Finite Group Databasebeta

← C31×#33020 #21489779

Subgroups — C31×#33020 #21489779

Order 7936.

1824 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
1C2×C31×#518C211yesmaximal, characteristic, complemented
2C31×#2405C212yesmaximal, complemented
3C31×#2403C211yesmaximal, characteristic
4C31×#1889C214yesmaximal, complemented
5C31×#1867C214yesmaximal, complemented
6C31×#1819C212yesmaximal, complemented
7C31×#1781C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C23×D4×C31C2211yescharacteristic
10C2×C31×#123—22no—
11C2×C31×#120—21no—
12C2×C31×#120C2212yes—
13C31×#518—22no—
14C31×#518—24no—
15C31×#518C2214yes—
16C2×C4×D4×C31—22no—
17C2×C4×D4×C31—22no—
18C2×C31×#117—21no—
19C22×C22⋊C4×C31—21no—
20C22×C22⋊C4×C31C2212yes—
21C2×C31×#99C2214yes—
22C31×#394—24no—
23C31×#392—22no—
24C31×#386—21no—
25C31×#386—22no—
26C31×#386C2212yes—
27C31×#385C2214yescomplemented
28C31×#379C2211yescharacteristic
29C31×#379C2212yes—
30C31×#379C2214yescomplemented
31C31×#342C2218yescomplemented
32C25×C31D411yescharacteristic
33C25×C31C2311yescharacteristic
34C25×C31C2311yescharacteristic
35C22×D4×C31—22no—
36C22×D4×C31—22no—
37C22×D4×C31—28no—
38C22×D4×C31—21no—
39C22×D4×C31—22no—
40C22×D4×C31—21no—
41C22×D4×C31—22no—
42C22×D4×C31—22no—
43C22×D4×C31—44no—
44C22×D4×C31D412yes—
45C22×D4×C31C2312yes—
46C23×C4×C31—21no—
47C23×C4×C31—21no—
48C23×C4×C31D411yescharacteristic
49C23×C4×C31D412yescomplemented
50C23×C4×C31D412yescomplemented
51C23×C4×C31C2311yescharacteristic
52C31×#123—48no—
53C31×#120—28no—
54C31×#120—44no—
55C4×D4×C31—28no—
56C4×D4×C31—28no—
57C4×D4×C31—28no—
58C4×D4×C31—28no—
59C31×#117—24no—
60C31×#117—24no—
61C2×C4⋊C4×C31—21no—
62C2×C4⋊C4×C31—21no—
63C2×C4⋊C4×C31—24no—
64C2×C22⋊C4×C31—22no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31—22no—
67C2×C22⋊C4×C31—24no—
68C2×C22⋊C4×C31—22no—
69C2×C22⋊C4×C31—22no—
70C2×C22⋊C4×C31—22no—
71C2×C22⋊C4×C31—21no—
72C2×C22⋊C4×C31—22no—
73C2×C22⋊C4×C31—22no—
74C2×C22⋊C4×C31—22no—
75C2×C22⋊C4×C31—24no—
76C2×C22⋊C4×C31—21no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31D414yescomplemented
80C2×C22⋊C4×C31C2314yes—
81C2×C22⋊C4×C31C2312yes—
82C2×C22⋊C4×C31C2314yes—
83C2×C42×C31—22no—
84C31×#99—28no—
85C31×#95—24no—
86C31×#95—22no—
87C24×C31—21no—
88C24×C31—21no—
89C24×C31—24no—
90C24×C31—24no—
91C24×C31—22no—
92C24×C31—21no—
93C24×C31—24no—
94C24×C31—42no—
95C24×C31—42no—
96C24×C31—42no—
97C24×C31—81no—
98C24×C31—81no—
99C24×C31—81no—
100C24×C31C2×D411yescharacteristic
101C24×C31C2×D412yes—
102C24×C31C2×D411yescharacteristic
103C24×C31C2×D412yes—
104C24×C31C2×D412yes—
105C24×C31C2411yescharacteristic
106C2×D4×C31—216no—
107C2×D4×C31—216no—
108C2×D4×C31—24no—
109C2×D4×C31—24no—
110C2×D4×C31—24no—
111C2×D4×C31—24no—
112C2×D4×C31—24no—
113C2×D4×C31—28no—
114C2×D4×C31—24no—
115C2×D4×C31—42no—
116C2×D4×C31—44no—
117C2×D4×C31—44no—
118C2×D4×C31—42no—
119C2×D4×C31—44no—
120C2×D4×C31—42no—
121C2×D4×C31—41no—
122C2×D4×C31—42no—
123C2×D4×C31—41no—
124C2×D4×C31—44no—
125C2×D4×C31—44no—
126C2×D4×C31—82no—
127C2×D4×C31#4118yes—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—24no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—24no—
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—24no—
140C22×C4×C31—22no—
141C22×C4×C31—42no—
142C22×C4×C31—44no—
143C22×C4×C31—82no—
144C22×C4×C31—82no—
145C22×C4×C31—82no—
146C22×C4×C31C2×D412yes—
147C22×C4×C31C2×D414yes—
148C22×C4×C31C2×D414yes—
149C4⋊C4×C31—24no—
150C4⋊C4×C31—24no—
151C4⋊C4×C31—48no—
152C22⋊C4×C31—28no—
153C22⋊C4×C31—24no—
154C22⋊C4×C31—24no—
155C22⋊C4×C31—24no—
156C22⋊C4×C31—24no—
157C22⋊C4×C31—28no—
158C22⋊C4×C31—24no—
159C22⋊C4×C31—44no—
160C22⋊C4×C31—42no—
161C22⋊C4×C31—48no—
162C22⋊C4×C31—44no—
163C22⋊C4×C31—44no—
164C22⋊C4×C31—84no—
165C22⋊C4×C31—82no—
166C22⋊C4×C31—81no—
167C42×C31—28no—
168#33020C3111yesmaximal, characteristic, direct product factor, Sylow
169C23×C31—24no—
170C23×C31—24no—
171C23×C31—22no—
172C23×C31—22no—
173C23×C31—24no—
174C23×C31—24no—
175C23×C31—22no—
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—24no—
179C23×C31—24no—
180C23×C31—22no—
181C23×C31—41no—
182C23×C31—42no—
183C23×C31—41no—
184C23×C31—41no—
185C23×C31—42no—
186C23×C31—41no—
187C23×C31—42no—
188C23×C31—41no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31—42no—
192C23×C31—44no—
193C23×C31—42no—
194C23×C31—41no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—41no—
198C23×C31—42no—
199C23×C31—44no—
200C23×C31—81no—
201C23×C31—81no—
202C23×C31—88no—
203C23×C31—88no—
204C23×C31—88no—
205C23×C31#12011yescharacteristic
206C23×C31#12012yes—
207C23×C31#12011yescharacteristic
208C23×C31#12314yescomplemented
209C23×C31C22×D411yescharacteristic
210C23×C31C22×D412yes—
211C23×C31C2×#4114yes—
212D4×C31—216no—
213D4×C31—216no—
214D4×C31—48no—
215D4×C31—44no—
216D4×C31—44no—
217D4×C31—88no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—24no—
224C2×C4×C31—24no—
225C2×C4×C31—24no—
226C2×C4×C31—42no—
227C2×C4×C31—41no—
228C2×C4×C31—44no—
229C2×C4×C31—41no—
230C2×C4×C31—44no—
231C2×C4×C31—44no—
232C2×C4×C31—44no—
233C2×C4×C31—44no—
234C2×C4×C31—42no—
235C2×C4×C31—44no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—44no—
239C2×C4×C31—82no—
240C2×C4×C31—82no—
241C2×C4×C31—84no—
242C2×C4×C31—84no—
243C2×C4×C31#12314yescomplemented
244C2×#518C2×C3111yescharacteristic, complemented
245#2405C2×C3112yescomplemented
246#2403C2×C3111yescharacteristic
247#1889C2×C3114yescomplemented
248#1867C2×C3114yescomplemented
249#1819C2×C3112yescomplemented
250#1781C2×C3111yescharacteristic, complemented
251C22×C31—21no—
252C22×C31—22no—
253C22×C31—21no—
254C22×C31—21no—
255C22×C31—22no—
256C22×C31—21no—
257C22×C31—21no—
258C22×C31—22no—
259C22×C31—24no—
260C22×C31—22no—
261C22×C31—21no—
262C22×C31—22no—
263C22×C31—21no—
264C22×C31—44no—
265C22×C31—48no—
266C22×C31—44no—
267C22×C31—44no—
268C22×C31—48no—
269C22×C31—44no—
270C22×C31—48no—
271C22×C31—42no—
272C22×C31—42no—
273C22×C31—42no—
274C22×C31—82no—
275C22×C31—82no—
276C22×C31—84no—
277C22×C31—82no—
278C22×C31—84no—
279C22×C31—84no—
280C22×C31—81no—
281C22×C31—81no—
282C22×C31B(4,𝔽2)12yes—
283C22×C31C2×#12011yescharacteristic
284C22×C31C2×#12312yes—
285C22×C31#52514yes—
286C4×C31—24no—
287C4×C31—42no—
288C4×C31—44no—
289C4×C31—44no—
290C4×C31—84no—
291C4×C31—82no—
292C23×D4C22×C3111yescharacteristic
293C23×D4C22×C3111yescharacteristic
294C2×#123—22no—
295C2×#120—21no—
296C2×#120C22×C3112yes—
297#518—22no—
298#518—24no—
299#518C22×C3114yes—
300C2×C4×D4—22no—
301C2×C4×D4—22no—
302C2×#117—21no—
303C22×C22⋊C4—21no—
304C22×C22⋊C4C22×C3112yes—
305C2×#99C22×C3114yes—
306#394—24no—
307#392—22no—
308#386—21no—
309#386—22no—
310#386C22×C3112yes—
311#385C22×C3114yescomplemented
312#379C22×C3111yescharacteristic
313#379C22×C3112yes—
314#379C22×C3114yescomplemented
315#342C22×C3118yescomplemented
316C2×C31—22no—
317C2×C31—24no—
318C2×C31—22no—
319C2×C31—42no—
320C2×C31—41no—
321C2×C31—44no—
322C2×C31—82no—
323C2×C31#284911yescharacteristic
324C2×C31C2×B(4,𝔽2)11yescharacteristic
325C2×C31#302611yescharacteristic
326C25D4×C3111yescharacteristic
327C25C23×C3111yescharacteristic
328C25C23×C3111yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—28no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—44no—
338C22×D4D4×C3112yes—
339C22×D4C23×C3112yes—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4D4×C3111yescharacteristic
343C23×C4D4×C3112yescomplemented
344C23×C4D4×C3112yescomplemented
345C23×C4C23×C3111yescharacteristic
346#123—48no—
347#120—28no—
348#120—44no—
349C4×D4—28no—
350C4×D4—28no—
351C4×D4—28no—
352C4×D4—28no—
353#117—24no—
354#117—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4D4×C3114yescomplemented
374C2×C22⋊C4C23×C3112yes—
375C2×C22⋊C4C23×C3114yes—
376C2×C22⋊C4C23×C3114yes—
377C2×C42—22no—
378#99—28no—
379#95—24no—
380#95—22no—
381C31#3302011yescharacteristic, direct product factor, Sylow
382C24—21no—
383C24—21no—
384C24—24no—
385C24—24no—
386C24—22no—
387C24—21no—
388C24—24no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—81no—
393C24—81no—
394C24—81no—
395C24C2×D4×C3111yescharacteristic
396C24C2×D4×C3112yes—
397C24C2×D4×C3111yescharacteristic
398C24C2×D4×C3112yes—
399C24C2×D4×C3112yes—
400C24C24×C3111yescharacteristic
401C2×D4—216no—
402C2×D4—216no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—28no—
409C2×D4—24no—
410C2×D4—42no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—82no—
422C2×D4#41×C3118yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—82no—
441C22×C4C2×D4×C3112yes—
442C22×C4C2×D4×C3114yes—
443C22×C4C2×D4×C3114yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—48no—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—42no—
456C22⋊C4—48no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—84no—
460C22⋊C4—82no—
461C22⋊C4—81no—
462C42—28no—
463C23—24no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—41no—
492C23—42no—
493C23—44no—
494C23—81no—
495C23—81no—
496C23—88no—
497C23—88no—
498C23—88no—
499C23C31×#12011yescharacteristic
500C23C31×#12012yes—
501C23C31×#12011yescharacteristic
502C23C31×#12314yescomplemented
503C23C22×D4×C3111yescharacteristic
504C23C22×D4×C3112yes—
505C23C2×#41×C3114yes—
506D4—216no—
507D4—216no—
508D4—48no—
509D4—44no—
510D4—44no—
511D4—88no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—41no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4—84no—
537C2×C4C31×#12314yescomplemented
538C22—21no—
539C22—22no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—24no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—44no—
552C22—44no—
553C22—48no—
554C22—44no—
555C22—48no—
556C22—44no—
557C22—48no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—82no—
563C22—84no—
564C22—82no—
565C22—84no—
566C22—84no—
567C22—81no—
568C22—81no—
569C22C31×B(4,𝔽2)12yes—
570C22C2×C31×#12011yescharacteristic
571C22C2×C31×#12312yes—
572C22C31×#52514yes—
573C4—24no—
574C4—42no—
575C4—44no—
576C4—44no—
577C4—82no—
578C4—84no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—41no—
583C2—42no—
584C2—44no—
585C2—82no—
586C2C31×#284911yescharacteristic
587C2C2×C31×B(4,𝔽2)11yescharacteristic
588C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#2403C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#518C2semidirect
2. C31×#2405C2semidirect
4. C31×#1889C2semidirect
5. C31×#1867C2semidirect
6. C31×#1819C2semidirect
7. C31×#1781C2semidirect
27. C31×#385C22semidirect
30. C31×#379C22semidirect
31. C31×#342C22semidirect
49. C23×C4×C31D4semidirect
50. C23×C4×C31D4semidirect
79. C2×C22⋊C4×C31D4semidirect
168. #33020C31direct (N × H)
208. C23×C31#123semidirect
243. C2×C4×C31#123semidirect
244. C2×#518C2×C31semidirect
245. #2405C2×C31semidirect
247. #1889C2×C31semidirect
248. #1867C2×C31semidirect
249. #1819C2×C31semidirect
250. #1781C2×C31semidirect
311. #385C22×C31semidirect
314. #379C22×C31semidirect
315. #342C22×C31semidirect
343. C23×C4D4×C31semidirect
344. C23×C4D4×C31semidirect
373. C2×C22⋊C4D4×C31semidirect
381. C31#33020direct (N × H)
502. C23C31×#123semidirect
537. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5182
C31×#24052
C31×#24032
C31×#18892
C31×#18672
C31×#18192
C31×#17812
#3302031