Finite Group Databasebeta

← C31×#14241 #21471000

Subgroups — C31×#14241 #21471000

Order 7936.

1470 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#395C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
4C31×#1446C211yesmaximal, characteristic
5C31×#1444C211yesmaximal, characteristic
6C31×#1441C211yesmaximal, characteristic
7C31×#1436C212yesmaximal
8C31×#1436C212yesmaximal
9C31×#1436C212yesmaximal
10C31×C4⋊#95C212yesmaximal
11C4×C31×#95C211yesmaximal, characteristic
12C23×Q8×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2212yes—
18C22×C42×C31C2211yescharacteristic
19C22×C42×C31C2212yes—
20C22×C42×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C31×#395C418yescomplemented
23C31×#391—24no—
24C4×C4⋊C4×C31—24no—
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2211yescharacteristic
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C22×Q8×C31—22no—
39C22×Q8×C31—22no—
40C22×Q8×C31—42no—
41C22×Q8×C31—42no—
42C22×Q8×C31C2×C414yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—42no—
62C2×C4⋊C4×C31—42no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31—42no—
65C2×C4⋊C4×C31C2×C414yes—
66C2×C4⋊C4×C31C2×C418yes—
67C2×C4⋊C4×C31Q814yescomplemented
68C2×C42×C31—22no—
69C2×C42×C31—22no—
70C2×C42×C31—22no—
71C2×C42×C31—22no—
72C2×C42×C31—24no—
73C2×C42×C31—24no—
74C2×C42×C31—42no—
75C2×C42×C31—42no—
76C2×C42×C31—42no—
77C2×C42×C31D414yes—
78C31×#95—22no—
79C31×#95—22no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—22no—
83C31×#95—24no—
84C31×#95—24no—
85C31×#95—42no—
86C31×#95—42no—
87C31×#95—42no—
88C31×#95C2×C418yes—
89C31×#95C2×C414yes—
90C31×#95Q818yescomplemented
91C24×C31C2411yescharacteristic
92C2×Q8×C31—28no—
93C2×Q8×C31—48no—
94C2×Q8×C31—44no—
95C2×Q8×C31—44no—
96C2×Q8×C31—48no—
97C22×C4×C31—21no—
98C22×C4×C31—21no—
99C22×C4×C31—22no—
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
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—22no—
140C22×C4×C31—22no—
141C22×C4×C31—22no—
142C22×C4×C31—22no—
143C22×C4×C31C22×C414yes—
144C22×C4×C31C22×C412yes—
145C22×C4×C31C22×C412yes—
146C22×C4×C31C22×C412yes—
147C22×C4×C31C22×C414yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D412yes—
150C22×C4×C31C2×D412yes—
151C22×C4×C31C2×Q814yes—
152C22×C4×C31C2×Q812yes—
153C22×C4×C31C2×Q814yes—
154C22×C4×C31C2×Q812yes—
155C22×C4×C31C2×Q812yes—
156C22×C4×C31C2×Q814yes—
157C22×C4×C31#4112yes—
158C22×C4×C31#4112yes—
159C22×C4×C31#4112yes—
160C22×C4×C31#4114yes—
161C22×C4×C31#4112yes—
162C4⋊C4×C31—28no—
163C4⋊C4×C31—28no—
164C4⋊C4×C31—48no—
165C4⋊C4×C31—48no—
166C4⋊C4×C31—44no—
167C42×C31—28no—
168C42×C31—44no—
169C42×C31—48no—
170C42×C31—44no—
171#14241C3111yesmaximal, characteristic, direct product factor, Sylow
172C23×C31C23×C411yescharacteristic
173C23×C31C22×D411yescharacteristic
174C23×C31C22×Q811yescharacteristic
175C23×C31C22×Q812yes—
176C23×C31C2×#4111yescharacteristic
177C23×C31C2×#4111yescharacteristic
178C23×C31C2×#4112yes—
179C23×C31C2×#4111yescharacteristic
180C23×C31C2×#4111yescharacteristic
181C23×C31H(5,𝔽2)12yes—
182C23×C31H(5,𝔽2)12yes—
183Q8×C31—416no—
184C2×C4×C31—22no—
185C2×C4×C31—24no—
186C2×C4×C31—22no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—22no—
190C2×C4×C31—22no—
191C2×C4×C31—22no—
192C2×C4×C31—22no—
193C2×C4×C31—22no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—22no—
199C2×C4×C31—24no—
200C2×C4×C31—24no—
201C2×C4×C31—24no—
202C2×C4×C31—24no—
203C2×C4×C31—24no—
204C2×C4×C31—24no—
205C2×C4×C31—24no—
206C2×C4×C31—24no—
207C2×C4×C31—24no—
208C2×C4×C31—22no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—24no—
216C2×C4×C31—24no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—42no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—42no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
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×C31C4×D414yes—
245C2×C4×C31C4×Q818yes—
246C2×C4×C31C4×Q814yes—
247C2×C4×C31C22⋊Q814yes—
248C2×C4×C31C4⋊Q814yes—
249C2×#395C2×C3111yescharacteristic
250C2×#391C2×C3111yescharacteristic
251C2×C4×C4⋊C4C2×C3111yescharacteristic
252#1446C2×C3111yescharacteristic
253#1444C2×C3111yescharacteristic
254#1441C2×C3111yescharacteristic
255#1436C2×C3112yes—
256#1436C2×C3112yes—
257#1436C2×C3112yes—
258C4⋊#95C2×C3112yes—
259C4×#95C2×C3111yescharacteristic
260C22×C31C2×C4×D411yescharacteristic
261C22×C31C2×C4×Q812yes—
262C22×C31C2×C4×Q811yescharacteristic
263C22×C31C4×#4111yescharacteristic
264C22×C31#51812yes—
265C22×C31C2×C22⋊Q811yescharacteristic
266C22×C31#52511yescharacteristic
267C22×C31#52911yescharacteristic
268C22×C31C2×C4⋊Q811yescharacteristic
269C22×C31#53211yescharacteristic
270C22×C31#53312yes—
271C22×C31#53311yescharacteristic
272C22×C31#53411yescharacteristic
273C22×C31#53511yescharacteristic
274C22×C31#53812yes—
275C22×C31#55112yes—
276C22×C31#55112yes—
277C22×C31#55412yes—
278C22×C31#55412yes—
279C22×C31#55412yes—
280C22×C31#55412yes—
281C22×C31#55512yes—
282C22×C31Q8212yes—
283C4×C31—24no—
284C4×C31—24no—
285C4×C31—24no—
286C4×C31—28no—
287C4×C31—24no—
288C4×C31—42no—
289C4×C31—44no—
290C4×C31—42no—
291C4×C31—44no—
292C4×C31—42no—
293C4×C31—82no—
294C23×Q8C22×C3111yescharacteristic
295C22×C4⋊C4C22×C3112yes—
296C22×C4⋊C4C22×C3111yescharacteristic
297C22×C4⋊C4C22×C3111yescharacteristic
298C22×C4⋊C4C22×C3111yescharacteristic
299C22×C4⋊C4C22×C3112yes—
300C22×C42C22×C3111yescharacteristic
301C22×C42C22×C3112yes—
302C22×C42C22×C3111yescharacteristic
303C22×C42C22×C3111yescharacteristic
304#395C4×C3118yescomplemented
305#391—24no—
306C4×C4⋊C4—24no—
307C2×#95C22×C3111yescharacteristic
308C2×#95C22×C3111yescharacteristic
309C2×#95C22×C3112yes—
310C2×#95C22×C3112yes—
311C2×#95C22×C3112yes—
312C2×#95C22×C3112yes—
313C2×#95C22×C3111yescharacteristic
314C2×#95C22×C3112yes—
315C2×#95C22×C3112yes—
316C2×#95C22×C3112yes—
317C2×#95C22×C3111yescharacteristic
318C2×#95C22×C3112yes—
319C2×#95C22×C3112yes—
320C2×C31C4×C22⋊Q811yescharacteristic
321C2×C31C4×C4⋊Q811yescharacteristic
322C2×C31#232111yescharacteristic
323C2×C31#236812yes—
324C2×C31#236912yes—
325C2×C31#256411yescharacteristic
326C2×C31#256711yescharacteristic
327C2×C31#257412yes—
328C2×C31#258311yescharacteristic
329C2×C31#258612yes—
330C2×C31#261011yescharacteristic
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—42no—
334C22×Q8—42no—
335C22×Q8C2×C4×C3114yes—
336C23×C4C23×C3112yes—
337C23×C4C23×C3111yescharacteristic
338C23×C4C23×C3112yes—
339C23×C4C23×C3111yescharacteristic
340C23×C4C23×C3112yes—
341C23×C4C23×C3111yescharacteristic
342C23×C4C23×C3111yescharacteristic
343C23×C4C23×C3111yescharacteristic
344C23×C4C23×C3112yes—
345C23×C4C23×C3111yescharacteristic
346C23×C4C23×C3111yescharacteristic
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4C2×C4×C3114yes—
359C2×C4⋊C4C2×C4×C3118yes—
360C2×C4⋊C4Q8×C3114yescomplemented
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42D4×C3114yes—
371#95—22no—
372#95—22no—
373#95—24no—
374#95—24no—
375#95—22no—
376#95—24no—
377#95—24no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95C2×C4×C3118yes—
382#95C2×C4×C3114yes—
383#95Q8×C3118yescomplemented
384C31#1424111yescharacteristic, direct product factor, Sylow
385C24C24×C3111yescharacteristic
386C2×Q8—28no—
387C2×Q8—48no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—48no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4C22×C4×C3114yes—
438C22×C4C22×C4×C3112yes—
439C22×C4C22×C4×C3112yes—
440C22×C4C22×C4×C3112yes—
441C22×C4C22×C4×C3114yes—
442C22×C4C2×D4×C3112yes—
443C22×C4C2×D4×C3112yes—
444C22×C4C2×D4×C3112yes—
445C22×C4C2×Q8×C3114yes—
446C22×C4C2×Q8×C3112yes—
447C22×C4C2×Q8×C3114yes—
448C22×C4C2×Q8×C3112yes—
449C22×C4C2×Q8×C3112yes—
450C22×C4C2×Q8×C3114yes—
451C22×C4#41×C3112yes—
452C22×C4#41×C3112yes—
453C22×C4#41×C3112yes—
454C22×C4#41×C3114yes—
455C22×C4#41×C3112yes—
456C4⋊C4—28no—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—48no—
460C4⋊C4—44no—
461C42—28no—
462C42—44no—
463C42—48no—
464C42—44no—
465C23C23×C4×C3111yescharacteristic
466C23C22×D4×C3111yescharacteristic
467C23C22×Q8×C3111yescharacteristic
468C23C22×Q8×C3112yes—
469C23C2×#41×C3111yescharacteristic
470C23C2×#41×C3111yescharacteristic
471C23C2×#41×C3112yes—
472C23C2×#41×C3111yescharacteristic
473C23C2×#41×C3111yescharacteristic
474C23C31×H(5,𝔽2)12yes—
475C23C31×H(5,𝔽2)12yes—
476Q8—416no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4C4×D4×C3114yes—
538C2×C4C4×Q8×C3118yes—
539C2×C4C4×Q8×C3114yes—
540C2×C4C31×C22⋊Q814yes—
541C2×C4C31×C4⋊Q814yes—
542C22C2×C4×D4×C3111yescharacteristic
543C22C2×C4×Q8×C3112yes—
544C22C2×C4×Q8×C3111yescharacteristic
545C22C4×#41×C3111yescharacteristic
546C22C31×#51812yes—
547C22C2×C31×C22⋊Q811yescharacteristic
548C22C31×#52511yescharacteristic
549C22C31×#52911yescharacteristic
550C22C2×C31×C4⋊Q811yescharacteristic
551C22C31×#53211yescharacteristic
552C22C31×#53312yes—
553C22C31×#53311yescharacteristic
554C22C31×#53411yescharacteristic
555C22C31×#53511yescharacteristic
556C22C31×#53812yes—
557C22C31×#55112yes—
558C22C31×#55112yes—
559C22C31×#55412yes—
560C22C31×#55412yes—
561C22C31×#55412yes—
562C22C31×#55412yes—
563C22C31×#55512yes—
564C22Q82×C3112yes—
565C4—24no—
566C4—24no—
567C4—24no—
568C4—28no—
569C4—24no—
570C4—42no—
571C4—44no—
572C4—44no—
573C4—42no—
574C4—42no—
575C4—82no—
576C2C4×C31×C22⋊Q811yescharacteristic
577C2C4×C31×C4⋊Q811yescharacteristic
578C2C31×#232111yescharacteristic
579C2C31×#236812yes—
580C2C31×#236912yes—
581C2C31×#256411yescharacteristic
582C2C31×#256711yescharacteristic
583C2C31×#257412yes—
584C2C31×#258311yescharacteristic
585C2C31×#258612yes—
586C2C31×#261011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
22. C31×#395C4semidirect
67. C2×C4⋊C4×C31Q8semidirect
90. C31×#95Q8semidirect
171. #14241C31direct (N × H)
304. #395C4×C31semidirect
360. C2×C4⋊C4Q8×C31semidirect
383. #95Q8×C31semidirect
384. C31#14241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3952
C2×C31×#3912
C2×C4×C4⋊C4×C312
C31×#14462
C31×#14442
C31×#14412
C31×#14362
C31×C4⋊#952
C4×C31×#952
#1424131