Finite Group Databasebeta

← C31×#9511 #21466270

Subgroups — C31×#9511 #21466270

Order 7936.

812 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2879C211yesmaximal, characteristic, complemented
2C31×#2404C211yesmaximal, characteristic
3C31×#1785C211yesmaximal, characteristic, complemented
4C31×#1462C212yesmaximal, complemented
5C31×#1306C212yesmaximal, complemented
6C22×#41×C31C2211yescharacteristic
7C22×M16×C31—21no—
8C2×C31×#120C411yescharacteristic
9C2×C31×#120C411yescharacteristic
10C22×C22⋊C4×C31C2211yescharacteristic
11C2×C31×#101—21no—
12C2×C31×#100—21no—
13C31×#408—24no—
14C31×#407—21no—
15C31×#407C2212yes—
16C31×#407C2212yes—
17C31×#393—21no—
18C31×#392—21no—
19C31×#386—21no—
20C31×#386—21no—
21C31×#386C411yescharacteristic
22C31×#386C411yescharacteristic
23C31×#381C2211yescharacteristic
24C31×#323—24no—
25C25×C31C2×C411yescharacteristic
26C2×#41×C31—22no—
27C2×#41×C31—22no—
28C2×#41×C31—42no—
29C2×#41×C31—42no—
30C22×Q8×C31D411yescharacteristic
31C22×D4×C31—21no—
32C22×D4×C31—21no—
33C22×D4×C31C2×C411yescharacteristic
34C22×D4×C31C2×C411yescharacteristic
35C22×D4×C31D411yescharacteristic
36C23×C4×C31C2×C411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31D411yescharacteristic
39C23×C4×C31C2311yescharacteristic
40C2×M16×C31—22no—
41C2×M16×C31—22no—
42C2×M16×C31—22no—
43C2×M16×C31—42no—
44C2×M16×C31—42no—
45C22×C8×C31—22no—
46C31×#120—42no—
47C31×#120—42no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—22no—
51C2×C22⋊C4×C31—21no—
52C2×C22⋊C4×C31—21no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—21no—
55C2×C22⋊C4×C31—21no—
56C2×C22⋊C4×C31C2×C411yescharacteristic
57C2×C22⋊C4×C31C2×C411yescharacteristic
58C31×#101—42no—
59C31×#100—42no—
60C31×C22⋊C8—24no—
61C31×C22⋊C8—22no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—22no—
64C31×C22⋊C8D414yescomplemented
65C31×#95—21no—
66C31×#95—21no—
67C31×#95—21no—
68C31×#95—21no—
69C24×C31—21no—
70C24×C31—22no—
71C24×C31—42no—
72C24×C31—41no—
73C24×C31—41no—
74C24×C31—81no—
75C24×C31C22⋊C411yescharacteristic
76C24×C31C22⋊C411yescharacteristic
77C24×C31C22×C411yescharacteristic
78#41×C31—44no—
79#41×C31—44no—
80#41×C31—48no—
81C2×Q8×C31—22no—
82C2×Q8×C31—22no—
83C2×Q8×C31—41no—
84C2×D4×C31—22no—
85C2×D4×C31—22no—
86C2×D4×C31—22no—
87C2×D4×C31—22no—
88C2×D4×C31—22no—
89C2×D4×C31—22no—
90C2×D4×C31—41no—
91C2×D4×C31—41no—
92C2×D4×C31—41no—
93C2×D4×C31—42no—
94C2×D4×C31—42no—
95C2×D4×C31—42no—
96C2×D4×C31—42no—
97C2×D4×C31—81no—
98C2×D4×C31—81no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—21no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—41no—
110C22×C4×C31—41no—
111C22×C4×C31—41no—
112C22×C4×C31—41no—
113C22×C4×C31—81no—
114C22×C4×C31C22⋊C411yescharacteristic
115C22×C4×C31C22⋊C411yescharacteristic
116C22×C4×C31C2×D411yescharacteristic
117C22×C4×C31C2×D411yescharacteristic
118C22×C4×C31C2×D412yes—
119C22×C4×C31#4112yes—
120M16×C31—44no—
121M16×C31—42no—
122M16×C31—42no—
123M16×C31—42no—
124M16×C31—42no—
125C2×C8×C31—24no—
126C2×C8×C31—44no—
127C2×C8×C31—42no—
128C22⋊C4×C31—42no—
129C22⋊C4×C31—42no—
130C22⋊C4×C31—41no—
131C22⋊C4×C31—42no—
132C22⋊C4×C31—41no—
133C22⋊C4×C31—41no—
134C22⋊C4×C31—41no—
135C22⋊C4×C31—81no—
136C22⋊C4×C31—81no—
137#9511C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—21no—
139C23×C31—21no—
140C23×C31—21no—
141C23×C31—21no—
142C23×C31—22no—
143C23×C31—24no—
144C23×C31—21no—
145C23×C31—21no—
146C23×C31—21no—
147C23×C31—41no—
148C23×C31—41no—
149C23×C31—41no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—41no—
155C23×C31—41no—
156C23×C31—42no—
157C23×C31—41no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31—82no—
161C23×C31—82no—
162C23×C31—84no—
163C23×C31—84no—
164C23×C31#9912yes—
165C23×C31C2×C22⋊C411yescharacteristic
166C23×C31C4×D412yes—
167Q8×C31—44no—
168D4×C31—44no—
169D4×C31—44no—
170D4×C31—44no—
171D4×C31—84no—
172D4×C31—84no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—24no—
176C2×C4×C31—21no—
177C2×C4×C31—21no—
178C2×C4×C31—21no—
179C2×C4×C31—21no—
180C2×C4×C31—21no—
181C2×C4×C31—21no—
182C2×C4×C31—21no—
183C2×C4×C31—21no—
184C2×C4×C31—21no—
185C2×C4×C31—42no—
186C2×C4×C31—42no—
187C2×C4×C31—42no—
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—41no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—82no—
199C2×C4×C31#9912yes—
200C2×C4×C31#12011yescharacteristic
201C2×C4×C31#12112yes—
202C2×C4×C31#12311yescharacteristic
203C8×C31—44no—
204C8×C31—82no—
205#2879C2×C3111yescharacteristic, complemented
206#2404C2×C3111yescharacteristic
207#1785C2×C3111yescharacteristic, complemented
208#1462C2×C3112yescomplemented
209#1306C2×C3112yescomplemented
210C22×C31—21no—
211C22×C31—21no—
212C22×C31—22no—
213C22×C31—22no—
214C22×C31—22no—
215C22×C31—22no—
216C22×C31—42no—
217C22×C31—42no—
218C22×C31—42no—
219C22×C31—42no—
220C22×C31—42no—
221C22×C31—42no—
222C22×C31—41no—
223C22×C31—41no—
224C22×C31—42no—
225C22×C31—41no—
226C22×C31—41no—
227C22×C31—41no—
228C22×C31—81no—
229C22×C31—81no—
230C22×C31—81no—
231C22×C31—81no—
232C22×C31—84no—
233C22×C31—84no—
234C22×C31—81no—
235C22×C31—81no—
236C22×C31#38611yescharacteristic
237C22×C31C2×#9911yescharacteristic
238C22×C31C2×#9911yescharacteristic
239C4×C31—21no—
240C4×C31—22no—
241C4×C31—21no—
242C4×C31—22no—
243C4×C31—41no—
244C4×C31—81no—
245C4×C31—81no—
246C4×C31—81no—
247C22×#41C22×C3111yescharacteristic
248C22×M16—21no—
249C2×#120C4×C3111yescharacteristic
250C2×#120C4×C3111yescharacteristic
251C22×C22⋊C4C22×C3111yescharacteristic
252C2×#101—21no—
253C2×#100—21no—
254#408—24no—
255#407—21no—
256#407C22×C3112yes—
257#407C22×C3112yes—
258#393—21no—
259#392—21no—
260#386—21no—
261#386—21no—
262#386C4×C3111yescharacteristic
263#386C4×C3111yescharacteristic
264#381C22×C3111yescharacteristic
265#323—24no—
266C2×C31—21no—
267C2×C31—21no—
268C2×C31—42no—
269C2×C31—42no—
270C2×C31—81no—
271C2×C31—82no—
272C2×C31#189111yescharacteristic
273C2×C31#189811yescharacteristic
274C2×C31#191411yescharacteristic
275C25C2×C4×C3111yescharacteristic
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—42no—
279C2×#41—42no—
280C22×Q8D4×C3111yescharacteristic
281C22×D4—21no—
282C22×D4—21no—
283C22×D4C2×C4×C3111yescharacteristic
284C22×D4C2×C4×C3111yescharacteristic
285C22×D4D4×C3111yescharacteristic
286C23×C4C2×C4×C3111yescharacteristic
287C23×C4D4×C3111yescharacteristic
288C23×C4D4×C3111yescharacteristic
289C23×C4C23×C3111yescharacteristic
290C2×M16—22no—
291C2×M16—22no—
292C2×M16—22no—
293C2×M16—42no—
294C2×M16—42no—
295C22×C8—22no—
296#120—42no—
297#120—42no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—21no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4C2×C4×C3111yescharacteristic
307C2×C22⋊C4C2×C4×C3111yescharacteristic
308#101—42no—
309#100—42no—
310C22⋊C8—24no—
311C22⋊C8—22no—
312C22⋊C8—22no—
313C22⋊C8—22no—
314C22⋊C8D4×C3114yescomplemented
315#95—21no—
316#95—21no—
317#95—21no—
318#95—21no—
319C31#951111yescharacteristic, direct product factor, Sylow
320C24—21no—
321C24—22no—
322C24—42no—
323C24—41no—
324C24—41no—
325C24—81no—
326C24C22⋊C4×C3111yescharacteristic
327C24C22⋊C4×C3111yescharacteristic
328C24C22×C4×C3111yescharacteristic
329#41—44no—
330#41—44no—
331#41—48no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—41no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—42no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—42no—
348C2×D4—81no—
349C2×D4—81no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—81no—
365C22×C4C22⋊C4×C3111yescharacteristic
366C22×C4C22⋊C4×C3111yescharacteristic
367C22×C4C2×D4×C3111yescharacteristic
368C22×C4C2×D4×C3111yescharacteristic
369C22×C4C2×D4×C3112yes—
370C22×C4#41×C3112yes—
371M16—44no—
372M16—42no—
373M16—42no—
374M16—42no—
375M16—42no—
376C2×C8—24no—
377C2×C8—44no—
378C2×C8—42no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—41no—
382C22⋊C4—42no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—81no—
387C22⋊C4—81no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—22no—
393C23—24no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—82no—
411C23—82no—
412C23—84no—
413C23—84no—
414C23C31×#9912yes—
415C23C2×C22⋊C4×C3111yescharacteristic
416C23C4×D4×C3112yes—
417Q8—44no—
418D4—44no—
419D4—44no—
420D4—44no—
421D4—84no—
422D4—84no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4C31×#9912yes—
450C2×C4C31×#12011yescharacteristic
451C2×C4C31×#12112yes—
452C2×C4C31×#12311yescharacteristic
453C8—44no—
454C8—82no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22—42no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—84no—
478C22—84no—
479C22—81no—
480C22—81no—
481C22C31×#38611yescharacteristic
482C22C2×C31×#9911yescharacteristic
483C22C2×C31×#9911yescharacteristic
484C4—21no—
485C4—22no—
486C4—21no—
487C4—22no—
488C4—41no—
489C4—81no—
490C4—81no—
491C4—81no—
492C2—21no—
493C2—21no—
494C2—42no—
495C2—42no—
496C2—81no—
497C2—82no—
498C2C31×#189111yescharacteristic
499C2C31×#189811yescharacteristic
500C2C31×#191411yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC24C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#2404C2
LCSG ▷ C24 ▷ 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×#2879C2semidirect
3. C31×#1785C2semidirect
4. C31×#1462C2semidirect
5. C31×#1306C2semidirect
64. C31×C22⋊C8D4semidirect
137. #9511C31direct (N × H)
205. #2879C2×C31semidirect
207. #1785C2×C31semidirect
208. #1462C2×C31semidirect
209. #1306C2×C31semidirect
314. C22⋊C8D4×C31semidirect
319. C31#9511direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#28792
C31×#24042
C31×#17852
C31×#14622
C31×#13062
#951131