Finite Group Databasebeta

← C31×#23589 #21480348

Subgroups — C31×#23589 #21480348

Order 7936.

1138 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3460C211yesmaximal, characteristic
2C4×C31×#137C212yesmaximal, complemented
3C4×C31×#124C211yesmaximal, characteristic, complemented
4C31×#2061C211yesmaximal, characteristic, complemented
5C31×#2040C211yesmaximal, characteristic, complemented
6C31×#2037C212yesmaximal, complemented
7C31×#2028C211yesmaximal, characteristic, complemented
8C31×#2007C211yesmaximal, characteristic, complemented
9C31×#2004C212yesmaximal, complemented
10C4×C31×#104C212yesmaximal, complemented
11C4×C31×#100C211yesmaximal, characteristic, complemented
12C2×C31×#137C2212yes—
13C31×#544C2211yescharacteristic
14C31×#542—22no—
15C31×#540—22no—
16C31×#538—22no—
17C31×#537C2211yescharacteristic
18C31×#535C2212yes—
19C31×#532—22no—
20C31×#529—22no—
21C2×C31×#124C2211yescharacteristic
22C31×#525—22no—
23C4×#41×C31C2212yes—
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C31×#441—22no—
27C31×#440—22no—
28C4×Q16×C31—22no—
29C4×SD16×C31—22no—
30C31×#428C2212yes—
31C2×C31×#104C2212yes—
32C2×C31×#104C2212yes—
33C31×#419C2212yes—
34C31×#417C2212yes—
35C2×C31×#100C2212yes—
36C4×M16×C31C2212yes—
37C31×#391C2211yescharacteristic
38C31×#390C2211yescharacteristic
39C31×#388—22no—
40C31×#382C2211yescharacteristic
41C4×C22⋊C4×C31—22no—
42C43×C31C2211yescharacteristic
43C31×#343C2211yescharacteristic
44C31×#343C2211yescharacteristic
45C31×#339C2212yes—
46C31×#339C2212yes—
47C2×#41×C31—22no—
48C2×#41×C31C2312yes—
49C22×Q8×C31C2311yescharacteristic
50C22×D4×C31C2311yescharacteristic
51C23×C4×C31D412yes—
52C31×#137—24no—
53C31×#137—24no—
54C2×Q16×C31—22no—
55C2×SD16×C31—22no—
56C2×M16×C31C2312yes—
57C2×M16×C31C2312yes—
58C31×C4⋊Q8—22no—
59C31×#127—22no—
60C31×#126—24no—
61C31×#125—22no—
62C31×#124—24no—
63C31×#124—22no—
64C31×#124—22no—
65C31×#124—22no—
66C31×#123—24no—
67C31×#123—24no—
68C31×C22⋊Q8—22no—
69C31×C22⋊Q8—22no—
70C31×C22⋊Q8—22no—
71C31×#121—22no—
72C31×#121—24no—
73C31×#121—22no—
74C31×#121—22no—
75C31×#121—22no—
76C31×#121—22no—
77C31×#120—24no—
78C4×Q8×C31—22no—
79C4×Q8×C31—22no—
80C4×Q8×C31D412yes—
81C4×Q8×C31D412yes—
82C4×D4×C31—24no—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31D412yes—
88C4×D4×C31D412yes—
89C31×#117—22no—
90C31×#117—22no—
91C31×#117C2312yes—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31D412yes—
98C2×C42×C31—22no—
99C2×C42×C31—21no—
100C2×C42×C31—21no—
101C2×C42×C31—21no—
102C2×C42×C31C2311yescharacteristic
103C2×C42×C31C2311yescharacteristic
104C2×C42×C31C2311yescharacteristic
105C31×#107—22no—
106C31×#106—22no—
107C31×#104—24no—
108C31×#104—24no—
109C31×#103—22no—
110C31×#103—22no—
111C31×#103—22no—
112C31×#102—22no—
113C31×#100—24no—
114C31×#97—22no—
115C4×C8×C31—22no—
116C31×#95—22no—
117C31×#95—22no—
118C24×C31C2×D412yes—
119#41×C31—22no—
120#41×C31—22no—
121#41×C31—22no—
122#41×C31—22no—
123#41×C31—84no—
124C2×Q8×C31—22no—
125C2×Q8×C31—21no—
126C2×Q8×C31—22no—
127C2×Q8×C31—22no—
128C2×Q8×C31C2×D412yes—
129C2×Q8×C31#4112yescomplemented
130C2×D4×C31—22no—
131C2×D4×C31—24no—
132C2×D4×C31—24no—
133C2×D4×C31—22no—
134C2×D4×C31—22no—
135C2×D4×C31—22no—
136C2×D4×C31—21no—
137C2×D4×C31—21no—
138C2×D4×C31C2×D412yes—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—21no—
148C22×C4×C31—44no—
149C22×C4×C31C2×D411yescharacteristic
150C22×C4×C31C2×D412yes—
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2411yescharacteristic
153Q16×C31—28no—
154SD16×C31—28no—
155M16×C31—22no—
156M16×C31—22no—
157M16×C31—22no—
158M16×C31#4114yescomplemented
159C2×C8×C31—22no—
160C2×C8×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—24no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—42no—
169C4⋊C4×C31C2×D412yes—
170C4⋊C4×C31C2×D412yes—
171C22⋊C4×C31—28no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—24no—
174C22⋊C4×C31—24no—
175C22⋊C4×C31—22no—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—22no—
178C22⋊C4×C31—22no—
179C22⋊C4×C31—44no—
180C42×C31—22no—
181C42×C31—22no—
182C42×C31—22no—
183C42×C31—21no—
184C42×C31—22no—
185C42×C31—42no—
186C42×C31—42no—
187C42×C31—41no—
188C42×C31—41no—
189C42×C31C2×D412yes—
190C42×C31C2×D412yes—
191C42×C31#4112yescomplemented
192#23589C3111yesmaximal, characteristic, direct product factor, Sylow
193C23×C31—22no—
194C23×C31—22no—
195C23×C31—22no—
196C23×C31—22no—
197C23×C31—42no—
198C23×C31—42no—
199C23×C31C22×D411yescharacteristic
200Q8×C31—24no—
201Q8×C31—22no—
202Q8×C31—22no—
203Q8×C31—42no—
204Q8×C31—82no—
205D4×C31—22no—
206D4×C31—22no—
207D4×C31—42no—
208D4×C31—42no—
209D4×C31—42no—
210D4×C31—42no—
211D4×C31—84no—
212D4×C31—82no—
213D4×C31—84no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—41no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—42no—
231C2×C4×C31—44no—
232C2×C4×C31—44no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—41no—
236C2×C4×C31—82no—
237C2×C4×C31—82no—
238C2×C4×C31#12012yes—
239C2×C4×C31#12011yescharacteristic
240C2×C4×C31#12011yescharacteristic
241C2×C4×C31C22×D412yes—
242C2×C4×C31C2×#4111yescharacteristic
243C2×C4×C31C2×#4112yes—
244C2×C4×C31C2×#4111yescharacteristic
245C8×C31—24no—
246C8×C31—42no—
247#3460C2×C3111yescharacteristic
248C4×#137C2×C3112yescomplemented
249C4×#124C2×C3111yescharacteristic, complemented
250#2061C2×C3111yescharacteristic, complemented
251#2040C2×C3111yescharacteristic, complemented
252#2037C2×C3112yescomplemented
253#2028C2×C3111yescharacteristic, complemented
254#2007C2×C3111yescharacteristic, complemented
255#2004C2×C3112yescomplemented
256C4×#104C2×C3112yescomplemented
257C4×#100C2×C3111yescharacteristic, complemented
258C22×C31—21no—
259C22×C31—21no—
260C22×C31—44no—
261C22×C31—42no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—82no—
268C22×C31C2×#12011yescharacteristic
269C22×C31#52511yescharacteristic
270C22×C31#53211yescharacteristic
271C4×C31—21no—
272C4×C31—22no—
273C4×C31—42no—
274C4×C31—42no—
275C4×C31—42no—
276C4×C31—42no—
277C4×C31—42no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—81no—
281C4×C31#45512yes—
282C4×C31#52512yes—
283C4×C31#53212yes—
284C2×#137C22×C3112yes—
285#544C22×C3111yescharacteristic
286#542—22no—
287#540—22no—
288#538—22no—
289#537C22×C3111yescharacteristic
290#535C22×C3112yes—
291#532—22no—
292#529—22no—
293C2×#124C22×C3111yescharacteristic
294#525—22no—
295C4×#41C22×C3112yes—
296C2×C4×Q8C22×C3111yescharacteristic
297C2×C4×D4C22×C3111yescharacteristic
298#441—22no—
299#440—22no—
300C4×Q16—22no—
301C4×SD16—22no—
302#428C22×C3112yes—
303C2×#104C22×C3112yes—
304C2×#104C22×C3112yes—
305#419C22×C3112yes—
306#417C22×C3112yes—
307C2×#100C22×C3112yes—
308C4×M16C22×C3112yes—
309#391C22×C3111yescharacteristic
310#390C22×C3111yescharacteristic
311#388—22no—
312#382C22×C3111yescharacteristic
313C4×C22⋊C4—22no—
314C43C22×C3111yescharacteristic
315#343C22×C3111yescharacteristic
316#343C22×C3111yescharacteristic
317#339C22×C3112yes—
318#339C22×C3112yes—
319C2×C31—21no—
320C2×C31—21no—
321C2×C31—82no—
322C2×C31—82no—
323C2×C31#238811yescharacteristic
324C2×C31C2×#45511yescharacteristic
325C2×C31#301811yescharacteristic
326C2×#41—22no—
327C2×#41C23×C3112yes—
328C22×Q8C23×C3111yescharacteristic
329C22×D4C23×C3111yescharacteristic
330C23×C4D4×C3112yes—
331#137—24no—
332#137—24no—
333C2×Q16—22no—
334C2×SD16—22no—
335C2×M16C23×C3112yes—
336C2×M16C23×C3112yes—
337C4⋊Q8—22no—
338#127—22no—
339#126—24no—
340#125—22no—
341#124—24no—
342#124—22no—
343#124—22no—
344#124—22no—
345#123—24no—
346#123—24no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350#121—22no—
351#121—24no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#120—24no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8D4×C3112yes—
360C4×Q8D4×C3112yes—
361C4×D4—24no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4D4×C3112yes—
367C4×D4D4×C3112yes—
368#117—22no—
369#117—22no—
370#117C23×C3112yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C23×C3111yescharacteristic
373C2×C4⋊C4C23×C3111yescharacteristic
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4D4×C3112yes—
377C2×C42—22no—
378C2×C42—21no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42C23×C3111yescharacteristic
382C2×C42C23×C3111yescharacteristic
383C2×C42C23×C3111yescharacteristic
384#107—22no—
385#106—22no—
386#104—24no—
387#104—24no—
388#103—22no—
389#103—22no—
390#103—22no—
391#102—22no—
392#100—24no—
393#97—22no—
394C4×C8—22no—
395#95—22no—
396#95—22no—
397C31#2358911yescharacteristic, direct product factor, Sylow
398C24C2×D4×C3112yes—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—84no—
404C2×Q8—22no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8C2×D4×C3112yes—
409C2×Q8#41×C3112yescomplemented
410C2×D4—22no—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4C2×D4×C3112yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—44no—
429C22×C4C2×D4×C3111yescharacteristic
430C22×C4C2×D4×C3112yes—
431C22×C4C2×D4×C3111yescharacteristic
432C22×C4C24×C3111yescharacteristic
433Q16—28no—
434SD16—28no—
435M16—22no—
436M16—22no—
437M16—22no—
438M16#41×C3114yescomplemented
439C2×C8—22no—
440C2×C8—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—42no—
449C4⋊C4C2×D4×C3112yes—
450C4⋊C4C2×D4×C3112yes—
451C22⋊C4—28no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—44no—
460C42—22no—
461C42—22no—
462C42—22no—
463C42—21no—
464C42—22no—
465C42—42no—
466C42—42no—
467C42—41no—
468C42—41no—
469C42C2×D4×C3112yes—
470C42C2×D4×C3112yes—
471C42#41×C3112yescomplemented
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—42no—
477C23—42no—
478C23C22×D4×C3111yescharacteristic
479Q8—24no—
480Q8—22no—
481Q8—22no—
482Q8—42no—
483Q8—82no—
484D4—22no—
485D4—22no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—84no—
491D4—82no—
492D4—84no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4C31×#12012yes—
518C2×C4C31×#12011yescharacteristic
519C2×C4C31×#12011yescharacteristic
520C2×C4C22×D4×C3112yes—
521C2×C4C2×#41×C3111yescharacteristic
522C2×C4C2×#41×C3112yes—
523C2×C4C2×#41×C3111yescharacteristic
524C8—24no—
525C8—42no—
526C22—21no—
527C22—21no—
528C22—44no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—82no—
536C22C2×C31×#12011yescharacteristic
537C22C31×#52511yescharacteristic
538C22C31×#53211yescharacteristic
539C4—21no—
540C4—22no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—81no—
549C4C31×#45512yes—
550C4C31×#52512yes—
551C4C31×#53212yes—
552C2—21no—
553C2—21no—
554C2—82no—
555C2—82no—
556C2C31×#238811yescharacteristic
557C2C2×C31×#45511yescharacteristic
558C2C31×#301811yescharacteristic
subgroupG/H
centerC2×C4×C31#120
commutator, Frattini, cosocleC22×C4C24×C31
socleC22×C31C2×#120
prime radicalC31×#3460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C31×#137C2semidirect
3. C4×C31×#124C2semidirect
4. C31×#2061C2semidirect
5. C31×#2040C2semidirect
6. C31×#2037C2semidirect
7. C31×#2028C2semidirect
8. C31×#2007C2semidirect
9. C31×#2004C2semidirect
10. C4×C31×#104C2semidirect
11. C4×C31×#100C2semidirect
129. C2×Q8×C31#41semidirect
158. M16×C31#41semidirect
191. C42×C31#41semidirect
192. #23589C31direct (N × H)
248. C4×#137C2×C31semidirect
249. C4×#124C2×C31semidirect
250. #2061C2×C31semidirect
251. #2040C2×C31semidirect
252. #2037C2×C31semidirect
253. #2028C2×C31semidirect
254. #2007C2×C31semidirect
255. #2004C2×C31semidirect
256. C4×#104C2×C31semidirect
257. C4×#100C2×C31semidirect
397. C31#23589direct (N × H)
409. C2×Q8#41×C31semidirect
438. M16#41×C31semidirect
471. C42#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34602
C4×C31×#1372
C4×C31×#1242
C31×#20612
C31×#20402
C31×#20372
C31×#20282
C31×#20072
C31×#20042
C4×C31×#1042
C4×C31×#1002
#2358931