Finite Group Databasebeta

← C31×#24660 #21481419

Subgroups — C31×#24660 #21481419

Order 7936.

876 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#462C211yesmaximal, characteristic, complemented
2C2×C31×#432C211yesmaximal, characteristic
3C31×#2857C211yesmaximal, characteristic
4C4×C31×C22⋊Q8C211yesmaximal, characteristic
5C31×#2035C212yesmaximal
6C31×#2001C212yesmaximal
7C31×#1981C211yesmaximal, characteristic, complemented
8C31×#1971C212yesmaximal, complemented
9C31×#1948C211yesmaximal, characteristic, complemented
10C31×#1935C212yesmaximal, complemented
11C31×#1803C211yesmaximal, characteristic, complemented
12C22×Q16×C31C2212yes—
13C2×C31×C4⋊Q8C2211yescharacteristic
14C2×C31×C22⋊Q8C2211yescharacteristic
15C2×C31×C22⋊Q8C2212yes—
16C2×C4×Q8×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C31×#462—24no—
19C31×#432—24no—
20C2×C31×#106C2212yes—
21C2×C31×C4⋊C8C2211yescharacteristic
22C2×C31×C4⋊C8C2211yescharacteristic
23C2×C31×#103C2212yes—
24C2×C31×#103C2212yes—
25C2×C31×#103C2212yes—
26C2×C31×#103C2212yes—
27C2×C31×C22⋊C8C2212yes—
28C2×C31×#97C2212yes—
29C31×#391C2212yes—
30C31×#391C2211yescharacteristic
31C31×#389—21no—
32C31×#389—21no—
33C31×#389C2211yescharacteristic
34C31×#387—21no—
35C31×#385—21no—
36C31×#384C2211yescharacteristic
37C31×#380—21no—
38C31×#380—21no—
39C31×#380C2211yescharacteristic
40C4×C4⋊C4×C31—21no—
41C4×C4⋊C4×C31C2211yescharacteristic
42C4×C22⋊C4×C31—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C22×Q8×C31C2312yes—
46C22×Q8×C31C2311yescharacteristic
47C23×C4×C31D411yescharacteristic
48C23×C4×C31D411yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C2×Q16×C31—24no—
51C2×Q16×C31—24no—
52C2×Q16×C31—42no—
53C22×C8×C31C2312yes—
54C22×C8×C31C2312yes—
55C31×C4⋊Q8—22no—
56C31×C4⋊Q8—22no—
57C31×C22⋊Q8—22no—
58C31×C22⋊Q8—22no—
59C31×C22⋊Q8—42no—
60C31×C22⋊Q8—42no—
61C4×Q8×C31—22no—
62C4×Q8×C31—22no—
63C2×C4⋊C4×C31—21no—
64C2×C4⋊C4×C31—21no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—21no—
67C2×C4⋊C4×C31—21no—
68C2×C4⋊C4×C31—21no—
69C2×C4⋊C4×C31—21no—
70C2×C4⋊C4×C31—21no—
71C2×C4⋊C4×C31C2311yescharacteristic
72C2×C4⋊C4×C31C2311yescharacteristic
73C2×C4⋊C4×C31C2312yes—
74C2×C4⋊C4×C31C2311yescharacteristic
75C2×C22⋊C4×C31—21no—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—21no—
78C2×C42×C31—22no—
79C2×C42×C31—22no—
80C2×C42×C31—21no—
81C2×C42×C31—21no—
82C2×C42×C31D411yescharacteristic
83C2×C42×C31D411yescharacteristic
84C2×C42×C31C2311yescharacteristic
85C2×C42×C31C2311yescharacteristic
86C31×#106—42no—
87C31×C4⋊C8—22no—
88C31×C4⋊C8D414yes—
89C31×#103—24no—
90C31×#103—24no—
91C31×#103—42no—
92C31×#103—42no—
93C31×C22⋊C8—24no—
94C31×#97—24no—
95C31×#95—21no—
96C31×#95—21no—
97C31×#95—21no—
98C31×#95—21no—
99C31×#95—21no—
100C31×#95—22no—
101C31×#95—22no—
102C24×C31C2×D411yescharacteristic
103C2×Q8×C31—21no—
104C2×Q8×C31—21no—
105C2×Q8×C31—22no—
106C2×Q8×C31—21no—
107C2×Q8×C31—22no—
108C2×Q8×C31—22no—
109C2×Q8×C31—22no—
110C2×Q8×C31—21no—
111C2×Q8×C31—21no—
112C2×Q8×C31—22no—
113C2×Q8×C31—22no—
114C2×Q8×C31#4112yes—
115C22×C4×C31—22no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—41no—
133C22×C4×C31C2×D411yescharacteristic
134C22×C4×C31C2×D411yescharacteristic
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2411yescharacteristic
139Q16×C31—48no—
140C2×C8×C31—22no—
141C2×C8×C31—22no—
142C2×C8×C31—22no—
143C2×C8×C31—22no—
144C2×C8×C31—22no—
145C2×C8×C31C2×D414yes—
146C4⋊C4×C31—24no—
147C4⋊C4×C31—21no—
148C4⋊C4×C31—21no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—22no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—42no—
155C4⋊C4×C31—42no—
156C4⋊C4×C31—44no—
157C4⋊C4×C31—42no—
158C4⋊C4×C31—42no—
159C4⋊C4×C31—42no—
160C4⋊C4×C31—42no—
161C4⋊C4×C31#4112yes—
162C22⋊C4×C31—24no—
163C22⋊C4×C31—44no—
164C22⋊C4×C31—42no—
165C42×C31—22no—
166C42×C31—22no—
167C42×C31—21no—
168C42×C31—21no—
169C42×C31—42no—
170C42×C31—42no—
171C42×C31C2×D412yes—
172C42×C31#4112yes—
173#24660C3111yesmaximal, characteristic, direct product factor, Sylow
174C23×C31—21no—
175C23×C31—21no—
176C23×C31—21no—
177C23×C31—21no—
178C23×C31—21no—
179C23×C31—21no—
180C23×C31#13712yes—
181C23×C31C22×D411yescharacteristic
182Q8×C31—22no—
183Q8×C31—22no—
184Q8×C31—41no—
185Q8×C31—41no—
186Q8×C31—42no—
187Q8×C31—42no—
188Q8×C31—42no—
189Q8×C31—42no—
190C2×C4×C31—21no—
191C2×C4×C31—21no—
192C2×C4×C31—21no—
193C2×C4×C31—21no—
194C2×C4×C31—21no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—21no—
198C2×C4×C31—21no—
199C2×C4×C31—21no—
200C2×C4×C31—21no—
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—44no—
204C2×C4×C31—41no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—41no—
208C2×C4×C31—41no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31—41no—
212C2×C4×C31—44no—
213C2×C4×C31—41no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—42no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—41no—
225C2×C4×C31#12112yes—
226C2×C4×C31#12112yes—
227C2×C4×C31#13712yes—
228C2×C4×C31#13712yes—
229C2×C4×C31C22×D411yescharacteristic
230C2×C4×C31C2×#4111yescharacteristic
231C2×C4×C31C2×#4111yescharacteristic
232C2×C4×C31C2×#4111yescharacteristic
233C2×C4×C31H(5,𝔽2)11yescharacteristic
234C2×C4×C31H(5,𝔽2)11yescharacteristic
235C8×C31—24no—
236C8×C31—42no—
237C2×#462C2×C3111yescharacteristic, complemented
238C2×#432C2×C3111yescharacteristic
239#2857C2×C3111yescharacteristic
240C4×C22⋊Q8C2×C3111yescharacteristic
241#2035C2×C3112yes—
242#2001C2×C3112yes—
243#1981C2×C3111yescharacteristic, complemented
244#1971C2×C3112yescomplemented
245#1948C2×C3111yescharacteristic, complemented
246#1935C2×C3112yescomplemented
247#1803C2×C3111yescharacteristic, complemented
248C22×C31—22no—
249C22×C31—22no—
250C22×C31—22no—
251C22×C31—41no—
252C22×C31—41no—
253C22×C31—41no—
254C22×C31—41no—
255C22×C31C2×#12111yescharacteristic
256C22×C31#52511yescharacteristic
257C22×C31#53511yescharacteristic
258C22×C31C2×#13711yescharacteristic
259C22×C31C2×#13711yescharacteristic
260C22×C31C2×#13711yescharacteristic
261C22×C31#57511yescharacteristic
262C4×C31—22no—
263C4×C31—42no—
264C4×C31—41no—
265C4×C31—42no—
266C4×C31—41no—
267C4×C31—41no—
268C4×C31—82no—
269C4×C31—82no—
270C4×C31—81no—
271C4×C31—81no—
272C4×C31#47014yes—
273C4×C31#54611yescharacteristic
274C4×C31#55011yescharacteristic
275C4×C31#55311yescharacteristic
276C4×C31#55511yescharacteristic
277C22×Q16C22×C3112yes—
278C2×C4⋊Q8C22×C3111yescharacteristic
279C2×C22⋊Q8C22×C3111yescharacteristic
280C2×C22⋊Q8C22×C3112yes—
281C2×C4×Q8C22×C3111yescharacteristic
282C22×C42C22×C3111yescharacteristic
283#462—24no—
284#432—24no—
285C2×#106C22×C3112yes—
286C2×C4⋊C8C22×C3111yescharacteristic
287C2×C4⋊C8C22×C3111yescharacteristic
288C2×#103C22×C3112yes—
289C2×#103C22×C3112yes—
290C2×#103C22×C3112yes—
291C2×#103C22×C3112yes—
292C2×C22⋊C8C22×C3112yes—
293C2×#97C22×C3112yes—
294#391C22×C3112yes—
295#391C22×C3111yescharacteristic
296#389—21no—
297#389—21no—
298#389C22×C3111yescharacteristic
299#387—21no—
300#385—21no—
301#384C22×C3111yescharacteristic
302#380—21no—
303#380—21no—
304#380C22×C3111yescharacteristic
305C4×C4⋊C4—21no—
306C4×C4⋊C4C22×C3111yescharacteristic
307C4×C22⋊C4—21no—
308#340C22×C3112yes—
309#340C22×C3112yes—
310C2×C31—42no—
311C2×C31#241411yescharacteristic
312C2×C31C2×#47011yescharacteristic
313C2×C31#305611yescharacteristic
314C2×C31#311311yescharacteristic
315C2×C31#311611yescharacteristic
316C2×C31#321611yescharacteristic
317C2×C31#321811yescharacteristic
318C22×Q8C23×C3112yes—
319C22×Q8C23×C3111yescharacteristic
320C23×C4D4×C3111yescharacteristic
321C23×C4D4×C3111yescharacteristic
322C23×C4C23×C3111yescharacteristic
323C2×Q16—24no—
324C2×Q16—24no—
325C2×Q16—42no—
326C22×C8C23×C3112yes—
327C22×C8C23×C3112yes—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—42no—
333C22⋊Q8—42no—
334C4×Q8—22no—
335C4×Q8—22no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4C23×C3111yescharacteristic
345C2×C4⋊C4C23×C3112yes—
346C2×C4⋊C4C23×C3111yescharacteristic
347C2×C4⋊C4C23×C3111yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42D4×C3111yescharacteristic
356C2×C42D4×C3111yescharacteristic
357C2×C42C23×C3111yescharacteristic
358C2×C42C23×C3111yescharacteristic
359#106—42no—
360C4⋊C8—22no—
361C4⋊C8D4×C3114yes—
362#103—24no—
363#103—24no—
364#103—42no—
365#103—42no—
366C22⋊C8—24no—
367#97—24no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—22no—
374#95—22no—
375C31#2466011yescharacteristic, direct product factor, Sylow
376C24C2×D4×C3111yescharacteristic
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8#41×C3112yes—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—41no—
407C22×C4C2×D4×C3111yescharacteristic
408C22×C4C2×D4×C3111yescharacteristic
409C22×C4C2×D4×C3111yescharacteristic
410C22×C4C2×D4×C3111yescharacteristic
411C22×C4C2×D4×C3111yescharacteristic
412C22×C4C24×C3111yescharacteristic
413Q16—48no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8C2×D4×C3114yes—
420C4⋊C4—24no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—42no—
429C4⋊C4—42no—
430C4⋊C4—44no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4—42no—
435C4⋊C4#41×C3112yes—
436C22⋊C4—24no—
437C22⋊C4—44no—
438C22⋊C4—42no—
439C42—22no—
440C42—22no—
441C42—21no—
442C42—21no—
443C42—42no—
444C42—42no—
445C42C2×D4×C3112yes—
446C42#41×C3112yes—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23C31×#13712yes—
454C23C22×D4×C3111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—41no—
458Q8—41no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—44no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—44no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4C31×#12112yes—
499C2×C4C31×#12112yes—
500C2×C4C31×#13712yes—
501C2×C4C31×#13712yes—
502C2×C4C22×D4×C3111yescharacteristic
503C2×C4C2×#41×C3111yescharacteristic
504C2×C4C2×#41×C3111yescharacteristic
505C2×C4C2×#41×C3111yescharacteristic
506C2×C4C31×H(5,𝔽2)11yescharacteristic
507C2×C4C31×H(5,𝔽2)11yescharacteristic
508C8—24no—
509C8—42no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22C2×C31×#12111yescharacteristic
518C22C31×#52511yescharacteristic
519C22C31×#53511yescharacteristic
520C22C2×C31×#13711yescharacteristic
521C22C2×C31×#13711yescharacteristic
522C22C2×C31×#13711yescharacteristic
523C22C31×#57511yescharacteristic
524C4—22no—
525C4—42no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—82no—
531C4—82no—
532C4—81no—
533C4—81no—
534C4C31×#47014yes—
535C4C31×#54611yescharacteristic
536C4C31×#55011yescharacteristic
537C4C31×#55311yescharacteristic
538C4C31×#55511yescharacteristic
539C2—42no—
540C2C31×#241411yescharacteristic
541C2C2×C31×#47011yescharacteristic
542C2C31×#305611yescharacteristic
543C2C31×#311311yescharacteristic
544C2C31×#311611yescharacteristic
545C2C31×#321611yescharacteristic
546C2C31×#321811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
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×#462C2semidirect
7. C31×#1981C2semidirect
8. C31×#1971C2semidirect
9. C31×#1948C2semidirect
10. C31×#1935C2semidirect
11. C31×#1803C2semidirect
173. #24660C31direct (N × H)
237. C2×#462C2×C31semidirect
243. #1981C2×C31semidirect
244. #1971C2×C31semidirect
245. #1948C2×C31semidirect
246. #1935C2×C31semidirect
247. #1803C2×C31semidirect
375. C31#24660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4622
C2×C31×#4322
C31×#28572
C4×C31×C22⋊Q82
C31×#20352
C31×#20012
C31×#19812
C31×#19712
C31×#19482
C31×#19352
C31×#18032
#2466031