Finite Group Databasebeta

← C31×#12574 #21469333

Subgroups — C31×#12574 #21469333

Order 7936.

994 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#100C211yesmaximal, characteristic
2C22×C31×#99C211yesmaximal, characteristic
3C31×#2308C211yesmaximal, characteristic
4C31×#1390C214yesmaximal, complemented
5C23×D4×C31C2211yescharacteristic
6C22×M16×C31—21no—
7C22×C22⋊C4×C31—21no—
8C22×C22⋊C4×C31C411yescharacteristic, complemented
9C22×C22⋊C4×C31C411yescharacteristic, complemented
10C2×C31×#100—21no—
11C2×C31×#100—22no—
12C2×C31×#100C414yescomplemented
13C2×C31×#100C2212yes—
14C2×C31×#99—21no—
15C2×C31×#99—22no—
16C2×C31×#99C414yescomplemented
17C2×C31×#99C2212yes—
18C31×#386—21no—
19C31×#386—21no—
20C31×#386C412yescomplemented
21C31×#386C2212yes—
22C31×#381—21no—
23C31×#379—21no—
24C25×C31C2×C411yescharacteristic
25C25×C31D411yescharacteristic
26C22×D4×C31—41no—
27C22×D4×C31—41no—
28C22×D4×C31—42no—
29C22×D4×C31C2×C411yescharacteristic
30C22×D4×C31C2×C412yes—
31C22×D4×C31C2×C412yes—
32C22×D4×C31D411yescharacteristic
33C22×D4×C31D412yes—
34C22×D4×C31D411yescharacteristic
35C22×D4×C31Q812yes—
36C22×D4×C31C2311yescharacteristic
37C23×C4×C31—21no—
38C23×C4×C31—41no—
39C23×C4×C31C2×C412yescomplemented
40C23×C4×C31D411yescharacteristic
41C2×M16×C31—24no—
42C2×M16×C31—22no—
43C2×M16×C31—42no—
44C2×M16×C31—41no—
45C22×C8×C31—41no—
46C2×C22⋊C4×C31—24no—
47C2×C22⋊C4×C31—22no—
48C2×C22⋊C4×C31—21no—
49C2×C22⋊C4×C31—21no—
50C2×C22⋊C4×C31—21no—
51C2×C22⋊C4×C31—22no—
52C2×C22⋊C4×C31—22no—
53C2×C22⋊C4×C31—41no—
54C2×C22⋊C4×C31—42no—
55C2×C22⋊C4×C31—41no—
56C2×C22⋊C4×C31—41no—
57C2×C22⋊C4×C31—42no—
58C2×C22⋊C4×C31C2×C412yescomplemented
59C31×#100—24no—
60C31×#100—22no—
61C31×#100C2×C414yescomplemented
62C31×#99—24no—
63C31×#99—22no—
64C31×#99C2×C414yescomplemented
65C31×#95—22no—
66C31×#95—22no—
67C24×C31—21no—
68C24×C31—22no—
69C24×C31—21no—
70C24×C31—21no—
71C24×C31—22no—
72C24×C31—21no—
73C24×C31—82no—
74C24×C31—82no—
75C24×C31C4212yes—
76C24×C31C22⋊C411yescharacteristic
77C24×C31C22⋊C411yescharacteristic
78C24×C31C22⋊C412yes—
79C24×C31C22⋊C411yescharacteristic
80C24×C31C4⋊C412yes—
81C24×C31C4⋊C412yes—
82C24×C31C22×C411yescharacteristic
83C24×C31C2×D411yescharacteristic
84C2×D4×C31—42no—
85C2×D4×C31—42no—
86C2×D4×C31—42no—
87C2×D4×C31—42no—
88C2×D4×C31—41no—
89C2×D4×C31—41no—
90C2×D4×C31—42no—
91C2×D4×C31—42no—
92C2×D4×C31—41no—
93C2×D4×C31—41no—
94C2×D4×C31—41no—
95C2×D4×C31—41no—
96C2×D4×C31—42no—
97C2×D4×C31—42no—
98C2×D4×C31—41no—
99C2×D4×C31—41no—
100C2×D4×C31C4212yes—
101C2×D4×C31C22⋊C412yes—
102C2×D4×C31C22⋊C412yes—
103C2×D4×C31C4⋊C412yes—
104C2×D4×C31C4⋊C412yes—
105C2×D4×C31C4⋊C412yes—
106C2×D4×C31C22×C411yescharacteristic
107C2×D4×C31C22×C411yescharacteristic
108C2×D4×C31C2×D411yescharacteristic
109C2×D4×C31C2×Q811yescharacteristic
110C22×C4×C31—21no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—44no—
116C22×C4×C31—42no—
117C22×C4×C31—42no—
118C22×C4×C31—42no—
119C22×C4×C31—82no—
120C22×C4×C31—82no—
121C22×C4×C31—84no—
122C22×C4×C31C22⋊C411yescharacteristic
123C22×C4×C31C22⋊C412yes—
124C22×C4×C31C4⋊C412yes—
125C22×C4×C31C2×D411yescharacteristic
126M16×C31—24no—
127M16×C31—44no—
128M16×C31—42no—
129C2×C8×C31—44no—
130C2×C8×C31—42no—
131C22⋊C4×C31—24no—
132C22⋊C4×C31—44no—
133C22⋊C4×C31—42no—
134C22⋊C4×C31—42no—
135C22⋊C4×C31—42no—
136C22⋊C4×C31—41no—
137C22⋊C4×C31—41no—
138C22⋊C4×C31—42no—
139C22⋊C4×C31—82no—
140C22⋊C4×C31—82no—
141#12574C3111yesmaximal, characteristic, direct product factor, Sylow
142C23×C31—22no—
143C23×C31—22no—
144C23×C31—21no—
145C23×C31—21no—
146C23×C31—21no—
147C23×C31—21no—
148C23×C31—21no—
149C23×C31—21no—
150C23×C31—22no—
151C23×C31—22no—
152C23×C31—22no—
153C23×C31—22no—
154C23×C31—22no—
155C23×C31—22no—
156C23×C31—21no—
157C23×C31—21no—
158C23×C31—42no—
159C23×C31—42no—
160C23×C31—42no—
161C23×C31—44no—
162C23×C31—42no—
163C23×C31—42no—
164C23×C31—82no—
165C23×C31—82no—
166C23×C31—82no—
167C23×C31—82no—
168C23×C31—82no—
169C23×C31—82no—
170C23×C31—82no—
171C23×C31—84no—
172C23×C31—84no—
173C23×C31#9512yes—
174C23×C31#9512yes—
175C23×C31#9512yes—
176C23×C31#9911yescharacteristic
177C23×C31#9911yescharacteristic
178C23×C31#9912yes—
179C23×C31C2×C4211yescharacteristic
180C23×C31C2×C22⋊C411yescharacteristic
181C23×C31C2×C22⋊C411yescharacteristic
182C23×C31C2×C4⋊C411yescharacteristic
183C23×C31C2×C4⋊C411yescharacteristic
184D4×C31—42no—
185D4×C31—42no—
186D4×C31—42no—
187D4×C31—42no—
188D4×C31—42no—
189D4×C31—42no—
190D4×C31—41no—
191D4×C31—41no—
192D4×C31—41no—
193D4×C31—41no—
194C2×C4×C31—22no—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—21no—
199C2×C4×C31—21no—
200C2×C4×C31—21no—
201C2×C4×C31—21no—
202C2×C4×C31—44no—
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—84no—
210C2×C4×C31—88no—
211C2×C4×C31—84no—
212C2×C4×C31—84no—
213C2×C4×C31#9512yes—
214C2×C4×C31C2×C22⋊C411yescharacteristic
215C2×C4×C31C2×C4⋊C411yescharacteristic
216C8×C31—44no—
217C22×#100C2×C3111yescharacteristic
218C22×#99C2×C3111yescharacteristic
219#2308C2×C3111yescharacteristic
220#1390C2×C3114yescomplemented
221C22×C31—22no—
222C22×C31—22no—
223C22×C31—22no—
224C22×C31—21no—
225C22×C31—22no—
226C22×C31—22no—
227C22×C31—21no—
228C22×C31—21no—
229C22×C31—21no—
230C22×C31—42no—
231C22×C31—42no—
232C22×C31—42no—
233C22×C31—42no—
234C22×C31—41no—
235C22×C31—41no—
236C22×C31—41no—
237C22×C31—41no—
238C22×C31—42no—
239C22×C31—44no—
240C22×C31—42no—
241C22×C31—44no—
242C22×C31—42no—
243C22×C31—42no—
244C22×C31—42no—
245C22×C31—42no—
246C22×C31—81no—
247C22×C31—81no—
248C22×C31—82no—
249C22×C31—82no—
250C22×C31—82no—
251C22×C31—82no—
252C22×C31—82no—
253C22×C31—82no—
254C22×C31#34212yes—
255C22×C31#34212yes—
256C22×C31C2×#9511yescharacteristic
257C22×C31C2×#9911yescharacteristic
258C22×C31C2×#9911yescharacteristic
259C4×C31—21no—
260C4×C31—22no—
261C4×C31—21no—
262C4×C31—82no—
263C4×C31—84no—
264C4×C31—82no—
265C23×D4C22×C3111yescharacteristic
266C22×M16—21no—
267C22×C22⋊C4—21no—
268C22×C22⋊C4C4×C3111yescharacteristic, complemented
269C22×C22⋊C4C4×C3111yescharacteristic, complemented
270C2×#100—21no—
271C2×#100—22no—
272C2×#100C4×C3114yescomplemented
273C2×#100C22×C3112yes—
274C2×#99—21no—
275C2×#99—22no—
276C2×#99C4×C3114yescomplemented
277C2×#99C22×C3112yes—
278#386—21no—
279#386—21no—
280#386C4×C3112yescomplemented
281#386C22×C3112yes—
282#381—21no—
283#379—21no—
284C2×C31—21no—
285C2×C31—21no—
286C2×C31—22no—
287C2×C31—22no—
288C2×C31—41no—
289C2×C31—42no—
290C2×C31—41no—
291C2×C31—42no—
292C2×C31—41no—
293C2×C31—41no—
294C2×C31C2×#34211yescharacteristic
295C2×C31#212112yes—
296C25C2×C4×C3111yescharacteristic
297C25D4×C3111yescharacteristic
298C22×D4—41no—
299C22×D4—41no—
300C22×D4—42no—
301C22×D4C2×C4×C3111yescharacteristic
302C22×D4C2×C4×C3112yes—
303C22×D4C2×C4×C3112yes—
304C22×D4D4×C3111yescharacteristic
305C22×D4D4×C3112yes—
306C22×D4D4×C3111yescharacteristic
307C22×D4Q8×C3112yes—
308C22×D4C23×C3111yescharacteristic
309C23×C4—21no—
310C23×C4—41no—
311C23×C4C2×C4×C3112yescomplemented
312C23×C4D4×C3111yescharacteristic
313C2×M16—24no—
314C2×M16—22no—
315C2×M16—41no—
316C2×M16—42no—
317C22×C8—41no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—41no—
327C2×C22⋊C4—41no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4C2×C4×C3112yescomplemented
331#100—24no—
332#100—22no—
333#100C2×C4×C3114yescomplemented
334#99—24no—
335#99—22no—
336#99C2×C4×C3114yescomplemented
337#95—22no—
338#95—22no—
339C31#1257411yescharacteristic, direct product factor, Sylow
340C24—21no—
341C24—21no—
342C24—21no—
343C24—22no—
344C24—21no—
345C24—22no—
346C24—82no—
347C24—82no—
348C24C42×C3112yes—
349C24C22⋊C4×C3111yescharacteristic
350C24C22⋊C4×C3111yescharacteristic
351C24C22⋊C4×C3112yes—
352C24C22⋊C4×C3111yescharacteristic
353C24C4⋊C4×C3112yes—
354C24C4⋊C4×C3112yes—
355C24C22×C4×C3111yescharacteristic
356C24C2×D4×C3111yescharacteristic
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4C42×C3112yes—
374C2×D4C22⋊C4×C3112yes—
375C2×D4C22⋊C4×C3112yes—
376C2×D4C4⋊C4×C3112yes—
377C2×D4C4⋊C4×C3112yes—
378C2×D4C4⋊C4×C3112yes—
379C2×D4C22×C4×C3111yescharacteristic
380C2×D4C22×C4×C3111yescharacteristic
381C2×D4C2×D4×C3111yescharacteristic
382C2×D4C2×Q8×C3111yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—42no—
389C22×C4—44no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—82no—
393C22×C4—82no—
394C22×C4—84no—
395C22×C4C22⋊C4×C3111yescharacteristic
396C22×C4C22⋊C4×C3112yes—
397C22×C4C4⋊C4×C3112yes—
398C22×C4C2×D4×C3111yescharacteristic
399M16—24no—
400M16—42no—
401M16—44no—
402C2×C8—42no—
403C2×C8—44no—
404C22⋊C4—24no—
405C22⋊C4—42no—
406C22⋊C4—44no—
407C22⋊C4—42no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—82no—
413C22⋊C4—82no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—22no—
421C23—22no—
422C23—21no—
423C23—21no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23—82no—
440C23—82no—
441C23—82no—
442C23—82no—
443C23—84no—
444C23—84no—
445C23C31×#9512yes—
446C23C31×#9512yes—
447C23C31×#9512yes—
448C23C31×#9911yescharacteristic
449C23C31×#9911yescharacteristic
450C23C31×#9912yes—
451C23C2×C42×C3111yescharacteristic
452C23C2×C22⋊C4×C3111yescharacteristic
453C23C2×C22⋊C4×C3111yescharacteristic
454C23C2×C4⋊C4×C3111yescharacteristic
455C23C2×C4⋊C4×C3111yescharacteristic
456D4—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—41no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—84no—
482C2×C4—88no—
483C2×C4—84no—
484C2×C4—84no—
485C2×C4C31×#9512yes—
486C2×C4C2×C22⋊C4×C3111yescharacteristic
487C2×C4C2×C4⋊C4×C3111yescharacteristic
488C8—44no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—21no—
493C22—22no—
494C22—22no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—42no—
507C22—44no—
508C22—42no—
509C22—44no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—82no—
517C22—82no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22C31×#34212yes—
523C22C31×#34212yes—
524C22C2×C31×#9511yescharacteristic
525C22C2×C31×#9911yescharacteristic
526C22C2×C31×#9911yescharacteristic
527C4—21no—
528C4—22no—
529C4—21no—
530C4—82no—
531C4—84no—
532C4—82no—
533C2—21no—
534C2—21no—
535C2—22no—
536C2—22no—
537C2—41no—
538C2—42no—
539C2—41no—
540C2—42no—
541C2—41no—
542C2—41no—
543C2C2×C31×#34211yescharacteristic
544C2C31×#212112yes—
subgroupG/H
center, socleC22×C31C2×#99
commutatorC23C2×C42×C31
Frattini, cosocleC22×D4C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C31 ◁ C23×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1390C2semidirect
8. C22×C22⋊C4×C31C4semidirect
9. C22×C22⋊C4×C31C4semidirect
12. C2×C31×#100C4semidirect
16. C2×C31×#99C4semidirect
20. C31×#386C4semidirect
39. C23×C4×C31C2×C4semidirect
58. C2×C22⋊C4×C31C2×C4semidirect
61. C31×#100C2×C4semidirect
64. C31×#99C2×C4semidirect
141. #12574C31direct (N × H)
220. #1390C2×C31semidirect
268. C22×C22⋊C4C4×C31semidirect
269. C22×C22⋊C4C4×C31semidirect
272. C2×#100C4×C31semidirect
276. C2×#99C4×C31semidirect
280. #386C4×C31semidirect
311. C23×C4C2×C4×C31semidirect
330. C2×C22⋊C4C2×C4×C31semidirect
333. #100C2×C4×C31semidirect
336. #99C2×C4×C31semidirect
339. C31#12574direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1002
C22×C31×#992
C31×#23082
C31×#13902
#1257431