Finite Group Databasebeta

← C31×#16629 #21473388

Subgroups — C31×#16629 #21473388

Order 7936.

1286 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C211yesmaximal, characteristic
2C2×C31×#395C212yesmaximal
3C2×C31×#391C211yesmaximal, characteristic
4C31×#1444C212yesmaximal
5C31×#1443C212yesmaximal
6C31×#1442C212yesmaximal
7C31×#1441C212yesmaximal
8C31×#1441C211yesmaximal, characteristic
9C31×#1436C212yesmaximal
10C23×Q8×C31C2211yescharacteristic
11C22×C4⋊C4×C31C2212yes—
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C42×C31C2211yescharacteristic
18C31×#398—24no—
19C31×#395—28no—
20C31×#391—24no—
21C2×C31×#95C2212yes—
22C2×C31×#95C2212yes—
23C2×C31×#95C2212yes—
24C2×C31×#95C2212yes—
25C2×C31×#95C2211yescharacteristic
26C2×C31×#95C2212yes—
27C2×C31×#95C2212yes—
28C2×C31×#95C2212yes—
29C2×C31×#95C2212yes—
30C2×C31×#95C2212yes—
31C2×C31×#95C2212yes—
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2212yes—
34C22×Q8×C31—22no—
35C22×Q8×C31—22no—
36C22×Q8×C31—41no—
37C22×Q8×C31—41no—
38C22×Q8×C31—41no—
39C22×Q8×C31—41no—
40C22×Q8×C31D414yes—
41C23×C4×C31C2312yes—
42C23×C4×C31C2312yes—
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2312yes—
47C23×C4×C31C2312yes—
48C23×C4×C31C2312yes—
49C23×C4×C31C2311yescharacteristic
50C2×C4⋊C4×C31—24no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—24no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—24no—
57C2×C4⋊C4×C31—41no—
58C2×C4⋊C4×C31—41no—
59C2×C4⋊C4×C31—41no—
60C2×C4⋊C4×C31—42no—
61C2×C4⋊C4×C31—42no—
62C2×C4⋊C4×C31—42no—
63C2×C4⋊C4×C31—42no—
64C2×C4⋊C4×C31—41no—
65C2×C4⋊C4×C31—41no—
66C2×C4⋊C4×C31D414yes—
67C2×C42×C31—22no—
68C2×C42×C31—41no—
69C2×C42×C31—41no—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95—22no—
74C31×#95—24no—
75C31×#95—24no—
76C31×#95—24no—
77C31×#95—24no—
78C31×#95—24no—
79C31×#95—42no—
80C31×#95—42no—
81C31×#95—41no—
82C31×#95Q818yescomplemented
83C24×C31C2411yescharacteristic
84C2×Q8×C31—28no—
85C2×Q8×C31—44no—
86C2×Q8×C31—44no—
87C2×Q8×C31—44no—
88C2×Q8×C31—44no—
89C2×Q8×C31—44no—
90C2×Q8×C31—44no—
91C22×C4×C31—21no—
92C22×C4×C31—21no—
93C22×C4×C31—21no—
94C22×C4×C31—21no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—22no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—22no—
105C22×C4×C31—22no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—21no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—21no—
116C22×C4×C31—21no—
117C22×C4×C31—21no—
118C22×C4×C31—22no—
119C22×C4×C31—22no—
120C22×C4×C31—22no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D414yes—
143C22×C4×C31C2×D412yes—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×Q814yes—
146C22×C4×C31C2×Q814yes—
147C22×C4×C31C2×Q814yes—
148C22×C4×C31#4114yes—
149C22×C4×C31#4112yes—
150C4⋊C4×C31—44no—
151C4⋊C4×C31—44no—
152C4⋊C4×C31—44no—
153C4⋊C4×C31—48no—
154C4⋊C4×C31—48no—
155C4⋊C4×C31—48no—
156C42×C31—44no—
157#16629C3111yesmaximal, characteristic, direct product factor, Sylow
158C23×C31C22×D411yescharacteristic
159C23×C31C22×D411yescharacteristic
160C23×C31C22×Q812yes—
161C23×C31C2×#4111yescharacteristic
162C23×C31C2×#4112yes—
163C23×C31H(5,𝔽2)11yescharacteristic
164C23×C31H(5,𝔽2)11yescharacteristic
165C23×C31H(5,𝔽2)11yescharacteristic
166C23×C31H(5,𝔽2)11yescharacteristic
167C23×C312−1+412yes—
168C23×C312−1+412yes—
169Q8×C31—416no—
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—24no—
177C2×C4×C31—24no—
178C2×C4×C31—22no—
179C2×C4×C31—22no—
180C2×C4×C31—24no—
181C2×C4×C31—24no—
182C2×C4×C31—24no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—24no—
195C2×C4×C31—42no—
196C2×C4×C31—42no—
197C2×C4×C31—42no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—42no—
203C2×C4×C31—42no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—41no—
215C2×C4×C31—41no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—42no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31#12114yes—
229C2×#398C2×C3111yescharacteristic
230C2×#395C2×C3112yes—
231C2×#391C2×C3111yescharacteristic
232#1444C2×C3112yes—
233#1443C2×C3112yes—
234#1442C2×C3112yes—
235#1441C2×C3112yes—
236#1441C2×C3111yescharacteristic
237#1436C2×C3112yes—
238C22×C31C2×#12111yescharacteristic
239C22×C31#53312yes—
240C22×C31#53411yescharacteristic
241C22×C31#53411yescharacteristic
242C22×C31#53411yescharacteristic
243C22×C31#53511yescharacteristic
244C22×C31#53811yescharacteristic
245C22×C31#53811yescharacteristic
246C22×C31#53912yes—
247C22×C31#54112yes—
248C22×C31#54212yes—
249C22×C31#54412yes—
250C22×C31#54412yes—
251C22×C31#54712yes—
252C22×C31#54812yes—
253C22×C31D4×Q812yes—
254C22×C31D4×Q812yes—
255C22×C31#55111yescharacteristic
256C22×C31#55412yes—
257C22×C31Q8211yescharacteristic
258C22×C31#56311yescharacteristic
259C22×C31#56312yes—
260C22×C31#56311yescharacteristic
261C4×C31—24no—
262C4×C31—44no—
263C4×C31—44no—
264C4×C31—42no—
265C4×C31—42no—
266C4×C31—44no—
267C4×C31—44no—
268C4×C31—44no—
269C4×C31—82no—
270C23×Q8C22×C3111yescharacteristic
271C22×C4⋊C4C22×C3112yes—
272C22×C4⋊C4C22×C3111yescharacteristic
273C22×C4⋊C4C22×C3112yes—
274C22×C4⋊C4C22×C3112yes—
275C22×C4⋊C4C22×C3111yescharacteristic
276C22×C4⋊C4C22×C3111yescharacteristic
277C22×C42C22×C3111yescharacteristic
278#398—24no—
279#395—28no—
280#391—24no—
281C2×#95C22×C3112yes—
282C2×#95C22×C3112yes—
283C2×#95C22×C3112yes—
284C2×#95C22×C3112yes—
285C2×#95C22×C3111yescharacteristic
286C2×#95C22×C3112yes—
287C2×#95C22×C3112yes—
288C2×#95C22×C3112yes—
289C2×#95C22×C3112yes—
290C2×#95C22×C3112yes—
291C2×#95C22×C3112yes—
292C2×#95C22×C3111yescharacteristic
293C2×#95C22×C3112yes—
294C2×C31#242912yes—
295C2×C31#258611yescharacteristic
296C2×C31#261711yescharacteristic
297C2×C31#266612yes—
298C2×C31#271711yescharacteristic
299C2×C31#272012yes—
300C2×C31#272811yescharacteristic
301C2×C31#272912yes—
302C2×C31#273411yescharacteristic
303C2×C31#273411yescharacteristic
304C2×C31#283311yescharacteristic
305C22×Q8—22no—
306C22×Q8—22no—
307C22×Q8—41no—
308C22×Q8—41no—
309C22×Q8—41no—
310C22×Q8—41no—
311C22×Q8D4×C3114yes—
312C23×C4C23×C3112yes—
313C23×C4C23×C3112yes—
314C23×C4C23×C3111yescharacteristic
315C23×C4C23×C3111yescharacteristic
316C23×C4C23×C3112yes—
317C23×C4C23×C3112yes—
318C23×C4C23×C3112yes—
319C23×C4C23×C3112yes—
320C23×C4C23×C3111yescharacteristic
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4D4×C3114yes—
338C2×C42—22no—
339C2×C42—41no—
340C2×C42—41no—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—24no—
345#95—24no—
346#95—22no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—42no—
351#95—42no—
352#95—41no—
353#95Q8×C3118yescomplemented
354C31#1662911yescharacteristic, direct product factor, Sylow
355C24C24×C3111yescharacteristic
356C2×Q8—28no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—44no—
360C2×Q8—44no—
361C2×Q8—44no—
362C2×Q8—44no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4C2×D4×C3112yes—
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3114yes—
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3112yes—
417C22×C4C2×Q8×C3114yes—
418C22×C4C2×Q8×C3114yes—
419C22×C4C2×Q8×C3114yes—
420C22×C4#41×C3114yes—
421C22×C4#41×C3112yes—
422C4⋊C4—44no—
423C4⋊C4—44no—
424C4⋊C4—44no—
425C4⋊C4—48no—
426C4⋊C4—48no—
427C4⋊C4—48no—
428C42—44no—
429C23C22×D4×C3111yescharacteristic
430C23C22×D4×C3111yescharacteristic
431C23C22×Q8×C3112yes—
432C23C2×#41×C3111yescharacteristic
433C23C2×#41×C3112yes—
434C23C31×H(5,𝔽2)11yescharacteristic
435C23C31×H(5,𝔽2)11yescharacteristic
436C23C31×H(5,𝔽2)11yescharacteristic
437C23C31×H(5,𝔽2)11yescharacteristic
438C23C31×2−1+412yes—
439C23C31×2−1+412yes—
440Q8—416no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4C31×#12114yes—
500C22C2×C31×#12111yescharacteristic
501C22C31×#53312yes—
502C22C31×#53411yescharacteristic
503C22C31×#53411yescharacteristic
504C22C31×#53411yescharacteristic
505C22C31×#53511yescharacteristic
506C22C31×#53811yescharacteristic
507C22C31×#53811yescharacteristic
508C22C31×#53912yes—
509C22C31×#54112yes—
510C22C31×#54212yes—
511C22C31×#54412yes—
512C22C31×#54412yes—
513C22C31×#54712yes—
514C22C31×#54812yes—
515C22D4×Q8×C3112yes—
516C22D4×Q8×C3112yes—
517C22C31×#55111yescharacteristic
518C22C31×#55412yes—
519C22Q82×C3111yescharacteristic
520C22C31×#56311yescharacteristic
521C22C31×#56312yes—
522C22C31×#56311yescharacteristic
523C4—24no—
524C4—44no—
525C4—44no—
526C4—42no—
527C4—42no—
528C4—44no—
529C4—44no—
530C4—44no—
531C4—82no—
532C2C31×#242912yes—
533C2C31×#258611yescharacteristic
534C2C31×#261711yescharacteristic
535C2C31×#266612yes—
536C2C31×#271711yescharacteristic
537C2C31×#272012yes—
538C2C31×#272811yescharacteristic
539C2C31×#272912yes—
540C2C31×#273411yescharacteristic
541C2C31×#273411yescharacteristic
542C2C31×#283311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
82. C31×#95Q8semidirect
157. #16629C31direct (N × H)
353. #95Q8×C31semidirect
354. C31#16629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C2×C31×#3952
C2×C31×#3912
C31×#14442
C31×#14432
C31×#14422
C31×#14412
C31×#14362
#1662931