Finite Group Databasebeta

← C2×C31×#1282 #21464682

Subgroups — C2×C31×#1282 #21464682

Order 7936.

1130 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊C8C211yesmaximal, characteristic
2C22×C31×C22⋊C8C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1282C214yesmaximal, direct product factor
5C24×C4×C31C2211yescharacteristic
6C23×C8×C31—21no—
7C23×C8×C31C412yescomplemented
8C22×C22⋊C4×C31C412yes—
9C22×C42×C31—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×C22⋊C8—21no—
12C2×C31×C22⋊C8—21no—
13C2×C31×C22⋊C8—21no—
14C2×C31×C22⋊C8—21no—
15C2×C31×C22⋊C8—21no—
16C2×C31×C22⋊C8—21no—
17C2×C31×C22⋊C8C412yescomplemented
18C2×C31×C22⋊C8C412yescomplemented
19C2×C31×C22⋊C8C412yescomplemented
20C2×C31×C22⋊C8C2212yes—
21C2×C31×C22⋊C8C2212yes—
22C4×C22⋊C4×C31—21no—
23C4×C22⋊C4×C31—21no—
24C4×C22⋊C4×C31C412yes—
25C4×C22⋊C4×C31C2212yes—
26C2×C31×#95—21no—
27C25×C31C2×C411yescharacteristic
28C23×C4×C31—22no—
29C23×C4×C31—44no—
30C23×C4×C31C2×C411yescharacteristic
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31C2×C411yescharacteristic
35C23×C4×C31D411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31D411yescharacteristic
39C23×C4×C31D411yescharacteristic
40C23×C4×C31D411yescharacteristic
41C23×C4×C31Q811yescharacteristic
42C23×C4×C31Q811yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C22×C8×C31—22no—
45C22×C8×C31—22no—
46C22×C8×C31—22no—
47C22×C8×C31—22no—
48C22×C8×C31—22no—
49C22×C8×C31—44no—
50C22×C8×C31—44no—
51C22×C8×C31C2×C414yescomplemented
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—24no—
54C2×C22⋊C4×C31C818yescomplemented
55C2×C22⋊C4×C31C2×C414yes—
56C2×C42×C31—22no—
57C2×C42×C31—22no—
58C2×C42×C31—44no—
59C31×C22⋊C8—22no—
60C31×C22⋊C8—22no—
61C31×C22⋊C8—22no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—22no—
64C31×C22⋊C8—22no—
65C31×C22⋊C8—22no—
66C31×C22⋊C8C2×C414yescomplemented
67C31×#95—22no—
68C31×#95—22no—
69C24×C31—42no—
70C24×C31—42no—
71C24×C31C4211yescharacteristic
72C24×C31C4211yescharacteristic
73C24×C31C22⋊C411yescharacteristic
74C24×C31C22⋊C411yescharacteristic
75C24×C31C4⋊C411yescharacteristic
76C24×C31C4⋊C411yescharacteristic
77C24×C31C2×C814yes—
78C24×C31M1614yes—
79C24×C31C22×C411yescharacteristic
80C22×C4×C31—24no—
81C22×C4×C31—24no—
82C22×C4×C31—24no—
83C22×C4×C31—28no—
84C22×C4×C31—24no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—42no—
95C22×C4×C31—42no—
96C22×C4×C31—44no—
97C22×C4×C31—44no—
98C22×C4×C31C4211yescharacteristic
99C22×C4×C31C4211yescharacteristic
100C22×C4×C31C22⋊C411yescharacteristic
101C22×C4×C31C22⋊C411yescharacteristic
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22⋊C411yescharacteristic
105C22×C4×C31C22⋊C411yescharacteristic
106C22×C4×C31C22⋊C411yescharacteristic
107C22×C4×C31C22⋊C411yescharacteristic
108C22×C4×C31C22⋊C411yescharacteristic
109C22×C4×C31C22⋊C411yescharacteristic
110C22×C4×C31C4⋊C411yescharacteristic
111C22×C4×C31C4⋊C411yescharacteristic
112C22×C4×C31C4⋊C411yescharacteristic
113C22×C4×C31C4⋊C411yescharacteristic
114C22×C4×C31C4⋊C411yescharacteristic
115C22×C4×C31C4⋊C411yescharacteristic
116C22×C4×C31C4⋊C411yescharacteristic
117C22×C4×C31C4⋊C411yescharacteristic
118C22×C4×C31C4⋊C411yescharacteristic
119C22×C4×C31C4⋊C411yescharacteristic
120C22×C4×C31C22×C411yescharacteristic
121C22×C4×C31C22×C411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×D411yescharacteristic
124C22×C4×C31C2×D411yescharacteristic
125C22×C4×C31C2×Q811yescharacteristic
126C2×C8×C31—24no—
127C2×C8×C31—24no—
128C2×C8×C31—44no—
129C2×C8×C31—44no—
130C2×C8×C31—44no—
131C2×C8×C31—44no—
132C2×C8×C31—44no—
133C2×C8×C31—44no—
134C22⋊C4×C31—28no—
135C22⋊C4×C31—24no—
136C22⋊C4×C31C2×C818yescomplemented
137C42×C31—44no—
138C42×C31—44no—
139C2×#1282C3111yesmaximal, characteristic, direct product factor, Sylow
140C23×C31—22no—
141C23×C31—22no—
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—41no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—48no—
154C23×C31—48no—
155C23×C31—41no—
156C23×C31#9511yescharacteristic
157C23×C31#9511yescharacteristic
158C23×C31#9511yescharacteristic
159C23×C31#9511yescharacteristic
160C23×C31C4×C812yes—
161C23×C31C4×C812yes—
162C23×C31#9712yes—
163C23×C31#9712yes—
164C23×C31C22⋊C814yes—
165C23×C31C22⋊C814yes—
166C23×C31C4⋊C814yes—
167C23×C31C4⋊C814yes—
168C23×C31C2×C4211yescharacteristic
169C23×C31C2×C22⋊C411yescharacteristic
170C23×C31C2×C4⋊C411yescharacteristic
171C23×C31C22×C812yes—
172C23×C31C2×M1612yes—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—28no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—41no—
195C2×C4×C31—41no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—41no—
200C2×C4×C31—41no—
201C2×C4×C31—44no—
202C2×C4×C31—416no—
203C2×C4×C31—44no—
204C2×C4×C31#9511yescharacteristic
205C2×C4×C31#9511yescharacteristic
206C2×C4×C31#9511yescharacteristic
207C2×C4×C31#9511yescharacteristic
208C2×C4×C31#9914yes—
209C2×C4×C31C2×C22⋊C411yescharacteristic
210C2×C4×C31C2×C22⋊C411yescharacteristic
211C2×C4×C31C2×C4⋊C411yescharacteristic
212C2×C4×C31C2×C4⋊C411yescharacteristic
213C8×C31—44no—
214C8×C31—44no—
215C22×C22⋊C8C2×C3111yescharacteristic
216C22×C22⋊C8C2×C3111yescharacteristic
217C2×C4×C22⋊C4C2×C3111yescharacteristic
218#1282C2×C3114yesdirect product factor
219C22×C31—28no—
220C22×C31—24no—
221C22×C31—24no—
222C22×C31—28no—
223C22×C31—21no—
224C22×C31—21no—
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—42no—
236C22×C31—42no—
237C22×C31—44no—
238C22×C31—44no—
239C22×C31—42no—
240C22×C31—42no—
241C22×C31#33612yes—
242C22×C31#33612yes—
243C22×C31#33612yes—
244C22×C31#33612yes—
245C22×C31#34212yes—
246C22×C31#34412yes—
247C22×C31C2×#9511yescharacteristic
248C22×C31C2×C4×C811yescharacteristic
249C22×C31C2×#9711yescharacteristic
250C22×C31C2×C22⋊C812yes—
251C22×C31C2×C4⋊C812yes—
252C4×C31—21no—
253C4×C31—21no—
254C4×C31—21no—
255C4×C31—21no—
256C4×C31—21no—
257C4×C31—21no—
258C4×C31—48no—
259C4×C31#34212yes—
260C4×C31C2×#9912yes—
261C24×C4C22×C3111yescharacteristic
262C23×C8—21no—
263C23×C8C4×C3112yescomplemented
264C22×C22⋊C4C4×C3112yes—
265C22×C42—21no—
266C2×C22⋊C8—21no—
267C2×C22⋊C8—21no—
268C2×C22⋊C8—21no—
269C2×C22⋊C8—21no—
270C2×C22⋊C8—21no—
271C2×C22⋊C8—21no—
272C2×C22⋊C8—21no—
273C2×C22⋊C8C4×C3112yescomplemented
274C2×C22⋊C8C4×C3112yescomplemented
275C2×C22⋊C8C4×C3112yescomplemented
276C2×C22⋊C8C22×C3112yes—
277C2×C22⋊C8C22×C3112yes—
278C4×C22⋊C4—21no—
279C4×C22⋊C4—21no—
280C4×C22⋊C4C4×C3112yes—
281C4×C22⋊C4C22×C3112yes—
282C2×#95—21no—
283C2×C31—22no—
284C2×C31—22no—
285C2×C31—22no—
286C2×C31—22no—
287C2×C31—21no—
288C2×C31—21no—
289C2×C31—22no—
290C2×C31#128214yesdirect product factor
291C2×C31C2×#33611yescharacteristic
292C2×C31C2×#34211yescharacteristic
293C2×C31C2×#34411yescharacteristic
294C25C2×C4×C3111yescharacteristic
295C23×C4—22no—
296C23×C4—44no—
297C23×C4C2×C4×C3111yescharacteristic
298C23×C4C2×C4×C3111yescharacteristic
299C23×C4C2×C4×C3111yescharacteristic
300C23×C4C2×C4×C3111yescharacteristic
301C23×C4C2×C4×C3111yescharacteristic
302C23×C4D4×C3111yescharacteristic
303C23×C4D4×C3111yescharacteristic
304C23×C4D4×C3111yescharacteristic
305C23×C4D4×C3111yescharacteristic
306C23×C4D4×C3111yescharacteristic
307C23×C4D4×C3111yescharacteristic
308C23×C4Q8×C3111yescharacteristic
309C23×C4Q8×C3111yescharacteristic
310C23×C4C23×C3111yescharacteristic
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—44no—
317C22×C8—44no—
318C22×C8C2×C4×C3114yescomplemented
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4C8×C3118yescomplemented
322C2×C22⋊C4C2×C4×C3114yes—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—44no—
326C22⋊C8—22no—
327C22⋊C8—22no—
328C22⋊C8—22no—
329C22⋊C8—22no—
330C22⋊C8—22no—
331C22⋊C8—22no—
332C22⋊C8—22no—
333C22⋊C8C2×C4×C3114yescomplemented
334#95—22no—
335#95—22no—
336C31C2×#128211yescharacteristic, direct product factor, Sylow
337C24—42no—
338C24—42no—
339C24C42×C3111yescharacteristic
340C24C42×C3111yescharacteristic
341C24C22⋊C4×C3111yescharacteristic
342C24C22⋊C4×C3111yescharacteristic
343C24C4⋊C4×C3111yescharacteristic
344C24C4⋊C4×C3111yescharacteristic
345C24C2×C8×C3114yes—
346C24M16×C3114yes—
347C24C22×C4×C3111yescharacteristic
348C22×C4—24no—
349C22×C4—24no—
350C22×C4—24no—
351C22×C4—28no—
352C22×C4—24no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—44no—
365C22×C4—44no—
366C22×C4C42×C3111yescharacteristic
367C22×C4C42×C3111yescharacteristic
368C22×C4C22⋊C4×C3111yescharacteristic
369C22×C4C22⋊C4×C3111yescharacteristic
370C22×C4C22⋊C4×C3111yescharacteristic
371C22×C4C22⋊C4×C3111yescharacteristic
372C22×C4C22⋊C4×C3111yescharacteristic
373C22×C4C22⋊C4×C3111yescharacteristic
374C22×C4C22⋊C4×C3111yescharacteristic
375C22×C4C22⋊C4×C3111yescharacteristic
376C22×C4C22⋊C4×C3111yescharacteristic
377C22×C4C22⋊C4×C3111yescharacteristic
378C22×C4C4⋊C4×C3111yescharacteristic
379C22×C4C4⋊C4×C3111yescharacteristic
380C22×C4C4⋊C4×C3111yescharacteristic
381C22×C4C4⋊C4×C3111yescharacteristic
382C22×C4C4⋊C4×C3111yescharacteristic
383C22×C4C4⋊C4×C3111yescharacteristic
384C22×C4C4⋊C4×C3111yescharacteristic
385C22×C4C4⋊C4×C3111yescharacteristic
386C22×C4C4⋊C4×C3111yescharacteristic
387C22×C4C4⋊C4×C3111yescharacteristic
388C22×C4C22×C4×C3111yescharacteristic
389C22×C4C22×C4×C3111yescharacteristic
390C22×C4C2×D4×C3111yescharacteristic
391C22×C4C2×D4×C3111yescharacteristic
392C22×C4C2×D4×C3111yescharacteristic
393C22×C4C2×Q8×C3111yescharacteristic
394C2×C8—24no—
395C2×C8—24no—
396C2×C8—44no—
397C2×C8—44no—
398C2×C8—44no—
399C2×C8—44no—
400C2×C8—44no—
401C2×C8—44no—
402C22⋊C4—28no—
403C22⋊C4—24no—
404C22⋊C4C2×C8×C3118yescomplemented
405C42—44no—
406C42—44no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—48no—
421C23—48no—
422C23—41no—
423C23C31×#9511yescharacteristic
424C23C31×#9511yescharacteristic
425C23C31×#9511yescharacteristic
426C23C31×#9511yescharacteristic
427C23C4×C8×C3112yes—
428C23C4×C8×C3112yes—
429C23C31×#9712yes—
430C23C31×#9712yes—
431C23C31×C22⋊C814yes—
432C23C31×C22⋊C814yes—
433C23C31×C4⋊C814yes—
434C23C31×C4⋊C814yes—
435C23C2×C42×C3111yescharacteristic
436C23C2×C22⋊C4×C3111yescharacteristic
437C23C2×C4⋊C4×C3111yescharacteristic
438C23C22×C8×C3112yes—
439C23C2×M16×C3112yes—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—28no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—416no—
471C2×C4C31×#9511yescharacteristic
472C2×C4C31×#9511yescharacteristic
473C2×C4C31×#9511yescharacteristic
474C2×C4C31×#9511yescharacteristic
475C2×C4C31×#9914yes—
476C2×C4C2×C22⋊C4×C3111yescharacteristic
477C2×C4C2×C22⋊C4×C3111yescharacteristic
478C2×C4C2×C4⋊C4×C3111yescharacteristic
479C2×C4C2×C4⋊C4×C3111yescharacteristic
480C8—44no—
481C8—44no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—28no—
495C22—24no—
496C22—24no—
497C22—28no—
498C22—42no—
499C22—42no—
500C22—44no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22C31×#33612yes—
505C22C31×#33612yes—
506C22C31×#33612yes—
507C22C31×#33612yes—
508C22C31×#34212yes—
509C22C31×#34412yes—
510C22C2×C31×#9511yescharacteristic
511C22C2×C4×C8×C3111yescharacteristic
512C22C2×C31×#9711yescharacteristic
513C22C2×C31×C22⋊C812yes—
514C22C2×C31×C4⋊C812yes—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—48no—
522C4C31×#34212yes—
523C4C2×C31×#9912yes—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—22no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2C31×#128214yesdirect product factor
532C2C2×C31×#33611yescharacteristic
533C2C2×C31×#34211yescharacteristic
534C2C2×C31×#34411yescharacteristic
subgroupG/H
centerC22×C4×C31C22⋊C4
commutatorC22C2×C4×C8×C31
Frattini, cosocleC23×C4C23×C31
socleC23×C31#95
prime radicalC25×C31C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1282C2direct (N × H)
7. C23×C8×C31C4semidirect
17. C2×C31×C22⋊C8C4semidirect
18. C2×C31×C22⋊C8C4semidirect
19. C2×C31×C22⋊C8C4semidirect
51. C22×C8×C31C2×C4semidirect
54. C2×C22⋊C4×C31C8semidirect
66. C31×C22⋊C8C2×C4semidirect
136. C22⋊C4×C31C2×C8semidirect
139. C2×#1282C31direct (N × H)
218. #1282C2×C31direct (N × H)
263. C23×C8C4×C31semidirect
273. C2×C22⋊C8C4×C31semidirect
274. C2×C22⋊C8C4×C31semidirect
275. C2×C22⋊C8C4×C31semidirect
290. C2×C31#1282direct (N × H)
318. C22×C8C2×C4×C31semidirect
321. C2×C22⋊C4C8×C31semidirect
333. C22⋊C8C2×C4×C31semidirect
336. C31C2×#1282direct (N × H)
404. C22⋊C4C2×C8×C31semidirect
531. C2C31×#1282direct (N × H)

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×C4×C22⋊C4×C312
C31×#12822
C2×#128231