Finite Group Databasebeta

← C31×#14449 #21471208

Subgroups — C31×#14449 #21471208

Order 7936.

1810 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#391C212yesmaximal, complemented
3C31×#1445C212yesmaximal, complemented
4C31×#1441C212yesmaximal, complemented
5C31×#1439C212yesmaximal
6C31×#1437C212yesmaximal
7C31×#1436C212yesmaximal, complemented
8C31×C22⋊#95C211yesmaximal, characteristic
9C31×C22⋊#95C211yesmaximal, characteristic
10C23×Q8×C31C2211yescharacteristic
11C24×C4×C31C2211yescharacteristic
12C2×C31×C22⋊Q8—28no—
13C2×C31×C22⋊Q8C418yescomplemented
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2212yes—
17C22×C22⋊C4×C31C2212yes—
18C22×C22⋊C4×C31C2212yes—
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C42×C31C2212yes—
22C31×#391—28no—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2211yescharacteristic
30C2×C31×#95C2212yes—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C25×C31C2311yescharacteristic
35C22×Q8×C31—41no—
36C22×Q8×C31—42no—
37C22×Q8×C31—41no—
38C22×Q8×C31C2×C414yes—
39C22×Q8×C31D418yes—
40C23×C4×C31—24no—
41C23×C4×C31—41no—
42C23×C4×C31—41no—
43C23×C4×C31—42no—
44C23×C4×C31C2×C414yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2312yes—
50C23×C4×C31C2312yes—
51C23×C4×C31C2312yes—
52C23×C4×C31C2311yescharacteristic
53C31×C22⋊Q8—232no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—24no—
58C2×C4⋊C4×C31—42no—
59C2×C4⋊C4×C31—42no—
60C2×C4⋊C4×C31C2×C414yes—
61C2×C4⋊C4×C31C2×C418yes—
62C2×C22⋊C4×C31—24no—
63C2×C22⋊C4×C31—24no—
64C2×C22⋊C4×C31—24no—
65C2×C22⋊C4×C31—22no—
66C2×C22⋊C4×C31—24no—
67C2×C22⋊C4×C31—41no—
68C2×C22⋊C4×C31—41no—
69C2×C22⋊C4×C31—42no—
70C2×C22⋊C4×C31—41no—
71C2×C22⋊C4×C31—41no—
72C2×C22⋊C4×C31C2×C418yes—
73C2×C22⋊C4×C31Q814yescomplemented
74C2×C42×C31—24no—
75C2×C42×C31—42no—
76C2×C42×C31—42no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—24no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—24no—
83C31×#95—42no—
84C31×#95—42no—
85C31×#95—41no—
86C31×#95—42no—
87C31×#95—41no—
88C24×C31—22no—
89C24×C31—22no—
90C24×C31—21no—
91C24×C31—21no—
92C24×C31—21no—
93C24×C31—22no—
94C24×C31—22no—
95C24×C31—21no—
96C24×C31C22×C412yes—
97C24×C31C2×Q812yes—
98C24×C31#4112yes—
99C24×C31C2411yescharacteristic
100C2×Q8×C31—44no—
101C2×Q8×C31—44no—
102C2×Q8×C31—48no—
103C2×Q8×C31—48no—
104C2×Q8×C31C22⋊C4116yescomplemented
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—21no—
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
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—28no—
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×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—44no—
150C22×C4×C31—44no—
151C22×C4×C31—48no—
152C22×C4×C31—48no—
153C22×C4×C31C22×C414yes—
154C22×C4×C31C22×C412yes—
155C22×C4×C31C22×C414yes—
156C22×C4×C31C22×C412yes—
157C22×C4×C31C2×D414yes—
158C22×C4×C31C2×D414yes—
159C22×C4×C31C2×D414yes—
160C22×C4×C31C2×Q814yes—
161C22×C4×C31#4114yes—
162C4⋊C4×C31—28no—
163C4⋊C4×C31—216no—
164C4⋊C4×C31—48no—
165C22⋊C4×C31—216no—
166C22⋊C4×C31—44no—
167C22⋊C4×C31—48no—
168C22⋊C4×C31—44no—
169C42×C31—48no—
170#14449C3111yesmaximal, characteristic, direct product factor, Sylow
171C23×C31—22no—
172C23×C31—22no—
173C23×C31—22no—
174C23×C31—22no—
175C23×C31—22no—
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—22no—
179C23×C31—22no—
180C23×C31—22no—
181C23×C31—24no—
182C23×C31—24no—
183C23×C31—24no—
184C23×C31—24no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—42no—
193C23×C31C4×Q814yes—
194C23×C31C23×C411yescharacteristic
195C23×C31C22×D412yes—
196C23×C31C22×Q811yescharacteristic
197C23×C31C2×#4111yescharacteristic
198C23×C31C2×#4112yes—
199C23×C31H(5,𝔽2)11yescharacteristic
200C23×C31H(5,𝔽2)11yescharacteristic
201C23×C31H(5,𝔽2)12yes—
202C23×C31H(5,𝔽2)11yescharacteristic
203C23×C312−1+412yes—
204C23×C312−1+411yescharacteristic
205Q8×C31—416no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—24no—
209C2×C4×C31—24no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—24no—
215C2×C4×C31—24no—
216C2×C4×C31—24no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—416no—
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×C31—42no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—42no—
248C2×C4×C31—42no—
249C2×C4×C31—42no—
250C2×C4×C31—42no—
251C2×C4×C31—42no—
252C2×C4×C31—42no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—42no—
257C2×C4×C31C2×C22⋊C418yes—
258C2×C4×C31C2×C22⋊C414yes—
259C22×C22⋊Q8C2×C3111yescharacteristic
260C2×#391C2×C3112yescomplemented
261#1445C2×C3112yescomplemented
262#1441C2×C3112yescomplemented
263#1439C2×C3112yes—
264#1437C2×C3112yes—
265#1436C2×C3112yescomplemented
266C22⋊#95C2×C3111yescharacteristic
267C22⋊#95C2×C3111yescharacteristic
268C22×C31—24no—
269C22×C31—24no—
270C22×C31—24no—
271C22×C31—42no—
272C22×C31—42no—
273C22×C31—42no—
274C22×C31—42no—
275C22×C31—44no—
276C22×C31—44no—
277C22×C31—44no—
278C22×C31—44no—
279C22×C31C22×C22⋊C411yescharacteristic
280C22×C31C2×C4×Q811yescharacteristic
281C22×C31C4×#4111yescharacteristic
282C22×C31#51811yescharacteristic
283C22×C31#51811yescharacteristic
284C22×C31#51911yescharacteristic
285C22×C31#52011yescharacteristic
286C22×C31#53412yes—
287C22×C31#53412yes—
288C22×C31#53811yescharacteristic
289C22×C31#53911yescharacteristic
290C22×C31#53912yes—
291C22×C31#54212yes—
292C22×C31#54311yescharacteristic
293C22×C31#54411yescharacteristic
294C22×C31#54812yes—
295C22×C31#54812yes—
296C22×C31D4×Q812yes—
297C22×C31#55012yes—
298C22×C31#55112yes—
299C22×C31#55412yes—
300C22×C31#56212yes—
301C22×C31#56312yes—
302C4×C31—24no—
303C4×C31—28no—
304C4×C31—42no—
305C4×C31—44no—
306C4×C31—44no—
307C4×C31—44no—
308C4×C31—82no—
309C4×C31—82no—
310C23×Q8C22×C3111yescharacteristic
311C24×C4C22×C3111yescharacteristic
312C2×C22⋊Q8—28no—
313C2×C22⋊Q8C4×C3118yescomplemented
314C22×C4⋊C4C22×C3112yes—
315C22×C4⋊C4C22×C3111yescharacteristic
316C22×C4⋊C4C22×C3112yes—
317C22×C22⋊C4C22×C3112yes—
318C22×C22⋊C4C22×C3112yes—
319C22×C22⋊C4C22×C3111yescharacteristic
320C22×C22⋊C4C22×C3111yescharacteristic
321C22×C42C22×C3112yes—
322#391—28no—
323C2×#95C22×C3112yes—
324C2×#95C22×C3112yes—
325C2×#95C22×C3112yes—
326C2×#95C22×C3112yes—
327C2×#95C22×C3112yes—
328C2×#95C22×C3112yes—
329C2×#95C22×C3111yescharacteristic
330C2×#95C22×C3112yes—
331C2×#95C22×C3111yescharacteristic
332C2×#95C22×C3112yes—
333C2×#95C22×C3112yes—
334C2×C31—44no—
335C2×C31#230811yescharacteristic
336C2×C31#232911yescharacteristic
337C2×C31#233211yescharacteristic
338C2×C31Q8×C22⋊C411yescharacteristic
339C2×C31#234111yescharacteristic
340C2×C31#236811yescharacteristic
341C2×C31#237811yescharacteristic
342C2×C31#272812yes—
343C2×C31#272912yes—
344C2×C31#273012yes—
345C2×C31#273212yes—
346C25C23×C3111yescharacteristic
347C22×Q8—41no—
348C22×Q8—42no—
349C22×Q8—41no—
350C22×Q8C2×C4×C3114yes—
351C22×Q8D4×C3118yes—
352C23×C4—24no—
353C23×C4—41no—
354C23×C4—41no—
355C23×C4—42no—
356C23×C4C2×C4×C3114yes—
357C23×C4C23×C3112yes—
358C23×C4C23×C3112yes—
359C23×C4C23×C3112yes—
360C23×C4C23×C3111yescharacteristic
361C23×C4C23×C3112yes—
362C23×C4C23×C3112yes—
363C23×C4C23×C3112yes—
364C23×C4C23×C3111yescharacteristic
365C22⋊Q8—232no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4C2×C4×C3114yes—
373C2×C4⋊C4C2×C4×C3118yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4C2×C4×C3118yes—
385C2×C22⋊C4Q8×C3114yescomplemented
386C2×C42—24no—
387C2×C42—42no—
388C2×C42—42no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—42no—
396#95—42no—
397#95—41no—
398#95—42no—
399#95—41no—
400C31#1444911yescharacteristic, direct product factor, Sylow
401C24—22no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24C22×C4×C3112yes—
410C24C2×Q8×C3112yes—
411C24#41×C3112yes—
412C24C24×C3111yescharacteristic
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—48no—
416C2×Q8—48no—
417C2×Q8C22⋊C4×C31116yescomplemented
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
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×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4C22×C4×C3114yes—
467C22×C4C22×C4×C3112yes—
468C22×C4C22×C4×C3114yes—
469C22×C4C22×C4×C3112yes—
470C22×C4C2×D4×C3114yes—
471C22×C4C2×D4×C3114yes—
472C22×C4C2×D4×C3114yes—
473C22×C4C2×Q8×C3114yes—
474C22×C4#41×C3114yes—
475C4⋊C4—28no—
476C4⋊C4—216no—
477C4⋊C4—48no—
478C22⋊C4—216no—
479C22⋊C4—44no—
480C22⋊C4—48no—
481C22⋊C4—44no—
482C42—48no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23C4×Q8×C3114yes—
506C23C23×C4×C3111yescharacteristic
507C23C22×D4×C3112yes—
508C23C22×Q8×C3111yescharacteristic
509C23C2×#41×C3111yescharacteristic
510C23C2×#41×C3112yes—
511C23C31×H(5,𝔽2)11yescharacteristic
512C23C31×H(5,𝔽2)11yescharacteristic
513C23C31×H(5,𝔽2)12yes—
514C23C31×H(5,𝔽2)11yescharacteristic
515C23C31×2−1+412yes—
516C23C31×2−1+411yescharacteristic
517Q8—416no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—416no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4C2×C22⋊C4×C3118yes—
570C2×C4C2×C22⋊C4×C3114yes—
571C22—24no—
572C22—24no—
573C22—24no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—44no—
582C22C22×C22⋊C4×C3111yescharacteristic
583C22C2×C4×Q8×C3111yescharacteristic
584C22C4×#41×C3111yescharacteristic
585C22C31×#51811yescharacteristic
586C22C31×#51811yescharacteristic
587C22C31×#51911yescharacteristic
588C22C31×#52011yescharacteristic
589C22C31×#53412yes—
590C22C31×#53412yes—
591C22C31×#53811yescharacteristic
592C22C31×#53911yescharacteristic
593C22C31×#53912yes—
594C22C31×#54212yes—
595C22C31×#54311yescharacteristic
596C22C31×#54411yescharacteristic
597C22C31×#54812yes—
598C22C31×#54812yes—
599C22D4×Q8×C3112yes—
600C22C31×#55012yes—
601C22C31×#55112yes—
602C22C31×#55412yes—
603C22C31×#56212yes—
604C22C31×#56312yes—
605C4—24no—
606C4—28no—
607C4—42no—
608C4—44no—
609C4—44no—
610C4—44no—
611C4—82no—
612C4—82no—
613C2—44no—
614C2C31×#230811yescharacteristic
615C2C31×#232911yescharacteristic
616C2C31×#233211yescharacteristic
617C2Q8×C22⋊C4×C3111yescharacteristic
618C2C31×#234111yescharacteristic
619C2C31×#236811yescharacteristic
620C2C31×#237811yescharacteristic
621C2C31×#272812yes—
622C2C31×#272912yes—
623C2C31×#273012yes—
624C2C31×#273212yes—
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×#391C2semidirect
3. C31×#1445C2semidirect
4. C31×#1441C2semidirect
7. C31×#1436C2semidirect
13. C2×C31×C22⋊Q8C4semidirect
73. C2×C22⋊C4×C31Q8semidirect
104. C2×Q8×C31C22⋊C4semidirect
170. #14449C31direct (N × H)
260. C2×#391C2×C31semidirect
261. #1445C2×C31semidirect
262. #1441C2×C31semidirect
265. #1436C2×C31semidirect
313. C2×C22⋊Q8C4×C31semidirect
385. C2×C22⋊C4Q8×C31semidirect
400. C31#14449direct (N × H)
417. C2×Q8C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3912
C31×#14452
C31×#14412
C31×#14392
C31×#14372
C31×#14362
C31×C22⋊#952
#1444931