Finite Group Databasebeta

← C31×#21454 #21478213

Subgroups — C31×#21454 #21478213

Order 7936.

1520 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic, complemented
2C2×C31×#448C211yesmaximal, characteristic
3C2×C31×#440C212yesmaximal, complemented
4C4×C31×#121C211yesmaximal, characteristic
5C31×#1880C212yesmaximal, complemented
6C31×#1874C211yesmaximal, characteristic
7C31×#1863C212yesmaximal, complemented
8C31×#1852C211yesmaximal, characteristic, complemented
9C31×#1787C211yesmaximal, characteristic, complemented
10C31×#1763C212yesmaximal, complemented
11C31×#1749C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C22×SD16×C31C2212yes—
14C2×C31×#121C2211yescharacteristic
15C2×C4×Q8×C31—28no—
16C2×C4×Q8×C31—21no—
17C2×C4×Q8×C31—21no—
18C2×C4×Q8×C31C2212yes—
19C2×C4×Q8×C31C2212yes—
20C2×C4×D4×C31—21no—
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31—21no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C42×C31—21no—
25C22×C42×C31C2211yescharacteristic
26C31×#448C418yescomplemented
27C31×#440—28no—
28C2×C31×#107C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#103C2212yes—
31C2×C31×#103C2212yes—
32C2×C31×#102C2212yes—
33C2×C31×C22⋊C8C2211yescharacteristic
34C2×C31×C22⋊C8C2211yescharacteristic
35C2×C31×#97C2212yes—
36C31×#390C2211yescharacteristic
37C31×#389C2211yescharacteristic
38C31×#388—21no—
39C31×#386—21no—
40C31×#380C2211yescharacteristic
41C4×C4⋊C4×C31C2211yescharacteristic
42C4×C22⋊C4×C31—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C31×#336C2212yes—
46C22×Q8×C31—24no—
47C22×Q8×C31—24no—
48C22×Q8×C31—21no—
49C22×Q8×C31—22no—
50C22×Q8×C31C2×C414yescomplemented
51C22×Q8×C31C2312yes—
52C22×D4×C31—21no—
53C22×D4×C31C2311yescharacteristic
54C23×C4×C31—21no—
55C23×C4×C31—21no—
56C23×C4×C31—21no—
57C23×C4×C31D411yescharacteristic
58C23×C4×C31D411yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C2×SD16×C31—24no—
61C2×SD16×C31—24no—
62C2×SD16×C31C2×C418yescomplemented
63C22×C8×C31C2312yes—
64C22×C8×C31C2312yes—
65C31×#121—22no—
66C31×#121C2×C414yes—
67C4×Q8×C31—28no—
68C4×Q8×C31—28no—
69C4×Q8×C31—24no—
70C4×Q8×C31—24no—
71C4×Q8×C31—24no—
72C4×Q8×C31D418yescomplemented
73C4×D4×C31—24no—
74C4×D4×C31—44no—
75C2×C4⋊C4×C31—28no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2311yescharacteristic
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31C2312yes—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C42×C31—28no—
91C2×C42×C31—22no—
92C2×C42×C31—22no—
93C2×C42×C31—24no—
94C2×C42×C31—21no—
95C2×C42×C31D411yescharacteristic
96C2×C42×C31D411yescharacteristic
97C2×C42×C31C2311yescharacteristic
98C2×C42×C31C2311yescharacteristic
99C31×#107—24no—
100C31×#103—24no—
101C31×#103—24no—
102C31×#103C2×C418yescomplemented
103C31×#102—24no—
104C31×C22⋊C8—22no—
105C31×C22⋊C8C2×C414yescomplemented
106C31×#97—24no—
107C31×#95—21no—
108C31×#95—21no—
109C31×#95—21no—
110C24×C31—21no—
111C24×C31C2×D411yescharacteristic
112C2×Q8×C31—24no—
113C2×Q8×C31—216no—
114C2×Q8×C31—24no—
115C2×Q8×C31—216no—
116C2×Q8×C31—24no—
117C2×Q8×C31—22no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31C22×C414yes—
121C2×Q8×C31C2×D414yes—
122C2×Q8×C31#4114yes—
123C2×D4×C31—24no—
124C2×D4×C31—22no—
125C2×D4×C31—22no—
126C2×D4×C31—21no—
127C2×D4×C31—42no—
128C2×D4×C31—42no—
129C2×D4×C31C22×C412yes—
130C22×C4×C31—24no—
131C22×C4×C31—24no—
132C22×C4×C31—24no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—24no—
140C22×C4×C31—22no—
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—41no—
147C22×C4×C31—42no—
148C22×C4×C31—42no—
149C22×C4×C31—42no—
150C22×C4×C31—42no—
151C22×C4×C31—42no—
152C22×C4×C31C22×C412yes—
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D411yescharacteristic
157C22×C4×C31C2×D411yescharacteristic
158C22×C4×C31#4112yes—
159C22×C4×C31C2411yescharacteristic
160SD16×C31—216no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31—22no—
164C2×C8×C31—22no—
165C2×C8×C31—22no—
166C2×C8×C31C22×C414yes—
167C4⋊C4×C31—28no—
168C4⋊C4×C31—24no—
169C4⋊C4×C31—28no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—42no—
175C4⋊C4×C31C22×C412yes—
176C4⋊C4×C31C2×D414yes—
177C22⋊C4×C31—24no—
178C22⋊C4×C31—42no—
179C22⋊C4×C31—42no—
180C22⋊C4×C31—42no—
181C22⋊C4×C31—42no—
182C42×C31—28no—
183C42×C31—28no—
184C42×C31—22no—
185C42×C31—22no—
186C42×C31—22no—
187C42×C31—42no—
188C42×C31C2×D414yes—
189#21454C3111yesmaximal, characteristic, direct product factor, Sylow
190C23×C31—21no—
191C23×C31—21no—
192C23×C31—21no—
193C23×C31—21no—
194C23×C31—22no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31—41no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—41no—
201C23×C31C4×D412yes—
202C23×C31AGL(1,ℤ/8)12yes—
203C23×C31#13712yes—
204C23×C31C22×D411yescharacteristic
205Q8×C31—216no—
206Q8×C31—24no—
207Q8×C31—24no—
208Q8×C31—24no—
209Q8×C31C4×D418yescomplemented
210D4×C31—24no—
211D4×C31—48no—
212D4×C31—42no—
213C2×C4×C31—28no—
214C2×C4×C31—216no—
215C2×C4×C31—24no—
216C2×C4×C31—21no—
217C2×C4×C31—24no—
218C2×C4×C31—21no—
219C2×C4×C31—24no—
220C2×C4×C31—21no—
221C2×C4×C31—21no—
222C2×C4×C31—21no—
223C2×C4×C31—21no—
224C2×C4×C31—21no—
225C2×C4×C31—21no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—22no—
229C2×C4×C31—21no—
230C2×C4×C31—24no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—44no—
234C2×C4×C31—48no—
235C2×C4×C31—41no—
236C2×C4×C31—42no—
237C2×C4×C31—41no—
238C2×C4×C31—42no—
239C2×C4×C31—41no—
240C2×C4×C31—41no—
241C2×C4×C31—41no—
242C2×C4×C31—41no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—84no—
246C2×C4×C31C4×D412yes—
247C2×C4×C31#12012yes—
248C2×C4×C31#12012yes—
249C2×C4×C31#13712yes—
250C2×C4×C31C23×C411yescharacteristic
251C2×C4×C31C22×D412yes—
252C2×C4×C31C2×#4112yes—
253C2×C4×C31C2×#4111yescharacteristic
254C8×C31—24no—
255C8×C31—42no—
256C22×C4×Q8C2×C3111yescharacteristic, complemented
257C2×#448C2×C3111yescharacteristic
258C2×#440C2×C3112yescomplemented
259C4×#121C2×C3111yescharacteristic
260#1880C2×C3112yescomplemented
261#1874C2×C3111yescharacteristic
262#1863C2×C3112yescomplemented
263#1852C2×C3111yescharacteristic, complemented
264#1787C2×C3111yescharacteristic, complemented
265#1763C2×C3112yescomplemented
266#1749C2×C3111yescharacteristic, complemented
267C22×C31—22no—
268C22×C31—22no—
269C22×C31—22no—
270C22×C31—22no—
271C22×C31—22no—
272C22×C31—22no—
273C22×C31—42no—
274C22×C31—42no—
275C22×C31—42no—
276C22×C31—81no—
277C22×C31—81no—
278C22×C31—81no—
279C22×C31—81no—
280C22×C31#44014yescomplemented
281C22×C31C2×C4×D411yescharacteristic
282C22×C31C2×#12011yescharacteristic
283C22×C31#52511yescharacteristic
284C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C31C2×#13711yescharacteristic
286C22×C31C2×#13711yescharacteristic
287C22×C31#57511yescharacteristic
288C4×C31—22no—
289C4×C31—22no—
290C4×C31—22no—
291C4×C31—28no—
292C4×C31—22no—
293C4×C31—42no—
294C4×C31—41no—
295C4×C31—44no—
296C4×C31—81no—
297C4×C31—81no—
298C4×C31C2×C4×D412yes—
299C4×C31#52512yes—
300C23×Q8C22×C3111yescharacteristic
301C22×SD16C22×C3112yes—
302C2×#121C22×C3111yescharacteristic
303C2×C4×Q8—28no—
304C2×C4×Q8—21no—
305C2×C4×Q8—21no—
306C2×C4×Q8C22×C3112yes—
307C2×C4×Q8C22×C3112yes—
308C2×C4×D4—21no—
309C2×C4×D4C22×C3111yescharacteristic
310C22×C4⋊C4—21no—
311C22×C4⋊C4C22×C3111yescharacteristic
312C22×C42—21no—
313C22×C42C22×C3111yescharacteristic
314#448C4×C3118yescomplemented
315#440—28no—
316C2×#107C22×C3112yes—
317C2×#103C22×C3112yes—
318C2×#103C22×C3112yes—
319C2×#103C22×C3112yes—
320C2×#102C22×C3112yes—
321C2×C22⋊C8C22×C3111yescharacteristic
322C2×C22⋊C8C22×C3111yescharacteristic
323C2×#97C22×C3112yes—
324#390C22×C3111yescharacteristic
325#389C22×C3111yescharacteristic
326#388—21no—
327#386—21no—
328#380C22×C3111yescharacteristic
329C4×C4⋊C4C22×C3111yescharacteristic
330C4×C22⋊C4—21no—
331#340C22×C3112yes—
332#340C22×C3112yes—
333#336C22×C3112yes—
334C2×C31—24no—
335C2×C31—82no—
336C2×C31C4×#12011yescharacteristic
337C2×C31C2×#44011yescharacteristic
338C2×C31C4×#13711yescharacteristic
339C2×C31#300411yescharacteristic
340C2×C31#300611yescharacteristic
341C2×C31#311211yescharacteristic
342C2×C31#311711yescharacteristic
343C22×Q8—24no—
344C22×Q8—24no—
345C22×Q8—21no—
346C22×Q8—22no—
347C22×Q8C2×C4×C3114yescomplemented
348C22×Q8C23×C3112yes—
349C22×D4—21no—
350C22×D4C23×C3111yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4D4×C3111yescharacteristic
355C23×C4D4×C3111yescharacteristic
356C23×C4C23×C3111yescharacteristic
357C2×SD16—24no—
358C2×SD16—24no—
359C2×SD16C2×C4×C3118yescomplemented
360C22×C8C23×C3112yes—
361C22×C8C23×C3112yes—
362#121—22no—
363#121C2×C4×C3114yes—
364C4×Q8—28no—
365C4×Q8—28no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—24no—
369C4×Q8D4×C3118yescomplemented
370C4×D4—24no—
371C4×D4—44no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C23×C3111yescharacteristic
379C2×C4⋊C4C23×C3111yescharacteristic
380C2×C4⋊C4C23×C3111yescharacteristic
381C2×C4⋊C4C23×C3112yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C42—28no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—21no—
392C2×C42D4×C3111yescharacteristic
393C2×C42D4×C3111yescharacteristic
394C2×C42C23×C3111yescharacteristic
395C2×C42C23×C3111yescharacteristic
396#107—24no—
397#103—24no—
398#103—24no—
399#103C2×C4×C3118yescomplemented
400#102—24no—
401C22⋊C8—22no—
402C22⋊C8C2×C4×C3114yescomplemented
403#97—24no—
404#95—21no—
405#95—21no—
406#95—21no—
407C31#2145411yescharacteristic, direct product factor, Sylow
408C24—21no—
409C24C2×D4×C3111yescharacteristic
410C2×Q8—24no—
411C2×Q8—216no—
412C2×Q8—24no—
413C2×Q8—216no—
414C2×Q8—24no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8C22×C4×C3114yes—
419C2×Q8C2×D4×C3114yes—
420C2×Q8#41×C3114yes—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C22×C4×C3112yes—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4C22×C4×C3112yes—
451C22×C4C2×D4×C3111yescharacteristic
452C22×C4C2×D4×C3111yescharacteristic
453C22×C4C2×D4×C3111yescharacteristic
454C22×C4C2×D4×C3111yescharacteristic
455C22×C4C2×D4×C3111yescharacteristic
456C22×C4#41×C3112yes—
457C22×C4C24×C3111yescharacteristic
458SD16—216no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8C22×C4×C3114yes—
465C4⋊C4—28no—
466C4⋊C4—24no—
467C4⋊C4—28no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—42no—
473C4⋊C4C22×C4×C3112yes—
474C4⋊C4C2×D4×C3114yes—
475C22⋊C4—24no—
476C22⋊C4—42no—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C42—28no—
481C42—28no—
482C42—22no—
483C42—22no—
484C42—22no—
485C42—42no—
486C42C2×D4×C3114yes—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C4×D4×C3112yes—
499C23C31×AGL(1,ℤ/8)12yes—
500C23C31×#13712yes—
501C23C22×D4×C3111yescharacteristic
502Q8—216no—
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8C4×D4×C3118yescomplemented
507D4—24no—
508D4—48no—
509D4—42no—
510C2×C4—28no—
511C2×C4—216no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—24no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—44no—
531C2×C4—48no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
543C2×C4C4×D4×C3112yes—
544C2×C4C31×#12012yes—
545C2×C4C31×#12012yes—
546C2×C4C31×#13712yes—
547C2×C4C23×C4×C3111yescharacteristic
548C2×C4C22×D4×C3112yes—
549C2×C4C2×#41×C3112yes—
550C2×C4C2×#41×C3111yescharacteristic
551C8—24no—
552C8—42no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22C31×#44014yescomplemented
567C22C2×C4×D4×C3111yescharacteristic
568C22C2×C31×#12011yescharacteristic
569C22C31×#52511yescharacteristic
570C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
571C22C2×C31×#13711yescharacteristic
572C22C2×C31×#13711yescharacteristic
573C22C31×#57511yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—28no—
578C4—22no—
579C4—42no—
580C4—41no—
581C4—44no—
582C4—81no—
583C4—81no—
584C4C2×C4×D4×C3112yes—
585C4C31×#52512yes—
586C2—24no—
587C2—82no—
588C2C4×C31×#12011yescharacteristic
589C2C2×C31×#44011yescharacteristic
590C2C4×C31×#13711yescharacteristic
591C2C31×#300411yescharacteristic
592C2C31×#300611yescharacteristic
593C2C31×#311211yescharacteristic
594C2C31×#311711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q8×C31C2semidirect
3. C2×C31×#440C2semidirect
5. C31×#1880C2semidirect
7. C31×#1863C2semidirect
8. C31×#1852C2semidirect
9. C31×#1787C2semidirect
10. C31×#1763C2semidirect
11. C31×#1749C2semidirect
26. C31×#448C4semidirect
50. C22×Q8×C31C2×C4semidirect
62. C2×SD16×C31C2×C4semidirect
72. C4×Q8×C31D4semidirect
102. C31×#103C2×C4semidirect
105. C31×C22⋊C8C2×C4semidirect
189. #21454C31direct (N × H)
209. Q8×C31C4×D4semidirect
256. C22×C4×Q8C2×C31semidirect
258. C2×#440C2×C31semidirect
260. #1880C2×C31semidirect
262. #1863C2×C31semidirect
263. #1852C2×C31semidirect
264. #1787C2×C31semidirect
265. #1763C2×C31semidirect
266. #1749C2×C31semidirect
280. C22×C31#440semidirect
314. #448C4×C31semidirect
347. C22×Q8C2×C4×C31semidirect
359. C2×SD16C2×C4×C31semidirect
369. C4×Q8D4×C31semidirect
399. #103C2×C4×C31semidirect
402. C22⋊C8C2×C4×C31semidirect
407. C31#21454direct (N × H)
506. Q8C4×D4×C31semidirect
566. C22C31×#440semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#4482
C2×C31×#4402
C4×C31×#1212
C31×#18802
C31×#18742
C31×#18632
C31×#18522
C31×#17872
C31×#17632
C31×#17492
#2145431