Finite Group Databasebeta

← C31×#25949 #21482708

Subgroups — C31×#25949 #21482708

Order 7936.

1202 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic, complemented
2C31×#2561C212yesmaximal, complemented
3C31×#2534C211yesmaximal, characteristic
4C31×#2030C212yesmaximal, complemented
5C31×#2029C212yesmaximal, complemented
6C31×#1996C212yesmaximal, complemented
7C31×#1890C212yesmaximal, complemented
8C31×#1889C212yesmaximal
9C4×C31×#99C211yesmaximal, characteristic, complemented
10C31×#554—22no—
11C31×#554—24no—
12D4×Q8×C31—22no—
13C31×#544—21no—
14C31×#543—21no—
15C31×#543C2212yes—
16C31×#533—21no—
17C2×C31×#123C2211yescharacteristic
18C2×C31×C22⋊Q8—21no—
19C2×C31×C22⋊Q8C2212yes—
20C2×C31×#120C2211yescharacteristic
21C31×#518C2212yes—
22C2×C4×D4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C2×C31×#99C2212yes—
25C31×#397—22no—
26C31×#396—21no—
27C31×#394—21no—
28C31×#393—22no—
29C31×#388—24no—
30C31×#388—21no—
31C31×#386—21no—
32C31×#381C2214yes—
33C31×#381C2211yescharacteristic
34C31×#380C2211yescharacteristic
35C31×#379C2214yes—
36C31×#379C2211yescharacteristic
37C4×C22⋊C4×C31C2212yes—
38C31×#342C2214yes—
39C31×#342C2214yes—
40C31×#342C2212yes—
41C25×C31C2311yescharacteristic
42C22×Q8×C31—21no—
43C22×Q8×C31D412yescomplemented
44C22×D4×C31—21no—
45C22×D4×C31C2311yescharacteristic
46C23×C4×C31D411yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C31×C4⋊Q8—21no—
50C31×C4⋊Q8—21no—
51C31×C4⋊Q8—24no—
52C31×#125—22no—
53C31×#125—24no—
54C31×#123—24no—
55C31×C22⋊Q8—22no—
56C31×C22⋊Q8—22no—
57C31×C22⋊Q8—24no—
58C31×C22⋊Q8—24no—
59C31×C22⋊Q8—22no—
60C31×C22⋊Q8—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—22no—
64C31×C22⋊Q8—22no—
65C31×C22⋊Q8—24no—
66C31×C22⋊Q8—24no—
67C31×#120—24no—
68C4×Q8×C31—22no—
69C4×Q8×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31—24no—
73C4×D4×C31—24no—
74C31×#117—22no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31D411yescharacteristic
80C2×C4⋊C4×C31D412yescomplemented
81C2×C4⋊C4×C31D414yescomplemented
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31D411yescharacteristic
94C2×C22⋊C4×C31C2314yes—
95C2×C22⋊C4×C31C2311yescharacteristic
96C2×C22⋊C4×C31C2311yescharacteristic
97C2×C22⋊C4×C31C2311yescharacteristic
98C2×C22⋊C4×C31C2314yes—
99C2×C42×C31—22no—
100C2×C42×C31D411yescharacteristic
101C31×#99—24no—
102C31×#95—21no—
103C31×#95—22no—
104C31×#95—24no—
105C31×#95—21no—
106C31×#95—24no—
107C31×#95—21no—
108C24×C31—22no—
109C24×C31—21no—
110C24×C31—22no—
111C24×C31—22no—
112C24×C31—42no—
113C24×C31—81no—
114C24×C31C2×D411yescharacteristic
115C24×C31C2411yescharacteristic
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31—22no—
119C2×Q8×C31—22no—
120C2×Q8×C31—82no—
121C2×Q8×C31—82no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—42no—
125C2×D4×C31—42no—
126C2×D4×C31—81no—
127C2×D4×C31#4114yes—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—22no—
133C22×C4×C31—24no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—81no—
140C22×C4×C31—81no—
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D414yes—
145C22×C4×C31C2×D414yes—
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2×D411yescharacteristic
150C4⋊C4×C31—22no—
151C4⋊C4×C31—24no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—24no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—24no—
161C4⋊C4×C31—42no—
162C4⋊C4×C31—81no—
163C22⋊C4×C31—24no—
164C22⋊C4×C31—24no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—24no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—24no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—22no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—48no—
173C22⋊C4×C31—42no—
174C22⋊C4×C31—42no—
175C22⋊C4×C31—41no—
176C22⋊C4×C31—41no—
177C22⋊C4×C31—42no—
178C22⋊C4×C31—42no—
179C22⋊C4×C31—81no—
180C22⋊C4×C31—84no—
181C42×C31—24no—
182C42×C31—21no—
183C42×C31—21no—
184C42×C31—82no—
185#25949C3111yesmaximal, characteristic, direct product factor, Sylow
186C23×C31—21no—
187C23×C31—21no—
188C23×C31—24no—
189C23×C31—22no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—44no—
195C23×C31—41no—
196C23×C31—41no—
197C23×C31—42no—
198C23×C31—41no—
199C23×C31—41no—
200C23×C31—41no—
201C23×C31—41no—
202C23×C31—44no—
203C23×C31—84no—
204C23×C31—84no—
205C23×C31#12412yes—
206C23×C31C22×D411yescharacteristic
207C23×C31C22×D412yes—
208C23×C31C2×#4112yes—
209C23×C312−1+412yes—
210Q8×C31—44no—
211Q8×C31—82no—
212Q8×C31—82no—
213Q8×C31—82no—
214D4×C31—28no—
215D4×C31—84no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—21no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—21no—
222C2×C4×C31—42no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—44no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—44no—
231C2×C4×C31—44no—
232C2×C4×C31—44no—
233C2×C4×C31—41no—
234C2×C4×C31—41no—
235C2×C4×C31—41no—
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—44no—
243C2×C4×C31—44no—
244C2×C4×C31—81no—
245C2×C4×C31—82no—
246C2×C4×C31—82no—
247C2×C4×C31#12011yescharacteristic
248C2×C4×C31#12011yescharacteristic
249C2×C4×C31#12012yes—
250C2×C4×C31#12412yes—
251#3501C2×C3111yescharacteristic, complemented
252#2561C2×C3112yescomplemented
253#2534C2×C3111yescharacteristic
254#2030C2×C3112yescomplemented
255#2029C2×C3112yescomplemented
256#1996C2×C3112yescomplemented
257#1890C2×C3112yescomplemented
258#1889C2×C3112yes—
259C4×#99C2×C3111yescharacteristic, complemented
260C22×C31—22no—
261C22×C31—21no—
262C22×C31—22no—
263C22×C31—21no—
264C22×C31—22no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—42no—
268C22×C31—42no—
269C22×C31—48no—
270C22×C31—42no—
271C22×C31—41no—
272C22×C31—41no—
273C22×C31—42no—
274C22×C31—81no—
275C22×C31—81no—
276C22×C31—84no—
277C22×C31—81no—
278C22×C31—81no—
279C22×C31—81no—
280C22×C31C2×#12011yescharacteristic
281C22×C31C2×#12411yescharacteristic
282C22×C31#53611yescharacteristic
283C22×C31#54814yes—
284C4×C31—22no—
285C4×C31—21no—
286C4×C31—21no—
287C4×C31—22no—
288C4×C31—44no—
289C4×C31—41no—
290C4×C31—41no—
291C4×C31—44no—
292C4×C31—81no—
293C4×C31—84no—
294C4×C31—81no—
295C4×C31—81no—
296#554—24no—
297#554—22no—
298D4×Q8—22no—
299#544—21no—
300#543—21no—
301#543C22×C3112yes—
302#533—21no—
303C2×#123C22×C3111yescharacteristic
304C2×C22⋊Q8—21no—
305C2×C22⋊Q8C22×C3112yes—
306C2×#120C22×C3111yescharacteristic
307#518C22×C3112yes—
308C2×C4×D4C22×C3111yescharacteristic
309C22×C22⋊C4C22×C3111yescharacteristic
310C2×#99C22×C3112yes—
311#397—22no—
312#396—21no—
313#394—21no—
314#393—22no—
315#388—24no—
316#388—21no—
317#386—21no—
318#381C22×C3114yes—
319#381C22×C3111yescharacteristic
320#380C22×C3111yescharacteristic
321#379C22×C3114yes—
322#379C22×C3111yescharacteristic
323C4×C22⋊C4C22×C3112yes—
324#342C22×C3114yes—
325#342C22×C3114yes—
326#342C22×C3112yes—
327C2×C31—21no—
328C2×C31—24no—
329C2×C31—21no—
330C2×C31—42no—
331C2×C31—82no—
332C2×C31#243611yescharacteristic
333C2×C31#302511yescharacteristic
334C2×C31#302611yescharacteristic
335C25C23×C3111yescharacteristic
336C22×Q8—21no—
337C22×Q8D4×C3112yescomplemented
338C22×D4—21no—
339C22×D4C23×C3111yescharacteristic
340C23×C4D4×C3111yescharacteristic
341C23×C4C23×C3111yescharacteristic
342C23×C4C23×C3111yescharacteristic
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—24no—
346#125—22no—
347#125—24no—
348#123—24no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—24no—
360C22⋊Q8—24no—
361#120—24no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—24no—
367C4×D4—24no—
368#117—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C3111yescharacteristic
374C2×C4⋊C4D4×C3114yescomplemented
375C2×C4⋊C4D4×C3112yescomplemented
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4D4×C3111yescharacteristic
388C2×C22⋊C4C23×C3111yescharacteristic
389C2×C22⋊C4C23×C3111yescharacteristic
390C2×C22⋊C4C23×C3114yes—
391C2×C22⋊C4C23×C3111yescharacteristic
392C2×C22⋊C4C23×C3114yes—
393C2×C42—22no—
394C2×C42D4×C3111yescharacteristic
395#99—24no—
396#95—22no—
397#95—21no—
398#95—21no—
399#95—24no—
400#95—21no—
401#95—24no—
402C31#2594911yescharacteristic, direct product factor, Sylow
403C24—22no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—42no—
408C24—81no—
409C24C2×D4×C3111yescharacteristic
410C24C24×C3111yescharacteristic
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—82no—
416C2×Q8—82no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—81no—
422C2×D4#41×C3114yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4C2×D4×C3111yescharacteristic
437C22×C4C2×D4×C3111yescharacteristic
438C22×C4C2×D4×C3111yescharacteristic
439C22×C4C2×D4×C3114yes—
440C22×C4C2×D4×C3114yes—
441C22×C4C2×D4×C3111yescharacteristic
442C22×C4C2×D4×C3112yes—
443C22×C4C2×D4×C3112yes—
444C22×C4C2×D4×C3111yescharacteristic
445C4⋊C4—22no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—24no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—42no—
457C4⋊C4—81no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—22no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—24no—
467C22⋊C4—48no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—84no—
476C42—24no—
477C42—21no—
478C42—21no—
479C42—82no—
480C23—21no—
481C23—21no—
482C23—24no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—44no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—44no—
497C23—84no—
498C23—84no—
499C23C31×#12412yes—
500C23C22×D4×C3111yescharacteristic
501C23C22×D4×C3112yes—
502C23C2×#41×C3112yes—
503C23C31×2−1+412yes—
504Q8—44no—
505Q8—82no—
506Q8—82no—
507Q8—82no—
508D4—28no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—81no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4C31×#12011yescharacteristic
542C2×C4C31×#12011yescharacteristic
543C2×C4C31×#12012yes—
544C2×C4C31×#12412yes—
545C22—22no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—48no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—84no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×C31×#12011yescharacteristic
566C22C2×C31×#12411yescharacteristic
567C22C31×#53611yescharacteristic
568C22C31×#54814yes—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—41no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—84no—
580C4—81no—
581C2—21no—
582C2—24no—
583C2—21no—
584C2—42no—
585C2—82no—
586C2C31×#243611yescharacteristic
587C2C31×#302511yescharacteristic
588C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#120C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3501C2semidirect
2. C31×#2561C2semidirect
4. C31×#2030C2semidirect
5. C31×#2029C2semidirect
6. C31×#1996C2semidirect
7. C31×#1890C2semidirect
9. C4×C31×#99C2semidirect
43. C22×Q8×C31D4semidirect
80. C2×C4⋊C4×C31D4semidirect
81. C2×C4⋊C4×C31D4semidirect
185. #25949C31direct (N × H)
251. #3501C2×C31semidirect
252. #2561C2×C31semidirect
254. #2030C2×C31semidirect
255. #2029C2×C31semidirect
256. #1996C2×C31semidirect
257. #1890C2×C31semidirect
259. C4×#99C2×C31semidirect
337. C22×Q8D4×C31semidirect
374. C2×C4⋊C4D4×C31semidirect
375. C2×C4⋊C4D4×C31semidirect
402. C31#25949direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#25612
C31×#25342
C31×#20302
C31×#20292
C31×#19962
C31×#18902
C31×#18892
C4×C31×#992
#2594931