Finite Group Databasebeta

← C31×#9920 #21466679

Subgroups — C31×#9920 #21466679

Order 7936.

856 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#481C211yesmaximal, characteristic, complemented
2C31×#2617C211yesmaximal, characteristic
3C2×C31×#399C211yesmaximal, characteristic, complemented
4C31×#1824C211yesmaximal, characteristic, complemented
5C2×C31×#327C211yesmaximal, characteristic, complemented
6C2×C31×#323C211yesmaximal, characteristic, complemented
7C31×#1294C211yesmaximal, characteristic, complemented
8C2×C31×#121C2211yescharacteristic
9C2×C31×#120—21no—
10C22×C4⋊C4×C31—21no—
11C22×C4⋊C4×C31C2211yescharacteristic
12C22×C22⋊C4×C31—21no—
13C22×C22⋊C4×C31C2211yescharacteristic
14C31×#481—22no—
15C31×#481—22no—
16C2×C31×#106—21no—
17C2×C31×#102—21no—
18C2×C31×C22⋊C8C2211yescharacteristic
19C2×C31×C22⋊C8C2211yescharacteristic
20C31×#399—22no—
21C31×#399—22no—
22C31×#397—21no—
23C31×#394—22no—
24C31×#392—21no—
25C31×#386—21no—
26C31×#380C2211yescharacteristic
27C2×C31×#95C2211yescharacteristic
28C31×#340—22no—
29C31×#327—22no—
30C31×#323—22no—
31C25×C31D411yescharacteristic
32C22×D4×C31—21no—
33C22×D4×C31—22no—
34C22×D4×C31D411yescharacteristic
35C23×C4×C31—21no—
36C23×C4×C31—21no—
37C23×C4×C31D411yescharacteristic
38C23×C4×C31C2311yescharacteristic
39C22×C8×C31—21no—
40C22×C8×C31—21no—
41C31×#121—21no—
42C31×#121—21no—
43C31×#121—21no—
44C31×#121—21no—
45C31×#120—42no—
46C31×#120—42no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—21no—
53C2×C4⋊C4×C31—44no—
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C4⋊C4×C31D412yes—
56C2×C4⋊C4×C31D412yescomplemented
57C2×C22⋊C4×C31—22no—
58C2×C22⋊C4×C31—24no—
59C2×C22⋊C4×C31—21no—
60C2×C22⋊C4×C31—21no—
61C2×C22⋊C4×C31—21no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—21no—
65C2×C22⋊C4×C31—21no—
66C2×C22⋊C4×C31—21no—
67C2×C22⋊C4×C31—22no—
68C2×C22⋊C4×C31—44no—
69C31×#106—24no—
70C31×#102—24no—
71C31×C22⋊C8—21no—
72C31×C22⋊C8—21no—
73C31×C22⋊C8—21no—
74C31×C22⋊C8D412yescomplemented
75C31×#95—22no—
76C31×#95—21no—
77C31×#95—21no—
78C31×#95D412yescomplemented
79C24×C31—21no—
80C24×C31—21no—
81C24×C31—21no—
82C24×C31—21no—
83C24×C31—21no—
84C24×C31—21no—
85C24×C31—21no—
86C24×C31—42no—
87C24×C31—42no—
88C24×C31SD1612yes—
89C24×C31C2×D411yescharacteristic
90C2×D4×C31—21no—
91C2×D4×C31—21no—
92C2×D4×C31—42no—
93C2×D4×C31—44no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31—41no—
97C2×D4×C31—41no—
98C2×D4×C31—41no—
99C2×D4×C31—41no—
100C2×D4×C31—82no—
101C2×D4×C31—82no—
102C22×C4×C31—24no—
103C22×C4×C31—22no—
104C22×C4×C31—21no—
105C22×C4×C31—22no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—21no—
110C22×C4×C31—42no—
111C22×C4×C31—42no—
112C22×C4×C31—41no—
113C22×C4×C31—41no—
114C22×C4×C31—42no—
115C22×C4×C31—42no—
116C22×C4×C31—42no—
117C22×C4×C31—41no—
118C22×C4×C31—41no—
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×D411yescharacteristic
124C22×C4×C31#4111yescharacteristic
125C2×C8×C31—22no—
126C2×C8×C31—42no—
127C2×C8×C31—42no—
128C2×C8×C31—41no—
129C4⋊C4×C31—22no—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—22no—
132C4⋊C4×C31—21no—
133C4⋊C4×C31—48no—
134C4⋊C4×C31—42no—
135C4⋊C4×C31—41no—
136C4⋊C4×C31—41no—
137C22⋊C4×C31—48no—
138C22⋊C4×C31—44no—
139C22⋊C4×C31—41no—
140C22⋊C4×C31—41no—
141C22⋊C4×C31—41no—
142C22⋊C4×C31—41no—
143C22⋊C4×C31—41no—
144C22⋊C4×C31—41no—
145C22⋊C4×C31—41no—
146C22⋊C4×C31—41no—
147C22⋊C4×C31—82no—
148#9920C3111yesmaximal, characteristic, direct product factor, Sylow
149C23×C31—22no—
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—22no—
153C23×C31—22no—
154C23×C31—44no—
155C23×C31—42no—
156C23×C31—44no—
157C23×C31—42no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31—41no—
161C23×C31—42no—
162C23×C31—42no—
163C23×C31—41no—
164C23×C31—41no—
165C23×C31—41no—
166C23×C31—41no—
167C23×C31—42no—
168C23×C31—42no—
169C23×C31—82no—
170C23×C31—82no—
171C23×C31—81no—
172C23×C31—81no—
173C23×C31#12011yescharacteristic
174C23×C31#12011yescharacteristic
175C23×C31#12111yescharacteristic
176C23×C31C2×SD1611yescharacteristic
177C23×C31#13511yescharacteristic
178C23×C31AGL(1,ℤ/8)11yescharacteristic
179C23×C31#13711yescharacteristic
180D4×C31—42no—
181D4×C31—81no—
182D4×C31—88no—
183D4×C31—81no—
184D4×C31—81no—
185D4×C31—81no—
186D4×C31—81no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—24no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—44no—
195C2×C4×C31—44no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—41no—
202C2×C4×C31—41no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—41no—
206C2×C4×C31—41no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—82no—
211C2×C4×C31—82no—
212C2×C4×C31—81no—
213C2×C4×C31#12011yescharacteristic
214C2×C4×C31#12111yescharacteristic
215C2×C4×C31#12111yescharacteristic
216C2×C4×C31#12711yescharacteristic
217C8×C31—42no—
218C8×C31—81no—
219C2×#481C2×C3111yescharacteristic, complemented
220#2617C2×C3111yescharacteristic
221C2×#399C2×C3111yescharacteristic, complemented
222#1824C2×C3111yescharacteristic, complemented
223C2×#327C2×C3111yescharacteristic, complemented
224C2×#323C2×C3111yescharacteristic, complemented
225#1294C2×C3111yescharacteristic, complemented
226C22×C31—22no—
227C22×C31—22no—
228C22×C31—22no—
229C22×C31—22no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—44no—
235C22×C31—44no—
236C22×C31—42no—
237C22×C31—82no—
238C22×C31—82no—
239C22×C31—82no—
240C22×C31—82no—
241C22×C31—81no—
242C22×C31—81no—
243C22×C31—82no—
244C22×C31—82no—
245C22×C31—81no—
246C22×C31—81no—
247C22×C31—81no—
248C22×C31#39211yescharacteristic
249C22×C31#44811yescharacteristic
250C22×C31#44911yescharacteristic
251C22×C31#45011yescharacteristic
252C22×C31#45211yescharacteristic
253C22×C31#45312yes—
254C22×C31#45812yes—
255C22×C31#46511yescharacteristic
256C22×C31#46811yescharacteristic
257C4×C31—21no—
258C4×C31—21no—
259C4×C31—21no—
260C4×C31—21no—
261C4×C31—44no—
262C4×C31—82no—
263C4×C31—81no—
264C4×C31—81no—
265C4×C31—82no—
266C2×#121C22×C3111yescharacteristic
267C2×#120—21no—
268C22×C4⋊C4—21no—
269C22×C4⋊C4C22×C3111yescharacteristic
270C22×C22⋊C4—21no—
271C22×C22⋊C4C22×C3111yescharacteristic
272#481—22no—
273#481—22no—
274C2×#106—21no—
275C2×#102—21no—
276C2×C22⋊C8C22×C3111yescharacteristic
277C2×C22⋊C8C22×C3111yescharacteristic
278#399—22no—
279#399—22no—
280#397—21no—
281#394—22no—
282#392—21no—
283#386—21no—
284#380C22×C3111yescharacteristic
285C2×#95C22×C3111yescharacteristic
286#340—22no—
287#327—22no—
288#323—22no—
289C2×C31—21no—
290C2×C31—21no—
291C2×C31—21no—
292C2×C31—21no—
293C2×C31—82no—
294C2×C31—161no—
295C2×C31#161312yes—
296C2×C31#161812yes—
297C2×C31#200011yescharacteristic
298C2×C31#200211yescharacteristic
299C2×C31#202211yescharacteristic
300C25D4×C3111yescharacteristic
301C22×D4—21no—
302C22×D4—22no—
303C22×D4D4×C3111yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C23×C4D4×C3111yescharacteristic
307C23×C4C23×C3111yescharacteristic
308C22×C8—21no—
309C22×C8—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#120—42no—
315#120—42no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4D4×C3111yescharacteristic
324C2×C4⋊C4D4×C3112yes—
325C2×C4⋊C4D4×C3112yescomplemented
326C2×C22⋊C4—24no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—44no—
338#106—24no—
339#102—24no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8D4×C3112yescomplemented
344#95—22no—
345#95—21no—
346#95—21no—
347#95D4×C3112yescomplemented
348C31#992011yescharacteristic, direct product factor, Sylow
349C24—21no—
350C24—21no—
351C24—21no—
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—42no—
357C24—42no—
358C24SD16×C3112yes—
359C24C2×D4×C3111yescharacteristic
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—42no—
363C2×D4—44no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—82no—
371C2×D4—82no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—42no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4C2×D4×C3111yescharacteristic
390C22×C4C2×D4×C3111yescharacteristic
391C22×C4C2×D4×C3111yescharacteristic
392C22×C4C2×D4×C3111yescharacteristic
393C22×C4C2×D4×C3111yescharacteristic
394C22×C4#41×C3111yescharacteristic
395C2×C8—22no—
396C2×C8—42no—
397C2×C8—42no—
398C2×C8—41no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—42no—
404C4⋊C4—48no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C22⋊C4—48no—
408C22⋊C4—44no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—82no—
418C23—22no—
419C23—22no—
420C23—22no—
421C23—22no—
422C23—22no—
423C23—44no—
424C23—42no—
425C23—44no—
426C23—42no—
427C23—41no—
428C23—41no—
429C23—42no—
430C23—42no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—42no—
436C23—42no—
437C23—41no—
438C23—82no—
439C23—82no—
440C23—81no—
441C23—81no—
442C23C31×#12011yescharacteristic
443C23C31×#12011yescharacteristic
444C23C31×#12111yescharacteristic
445C23C2×SD16×C3111yescharacteristic
446C23C31×#13511yescharacteristic
447C23C31×AGL(1,ℤ/8)11yescharacteristic
448C23C31×#13711yescharacteristic
449D4—42no—
450D4—81no—
451D4—88no—
452D4—81no—
453D4—81no—
454D4—81no—
455D4—81no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4—81no—
482C2×C4C31×#12011yescharacteristic
483C2×C4C31×#12111yescharacteristic
484C2×C4C31×#12111yescharacteristic
485C2×C4C31×#12711yescharacteristic
486C8—42no—
487C8—81no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—44no—
498C22—42no—
499C22—82no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—81no—
504C22—81no—
505C22—82no—
506C22—82no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22C31×#39211yescharacteristic
511C22C31×#44811yescharacteristic
512C22C31×#44911yescharacteristic
513C22C31×#45011yescharacteristic
514C22C31×#45211yescharacteristic
515C22C31×#45312yes—
516C22C31×#45812yes—
517C22C31×#46511yescharacteristic
518C22C31×#46811yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—44no—
524C4—82no—
525C4—81no—
526C4—81no—
527C4—82no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—82no—
533C2—161no—
534C2C31×#161312yes—
535C2C31×#161812yes—
536C2C31×#200011yescharacteristic
537C2C31×#200211yescharacteristic
538C2C31×#202211yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC31×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#481C2semidirect
3. C2×C31×#399C2semidirect
4. C31×#1824C2semidirect
5. C2×C31×#327C2semidirect
6. C2×C31×#323C2semidirect
7. C31×#1294C2semidirect
56. C2×C4⋊C4×C31D4semidirect
74. C31×C22⋊C8D4semidirect
78. C31×#95D4semidirect
148. #9920C31direct (N × H)
219. C2×#481C2×C31semidirect
221. C2×#399C2×C31semidirect
222. #1824C2×C31semidirect
223. C2×#327C2×C31semidirect
224. C2×#323C2×C31semidirect
225. #1294C2×C31semidirect
325. C2×C4⋊C4D4×C31semidirect
343. C22⋊C8D4×C31semidirect
347. #95D4×C31semidirect
348. C31#9920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4812
C31×#26172
C2×C31×#3992
C31×#18242
C2×C31×#3272
C2×C31×#3232
C31×#12942
#992031