Finite Group Databasebeta

← C31×#7929 #21464688

Subgroups — C31×#7929 #21464688

Order 7936.

1058 conjugacy classes of subgroups.

The subgroup lattice has 514 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×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1282C214yesmaximal, complemented
5C24×C4×C31C2211yescharacteristic
6C22×M16×C31—21no—
7C22×M16×C31C412yescomplemented
8C22×C22⋊C4×C31C412yes—
9C22×C42×C31—21no—
10C31×#407—21no—
11C31×#407—21no—
12C31×#407—21no—
13C31×#407—21no—
14C31×#407—21no—
15C31×#407—21no—
16C31×#407C412yescomplemented
17C31×#407C412yescomplemented
18C2×C31×C22⋊C8—21no—
19C2×C31×C22⋊C8C412yescomplemented
20C2×C31×C22⋊C8C2212yes—
21C2×C31×C22⋊C8C2212yes—
22C4×C22⋊C4×C31—21no—
23C4×C22⋊C4×C31—21no—
24C4×C22⋊C4×C31C412yes—
25C4×C22⋊C4×C31C2212yes—
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—22no—
48C2×M16×C31—44no—
49C2×M16×C31—44no—
50C22×C8×C31—22no—
51C22×C8×C31C2×C414yescomplemented
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—28no—
54C2×C22⋊C4×C31C2×C414yes—
55C2×C42×C31—22no—
56C2×C42×C31—22no—
57C2×C42×C31—44no—
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—24no—
69C24×C31—42no—
70C24×C31—42no—
71C24×C31C4211yescharacteristic
72C24×C31C4211yescharacteristic
73C24×C31C22⋊C411yescharacteristic
74C24×C31C22⋊C411yescharacteristic
75C24×C31C4⋊C411yescharacteristic
76C24×C31C4⋊C411yescharacteristic
77C24×C31C22×C411yescharacteristic
78C22×C4×C31—24no—
79C22×C4×C31—24no—
80C22×C4×C31—24no—
81C22×C4×C31—28no—
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×C31C4211yescharacteristic
97C22×C4×C31C4211yescharacteristic
98C22×C4×C31C22⋊C411yescharacteristic
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×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×C31C2×D411yescharacteristic
121C22×C4×C31C2×D411yescharacteristic
122C22×C4×C31C2×D411yescharacteristic
123C22×C4×C31C2×Q811yescharacteristic
124M16×C31—44no—
125M16×C31—44no—
126M16×C31—44no—
127M16×C31—44no—
128C2×C8×C31—24no—
129C2×C8×C31—24no—
130C2×C8×C31—44no—
131C2×C8×C31—44no—
132C22⋊C4×C31—28no—
133C22⋊C4×C31—24no—
134C22⋊C4×C31M1618yescomplemented
135C42×C31—44no—
136C42×C31—44no—
137#7929C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
149C23×C31—22no—
150C23×C31—41no—
151C23×C31—41no—
152C23×C31—41no—
153C23×C31—41no—
154C23×C31—41no—
155C23×C31—41no—
156C23×C31—41no—
157C23×C31—41no—
158C23×C31—416no—
159C23×C31#9511yescharacteristic
160C23×C31#9511yescharacteristic
161C23×C31#9511yescharacteristic
162C23×C31#9511yescharacteristic
163C23×C31C2×C4211yescharacteristic
164C23×C31C2×C22⋊C411yescharacteristic
165C23×C31C2×C4⋊C411yescharacteristic
166C23×C31C2×M1614yes—
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—22no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—22no—
181C2×C4×C31—22no—
182C2×C4×C31—28no—
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—41no—
194C2×C4×C31—41no—
195C2×C4×C31—44no—
196C2×C4×C31—416no—
197C2×C4×C31—44no—
198C2×C4×C31#9511yescharacteristic
199C2×C4×C31#9511yescharacteristic
200C2×C4×C31#9511yescharacteristic
201C2×C4×C31#9511yescharacteristic
202C2×C4×C31#9914yes—
203C2×C4×C31C2×C22⋊C411yescharacteristic
204C2×C4×C31C2×C22⋊C411yescharacteristic
205C2×C4×C31C2×C4⋊C411yescharacteristic
206C2×C4×C31C2×C4⋊C411yescharacteristic
207C8×C31—44no—
208C8×C31—44no—
209C2×#407C2×C3111yescharacteristic
210C2×#407C2×C3111yescharacteristic
211C2×C4×C22⋊C4C2×C3111yescharacteristic
212#1282C2×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×C31#34212yes—
237C22×C31#34412yes—
238C22×C31C2×#9511yescharacteristic
239C22×C31C4×M1612yes—
240C22×C31#40712yes—
241C22×C31#42312yes—
242C4×C31—21no—
243C4×C31—21no—
244C4×C31—21no—
245C4×C31—21no—
246C4×C31—21no—
247C4×C31—21no—
248C4×C31—48no—
249C4×C31#34212yes—
250C4×C31C2×#9912yes—
251C24×C4C22×C3111yescharacteristic
252C22×M16—21no—
253C22×M16C4×C3112yescomplemented
254C22×C22⋊C4C4×C3112yes—
255C22×C42—21no—
256#407—21no—
257#407—21no—
258#407—21no—
259#407—21no—
260#407—21no—
261#407—21no—
262#407C4×C3112yescomplemented
263#407C4×C3112yescomplemented
264C2×C22⋊C8—21no—
265C2×C22⋊C8C4×C3112yescomplemented
266C2×C22⋊C8C22×C3112yes—
267C2×C22⋊C8C22×C3112yes—
268C4×C22⋊C4—21no—
269C4×C22⋊C4—21no—
270C4×C22⋊C4C4×C3112yes—
271C4×C22⋊C4C22×C3112yes—
272C2×#95—21no—
273C2×C31—22no—
274C2×C31—22no—
275C2×C31—22no—
276C2×C31—22no—
277C2×C31—22no—
278C2×C31—41no—
279C2×C31—41no—
280C2×C31#172811yescharacteristic
281C2×C31C2×#34211yescharacteristic
282C2×C31C2×#34411yescharacteristic
283C25C2×C4×C3111yescharacteristic
284C23×C4—22no—
285C23×C4—44no—
286C23×C4C2×C4×C3111yescharacteristic
287C23×C4C2×C4×C3111yescharacteristic
288C23×C4C2×C4×C3111yescharacteristic
289C23×C4C2×C4×C3111yescharacteristic
290C23×C4C2×C4×C3111yescharacteristic
291C23×C4D4×C3111yescharacteristic
292C23×C4D4×C3111yescharacteristic
293C23×C4D4×C3111yescharacteristic
294C23×C4D4×C3111yescharacteristic
295C23×C4D4×C3111yescharacteristic
296C23×C4D4×C3111yescharacteristic
297C23×C4Q8×C3111yescharacteristic
298C23×C4Q8×C3111yescharacteristic
299C23×C4C23×C3111yescharacteristic
300C2×M16—22no—
301C2×M16—22no—
302C2×M16—22no—
303C2×M16—22no—
304C2×M16—44no—
305C2×M16—44no—
306C22×C8—22no—
307C22×C8C2×C4×C3114yescomplemented
308C2×C22⋊C4—22no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4C2×C4×C3114yes—
311C2×C42—22no—
312C2×C42—22no—
313C2×C42—44no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317C22⋊C8—22no—
318C22⋊C8—22no—
319C22⋊C8—22no—
320C22⋊C8—22no—
321C22⋊C8C2×C4×C3114yescomplemented
322#95—22no—
323#95—22no—
324C31#792911yescharacteristic, direct product factor, Sylow
325C24—24no—
326C24—42no—
327C24—42no—
328C24C42×C3111yescharacteristic
329C24C42×C3111yescharacteristic
330C24C22⋊C4×C3111yescharacteristic
331C24C22⋊C4×C3111yescharacteristic
332C24C4⋊C4×C3111yescharacteristic
333C24C4⋊C4×C3111yescharacteristic
334C24C22×C4×C3111yescharacteristic
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—28no—
339C22×C4—24no—
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×C4C42×C3111yescharacteristic
354C22×C4C42×C3111yescharacteristic
355C22×C4C22⋊C4×C3111yescharacteristic
356C22×C4C22⋊C4×C3111yescharacteristic
357C22×C4C22⋊C4×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×C4C4⋊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×C4C22×C4×C3111yescharacteristic
376C22×C4C22×C4×C3111yescharacteristic
377C22×C4C2×D4×C3111yescharacteristic
378C22×C4C2×D4×C3111yescharacteristic
379C22×C4C2×D4×C3111yescharacteristic
380C22×C4C2×Q8×C3111yescharacteristic
381M16—44no—
382M16—44no—
383M16—44no—
384M16—44no—
385C2×C8—24no—
386C2×C8—24no—
387C2×C8—44no—
388C2×C8—44no—
389C22⋊C4—28no—
390C22⋊C4—24no—
391C22⋊C4M16×C3118yescomplemented
392C42—44no—
393C42—44no—
394C23—22no—
395C23—22no—
396C23—22no—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—416no—
415C23C31×#9511yescharacteristic
416C23C31×#9511yescharacteristic
417C23C31×#9511yescharacteristic
418C23C31×#9511yescharacteristic
419C23C2×C42×C3111yescharacteristic
420C23C2×C22⋊C4×C3111yescharacteristic
421C23C2×C4⋊C4×C3111yescharacteristic
422C23C2×M16×C3114yes—
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—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—28no—
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—41no—
451C2×C4—44no—
452C2×C4—416no—
453C2×C4—44no—
454C2×C4C31×#9511yescharacteristic
455C2×C4C31×#9511yescharacteristic
456C2×C4C31×#9511yescharacteristic
457C2×C4C31×#9511yescharacteristic
458C2×C4C31×#9914yes—
459C2×C4C2×C22⋊C4×C3111yescharacteristic
460C2×C4C2×C22⋊C4×C3111yescharacteristic
461C2×C4C2×C4⋊C4×C3111yescharacteristic
462C2×C4C2×C4⋊C4×C3111yescharacteristic
463C8—44no—
464C8—44no—
465C22—28no—
466C22—21no—
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—44no—
483C22—44no—
484C22—44no—
485C22—44no—
486C22—44no—
487C22—44no—
488C22C31×#34212yes—
489C22C31×#34412yes—
490C22C2×C31×#9511yescharacteristic
491C22C4×M16×C3112yes—
492C22C31×#40712yes—
493C22C31×#42312yes—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4—48no—
501C4C31×#34212yes—
502C4C2×C31×#9912yes—
503C2—22no—
504C2—22no—
505C2—22no—
506C2—22no—
507C2—22no—
508C2—41no—
509C2—41no—
510C2C31×#172811yescharacteristic
511C2C2×C31×#34211yescharacteristic
512C2C2×C31×#34411yescharacteristic
subgroupG/H
centerC2×C4×C31C2×C22⋊C4
commutatorC23C2×C42×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31C2×#95
prime radicalC25×C31C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1282C2semidirect
7. C22×M16×C31C4semidirect
16. C31×#407C4semidirect
17. C31×#407C4semidirect
19. C2×C31×C22⋊C8C4semidirect
51. C22×C8×C31C2×C4semidirect
65. C31×C22⋊C8C2×C4semidirect
134. C22⋊C4×C31M16semidirect
137. #7929C31direct (N × H)
212. #1282C2×C31semidirect
253. C22×M16C4×C31semidirect
262. #407C4×C31semidirect
263. #407C4×C31semidirect
265. C2×C22⋊C8C4×C31semidirect
307. C22×C8C2×C4×C31semidirect
321. C22⋊C8C2×C4×C31semidirect
324. C31#7929direct (N × H)
391. C22⋊C4M16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4072
C2×C4×C22⋊C4×C312
C31×#12822
#792931