Finite Group Databasebeta

← C31×#9947 #21466706

Subgroups — C31×#9947 #21466706

Order 7936.

930 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3187C211yesmaximal, characteristic, complemented
2C2×C31×#447C211yesmaximal, characteristic
3C31×#2435C211yesmaximal, characteristic, complemented
4C31×#1964C211yesmaximal, characteristic, complemented
5C31×#1786C211yesmaximal, characteristic, complemented
6C31×#1520C211yesmaximal, characteristic, complemented
7C31×#1282C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C22×D8×C31—21no—
10C2×C31×#124—21no—
11C2×C31×C22⋊Q8C2211yescharacteristic
12C2×C31×#121C2211yescharacteristic
13C31×#483—21no—
14C31×#481—21no—
15C31×#465—22no—
16C31×#450—21no—
17C31×#448—21no—
18C31×#447—22no—
19C31×#447—22no—
20C2×C31×#102—21no—
21C2×C31×#102—22no—
22C2×C31×#99—22no—
23C2×C31×C22⋊C8C2211yescharacteristic
24C2×C31×C22⋊C8C2211yescharacteristic
25C31×#394—22no—
26C31×#390—21no—
27C31×#380C2211yescharacteristic
28C31×#379—22no—
29C4×C22⋊C4×C31C2211yescharacteristic
30C31×#328—22no—
31C25×C31—21no—
32C22×Q8×C31D411yescharacteristic
33C22×D4×C31—21no—
34C22×D4×C31—21no—
35C22×D4×C31—21no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—44no—
40C22×D4×C31D412yes—
41C22×D4×C31D411yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C2×SD16×C31—22no—
44C2×D8×C31—24no—
45C2×D8×C31—44no—
46C22×C8×C31—21no—
47C22×C8×C31D412yes—
48C31×#124—44no—
49C31×C22⋊Q8—21no—
50C31×C22⋊Q8—21no—
51C31×C22⋊Q8—21no—
52C31×C22⋊Q8—21no—
53C31×#121—21no—
54C31×#121—21no—
55C31×#121—21no—
56C31×#121—21no—
57C2×C4⋊C4×C31—21no—
58C2×C4⋊C4×C31—21no—
59C2×C4⋊C4×C31D411yescharacteristic
60C2×C4⋊C4×C31D411yescharacteristic
61C2×C22⋊C4×C31—24no—
62C2×C22⋊C4×C31—21no—
63C2×C22⋊C4×C31—21no—
64C2×C22⋊C4×C31—21no—
65C2×C22⋊C4×C31—24no—
66C2×C22⋊C4×C31D412yes—
67C2×C42×C31—21no—
68C31×#106—22no—
69C31×#103—22no—
70C31×#102—24no—
71C31×#102—22no—
72C31×#102—44no—
73C31×#99—44no—
74C31×C22⋊C8—21no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8—21no—
77C31×C22⋊C8D412yes—
78C31×#95—21no—
79C31×#95—21no—
80C24×C31—22no—
81C24×C31—21no—
82C24×C31—44no—
83C24×C31—41no—
84C24×C31—41no—
85C24×C31—42no—
86C24×C31—42no—
87C24×C31—82no—
88C24×C31C2×D411yescharacteristic
89C2×Q8×C31—21no—
90C2×Q8×C31—21no—
91C2×Q8×C31—42no—
92C2×D4×C31—24no—
93C2×D4×C31—24no—
94C2×D4×C31—24no—
95C2×D4×C31—22no—
96C2×D4×C31—21no—
97C2×D4×C31—21no—
98C2×D4×C31—22no—
99C2×D4×C31—42no—
100C2×D4×C31—42no—
101C2×D4×C31—42no—
102C2×D4×C31—42no—
103C2×D4×C31—44no—
104C2×D4×C31—44no—
105C2×D4×C31—44no—
106C2×D4×C31—41no—
107C2×D4×C31—41no—
108C2×D4×C31—42no—
109C2×D4×C31—42no—
110C2×D4×C31—41no—
111C2×D4×C31—41no—
112C22×C4×C31—22no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—42no—
117C22×C4×C31—41no—
118C22×C4×C31C2×D411yescharacteristic
119C22×C4×C31C2×D411yescharacteristic
120C22×C4×C31C2×D411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31#4111yescharacteristic
124SD16×C31—82no—
125D8×C31—48no—
126C2×C8×C31—22no—
127C2×C8×C31—22no—
128C2×C8×C31—42no—
129C2×C8×C31—42no—
130C4⋊C4×C31—21no—
131C4⋊C4×C31—21no—
132C4⋊C4×C31—21no—
133C4⋊C4×C31—21no—
134C4⋊C4×C31—42no—
135C4⋊C4×C31—41no—
136C4⋊C4×C31—41no—
137C22⋊C4×C31—22no—
138C22⋊C4×C31—22no—
139C22⋊C4×C31—48no—
140C22⋊C4×C31—41no—
141C22⋊C4×C31—41no—
142C22⋊C4×C31—41no—
143C22⋊C4×C31—41no—
144C22⋊C4×C31—42no—
145C22⋊C4×C31—84no—
146C42×C31—42no—
147#9947C3111yesmaximal, characteristic, direct product factor, Sylow
148C23×C31—24no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—44no—
152C23×C31—44no—
153C23×C31—44no—
154C23×C31—42no—
155C23×C31—42no—
156C23×C31—44no—
157C23×C31—41no—
158C23×C31—42no—
159C23×C31—82no—
160C23×C31—82no—
161C23×C31—81no—
162C23×C31—81no—
163C23×C31—88no—
164C23×C31—88no—
165C23×C31—82no—
166C23×C31—81no—
167C23×C31—81no—
168C23×C31#12011yescharacteristic
169C23×C31#12111yescharacteristic
170C23×C31#12711yescharacteristic
171C23×C31#13512yes—
172C23×C31AGL(1,ℤ/8)12yes—
173Q8×C31—42no—
174Q8×C31—81no—
175D4×C31—24no—
176D4×C31—24no—
177D4×C31—42no—
178D4×C31—42no—
179D4×C31—44no—
180D4×C31—42no—
181D4×C31—44no—
182D4×C31—42no—
183D4×C31—82no—
184D4×C31—81no—
185D4×C31—81no—
186C2×C4×C31—22no—
187C2×C4×C31—22no—
188C2×C4×C31—22no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—42no—
193C2×C4×C31—42no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—41no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—81no—
202C2×C4×C31—81no—
203C2×C4×C31—81no—
204C2×C4×C31#12011yescharacteristic
205C2×C4×C31#12011yescharacteristic
206C2×C4×C31#12111yescharacteristic
207C2×C4×C31#12111yescharacteristic
208C8×C31—42no—
209C8×C31—42no—
210#3187C2×C3111yescharacteristic, complemented
211C2×#447C2×C3111yescharacteristic
212#2435C2×C3111yescharacteristic, complemented
213#1964C2×C3111yescharacteristic, complemented
214#1786C2×C3111yescharacteristic, complemented
215#1520C2×C3111yescharacteristic, complemented
216#1282C2×C3111yescharacteristic, complemented
217C22×C31—21no—
218C22×C31—21no—
219C22×C31—21no—
220C22×C31—21no—
221C22×C31—21no—
222C22×C31—21no—
223C22×C31—42no—
224C22×C31—42no—
225C22×C31—48no—
226C22×C31—44no—
227C22×C31—84no—
228C22×C31—84no—
229C22×C31—88no—
230C22×C31—84no—
231C22×C31—82no—
232C22×C31—82no—
233C22×C31—81no—
234C22×C31—81no—
235C22×C31—81no—
236C22×C31—162no—
237C22×C31#39211yescharacteristic
238C22×C31#44912yes—
239C22×C31#46312yes—
240C22×C31#49511yescharacteristic
241C22×C31#49611yescharacteristic
242C4×C31—21no—
243C4×C31—21no—
244C4×C31—21no—
245C4×C31—82no—
246C4×C31—81no—
247C4×C31—81no—
248C4×C31—81no—
249C4×C31—161no—
250C4×C31B(4,𝔽2)12yes—
251C23×D4C22×C3111yescharacteristic
252C22×D8—21no—
253C2×#124—21no—
254C2×C22⋊Q8C22×C3111yescharacteristic
255C2×#121C22×C3111yescharacteristic
256#483—21no—
257#481—21no—
258#465—22no—
259#450—21no—
260#448—21no—
261#447—22no—
262#447—22no—
263C2×#102—21no—
264C2×#102—22no—
265C2×#99—22no—
266C2×C22⋊C8C22×C3111yescharacteristic
267C2×C22⋊C8C22×C3111yescharacteristic
268#394—22no—
269#390—21no—
270#380C22×C3111yescharacteristic
271#379—22no—
272C4×C22⋊C4C22×C3111yescharacteristic
273#328—22no—
274C2×C31—22no—
275C2×C31—21no—
276C2×C31—22no—
277C2×C31—21no—
278C2×C31—84no—
279C2×C31—161no—
280C2×C31#200811yescharacteristic
281C2×C31#201211yescharacteristic
282C2×C31#202111yescharacteristic
283C25—21no—
284C22×Q8D4×C3111yescharacteristic
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—44no—
292C22×D4D4×C3111yescharacteristic
293C22×D4D4×C3112yes—
294C23×C4C23×C3111yescharacteristic
295C2×SD16—22no—
296C2×D8—24no—
297C2×D8—44no—
298C22×C8—21no—
299C22×C8D4×C3112yes—
300#124—44no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4D4×C3111yescharacteristic
312C2×C4⋊C4D4×C3111yescharacteristic
313C2×C22⋊C4—24no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4D4×C3112yes—
319C2×C42—21no—
320#106—22no—
321#103—22no—
322#102—24no—
323#102—22no—
324#102—44no—
325#99—44no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8D4×C3112yes—
330#95—21no—
331#95—21no—
332C31#994711yescharacteristic, direct product factor, Sylow
333C24—22no—
334C24—21no—
335C24—44no—
336C24—41no—
337C24—41no—
338C24—42no—
339C24—42no—
340C24—82no—
341C24C2×D4×C3111yescharacteristic
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—42no—
345C2×D4—24no—
346C2×D4—24no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—44no—
357C2×D4—44no—
358C2×D4—44no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—42no—
370C22×C4—41no—
371C22×C4C2×D4×C3111yescharacteristic
372C22×C4C2×D4×C3111yescharacteristic
373C22×C4C2×D4×C3111yescharacteristic
374C22×C4C2×D4×C3111yescharacteristic
375C22×C4C2×D4×C3111yescharacteristic
376C22×C4#41×C3111yescharacteristic
377SD16—82no—
378D8—48no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—42no—
382C2×C8—42no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—42no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—48no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—42no—
398C22⋊C4—84no—
399C42—42no—
400C23—24no—
401C23—41no—
402C23—41no—
403C23—44no—
404C23—44no—
405C23—44no—
406C23—42no—
407C23—44no—
408C23—42no—
409C23—41no—
410C23—42no—
411C23—82no—
412C23—82no—
413C23—81no—
414C23—81no—
415C23—88no—
416C23—88no—
417C23—82no—
418C23—81no—
419C23—81no—
420C23C31×#12011yescharacteristic
421C23C31×#12111yescharacteristic
422C23C31×#12711yescharacteristic
423C23C31×#13512yes—
424C23C31×AGL(1,ℤ/8)12yes—
425Q8—42no—
426Q8—81no—
427D4—24no—
428D4—24no—
429D4—42no—
430D4—42no—
431D4—44no—
432D4—42no—
433D4—44no—
434D4—42no—
435D4—82no—
436D4—81no—
437D4—81no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4C31×#12011yescharacteristic
457C2×C4C31×#12011yescharacteristic
458C2×C4C31×#12111yescharacteristic
459C2×C4C31×#12111yescharacteristic
460C8—42no—
461C8—42no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—42no—
469C22—42no—
470C22—48no—
471C22—44no—
472C22—84no—
473C22—84no—
474C22—88no—
475C22—84no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—162no—
482C22C31×#39211yescharacteristic
483C22C31×#44912yes—
484C22C31×#46312yes—
485C22C31×#49511yescharacteristic
486C22C31×#49611yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—82no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—161no—
495C4C31×B(4,𝔽2)12yes—
496C2—22no—
497C2—21no—
498C2—22no—
499C2—21no—
500C2—84no—
501C2—161no—
502C2C31×#200811yescharacteristic
503C2C31×#201211yescharacteristic
504C2C31×#202111yescharacteristic
subgroupG/H
center, socleC22×C31#392
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC2×C31×#447C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3187C2semidirect
3. C31×#2435C2semidirect
4. C31×#1964C2semidirect
5. C31×#1786C2semidirect
6. C31×#1520C2semidirect
7. C31×#1282C2semidirect
147. #9947C31direct (N × H)
210. #3187C2×C31semidirect
212. #2435C2×C31semidirect
213. #1964C2×C31semidirect
214. #1786C2×C31semidirect
215. #1520C2×C31semidirect
216. #1282C2×C31semidirect
332. C31#9947direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#31872
C2×C31×#4472
C31×#24352
C31×#19642
C31×#17862
C31×#15202
C31×#12822
#994731