Finite Group Databasebeta

← C31×#8107 #21464866

Subgroups — C31×#8107 #21464866

Order 7936.

986 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#407C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic
3C2×C31×#380C211yesmaximal, characteristic
4C31×#1305C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×M16×C31—21no—
7C22×M16×C31C412yescomplemented
8C22×C4⋊C4×C31—21no—
9C22×C22⋊C4×C31C412yes—
10C31×#407—21no—
11C31×#407—21no—
12C31×#407—21no—
13C31×#407—21no—
14C31×#407C412yescomplemented
15C31×#407C412yescomplemented
16C31×#407C2212yes—
17C31×#407C2212yes—
18C2×C31×C22⋊C8—21no—
19C2×C31×C22⋊C8—21no—
20C2×C31×C22⋊C8—21no—
21C2×C31×C22⋊C8C412yescomplemented
22C31×#380—21no—
23C31×#380—21no—
24C31×#380C412yes—
25C31×#380C2212yes—
26C2×C31×#95—21no—
27C25×C31C2×C411yescharacteristic
28C23×C4×C31—22no—
29C23×C4×C31—44no—
30C23×C4×C31C2×C411yescharacteristic
31C23×C4×C31C2×C411yescharacteristic
32C23×C4×C31C2×C411yescharacteristic
33C23×C4×C31C2×C411yescharacteristic
34C23×C4×C31C2×C411yescharacteristic
35C23×C4×C31D411yescharacteristic
36C23×C4×C31D411yescharacteristic
37C23×C4×C31D411yescharacteristic
38C23×C4×C31D411yescharacteristic
39C23×C4×C31D411yescharacteristic
40C23×C4×C31D411yescharacteristic
41C23×C4×C31Q811yescharacteristic
42C23×C4×C31Q811yescharacteristic
43C23×C4×C31C2311yescharacteristic
44C2×M16×C31—22no—
45C2×M16×C31—22no—
46C2×M16×C31—22no—
47C2×M16×C31—44no—
48C2×M16×C31—44no—
49C2×M16×C31C2×C414yescomplemented
50C22×C8×C31—22no—
51C22×C8×C31—22no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—44no—
55C2×C22⋊C4×C31—22no—
56C2×C22⋊C4×C31—44no—
57C2×C22⋊C4×C31C2×C414yes—
58C31×C22⋊C8—22no—
59C31×C22⋊C8—22no—
60C31×C22⋊C8—22no—
61C31×C22⋊C8—22no—
62C31×C22⋊C8—22no—
63C31×C22⋊C8—22no—
64C31×C22⋊C8—22no—
65C31×C22⋊C8C2×C414yescomplemented
66C31×#95—22no—
67C31×#95—22no—
68C24×C31—22no—
69C24×C31—22no—
70C24×C31—42no—
71C24×C31—42no—
72C24×C31C4211yescharacteristic
73C24×C31C4211yescharacteristic
74C24×C31C22⋊C411yescharacteristic
75C24×C31C22⋊C411yescharacteristic
76C24×C31C4⋊C411yescharacteristic
77C24×C31C4⋊C411yescharacteristic
78C24×C31C22×C411yescharacteristic
79C22×C4×C31—24no—
80C22×C4×C31—24no—
81C22×C4×C31—24no—
82C22×C4×C31—24no—
83C22×C4×C31—42no—
84C22×C4×C31—42no—
85C22×C4×C31—42no—
86C22×C4×C31—42no—
87C22×C4×C31—42no—
88C22×C4×C31—42no—
89C22×C4×C31—42no—
90C22×C4×C31—42no—
91C22×C4×C31—42no—
92C22×C4×C31—42no—
93C22×C4×C31—42no—
94C22×C4×C31—44no—
95C22×C4×C31—44no—
96C22×C4×C31—44no—
97C22×C4×C31C4211yescharacteristic
98C22×C4×C31C4211yescharacteristic
99C22×C4×C31C22⋊C411yescharacteristic
100C22×C4×C31C22⋊C411yescharacteristic
101C22×C4×C31C22⋊C411yescharacteristic
102C22×C4×C31C22⋊C411yescharacteristic
103C22×C4×C31C22⋊C411yescharacteristic
104C22×C4×C31C22⋊C411yescharacteristic
105C22×C4×C31C22⋊C411yescharacteristic
106C22×C4×C31C22⋊C411yescharacteristic
107C22×C4×C31C22⋊C411yescharacteristic
108C22×C4×C31C22⋊C411yescharacteristic
109C22×C4×C31C4⋊C411yescharacteristic
110C22×C4×C31C4⋊C411yescharacteristic
111C22×C4×C31C4⋊C411yescharacteristic
112C22×C4×C31C4⋊C411yescharacteristic
113C22×C4×C31C4⋊C411yescharacteristic
114C22×C4×C31C4⋊C411yescharacteristic
115C22×C4×C31C4⋊C411yescharacteristic
116C22×C4×C31C4⋊C411yescharacteristic
117C22×C4×C31C4⋊C411yescharacteristic
118C22×C4×C31C4⋊C411yescharacteristic
119C22×C4×C31C22×C411yescharacteristic
120C22×C4×C31C22×C411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×D411yescharacteristic
124C22×C4×C31C2×Q811yescharacteristic
125M16×C31—44no—
126M16×C31—44no—
127M16×C31—44no—
128M16×C31—44no—
129C2×C8×C31—24no—
130C2×C8×C31—24no—
131C2×C8×C31—44no—
132C2×C8×C31—44no—
133C4⋊C4×C31—44no—
134C4⋊C4×C31—44no—
135C22⋊C4×C31—44no—
136C22⋊C4×C31—44no—
137#8107C3111yesmaximal, characteristic, direct product factor, Sylow
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—21no—
141C23×C31—21no—
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—22no—
147C23×C31—22no—
148C23×C31—22no—
149C23×C31—22no—
150C23×C31—21no—
151C23×C31—21no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—41no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—41no—
158C23×C31—41no—
159C23×C31—41no—
160C23×C31—48no—
161C23×C31—48no—
162C23×C31#9511yescharacteristic
163C23×C31#9511yescharacteristic
164C23×C31#9511yescharacteristic
165C23×C31#9511yescharacteristic
166C23×C31#10012yes—
167C23×C31#10112yes—
168C23×C31C2×C4211yescharacteristic
169C23×C31C2×C22⋊C411yescharacteristic
170C23×C31C2×C4⋊C411yescharacteristic
171C2×C4×C31—22no—
172C2×C4×C31—22no—
173C2×C4×C31—22no—
174C2×C4×C31—22no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—22no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—22no—
184C2×C4×C31—22no—
185C2×C4×C31—22no—
186C2×C4×C31—41no—
187C2×C4×C31—41no—
188C2×C4×C31—41no—
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—44no—
199C2×C4×C31—44no—
200C2×C4×C31—44no—
201C2×C4×C31—88no—
202C2×C4×C31#9511yescharacteristic
203C2×C4×C31#9511yescharacteristic
204C2×C4×C31#9511yescharacteristic
205C2×C4×C31#9511yescharacteristic
206C2×C4×C31#9914yes—
207C2×C4×C31C2×C22⋊C411yescharacteristic
208C2×C4×C31C2×C22⋊C411yescharacteristic
209C2×C4×C31C2×C4⋊C411yescharacteristic
210C2×C4×C31C2×C4⋊C411yescharacteristic
211C8×C31—44no—
212C8×C31—44no—
213C2×#407C2×C3111yescharacteristic
214C2×#407C2×C3111yescharacteristic
215C2×#380C2×C3111yescharacteristic
216#1305C2×C3114yescomplemented
217C22×C31—24no—
218C22×C31—24no—
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—21no—
230C22×C31—21no—
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—21no—
234C22×C31—21no—
235C22×C31—42no—
236C22×C31—42no—
237C22×C31—44no—
238C22×C31—44no—
239C22×C31—44no—
240C22×C31—44no—
241C22×C31—42no—
242C22×C31—42no—
243C22×C31#34212yes—
244C22×C31#34312yes—
245C22×C31#34312yes—
246C22×C31#34412yes—
247C22×C31C2×#9511yescharacteristic
248C22×C31C2×#10011yescharacteristic
249C22×C31C2×#10111yescharacteristic
250C4×C31—21no—
251C4×C31—21no—
252C4×C31—21no—
253C4×C31—21no—
254C4×C31—21no—
255C4×C31—21no—
256C4×C31—84no—
257C4×C31#34212yes—
258C4×C31C2×#9912yes—
259C24×C4C22×C3111yescharacteristic
260C22×M16—21no—
261C22×M16C4×C3112yescomplemented
262C22×C4⋊C4—21no—
263C22×C22⋊C4C4×C3112yes—
264#407—21no—
265#407—21no—
266#407—21no—
267#407—21no—
268#407C4×C3112yescomplemented
269#407C4×C3112yescomplemented
270#407C22×C3112yes—
271#407C22×C3112yes—
272C2×C22⋊C8—21no—
273C2×C22⋊C8—21no—
274C2×C22⋊C8—21no—
275C2×C22⋊C8C4×C3112yescomplemented
276#380—21no—
277#380—21no—
278#380C4×C3112yes—
279#380C22×C3112yes—
280C2×#95—21no—
281C2×C31—21no—
282C2×C31—22no—
283C2×C31—22no—
284C2×C31—21no—
285C2×C31—22no—
286C2×C31—22no—
287C2×C31—41no—
288C2×C31—41no—
289C2×C31C2×#34211yescharacteristic
290C2×C31C2×#34311yescharacteristic
291C2×C31C2×#34411yescharacteristic
292C25C2×C4×C3111yescharacteristic
293C23×C4—22no—
294C23×C4—44no—
295C23×C4C2×C4×C3111yescharacteristic
296C23×C4C2×C4×C3111yescharacteristic
297C23×C4C2×C4×C3111yescharacteristic
298C23×C4C2×C4×C3111yescharacteristic
299C23×C4C2×C4×C3111yescharacteristic
300C23×C4D4×C3111yescharacteristic
301C23×C4D4×C3111yescharacteristic
302C23×C4D4×C3111yescharacteristic
303C23×C4D4×C3111yescharacteristic
304C23×C4D4×C3111yescharacteristic
305C23×C4D4×C3111yescharacteristic
306C23×C4Q8×C3111yescharacteristic
307C23×C4Q8×C3111yescharacteristic
308C23×C4C23×C3111yescharacteristic
309C2×M16—22no—
310C2×M16—22no—
311C2×M16—22no—
312C2×M16—44no—
313C2×M16—44no—
314C2×M16C2×C4×C3114yescomplemented
315C22×C8—22no—
316C22×C8—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—44no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4C2×C4×C3114yes—
323C22⋊C8—22no—
324C22⋊C8—22no—
325C22⋊C8—22no—
326C22⋊C8—22no—
327C22⋊C8—22no—
328C22⋊C8—22no—
329C22⋊C8—22no—
330C22⋊C8C2×C4×C3114yescomplemented
331#95—22no—
332#95—22no—
333C31#810711yescharacteristic, direct product factor, Sylow
334C24—22no—
335C24—22no—
336C24—42no—
337C24—42no—
338C24C42×C3111yescharacteristic
339C24C42×C3111yescharacteristic
340C24C22⋊C4×C3111yescharacteristic
341C24C22⋊C4×C3111yescharacteristic
342C24C4⋊C4×C3111yescharacteristic
343C24C4⋊C4×C3111yescharacteristic
344C24C22×C4×C3111yescharacteristic
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4—44no—
363C22×C4C42×C3111yescharacteristic
364C22×C4C42×C3111yescharacteristic
365C22×C4C22⋊C4×C3111yescharacteristic
366C22×C4C22⋊C4×C3111yescharacteristic
367C22×C4C22⋊C4×C3111yescharacteristic
368C22×C4C22⋊C4×C3111yescharacteristic
369C22×C4C22⋊C4×C3111yescharacteristic
370C22×C4C22⋊C4×C3111yescharacteristic
371C22×C4C22⋊C4×C3111yescharacteristic
372C22×C4C22⋊C4×C3111yescharacteristic
373C22×C4C22⋊C4×C3111yescharacteristic
374C22×C4C22⋊C4×C3111yescharacteristic
375C22×C4C4⋊C4×C3111yescharacteristic
376C22×C4C4⋊C4×C3111yescharacteristic
377C22×C4C4⋊C4×C3111yescharacteristic
378C22×C4C4⋊C4×C3111yescharacteristic
379C22×C4C4⋊C4×C3111yescharacteristic
380C22×C4C4⋊C4×C3111yescharacteristic
381C22×C4C4⋊C4×C3111yescharacteristic
382C22×C4C4⋊C4×C3111yescharacteristic
383C22×C4C4⋊C4×C3111yescharacteristic
384C22×C4C4⋊C4×C3111yescharacteristic
385C22×C4C22×C4×C3111yescharacteristic
386C22×C4C22×C4×C3111yescharacteristic
387C22×C4C2×D4×C3111yescharacteristic
388C22×C4C2×D4×C3111yescharacteristic
389C22×C4C2×D4×C3111yescharacteristic
390C22×C4C2×Q8×C3111yescharacteristic
391M16—44no—
392M16—44no—
393M16—44no—
394M16—44no—
395C2×C8—24no—
396C2×C8—24no—
397C2×C8—44no—
398C2×C8—44no—
399C4⋊C4—44no—
400C4⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C23—21no—
404C23—21no—
405C23—22no—
406C23—22no—
407C23—21no—
408C23—21no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—22no—
415C23—22no—
416C23—22no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—48no—
426C23—48no—
427C23C31×#9511yescharacteristic
428C23C31×#9511yescharacteristic
429C23C31×#9511yescharacteristic
430C23C31×#9511yescharacteristic
431C23C31×#10012yes—
432C23C31×#10112yes—
433C23C2×C42×C3111yescharacteristic
434C23C2×C22⋊C4×C3111yescharacteristic
435C23C2×C4⋊C4×C3111yescharacteristic
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—44no—
464C2×C4—44no—
465C2×C4—44no—
466C2×C4—88no—
467C2×C4C31×#9511yescharacteristic
468C2×C4C31×#9511yescharacteristic
469C2×C4C31×#9511yescharacteristic
470C2×C4C31×#9511yescharacteristic
471C2×C4C31×#9914yes—
472C2×C4C2×C22⋊C4×C3111yescharacteristic
473C2×C4C2×C22⋊C4×C3111yescharacteristic
474C2×C4C2×C4⋊C4×C3111yescharacteristic
475C2×C4C2×C4⋊C4×C3111yescharacteristic
476C8—44no—
477C8—44no—
478C22—24no—
479C22—24no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—42no—
497C22—42no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—42no—
503C22—42no—
504C22C31×#34212yes—
505C22C31×#34312yes—
506C22C31×#34312yes—
507C22C31×#34412yes—
508C22C2×C31×#9511yescharacteristic
509C22C2×C31×#10011yescharacteristic
510C22C2×C31×#10111yescharacteristic
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—84no—
518C4C31×#34212yes—
519C4C2×C31×#9912yes—
520C2—21no—
521C2—21no—
522C2—22no—
523C2—22no—
524C2—22no—
525C2—22no—
526C2—41no—
527C2—41no—
528C2C2×C31×#34211yescharacteristic
529C2C2×C31×#34311yescharacteristic
530C2C2×C31×#34411yescharacteristic
subgroupG/H
center, socleC22×C31C2×#95
commutatorC23C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1305C2semidirect
7. C22×M16×C31C4semidirect
14. C31×#407C4semidirect
15. C31×#407C4semidirect
21. C2×C31×C22⋊C8C4semidirect
49. C2×M16×C31C2×C4semidirect
65. C31×C22⋊C8C2×C4semidirect
137. #8107C31direct (N × H)
216. #1305C2×C31semidirect
261. C22×M16C4×C31semidirect
268. #407C4×C31semidirect
269. #407C4×C31semidirect
275. C2×C22⋊C8C4×C31semidirect
314. C2×M16C2×C4×C31semidirect
330. C22⋊C8C2×C4×C31semidirect
333. C31#8107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4072
C2×C31×#3802
C31×#13052
#810731