Finite Group Databasebeta

← C31×#10745 #21467504

Subgroups — C31×#10745 #21467504

Order 7936.

1794 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#518C211yesmaximal, characteristic
2C22×C31×#99C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#342C212yesmaximal, complemented
5C31×C22⋊#95C212yesmaximal, complemented
6C23×D4×C31C2211yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C31×#518—22no—
9C31×#518—24no—
10C31×#518C414yescomplemented
11C2×C4×D4×C31—24no—
12C2×C31×#117—21no—
13C22×C22⋊C4×C31—21no—
14C22×C22⋊C4×C31—21no—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2211yescharacteristic
17C22×C22⋊C4×C31C2212yes—
18C2×C31×#99—22no—
19C2×C31×#99—22no—
20C2×C31×#99C414yescomplemented
21C31×#386—22no—
22C31×#386C414yescomplemented
23C2×C31×#95—21no—
24C2×C31×#95—24no—
25C31×#342—24no—
26C25×C31D411yescharacteristic
27C25×C31C2311yescharacteristic
28C22×D4×C31—22no—
29C22×D4×C31—22no—
30C22×D4×C31—22no—
31C22×D4×C31—22no—
32C22×D4×C31C2×C412yes—
33C22×D4×C31C2×C412yes—
34C22×D4×C31C2×C412yes—
35C22×D4×C31D412yes—
36C22×D4×C31D412yes—
37C22×D4×C31Q812yes—
38C23×C4×C31—21no—
39C23×C4×C31—22no—
40C23×C4×C31—22no—
41C23×C4×C31—21no—
42C23×C4×C31—22no—
43C23×C4×C31—21no—
44C23×C4×C31—22no—
45C23×C4×C31—44no—
46C23×C4×C31C2×C412yescomplemented
47C23×C4×C31D411yescharacteristic
48C23×C4×C31D414yes—
49C4×D4×C31—216no—
50C4×D4×C31—216no—
51C31×#117—24no—
52C31×#117—24no—
53C2×C4⋊C4×C31—22no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31—24no—
56C2×C22⋊C4×C31—24no—
57C2×C22⋊C4×C31—22no—
58C2×C22⋊C4×C31—22no—
59C2×C22⋊C4×C31—22no—
60C2×C22⋊C4×C31—22no—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—44no—
71C2×C22⋊C4×C31C2×C414yes—
72C2×C22⋊C4×C31C2×C414yescomplemented
73C2×C22⋊C4×C31C2×C412yescomplemented
74C2×C22⋊C4×C31D414yes—
75C2×C42×C31—22no—
76C31×#99—28no—
77C31×#95—24no—
78C31×#95—48no—
79C24×C31—21no—
80C24×C31—21no—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—42no—
84C24×C31—42no—
85C24×C31—42no—
86C24×C31—42no—
87C24×C31C22⋊C412yes—
88C24×C31C22⋊C412yes—
89C24×C31C4⋊C412yes—
90C24×C31C22×C411yescharacteristic
91C24×C31C22×C411yescharacteristic
92C24×C31C22×C411yescharacteristic
93C24×C31C2×D411yescharacteristic
94C24×C31C2×D412yes—
95C24×C31C2×D411yescharacteristic
96C24×C31C2×D411yescharacteristic
97C24×C31C2×D412yes—
98C24×C31C2×Q811yescharacteristic
99C24×C31#4112yes—
100C24×C31#4112yes—
101C2×D4×C31—24no—
102C2×D4×C31—24no—
103C2×D4×C31—24no—
104C2×D4×C31—24no—
105C2×D4×C31—24no—
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×C31C4214yes—
114C2×D4×C31C22⋊C414yes—
115C2×D4×C31C4⋊C414yes—
116C2×D4×C31C4⋊C414yes—
117C22×C4×C31—21no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—28no—
122C22×C4×C31—24no—
123C22×C4×C31—22no—
124C22×C4×C31—24no—
125C22×C4×C31—24no—
126C22×C4×C31—28no—
127C22×C4×C31—24no—
128C22×C4×C31—22no—
129C22×C4×C31—24no—
130C22×C4×C31—44no—
131C22×C4×C31—44no—
132C22×C4×C31—48no—
133C22×C4×C31—44no—
134C22×C4×C31—42no—
135C22×C4×C31—41no—
136C22×C4×C31—42no—
137C22×C4×C31—41no—
138C22×C4×C31—44no—
139C22×C4×C31—44no—
140C22×C4×C31—44no—
141C22×C4×C31—42no—
142C22×C4×C31—44no—
143C22×C4×C31—42no—
144C22×C4×C31—41no—
145C22×C4×C31—42no—
146C22×C4×C31—42no—
147C22×C4×C31—41no—
148C22×C4×C31—82no—
149C22×C4×C31—82no—
150C22×C4×C31C22⋊C412yes—
151C22×C4×C31C22⋊C412yes—
152C22×C4×C31C22⋊C418yescomplemented
153C22×C4×C31C4⋊C412yes—
154C4⋊C4×C31—28no—
155C22⋊C4×C31—28no—
156C22⋊C4×C31—24no—
157C22⋊C4×C31—24no—
158C22⋊C4×C31—24no—
159C22⋊C4×C31—24no—
160C22⋊C4×C31—24no—
161C22⋊C4×C31—24no—
162C22⋊C4×C31—24no—
163C22⋊C4×C31—48no—
164C22⋊C4×C31—42no—
165C22⋊C4×C31—42no—
166C22⋊C4×C31—42no—
167C42×C31—28no—
168#10745C3111yesmaximal, characteristic, direct product factor, Sylow
169C23×C31—24no—
170C23×C31—22no—
171C23×C31—24no—
172C23×C31—22no—
173C23×C31—22no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—41no—
180C23×C31—41no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31—41no—
184C23×C31—42no—
185C23×C31—41no—
186C23×C31—44no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—44no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—44no—
194C23×C31—44no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—82no—
198C23×C31—81no—
199C23×C31—81no—
200C23×C31—82no—
201C23×C31#9514yescomplemented
202C23×C31C2×C4211yescharacteristic
203C23×C31C2×C22⋊C411yescharacteristic
204C23×C31C2×C22⋊C411yescharacteristic
205C23×C31C2×C22⋊C412yes—
206C23×C31C2×C22⋊C411yescharacteristic
207C23×C31C2×C4⋊C411yescharacteristic
208C23×C31C2×C4⋊C411yescharacteristic
209C23×C31C2×C4⋊C411yescharacteristic
210C23×C31#11712yes—
211C23×C31C4×D412yes—
212C23×C31C4×D412yes—
213C23×C31C4×D412yes—
214C23×C31C4×D412yes—
215C23×C31#12011yescharacteristic
216C23×C31#12012yes—
217C23×C31#12011yescharacteristic
218C23×C31#12112yes—
219C23×C31#12112yes—
220C23×C31C22⋊Q812yes—
221C23×C31C22⋊Q812yes—
222C23×C31#12311yescharacteristic
223C23×C31#12311yescharacteristic
224C23×C31#12312yes—
225D4×C31—28no—
226D4×C31—28no—
227D4×C31—28no—
228D4×C31—28no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—24no—
236C2×C4×C31—28no—
237C2×C4×C31—28no—
238C2×C4×C31—42no—
239C2×C4×C31—44no—
240C2×C4×C31—48no—
241C2×C4×C31—44no—
242C2×C4×C31—42no—
243C2×C4×C31—44no—
244C2×C4×C31—44no—
245C2×C4×C31—44no—
246C2×C4×C31—48no—
247C2×C4×C31—42no—
248C2×C4×C31—48no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—44no—
252C2×C4×C31—84no—
253C2×C4×C31—88no—
254C2×C4×C31—82no—
255C2×C4×C31—82no—
256C2×C4×C31—82no—
257C2×C4×C31—84no—
258C2×C4×C31—82no—
259C2×C4×C31#9514yescomplemented
260C2×#518C2×C3111yescharacteristic
261C22×#99C2×C3111yescharacteristic
262C2×#386C2×C3111yescharacteristic
263C2×#342C2×C3112yescomplemented
264C22⋊#95C2×C3112yescomplemented
265C22×C31—24no—
266C22×C31—22no—
267C22×C31—22no—
268C22×C31—24no—
269C22×C31—21no—
270C22×C31—22no—
271C22×C31—22no—
272C22×C31—21no—
273C22×C31—21no—
274C22×C31—22no—
275C22×C31—21no—
276C22×C31—22no—
277C22×C31—24no—
278C22×C31—24no—
279C22×C31—22no—
280C22×C31—22no—
281C22×C31—24no—
282C22×C31—41no—
283C22×C31—41no—
284C22×C31—41no—
285C22×C31—41no—
286C22×C31—42no—
287C22×C31—42no—
288C22×C31—42no—
289C22×C31—42no—
290C22×C31—42no—
291C22×C31—42no—
292C22×C31—44no—
293C22×C31—44no—
294C22×C31—42no—
295C22×C31—42no—
296C22×C31—44no—
297C22×C31—82no—
298C22×C31—82no—
299C22×C31—82no—
300C22×C31C2×#9511yescharacteristic
301C22×C31C4×C22⋊C412yes—
302C22×C31#37911yescharacteristic
303C22×C31#38012yes—
304C22×C31#38111yescharacteristic
305C22×C31#38511yescharacteristic
306C22×C31#38512yes—
307C22×C31#38511yescharacteristic
308C22×C31#38611yescharacteristic
309C22×C31#38612yes—
310C22×C31#38611yescharacteristic
311C22×C31B(4,𝔽2)12yes—
312C22×C31#45812yes—
313C4×C31—24no—
314C4×C31—44no—
315C4×C31—48no—
316C4×C31—82no—
317C4×C31—84no—
318C23×D4C22×C3111yescharacteristic
319C24×C4C22×C3111yescharacteristic
320#518—22no—
321#518—24no—
322#518C4×C3114yescomplemented
323C2×C4×D4—24no—
324C2×#117—21no—
325C22×C22⋊C4—21no—
326C22×C22⋊C4—21no—
327C22×C22⋊C4C22×C3112yes—
328C22×C22⋊C4C22×C3111yescharacteristic
329C22×C22⋊C4C22×C3112yes—
330C2×#99—22no—
331C2×#99—22no—
332C2×#99C4×C3114yescomplemented
333#386—22no—
334#386C4×C3114yescomplemented
335C2×#95—21no—
336C2×#95—24no—
337#342—24no—
338C2×C31—21no—
339C2×C31—22no—
340C2×C31—21no—
341C2×C31—21no—
342C2×C31—21no—
343C2×C31—22no—
344C2×C31—22no—
345C2×C31—22no—
346C2×C31—44no—
347C2×C31C22⋊#9511yescharacteristic
348C2×C31#179012yes—
349C2×C31#186712yes—
350C2×C31#188911yescharacteristic
351C2×C31#189011yescharacteristic
352C25D4×C3111yescharacteristic
353C25C23×C3111yescharacteristic
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C3112yes—
359C22×D4C2×C4×C3112yes—
360C22×D4C2×C4×C3112yes—
361C22×D4D4×C3112yes—
362C22×D4D4×C3112yes—
363C22×D4Q8×C3112yes—
364C23×C4—21no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—21no—
368C23×C4—22no—
369C23×C4—21no—
370C23×C4—22no—
371C23×C4—44no—
372C23×C4C2×C4×C3112yescomplemented
373C23×C4D4×C3111yescharacteristic
374C23×C4D4×C3114yes—
375C4×D4—216no—
376C4×D4—216no—
377#117—24no—
378#117—24no—
379C2×C4⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4C2×C4×C3114yes—
398C2×C22⋊C4C2×C4×C3112yescomplemented
399C2×C22⋊C4C2×C4×C3114yescomplemented
400C2×C22⋊C4D4×C3114yes—
401C2×C42—22no—
402#99—28no—
403#95—24no—
404#95—48no—
405C31#1074511yescharacteristic, direct product factor, Sylow
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24C22⋊C4×C3112yes—
415C24C22⋊C4×C3112yes—
416C24C4⋊C4×C3112yes—
417C24C22×C4×C3111yescharacteristic
418C24C22×C4×C3111yescharacteristic
419C24C22×C4×C3111yescharacteristic
420C24C2×D4×C3111yescharacteristic
421C24C2×D4×C3112yes—
422C24C2×D4×C3111yescharacteristic
423C24C2×D4×C3111yescharacteristic
424C24C2×D4×C3112yes—
425C24C2×Q8×C3111yescharacteristic
426C24#41×C3112yes—
427C24#41×C3112yes—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C42×C3114yes—
441C2×D4C22⋊C4×C3114yes—
442C2×D4C4⋊C4×C3114yes—
443C2×D4C4⋊C4×C3114yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4C22⋊C4×C3112yes—
478C22×C4C22⋊C4×C3112yes—
479C22×C4C22⋊C4×C3118yescomplemented
480C22×C4C4⋊C4×C3112yes—
481C4⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—48no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—44no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—44no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—82no—
524C23—81no—
525C23—81no—
526C23—82no—
527C23C31×#9514yescomplemented
528C23C2×C42×C3111yescharacteristic
529C23C2×C22⋊C4×C3111yescharacteristic
530C23C2×C22⋊C4×C3111yescharacteristic
531C23C2×C22⋊C4×C3112yes—
532C23C2×C22⋊C4×C3111yescharacteristic
533C23C2×C4⋊C4×C3111yescharacteristic
534C23C2×C4⋊C4×C3111yescharacteristic
535C23C2×C4⋊C4×C3111yescharacteristic
536C23C31×#11712yes—
537C23C4×D4×C3112yes—
538C23C4×D4×C3112yes—
539C23C4×D4×C3112yes—
540C23C4×D4×C3112yes—
541C23C31×#12011yescharacteristic
542C23C31×#12012yes—
543C23C31×#12011yescharacteristic
544C23C31×#12112yes—
545C23C31×#12112yes—
546C23C31×C22⋊Q812yes—
547C23C31×C22⋊Q812yes—
548C23C31×#12311yescharacteristic
549C23C31×#12311yescharacteristic
550C23C31×#12312yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—84no—
579C2×C4—88no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—84no—
584C2×C4—82no—
585C2×C4C31×#9514yescomplemented
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—21no—
591C22—22no—
592C22—22no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—22no—
598C22—24no—
599C22—24no—
600C22—22no—
601C22—22no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—44no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×C31×#9511yescharacteristic
622C22C4×C22⋊C4×C3112yes—
623C22C31×#37911yescharacteristic
624C22C31×#38012yes—
625C22C31×#38111yescharacteristic
626C22C31×#38511yescharacteristic
627C22C31×#38512yes—
628C22C31×#38511yescharacteristic
629C22C31×#38611yescharacteristic
630C22C31×#38612yes—
631C22C31×#38611yescharacteristic
632C22C31×B(4,𝔽2)12yes—
633C22C31×#45812yes—
634C4—24no—
635C4—44no—
636C4—48no—
637C4—82no—
638C4—84no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2C31×C22⋊#9511yescharacteristic
649C2C31×#179012yes—
650C2C31×#186712yes—
651C2C31×#188911yescharacteristic
652C2C31×#189011yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutatorC23C2×C42×C31
Frattini, cosocleC25C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#342C2semidirect
5. C31×C22⋊#95C2semidirect
10. C31×#518C4semidirect
20. C2×C31×#99C4semidirect
22. C31×#386C4semidirect
46. C23×C4×C31C2×C4semidirect
72. C2×C22⋊C4×C31C2×C4semidirect
73. C2×C22⋊C4×C31C2×C4semidirect
152. C22×C4×C31C22⋊C4semidirect
168. #10745C31direct (N × H)
201. C23×C31#95semidirect
259. C2×C4×C31#95semidirect
263. C2×#342C2×C31semidirect
264. C22⋊#95C2×C31semidirect
322. #518C4×C31semidirect
332. C2×#99C4×C31semidirect
334. #386C4×C31semidirect
372. C23×C4C2×C4×C31semidirect
398. C2×C22⋊C4C2×C4×C31semidirect
399. C2×C22⋊C4C2×C4×C31semidirect
405. C31#10745direct (N × H)
479. C22×C4C22⋊C4×C31semidirect
527. C23C31×#95semidirect
585. C2×C4C31×#95semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5182
C22×C31×#992
C2×C31×#3862
C2×C31×#3422
C31×C22⋊#952
#1074531