Finite Group Databasebeta

← C31×#25603 #21482362

Subgroups — C31×#25603 #21482362

Order 7936.

1172 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#533C211yesmaximal, characteristic, complemented
2C2×C31×#497C211yesmaximal, characteristic, complemented
3C2×C31×#489C211yesmaximal, characteristic, complemented
4C31×#2850C211yesmaximal, characteristic
5C31×#2001C212yesmaximal, complemented
6C31×#2000C212yesmaximal
7C31×#1993C211yesmaximal, characteristic, complemented
8C31×#1960C211yesmaximal, characteristic, complemented
9C31×#1880C212yesmaximal, complemented
10C31×#1878C212yesmaximal, complemented
11C31×#1749C211yesmaximal, characteristic, complemented
12C22×Q16×C31C2212yes—
13C22×SD16×C31C2212yes—
14C31×#533—24no—
15C31×#533—24no—
16C2×C31×C4⋊Q8C2211yescharacteristic
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×#125—21no—
19C2×C31×#124C2211yescharacteristic
20C2×C31×C22⋊Q8—21no—
21C2×C31×C22⋊Q8C2212yes—
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×Q8×C31—21no—
25C2×C4×Q8×C31C2212yes—
26C2×C31×#117—21no—
27C22×C42×C31C2211yescharacteristic
28C31×#497—24no—
29C31×#489—24no—
30C2×C31×#103C2212yes—
31C2×C31×#103C2212yes—
32C2×C31×#103C2212yes—
33C2×C31×#102C2212yes—
34C2×C31×C22⋊C8C2212yes—
35C2×C31×#97C2211yescharacteristic
36C2×C31×#97C2211yescharacteristic
37C31×#391C2211yescharacteristic
38C31×#390C2211yescharacteristic
39C31×#388—21no—
40C31×#388—21no—
41C31×#386—21no—
42C31×#386—21no—
43C31×#382C2211yescharacteristic
44C31×#340C2212yes—
45C31×#340C2212yes—
46C31×#336C2212yes—
47C22×Q8×C31—21no—
48C22×Q8×C31C2311yescharacteristic
49C22×Q8×C31C2312yes—
50C22×D4×C31—21no—
51C22×D4×C31C2311yescharacteristic
52C23×C4×C31D411yescharacteristic
53C23×C4×C31D411yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C2×Q16×C31—24no—
56C2×Q16×C31—24no—
57C2×Q16×C31—42no—
58C2×SD16×C31—24no—
59C2×SD16×C31—24no—
60C2×SD16×C31—42no—
61C22×C8×C31C2312yes—
62C22×C8×C31C2312yes—
63C31×C4⋊Q8—22no—
64C31×C4⋊Q8—22no—
65C31×C4⋊Q8D414yescomplemented
66C31×C4⋊Q8D414yescomplemented
67C31×#125—28no—
68C31×#124—22no—
69C31×#124—22no—
70C31×C22⋊Q8—28no—
71C31×C22⋊Q8—24no—
72C31×C22⋊Q8—24no—
73C31×C22⋊Q8—42no—
74C31×#121—42no—
75C4×Q8×C31—28no—
76C4×Q8×C31—24no—
77C4×Q8×C31—24no—
78C31×#117—28no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—21no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31C2311yescharacteristic
86C2×C4⋊C4×C31C2311yescharacteristic
87C2×C4⋊C4×C31C2312yes—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31—21no—
94C2×C22⋊C4×C31—21no—
95C2×C42×C31—22no—
96C2×C42×C31—22no—
97C2×C42×C31—22no—
98C2×C42×C31D411yescharacteristic
99C2×C42×C31D411yescharacteristic
100C2×C42×C31C2311yescharacteristic
101C2×C42×C31C2311yescharacteristic
102C31×#103—24no—
103C31×#103—42no—
104C31×#103—42no—
105C31×#102—24no—
106C31×C22⋊C8—24no—
107C31×#97—22no—
108C31×#97—22no—
109C31×#95—21no—
110C31×#95—21no—
111C31×#95—21no—
112C31×#95—21no—
113C24×C31—21no—
114C24×C31C2×D411yescharacteristic
115C2×Q8×C31—24no—
116C2×Q8×C31—22no—
117C2×Q8×C31—21no—
118C2×Q8×C31—21no—
119C2×Q8×C31—22no—
120C2×Q8×C31—22no—
121C2×Q8×C31—22no—
122C2×Q8×C31—22no—
123C2×Q8×C31—22no—
124C2×Q8×C31—22no—
125C2×Q8×C31—42no—
126C2×Q8×C31—42no—
127C2×Q8×C31C2×D414yes—
128C2×D4×C31—21no—
129C2×D4×C31—21no—
130C2×D4×C31—22no—
131C2×D4×C31—22no—
132C2×D4×C31—42no—
133C2×D4×C31—42no—
134C2×D4×C31—42no—
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—21no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—41no—
149C22×C4×C31—41no—
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2411yescharacteristic
156Q16×C31—48no—
157SD16×C31—48no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C2×C8×C31#4114yes—
164C4⋊C4×C31—28no—
165C4⋊C4×C31—28no—
166C4⋊C4×C31—24no—
167C4⋊C4×C31—24no—
168C4⋊C4×C31—24no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—42no—
173C4⋊C4×C31C2×D414yes—
174C22⋊C4×C31—28no—
175C22⋊C4×C31—42no—
176C22⋊C4×C31—42no—
177C22⋊C4×C31—42no—
178C22⋊C4×C31—42no—
179C22⋊C4×C31—42no—
180C22⋊C4×C31—42no—
181C42×C31—28no—
182C42×C31—22no—
183C42×C31—22no—
184C42×C31—21no—
185C42×C31—21no—
186C42×C31C2×D412yes—
187C42×C31C2×D412yes—
188#25603C3111yesmaximal, characteristic, direct product factor, Sylow
189C23×C31—21no—
190C23×C31—21no—
191C23×C31—21no—
192C23×C31—21no—
193C23×C31—21no—
194C23×C31—21no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31—41no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—41no—
201C23×C31—41no—
202C23×C31#13712yes—
203C23×C31C22×D411yescharacteristic
204Q8×C31—24no—
205Q8×C31—24no—
206Q8×C31—48no—
207Q8×C31—42no—
208Q8×C31—42no—
209Q8×C31—42no—
210Q8×C31—42no—
211D4×C31—42no—
212D4×C31—42no—
213D4×C31—84no—
214C2×C4×C31—28no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—21no—
220C2×C4×C31—21no—
221C2×C4×C31—21no—
222C2×C4×C31—21no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—21no—
226C2×C4×C31—21no—
227C2×C4×C31—21no—
228C2×C4×C31—21no—
229C2×C4×C31—44no—
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—41no—
237C2×C4×C31—41no—
238C2×C4×C31—41no—
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#12012yes—
246C2×C4×C31#12012yes—
247C2×C4×C31#13712yes—
248C2×C4×C31C22×D411yescharacteristic
249C2×C4×C31C22×D411yescharacteristic
250C2×C4×C31C2×#4112yes—
251C2×C4×C31H(5,𝔽2)12yes—
252C8×C31—24no—
253C8×C31—42no—
254C2×#533C2×C3111yescharacteristic, complemented
255C2×#497C2×C3111yescharacteristic, complemented
256C2×#489C2×C3111yescharacteristic, complemented
257#2850C2×C3111yescharacteristic
258#2001C2×C3112yescomplemented
259#2000C2×C3112yes—
260#1993C2×C3111yescharacteristic, complemented
261#1960C2×C3111yescharacteristic, complemented
262#1880C2×C3112yescomplemented
263#1878C2×C3112yescomplemented
264#1749C2×C3111yescharacteristic, complemented
265C22×C31—22no—
266C22×C31—22no—
267C22×C31—22no—
268C22×C31—41no—
269C22×C31—41no—
270C22×C31—41no—
271C22×C31—41no—
272C22×C31—81no—
273C22×C31—81no—
274C22×C31—81no—
275C22×C31—81no—
276C22×C31—81no—
277C22×C31—81no—
278C22×C31—81no—
279C22×C31C2×#12011yescharacteristic
280C22×C31#53211yescharacteristic
281C22×C31#53511yescharacteristic
282C22×C31C2×#13711yescharacteristic
283C22×C31C2×#13711yescharacteristic
284C22×C31#57511yescharacteristic
285C22×C31#57511yescharacteristic
286C4×C31—22no—
287C4×C31—22no—
288C4×C31—22no—
289C4×C31—41no—
290C4×C31—44no—
291C4×C31—41no—
292C4×C31—44no—
293C4×C31—81no—
294C4×C31—81no—
295C4×C31—81no—
296C4×C31#54612yes—
297C4×C31#55012yes—
298C22×Q16C22×C3112yes—
299C22×SD16C22×C3112yes—
300#533—24no—
301#533—24no—
302C2×C4⋊Q8C22×C3111yescharacteristic
303C2×C4⋊Q8C22×C3111yescharacteristic
304C2×#125—21no—
305C2×#124C22×C3111yescharacteristic
306C2×C22⋊Q8—21no—
307C2×C22⋊Q8C22×C3112yes—
308C2×C22⋊Q8C22×C3111yescharacteristic
309C2×#121C22×C3111yescharacteristic
310C2×C4×Q8—21no—
311C2×C4×Q8C22×C3112yes—
312C2×#117—21no—
313C22×C42C22×C3111yescharacteristic
314#497—24no—
315#489—24no—
316C2×#103C22×C3112yes—
317C2×#103C22×C3112yes—
318C2×#103C22×C3112yes—
319C2×#102C22×C3112yes—
320C2×C22⋊C8C22×C3112yes—
321C2×#97C22×C3111yescharacteristic
322C2×#97C22×C3111yescharacteristic
323#391C22×C3111yescharacteristic
324#390C22×C3111yescharacteristic
325#388—21no—
326#388—21no—
327#386—21no—
328#386—21no—
329#382C22×C3111yescharacteristic
330#340C22×C3112yes—
331#340C22×C3112yes—
332#336C22×C3112yes—
333C2×C31—42no—
334C2×C31—161no—
335C2×C31#243111yescharacteristic
336C2×C31#300411yescharacteristic
337C2×C31#300511yescharacteristic
338C2×C31#317211yescharacteristic
339C2×C31#318111yescharacteristic
340C2×C31#321511yescharacteristic
341C2×C31#321611yescharacteristic
342C22×Q8—21no—
343C22×Q8C23×C3111yescharacteristic
344C22×Q8C23×C3112yes—
345C22×D4—21no—
346C22×D4C23×C3111yescharacteristic
347C23×C4D4×C3111yescharacteristic
348C23×C4D4×C3111yescharacteristic
349C23×C4C23×C3111yescharacteristic
350C2×Q16—24no—
351C2×Q16—24no—
352C2×Q16—42no—
353C2×SD16—24no—
354C2×SD16—24no—
355C2×SD16—42no—
356C22×C8C23×C3112yes—
357C22×C8C23×C3112yes—
358C4⋊Q8—22no—
359C4⋊Q8—22no—
360C4⋊Q8D4×C3114yescomplemented
361C4⋊Q8D4×C3114yescomplemented
362#125—28no—
363#124—22no—
364#124—22no—
365C22⋊Q8—28no—
366C22⋊Q8—24no—
367C22⋊Q8—24no—
368C22⋊Q8—42no—
369#121—42no—
370C4×Q8—28no—
371C4×Q8—24no—
372C4×Q8—24no—
373#117—28no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C23×C3111yescharacteristic
381C2×C4⋊C4C23×C3111yescharacteristic
382C2×C4⋊C4C23×C3112yes—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42D4×C3111yescharacteristic
394C2×C42D4×C3111yescharacteristic
395C2×C42C23×C3111yescharacteristic
396C2×C42C23×C3111yescharacteristic
397#103—24no—
398#103—42no—
399#103—42no—
400#102—24no—
401C22⋊C8—24no—
402#97—22no—
403#97—22no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408C31#2560311yescharacteristic, direct product factor, Sylow
409C24—21no—
410C24C2×D4×C3111yescharacteristic
411C2×Q8—24no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8C2×D4×C3114yes—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—42no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4C2×D4×C3111yescharacteristic
447C22×C4C2×D4×C3111yescharacteristic
448C22×C4C2×D4×C3111yescharacteristic
449C22×C4C2×D4×C3111yescharacteristic
450C22×C4C2×D4×C3111yescharacteristic
451C22×C4C24×C3111yescharacteristic
452Q16—48no—
453SD16—48no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8#41×C3114yes—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—42no—
469C4⋊C4C2×D4×C3114yes—
470C22⋊C4—28no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C42—28no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42C2×D4×C3112yes—
483C42C2×D4×C3112yes—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C31×#13712yes—
498C23C22×D4×C3111yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—48no—
502Q8—42no—
503Q8—42no—
504Q8—42no—
505Q8—42no—
506D4—42no—
507D4—42no—
508D4—84no—
509C2×C4—28no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4C31×#12012yes—
541C2×C4C31×#12012yes—
542C2×C4C31×#13712yes—
543C2×C4C22×D4×C3111yescharacteristic
544C2×C4C22×D4×C3111yescharacteristic
545C2×C4C2×#41×C3112yes—
546C2×C4C31×H(5,𝔽2)12yes—
547C8—24no—
548C8—42no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C2×C31×#12011yescharacteristic
564C22C31×#53211yescharacteristic
565C22C31×#53511yescharacteristic
566C22C2×C31×#13711yescharacteristic
567C22C2×C31×#13711yescharacteristic
568C22C31×#57511yescharacteristic
569C22C31×#57511yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—44no—
575C4—41no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4C31×#54612yes—
581C4C31×#55012yes—
582C2—42no—
583C2—161no—
584C2C31×#243111yescharacteristic
585C2C31×#300411yescharacteristic
586C2C31×#300511yescharacteristic
587C2C31×#317211yescharacteristic
588C2C31×#318111yescharacteristic
589C2C31×#321511yescharacteristic
590C2C31×#321611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×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. C2×C31×#533C2semidirect
2. C2×C31×#497C2semidirect
3. C2×C31×#489C2semidirect
5. C31×#2001C2semidirect
7. C31×#1993C2semidirect
8. C31×#1960C2semidirect
9. C31×#1880C2semidirect
10. C31×#1878C2semidirect
11. C31×#1749C2semidirect
65. C31×C4⋊Q8D4semidirect
66. C31×C4⋊Q8D4semidirect
188. #25603C31direct (N × H)
254. C2×#533C2×C31semidirect
255. C2×#497C2×C31semidirect
256. C2×#489C2×C31semidirect
258. #2001C2×C31semidirect
260. #1993C2×C31semidirect
261. #1960C2×C31semidirect
262. #1880C2×C31semidirect
263. #1878C2×C31semidirect
264. #1749C2×C31semidirect
360. C4⋊Q8D4×C31semidirect
361. C4⋊Q8D4×C31semidirect
408. C31#25603direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5332
C2×C31×#4972
C2×C31×#4892
C31×#28502
C31×#20012
C31×#20002
C31×#19932
C31×#19602
C31×#18802
C31×#18782
C31×#17492
#2560331