Finite Group Databasebeta

← C31×#9520 #21466279

Subgroups — C31×#9520 #21466279

Order 7936.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3003C211yesmaximal, characteristic
2C31×#2976C211yesmaximal, characteristic, complemented
3C31×#1786C211yesmaximal, characteristic, complemented
4C31×#1783C211yesmaximal, characteristic, complemented
5C31×#1513C211yesmaximal, characteristic, complemented
6C31×#1305C211yesmaximal, characteristic, complemented
7C31×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C2×C31×AGL(1,ℤ/8)—21no—
10C31×#525C2211yescharacteristic
11C31×#450—21no—
12C31×#450C412yescomplemented
13C31×#447—21no—
14C31×#447C412yescomplemented
15C31×#436—21no—
16C31×#435—21no—
17C31×#435—21no—
18C8×D4×C31—21no—
19C31×#433—21no—
20C31×#418—21no—
21C2×C31×#102—21no—
22C2×C31×#102—21no—
23C2×C31×#100—21no—
24C2×C31×#100—21no—
25C31×#408—21no—
26C31×#407C2211yescharacteristic
27C31×#407C2211yescharacteristic
28C31×#407C2211yescharacteristic
29C2×C31×C22⋊C8C2211yescharacteristic
30C31×#380C2211yescharacteristic
31C31×#328—21no—
32C31×#327—21no—
33C25×C31—21no—
34C2×#41×C31D411yescharacteristic
35C22×D4×C31—21no—
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—21no—
40C22×D4×C31—42no—
41C22×D4×C31—42no—
42C22×D4×C31C2×C412yes—
43C23×C4×C31C2311yescharacteristic
44C31×AGL(1,ℤ/8)—42no—
45C31×AGL(1,ℤ/8)—42no—
46C2×SD16×C31—22no—
47C2×D8×C31—22no—
48C2×M16×C31—21no—
49C2×M16×C31—21no—
50C2×M16×C31—21no—
51C2×M16×C31D411yescharacteristic
52C2×M16×C31D411yescharacteristic
53C22×C8×C31—21no—
54C22×C8×C31D411yescharacteristic
55C22×C8×C31D411yescharacteristic
56C31×#123—21no—
57C31×C22⋊Q8C2×C411yescharacteristic
58C31×C22⋊Q8D411yescharacteristic
59C31×#121C2×C411yescharacteristic
60C31×#121D411yescharacteristic
61C31×#120—21no—
62C4×D4×C31—21no—
63C4×D4×C31—21no—
64C31×#117D411yescharacteristic
65C2×C4⋊C4×C31—21no—
66C2×C22⋊C4×C31—21no—
67C31×C4⋊C8—21no—
68C31×C4⋊C8—21no—
69C31×#102—22no—
70C31×#102—22no—
71C31×#102—42no—
72C31×#102—42no—
73C31×#100—42no—
74C31×#100—42no—
75C31×C22⋊C8—21no—
76C31×C22⋊C8—21no—
77C31×C22⋊C8—21no—
78C31×C22⋊C8—21no—
79C31×C22⋊C8—21no—
80C31×C22⋊C8—21no—
81C31×C22⋊C8—21no—
82C31×C22⋊C8—21no—
83C31×C22⋊C8—21no—
84C31×C22⋊C8C2×C412yes—
85C31×#97—21no—
86C4×C8×C31—21no—
87C31×#95—21no—
88C24×C31—22no—
89C24×C31—44no—
90C24×C31—41no—
91C24×C31—41no—
92C24×C31—81no—
93C24×C31—81no—
94C24×C31—82no—
95C24×C31#4111yescharacteristic
96#41×C31—41no—
97#41×C31—41no—
98C2×Q8×C31C22⋊C411yescharacteristic
99C2×D4×C31—22no—
100C2×D4×C31—22no—
101C2×D4×C31—22no—
102C2×D4×C31—22no—
103C2×D4×C31—22no—
104C2×D4×C31—22no—
105C2×D4×C31—21no—
106C2×D4×C31—21no—
107C2×D4×C31—21no—
108C2×D4×C31—22no—
109C2×D4×C31—22no—
110C2×D4×C31—41no—
111C2×D4×C31—41no—
112C2×D4×C31—41no—
113C2×D4×C31—41no—
114C2×D4×C31—41no—
115C2×D4×C31—41no—
116C2×D4×C31—44no—
117C2×D4×C31—44no—
118C2×D4×C31—44no—
119C2×D4×C31—41no—
120C2×D4×C31—41no—
121C2×D4×C31C22⋊C411yescharacteristic
122C22×C4×C31—21no—
123C22×C4×C31—41no—
124C22×C4×C31—41no—
125C22×C4×C31—41no—
126C22×C4×C31C22×C411yescharacteristic
127C22×C4×C31C2×D411yescharacteristic
128C22×C4×C31C2×D411yescharacteristic
129C22×C4×C31C2×D411yescharacteristic
130C22×C4×C31C2×D411yescharacteristic
131C22×C4×C31#4111yescharacteristic
132SD16×C31—44no—
133D8×C31—44no—
134M16×C31—41no—
135M16×C31—41no—
136M16×C31—41no—
137M16×C31—41no—
138M16×C31—41no—
139M16×C31—41no—
140M16×C31—81no—
141C2×C8×C31—22no—
142C2×C8×C31—21no—
143C2×C8×C31—21no—
144C2×C8×C31—21no—
145C2×C8×C31—21no—
146C2×C8×C31—41no—
147C2×C8×C31—41no—
148C2×C8×C31—41no—
149C2×C8×C31—81no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—41no—
153C4⋊C4×C31—41no—
154C4⋊C4×C31C22⋊C411yescharacteristic
155C4⋊C4×C31C22⋊C411yescharacteristic
156C22⋊C4×C31—21no—
157C22⋊C4×C31—21no—
158C22⋊C4×C31—21no—
159C22⋊C4×C31—21no—
160C22⋊C4×C31—21no—
161C22⋊C4×C31—81no—
162C42×C31—21no—
163#9520C3111yesmaximal, characteristic, direct product factor, Sylow
164C23×C31—21no—
165C23×C31—21no—
166C23×C31—24no—
167C23×C31—21no—
168C23×C31—41no—
169C23×C31—41no—
170C23×C31—42no—
171C23×C31—42no—
172C23×C31—42no—
173C23×C31—42no—
174C23×C31—42no—
175C23×C31—42no—
176C23×C31—82no—
177C23×C31—82no—
178C23×C31—82no—
179C23×C31—81no—
180C23×C31—81no—
181C23×C31—82no—
182C23×C31—88no—
183C23×C31—88no—
184C23×C31—81no—
185C23×C31—81no—
186C23×C31C4×D411yescharacteristic
187C23×C31#12111yescharacteristic
188C23×C31#12311yescharacteristic
189Q8×C31—41no—
190D4×C31—24no—
191D4×C31—24no—
192D4×C31—41no—
193D4×C31—42no—
194D4×C31—42no—
195D4×C31—42no—
196D4×C31—42no—
197D4×C31—41no—
198D4×C31—41no—
199D4×C31—42no—
200D4×C31—42no—
201D4×C31—81no—
202D4×C31—81no—
203C2×C4×C31—21no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—21no—
208C2×C4×C31—21no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—41no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—81no—
218C2×C4×C31—81no—
219C2×C4×C31—81no—
220C2×C4×C31C2×C22⋊C411yescharacteristic
221C2×C4×C31C4×D411yescharacteristic
222C2×C4×C31#12011yescharacteristic
223C2×C4×C31#12111yescharacteristic
224C8×C31—42no—
225C8×C31—41no—
226C8×C31—41no—
227C8×C31—41no—
228C8×C31—41no—
229C8×C31—81no—
230#3003C2×C3111yescharacteristic
231#2976C2×C3111yescharacteristic, complemented
232#1786C2×C3111yescharacteristic, complemented
233#1783C2×C3111yescharacteristic, complemented
234#1513C2×C3111yescharacteristic, complemented
235#1305C2×C3111yescharacteristic, complemented
236#1293C2×C3111yescharacteristic, complemented
237C22×C31—21no—
238C22×C31—21no—
239C22×C31—21no—
240C22×C31—21no—
241C22×C31—21no—
242C22×C31—21no—
243C22×C31—21no—
244C22×C31—21no—
245C22×C31—42no—
246C22×C31—42no—
247C22×C31—41no—
248C22×C31—44no—
249C22×C31—41no—
250C22×C31—41no—
251C22×C31—82no—
252C22×C31—82no—
253C22×C31—82no—
254C22×C31—82no—
255C22×C31—84no—
256C22×C31—84no—
257C22×C31—84no—
258C22×C31—84no—
259C22×C31—82no—
260C22×C31—82no—
261C22×C31#38611yescharacteristic
262C22×C31#47111yescharacteristic
263C22×C31#47211yescharacteristic
264C4×C31—21no—
265C4×C31—21no—
266C4×C31—21no—
267C4×C31—41no—
268C4×C31—41no—
269C4×C31—41no—
270C4×C31—161no—
271C4×C31B(4,𝔽2)11yescharacteristic
272C4×C31B(4,𝔽2)11yescharacteristic
273C23×D4C22×C3111yescharacteristic
274C2×AGL(1,ℤ/8)—21no—
275#525C22×C3111yescharacteristic
276#450—21no—
277#450C4×C3112yescomplemented
278#447—21no—
279#447C4×C3112yescomplemented
280#436—21no—
281#435—21no—
282#435—21no—
283C8×D4—21no—
284#433—21no—
285#418—21no—
286C2×#102—21no—
287C2×#102—21no—
288C2×#100—21no—
289C2×#100—21no—
290#408—21no—
291#407C22×C3111yescharacteristic
292#407C22×C3111yescharacteristic
293#407C22×C3111yescharacteristic
294C2×C22⋊C8C22×C3111yescharacteristic
295#380C22×C3111yescharacteristic
296#328—21no—
297#327—21no—
298C2×C31—21no—
299C2×C31—21no—
300C2×C31—41no—
301C2×C31—41no—
302C2×C31—81no—
303C2×C31—84no—
304C2×C31#188911yescharacteristic
305C2×C31#190311yescharacteristic
306C2×C31#190711yescharacteristic
307C25—21no—
308C2×#41D4×C3111yescharacteristic
309C22×D4—21no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4C2×C4×C3112yes—
317C23×C4C23×C3111yescharacteristic
318AGL(1,ℤ/8)—42no—
319AGL(1,ℤ/8)—42no—
320C2×SD16—22no—
321C2×D8—22no—
322C2×M16—21no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16D4×C3111yescharacteristic
326C2×M16D4×C3111yescharacteristic
327C22×C8—21no—
328C22×C8D4×C3111yescharacteristic
329C22×C8D4×C3111yescharacteristic
330#123—21no—
331C22⋊Q8C2×C4×C3111yescharacteristic
332C22⋊Q8D4×C3111yescharacteristic
333#121C2×C4×C3111yescharacteristic
334#121D4×C3111yescharacteristic
335#120—21no—
336C4×D4—21no—
337C4×D4—21no—
338#117D4×C3111yescharacteristic
339C2×C4⋊C4—21no—
340C2×C22⋊C4—21no—
341C4⋊C8—21no—
342C4⋊C8—21no—
343#102—22no—
344#102—22no—
345#102—42no—
346#102—42no—
347#100—42no—
348#100—42no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8C2×C4×C3112yes—
359#97—21no—
360C4×C8—21no—
361#95—21no—
362C31#952011yescharacteristic, direct product factor, Sylow
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C3111yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C3111yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C3111yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C3111yescharacteristic
402C22×C4C2×D4×C3111yescharacteristic
403C22×C4C2×D4×C3111yescharacteristic
404C22×C4C2×D4×C3111yescharacteristic
405C22×C4C2×D4×C3111yescharacteristic
406C22×C4#41×C3111yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C3111yescharacteristic
430C4⋊C4C22⋊C4×C3111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—82no—
453C23—81no—
454C23—81no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C3111yescharacteristic
461C23C31×#12111yescharacteristic
462C23C31×#12311yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C3111yescharacteristic
495C2×C4C4×D4×C3111yescharacteristic
496C2×C4C31×#12011yescharacteristic
497C2×C4C31×#12111yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C31×#38611yescharacteristic
529C22C31×#47111yescharacteristic
530C22C31×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C31×B(4,𝔽2)11yescharacteristic
539C4C31×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C31×#188911yescharacteristic
547C2C31×#190311yescharacteristic
548C2C31×#190711yescharacteristic
subgroupG/H
center, socleC22×C31#386
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC31×#3003C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2976C2semidirect
3. C31×#1786C2semidirect
4. C31×#1783C2semidirect
5. C31×#1513C2semidirect
6. C31×#1305C2semidirect
7. C31×#1293C2semidirect
12. C31×#450C4semidirect
14. C31×#447C4semidirect
163. #9520C31direct (N × H)
231. #2976C2×C31semidirect
232. #1786C2×C31semidirect
233. #1783C2×C31semidirect
234. #1513C2×C31semidirect
235. #1305C2×C31semidirect
236. #1293C2×C31semidirect
277. #450C4×C31semidirect
279. #447C4×C31semidirect
362. C31#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#30032
C31×#29762
C31×#17862
C31×#17832
C31×#15132
C31×#13052
C31×#12932
#952031