Finite Group Databasebeta

← C31×#10995 #21467754

Subgroups — C31×#10995 #21467754

Order 7936.

1934 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#534C211yesmaximal, characteristic
2C22×C31×#99C212yesmaximal, complemented
3C2×C31×#386C212yesmaximal, complemented
4C2×C31×#342C211yesmaximal, characteristic, complemented
5C31×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C31C2212yes—
7C24×C4×C31C2211yescharacteristic
8C31×#534—24no—
9C31×#534—22no—
10C31×#534C414yescomplemented
11C2×C31×#123—22no—
12C2×C31×#121—22no—
13C2×C31×#120—22no—
14C22×C22⋊C4×C31—22no—
15C22×C22⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C2×C31×#99—24no—
19C2×C31×#99—24no—
20C2×C31×#99—24no—
21C31×#386—24no—
22C31×#386—24no—
23C2×C31×#95—22no—
24C2×C31×#95—22no—
25C31×#342—22no—
26C25×C31D412yes—
27C25×C31C2311yescharacteristic
28C22×D4×C31—22no—
29C22×D4×C31—22no—
30C22×D4×C31—22no—
31C22×D4×C31—22no—
32C22×D4×C31—22no—
33C22×D4×C31—22no—
34C22×D4×C31—22no—
35C22×D4×C31—22no—
36C22×D4×C31—22no—
37C22×D4×C31—22no—
38C22×D4×C31—22no—
39C22×D4×C31—22no—
40C22×D4×C31—22no—
41C22×D4×C31C2×C414yes—
42C22×D4×C31D414yes—
43C23×C4×C31—22no—
44C23×C4×C31—21no—
45C23×C4×C31—22no—
46C23×C4×C31—21no—
47C23×C4×C31—22no—
48C23×C4×C31—21no—
49C23×C4×C31—44no—
50C23×C4×C31D412yes—
51C23×C4×C31D412yes—
52C23×C4×C31D412yescomplemented
53C31×#123—28no—
54C31×#123—28no—
55C31×#121—28no—
56C31×#121—28no—
57C31×#120—28no—
58C31×#120—28no—
59C2×C4⋊C4×C31—22no—
60C2×C22⋊C4×C31—24no—
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—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—28no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—21no—
72C2×C22⋊C4×C31—48no—
73C2×C22⋊C4×C31C2×C412yes—
74C2×C22⋊C4×C31D412yes—
75C2×C22⋊C4×C31D412yescomplemented
76C2×C22⋊C4×C31D414yescomplemented
77C31×#99—216no—
78C31×#95—28no—
79C31×#95—44no—
80C24×C31—22no—
81C24×C31—22no—
82C24×C31—22no—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31—22no—
86C24×C31—42no—
87C24×C31—42no—
88C24×C31—44no—
89C24×C31—44no—
90C24×C31C22⋊C414yescomplemented
91C24×C31C22×C411yescharacteristic
92C24×C31C2×D412yes—
93C24×C31C2×D411yescharacteristic
94C24×C31C2×D412yes—
95C24×C31C2×D411yescharacteristic
96C24×C31C2×D411yescharacteristic
97C24×C31C2×D411yescharacteristic
98C24×C31C2×D412yes—
99C24×C31#4112yes—
100C24×C31#4111yescharacteristic
101C24×C31#4111yescharacteristic
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×C31—24no—
114C2×D4×C31—28no—
115C2×D4×C31—42no—
116C2×D4×C31—42no—
117C2×D4×C31—42no—
118C2×D4×C31—42no—
119C2×D4×C31—42no—
120C2×D4×C31—42no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31—42no—
124C2×D4×C31—42no—
125C2×D4×C31—42no—
126C2×D4×C31—42no—
127C2×D4×C31—42no—
128C2×D4×C31—42no—
129C2×D4×C31—42no—
130C2×D4×C31—42no—
131C2×D4×C31—82no—
132C2×D4×C31—82no—
133C22×C4×C31—24no—
134C22×C4×C31—28no—
135C22×C4×C31—22no—
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—24no—
146C22×C4×C31—22no—
147C22×C4×C31—44no—
148C22×C4×C31—48no—
149C22×C4×C31—44no—
150C22×C4×C31—42no—
151C22×C4×C31—44no—
152C22×C4×C31—41no—
153C22×C4×C31—42no—
154C22×C4×C31—41no—
155C22×C4×C31—42no—
156C22×C4×C31—42no—
157C22×C4×C31—42no—
158C22×C4×C31—44no—
159C22×C4×C31—42no—
160C22×C4×C31—44no—
161C22×C4×C31—42no—
162C22×C4×C31—41no—
163C22×C4×C31—42no—
164C22×C4×C31—41no—
165C22×C4×C31C22⋊C414yescomplemented
166C22×C4×C31C22⋊C414yescomplemented
167C4⋊C4×C31—28no—
168C22⋊C4×C31—216no—
169C22⋊C4×C31—24no—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—24no—
174C22⋊C4×C31—416no—
175C22⋊C4×C31—42no—
176C22⋊C4×C31—42no—
177C22⋊C4×C31—42no—
178#10995C3111yesmaximal, characteristic, direct product factor, Sylow
179C23×C31—22no—
180C23×C31—24no—
181C23×C31—22no—
182C23×C31—24no—
183C23×C31—24no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—41no—
187C23×C31—42no—
188C23×C31—41no—
189C23×C31—42no—
190C23×C31—41no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31—42no—
194C23×C31—44no—
195C23×C31—41no—
196C23×C31—42no—
197C23×C31—44no—
198C23×C31—48no—
199C23×C31—44no—
200C23×C31—44no—
201C23×C31—48no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—42no—
205C23×C31—42no—
206C23×C31—44no—
207C23×C31—44no—
208C23×C31—84no—
209C23×C31—82no—
210C23×C31—82no—
211C23×C31—84no—
212C23×C31C2×C22⋊C412yes—
213C23×C31C2×C22⋊C411yescharacteristic
214C23×C31C4×D411yescharacteristic
215C23×C31C4×D411yescharacteristic
216C23×C31C4×D412yes—
217C23×C31#12012yes—
218C23×C31#12011yescharacteristic
219C23×C31#12012yes—
220C23×C31#12012yes—
221C23×C31#12011yescharacteristic
222C23×C31#12112yes—
223C23×C31#12112yes—
224C23×C31#12111yescharacteristic
225C23×C31#12111yescharacteristic
226C23×C31#12112yes—
227C23×C31#12112yes—
228C23×C31#12112yes—
229C23×C31#12312yes—
230C23×C31#12312yes—
231C23×C31#12411yescharacteristic
232C23×C31#12411yescharacteristic
233C23×C31#12711yescharacteristic
234C23×C31#12711yescharacteristic
235D4×C31—44no—
236D4×C31—44no—
237D4×C31—44no—
238D4×C31—44no—
239D4×C31—44no—
240D4×C31—44no—
241D4×C31—44no—
242D4×C31—44no—
243D4×C31—88no—
244C2×C4×C31—28no—
245C2×C4×C31—24no—
246C2×C4×C31—24no—
247C2×C4×C31—24no—
248C2×C4×C31—24no—
249C2×C4×C31—24no—
250C2×C4×C31—44no—
251C2×C4×C31—42no—
252C2×C4×C31—44no—
253C2×C4×C31—48no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—42no—
259C2×C4×C31—44no—
260C2×C4×C31—42no—
261C2×C4×C31—42no—
262C2×C4×C31—44no—
263C2×C4×C31—44no—
264C2×C4×C31—44no—
265C2×C4×C31—44no—
266C2×C4×C31—44no—
267C2×C4×C31—42no—
268C2×C4×C31—82no—
269C2×C4×C31—81no—
270C2×C4×C31—81no—
271C2×C4×C31—84no—
272C2×C4×C31—82no—
273C2×C4×C31—84no—
274C2×#534C2×C3111yescharacteristic
275C22×#99C2×C3112yescomplemented
276C2×#386C2×C3112yescomplemented
277C2×#342C2×C3111yescharacteristic, complemented
278C22⋊#95C2×C3111yescharacteristic, complemented
279C22×C31—22no—
280C22×C31—21no—
281C22×C31—21no—
282C22×C31—22no—
283C22×C31—22no—
284C22×C31—21no—
285C22×C31—22no—
286C22×C31—21no—
287C22×C31—22no—
288C22×C31—24no—
289C22×C31—24no—
290C22×C31—22no—
291C22×C31—22no—
292C22×C31—22no—
293C22×C31—24no—
294C22×C31—24no—
295C22×C31—41no—
296C22×C31—42no—
297C22×C31—41no—
298C22×C31—42no—
299C22×C31—42no—
300C22×C31—42no—
301C22×C31—42no—
302C22×C31—42no—
303C22×C31—41no—
304C22×C31—41no—
305C22×C31—48no—
306C22×C31—44no—
307C22×C31—48no—
308C22×C31—84no—
309C22×C31—84no—
310C22×C31—84no—
311C22×C31—82no—
312C22×C31—82no—
313C22×C31—84no—
314C22×C31#37911yescharacteristic
315C22×C31#38612yes—
316C22×C31#38612yes—
317C22×C31#39011yescharacteristic
318C22×C31#39011yescharacteristic
319C22×C31#39212yes—
320C22×C31#39211yescharacteristic
321C22×C31#39211yescharacteristic
322C22×C31#39412yes—
323C22×C31#39411yescharacteristic
324C22×C31#39411yescharacteristic
325C22×C31B(4,𝔽2)12yes—
326C22×C31#45812yes—
327C4×C31—44no—
328C4×C31—44no—
329C4×C31—44no—
330C4×C31—84no—
331C4×C31—82no—
332C23×D4C22×C3112yes—
333C24×C4C22×C3111yescharacteristic
334#534—24no—
335#534—22no—
336#534C4×C3114yescomplemented
337C2×#123—22no—
338C2×#121—22no—
339C2×#120—22no—
340C22×C22⋊C4—22no—
341C22×C22⋊C4C22×C3111yescharacteristic
342C22×C22⋊C4C22×C3112yes—
343C22×C22⋊C4C22×C3111yescharacteristic
344C2×#99—24no—
345C2×#99—24no—
346C2×#99—24no—
347#386—24no—
348#386—24no—
349C2×#95—22no—
350C2×#95—22no—
351#342—22no—
352C2×C31—22no—
353C2×C31—21no—
354C2×C31—22no—
355C2×C31—22no—
356C2×C31—22no—
357C2×C31—21no—
358C2×C31—21no—
359C2×C31—21no—
360C2×C31—84no—
361C2×C31#143811yescharacteristic
362C2×C31#179012yes—
363C2×C31#202111yescharacteristic
364C2×C31#202211yescharacteristic
365C2×C31#204412yes—
366C25D4×C3112yes—
367C25C23×C3111yescharacteristic
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—22no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4C2×C4×C3114yes—
382C22×D4D4×C3114yes—
383C23×C4—22no—
384C23×C4—21no—
385C23×C4—22no—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4—21no—
389C23×C4—44no—
390C23×C4D4×C3112yes—
391C23×C4D4×C3112yes—
392C23×C4D4×C3112yescomplemented
393#123—28no—
394#123—28no—
395#121—28no—
396#121—28no—
397#120—28no—
398#120—28no—
399C2×C4⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—28no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—48no—
413C2×C22⋊C4C2×C4×C3112yes—
414C2×C22⋊C4D4×C3112yes—
415C2×C22⋊C4D4×C3114yescomplemented
416C2×C22⋊C4D4×C3112yescomplemented
417#99—216no—
418#95—28no—
419#95—44no—
420C31#1099511yescharacteristic, direct product factor, Sylow
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—44no—
430C24—44no—
431C24C22⋊C4×C3114yescomplemented
432C24C22×C4×C3111yescharacteristic
433C24C2×D4×C3112yes—
434C24C2×D4×C3111yescharacteristic
435C24C2×D4×C3112yes—
436C24C2×D4×C3111yescharacteristic
437C24C2×D4×C3111yescharacteristic
438C24C2×D4×C3111yescharacteristic
439C24C2×D4×C3112yes—
440C24#41×C3112yes—
441C24#41×C3111yescharacteristic
442C24#41×C3111yescharacteristic
443C2×D4—24no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—28no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—82no—
473C2×D4—82no—
474C22×C4—24no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—24no—
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—24no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—44no—
491C22×C4—42no—
492C22×C4—44no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—44no—
500C22×C4—42no—
501C22×C4—44no—
502C22×C4—42no—
503C22×C4—41no—
504C22×C4—42no—
505C22×C4—41no—
506C22×C4C22⋊C4×C3114yescomplemented
507C22×C4C22⋊C4×C3114yescomplemented
508C4⋊C4—28no—
509C22⋊C4—216no—
510C22⋊C4—24no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—416no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C23—22no—
520C23—24no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—42no—
530C23—41no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—44no—
535C23—41no—
536C23—42no—
537C23—44no—
538C23—48no—
539C23—44no—
540C23—44no—
541C23—48no—
542C23—44no—
543C23—44no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—84no—
549C23—82no—
550C23—82no—
551C23—84no—
552C23C2×C22⋊C4×C3112yes—
553C23C2×C22⋊C4×C3111yescharacteristic
554C23C4×D4×C3111yescharacteristic
555C23C4×D4×C3111yescharacteristic
556C23C4×D4×C3112yes—
557C23C31×#12012yes—
558C23C31×#12011yescharacteristic
559C23C31×#12012yes—
560C23C31×#12012yes—
561C23C31×#12011yescharacteristic
562C23C31×#12112yes—
563C23C31×#12112yes—
564C23C31×#12111yescharacteristic
565C23C31×#12111yescharacteristic
566C23C31×#12112yes—
567C23C31×#12112yes—
568C23C31×#12112yes—
569C23C31×#12312yes—
570C23C31×#12312yes—
571C23C31×#12411yescharacteristic
572C23C31×#12411yescharacteristic
573C23C31×#12711yescharacteristic
574C23C31×#12711yescharacteristic
575D4—44no—
576D4—44no—
577D4—44no—
578D4—44no—
579D4—44no—
580D4—44no—
581D4—44no—
582D4—44no—
583D4—88no—
584C2×C4—28no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—44no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—48no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—44no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—44no—
607C2×C4—42no—
608C2×C4—82no—
609C2×C4—81no—
610C2×C4—81no—
611C2×C4—84no—
612C2×C4—82no—
613C2×C4—84no—
614C22—22no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—22no—
619C22—21no—
620C22—22no—
621C22—21no—
622C22—22no—
623C22—24no—
624C22—24no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—24no—
629C22—24no—
630C22—41no—
631C22—42no—
632C22—41no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—41no—
640C22—48no—
641C22—44no—
642C22—48no—
643C22—84no—
644C22—84no—
645C22—84no—
646C22—82no—
647C22—82no—
648C22—84no—
649C22C31×#37911yescharacteristic
650C22C31×#38612yes—
651C22C31×#38612yes—
652C22C31×#39011yescharacteristic
653C22C31×#39011yescharacteristic
654C22C31×#39212yes—
655C22C31×#39211yescharacteristic
656C22C31×#39211yescharacteristic
657C22C31×#39412yes—
658C22C31×#39411yescharacteristic
659C22C31×#39411yescharacteristic
660C22C31×B(4,𝔽2)12yes—
661C22C31×#45812yes—
662C4—44no—
663C4—44no—
664C4—44no—
665C4—84no—
666C4—82no—
667C2—22no—
668C2—21no—
669C2—22no—
670C2—22no—
671C2—22no—
672C2—21no—
673C2—21no—
674C2—21no—
675C2—84no—
676C2C31×#143811yescharacteristic
677C2C31×#179012yes—
678C2C31×#202111yescharacteristic
679C2C31×#202211yescharacteristic
680C2C31×#204412yes—
subgroupG/H
center, socleC23×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC2×C31×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C31×#99C2semidirect
3. C2×C31×#386C2semidirect
4. C2×C31×#342C2semidirect
5. C31×C22⋊#95C2semidirect
10. C31×#534C4semidirect
52. C23×C4×C31D4semidirect
75. C2×C22⋊C4×C31D4semidirect
76. C2×C22⋊C4×C31D4semidirect
90. C24×C31C22⋊C4semidirect
165. C22×C4×C31C22⋊C4semidirect
166. C22×C4×C31C22⋊C4semidirect
178. #10995C31direct (N × H)
275. C22×#99C2×C31semidirect
276. C2×#386C2×C31semidirect
277. C2×#342C2×C31semidirect
278. C22⋊#95C2×C31semidirect
336. #534C4×C31semidirect
392. C23×C4D4×C31semidirect
415. C2×C22⋊C4D4×C31semidirect
416. C2×C22⋊C4D4×C31semidirect
420. C31#10995direct (N × H)
431. C24C22⋊C4×C31semidirect
506. C22×C4C22⋊C4×C31semidirect
507. C22×C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5342
C22×C31×#992
C2×C31×#3862
C2×C31×#3422
C31×C22⋊#952
#1099531