Finite Group Databasebeta

← C2×C31×#1468 #21474132

Subgroups — C2×C31×#1468 #21474132

Order 7936.

1490 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C22×C31×C22⋊C8C211yesmaximal, characteristic, complemented
4C31×#1468C218yesmaximal, direct product factor
5C2×C31×#324C212yesmaximal, complemented
6C2×C31×#323C212yesmaximal, complemented
7C23×D4×C31C411yescharacteristic
8C24×C4×C31C2211yescharacteristic
9C22×M16×C31—21no—
10C23×C8×C31—21no—
11C2×C31×#123—21no—
12C2×C31×#123—21no—
13C2×C31×#123—22no—
14C2×C31×#123—21no—
15C2×C31×#123—21no—
16C2×C31×#123—22no—
17C2×C31×#123C414yes—
18C2×C31×#123C2214yes—
19C22×C4⋊C4×C31C411yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C411yescharacteristic
22C22×C22⋊C4×C31C411yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C31×#407—22no—
25C31×#407C2214yescomplemented
26C2×C31×C22⋊C8—22no—
27C2×C31×C22⋊C8—21no—
28C2×C31×C22⋊C8—21no—
29C2×C31×C22⋊C8C2212yes—
30C2×C31×C22⋊C8C2212yes—
31C2×C31×C22⋊C8C2214yescomplemented
32C31×#324C2218yescomplemented
33C31×#323C2218yescomplemented
34C25×C31C2×C411yescharacteristic
35C25×C31C2×C411yescharacteristic
36C22×D4×C31—22no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—44no—
40C22×D4×C31C2×C414yes—
41C23×C4×C31—44no—
42C23×C4×C31C2×C411yescharacteristic
43C23×C4×C31C2×C411yescharacteristic
44C23×C4×C31C2×C411yescharacteristic
45C23×C4×C31C2×C411yescharacteristic
46C23×C4×C31C2×C412yes—
47C23×C4×C31D411yescharacteristic
48C23×C4×C31D411yescharacteristic
49C23×C4×C31D412yes—
50C23×C4×C31D411yescharacteristic
51C23×C4×C31D411yescharacteristic
52C23×C4×C31D412yes—
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2312yes—
55C2×M16×C31—24no—
56C2×M16×C31—44no—
57C22×C8×C31—22no—
58C22×C8×C31—22no—
59C22×C8×C31—24no—
60C22×C8×C31—44no—
61C31×#123—24no—
62C31×#123—24no—
63C31×#123—24no—
64C31×#123—24no—
65C31×#123—24no—
66C31×#123—24no—
67C31×#123—24no—
68C31×#123—24no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—21no—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31C2×C414yes—
77C2×C4⋊C4×C31C2×C412yes—
78C2×C4⋊C4×C31C2312yes—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—21no—
81C2×C22⋊C4×C31—21no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31C2×C414yes—
90C2×C22⋊C4×C31C2×C414yes—
91C2×C22⋊C4×C31C2×C412yes—
92C2×C22⋊C4×C31C2312yes—
93C31×C22⋊C8—22no—
94C31×C22⋊C8—24no—
95C31×C22⋊C8—24no—
96C31×C22⋊C8—22no—
97C31×C22⋊C8C2314yes—
98C31×C22⋊C8C2314yes—
99C24×C31—24no—
100C24×C31—24no—
101C24×C31—21no—
102C24×C31—21no—
103C24×C31—24no—
104C24×C31—42no—
105C24×C31—42no—
106C24×C31—42no—
107C24×C31C22⋊C411yescharacteristic
108C24×C31C22⋊C412yes—
109C24×C31C22⋊C411yescharacteristic
110C24×C31C22×C412yes—
111C24×C31C22×C411yescharacteristic
112C24×C31C22×C412yes—
113C2×D4×C31—24no—
114C2×D4×C31—24no—
115C2×D4×C31—48no—
116C2×D4×C31—44no—
117C2×D4×C31—44no—
118C2×D4×C31—48no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—21no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—24no—
128C22×C4×C31—42no—
129C22×C4×C31—44no—
130C22×C4×C31—44no—
131C22×C4×C31—42no—
132C22×C4×C31—42no—
133C22×C4×C31—44no—
134C22×C4×C31—42no—
135C22×C4×C31—44no—
136C22×C4×C31—42no—
137C22×C4×C31—42no—
138C22×C4×C31C22⋊C412yes—
139C22×C4×C31C22⋊C412yes—
140C22×C4×C31C22⋊C411yescharacteristic
141C22×C4×C31C22⋊C411yescharacteristic
142C22×C4×C31C22⋊C412yes—
143C22×C4×C31C22⋊C412yes—
144C22×C4×C31C22⋊C412yes—
145C22×C4×C31C22×C412yes—
146C22×C4×C31C22×C412yes—
147C22×C4×C31C22×C412yes—
148C22×C4×C31C22×C412yes—
149C22×C4×C31C22×C411yescharacteristic
150C22×C4×C31C2×D412yes—
151C22×C4×C31C2×D412yes—
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2×D412yes—
158C22×C4×C31C2411yescharacteristic
159M16×C31—48no—
160C2×C8×C31—24no—
161C2×C8×C31—24no—
162C2×C8×C31—44no—
163C2×C8×C31—48no—
164C2×C8×C31—44no—
165C4⋊C4×C31—24no—
166C4⋊C4×C31—24no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—24no—
174C22⋊C4×C31—24no—
175C22⋊C4×C31—22no—
176C22⋊C4×C31—22no—
177C22⋊C4×C31—22no—
178C22⋊C4×C31—22no—
179C2×#1468C3111yesmaximal, characteristic, direct product factor, Sylow
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—24no—
185C23×C31—24no—
186C23×C31—22no—
187C23×C31—24no—
188C23×C31—22no—
189C23×C31—24no—
190C23×C31—22no—
191C23×C31—22no—
192C23×C31—24no—
193C23×C31—42no—
194C23×C31—42no—
195C23×C31—416no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31—42no—
202C23×C31—42no—
203C23×C31—42no—
204C23×C31—88no—
205C23×C31#9914yes—
206C23×C31C2×C22⋊C412yes—
207C23×C31C2×C22⋊C411yescharacteristic
208C23×C31C2×C22⋊C412yes—
209C23×C31C2×C22⋊C411yescharacteristic
210C23×C31#13114yes—
211C23×C31C23×C411yescharacteristic
212D4×C31—48no—
213D4×C31—48no—
214C2×C4×C31—24no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—22no—
225C2×C4×C31—24no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—41no—
230C2×C4×C31—42no—
231C2×C4×C31—41no—
232C2×C4×C31—41no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—41no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—42no—
241C2×C4×C31—42no—
242C2×C4×C31—42no—
243C2×C4×C31—42no—
244C2×C4×C31C2×C22⋊C411yescharacteristic
245C2×C4×C31C2×C22⋊C411yescharacteristic
246C2×C4×C31C2×C22⋊C412yes—
247C2×C4×C31C2×C22⋊C412yes—
248C2×C4×C31C22×D411yescharacteristic
249C2×C4×C31C22×D411yescharacteristic
250C8×C31—44no—
251C8×C31—44no—
252C22×#123C2×C3111yescharacteristic
253C2×#407C2×C3111yescharacteristic, complemented
254C22×C22⋊C8C2×C3111yescharacteristic, complemented
255#1468C2×C3118yesdirect product factor
256C2×#324C2×C3112yescomplemented
257C2×#323C2×C3112yescomplemented
258C22×C31—22no—
259C22×C31—21no—
260C22×C31—21no—
261C22×C31—21no—
262C22×C31—21no—
263C22×C31—22no—
264C22×C31—28no—
265C22×C31—28no—
266C22×C31—22no—
267C22×C31—22no—
268C22×C31—22no—
269C22×C31—48no—
270C22×C31—48no—
271C22×C31—44no—
272C22×C31—42no—
273C22×C31—42no—
274C22×C31—42no—
275C22×C31—84no—
276C22×C31—84no—
277C22×C31—84no—
278C22×C31#40812yes—
279C22×C31#40812yes—
280C22×C31C2×#9914yes—
281C22×C31C2×#9912yes—
282C22×C31#41312yes—
283C22×C31C22×C22⋊C411yescharacteristic
284C22×C31C2×#13112yes—
285C4×C31—21no—
286C4×C31—21no—
287C4×C31—22no—
288C4×C31—21no—
289C4×C31—21no—
290C4×C31—22no—
291C4×C31—42no—
292C4×C31—42no—
293C4×C31—42no—
294C23×D4C4×C3111yescharacteristic
295C24×C4C22×C3111yescharacteristic
296C22×M16—21no—
297C23×C8—21no—
298C2×#123—21no—
299C2×#123—21no—
300C2×#123—21no—
301C2×#123—21no—
302C2×#123—22no—
303C2×#123—22no—
304C2×#123C4×C3114yes—
305C2×#123C22×C3114yes—
306C22×C4⋊C4C4×C3111yescharacteristic
307C22×C4⋊C4C22×C3111yescharacteristic
308C22×C22⋊C4C4×C3111yescharacteristic
309C22×C22⋊C4C4×C3111yescharacteristic
310C22×C22⋊C4C22×C3111yescharacteristic
311#407—22no—
312#407C22×C3114yescomplemented
313C2×C22⋊C8—22no—
314C2×C22⋊C8—21no—
315C2×C22⋊C8—21no—
316C2×C22⋊C8C22×C3112yes—
317C2×C22⋊C8C22×C3112yes—
318C2×C22⋊C8C22×C3114yescomplemented
319#324C22×C3118yescomplemented
320#323C22×C3118yescomplemented
321C2×C31—22no—
322C2×C31—22no—
323C2×C31—24no—
324C2×C31—42no—
325C2×C31—82no—
326C2×C31#146814yesdirect product factor
327C2×C31C2×#40811yescharacteristic
328C2×C31C22×#9911yescharacteristic
329C2×C31C2×#41311yescharacteristic
330C25C2×C4×C3111yescharacteristic
331C25C2×C4×C3111yescharacteristic
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—44no—
336C22×D4C2×C4×C3114yes—
337C23×C4—44no—
338C23×C4C2×C4×C3111yescharacteristic
339C23×C4C2×C4×C3111yescharacteristic
340C23×C4C2×C4×C3111yescharacteristic
341C23×C4C2×C4×C3111yescharacteristic
342C23×C4C2×C4×C3112yes—
343C23×C4D4×C3111yescharacteristic
344C23×C4D4×C3111yescharacteristic
345C23×C4D4×C3111yescharacteristic
346C23×C4D4×C3111yescharacteristic
347C23×C4D4×C3112yes—
348C23×C4D4×C3112yes—
349C23×C4C23×C3111yescharacteristic
350C23×C4C23×C3112yes—
351C2×M16—24no—
352C2×M16—44no—
353C22×C8—22no—
354C22×C8—24no—
355C22×C8—22no—
356C22×C8—44no—
357#123—24no—
358#123—24no—
359#123—24no—
360#123—24no—
361#123—24no—
362#123—24no—
363#123—24no—
364#123—24no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C2×C4×C3114yes—
373C2×C4⋊C4C2×C4×C3112yes—
374C2×C4⋊C4C23×C3112yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4C2×C4×C3114yes—
386C2×C22⋊C4C2×C4×C3114yes—
387C2×C22⋊C4C2×C4×C3112yes—
388C2×C22⋊C4C23×C3112yes—
389C22⋊C8—22no—
390C22⋊C8—24no—
391C22⋊C8—24no—
392C22⋊C8—22no—
393C22⋊C8C23×C3114yes—
394C22⋊C8C23×C3114yes—
395C31C2×#146811yescharacteristic, direct product factor, Sylow
396C24—24no—
397C24—24no—
398C24—21no—
399C24—21no—
400C24—24no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24C22⋊C4×C3111yescharacteristic
405C24C22⋊C4×C3112yes—
406C24C22⋊C4×C3111yescharacteristic
407C24C22×C4×C3112yes—
408C24C22×C4×C3111yescharacteristic
409C24C22×C4×C3112yes—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—48no—
413C2×D4—44no—
414C2×D4—44no—
415C2×D4—48no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—42no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—44no—
431C22×C4—42no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4C22⋊C4×C3111yescharacteristic
436C22×C4C22⋊C4×C3111yescharacteristic
437C22×C4C22⋊C4×C3112yes—
438C22×C4C22⋊C4×C3112yes—
439C22×C4C22⋊C4×C3112yes—
440C22×C4C22⋊C4×C3112yes—
441C22×C4C22⋊C4×C3112yes—
442C22×C4C22×C4×C3112yes—
443C22×C4C22×C4×C3112yes—
444C22×C4C22×C4×C3112yes—
445C22×C4C22×C4×C3112yes—
446C22×C4C22×C4×C3111yescharacteristic
447C22×C4C2×D4×C3111yescharacteristic
448C22×C4C2×D4×C3111yescharacteristic
449C22×C4C2×D4×C3112yes—
450C22×C4C2×D4×C3112yes—
451C22×C4C2×D4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3112yes—
454C22×C4C2×D4×C3112yes—
455C22×C4C24×C3111yescharacteristic
456M16—48no—
457C2×C8—24no—
458C2×C8—24no—
459C2×C8—44no—
460C2×C8—48no—
461C2×C8—44no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—24no—
487C23—22no—
488C23—24no—
489C23—42no—
490C23—42no—
491C23—416no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—88no—
501C23C31×#9914yes—
502C23C2×C22⋊C4×C3112yes—
503C23C2×C22⋊C4×C3111yescharacteristic
504C23C2×C22⋊C4×C3112yes—
505C23C2×C22⋊C4×C3111yescharacteristic
506C23C31×#13114yes—
507C23C23×C4×C3111yescharacteristic
508D4—48no—
509D4—48no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4C2×C22⋊C4×C3112yes—
541C2×C4C2×C22⋊C4×C3112yes—
542C2×C4C2×C22⋊C4×C3111yescharacteristic
543C2×C4C2×C22⋊C4×C3111yescharacteristic
544C2×C4C22×D4×C3111yescharacteristic
545C2×C4C22×D4×C3111yescharacteristic
546C8—44no—
547C8—44no—
548C22—22no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—28no—
555C22—28no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—48no—
560C22—48no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—84no—
567C22—84no—
568C22C31×#40812yes—
569C22C31×#40812yes—
570C22C2×C31×#9914yes—
571C22C2×C31×#9912yes—
572C22C31×#41312yes—
573C22C22×C22⋊C4×C3111yescharacteristic
574C22C2×C31×#13112yes—
575C4—21no—
576C4—21no—
577C4—22no—
578C4—21no—
579C4—21no—
580C4—22no—
581C4—42no—
582C4—42no—
583C4—42no—
584C2—22no—
585C2—22no—
586C2—24no—
587C2—42no—
588C2—82no—
589C2C31×#146814yesdirect product factor
590C2C2×C31×#40811yescharacteristic
591C2C22×C31×#9911yescharacteristic
592C2C2×C31×#41311yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×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
2. C2×C31×#407C2semidirect
3. C22×C31×C22⋊C8C2semidirect
4. C31×#1468C2direct (N × H)
5. C2×C31×#324C2semidirect
6. C2×C31×#323C2semidirect
25. C31×#407C22semidirect
31. C2×C31×C22⋊C8C22semidirect
32. C31×#324C22semidirect
33. C31×#323C22semidirect
179. C2×#1468C31direct (N × H)
253. C2×#407C2×C31semidirect
254. C22×C22⋊C8C2×C31semidirect
255. #1468C2×C31direct (N × H)
256. C2×#324C2×C31semidirect
257. C2×#323C2×C31semidirect
312. #407C22×C31semidirect
318. C2×C22⋊C8C22×C31semidirect
319. #324C22×C31semidirect
320. #323C22×C31semidirect
326. C2×C31#1468direct (N × H)
395. C31C2×#1468direct (N × H)
589. C2C31×#1468direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C2×C31×#4072
C22×C31×C22⋊C82
C31×#14682
C2×C31×#3242
C2×C31×#3232
C2×#146831