Finite Group Databasebeta

← C31×#13879 #21470638

Subgroups — C31×#13879 #21470638

Order 7936.

2006 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#117C211yesmaximal, characteristic
2C2×C31×#384C211yesmaximal, characteristic, complemented
3C2×C31×#382C211yesmaximal, characteristic, complemented
4C2×C31×#380C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
6C31×#1439C214yesmaximal
7C31×#1436C214yesmaximal, complemented
8C31×C4⋊#95C211yesmaximal, characteristic, complemented
9C31×C4⋊#95C211yesmaximal, characteristic, complemented
10C24×C4×C31C2211yescharacteristic
11C2×C31×#117—24no—
12C2×C31×#117—24no—
13C2×C31×#117—24no—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2214yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2212yes—
20C22×C22⋊C4×C31C2212yes—
21C22×C22⋊C4×C31C2212yes—
22C22×C42×C31C2212yes—
23C22×C42×C31C2211yescharacteristic
24C22×C42×C31C2211yescharacteristic
25C31×#384—24no—
26C31×#382—24no—
27C31×#380—24no—
28C4×C22⋊C4×C31C418yescomplemented
29C2×C31×#95C2214yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2214yes—
32C2×C31×#95C2214yes—
33C2×C31×#95C2212yes—
34C25×C31C2311yescharacteristic
35C23×C4×C31—22no—
36C23×C4×C31—22no—
37C23×C4×C31—22no—
38C23×C4×C31—22no—
39C23×C4×C31C2×C414yes—
40C23×C4×C31D414yes—
41C23×C4×C31Q814yes—
42C23×C4×C31C2312yes—
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C31×#117—232no—
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—28no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—28no—
61C2×C4⋊C4×C31—22no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—44no—
64C2×C4⋊C4×C31D414yes—
65C2×C4⋊C4×C31D414yes—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—24no—
69C2×C22⋊C4×C31—24no—
70C2×C22⋊C4×C31—24no—
71C2×C22⋊C4×C31—24no—
72C2×C22⋊C4×C31—44no—
73C2×C22⋊C4×C31C2×C418yes—
74C2×C42×C31—24no—
75C2×C42×C31—24no—
76C2×C42×C31—24no—
77C2×C42×C31—22no—
78C2×C42×C31—22no—
79C2×C42×C31—22no—
80C2×C42×C31—22no—
81C2×C42×C31C2×C414yes—
82C2×C42×C31C2×C414yes—
83C31×#95—24no—
84C31×#95—28no—
85C31×#95—28no—
86C31×#95—44no—
87C31×#95C2×C418yes—
88C24×C31—21no—
89C24×C31—21no—
90C24×C31—22no—
91C24×C31—22no—
92C24×C31—21no—
93C24×C31—21no—
94C24×C31—22no—
95C24×C31—22no—
96C24×C31C22×C412yes—
97C24×C31C2×D412yes—
98C24×C31C2×Q812yes—
99C24×C31C2411yescharacteristic
100C22×C4×C31—21no—
101C22×C4×C31—21no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—21no—
105C22×C4×C31—21no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—28no—
109C22×C4×C31—28no—
110C22×C4×C31—28no—
111C22×C4×C31—28no—
112C22×C4×C31—28no—
113C22×C4×C31—28no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—24no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—24no—
124C22×C4×C31—22no—
125C22×C4×C31—24no—
126C22×C4×C31—22no—
127C22×C4×C31—24no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—24no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—24no—
136C22×C4×C31—24no—
137C22×C4×C31—24no—
138C22×C4×C31C4⋊C4116yescomplemented
139C22×C4×C31C22×C414yes—
140C22×C4×C31C22×C412yes—
141C22×C4×C31C22×C414yes—
142C22×C4×C31C22×C412yes—
143C22×C4×C31C2×D414yes—
144C22×C4×C31C2×D414yes—
145C22×C4×C31C2×D412yes—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×Q812yes—
150C22×C4×C31C2×Q812yes—
151C22×C4×C31#4114yes—
152C22×C4×C31#4114yes—
153C22×C4×C31#4112yes—
154C22×C4×C31#4112yes—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—28no—
157C4⋊C4×C31—416no—
158C4⋊C4×C31—44no—
159C4⋊C4×C31—44no—
160C22⋊C4×C31—216no—
161C22⋊C4×C31—216no—
162C22⋊C4×C31—48no—
163C42×C31—216no—
164C42×C31—28no—
165C42×C31—28no—
166#13879C3111yesmaximal, characteristic, direct product factor, Sylow
167C23×C31—24no—
168C23×C31—22no—
169C23×C31—22no—
170C23×C31—24no—
171C23×C31—22no—
172C23×C31—22no—
173C23×C31—22no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—22no—
177C23×C31—24no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—24no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31—42no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31C2×C4⋊C414yes—
190C23×C31C23×C411yescharacteristic
191C23×C31C22×D411yescharacteristic
192C23×C31C22×D411yescharacteristic
193C23×C31C22×D411yescharacteristic
194C23×C31C22×Q811yescharacteristic
195C23×C31C2×#4112yes—
196C23×C31C2×#4112yes—
197C23×C31C2×#4111yescharacteristic
198C23×C31C2×#4111yescharacteristic
199C23×C31H(5,𝔽2)12yes—
200C23×C312−1+412yes—
201C2×C4×C31—24no—
202C2×C4×C31—22no—
203C2×C4×C31—22no—
204C2×C4×C31—24no—
205C2×C4×C31—22no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—22no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—232no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—24no—
217C2×C4×C31—24no—
218C2×C4×C31—24no—
219C2×C4×C31—28no—
220C2×C4×C31—28no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—44no—
227C2×C4×C31—42no—
228C2×C4×C31—44no—
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—44no—
238C2×C4×C31—44no—
239C2×C4×C31—44no—
240C2×C4×C31—44no—
241C2×C4×C31C2×C4⋊C414yes—
242C2×C4×C31C2×C4⋊C414yes—
243C2×C4×C31#11718yescomplemented
244C2×C4×C31C4×D414yes—
245C2×C4×C31C4×D414yes—
246C2×C4×C31#12014yes—
247C2×C4×C31C22⋊Q814yes—
248C2×C4×C31C22⋊Q814yes—
249C2×C4×C31#12314yes—
250C22×#117C2×C3111yescharacteristic
251C2×#384C2×C3111yescharacteristic, complemented
252C2×#382C2×C3111yescharacteristic, complemented
253C2×#380C2×C3111yescharacteristic
254C2×C4×C22⋊C4C2×C3111yescharacteristic
255#1439C2×C3114yes—
256#1436C2×C3114yescomplemented
257C4⋊#95C2×C3111yescharacteristic, complemented
258C4⋊#95C2×C3111yescharacteristic, complemented
259C22×C31—24no—
260C22×C31—24no—
261C22×C31—24no—
262C22×C31—44no—
263C22×C31—44no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—44no—
267C22×C31—44no—
268C22×C31—42no—
269C22×C31—42no—
270C22×C31C22×C4⋊C411yescharacteristic
271C22×C31C2×#11712yes—
272C22×C31C2×C4×D411yescharacteristic
273C22×C31C2×C4×D411yescharacteristic
274C22×C31#52012yes—
275C22×C31C2×#12011yescharacteristic
276C22×C31C2×C22⋊Q811yescharacteristic
277C22×C31C2×C22⋊Q811yescharacteristic
278C22×C31C2×#12311yescharacteristic
279C22×C31#53211yescharacteristic
280C22×C31#53211yescharacteristic
281C22×C31#53312yes—
282C22×C31#53511yescharacteristic
283C22×C31#53611yescharacteristic
284C22×C31#54412yes—
285C22×C31#54612yes—
286C22×C31#54712yes—
287C22×C31#54812yes—
288C22×C31#55012yes—
289C22×C31#55212yes—
290C22×C31#55312yes—
291C22×C31#55512yes—
292C22×C31#55612yes—
293C4×C31—28no—
294C4×C31—24no—
295C4×C31—44no—
296C4×C31—44no—
297C4×C31—44no—
298C4×C31—82no—
299C4×C31—82no—
300C4×C31#38518yes—
301C24×C4C22×C3111yescharacteristic
302C2×#117—24no—
303C2×#117—24no—
304C2×#117—24no—
305C22×C4⋊C4C22×C3111yescharacteristic
306C22×C4⋊C4C22×C3111yescharacteristic
307C22×C4⋊C4C22×C3114yes—
308C22×C4⋊C4C22×C3111yescharacteristic
309C22×C4⋊C4C22×C3111yescharacteristic
310C22×C22⋊C4C22×C3112yes—
311C22×C22⋊C4C22×C3112yes—
312C22×C22⋊C4C22×C3112yes—
313C22×C42C22×C3112yes—
314C22×C42C22×C3111yescharacteristic
315C22×C42C22×C3111yescharacteristic
316#384—24no—
317#382—24no—
318#380—24no—
319C4×C22⋊C4C4×C3118yescomplemented
320C2×#95C22×C3114yes—
321C2×#95C22×C3112yes—
322C2×#95C22×C3114yes—
323C2×#95C22×C3114yes—
324C2×#95C22×C3112yes—
325C2×C31—44no—
326C2×C31#228511yescharacteristic
327C2×C31C2×#38511yescharacteristic
328C2×C31#231711yescharacteristic
329C2×C31#235212yes—
330C2×C31#235412yes—
331C2×C31#243111yescharacteristic
332C2×C31#243211yescharacteristic
333C2×C31#243912yes—
334C2×C31#244112yes—
335C2×C31#249911yescharacteristic
336C2×C31#250011yescharacteristic
337C25C23×C3111yescharacteristic
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4C2×C4×C3114yes—
343C23×C4D4×C3114yes—
344C23×C4Q8×C3114yes—
345C23×C4C23×C3112yes—
346C23×C4C23×C3112yes—
347C23×C4C23×C3112yes—
348C23×C4C23×C3112yes—
349C23×C4C23×C3112yes—
350C23×C4C23×C3111yescharacteristic
351C23×C4C23×C3112yes—
352C23×C4C23×C3111yescharacteristic
353#117—232no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4D4×C3114yes—
368C2×C4⋊C4D4×C3114yes—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×C4×C3118yes—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42C2×C4×C3114yes—
385C2×C42C2×C4×C3114yes—
386#95—24no—
387#95—28no—
388#95—28no—
389#95—44no—
390#95C2×C4×C3118yes—
391C31#1387911yescharacteristic, direct product factor, Sylow
392C24—21no—
393C24—21no—
394C24—22no—
395C24—22no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24C22×C4×C3112yes—
401C24C2×D4×C3112yes—
402C24C2×Q8×C3112yes—
403C24C24×C3111yescharacteristic
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—28no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4C4⋊C4×C31116yescomplemented
443C22×C4C22×C4×C3114yes—
444C22×C4C22×C4×C3112yes—
445C22×C4C22×C4×C3114yes—
446C22×C4C22×C4×C3112yes—
447C22×C4C2×D4×C3114yes—
448C22×C4C2×D4×C3114yes—
449C22×C4C2×D4×C3112yes—
450C22×C4C2×D4×C3112yes—
451C22×C4C2×D4×C3112yes—
452C22×C4C2×D4×C3112yes—
453C22×C4C2×Q8×C3112yes—
454C22×C4C2×Q8×C3112yes—
455C22×C4#41×C3114yes—
456C22×C4#41×C3114yes—
457C22×C4#41×C3112yes—
458C22×C4#41×C3112yes—
459C4⋊C4—28no—
460C4⋊C4—28no—
461C4⋊C4—416no—
462C4⋊C4—44no—
463C4⋊C4—44no—
464C22⋊C4—216no—
465C22⋊C4—216no—
466C22⋊C4—48no—
467C42—216no—
468C42—28no—
469C42—28no—
470C23—24no—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C2×C4⋊C4×C3114yes—
493C23C23×C4×C3111yescharacteristic
494C23C22×D4×C3111yescharacteristic
495C23C22×D4×C3111yescharacteristic
496C23C22×D4×C3111yescharacteristic
497C23C22×Q8×C3111yescharacteristic
498C23C2×#41×C3112yes—
499C23C2×#41×C3112yes—
500C23C2×#41×C3111yescharacteristic
501C23C2×#41×C3111yescharacteristic
502C23C31×H(5,𝔽2)12yes—
503C23C31×2−1+412yes—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—232no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—28no—
523C2×C4—28no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—44no—
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×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4C2×C4⋊C4×C3114yes—
545C2×C4C2×C4⋊C4×C3114yes—
546C2×C4C31×#11718yescomplemented
547C2×C4C4×D4×C3114yes—
548C2×C4C4×D4×C3114yes—
549C2×C4C31×#12014yes—
550C2×C4C31×C22⋊Q814yes—
551C2×C4C31×C22⋊Q814yes—
552C2×C4C31×#12314yes—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—44no—
557C22—44no—
558C22—42no—
559C22—42no—
560C22—44no—
561C22—44no—
562C22—42no—
563C22—42no—
564C22C22×C4⋊C4×C3111yescharacteristic
565C22C2×C31×#11712yes—
566C22C2×C4×D4×C3111yescharacteristic
567C22C2×C4×D4×C3111yescharacteristic
568C22C31×#52012yes—
569C22C2×C31×#12011yescharacteristic
570C22C2×C31×C22⋊Q811yescharacteristic
571C22C2×C31×C22⋊Q811yescharacteristic
572C22C2×C31×#12311yescharacteristic
573C22C31×#53211yescharacteristic
574C22C31×#53211yescharacteristic
575C22C31×#53312yes—
576C22C31×#53511yescharacteristic
577C22C31×#53611yescharacteristic
578C22C31×#54412yes—
579C22C31×#54612yes—
580C22C31×#54712yes—
581C22C31×#54812yes—
582C22C31×#55012yes—
583C22C31×#55212yes—
584C22C31×#55312yes—
585C22C31×#55512yes—
586C22C31×#55612yes—
587C4—28no—
588C4—24no—
589C4—44no—
590C4—44no—
591C4—44no—
592C4—82no—
593C4—82no—
594C4C31×#38518yes—
595C2—44no—
596C2C31×#228511yescharacteristic
597C2C2×C31×#38511yescharacteristic
598C2C31×#231711yescharacteristic
599C2C31×#235212yes—
600C2C31×#235412yes—
601C2C31×#243111yescharacteristic
602C2C31×#243211yescharacteristic
603C2C31×#243912yes—
604C2C31×#244112yes—
605C2C31×#249911yescharacteristic
606C2C31×#250011yescharacteristic
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×#384C2semidirect
3. C2×C31×#382C2semidirect
7. C31×#1436C2semidirect
8. C31×C4⋊#95C2semidirect
9. C31×C4⋊#95C2semidirect
28. C4×C22⋊C4×C31C4semidirect
138. C22×C4×C31C4⋊C4semidirect
166. #13879C31direct (N × H)
243. C2×C4×C31#117semidirect
251. C2×#384C2×C31semidirect
252. C2×#382C2×C31semidirect
256. #1436C2×C31semidirect
257. C4⋊#95C2×C31semidirect
258. C4⋊#95C2×C31semidirect
319. C4×C22⋊C4C4×C31semidirect
391. C31#13879direct (N × H)
442. C22×C4C4⋊C4×C31semidirect
546. C2×C4C31×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1172
C2×C31×#3842
C2×C31×#3822
C2×C31×#3802
C2×C4×C22⋊C4×C312
C31×#14392
C31×#14362
C31×C4⋊#952
#1387931