Finite Group Databasebeta

← C31×#8715 #21465474

Subgroups — C31×#8715 #21465474

Order 7936.

868 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2280C211yesmaximal, characteristic
2C31×#1779C211yesmaximal, characteristic
3C31×C22⋊#95C211yesmaximal, characteristic
4C31×#1294C212yesmaximal, complemented
5C31×#1294C212yesmaximal, complemented
6C24×C4×C31C2211yescharacteristic
7C2×C31×#117C411yescharacteristic, complemented
8C2×C31×#117C411yescharacteristic, complemented
9C22×C22⋊C4×C31—21no—
10C2×C31×C22⋊C8—21no—
11C2×C31×C22⋊C8—21no—
12C2×C31×C22⋊C8C2212yes—
13C31×#381—21no—
14C31×#380C411yescharacteristic, complemented
15C31×#380C411yescharacteristic, complemented
16C31×#380C2211yescharacteristic
17C31×#380C2211yescharacteristic
18C31×#379—21no—
19C4×C22⋊C4×C31—21no—
20C4×C22⋊C4×C31—21no—
21C2×C31×#95—21no—
22C2×C31×#95C2212yes—
23C25×C31D411yescharacteristic
24C23×C4×C31—24no—
25C23×C4×C31—22no—
26C23×C4×C31—42no—
27C23×C4×C31—42no—
28C23×C4×C31C2×C411yescharacteristic
29C23×C4×C31C2×C411yescharacteristic
30C23×C4×C31D411yescharacteristic
31C23×C4×C31D411yescharacteristic
32C23×C4×C31D411yescharacteristic
33C23×C4×C31C2311yescharacteristic
34C22×C8×C31—22no—
35C31×#117—42no—
36C31×#117—42no—
37C2×C4⋊C4×C31C2×C411yescharacteristic
38C2×C4⋊C4×C31C2×C411yescharacteristic
39C2×C4⋊C4×C31C2×C411yescharacteristic
40C2×C4⋊C4×C31C2×C411yescharacteristic
41C2×C22⋊C4×C31—24no—
42C2×C22⋊C4×C31—21no—
43C2×C22⋊C4×C31—21no—
44C2×C22⋊C4×C31—21no—
45C2×C22⋊C4×C31—21no—
46C2×C22⋊C4×C31—21no—
47C2×C22⋊C4×C31—21no—
48C2×C22⋊C4×C31—42no—
49C2×C22⋊C4×C31—42no—
50C2×C42×C31—21no—
51C2×C42×C31—21no—
52C31×C22⋊C8—24no—
53C31×C22⋊C8—42no—
54C31×C22⋊C8—42no—
55C31×#95—21no—
56C31×#95—21no—
57C31×#95—21no—
58C31×#95—21no—
59C31×#95—24no—
60C31×#95—42no—
61C24×C31—22no—
62C24×C31—22no—
63C24×C31—21no—
64C24×C31—21no—
65C24×C31—22no—
66C24×C31—22no—
67C24×C31—41no—
68C24×C31—41no—
69C24×C31C22⋊C411yescharacteristic
70C24×C31C22⋊C411yescharacteristic
71C24×C31C2×D411yescharacteristic
72C22×C4×C31—22no—
73C22×C4×C31—22no—
74C22×C4×C31—22no—
75C22×C4×C31—22no—
76C22×C4×C31—22no—
77C22×C4×C31—22no—
78C22×C4×C31—22no—
79C22×C4×C31—22no—
80C22×C4×C31—22no—
81C22×C4×C31—22no—
82C22×C4×C31—24no—
83C22×C4×C31—21no—
84C22×C4×C31—21no—
85C22×C4×C31—21no—
86C22×C4×C31—21no—
87C22×C4×C31—41no—
88C22×C4×C31—41no—
89C22×C4×C31—41no—
90C22×C4×C31—41no—
91C22×C4×C31—41no—
92C22×C4×C31—41no—
93C22×C4×C31—41no—
94C22×C4×C31—416no—
95C22×C4×C31—42no—
96C22×C4×C31—42no—
97C22×C4×C31—42no—
98C22×C4×C31—42no—
99C22×C4×C31—42no—
100C22×C4×C31—42no—
101C22×C4×C31C22⋊C411yescharacteristic
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22×C411yescharacteristic
104C22×C4×C31C2×D411yescharacteristic
105C22×C4×C31#4114yes—
106C2×C8×C31—42no—
107C2×C8×C31—42no—
108C2×C8×C31—42no—
109C4⋊C4×C31—41no—
110C4⋊C4×C31—41no—
111C4⋊C4×C31—41no—
112C4⋊C4×C31—41no—
113C22⋊C4×C31—42no—
114C22⋊C4×C31—48no—
115C22⋊C4×C31—42no—
116C22⋊C4×C31—42no—
117C22⋊C4×C31—42no—
118C22⋊C4×C31—42no—
119C22⋊C4×C31—41no—
120C22⋊C4×C31—41no—
121C42×C31—42no—
122C42×C31—42no—
123#8715C3111yesmaximal, characteristic, direct product factor, Sylow
124C23×C31—21no—
125C23×C31—21no—
126C23×C31—21no—
127C23×C31—21no—
128C23×C31—24no—
129C23×C31—24no—
130C23×C31—21no—
131C23×C31—21no—
132C23×C31—21no—
133C23×C31—21no—
134C23×C31—21no—
135C23×C31—21no—
136C23×C31—21no—
137C23×C31—21no—
138C23×C31—21no—
139C23×C31—21no—
140C23×C31—21no—
141C23×C31—21no—
142C23×C31—44no—
143C23×C31—44no—
144C23×C31—44no—
145C23×C31—44no—
146C23×C31—42no—
147C23×C31—42no—
148C23×C31—42no—
149C23×C31—42no—
150C23×C31#9912yes—
151C23×C31#10412yes—
152C23×C31C2×C22⋊C411yescharacteristic
153C23×C31#12312yes—
154C23×C31#13512yes—
155C23×C31AGL(1,ℤ/8)11yescharacteristic
156C23×C31#13711yescharacteristic
157C2×C4×C31—28no—
158C2×C4×C31—21no—
159C2×C4×C31—21no—
160C2×C4×C31—21no—
161C2×C4×C31—21no—
162C2×C4×C31—21no—
163C2×C4×C31—21no—
164C2×C4×C31—21no—
165C2×C4×C31—21no—
166C2×C4×C31—21no—
167C2×C4×C31—44no—
168C2×C4×C31—44no—
169C2×C4×C31—44no—
170C2×C4×C31—44no—
171C2×C4×C31—44no—
172C2×C4×C31—44no—
173C2×C4×C31—44no—
174C2×C4×C31—44no—
175C2×C4×C31—41no—
176C2×C4×C31—41no—
177C2×C4×C31—41no—
178C2×C4×C31—41no—
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—82no—
188C2×C4×C31—82no—
189C2×C4×C31—82no—
190C2×C4×C31—82no—
191C2×C4×C31#9912yes—
192C2×C4×C31#11712yes—
193C2×C4×C31#12312yes—
194C8×C31—82no—
195#2280C2×C3111yescharacteristic
196#1779C2×C3111yescharacteristic
197C22⋊#95C2×C3111yescharacteristic
198#1294C2×C3112yescomplemented
199#1294C2×C3112yescomplemented
200C22×C31—22no—
201C22×C31—22no—
202C22×C31—22no—
203C22×C31—21no—
204C22×C31—21no—
205C22×C31—21no—
206C22×C31—21no—
207C22×C31—22no—
208C22×C31—22no—
209C22×C31—22no—
210C22×C31—22no—
211C22×C31—22no—
212C22×C31—22no—
213C22×C31—22no—
214C22×C31—48no—
215C22×C31—48no—
216C22×C31—41no—
217C22×C31—41no—
218C22×C31—41no—
219C22×C31—41no—
220C22×C31—41no—
221C22×C31—41no—
222C22×C31—41no—
223C22×C31—41no—
224C22×C31#38111yescharacteristic
225C22×C31C2×#9911yescharacteristic
226C22×C31C2×#9911yescharacteristic
227C22×C31#41611yescharacteristic
228C22×C31#41711yescharacteristic
229C22×C31C2×#10411yescharacteristic
230C22×C31#42111yescharacteristic
231C22×C31#48212yes—
232C22×C31#48512yes—
233C4×C31—22no—
234C4×C31—22no—
235C4×C31—22no—
236C4×C31—41no—
237C4×C31—84no—
238C4×C31—81no—
239C4×C31—81no—
240C4×C31—81no—
241C4×C31—81no—
242C24×C4C22×C3111yescharacteristic
243C2×#117C4×C3111yescharacteristic, complemented
244C2×#117C4×C3111yescharacteristic, complemented
245C22×C22⋊C4—21no—
246C2×C22⋊C8—21no—
247C2×C22⋊C8—21no—
248C2×C22⋊C8C22×C3112yes—
249#381—21no—
250#380C4×C3111yescharacteristic, complemented
251#380C4×C3111yescharacteristic, complemented
252#380C22×C3111yescharacteristic
253#380C22×C3111yescharacteristic
254#379—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C2×#95—21no—
258C2×#95C22×C3112yes—
259C2×C31—22no—
260C2×C31—22no—
261C2×C31—42no—
262C2×C31—42no—
263C2×C31#150111yescharacteristic
264C2×C31#150411yescharacteristic
265C2×C31#151311yescharacteristic
266C2×C31#151611yescharacteristic
267C2×C31#181911yescharacteristic
268C2×C31#182511yescharacteristic
269C2×C31#182611yescharacteristic
270C25D4×C3111yescharacteristic
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4C2×C4×C3111yescharacteristic
276C23×C4C2×C4×C3111yescharacteristic
277C23×C4D4×C3111yescharacteristic
278C23×C4D4×C3111yescharacteristic
279C23×C4D4×C3111yescharacteristic
280C23×C4C23×C3111yescharacteristic
281C22×C8—22no—
282#117—42no—
283#117—42no—
284C2×C4⋊C4C2×C4×C3111yescharacteristic
285C2×C4⋊C4C2×C4×C3111yescharacteristic
286C2×C4⋊C4C2×C4×C3111yescharacteristic
287C2×C4⋊C4C2×C4×C3111yescharacteristic
288C2×C22⋊C4—24no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C42—21no—
298C2×C42—21no—
299C22⋊C8—24no—
300C22⋊C8—42no—
301C22⋊C8—42no—
302#95—21no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95—24no—
307#95—42no—
308C31#871511yescharacteristic, direct product factor, Sylow
309C24—22no—
310C24—22no—
311C24—21no—
312C24—21no—
313C24—22no—
314C24—22no—
315C24—41no—
316C24—41no—
317C24C22⋊C4×C3111yescharacteristic
318C24C22⋊C4×C3111yescharacteristic
319C24C2×D4×C3111yescharacteristic
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—416no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4C22⋊C4×C3111yescharacteristic
350C22×C4C22⋊C4×C3111yescharacteristic
351C22×C4C22×C4×C3111yescharacteristic
352C22×C4C2×D4×C3111yescharacteristic
353C22×C4#41×C3114yes—
354C2×C8—42no—
355C2×C8—42no—
356C2×C8—42no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C22⋊C4—42no—
362C22⋊C4—48no—
363C22⋊C4—42no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—42no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C42—42no—
370C42—42no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—24no—
376C23—24no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—44no—
390C23—44no—
391C23—44no—
392C23—44no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23C31×#9912yes—
398C23C31×#10412yes—
399C23C2×C22⋊C4×C3111yescharacteristic
400C23C31×#12312yes—
401C23C31×#13512yes—
402C23C31×AGL(1,ℤ/8)11yescharacteristic
403C23C31×#13711yescharacteristic
404C2×C4—28no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4C31×#9912yes—
439C2×C4C31×#11712yes—
440C2×C4C31×#12312yes—
441C8—82no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—48no—
457C22—48no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22C31×#38111yescharacteristic
467C22C2×C31×#9911yescharacteristic
468C22C2×C31×#9911yescharacteristic
469C22C31×#41611yescharacteristic
470C22C31×#41711yescharacteristic
471C22C2×C31×#10411yescharacteristic
472C22C31×#42111yescharacteristic
473C22C31×#48212yes—
474C22C31×#48512yes—
475C4—22no—
476C4—22no—
477C4—22no—
478C4—41no—
479C4—84no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—81no—
484C2—22no—
485C2—22no—
486C2—42no—
487C2—42no—
488C2C31×#150111yescharacteristic
489C2C31×#150411yescharacteristic
490C2C31×#151311yescharacteristic
491C2C31×#151611yescharacteristic
492C2C31×#181911yescharacteristic
493C2C31×#182511yescharacteristic
494C2C31×#182611yescharacteristic
subgroupG/H
center, socleC23×C31C2×C22⋊C4
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1294C2semidirect
5. C31×#1294C2semidirect
7. C2×C31×#117C4semidirect
8. C2×C31×#117C4semidirect
14. C31×#380C4semidirect
15. C31×#380C4semidirect
123. #8715C31direct (N × H)
198. #1294C2×C31semidirect
199. #1294C2×C31semidirect
243. C2×#117C4×C31semidirect
244. C2×#117C4×C31semidirect
250. #380C4×C31semidirect
251. #380C4×C31semidirect
308. C31#8715direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#22802
C31×#17792
C31×C22⋊#952
C31×#12942
#871531