no—
604C8—41no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—162no—
618C22C2×C31×#12011yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—81no—
632C2—41no—
633C2—82no—
634C2—81no—
635C2—161no—
636C2C31×#301911yescharacteristic
637C2C31×#302011yescharacteristic
638C2C31×#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×#3561C2semidirect
2. C31×#3235C2semidirect
3. C31×#3219C2semidirect
4. C31×#3213C2semidirect
5. C31×#1664C2semidirect
6. C31×#1661C2semidirect
7. C31×#1657C2semidirect
8. C31×#1656C2semidirect
9. C31×#1537C2semidirect
10. C31×#1535C2semidirect
11. C31×#1533C2semidirect
28. C31×#501C22semidirect
29. C31×#497C22semidirect
31. C31×#496C22semidirect
32. C31×#491C22semidirect
33. C31×#490C22semidirect
34. C31×#490C22semidirect
49. C31×#330C22semidirect
50. C31×#330C22semidirect
51. C31×#330C22semidirect
54. C31×#329C22semidirect
233. #19090C31direct (N × H)
286. #3561C2×C31semidirect
287. #3235C2×C31semidirect
288. #3219C2×C31semidirect
289. #3213C2×C31semidirect
290. #1664C2×C31semidirect
291. #1661C2×C31semidirect
292. #1657C2×C31semidirect
293. #1656C2×C31semidirect
294. #1537C2×C31semidirect
295. #1535C2×C31semidirect
296. #1533C2×C31semidirect
340. #501C22×C31semidirect
341. #497C22×C31semidirect
343. #496C22×C31semidirect
344. #491C22×C31semidirect
345. #490C22×C31semidirect
346. #490C22×C31semidirect
361. #330C22×C31semidirect
362. #330C22×C31semidirect
363. #330C22×C31semidirect
366. #329C22×C31semidirect
467. C31#19090direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35612
C31×#32352
C31×#32192
C31×#32132
C31×#16642
C31×#16612
C31×#16572
C31×#16562
C31×#15372
C31×#15352
C31×#15332
#1909031