Finite Group Databasebeta

← C31×#10991 #21467750

Subgroups — C31×#10991 #21467750

Order 7936.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#120C211yesmaximal, characteristic
2C22×C31×#99C211yesmaximal, characteristic, complemented
3C31×#2308C211yesmaximal, characteristic, complemented
4C2×C31×#379C212yesmaximal, complemented
5C2×C31×#342C212yesmaximal, complemented
6C26×C31C2211yescharacteristic
7C23×D4×C31—21no—
8C23×D4×C31C2211yescharacteristic
9C2×C31×#120—24no—
10C2×C31×#120—22no—
11C2×C31×#120—24no—
12C2×C31×#120C414yescomplemented
13C22×C22⋊C4×C31—21no—
14C22×C22⋊C4×C31—24no—
15C22×C22⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2211yescharacteristic
18C2×C31×#99—22no—
19C2×C31×#99—24no—
20C31×#386—24no—
21C31×#381—21no—
22C31×#379—21no—
23C31×#379—24no—
24C31×#379—24no—
25C31×#342—24no—
26C25×C31—22no—
27C25×C31—21no—
28C25×C31—21no—
29C25×C31—22no—
30C25×C31—22no—
31C25×C31—22no—
32C25×C31—22no—
33C25×C31—48no—
34C25×C31C2×C412yes—
35C25×C31D414yes—
36C25×C31D411yescharacteristic
37C25×C31C2311yescharacteristic
38C22×D4×C31—28no—
39C22×D4×C31—24no—
40C22×D4×C31—22no—
41C22×D4×C31—22no—
42C22×D4×C31—22no—
43C22×D4×C31—22no—
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—48no—
47C22×D4×C31C2×C412yes—
48C22×D4×C31D412yes—
49C23×C4×C31—21no—
50C23×C4×C31—22no—
51C23×C4×C31D411yescharacteristic
52C23×C4×C31D414yescomplemented
53C31×#120—216no—
54C31×#120—28no—
55C31×#120—28no—
56C2×C22⋊C4×C31—28no—
57C2×C22⋊C4×C31—22no—
58C2×C22⋊C4×C31—21no—
59C2×C22⋊C4×C31—24no—
60C2×C22⋊C4×C31—22no—
61C2×C22⋊C4×C31—22no—
62C2×C22⋊C4×C31—22no—
63C2×C22⋊C4×C31—22no—
64C2×C22⋊C4×C31—216no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—22no—
72C2×C22⋊C4×C31—24no—
73C2×C22⋊C4×C31—416no—
74C2×C22⋊C4×C31C2×C412yes—
75C2×C22⋊C4×C31D414yes—
76C2×C22⋊C4×C31D414yescomplemented
77C31×#99—28no—
78C31×#95—24no—
79C24×C31—216no—
80C24×C31—28no—
81C24×C31—22no—
82C24×C31—24no—
83C24×C31—24no—
84C24×C31—24no—
85C24×C31—24no—
86C24×C31—22no—
87C24×C31—24no—
88C24×C31—24no—
89C24×C31—22no—
90C24×C31—21no—
91C24×C31—24no—
92C24×C31—24no—
93C24×C31—22no—
94C24×C31—21no—
95C24×C31—48no—
96C24×C31—416no—
97C24×C31—44no—
98C24×C31—48no—
99C24×C31—44no—
100C24×C31—416no—
101C24×C31—48no—
102C24×C31—416no—
103C24×C31—416no—
104C24×C31—416no—
105C24×C31—44no—
106C24×C31—41no—
107C24×C31—41no—
108C24×C31—42no—
109C24×C31—42no—
110C24×C31—42no—
111C24×C31—42no—
112C24×C31—41no—
113C24×C31—41no—
114C24×C31—42no—
115C24×C31—42no—
116C24×C31C22⋊C414yescomplemented
117C24×C31C22⋊C412yescomplemented
118C24×C31C22×C411yescharacteristic
119C24×C31C2×D411yescharacteristic
120C24×C31C2×D412yes—
121C24×C31C2×D412yes—
122C24×C31C2×D411yescharacteristic
123C24×C31C2×D412yes—
124C24×C31C2×D412yes—
125C24×C31#4112yes—
126C24×C31#4112yes—
127C2×D4×C31—216no—
128C2×D4×C31—22no—
129C2×D4×C31—22no—
130C2×D4×C31—24no—
131C2×D4×C31—24no—
132C2×D4×C31—22no—
133C2×D4×C31—24no—
134C2×D4×C31—24no—
135C2×D4×C31—22no—
136C2×D4×C31—416no—
137C2×D4×C31—432no—
138C2×D4×C31—42no—
139C2×D4×C31—42no—
140C2×D4×C31—42no—
141C2×D4×C31—42no—
142C2×D4×C31—42no—
143C2×D4×C31—42no—
144C2×D4×C31—42no—
145C2×D4×C31—42no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—24no—
149C22×C4×C31—21no—
150C22×C4×C31—22no—
151C22×C4×C31—21no—
152C22×C4×C31—24no—
153C22×C4×C31—24no—
154C22×C4×C31—24no—
155C22×C4×C31—24no—
156C22×C4×C31—44no—
157C22×C4×C31—48no—
158C22×C4×C31—48no—
159C22×C4×C31—42no—
160C22×C4×C31—42no—
161C22×C4×C31C22⋊C412yescomplemented
162C22⋊C4×C31—216no—
163C22⋊C4×C31—22no—
164C22⋊C4×C31—24no—
165C22⋊C4×C31—24no—
166C22⋊C4×C31—24no—
167C22⋊C4×C31—432no—
168C22⋊C4×C31—42no—
169C22⋊C4×C31—42no—
170C22⋊C4×C31—42no—
171C22⋊C4×C31—42no—
172C22⋊C4×C31—42no—
173C22⋊C4×C31—42no—
174C22⋊C4×C31—84no—
175C22⋊C4×C31C22⋊C414yescomplemented
176#10991C3111yesmaximal, characteristic, direct product factor, Sylow
177C23×C31—28no—
178C23×C31—24no—
179C23×C31—216no—
180C23×C31—28no—
181C23×C31—216no—
182C23×C31—216no—
183C23×C31—216no—
184C23×C31—24no—
185C23×C31—28no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—48no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—44no—
193C23×C31—44no—
194C23×C31—44no—
195C23×C31—44no—
196C23×C31—44no—
197C23×C31—44no—
198C23×C31—416no—
199C23×C31—48no—
200C23×C31—48no—
201C23×C31—48no—
202C23×C31—48no—
203C23×C31—416no—
204C23×C31—416no—
205C23×C31—48no—
206C23×C31—416no—
207C23×C31—48no—
208C23×C31—416no—
209C23×C31—416no—
210C23×C31—416no—
211C23×C31—416no—
212C23×C31—44no—
213C23×C31—48no—
214C23×C31—48no—
215C23×C31—416no—
216C23×C31—48no—
217C23×C31—416no—
218C23×C31—42no—
219C23×C31—42no—
220C23×C31—44no—
221C23×C31—44no—
222C23×C31—44no—
223C23×C31—44no—
224C23×C31—44no—
225C23×C31—48no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31—44no—
229C23×C31—82no—
230C23×C31—84no—
231C23×C31C2×C22⋊C411yescharacteristic
232C23×C31C2×C22⋊C411yescharacteristic
233C23×C31C2×C22⋊C411yescharacteristic
234C23×C31C4×D412yes—
235C23×C31C4×D412yes—
236C23×C31#12012yes—
237C23×C31#12012yes—
238C23×C31#12012yes—
239C23×C31#12011yescharacteristic
240C23×C31#12011yescharacteristic
241C23×C31#12112yes—
242C23×C31#12112yes—
243C23×C31#12112yes—
244C23×C31#12112yes—
245C23×C31#12112yes—
246C23×C31#12112yes—
247C23×C31#12311yescharacteristic
248C23×C31#12311yescharacteristic
249C23×C31#12312yes—
250C23×C31#12412yes—
251C23×C31#12712yes—
252D4×C31—432no—
253D4×C31—44no—
254D4×C31—44no—
255D4×C31—44no—
256D4×C31—44no—
257C2×C4×C31—22no—
258C2×C4×C31—24no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—44no—
262C2×C4×C31—48no—
263C2×C4×C31—42no—
264C2×C4×C31—42no—
265C2×C4×C31—48no—
266C2×C4×C31—48no—
267C2×C4×C31—44no—
268C2×C4×C31—44no—
269C2×C4×C31—48no—
270C2×C4×C31—84no—
271C2×C4×C31—84no—
272C2×C4×C31—84no—
273C22×#120C2×C3111yescharacteristic
274C22×#99C2×C3111yescharacteristic, complemented
275#2308C2×C3111yescharacteristic, complemented
276C2×#379C2×C3112yescomplemented
277C2×#342C2×C3112yescomplemented
278C22×C31—22no—
279C22×C31—24no—
280C22×C31—24no—
281C22×C31—22no—
282C22×C31—24no—
283C22×C31—24no—
284C22×C31—24no—
285C22×C31—24no—
286C22×C31—24no—
287C22×C31—24no—
288C22×C31—28no—
289C22×C31—216no—
290C22×C31—41no—
291C22×C31—41no—
292C22×C31—42no—
293C22×C31—42no—
294C22×C31—41no—
295C22×C31—42no—
296C22×C31—42no—
297C22×C31—42no—
298C22×C31—41no—
299C22×C31—42no—
300C22×C31—44no—
301C22×C31—416no—
302C22×C31—48no—
303C22×C31—48no—
304C22×C31—416no—
305C22×C31—416no—
306C22×C31—416no—
307C22×C31—44no—
308C22×C31—48no—
309C22×C31—44no—
310C22×C31—416no—
311C22×C31—44no—
312C22×C31—42no—
313C22×C31—82no—
314C22×C31—84no—
315C22×C31—84no—
316C22×C31#37911yescharacteristic
317C22×C31#38611yescharacteristic
318C22×C31#38612yes—
319C22×C31#38611yescharacteristic
320C22×C31#39012yes—
321C22×C31#39212yes—
322C22×C31#39212yes—
323C22×C31#39412yes—
324C22×C31#39412yes—
325C22×C31B(4,𝔽2)14yes—
326C4×C31—44no—
327C4×C31—42no—
328C4×C31—84no—
329C4×C31—84no—
330C26C22×C3111yescharacteristic
331C23×D4—21no—
332C23×D4C22×C3111yescharacteristic
333C2×#120—24no—
334C2×#120—22no—
335C2×#120—24no—
336C2×#120C4×C3114yescomplemented
337C22×C22⋊C4—21no—
338C22×C22⋊C4—24no—
339C22×C22⋊C4C22×C3112yes—
340C22×C22⋊C4C22×C3112yes—
341C22×C22⋊C4C22×C3111yescharacteristic
342C2×#99—22no—
343C2×#99—24no—
344#386—24no—
345#381—21no—
346#379—21no—
347#379—24no—
348#379—24no—
349#342—24no—
350C2×C31—21no—
351C2×C31—22no—
352C2×C31—22no—
353C2×C31—21no—
354C2×C31—22no—
355C2×C31—22no—
356C2×C31—22no—
357C2×C31—48no—
358C2×C31—82no—
359C2×C31#143811yescharacteristic
360C2×C31#188912yes—
361C2×C31#202114yes—
362C25—22no—
363C25—21no—
364C25—21no—
365C25—22no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—48no—
370C25C2×C4×C3112yes—
371C25D4×C3114yes—
372C25D4×C3111yescharacteristic
373C25C23×C3111yescharacteristic
374C22×D4—28no—
375C22×D4—24no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—48no—
383C22×D4C2×C4×C3112yes—
384C22×D4D4×C3112yes—
385C23×C4—21no—
386C23×C4—22no—
387C23×C4D4×C3111yescharacteristic
388C23×C4D4×C3114yescomplemented
389#120—216no—
390#120—28no—
391#120—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—216no—
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—24no—
409C2×C22⋊C4—416no—
410C2×C22⋊C4C2×C4×C3112yes—
411C2×C22⋊C4D4×C3114yes—
412C2×C22⋊C4D4×C3114yescomplemented
413#99—28no—
414#95—24no—
415C31#1099111yescharacteristic, direct product factor, Sylow
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—48no—
439C24—416no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C3114yescomplemented
454C24C22⋊C4×C3112yescomplemented
455C24C22×C4×C3111yescharacteristic
456C24C2×D4×C3111yescharacteristic
457C24C2×D4×C3112yes—
458C24C2×D4×C3112yes—
459C24C2×D4×C3111yescharacteristic
460C24C2×D4×C3112yes—
461C24C2×D4×C3112yes—
462C24#41×C3112yes—
463C24#41×C3112yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C3112yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C3114yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—28no—
517C23—216no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—42no—
528C23—44no—
529C23—44no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—416no—
535C23—48no—
536C23—48no—
537C23—48no—
538C23—48no—
539C23—416no—
540C23—416no—
541C23—48no—
542C23—416no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—48no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—44no—
562C23—44no—
563C23—42no—
564C23—42no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C3111yescharacteristic
568C23C2×C22⋊C4×C3111yescharacteristic
569C23C2×C22⋊C4×C3111yescharacteristic
570C23C4×D4×C3112yes—
571C23C4×D4×C3112yes—
572C23C31×#12012yes—
573C23C31×#12012yes—
574C23C31×#12012yes—
575C23C31×#12011yescharacteristic
576C23C31×#12011yescharacteristic
577C23C31×#12112yes—
578C23C31×#12112yes—
579C23C31×#12112yes—
580C23C31×#12112yes—
581C23C31×#12112yes—
582C23C31×#12112yes—
583C23C31×#12311yescharacteristic
584C23C31×#12311yescharacteristic
585C23C31×#12312yes—
586C23C31×#12412yes—
587C23C31×#12712yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—44no—
605C2×C4—44no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—22no—
610C22—24no—
611C22—24no—
612C22—22no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—48no—
640C22—44no—
641C22—416no—
642C22—44no—
643C22—42no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22C31×#37911yescharacteristic
648C22C31×#38611yescharacteristic
649C22C31×#38612yes—
650C22C31×#38611yescharacteristic
651C22C31×#39012yes—
652C22C31×#39212yes—
653C22C31×#39212yes—
654C22C31×#39412yes—
655C22C31×#39412yes—
656C22C31×B(4,𝔽2)14yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2C31×#143811yescharacteristic
671C2C31×#188912yes—
672C2C31×#202114yes—
subgroupG/H
center, socleC23×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC22×C31×#120C2
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. C31×#2308C2semidirect
4. C2×C31×#379C2semidirect
5. C2×C31×#342C2semidirect
12. C2×C31×#120C4semidirect
52. C23×C4×C31D4semidirect
76. C2×C22⋊C4×C31D4semidirect
116. C24×C31C22⋊C4semidirect
117. C24×C31C22⋊C4semidirect
161. C22×C4×C31C22⋊C4semidirect
175. C22⋊C4×C31C22⋊C4semidirect
176. #10991C31direct (N × H)
274. C22×#99C2×C31semidirect
275. #2308C2×C31semidirect
276. C2×#379C2×C31semidirect
277. C2×#342C2×C31semidirect
336. C2×#120C4×C31semidirect
388. C23×C4D4×C31semidirect
412. C2×C22⋊C4D4×C31semidirect
415. C31#10991direct (N × H)
453. C24C22⋊C4×C31semidirect
454. C24C22⋊C4×C31semidirect
498. C22×C4C22⋊C4×C31semidirect
512. C22⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1202
C22×C31×#992
C31×#23082
C2×C31×#3792
C2×C31×#3422
#1099131