Finite Group Databasebeta

← C31×#9079 #21465838

Subgroups — C31×#9079 #21465838

Order 7936.

1136 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊C8C211yesmaximal, characteristic, complemented
2C2×C31×#386C211yesmaximal, characteristic
3C31×#1779C211yesmaximal, characteristic, complemented
4C2×C31×#323C212yesmaximal, complemented
5C31×#1280C212yesmaximal, complemented
6C23×D4×C31C411yescharacteristic
7C24×C4×C31C2211yescharacteristic
8C23×C8×C31—21no—
9C22×C22⋊C4×C31C411yescharacteristic
10C22×C22⋊C4×C31C411yescharacteristic
11C22×C22⋊C4×C31C2211yescharacteristic
12C2×C31×C22⋊C8—21no—
13C2×C31×C22⋊C8—24no—
14C2×C31×C22⋊C8—21no—
15C2×C31×C22⋊C8—21no—
16C2×C31×C22⋊C8C2212yes—
17C2×C31×C22⋊C8C2212yes—
18C31×#386—21no—
19C31×#386—21no—
20C31×#386—21no—
21C31×#386—21no—
22C2×C31×#95C411yescharacteristic
23C2×C31×#95C2211yescharacteristic
24C31×#323—24no—
25C25×C31C2×C411yescharacteristic
26C25×C31C2×C411yescharacteristic
27C22×D4×C31—21no—
28C22×D4×C31—21no—
29C22×D4×C31—22no—
30C22×D4×C31—42no—
31C22×D4×C31—42no—
32C22×D4×C31C814yescomplemented
33C23×C4×C31—22no—
34C23×C4×C31—22no—
35C23×C4×C31—42no—
36C23×C4×C31—42no—
37C23×C4×C31C2×C411yescharacteristic
38C23×C4×C31C2×C411yescharacteristic
39C23×C4×C31C2×C411yescharacteristic
40C23×C4×C31C2×C411yescharacteristic
41C23×C4×C31D411yescharacteristic
42C23×C4×C31D411yescharacteristic
43C23×C4×C31D411yescharacteristic
44C23×C4×C31D411yescharacteristic
45C23×C4×C31C2311yescharacteristic
46C22×C8×C31—24no—
47C22×C8×C31—22no—
48C22×C8×C31—22no—
49C22×C8×C31—42no—
50C22×C8×C31—42no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—21no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—22no—
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C2×C22⋊C4×C31—22no—
59C2×C22⋊C4×C31—42no—
60C2×C22⋊C4×C31—42no—
61C31×C22⋊C8—24no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—22no—
64C31×C22⋊C8—22no—
65C31×C22⋊C8—42no—
66C31×C22⋊C8—42no—
67C31×C22⋊C8D414yescomplemented
68C31×#95—21no—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—21no—
72C24×C31—22no—
73C24×C31—22no—
74C24×C31—22no—
75C24×C31—22no—
76C24×C31—21no—
77C24×C31—21no—
78C24×C31—22no—
79C24×C31—22no—
80C24×C31—41no—
81C24×C31—41no—
82C24×C31—41no—
83C24×C31—41no—
84C24×C31—41no—
85C24×C31—41no—
86C24×C31C22⋊C411yescharacteristic
87C24×C31C22⋊C411yescharacteristic
88C24×C31C2×C812yes—
89C24×C31C2×C812yescomplemented
90C24×C31M1612yes—
91C24×C31C22×C411yescharacteristic
92C2×D4×C31—24no—
93C2×D4×C31—24no—
94C2×D4×C31—48no—
95C2×D4×C31—42no—
96C2×D4×C31—42no—
97C2×D4×C31—42no—
98C2×D4×C31—42no—
99C2×D4×C31—48no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—22no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—41no—
119C22×C4×C31—41no—
120C22×C4×C31—41no—
121C22×C4×C31—41no—
122C22×C4×C31—41no—
123C22×C4×C31—41no—
124C22×C4×C31—41no—
125C22×C4×C31—48no—
126C22×C4×C31—48no—
127C22×C4×C31—41no—
128C22×C4×C31—41no—
129C22×C4×C31—41no—
130C22×C4×C31—41no—
131C22×C4×C31—41no—
132C22×C4×C31—41no—
133C22×C4×C31C22⋊C411yescharacteristic
134C22×C4×C31C22⋊C411yescharacteristic
135C22×C4×C31C2×C812yescomplemented
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D412yes—
139C22×C4×C31#4112yes—
140C2×C8×C31—24no—
141C2×C8×C31—48no—
142C2×C8×C31—42no—
143C2×C8×C31—42no—
144C2×C8×C31—42no—
145C2×C8×C31—42no—
146C2×C8×C31—42no—
147C22⋊C4×C31—42no—
148C22⋊C4×C31—42no—
149C22⋊C4×C31—42no—
150C22⋊C4×C31—42no—
151C22⋊C4×C31—41no—
152C22⋊C4×C31—42no—
153C22⋊C4×C31—41no—
154#9079C3111yesmaximal, characteristic, direct product factor, Sylow
155C23×C31—21no—
156C23×C31—21no—
157C23×C31—21no—
158C23×C31—21no—
159C23×C31—21no—
160C23×C31—21no—
161C23×C31—21no—
162C23×C31—21no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—21no—
166C23×C31—21no—
167C23×C31—21no—
168C23×C31—21no—
169C23×C31—21no—
170C23×C31—21no—
171C23×C31—24no—
172C23×C31—24no—
173C23×C31—22no—
174C23×C31—24no—
175C23×C31—42no—
176C23×C31—42no—
177C23×C31—44no—
178C23×C31—44no—
179C23×C31—44no—
180C23×C31—44no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31—42no—
184C23×C31—42no—
185C23×C31—41no—
186C23×C31—41no—
187C23×C31—41no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31—41no—
191C23×C31—42no—
192C23×C31—82no—
193C23×C31—82no—
194C23×C31—82no—
195C23×C31—82no—
196C23×C31C22⋊C812yes—
197C23×C31C22⋊C812yes—
198C23×C31#9912yes—
199C23×C31#10012yes—
200C23×C31C2×C22⋊C411yescharacteristic
201C23×C31C4×D412yes—
202C23×C31C22×C811yescharacteristic
203C23×C31C2×M1611yescharacteristic
204C23×C31#13112yes—
205D4×C31—48no—
206D4×C31—48no—
207C2×C4×C31—24no—
208C2×C4×C31—24no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—22no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—44no—
222C2×C4×C31—44no—
223C2×C4×C31—44no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—41no—
236C2×C4×C31—82no—
237C2×C4×C31—82no—
238C2×C4×C31#9912yes—
239C2×C4×C31#12011yescharacteristic
240C2×C4×C31#12112yes—
241C2×C4×C31#12311yescharacteristic
242C8×C31—44no—
243C8×C31—82no—
244C22×C22⋊C8C2×C3111yescharacteristic, complemented
245C2×#386C2×C3111yescharacteristic
246#1779C2×C3111yescharacteristic, complemented
247C2×#323C2×C3112yescomplemented
248#1280C2×C3112yescomplemented
249C22×C31—22no—
250C22×C31—22no—
251C22×C31—22no—
252C22×C31—22no—
253C22×C31—22no—
254C22×C31—21no—
255C22×C31—21no—
256C22×C31—21no—
257C22×C31—21no—
258C22×C31—22no—
259C22×C31—22no—
260C22×C31—22no—
261C22×C31—22no—
262C22×C31—22no—
263C22×C31—22no—
264C22×C31—22no—
265C22×C31—22no—
266C22×C31—48no—
267C22×C31—48no—
268C22×C31—41no—
269C22×C31—41no—
270C22×C31—41no—
271C22×C31—41no—
272C22×C31—42no—
273C22×C31—42no—
274C22×C31—42no—
275C22×C31—84no—
276C22×C31—84no—
277C22×C31—81no—
278C22×C31—81no—
279C22×C31—81no—
280C22×C31—81no—
281C22×C31#32314yescomplemented
282C22×C31#38611yescharacteristic
283C22×C31C2×C22⋊C811yescharacteristic
284C22×C31#40811yescharacteristic
285C22×C31C2×#9911yescharacteristic
286C22×C31C2×#9911yescharacteristic
287C22×C31C2×#10011yescharacteristic
288C22×C31#41311yescharacteristic
289C22×C31C8×D412yes—
290C22×C31#43512yes—
291C4×C31—21no—
292C4×C31—22no—
293C4×C31—22no—
294C4×C31—21no—
295C4×C31—41no—
296C4×C31—42no—
297C4×C31—81no—
298C4×C31—81no—
299C23×D4C4×C3111yescharacteristic
300C24×C4C22×C3111yescharacteristic
301C23×C8—21no—
302C22×C22⋊C4C4×C3111yescharacteristic
303C22×C22⋊C4C4×C3111yescharacteristic
304C22×C22⋊C4C22×C3111yescharacteristic
305C2×C22⋊C8—21no—
306C2×C22⋊C8—24no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C3112yes—
310C2×C22⋊C8C22×C3112yes—
311#386—21no—
312#386—21no—
313#386—21no—
314#386—21no—
315C2×#95C4×C3111yescharacteristic
316C2×#95C22×C3111yescharacteristic
317#323—24no—
318C2×C31—22no—
319C2×C31—22no—
320C2×C31—24no—
321C2×C31—42no—
322C2×C31—82no—
323C2×C31C2×#32311yescharacteristic
324C2×C31#145911yescharacteristic
325C2×C31#146811yescharacteristic
326C2×C31#147111yescharacteristic
327C2×C31#186911yescharacteristic
328C2×C31#189811yescharacteristic
329C2×C31#190011yescharacteristic
330C25C2×C4×C3111yescharacteristic
331C25C2×C4×C3111yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4C8×C3114yescomplemented
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4C2×C4×C3111yescharacteristic
343C23×C4C2×C4×C3111yescharacteristic
344C23×C4C2×C4×C3111yescharacteristic
345C23×C4C2×C4×C3111yescharacteristic
346C23×C4D4×C3111yescharacteristic
347C23×C4D4×C3111yescharacteristic
348C23×C4D4×C3111yescharacteristic
349C23×C4D4×C3111yescharacteristic
350C23×C4C23×C3111yescharacteristic
351C22×C8—24no—
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—42no—
355C22×C8—42no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C22⋊C8—24no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8D4×C3114yescomplemented
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377C31#907911yescharacteristic, direct product factor, Sylow
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24C22⋊C4×C3111yescharacteristic
393C24C22⋊C4×C3111yescharacteristic
394C24C2×C8×C3112yes—
395C24C2×C8×C3112yescomplemented
396C24M16×C3112yes—
397C24C22×C4×C3111yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—48no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C3111yescharacteristic
440C22×C4C22⋊C4×C3111yescharacteristic
441C22×C4C2×C8×C3112yescomplemented
442C22×C4C2×D4×C3111yescharacteristic
443C22×C4C2×D4×C3111yescharacteristic
444C22×C4C2×D4×C3112yes—
445C22×C4#41×C3112yes—
446C2×C8—24no—
447C2×C8—48no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—24no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23C31×C22⋊C812yes—
502C23C31×C22⋊C812yes—
503C23C31×#9912yes—
504C23C31×#10012yes—
505C23C2×C22⋊C4×C3111yescharacteristic
506C23C4×D4×C3112yes—
507C23C22×C8×C3111yescharacteristic
508C23C2×M16×C3111yescharacteristic
509C23C31×#13112yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C31×#9912yes—
544C2×C4C31×#12011yescharacteristic
545C2×C4C31×#12112yes—
546C2×C4C31×#12311yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—48no—
567C22—48no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—84no—
576C22—84no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C31×#32314yescomplemented
582C22C31×#38611yescharacteristic
583C22C2×C31×C22⋊C811yescharacteristic
584C22C31×#40811yescharacteristic
585C22C2×C31×#9911yescharacteristic
586C22C2×C31×#9911yescharacteristic
587C22C2×C31×#10011yescharacteristic
588C22C31×#41311yescharacteristic
589C22C8×D4×C3112yes—
590C22C31×#43512yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—42no—
603C2—82no—
604C2C2×C31×#32311yescharacteristic
605C2C31×#145911yescharacteristic
606C2C31×#146811yescharacteristic
607C2C31×#147111yescharacteristic
608C2C31×#186911yescharacteristic
609C2C31×#189811yescharacteristic
610C2C31×#190011yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C22×C8×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC23×D4×C31C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊C8C2semidirect
3. C31×#1779C2semidirect
4. C2×C31×#323C2semidirect
5. C31×#1280C2semidirect
32. C22×D4×C31C8semidirect
67. C31×C22⋊C8D4semidirect
89. C24×C31C2×C8semidirect
135. C22×C4×C31C2×C8semidirect
154. #9079C31direct (N × H)
244. C22×C22⋊C8C2×C31semidirect
246. #1779C2×C31semidirect
247. C2×#323C2×C31semidirect
248. #1280C2×C31semidirect
281. C22×C31#323semidirect
337. C22×D4C8×C31semidirect
372. C22⋊C8D4×C31semidirect
377. C31#9079direct (N × H)
395. C24C2×C8×C31semidirect
441. C22×C4C2×C8×C31semidirect
581. C22C31×#323semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊C82
C2×C31×#3862
C31×#17792
C2×C31×#3232
C31×#12802
#907931