Finite Group Databasebeta

← C31×#19044 #21475803

Subgroups — C31×#19044 #21475803

Order 7936.

956 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×#3180C211yesmaximal, characteristic, complemented
4C31×#3150C211yesmaximal, characteristic, complemented
5C31×#1661C212yesmaximal, complemented
6C31×#1660C212yesmaximal, complemented
7C31×#1657C212yesmaximal, complemented
8C31×#1656C212yesmaximal, complemented
9C31×#1532C211yesmaximal, characteristic, complemented
10C31×#1530C211yesmaximal, characteristic, complemented
11C2×C31×#330C211yesmaximal, characteristic, complemented
12C2×C31×#135—22no—
13C31×#563C2212yes—
14C31×#562C2212yes—
15C31×#554—21no—
16C31×#553—21no—
17C31×#553—21no—
18C31×#547—22no—
19C31×#547—21no—
20C31×#544—21no—
21C31×#540—21no—
22C31×#539—22no—
23C31×#539—21no—
24C31×#537—21no—
25C31×#532C2211yescharacteristic
26C31×#532C2211yescharacteristic
27C31×#529C2211yescharacteristic
28C2×C31×#125C2211yescharacteristic
29C31×#501C2211yescharacteristic
30C31×#501C2212yes—
31C31×#497—21no—
32C31×#497C2212yes—
33C31×#496—21no—
34C31×#496C2212yes—
35C31×#496C2211yescharacteristic
36C31×#490C2211yescharacteristic
37C31×#490C2212yes—
38C31×#489C2211yescharacteristic
39C31×#481—21no—
40C31×#480—21no—
41C31×#478—22no—
42C31×#466—21no—
43C31×#465—21no—
44C31×#442—21no—
45C31×#440—21no—
46C31×#432C2211yescharacteristic
47C2×C31×#97C2211yescharacteristic
48C2×C31×#97C2211yescharacteristic
49C31×#330C2212yes—
50C31×#330C2212yes—
51C31×#330C2212yes—
52C31×#329C2212yes—
53C31×#329C2212yes—
54C31×#329C2212yes—
55C2×#41×C31—22no—
56C2×#41×C31—21no—
57C2×#41×C31D412yes—
58C31×#135—48no—
59C2×Q16×C31—22no—
60C2×SD16×C31—21no—
61C2×SD16×C31—22no—
62C2×SD16×C31—22no—
63C2×D8×C31—21no—
64C2×D8×C31—22no—
65C22×C8×C31—21no—
66C22×C8×C31—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—22no—
69C31×C4⋊Q8D411yescharacteristic
70C31×C4⋊Q8C2311yescharacteristic
71C31×#127D411yescharacteristic
72C31×#127C2311yescharacteristic
73C31×#126—22no—
74C31×#126—22no—
75C31×#126—21no—
76C31×#125—22no—
77C31×#125—21no—
78C31×#125—21no—
79C31×#125—21no—
80C31×#125D412yes—
81C31×#125C2312yes—
82C31×#125C2311yescharacteristic
83C31×#124—21no—
84C31×#124C2311yescharacteristic
85C31×#124C2312yes—
86C31×#123—22no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—21no—
91C31×#123—22no—
92C31×#123—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8D411yescharacteristic
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—21no—
103C31×#121—21no—
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#121D411yescharacteristic
111C4×Q8×C31D411yescharacteristic
112C4×D4×C31—22no—
113C4×D4×C31—22no—
114C4×D4×C31—21no—
115C4×D4×C31—21no—
116C4×D4×C31—21no—
117C4×D4×C31—21no—
118C4×D4×C31—21no—
119C4×D4×C31—21no—
120C4×D4×C31—21no—
121C4×D4×C31D411yescharacteristic
122C31×#117—21no—
123C31×#117—21no—
124C2×C4⋊C4×C31—22no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31D411yescharacteristic
129C2×C4⋊C4×C31D411yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#107—21no—
132C31×#107—22no—
133C31×#106—21no—
134C31×#106—22no—
135C31×C4⋊C8—21no—
136C31×#103—21no—
137C31×#102—21no—
138C31×#102—21no—
139C31×#102—21no—
140C31×#102—22no—
141C31×#102—22no—
142C31×C22⋊C8—21no—
143C31×#97—21no—
144C31×#97—21no—
145C31×#97C2311yescharacteristic
146C31×#97C2312yes—
147C31×#97C2311yescharacteristic
148C31×#97C2312yes—
149#41×C31—44no—
150#41×C31—44no—
151#41×C31—84no—
152C2×Q8×C31—22no—
153C2×Q8×C31—21no—
154C2×Q8×C31C2×D411yescharacteristic
155C2×Q8×C31C2×D412yes—
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×D411yescharacteristic
167C2×D4×C31C2×D412yes—
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—44no—
180SD16×C31—42no—
181SD16×C31—44no—
182SD16×C31—44no—
183D8×C31—42no—
184D8×C31—44no—
185C2×C8×C31—24no—
186C2×C8×C31—21no—
187C2×C8×C31—22no—
188C2×C8×C31—21no—
189C2×C8×C31—22no—
190C2×C8×C31—42no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—22no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—22no—
195C4⋊C4×C31—22no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—22no—
204C4⋊C4×C31—22no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31C2×D412yes—
210C4⋊C4×C31C2×D411yescharacteristic
211C4⋊C4×C31C2×D412yes—
212C4⋊C4×C31C2×D411yescharacteristic
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—21no—
220C22⋊C4×C31—21no—
221C22⋊C4×C31—21no—
222C22⋊C4×C31—22no—
223C22⋊C4×C31—22no—
224C22⋊C4×C31—21no—
225C22⋊C4×C31—41no—
226C22⋊C4×C31—41no—
227C42×C31—22no—
228C42×C31—21no—
229C42×C31C2×D411yescharacteristic
230C42×C31C2×D411yescharacteristic
231C42×C31C2×D411yescharacteristic
232C42×C31C2411yescharacteristic
233#19044C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—22no—
235C23×C31—21no—
236C23×C31—41no—
237C23×C31#12011yescharacteristic
238Q8×C31—42no—
239Q8×C31—41no—
240Q8×C31—42no—
241Q8×C31—82no—
242D4×C31—42no—
243D4×C31—41no—
244D4×C31—42no—
245D4×C31—42no—
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—22no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
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—24no—
280C8×C31—22no—
281C8×C31—42no—
282C8×C31—41no—
283#3559C2×C3111yescharacteristic, complemented
284#3234C2×C3111yescharacteristic, complemented
285#3180C2×C3111yescharacteristic, complemented
286#3150C2×C3111yescharacteristic, complemented
287#1661C2×C3112yescomplemented
288#1660C2×C3112yescomplemented
289#1657C2×C3112yescomplemented
290#1656C2×C3112yescomplemented
291#1532C2×C3111yescharacteristic, complemented
292#1530C2×C3111yescharacteristic, complemented
293C2×#330C2×C3111yescharacteristic, complemented
294C22×C31—21no—
295C22×C31—21no—
296C22×C31—42no—
297C22×C31—41no—
298C22×C31—42no—
299C22×C31—41no—
300C22×C31—41no—
301C22×C31—42no—
302C22×C31—81no—
303C22×C31—81no—
304C22×C31—81no—
305C22×C31#45312yes—
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—42no—
317C4×C31—41no—
318C4×C31—41no—
319C4×C31—81no—
320C2×#135—22no—
321#563C22×C3112yes—
322#562C22×C3112yes—
323#554—21no—
324#553—21no—
325#553—21no—
326#547—22no—
327#547—21no—
328#544—21no—
329#540—21no—
330#539—22no—
331#539—21no—
332#537—21no—
333#532C22×C3111yescharacteristic
334#532C22×C3111yescharacteristic
335#529C22×C3111yescharacteristic
336C2×#125C22×C3111yescharacteristic
337#501C22×C3111yescharacteristic
338#501C22×C3112yes—
339#497—21no—
340#497C22×C3112yes—
341#496—21no—
342#496C22×C3112yes—
343#496C22×C3111yescharacteristic
344#490C22×C3111yescharacteristic
345#490C22×C3112yes—
346#489C22×C3111yescharacteristic
347#481—21no—
348#480—21no—
349#478—22no—
350#466—21no—
351#465—21no—
352#442—21no—
353#440—21no—
354#432C22×C3111yescharacteristic
355C2×#97C22×C3111yescharacteristic
356C2×#97C22×C3111yescharacteristic
357#330C22×C3112yes—
358#330C22×C3112yes—
359#330C22×C3112yes—
360#329C22×C3112yes—
361#329C22×C3112yes—
362#329C22×C3112yes—
363C2×C31—22no—
364C2×C31—82no—
365C2×C31—81no—
366C2×C31—161no—
367C2×C31C2×#45311yescharacteristic
368C2×C31#301811yescharacteristic
369C2×C31#302011yescharacteristic
370C2×#41—22no—
371C2×#41—21no—
372C2×#41D4×C3112yes—
373#135—48no—
374C2×Q16—22no—
375C2×SD16—22no—
376C2×SD16—21no—
377C2×SD16—22no—
378C2×D8—22no—
379C2×D8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—22no—
384C4⋊Q8D4×C3111yescharacteristic
385C4⋊Q8C23×C3111yescharacteristic
386#127D4×C3111yescharacteristic
387#127C23×C3111yescharacteristic
388#126—22no—
389#126—22no—
390#126—21no—
391#125—22no—
392#125—21no—
393#125—21no—
394#125—21no—
395#125D4×C3112yes—
396#125C23×C3112yes—
397#125C23×C3111yescharacteristic
398#124—21no—
399#124C23×C3111yescharacteristic
400#124C23×C3112yes—
401#123—22no—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—21no—
406#123—22no—
407#123—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8D4×C3111yescharacteristic
415#121—22no—
416#121—22no—
417#121—21no—
418#121—21no—
419#121—22no—
420#121—22no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121D4×C3111yescharacteristic
426C4×Q8D4×C3111yescharacteristic
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4D4×C3111yescharacteristic
437#117—21no—
438#117—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4D4×C3111yescharacteristic
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C42C23×C3111yescharacteristic
446#107—21no—
447#107—22no—
448#106—21no—
449#106—22no—
450C4⋊C8—21no—
451#103—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—22no—
456#102—22no—
457C22⋊C8—21no—
458#97—21no—
459#97—21no—
460#97C23×C3112yes—
461#97C23×C3111yescharacteristic
462#97C23×C3111yescharacteristic
463#97C23×C3112yes—
464C31#1904411yescharacteristic, direct product factor, Sylow
465#41—44no—
466#41—44no—
467#41—84no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8C2×D4×C3111yescharacteristic
471C2×Q8C2×D4×C3112yes—
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×C3111yescharacteristic
483C2×D4C2×D4×C3112yes—
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—44no—
496SD16—42no—
497SD16—44no—
498SD16—44no—
499D8—42no—
500D8—44no—
501C2×C8—24no—
502C2×C8—21no—
503C2×C8—22no—
504C2×C8—21no—
505C2×C8—22no—
506C2×C8—42no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4C2×D4×C3112yes—
526C4⋊C4C2×D4×C3111yescharacteristic
527C4⋊C4C2×D4×C3112yes—
528C4⋊C4C2×D4×C3111yescharacteristic
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—22no—
544C42—21no—
545C42C2×D4×C3111yescharacteristic
546C42C2×D4×C3111yescharacteristic
547C42C2×D4×C3111yescharacteristic
548C42C24×C3111yescharacteristic
549C23—22no—
550C23—21no—
551C23—41no—
552C23C31×#12011yescharacteristic
553Q8—42no—
554Q8—41no—
555Q8—42no—
556Q8—82no—
557D4—42no—
558D4—41no—
559D4—42no—
560D4—42no—
561D4—41no—
562D4—41no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
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—24no—
595C8—22no—
596C8—42no—
597C8—41no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—41no—
602C22—42no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22C31×#45312yes—
610C22C2×C31×#12011yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—81no—
624C2—22no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C2×C31×#45311yescharacteristic
629C2C31×#301811yescharacteristic
630C2C31×#302011yescharacteristic
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×#3180C2semidirect
4. C31×#3150C2semidirect
5. C31×#1661C2semidirect
6. C31×#1660C2semidirect
7. C31×#1657C2semidirect
8. C31×#1656C2semidirect
9. C31×#1532C2semidirect
10. C31×#1530C2semidirect
11. C2×C31×#330C2semidirect
233. #19044C31direct (N × H)
283. #3559C2×C31semidirect
284. #3234C2×C31semidirect
285. #3180C2×C31semidirect
286. #3150C2×C31semidirect
287. #1661C2×C31semidirect
288. #1660C2×C31semidirect
289. #1657C2×C31semidirect
290. #1656C2×C31semidirect
291. #1532C2×C31semidirect
292. #1530C2×C31semidirect
293. C2×#330C2×C31semidirect
464. C31#19044direct (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×#31802
C31×#31502
C31×#16612
C31×#16602
C31×#16572
C31×#16562
C31×#15322
C31×#15302
C2×C31×#3302
#1904431