Finite Group Databasebeta

← C31×#10969 #21467728

Subgroups — C31×#10969 #21467728

Order 7936.

1922 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C22×C31×#102C212yesmaximal, complemented
3C22×C31×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C31×#380C211yesmaximal, characteristic, complemented
5C2×C31×#340C212yesmaximal, complemented
6C23×D4×C31—21no—
7C23×D4×C31C2211yescharacteristic
8C24×C4×C31C2211yescharacteristic
9C23×C8×C31C2212yes—
10C2×C31×#121—24no—
11C2×C31×#121—22no—
12C2×C31×#121—24no—
13C2×C31×#121C414yescomplemented
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31—21no—
17C22×C22⋊C4×C31—21no—
18C2×C31×#102—24no—
19C2×C31×#102—24no—
20C2×C31×#102—24no—
21C2×C31×C22⋊C8—22no—
22C2×C31×C22⋊C8—24no—
23C31×#380—24no—
24C2×C31×#95—21no—
25C31×#340—24no—
26C25×C31—21no—
27C25×C31D411yescharacteristic
28C22×D4×C31—28no—
29C22×D4×C31—24no—
30C22×D4×C31—22no—
31C22×D4×C31—22no—
32C22×D4×C31—22no—
33C22×D4×C31—21no—
34C22×D4×C31—22no—
35C22×D4×C31—22no—
36C22×D4×C31—44no—
37C22×D4×C31—42no—
38C22×D4×C31—42no—
39C22×D4×C31C2×C412yes—
40C22×D4×C31D414yes—
41C23×C4×C31—21no—
42C23×C4×C31—22no—
43C23×C4×C31—22no—
44C23×C4×C31—22no—
45C23×C4×C31—22no—
46C23×C4×C31—22no—
47C23×C4×C31—22no—
48C23×C4×C31—22no—
49C23×C4×C31C2×C412yes—
50C23×C4×C31D411yescharacteristic
51C23×C4×C31D412yes—
52C23×C4×C31C2311yescharacteristic
53C22×C8×C31—22no—
54C22×C8×C31—22no—
55C22×C8×C31—22no—
56C22×C8×C31—22no—
57C22×C8×C31—22no—
58C22×C8×C31—22no—
59C22×C8×C31D414yescomplemented
60C31×#121—216no—
61C31×#121—28no—
62C31×#121—28no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—21no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31C2×C412yes—
71C2×C4⋊C4×C31D414yes—
72C2×C4⋊C4×C31D414yescomplemented
73C2×C22⋊C4×C31—28no—
74C2×C22⋊C4×C31—24no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—42no—
77C2×C22⋊C4×C31—42no—
78C31×#102—216no—
79C31×C22⋊C8—28no—
80C31×#95—24no—
81C24×C31—21no—
82C24×C31—22no—
83C24×C31—22no—
84C24×C31—21no—
85C24×C31—22no—
86C24×C31—21no—
87C24×C31—22no—
88C24×C31—21no—
89C24×C31—22no—
90C24×C31—24no—
91C24×C31—41no—
92C24×C31—42no—
93C24×C31—41no—
94C24×C31—41no—
95C24×C31—41no—
96C24×C31—42no—
97C24×C31—42no—
98C24×C31—41no—
99C24×C31—41no—
100C24×C31C22⋊C412yes—
101C24×C31D812yes—
102C24×C31SD1612yes—
103C24×C31C2×D411yescharacteristic
104C2×D4×C31—216no—
105C2×D4×C31—22no—
106C2×D4×C31—24no—
107C2×D4×C31—24no—
108C2×D4×C31—24no—
109C2×D4×C31—24no—
110C2×D4×C31—24no—
111C2×D4×C31—24no—
112C2×D4×C31—24no—
113C2×D4×C31—48no—
114C2×D4×C31—416no—
115C2×D4×C31—416no—
116C2×D4×C31—48no—
117C2×D4×C31—41no—
118C2×D4×C31—42no—
119C2×D4×C31—42no—
120C2×D4×C31—42no—
121C2×D4×C31—41no—
122C2×D4×C31—42no—
123C2×D4×C31—42no—
124C2×D4×C31C22⋊C414yescomplemented
125C22×C4×C31—22no—
126C22×C4×C31—21no—
127C22×C4×C31—22no—
128C22×C4×C31—24no—
129C22×C4×C31—22no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—24no—
134C22×C4×C31—24no—
135C22×C4×C31—22no—
136C22×C4×C31—24no—
137C22×C4×C31—24no—
138C22×C4×C31—22no—
139C22×C4×C31—24no—
140C22×C4×C31—41no—
141C22×C4×C31—41no—
142C22×C4×C31—42no—
143C22×C4×C31—42no—
144C22×C4×C31—42no—
145C22×C4×C31—42no—
146C22×C4×C31—42no—
147C22×C4×C31—42no—
148C22×C4×C31—42no—
149C22×C4×C31—42no—
150C22×C4×C31—42no—
151C22×C4×C31—42no—
152C22×C4×C31—42no—
153C22×C4×C31—42no—
154C22×C4×C31—42no—
155C22×C4×C31—42no—
156C22×C4×C31—42no—
157C22×C4×C31C22⋊C412yes—
158C22×C4×C31C22×C411yescharacteristic
159C22×C4×C31C2×D412yes—
160C22×C4×C31C2×D412yes—
161C22×C4×C31C2×D412yes—
162C22×C4×C31C2×D412yes—
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31#4112yes—
165C22×C4×C31#4112yes—
166C2×C8×C31—24no—
167C2×C8×C31—24no—
168C2×C8×C31—24no—
169C2×C8×C31—42no—
170C2×C8×C31—42no—
171C2×C8×C31—42no—
172C2×C8×C31—42no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—24no—
175C4⋊C4×C31—24no—
176C4⋊C4×C31—24no—
177C4⋊C4×C31—42no—
178C4⋊C4×C31—42no—
179C4⋊C4×C31C22⋊C414yescomplemented
180C22⋊C4×C31—216no—
181C22⋊C4×C31—48no—
182#10969C3111yesmaximal, characteristic, direct product factor, Sylow
183C23×C31—22no—
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—22no—
190C23×C31—24no—
191C23×C31—22no—
192C23×C31—24no—
193C23×C31—24no—
194C23×C31—24no—
195C23×C31—22no—
196C23×C31—22no—
197C23×C31—24no—
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—44no—
209C23×C31—44no—
210C23×C31—42no—
211C23×C31—42no—
212C23×C31—42no—
213C23×C31—42no—
214C23×C31—44no—
215C23×C31—44no—
216C23×C31—44no—
217C23×C31—44no—
218C23×C31—81no—
219C23×C31—81no—
220C23×C31—82no—
221C23×C31—82no—
222C23×C31—82no—
223C23×C31—82no—
224C23×C31—82no—
225C23×C31—81no—
226C23×C31—81no—
227C23×C31—82no—
228C23×C31#10214yescomplemented
229C23×C31C2×C22⋊C411yescharacteristic
230C23×C31#12012yes—
231C23×C31#12011yescharacteristic
232C23×C31#12112yes—
233C23×C31#12311yescharacteristic
234C23×C31C2×D811yescharacteristic
235C23×C31C2×SD1611yescharacteristic
236C23×C31#13512yes—
237C23×C31AGL(1,ℤ/8)11yescharacteristic
238C23×C31AGL(1,ℤ/8)12yes—
239C23×C31#13711yescharacteristic
240D4×C31—28no—
241D4×C31—432no—
242D4×C31—44no—
243D4×C31—44no—
244D4×C31—44no—
245C2×C4×C31—22no—
246C2×C4×C31—24no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—44no—
254C2×C4×C31—44no—
255C2×C4×C31—44no—
256C2×C4×C31—44no—
257C2×C4×C31—44no—
258C2×C4×C31—44no—
259C2×C4×C31—44no—
260C2×C4×C31—44no—
261C2×C4×C31—44no—
262C2×C4×C31—82no—
263C2×C4×C31—82no—
264C2×C4×C31—82no—
265C2×C4×C31—82no—
266C2×C4×C31C2×C22⋊C411yescharacteristic
267C2×C4×C31C2×C22⋊C411yescharacteristic
268C2×C4×C31C4×D412yes—
269C2×C4×C31C4×D412yes—
270C2×C4×C31#12012yes—
271C2×C4×C31#12011yescharacteristic
272C2×C4×C31#12012yes—
273C2×C4×C31#12112yes—
274C2×C4×C31#12112yes—
275C2×C4×C31#12112yes—
276C2×C4×C31#12112yes—
277C2×C4×C31#12112yes—
278C2×C4×C31#12312yes—
279C2×C4×C31#12311yescharacteristic
280C2×C4×C31#12412yes—
281C2×C4×C31#12712yes—
282C8×C31—44no—
283C22×#121C2×C3111yescharacteristic
284C22×#102C2×C3112yescomplemented
285C22×C22⋊C8C2×C3111yescharacteristic, complemented
286C2×#380C2×C3111yescharacteristic, complemented
287C2×#340C2×C3112yescomplemented
288C22×C31—24no—
289C22×C31—24no—
290C22×C31—24no—
291C22×C31—42no—
292C22×C31—42no—
293C22×C31—42no—
294C22×C31—44no—
295C22×C31—44no—
296C22×C31—44no—
297C22×C31—44no—
298C22×C31—42no—
299C22×C31—44no—
300C22×C31—44no—
301C22×C31—44no—
302C22×C31—82no—
303C22×C31—82no—
304C22×C31—82no—
305C22×C31—82no—
306C22×C31—84no—
307C22×C31—84no—
308C22×C31—84no—
309C22×C31—84no—
310C22×C31#37911yescharacteristic
311C22×C31#38611yescharacteristic
312C22×C31#38611yescharacteristic
313C22×C31#39212yes—
314C22×C31#39412yes—
315C22×C31C2×#10211yescharacteristic
316C22×C31#41611yescharacteristic
317C22×C31#41711yescharacteristic
318C22×C31#41811yescharacteristic
319C22×C31#44711yescharacteristic
320C22×C31#44712yes—
321C22×C31#44811yescharacteristic
322C22×C31#44912yes—
323C22×C31#44912yes—
324C22×C31#45012yes—
325C22×C31#45212yes—
326C22×C31#46512yes—
327C22×C31#46612yes—
328C22×C31#46812yes—
329C22×C31#46912yes—
330C22×C31#48011yescharacteristic
331C22×C31#48111yescharacteristic
332C22×C31#48212yes—
333C4×C31—42no—
334C4×C31—44no—
335C4×C31—84no—
336C4×C31#38612yes—
337C4×C31#39012yes—
338C4×C31#39212yes—
339C4×C31#39412yes—
340C23×D4—21no—
341C23×D4C22×C3111yescharacteristic
342C24×C4C22×C3111yescharacteristic
343C23×C8C22×C3112yes—
344C2×#121—24no—
345C2×#121—22no—
346C2×#121—24no—
347C2×#121C4×C3114yescomplemented
348C22×C4⋊C4C22×C3112yes—
349C22×C4⋊C4C22×C3111yescharacteristic
350C22×C22⋊C4—21no—
351C22×C22⋊C4—21no—
352C2×#102—24no—
353C2×#102—24no—
354C2×#102—24no—
355C2×C22⋊C8—22no—
356C2×C22⋊C8—24no—
357#380—24no—
358C2×#95—21no—
359#340—24no—
360C2×C31—44no—
361C2×C31—84no—
362C2×C31#143811yescharacteristic
363C2×C31#178611yescharacteristic
364C2×C31#178811yescharacteristic
365C2×C31#187411yescharacteristic
366C2×C31#187511yescharacteristic
367C2×C31#189311yescharacteristic
368C2×C31#189511yescharacteristic
369C2×C31#199912yes—
370C2×C31#200012yes—
371C2×C31#203312yes—
372C2×C31#203412yes—
373C25—21no—
374C25D4×C3111yescharacteristic
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—21no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—44no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4C2×C4×C3112yes—
387C22×D4D4×C3114yes—
388C23×C4—21no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4C2×C4×C3112yes—
397C23×C4D4×C3111yescharacteristic
398C23×C4D4×C3112yes—
399C23×C4C23×C3111yescharacteristic
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—22no—
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8D4×C3114yescomplemented
407#121—216no—
408#121—28no—
409#121—28no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4C2×C4×C3112yes—
418C2×C4⋊C4D4×C3114yes—
419C2×C4⋊C4D4×C3114yescomplemented
420C2×C22⋊C4—28no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425#102—216no—
426C22⋊C8—28no—
427#95—24no—
428C31#1096911yescharacteristic, direct product factor, Sylow
429C24—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—24no—
439C24—41no—
440C24—42no—
441C24—41no—
442C24—41no—
443C24—41no—
444C24—42no—
445C24—42no—
446C24—41no—
447C24—41no—
448C24C22⋊C4×C3112yes—
449C24D8×C3112yes—
450C24SD16×C3112yes—
451C24C2×D4×C3111yescharacteristic
452C2×D4—216no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—48no—
462C2×D4—416no—
463C2×D4—416no—
464C2×D4—48no—
465C2×D4—41no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—41no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4C22⋊C4×C3114yescomplemented
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4C22⋊C4×C3112yes—
506C22×C4C22×C4×C3111yescharacteristic
507C22×C4C2×D4×C3112yes—
508C22×C4C2×D4×C3112yes—
509C22×C4C2×D4×C3112yes—
510C22×C4C2×D4×C3112yes—
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4#41×C3112yes—
513C22×C4#41×C3112yes—
514C2×C8—24no—
515C2×C8—24no—
516C2×C8—24no—
517C2×C8—42no—
518C2×C8—42no—
519C2×C8—42no—
520C2×C8—42no—
521C4⋊C4—22no—
522C4⋊C4—24no—
523C4⋊C4—24no—
524C4⋊C4—24no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4C22⋊C4×C3114yescomplemented
528C22⋊C4—216no—
529C22⋊C4—48no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—22no—
534C23—24no—
535C23—22no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—24no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—42no—
562C23—42no—
563C23—44no—
564C23—44no—
565C23—81no—
566C23—81no—
567C23—82no—
568C23—82no—
569C23—82no—
570C23—82no—
571C23—82no—
572C23—81no—
573C23—81no—
574C23—82no—
575C23C31×#10214yescomplemented
576C23C2×C22⋊C4×C3111yescharacteristic
577C23C31×#12011yescharacteristic
578C23C31×#12012yes—
579C23C31×#12112yes—
580C23C31×#12311yescharacteristic
581C23C2×D8×C3111yescharacteristic
582C23C2×SD16×C3111yescharacteristic
583C23C31×#13512yes—
584C23C31×AGL(1,ℤ/8)11yescharacteristic
585C23C31×AGL(1,ℤ/8)12yes—
586C23C31×#13711yescharacteristic
587D4—28no—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—44no—
608C2×C4—44no—
609C2×C4—82no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4C2×C22⋊C4×C3111yescharacteristic
614C2×C4C2×C22⋊C4×C3111yescharacteristic
615C2×C4C4×D4×C3112yes—
616C2×C4C4×D4×C3112yes—
617C2×C4C31×#12012yes—
618C2×C4C31×#12011yescharacteristic
619C2×C4C31×#12012yes—
620C2×C4C31×#12112yes—
621C2×C4C31×#12112yes—
622C2×C4C31×#12112yes—
623C2×C4C31×#12112yes—
624C2×C4C31×#12112yes—
625C2×C4C31×#12312yes—
626C2×C4C31×#12311yescharacteristic
627C2×C4C31×#12412yes—
628C2×C4C31×#12712yes—
629C8—44no—
630C22—24no—
631C22—24no—
632C22—24no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—44no—
637C22—44no—
638C22—44no—
639C22—44no—
640C22—42no—
641C22—44no—
642C22—44no—
643C22—44no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—82no—
648C22—84no—
649C22—84no—
650C22—84no—
651C22—84no—
652C22C31×#37911yescharacteristic
653C22C31×#38611yescharacteristic
654C22C31×#38611yescharacteristic
655C22C31×#39212yes—
656C22C31×#39412yes—
657C22C2×C31×#10211yescharacteristic
658C22C31×#41611yescharacteristic
659C22C31×#41711yescharacteristic
660C22C31×#41811yescharacteristic
661C22C31×#44711yescharacteristic
662C22C31×#44712yes—
663C22C31×#44811yescharacteristic
664C22C31×#44912yes—
665C22C31×#44912yes—
666C22C31×#45012yes—
667C22C31×#45212yes—
668C22C31×#46512yes—
669C22C31×#46612yes—
670C22C31×#46812yes—
671C22C31×#46912yes—
672C22C31×#48011yescharacteristic
673C22C31×#48111yescharacteristic
674C22C31×#48212yes—
675C4—42no—
676C4—44no—
677C4—84no—
678C4C31×#38612yes—
679C4C31×#39012yes—
680C4C31×#39212yes—
681C4C31×#39412yes—
682C2—44no—
683C2—84no—
684C2C31×#143811yescharacteristic
685C2C31×#178611yescharacteristic
686C2C31×#178811yescharacteristic
687C2C31×#187411yescharacteristic
688C2C31×#187511yescharacteristic
689C2C31×#189311yescharacteristic
690C2C31×#189511yescharacteristic
691C2C31×#199912yes—
692C2C31×#200012yes—
693C2C31×#203312yes—
694C2C31×#203412yes—
subgroupG/H
center, socleC24×C31C2×D4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×C31×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#102C2semidirect
3. C22×C31×C22⋊C8C2semidirect
4. C2×C31×#380C2semidirect
5. C2×C31×#340C2semidirect
13. C2×C31×#121C4semidirect
59. C22×C8×C31D4semidirect
72. C2×C4⋊C4×C31D4semidirect
124. C2×D4×C31C22⋊C4semidirect
179. C4⋊C4×C31C22⋊C4semidirect
182. #10969C31direct (N × H)
228. C23×C31#102semidirect
284. C22×#102C2×C31semidirect
285. C22×C22⋊C8C2×C31semidirect
286. C2×#380C2×C31semidirect
287. C2×#340C2×C31semidirect
347. C2×#121C4×C31semidirect
406. C22×C8D4×C31semidirect
419. C2×C4⋊C4D4×C31semidirect
428. C31#10969direct (N × H)
472. C2×D4C22⋊C4×C31semidirect
527. C4⋊C4C22⋊C4×C31semidirect
575. C23C31×#102semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C22×C31×#1022
C22×C31×C22⋊C82
C2×C31×#3802
C2×C31×#3402
#1096931