Finite Group Databasebeta

← C31×#7943 #21464702

Subgroups — C31×#7943 #21464702

Order 7936.

982 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#407C211yesmaximal, characteristic
2C31×#2280C211yesmaximal, characteristic
3C2×C31×#381C211yesmaximal, characteristic
4C31×#1284C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×M16×C31—21no—
7C2×C31×#117C412yescomplemented
8C22×C22⋊C4×C31—21no—
9C31×#407—21no—
10C31×#407—21no—
11C31×#407C412yescomplemented
12C31×#407C2212yes—
13C2×C31×C22⋊C8—21no—
14C2×C31×C22⋊C8C412yescomplemented
15C31×#381—21no—
16C31×#381—21no—
17C31×#381—21no—
18C31×#381C412yescomplemented
19C31×#381C2212yes—
20C31×#380—21no—
21C31×#380—21no—
22C31×#379—21no—
23C4×C22⋊C4×C31C412yescomplemented
24C4×C22⋊C4×C31C2212yes—
25C2×C31×#95—21no—
26C2×C31×#95C412yescomplemented
27C25×C31D411yescharacteristic
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×C31C2×C411yescharacteristic
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—44no—
47C22×C8×C31—22no—
48C31×#117—44no—
49C2×C4⋊C4×C31—22no—
50C2×C22⋊C4×C31—22no—
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—22no—
54C2×C22⋊C4×C31—22no—
55C2×C22⋊C4×C31—44no—
56C2×C42×C31C2×C414yescomplemented
57C31×C22⋊C8—22no—
58C31×C22⋊C8—22no—
59C31×C22⋊C8—22no—
60C31×C22⋊C8C2×C414yescomplemented
61C31×#95—22no—
62C31×#95—22no—
63C31×#95—22no—
64C31×#95—22no—
65C31×#95—22no—
66C31×#95C2×C414yes—
67C24×C31—24no—
68C24×C31—42no—
69C24×C31—42no—
70C24×C31C22⋊C411yescharacteristic
71C24×C31C22⋊C411yescharacteristic
72C24×C31C22⋊C411yescharacteristic
73C24×C31C22⋊C411yescharacteristic
74C24×C31C4⋊C411yescharacteristic
75C24×C31C4⋊C411yescharacteristic
76C24×C31C2×D411yescharacteristic
77C22×C4×C31—24no—
78C22×C4×C31—24no—
79C22×C4×C31—24no—
80C22×C4×C31—24no—
81C22×C4×C31—42no—
82C22×C4×C31—42no—
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—44no—
94C22×C4×C31—44no—
95C22×C4×C31—44no—
96C22×C4×C31C4211yescharacteristic
97C22×C4×C31C4211yescharacteristic
98C22×C4×C31C4211yescharacteristic
99C22×C4×C31C4211yescharacteristic
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×C31C4⋊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×C31C22×C411yescharacteristic
119C22×C4×C31C22×C411yescharacteristic
120C22×C4×C31C22×C411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×Q811yescharacteristic
124M16×C31—44no—
125M16×C31—44no—
126C2×C8×C31—24no—
127C2×C8×C31—44no—
128C4⋊C4×C31—44no—
129C22⋊C4×C31—44no—
130C22⋊C4×C31—44no—
131C22⋊C4×C31—44no—
132C22⋊C4×C31—44no—
133C22⋊C4×C31—44no—
134C42×C31—44no—
135#7943C3111yesmaximal, characteristic, direct product factor, Sylow
136C23×C31—22no—
137C23×C31—22no—
138C23×C31—22no—
139C23×C31—22no—
140C23×C31—22no—
141C23×C31—22no—
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—22no—
145C23×C31—22no—
146C23×C31—22no—
147C23×C31—22no—
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—416no—
157C23×C31#9511yescharacteristic
158C23×C31#9511yescharacteristic
159C23×C31#9511yescharacteristic
160C23×C31#9511yescharacteristic
161C23×C31#9914yes—
162C23×C31C2×C22⋊C411yescharacteristic
163C23×C31C2×C22⋊C411yescharacteristic
164C23×C31C2×C4⋊C411yescharacteristic
165C2×C4×C31—22no—
166C2×C4×C31—22no—
167C2×C4×C31—22no—
168C2×C4×C31—22no—
169C2×C4×C31—22no—
170C2×C4×C31—22no—
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—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—41no—
188C2×C4×C31—41no—
189C2×C4×C31—41no—
190C2×C4×C31—41no—
191C2×C4×C31—41no—
192C2×C4×C31—41no—
193C2×C4×C31—44no—
194C2×C4×C31—44no—
195C2×C4×C31—44no—
196C2×C4×C31—44no—
197C2×C4×C31—44no—
198C2×C4×C31—44no—
199C2×C4×C31—88no—
200C2×C4×C31#9511yescharacteristic
201C2×C4×C31#9511yescharacteristic
202C2×C4×C31#9511yescharacteristic
203C2×C4×C31#9511yescharacteristic
204C2×C4×C31C2×C4211yescharacteristic
205C2×C4×C31C2×C22⋊C411yescharacteristic
206C2×C4×C31C2×C4⋊C411yescharacteristic
207C2×C4×C31C2×C4⋊C411yescharacteristic
208C8×C31—44no—
209C2×#407C2×C3111yescharacteristic
210#2280C2×C3111yescharacteristic
211C2×#381C2×C3111yescharacteristic
212#1284C2×C3114yescomplemented
213C22×C31—28no—
214C22×C31—21no—
215C22×C31—21no—
216C22×C31—21no—
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—21no—
230C22×C31—44no—
231C22×C31—44no—
232C22×C31—44no—
233C22×C31—44no—
234C22×C31—44no—
235C22×C31—44no—
236C22×C31H(3,ℤ/4)12yes—
237C22×C31#34212yes—
238C22×C31#34212yes—
239C22×C31C2×#9511yescharacteristic
240C22×C31C2×#9912yes—
241C22×C31#42112yes—
242C4×C31—21no—
243C4×C31—21no—
244C4×C31—21no—
245C4×C31—21no—
246C4×C31—21no—
247C4×C31—21no—
248C4×C31—21no—
249C4×C31—21no—
250C4×C31—84no—
251C4×C31—84no—
252C24×C4C22×C3111yescharacteristic
253C22×M16—21no—
254C2×#117C4×C3112yescomplemented
255C22×C22⋊C4—21no—
256#407—21no—
257#407—21no—
258#407C4×C3112yescomplemented
259#407C22×C3112yes—
260C2×C22⋊C8—21no—
261C2×C22⋊C8C4×C3112yescomplemented
262#381—21no—
263#381—21no—
264#381—21no—
265#381C4×C3112yescomplemented
266#381C22×C3112yes—
267#380—21no—
268#380—21no—
269#379—21no—
270C4×C22⋊C4C4×C3112yescomplemented
271C4×C22⋊C4C22×C3112yes—
272C2×#95—21no—
273C2×#95C4×C3112yescomplemented
274C2×C31—22no—
275C2×C31—22no—
276C2×C31—22no—
277C2×C31—22no—
278C2×C31—22no—
279C2×C31—41no—
280C2×C31—41no—
281C2×C31C2×H(3,ℤ/4)11yescharacteristic
282C2×C31#173311yescharacteristic
283C2×C31C2×#34211yescharacteristic
284C25D4×C3111yescharacteristic
285C23×C4—22no—
286C23×C4—44no—
287C23×C4C2×C4×C3111yescharacteristic
288C23×C4C2×C4×C3111yescharacteristic
289C23×C4C2×C4×C3111yescharacteristic
290C23×C4C2×C4×C3111yescharacteristic
291C23×C4C2×C4×C3111yescharacteristic
292C23×C4C2×C4×C3111yescharacteristic
293C23×C4D4×C3111yescharacteristic
294C23×C4D4×C3111yescharacteristic
295C23×C4D4×C3111yescharacteristic
296C23×C4D4×C3111yescharacteristic
297C23×C4D4×C3111yescharacteristic
298C23×C4Q8×C3111yescharacteristic
299C23×C4Q8×C3111yescharacteristic
300C23×C4C23×C3111yescharacteristic
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—44no—
304C22×C8—22no—
305#117—44no—
306C2×C4⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—44no—
313C2×C42C2×C4×C3114yescomplemented
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317C22⋊C8C2×C4×C3114yescomplemented
318#95—22no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95C2×C4×C3114yes—
324C31#794311yescharacteristic, direct product factor, Sylow
325C24—24no—
326C24—42no—
327C24—42no—
328C24C22⋊C4×C3111yescharacteristic
329C24C22⋊C4×C3111yescharacteristic
330C24C22⋊C4×C3111yescharacteristic
331C24C22⋊C4×C3111yescharacteristic
332C24C4⋊C4×C3111yescharacteristic
333C24C4⋊C4×C3111yescharacteristic
334C24C2×D4×C3111yescharacteristic
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—44no—
352C22×C4—44no—
353C22×C4—44no—
354C22×C4C42×C3111yescharacteristic
355C22×C4C42×C3111yescharacteristic
356C22×C4C42×C3111yescharacteristic
357C22×C4C42×C3111yescharacteristic
358C22×C4C22⋊C4×C3111yescharacteristic
359C22×C4C22⋊C4×C3111yescharacteristic
360C22×C4C22⋊C4×C3111yescharacteristic
361C22×C4C22⋊C4×C3111yescharacteristic
362C22×C4C22⋊C4×C3111yescharacteristic
363C22×C4C22⋊C4×C3111yescharacteristic
364C22×C4C22⋊C4×C3111yescharacteristic
365C22×C4C22⋊C4×C3111yescharacteristic
366C22×C4C4⋊C4×C3111yescharacteristic
367C22×C4C4⋊C4×C3111yescharacteristic
368C22×C4C4⋊C4×C3111yescharacteristic
369C22×C4C4⋊C4×C3111yescharacteristic
370C22×C4C4⋊C4×C3111yescharacteristic
371C22×C4C4⋊C4×C3111yescharacteristic
372C22×C4C4⋊C4×C3111yescharacteristic
373C22×C4C4⋊C4×C3111yescharacteristic
374C22×C4C4⋊C4×C3111yescharacteristic
375C22×C4C4⋊C4×C3111yescharacteristic
376C22×C4C22×C4×C3111yescharacteristic
377C22×C4C22×C4×C3111yescharacteristic
378C22×C4C22×C4×C3111yescharacteristic
379C22×C4C2×D4×C3111yescharacteristic
380C22×C4C2×D4×C3111yescharacteristic
381C22×C4C2×Q8×C3111yescharacteristic
382M16—44no—
383M16—44no—
384C2×C8—24no—
385C2×C8—44no—
386C4⋊C4—44no—
387C22⋊C4—44no—
388C22⋊C4—44no—
389C22⋊C4—44no—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C42—44no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—416no—
414C23C31×#9511yescharacteristic
415C23C31×#9511yescharacteristic
416C23C31×#9511yescharacteristic
417C23C31×#9511yescharacteristic
418C23C31×#9914yes—
419C23C2×C22⋊C4×C3111yescharacteristic
420C23C2×C22⋊C4×C3111yescharacteristic
421C23C2×C4⋊C4×C3111yescharacteristic
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
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—41no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—88no—
457C2×C4C31×#9511yescharacteristic
458C2×C4C31×#9511yescharacteristic
459C2×C4C31×#9511yescharacteristic
460C2×C4C31×#9511yescharacteristic
461C2×C4C2×C42×C3111yescharacteristic
462C2×C4C2×C22⋊C4×C3111yescharacteristic
463C2×C4C2×C4⋊C4×C3111yescharacteristic
464C2×C4C2×C4⋊C4×C3111yescharacteristic
465C8—44no—
466C22—28no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22—44no—
489C22C31×H(3,ℤ/4)12yes—
490C22C31×#34212yes—
491C22C31×#34212yes—
492C22C2×C31×#9511yescharacteristic
493C22C2×C31×#9912yes—
494C22C31×#42112yes—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—21no—
503C4—84no—
504C4—84no—
505C2—22no—
506C2—22no—
507C2—22no—
508C2—22no—
509C2—22no—
510C2—41no—
511C2—41no—
512C2C2×C31×H(3,ℤ/4)11yescharacteristic
513C2C31×#173311yescharacteristic
514C2C2×C31×#34211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#95
commutatorC2×C4C2×C42×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC25×C31D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1284C2semidirect
7. C2×C31×#117C4semidirect
11. C31×#407C4semidirect
14. C2×C31×C22⋊C8C4semidirect
18. C31×#381C4semidirect
23. C4×C22⋊C4×C31C4semidirect
26. C2×C31×#95C4semidirect
56. C2×C42×C31C2×C4semidirect
60. C31×C22⋊C8C2×C4semidirect
135. #7943C31direct (N × H)
212. #1284C2×C31semidirect
254. C2×#117C4×C31semidirect
258. #407C4×C31semidirect
261. C2×C22⋊C8C4×C31semidirect
265. #381C4×C31semidirect
270. C4×C22⋊C4C4×C31semidirect
273. C2×#95C4×C31semidirect
313. C2×C42C2×C4×C31semidirect
317. C22⋊C8C2×C4×C31semidirect
324. C31#7943direct (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
C31×#22802
C2×C31×#3812
C31×#12842
#794331