Finite Group Databasebeta

← C31×#14697 #21471456

Subgroups — C31×#14697 #21471456

Order 7936.

2574 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C31C211yesmaximal, characteristic
2C2×C31×#389C212yesmaximal, complemented
3C2×C31×#385C212yesmaximal
4C2×C31×#380C211yesmaximal, characteristic
5C2×C31×#380C211yesmaximal, characteristic
6C31×#1436C214yesmaximal, complemented
7C31×C4⋊#95C212yesmaximal, complemented
8C31×C22⋊#95C212yesmaximal
9C24×C4×C31C2211yescharacteristic
10C24×C4×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2214yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C22⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C42×C31—24no—
19C22×C42×C31—28no—
20C22×C42×C31C2212yes—
21C22×C42×C31C2212yes—
22C31×#389—28no—
23C31×#385—28no—
24C31×#380—24no—
25C31×#380C418yescomplemented
26C2×C31×#95C2214yes—
27C2×C31×#95C2214yes—
28C2×C31×#95C2214yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C25×C31C2311yescharacteristic
32C23×C4×C31—22no—
33C23×C4×C31—22no—
34C23×C4×C31—22no—
35C23×C4×C31—22no—
36C23×C4×C31—24no—
37C23×C4×C31—24no—
38C23×C4×C31—24no—
39C23×C4×C31—24no—
40C23×C4×C31—24no—
41C23×C4×C31—24no—
42C23×C4×C31C2×C414yes—
43C23×C4×C31D414yes—
44C23×C4×C31D414yes—
45C23×C4×C31Q814yes—
46C23×C4×C31Q814yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2314yes—
50C23×C4×C31C2311yescharacteristic
51C23×C4×C31C2312yes—
52C23×C4×C31C2312yes—
53C23×C4×C31C2311yescharacteristic
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—28no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—28no—
61C2×C4⋊C4×C31—28no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31C2×C418yescomplemented
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31C2×C418yes—
70C2×C42×C31—232no—
71C2×C42×C31—24no—
72C2×C42×C31—24no—
73C2×C42×C31—24no—
74C2×C42×C31—24no—
75C2×C42×C31—24no—
76C2×C42×C31D418yes—
77C31×#95—24no—
78C31×#95—28no—
79C31×#95—28no—
80C31×#95—28no—
81C31×#95C2×C418yescomplemented
82C24×C31—22no—
83C24×C31—22no—
84C24×C31—22no—
85C24×C31—22no—
86C24×C31C22×C412yes—
87C24×C31C2×D412yes—
88C24×C31C2×D412yes—
89C24×C31C2×Q812yes—
90C24×C31C2×Q812yes—
91C24×C31#4112yes—
92C24×C31#4112yes—
93C24×C31C2411yescharacteristic
94C22×C4×C31—28no—
95C22×C4×C31—28no—
96C22×C4×C31—216no—
97C22×C4×C31—216no—
98C22×C4×C31—28no—
99C22×C4×C31—28no—
100C22×C4×C31—28no—
101C22×C4×C31—28no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
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—216no—
113C22×C4×C31—28no—
114C22×C4×C31—216no—
115C22×C4×C31—216no—
116C22×C4×C31—216no—
117C22×C4×C31—28no—
118C22×C4×C31—24no—
119C22×C4×C31—24no—
120C22×C4×C31—24no—
121C22×C4×C31—24no—
122C22×C4×C31—24no—
123C22×C4×C31—24no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—24no—
128C22×C4×C31—22no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—24no—
133C22×C4×C31—24no—
134C22×C4×C31C4⋊C4116yescomplemented
135C22×C4×C31C22×C418yes—
136C22×C4×C31C22×C412yes—
137C22×C4×C31C22×C412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D414yes—
140C22×C4×C31C2×D414yes—
141C22×C4×C31C2×D414yes—
142C22×C4×C31C2×D412yes—
143C22×C4×C31C2×D414yes—
144C22×C4×C31C2×Q812yes—
145C22×C4×C31C2×Q814yes—
146C22×C4×C31C2×Q812yes—
147C22×C4×C31#4114yes—
148C22×C4×C31#4114yes—
149C22×C4×C31#4114yes—
150C4⋊C4×C31—216no—
151C4⋊C4×C31—44no—
152C4⋊C4×C31—416no—
153C4⋊C4×C31—44no—
154C22⋊C4×C31—216no—
155C22⋊C4×C31—48no—
156C42×C31—216no—
157C42×C31—216no—
158#14697C3111yesmaximal, characteristic, direct product factor, Sylow
159C23×C31—24no—
160C23×C31—24no—
161C23×C31—22no—
162C23×C31—24no—
163C23×C31—24no—
164C23×C31—24no—
165C23×C31—22no—
166C23×C31—22no—
167C23×C31—22no—
168C23×C31—24no—
169C23×C31—24no—
170C23×C31—24no—
171C23×C31—24no—
172C23×C31—24no—
173C23×C31—24no—
174C23×C31—24no—
175C23×C31C2×C4⋊C414yes—
176C23×C31C4×D414yes—
177C23×C31C4×Q814yes—
178C23×C31#12114yes—
179C23×C31C22⋊Q814yes—
180C23×C31#12514yes—
181C23×C31C4⋊Q814yes—
182C23×C31C23×C411yescharacteristic
183C23×C31C22×D411yescharacteristic
184C23×C31C22×D412yes—
185C23×C31C22×D411yescharacteristic
186C23×C31C22×Q811yescharacteristic
187C23×C31C22×Q811yescharacteristic
188C23×C31C2×#4112yes—
189C23×C31C2×#4111yescharacteristic
190C23×C31C2×#4111yescharacteristic
191C23×C31C2×#4112yes—
192C23×C31C2×#4112yes—
193C2×C4×C31—232no—
194C2×C4×C31—232no—
195C2×C4×C31—24no—
196C2×C4×C31—24no—
197C2×C4×C31—24no—
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—22no—
205C2×C4×C31—24no—
206C2×C4×C31—24no—
207C2×C4×C31—24no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—232no—
212C2×C4×C31—28no—
213C2×C4×C31—28no—
214C2×C4×C31—28no—
215C2×C4×C31—44no—
216C2×C4×C31—44no—
217C2×C4×C31—44no—
218C2×C4×C31—44no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—44no—
223C2×C4×C31—42no—
224C2×C4×C31—44no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—44no—
228C2×C4×C31—44no—
229C2×C4×C31C2×C4⋊C414yes—
230C2×C4×C31C2×C4⋊C414yes—
231C2×C4×C31C4×D418yes—
232C2×C4×C31#12014yes—
233C2×C4×C31#12118yes—
234C2×C4×C31C22⋊Q818yes—
235C2×C4×C31C22⋊Q818yes—
236C2×C4×C31#12314yes—
237C23×C42C2×C3111yescharacteristic
238C2×#389C2×C3112yescomplemented
239C2×#385C2×C3112yes—
240C2×#380C2×C3111yescharacteristic
241C2×#380C2×C3111yescharacteristic
242#1436C2×C3114yescomplemented
243C4⋊#95C2×C3112yescomplemented
244C22⋊#95C2×C3112yes—
245C22×C31—24no—
246C22×C31—24no—
247C22×C31—28no—
248C22×C31—24no—
249C22×C31—24no—
250C22×C31—28no—
251C22×C31—24no—
252C22×C31—24no—
253C22×C31—28no—
254C22×C31—28no—
255C22×C31#38918yescomplemented
256C22×C31C22×C4⋊C411yescharacteristic
257C22×C31C2×C4×D412yes—
258C22×C31C2×C4×D411yescharacteristic
259C22×C31C2×C4×Q811yescharacteristic
260C22×C31C4×#4112yes—
261C22×C31C2×#12011yescharacteristic
262C22×C31C2×#12111yescharacteristic
263C22×C31C2×#12112yes—
264C22×C31C2×C22⋊Q811yescharacteristic
265C22×C31C2×C22⋊Q812yes—
266C22×C31C2×C22⋊Q812yes—
267C22×C31C2×#12311yescharacteristic
268C22×C31#52512yes—
269C22×C31#52511yescharacteristic
270C22×C31#52512yes—
271C22×C31#52511yescharacteristic
272C22×C31C2×#12511yescharacteristic
273C22×C31#52912yes—
274C22×C31#52912yes—
275C22×C31C2×C4⋊Q811yescharacteristic
276C22×C31#53212yes—
277C22×C31#53312yes—
278C22×C31#53312yes—
279C4×C31—28no—
280C4×C31—28no—
281C4×C31—24no—
282C4×C31—48no—
283C4×C31—82no—
284C4×C31—82no—
285C4×C31#38518yescomplemented
286C24×C4C22×C3111yescharacteristic
287C24×C4C22×C3111yescharacteristic
288C24×C4C22×C3111yescharacteristic
289C22×C4⋊C4C22×C3111yescharacteristic
290C22×C4⋊C4C22×C3114yes—
291C22×C4⋊C4C22×C3111yescharacteristic
292C22×C4⋊C4C22×C3112yes—
293C22×C22⋊C4C22×C3112yes—
294C22×C22⋊C4C22×C3112yes—
295C22×C42—24no—
296C22×C42—28no—
297C22×C42C22×C3112yes—
298C22×C42C22×C3112yes—
299#389—28no—
300#385—28no—
301#380—24no—
302#380C4×C3118yescomplemented
303C2×#95C22×C3114yes—
304C2×#95C22×C3114yes—
305C2×#95C22×C3114yes—
306C2×#95C22×C3112yes—
307C2×#95C22×C3112yes—
308C2×C31—28no—
309C2×C31C2×#38511yescharacteristic
310C2×C31C2×#38911yescharacteristic
311C2×C31#229611yescharacteristic
312C2×C31C4×#12112yes—
313C2×C31C4×C22⋊Q812yes—
314C2×C31#284711yescharacteristic
315C2×C31#284811yescharacteristic
316C2×C31#285112yes—
317C2×C31#285411yescharacteristic
318C2×C31#285511yescharacteristic
319C2×C31#285712yes—
320C25C23×C3111yescharacteristic
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—24no—
328C23×C4—24no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4C2×C4×C3114yes—
332C23×C4D4×C3114yes—
333C23×C4D4×C3114yes—
334C23×C4Q8×C3114yes—
335C23×C4Q8×C3114yes—
336C23×C4C23×C3112yes—
337C23×C4C23×C3112yes—
338C23×C4C23×C3114yes—
339C23×C4C23×C3111yescharacteristic
340C23×C4C23×C3112yes—
341C23×C4C23×C3112yes—
342C23×C4C23×C3111yescharacteristic
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4C2×C4×C3118yescomplemented
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4C2×C4×C3118yes—
359C2×C42—232no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42D4×C3118yes—
366#95—24no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95C2×C4×C3118yescomplemented
371C31#1469711yescharacteristic, direct product factor, Sylow
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24C22×C4×C3112yes—
377C24C2×D4×C3112yes—
378C24C2×D4×C3112yes—
379C24C2×Q8×C3112yes—
380C24C2×Q8×C3112yes—
381C24#41×C3112yes—
382C24#41×C3112yes—
383C24C24×C3111yescharacteristic
384C22×C4—28no—
385C22×C4—28no—
386C22×C4—216no—
387C22×C4—216no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—28no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—216no—
403C22×C4—28no—
404C22×C4—216no—
405C22×C4—216no—
406C22×C4—216no—
407C22×C4—28no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4C4⋊C4×C31116yescomplemented
425C22×C4C22×C4×C3118yes—
426C22×C4C22×C4×C3112yes—
427C22×C4C22×C4×C3112yes—
428C22×C4C2×D4×C3112yes—
429C22×C4C2×D4×C3114yes—
430C22×C4C2×D4×C3114yes—
431C22×C4C2×D4×C3114yes—
432C22×C4C2×D4×C3112yes—
433C22×C4C2×D4×C3114yes—
434C22×C4C2×Q8×C3112yes—
435C22×C4C2×Q8×C3114yes—
436C22×C4C2×Q8×C3112yes—
437C22×C4#41×C3114yes—
438C22×C4#41×C3114yes—
439C22×C4#41×C3114yes—
440C4⋊C4—216no—
441C4⋊C4—44no—
442C4⋊C4—416no—
443C4⋊C4—44no—
444C22⋊C4—216no—
445C22⋊C4—48no—
446C42—216no—
447C42—216no—
448C23—24no—
449C23—24no—
450C23—22no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23C2×C4⋊C4×C3114yes—
465C23C4×D4×C3114yes—
466C23C4×Q8×C3114yes—
467C23C31×#12114yes—
468C23C31×C22⋊Q814yes—
469C23C31×#12514yes—
470C23C31×C4⋊Q814yes—
471C23C23×C4×C3111yescharacteristic
472C23C22×D4×C3111yescharacteristic
473C23C22×D4×C3112yes—
474C23C22×D4×C3111yescharacteristic
475C23C22×Q8×C3111yescharacteristic
476C23C22×Q8×C3111yescharacteristic
477C23C2×#41×C3112yes—
478C23C2×#41×C3111yescharacteristic
479C23C2×#41×C3111yescharacteristic
480C23C2×#41×C3112yes—
481C23C2×#41×C3112yes—
482C2×C4—232no—
483C2×C4—232no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—232no—
501C2×C4—28no—
502C2×C4—28no—
503C2×C4—28no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4C2×C4⋊C4×C3114yes—
519C2×C4C2×C4⋊C4×C3114yes—
520C2×C4C4×D4×C3118yes—
521C2×C4C31×#12014yes—
522C2×C4C31×#12118yes—
523C2×C4C31×C22⋊Q818yes—
524C2×C4C31×C22⋊Q818yes—
525C2×C4C31×#12314yes—
526C22—24no—
527C22—24no—
528C22—28no—
529C22—24no—
530C22—24no—
531C22—28no—
532C22—24no—
533C22—24no—
534C22—28no—
535C22—28no—
536C22C31×#38918yescomplemented
537C22C22×C4⋊C4×C3111yescharacteristic
538C22C2×C4×D4×C3112yes—
539C22C2×C4×D4×C3111yescharacteristic
540C22C2×C4×Q8×C3111yescharacteristic
541C22C4×#41×C3112yes—
542C22C2×C31×#12011yescharacteristic
543C22C2×C31×#12111yescharacteristic
544C22C2×C31×#12112yes—
545C22C2×C31×C22⋊Q811yescharacteristic
546C22C2×C31×C22⋊Q812yes—
547C22C2×C31×C22⋊Q812yes—
548C22C2×C31×#12311yescharacteristic
549C22C31×#52512yes—
550C22C31×#52511yescharacteristic
551C22C31×#52512yes—
552C22C31×#52511yescharacteristic
553C22C2×C31×#12511yescharacteristic
554C22C31×#52912yes—
555C22C31×#52912yes—
556C22C2×C31×C4⋊Q811yescharacteristic
557C22C31×#53212yes—
558C22C31×#53312yes—
559C22C31×#53312yes—
560C4—28no—
561C4—28no—
562C4—24no—
563C4—48no—
564C4—82no—
565C4—82no—
566C4C31×#38518yescomplemented
567C2—28no—
568C2C2×C31×#38511yescharacteristic
569C2C2×C31×#38911yescharacteristic
570C2C31×#229611yescharacteristic
571C2C4×C31×#12112yes—
572C2C4×C31×C22⋊Q812yes—
573C2C31×#284711yescharacteristic
574C2C31×#284811yescharacteristic
575C2C31×#285112yes—
576C2C31×#285411yescharacteristic
577C2C31×#285511yescharacteristic
578C2C31×#285712yes—
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#389C2semidirect
6. C31×#1436C2semidirect
7. C31×C4⋊#95C2semidirect
25. C31×#380C4semidirect
63. C2×C4⋊C4×C31C2×C4semidirect
81. C31×#95C2×C4semidirect
134. C22×C4×C31C4⋊C4semidirect
158. #14697C31direct (N × H)
238. C2×#389C2×C31semidirect
242. #1436C2×C31semidirect
243. C4⋊#95C2×C31semidirect
255. C22×C31#389semidirect
285. C4×C31#385semidirect
302. #380C4×C31semidirect
352. C2×C4⋊C4C2×C4×C31semidirect
370. #95C2×C4×C31semidirect
371. C31#14697direct (N × H)
424. C22×C4C4⋊C4×C31semidirect
536. C22C31×#389semidirect
566. C4C31×#385semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C312
C2×C31×#3892
C2×C31×#3852
C2×C31×#3802
C31×#14362
C31×C4⋊#952
C31×C22⋊#952
#1469731