Finite Group Databasebeta

← C31×#16094 #21472853

Subgroups — C31×#16094 #21472853

Order 7936.

1906 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#124C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic, complemented
3C2×C31×#388C212yesmaximal, complemented
4C31×#1446C211yesmaximal, characteristic, complemented
5C31×#1440C212yesmaximal, complemented
6C31×#1439C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1438C212yesmaximal
9C31×#1436C212yesmaximal, complemented
10C23×Q8×C31C2211yescharacteristic
11C23×D4×C31C2211yescharacteristic
12C2×C31×#124—24no—
13C2×C31×#124—28no—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C31×#391—24no—
25C31×#388—28no—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C25×C31C2312yes—
36C22×Q8×C31—24no—
37C22×Q8×C31—24no—
38C22×Q8×C31—41no—
39C22×Q8×C31—41no—
40C22×Q8×C31D414yes—
41C22×D4×C31—24no—
42C22×D4×C31—22no—
43C22×D4×C31—24no—
44C22×D4×C31—41no—
45C22×D4×C31—41no—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C31×#124—232no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—42no—
59C2×C4⋊C4×C31—41no—
60C2×C4⋊C4×C31—41no—
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—42no—
73C2×C22⋊C4×C31—42no—
74C2×C22⋊C4×C31—42no—
75C2×C22⋊C4×C31—42no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C2×C22⋊C4×C31D418yes—
79C2×C42×C31—24no—
80C2×C42×C31—22no—
81C2×C42×C31—24no—
82C2×C42×C31—22no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—24no—
86C31×#95—24no—
87C31×#95—24no—
88C31×#95—24no—
89C31×#95—41no—
90C31×#95—42no—
91C31×#95—41no—
92C24×C31—22no—
93C24×C31—22no—
94C24×C31—22no—
95C24×C31—22no—
96C24×C31—22no—
97C24×C31—22no—
98C24×C31—22no—
99C24×C31—22no—
100C24×C31—22no—
101C24×C31—22no—
102C24×C31—22no—
103C24×C31—22no—
104C24×C31—22no—
105C24×C31—22no—
106C24×C31C2×D414yes—
107C24×C31C2411yescharacteristic
108C2×Q8×C31—28no—
109C2×Q8×C31—28no—
110C2×Q8×C31—44no—
111C2×Q8×C31—48no—
112C2×Q8×C31—48no—
113C2×D4×C31—28no—
114C2×D4×C31—48no—
115C2×D4×C31—48no—
116C2×D4×C31—44no—
117C2×D4×C31—44no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—21no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
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—22no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31—22no—
157C22×C4×C31—22no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31C2×D412yes—
161C22×C4×C31C2×D414yes—
162C22×C4×C31C2×D414yes—
163C22×C4×C31C2×D412yes—
164C22×C4×C31C2×D412yes—
165C22×C4×C31#4114yes—
166C22×C4×C31#4114yes—
167C22×C4×C31#4114yes—
168C4⋊C4×C31—48no—
169C4⋊C4×C31—44no—
170C22⋊C4×C31—216no—
171C22⋊C4×C31—216no—
172C22⋊C4×C31—216no—
173C22⋊C4×C31—48no—
174C22⋊C4×C31—48no—
175C22⋊C4×C31—48no—
176C42×C31—28no—
177C42×C31—44no—
178#16094C3111yesmaximal, characteristic, direct product factor, Sylow
179C23×C31—24no—
180C23×C31—24no—
181C23×C31—24no—
182C23×C31—24no—
183C23×C31—24no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31—42no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—42no—
206C23×C31—42no—
207C23×C31—42no—
208C23×C31—42no—
209C23×C31—42no—
210C23×C31—42no—
211C23×C31—42no—
212C23×C31—42no—
213C23×C31—42no—
214C23×C31C22×D411yescharacteristic
215C23×C31C22×D412yes—
216C23×C31C2×#4112yes—
217C23×C31C2×#4112yes—
218C23×C31C2×#4112yes—
219C23×C31H(5,𝔽2)11yescharacteristic
220C23×C31H(5,𝔽2)11yescharacteristic
221C23×C31H(5,𝔽2)12yes—
222C23×C312−1+412yes—
223Q8×C31—416no—
224D4×C31—416no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—24no—
230C2×C4×C31—24no—
231C2×C4×C31—24no—
232C2×C4×C31—24no—
233C2×C4×C31—24no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—24no—
237C2×C4×C31—24no—
238C2×C4×C31—24no—
239C2×C4×C31—22no—
240C2×C4×C31—24no—
241C2×C4×C31—24no—
242C2×C4×C31—24no—
243C2×C4×C31—24no—
244C2×C4×C31—24no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—42no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—42no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—42no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—42no—
273C2×C4×C31#12014yes—
274C2×C4×C31#12314yes—
275C22×#124C2×C3111yescharacteristic
276C2×#391C2×C3111yescharacteristic, complemented
277C2×#388C2×C3112yescomplemented
278#1446C2×C3111yescharacteristic, complemented
279#1440C2×C3112yescomplemented
280#1439C2×C3112yescomplemented
281#1439C2×C3112yescomplemented
282#1438C2×C3112yes—
283#1436C2×C3112yescomplemented
284C22×C31—44no—
285C22×C31—44no—
286C22×C31—44no—
287C22×C31—44no—
288C22×C31—44no—
289C22×C31—44no—
290C22×C31—44no—
291C22×C31—82no—
292C22×C31—82no—
293C22×C31—82no—
294C22×C31—82no—
295C22×C31—82no—
296C22×C31—82no—
297C22×C31—82no—
298C22×C31—82no—
299C22×C31C2×#12011yescharacteristic
300C22×C31C2×#12311yescharacteristic
301C22×C31#52512yes—
302C22×C31#52912yes—
303C22×C31#53411yescharacteristic
304C22×C31#53712yes—
305C22×C31#53812yes—
306C22×C31#54212yes—
307C22×C31#54212yes—
308C22×C31#54612yes—
309C22×C31#54612yes—
310C22×C31#54612yes—
311C22×C31#54712yes—
312C22×C31#54812yes—
313C22×C31#55012yes—
314C22×C31#55511yescharacteristic
315C22×C31#55511yescharacteristic
316C22×C31#55612yes—
317C22×C31#55912yes—
318C22×C31H(3,𝔽4)11yescharacteristic
319C22×C31#56311yescharacteristic
320C4×C31—24no—
321C4×C31—24no—
322C4×C31—42no—
323C4×C31—44no—
324C4×C31—44no—
325C4×C31—44no—
326C4×C31—82no—
327C4×C31—82no—
328C23×Q8C22×C3111yescharacteristic
329C23×D4C22×C3111yescharacteristic
330C2×#124—24no—
331C2×#124—28no—
332C22×C4⋊C4C22×C3112yes—
333C22×C4⋊C4C22×C3111yescharacteristic
334C22×C22⋊C4C22×C3112yes—
335C22×C22⋊C4C22×C3112yes—
336C22×C22⋊C4C22×C3112yes—
337C22×C22⋊C4C22×C3112yes—
338C22×C22⋊C4C22×C3112yes—
339C22×C22⋊C4C22×C3112yes—
340C22×C42C22×C3111yescharacteristic
341C22×C42C22×C3111yescharacteristic
342#391—24no—
343#388—28no—
344C2×#95C22×C3112yes—
345C2×#95C22×C3112yes—
346C2×#95C22×C3112yes—
347C2×#95C22×C3112yes—
348C2×#95C22×C3112yes—
349C2×#95C22×C3112yes—
350C2×#95C22×C3112yes—
351C2×#95C22×C3111yescharacteristic
352C2×#95C22×C3111yescharacteristic
353C2×C31—84no—
354C2×C31#240511yescharacteristic
355C2×C31#240712yes—
356C2×C31#244812yes—
357C2×C31#245912yes—
358C2×C31#247412yes—
359C2×C31#271212yes—
360C2×C31#271512yes—
361C2×C31#273111yescharacteristic
362C2×C31#273311yescharacteristic
363C25C23×C3112yes—
364C22×Q8—24no—
365C22×Q8—24no—
366C22×Q8—41no—
367C22×Q8—41no—
368C22×Q8D4×C3114yes—
369C22×D4—24no—
370C22×D4—22no—
371C22×D4—24no—
372C22×D4—41no—
373C22×D4—41no—
374C23×C4C23×C3112yes—
375C23×C4C23×C3112yes—
376C23×C4C23×C3112yes—
377C23×C4C23×C3111yescharacteristic
378C23×C4C23×C3112yes—
379C23×C4C23×C3112yes—
380C23×C4C23×C3111yescharacteristic
381C23×C4C23×C3111yescharacteristic
382#124—232no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4D4×C3118yes—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—22no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—41no—
420C31#1609411yescharacteristic, direct product factor, Sylow
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24C2×D4×C3114yes—
436C24C24×C3111yescharacteristic
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—44no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×D4—28no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—44no—
446C2×D4—44no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4C2×D4×C3112yes—
490C22×C4C2×D4×C3114yes—
491C22×C4C2×D4×C3114yes—
492C22×C4C2×D4×C3112yes—
493C22×C4C2×D4×C3112yes—
494C22×C4#41×C3114yes—
495C22×C4#41×C3114yes—
496C22×C4#41×C3114yes—
497C4⋊C4—48no—
498C4⋊C4—44no—
499C22⋊C4—216no—
500C22⋊C4—216no—
501C22⋊C4—216no—
502C22⋊C4—48no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C42—28no—
506C42—44no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23C22×D4×C3111yescharacteristic
543C23C22×D4×C3112yes—
544C23C2×#41×C3112yes—
545C23C2×#41×C3112yes—
546C23C2×#41×C3112yes—
547C23C31×H(5,𝔽2)11yescharacteristic
548C23C31×H(5,𝔽2)11yescharacteristic
549C23C31×H(5,𝔽2)12yes—
550C23C31×2−1+412yes—
551Q8—416no—
552D4—416no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4C31×#12014yes—
602C2×C4C31×#12314yes—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—44no—
609C22—44no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—82no—
618C22C2×C31×#12011yescharacteristic
619C22C2×C31×#12311yescharacteristic
620C22C31×#52512yes—
621C22C31×#52912yes—
622C22C31×#53411yescharacteristic
623C22C31×#53712yes—
624C22C31×#53812yes—
625C22C31×#54212yes—
626C22C31×#54212yes—
627C22C31×#54612yes—
628C22C31×#54612yes—
629C22C31×#54612yes—
630C22C31×#54712yes—
631C22C31×#54812yes—
632C22C31×#55012yes—
633C22C31×#55511yescharacteristic
634C22C31×#55511yescharacteristic
635C22C31×#55612yes—
636C22C31×#55912yes—
637C22C31×H(3,𝔽4)11yescharacteristic
638C22C31×#56311yescharacteristic
639C4—24no—
640C4—24no—
641C4—42no—
642C4—44no—
643C4—44no—
644C4—44no—
645C4—82no—
646C4—82no—
647C2—84no—
648C2C31×#240511yescharacteristic
649C2C31×#240712yes—
650C2C31×#244812yes—
651C2C31×#245912yes—
652C2C31×#247412yes—
653C2C31×#271212yes—
654C2C31×#271512yes—
655C2C31×#273111yescharacteristic
656C2C31×#273311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#391C2semidirect
3. C2×C31×#388C2semidirect
4. C31×#1446C2semidirect
5. C31×#1440C2semidirect
6. C31×#1439C2semidirect
7. C31×#1439C2semidirect
9. C31×#1436C2semidirect
178. #16094C31direct (N × H)
276. C2×#391C2×C31semidirect
277. C2×#388C2×C31semidirect
278. #1446C2×C31semidirect
279. #1440C2×C31semidirect
280. #1439C2×C31semidirect
281. #1439C2×C31semidirect
283. #1436C2×C31semidirect
420. C31#16094direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1242
C2×C31×#3912
C2×C31×#3882
C31×#14462
C31×#14402
C31×#14392
C31×#14382
C31×#14362
#1609431