Finite Group Databasebeta

← C31×#10401 #21467160

Subgroups — C31×#10401 #21467160

Order 7936.

570 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2627C211yesmaximal, characteristic
2C31×#1872C211yesmaximal, characteristic
3C31×#1853C211yesmaximal, characteristic
4C2×C31×#328C211yesmaximal, characteristic
5C2×C31×#324C211yesmaximal, characteristic
6C31×#1441C211yesmaximal, characteristic
7C31×#1294C211yesmaximal, characteristic
8C2×C31×C22⋊Q8C2211yescharacteristic
9C22×C4⋊C4×C31C2211yescharacteristic
10C22×C4⋊C4×C31C2211yescharacteristic
11C2×C31×#106—21no—
12C2×C31×#103—21no—
13C2×C31×C22⋊C8C2211yescharacteristic
14C2×C31×C22⋊C8C2211yescharacteristic
15C31×#400—21no—
16C31×#398—21no—
17C31×#398—21no—
18C31×#395—21no—
19C31×#385—21no—
20C31×#381—21no—
21C31×#380C2211yescharacteristic
22C2×C31×#95—21no—
23C2×C31×#95—21no—
24C2×C31×#95C2211yescharacteristic
25C31×#340—21no—
26C31×#340—21no—
27C31×#328—22no—
28C31×#324—22no—
29C22×Q8×C31D411yescharacteristic
30C23×C4×C31—21no—
31C23×C4×C31—21no—
32C23×C4×C31D411yescharacteristic
33C23×C4×C31D411yescharacteristic
34C23×C4×C31C2311yescharacteristic
35C22×C8×C31—21no—
36C22×C8×C31—21no—
37C31×C22⋊Q8—21no—
38C31×C22⋊Q8—21no—
39C31×C22⋊Q8—21no—
40C31×C22⋊Q8—21no—
41C2×C4⋊C4×C31—21no—
42C2×C4⋊C4×C31—21no—
43C2×C4⋊C4×C31—21no—
44C2×C4⋊C4×C31—21no—
45C2×C4⋊C4×C31—21no—
46C2×C4⋊C4×C31—21no—
47C2×C4⋊C4×C31—21no—
48C2×C4⋊C4×C31—21no—
49C2×C4⋊C4×C31—21no—
50C2×C4⋊C4×C31—21no—
51C2×C4⋊C4×C31—21no—
52C2×C4⋊C4×C31—42no—
53C2×C4⋊C4×C31D411yescharacteristic
54C2×C4⋊C4×C31D411yescharacteristic
55C2×C4⋊C4×C31D411yescharacteristic
56C2×C22⋊C4×C31—21no—
57C2×C22⋊C4×C31—21no—
58C31×#106—42no—
59C31×#103—42no—
60C31×C22⋊C8—21no—
61C31×C22⋊C8—21no—
62C31×C22⋊C8—21no—
63C31×C22⋊C8D412yes—
64C31×#95—21no—
65C31×#95—21no—
66C31×#95—21no—
67C31×#95—21no—
68C31×#95—21no—
69C31×#95—21no—
70C31×#95—21no—
71C31×#95—21no—
72C31×#95—21no—
73C31×#95—42no—
74C31×#95—42no—
75C24×C31C2×D411yescharacteristic
76C2×Q8×C31—21no—
77C2×Q8×C31—21no—
78C2×Q8×C31—41no—
79C2×Q8×C31—41no—
80C22×C4×C31—21no—
81C22×C4×C31—21no—
82C22×C4×C31—21no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—21no—
89C22×C4×C31—21no—
90C22×C4×C31—21no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—41no—
96C22×C4×C31—41no—
97C22×C4×C31—41no—
98C22×C4×C31—41no—
99C22×C4×C31—41no—
100C22×C4×C31—41no—
101C22×C4×C31—41no—
102C22×C4×C31—41no—
103C22×C4×C31—41no—
104C22×C4×C31—41no—
105C22×C4×C31—41no—
106C22×C4×C31—41no—
107C22×C4×C31—41no—
108C22×C4×C31—41no—
109C22×C4×C31—41no—
110C22×C4×C31—41no—
111C22×C4×C31SD1612yes—
112C22×C4×C31C2×D411yescharacteristic
113C22×C4×C31C2×D411yescharacteristic
114C22×C4×C31C2×D411yescharacteristic
115C22×C4×C31#4111yescharacteristic
116C22×C4×C31#4111yescharacteristic
117C22×C4×C31#4111yescharacteristic
118C2×C8×C31—22no—
119C2×C8×C31—41no—
120C2×C8×C31—41no—
121C2×C8×C31—41no—
122C2×C8×C31—41no—
123C2×C8×C31—41no—
124C4⋊C4×C31—22no—
125C4⋊C4×C31—22no—
126C4⋊C4×C31—21no—
127C4⋊C4×C31—21no—
128C4⋊C4×C31—41no—
129C4⋊C4×C31—41no—
130C4⋊C4×C31—41no—
131C4⋊C4×C31—41no—
132C4⋊C4×C31—41no—
133C4⋊C4×C31—41no—
134C4⋊C4×C31—41no—
135C4⋊C4×C31—41no—
136C4⋊C4×C31—41no—
137C4⋊C4×C31—41no—
138C4⋊C4×C31—81no—
139C4⋊C4×C31—81no—
140C22⋊C4×C31—41no—
141C22⋊C4×C31—41no—
142C22⋊C4×C31—41no—
143C22⋊C4×C31—41no—
144#10401C3111yesmaximal, characteristic, direct product factor, Sylow
145C23×C31—21no—
146C23×C31—21no—
147C23×C31—21no—
148C23×C31—21no—
149C23×C31#12011yescharacteristic
150C23×C31#12111yescharacteristic
151C23×C31#12311yescharacteristic
152C23×C31C2×SD1611yescharacteristic
153C23×C31#13511yescharacteristic
154C23×C31#13711yescharacteristic
155C23×C31#13711yescharacteristic
156Q8×C31—42no—
157Q8×C31—81no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—22no—
163C2×C4×C31—22no—
164C2×C4×C31—22no—
165C2×C4×C31—41no—
166C2×C4×C31—41no—
167C2×C4×C31—41no—
168C2×C4×C31—41no—
169C2×C4×C31—41no—
170C2×C4×C31—41no—
171C2×C4×C31—41no—
172C2×C4×C31—41no—
173C2×C4×C31—42no—
174C2×C4×C31—42no—
175C2×C4×C31—42no—
176C2×C4×C31—42no—
177C2×C4×C31—42no—
178C2×C4×C31—42no—
179C2×C4×C31—41no—
180C2×C4×C31—41no—
181C2×C4×C31—41no—
182C2×C4×C31—41no—
183C2×C4×C31—41no—
184C2×C4×C31—41no—
185C2×C4×C31—41no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—42no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—41no—
194C2×C4×C31—41no—
195C2×C4×C31—81no—
196C2×C4×C31—81no—
197C2×C4×C31—81no—
198C2×C4×C31—81no—
199C2×C4×C31—81no—
200C2×C4×C31—81no—
201C2×C4×C31—81no—
202C2×C4×C31—81no—
203C2×C4×C31—81no—
204C2×C4×C31#12111yescharacteristic
205C2×C4×C31#12111yescharacteristic
206C2×C4×C31#12311yescharacteristic
207C2×C4×C31#12411yescharacteristic
208C8×C31—42no—
209C8×C31—81no—
210#2627C2×C3111yescharacteristic
211#1872C2×C3111yescharacteristic
212#1853C2×C3111yescharacteristic
213C2×#328C2×C3111yescharacteristic
214C2×#324C2×C3111yescharacteristic
215#1441C2×C3111yescharacteristic
216#1294C2×C3111yescharacteristic
217C22×C31—21no—
218C22×C31—21no—
219C22×C31—21no—
220C22×C31—21no—
221C22×C31—21no—
222C22×C31—21no—
223C22×C31—21no—
224C22×C31—21no—
225C22×C31—21no—
226C22×C31—21no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31#39411yescharacteristic
230C22×C31#44811yescharacteristic
231C22×C31#45211yescharacteristic
232C22×C31#45411yescharacteristic
233C22×C31#45611yescharacteristic
234C22×C31B(4,𝔽2)11yescharacteristic
235C22×C31#45811yescharacteristic
236C22×C31#46511yescharacteristic
237C22×C31#47011yescharacteristic
238C22×C31#48311yescharacteristic
239C22×C31#48511yescharacteristic
240C4×C31—21no—
241C4×C31—21no—
242C4×C31—21no—
243C4×C31—21no—
244C4×C31—42no—
245C4×C31—82no—
246C4×C31—82no—
247C4×C31—81no—
248C4×C31—81no—
249C4×C31—81no—
250C4×C31—81no—
251C4×C31—81no—
252C2×C22⋊Q8C22×C3111yescharacteristic
253C22×C4⋊C4C22×C3111yescharacteristic
254C22×C4⋊C4C22×C3111yescharacteristic
255C2×#106—21no—
256C2×#103—21no—
257C2×C22⋊C8C22×C3111yescharacteristic
258C2×C22⋊C8C22×C3111yescharacteristic
259#400—21no—
260#398—21no—
261#398—21no—
262#395—21no—
263#385—21no—
264#381—21no—
265#380C22×C3111yescharacteristic
266C2×#95—21no—
267C2×#95—21no—
268C2×#95C22×C3111yescharacteristic
269#340—21no—
270#340—21no—
271#328—22no—
272#324—22no—
273C2×C31—21no—
274C2×C31—21no—
275C2×C31—21no—
276C2×C31—21no—
277C2×C31#159911yescharacteristic
278C2×C31#160311yescharacteristic
279C2×C31#161111yescharacteristic
280C2×C31#161511yescharacteristic
281C2×C31#203511yescharacteristic
282C2×C31#203811yescharacteristic
283C2×C31#204411yescharacteristic
284C22×Q8D4×C3111yescharacteristic
285C23×C4—21no—
286C23×C4—21no—
287C23×C4D4×C3111yescharacteristic
288C23×C4D4×C3111yescharacteristic
289C23×C4C23×C3111yescharacteristic
290C22×C8—21no—
291C22×C8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4D4×C3111yescharacteristic
309C2×C4⋊C4D4×C3111yescharacteristic
310C2×C4⋊C4D4×C3111yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313#106—42no—
314#103—42no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8D4×C3112yes—
319#95—21no—
320#95—21no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95—21no—
328#95—42no—
329#95—42no—
330C31#1040111yescharacteristic, direct product factor, Sylow
331C24C2×D4×C3111yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—41no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4SD16×C3112yes—
368C22×C4C2×D4×C3111yescharacteristic
369C22×C4C2×D4×C3111yescharacteristic
370C22×C4C2×D4×C3111yescharacteristic
371C22×C4#41×C3111yescharacteristic
372C22×C4#41×C3111yescharacteristic
373C22×C4#41×C3111yescharacteristic
374C2×C8—22no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—81no—
395C4⋊C4—81no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23C31×#12011yescharacteristic
405C23C31×#12111yescharacteristic
406C23C31×#12311yescharacteristic
407C23C2×SD16×C3111yescharacteristic
408C23C31×#13511yescharacteristic
409C23C31×#13711yescharacteristic
410C23C31×#13711yescharacteristic
411Q8—42no—
412Q8—81no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4C31×#12111yescharacteristic
460C2×C4C31×#12111yescharacteristic
461C2×C4C31×#12311yescharacteristic
462C2×C4C31×#12411yescharacteristic
463C8—42no—
464C8—81no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22C31×#39411yescharacteristic
478C22C31×#44811yescharacteristic
479C22C31×#45211yescharacteristic
480C22C31×#45411yescharacteristic
481C22C31×#45611yescharacteristic
482C22C31×B(4,𝔽2)11yescharacteristic
483C22C31×#45811yescharacteristic
484C22C31×#46511yescharacteristic
485C22C31×#47011yescharacteristic
486C22C31×#48311yescharacteristic
487C22C31×#48511yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—82no—
494C4—82no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4—81no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2C31×#159911yescharacteristic
505C2C31×#160311yescharacteristic
506C2C31×#161111yescharacteristic
507C2C31×#161511yescharacteristic
508C2C31×#203511yescharacteristic
509C2C31×#203811yescharacteristic
510C2C31×#204411yescharacteristic
subgroupG/H
center, socleC23×C31#120
commutator, Frattini, cosocleC23×C4C23×C31
prime radicalC24×C31C2×D4
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
144. #10401C31direct (N × H)
330. C31#10401direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#26272
C31×#18722
C31×#18532
C2×C31×#3282
C2×C31×#3242
C31×#14412
C31×#12942
#1040131