Finite Group Databasebeta

← C31×#18431 #21475190

Subgroups — C31×#18431 #21475190

Order 7936.

928 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3559C211yesmaximal, characteristic
2C31×#3218C211yesmaximal, characteristic, complemented
3C31×#3206C211yesmaximal, characteristic, complemented
4C31×#2660C211yesmaximal, characteristic, complemented
5C31×#1604C214yesmaximal, complemented
6C31×#1603C214yesmaximal, complemented
7C31×#1505C211yesmaximal, characteristic, complemented
8C31×#1500C211yesmaximal, characteristic, complemented
9C31×#1470C211yesmaximal, characteristic, complemented
10C31×#563—21no—
11C31×#562—21no—
12C31×#554—21no—
13C31×#553—21no—
14C31×#553—21no—
15C31×#547—22no—
16C31×#547—21no—
17C31×#544—21no—
18C31×#540—21no—
19C31×#539—22no—
20C31×#539C2212yes—
21C31×#537C2212yes—
22C31×#532C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#529C2211yescharacteristic
25C2×C31×#125C2211yescharacteristic
26C31×#497—21no—
27C31×#492—21no—
28C31×#491—21no—
29C31×#487—21no—
30C31×#462—21no—
31C31×#461—22no—
32C31×#461—21no—
33C31×#451C2212yes—
34C31×#448C2214yes—
35C31×#448C2212yes—
36C31×#432C2211yescharacteristic
37C31×#431C2211yescharacteristic
38C31×#398—22no—
39C31×#395C2214yes—
40C31×#384—21no—
41C31×#382—21no—
42C31×#376C2211yescharacteristic
43C31×#328C2212yes—
44C31×#327C2214yes—
45C31×#327C2212yes—
46C31×#324C2214yes—
47C2×#41×C31—21no—
48C2×#41×C31—22no—
49C22×Q8×C31C2312yes—
50C2×Q16×C31—22no—
51C2×SD16×C31—24no—
52C2×SD16×C31—22no—
53C31×C4⋊Q8—21no—
54C31×C4⋊Q8—22no—
55C31×C4⋊Q8—21no—
56C31×C4⋊Q8—21no—
57C31×C4⋊Q8—21no—
58C31×C4⋊Q8—21no—
59C31×C4⋊Q8D411yescharacteristic
60C31×#127D411yescharacteristic
61C31×#126—22no—
62C31×#126—22no—
63C31×#126—21no—
64C31×#125—21no—
65C31×#125—22no—
66C31×#125—21no—
67C31×#125—21no—
68C31×#125—21no—
69C31×#125—21no—
70C31×#125D411yescharacteristic
71C31×#124—21no—
72C31×#124D411yescharacteristic
73C31×#123—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—21no—
79C31×#123—22no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—22no—
82C31×C22⋊Q8—22no—
83C31×C22⋊Q8—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—22no—
86C31×C22⋊Q8C2311yescharacteristic
87C31×#121—21no—
88C31×#121—22no—
89C31×#121—21no—
90C31×#121—22no—
91C31×#121—22no—
92C31×#121—21no—
93C31×#121—22no—
94C31×#121C2311yescharacteristic
95C31×#121C2312yes—
96C4×Q8×C31D411yescharacteristic
97C4×D4×C31—22no—
98C4×D4×C31—21no—
99C4×D4×C31—21no—
100C4×D4×C31—21no—
101C4×D4×C31—22no—
102C4×D4×C31—21no—
103C4×D4×C31D411yescharacteristic
104C4×D4×C31D412yes—
105C31×#117—21no—
106C31×#117—21no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—24no—
112C2×C4⋊C4×C31D412yes—
113C2×C4⋊C4×C31D411yescharacteristic
114C2×C4⋊C4×C31D411yescharacteristic
115C2×C4⋊C4×C31C2312yes—
116C2×C42×C31—21no—
117C2×C42×C31C2311yescharacteristic
118C31×C4⋊C8—21no—
119C31×C4⋊C8—21no—
120C31×#103—24no—
121C31×#103—22no—
122C31×#103—22no—
123C31×C22⋊C8C2312yes—
124C31×C22⋊C8C2312yes—
125C31×#97—21no—
126C4×C8×C31—21no—
127C31×#95—24no—
128C31×#95—21no—
129C31×#95C2312yes—
130#41×C31—82no—
131#41×C31—84no—
132C2×Q8×C31—22no—
133C2×Q8×C31—21no—
134C2×Q8×C31—22no—
135C2×Q8×C31—22no—
136C2×Q8×C31—82no—
137C2×Q8×C31C2×D411yescharacteristic
138C2×D4×C31—21no—
139C2×D4×C31—22no—
140C2×D4×C31—22no—
141C2×D4×C31—22no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31C2×D411yescharacteristic
145C2×D4×C31C2×D412yes—
146C22×C4×C31—22no—
147C22×C4×C31—22no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—21no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31C2×D412yes—
154C22×C4×C31C2×D411yescharacteristic
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D412yes—
157C22×C4×C31C2411yescharacteristic
158Q16×C31—82no—
159SD16×C31—84no—
160SD16×C31—82no—
161C2×C8×C31—22no—
162C2×C8×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—21no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—22no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—22no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—41no—
181C4⋊C4×C31—41no—
182C4⋊C4×C31—41no—
183C4⋊C4×C31—41no—
184C4⋊C4×C31—84no—
185C4⋊C4×C31C2×D412yes—
186C4⋊C4×C31C2×D411yescharacteristic
187C4⋊C4×C31C2×D411yescharacteristic
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—21no—
194C22⋊C4×C31—21no—
195C22⋊C4×C31—21no—
196C22⋊C4×C31—21no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—21no—
199C22⋊C4×C31—22no—
200C42×C31—24no—
201C42×C31—22no—
202C42×C31—21no—
203C42×C31C2×D411yescharacteristic
204C42×C31C2×D411yescharacteristic
205C42×C31C2×D411yescharacteristic
206C42×C31C2×D411yescharacteristic
207#18431C3111yesmaximal, characteristic, direct product factor, Sylow
208C23×C31—21no—
209C23×C31—22no—
210C23×C31C22×D411yescharacteristic
211Q8×C31—41no—
212Q8×C31—44no—
213Q8×C31—42no—
214Q8×C31—42no—
215Q8×C31—81no—
216Q8×C31—82no—
217D4×C31—42no—
218D4×C31—41no—
219D4×C31—44no—
220D4×C31—42no—
221D4×C31—42no—
222D4×C31—81no—
223D4×C31—82no—
224D4×C31—82no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—24no—
228C2×C4×C31—21no—
229C2×C4×C31—21no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—21no—
233C2×C4×C31—22no—
234C2×C4×C31—24no—
235C2×C4×C31—41no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—42no—
239C2×C4×C31—42no—
240C2×C4×C31—44no—
241C2×C4×C31—42no—
242C2×C4×C31—82no—
243C2×C4×C31—82no—
244C2×C4×C31—82no—
245C2×C4×C31—82no—
246C2×C4×C31#12011yescharacteristic
247C2×C4×C31#12011yescharacteristic
248C2×C4×C31#12011yescharacteristic
249C2×C4×C31#12011yescharacteristic
250C2×C4×C31C22×D411yescharacteristic
251C2×C4×C31C22×D411yescharacteristic
252C8×C31—42no—
253C8×C31—42no—
254#3559C2×C3111yescharacteristic
255#3218C2×C3111yescharacteristic, complemented
256#3206C2×C3111yescharacteristic, complemented
257#2660C2×C3111yescharacteristic, complemented
258#1604C2×C3114yescomplemented
259#1603C2×C3114yescomplemented
260#1505C2×C3111yescharacteristic, complemented
261#1500C2×C3111yescharacteristic, complemented
262#1470C2×C3111yescharacteristic, complemented
263C22×C31—21no—
264C22×C31—21no—
265C22×C31—42no—
266C22×C31—41no—
267C22×C31—41no—
268C22×C31—42no—
269C22×C31—42no—
270C22×C31—41no—
271C22×C31C2×#12011yescharacteristic
272C22×C31#57712yes—
273C4×C31—21no—
274C4×C31—21no—
275C4×C31—21no—
276C4×C31—21no—
277C4×C31—21no—
278C4×C31—44no—
279C4×C31—42no—
280C4×C31—42no—
281C4×C31—41no—
282C4×C31—41no—
283C4×C31—42no—
284C4×C31—41no—
285C4×C31—82no—
286C4×C31#45612yes—
287#563—21no—
288#562—21no—
289#554—21no—
290#553—21no—
291#553—21no—
292#547—22no—
293#547—21no—
294#544—21no—
295#540—21no—
296#539—22no—
297#539C22×C3112yes—
298#537C22×C3112yes—
299#532C22×C3111yescharacteristic
300C2×C4⋊Q8C22×C3111yescharacteristic
301#529C22×C3111yescharacteristic
302C2×#125C22×C3111yescharacteristic
303#497—21no—
304#492—21no—
305#491—21no—
306#487—21no—
307#462—21no—
308#461—22no—
309#461—21no—
310#451C22×C3112yes—
311#448C22×C3114yes—
312#448C22×C3112yes—
313#432C22×C3111yescharacteristic
314#431C22×C3111yescharacteristic
315#398—22no—
316#395C22×C3114yes—
317#384—21no—
318#382—21no—
319#376C22×C3111yescharacteristic
320#328C22×C3112yes—
321#327C22×C3114yes—
322#327C22×C3112yes—
323#324C22×C3114yes—
324C2×C31—22no—
325C2×C31—81no—
326C2×C31—82no—
327C2×C31#300911yescharacteristic
328C2×C31C2×#45611yescharacteristic
329C2×C31#302711yescharacteristic
330C2×#41—21no—
331C2×#41—22no—
332C22×Q8C23×C3112yes—
333C2×Q16—22no—
334C2×SD16—24no—
335C2×SD16—22no—
336C4⋊Q8—21no—
337C4⋊Q8—22no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8D4×C3111yescharacteristic
343#127D4×C3111yescharacteristic
344#126—22no—
345#126—22no—
346#126—21no—
347#125—21no—
348#125—22no—
349#125—21no—
350#125—21no—
351#125—21no—
352#125—21no—
353#125D4×C3111yescharacteristic
354#124—21no—
355#124D4×C3111yescharacteristic
356#123—22no—
357#123—22no—
358#123—22no—
359#123—22no—
360#123—22no—
361#123—21no—
362#123—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8C23×C3111yescharacteristic
370#121—21no—
371#121—22no—
372#121—21no—
373#121—22no—
374#121—22no—
375#121—21no—
376#121—22no—
377#121C23×C3111yescharacteristic
378#121C23×C3112yes—
379C4×Q8D4×C3111yescharacteristic
380C4×D4—22no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—22no—
385C4×D4—21no—
386C4×D4D4×C3111yescharacteristic
387C4×D4D4×C3112yes—
388#117—21no—
389#117—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4D4×C3111yescharacteristic
396C2×C4⋊C4D4×C3112yes—
397C2×C4⋊C4D4×C3111yescharacteristic
398C2×C4⋊C4C23×C3112yes—
399C2×C42—21no—
400C2×C42C23×C3111yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403#103—24no—
404#103—22no—
405#103—22no—
406C22⋊C8C23×C3112yes—
407C22⋊C8C23×C3112yes—
408#97—21no—
409C4×C8—21no—
410#95—21no—
411#95—24no—
412#95C23×C3112yes—
413C31#1843111yescharacteristic, direct product factor, Sylow
414#41—82no—
415#41—84no—
416C2×Q8—22no—
417C2×Q8—21no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—82no—
421C2×Q8C2×D4×C3111yescharacteristic
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4C2×D4×C3111yescharacteristic
429C2×D4C2×D4×C3112yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4C2×D4×C3112yes—
438C22×C4C2×D4×C3111yescharacteristic
439C22×C4C2×D4×C3111yescharacteristic
440C22×C4C2×D4×C3112yes—
441C22×C4C24×C3111yescharacteristic
442Q16—82no—
443SD16—84no—
444SD16—82no—
445C2×C8—22no—
446C2×C8—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—84no—
469C4⋊C4C2×D4×C3112yes—
470C4⋊C4C2×D4×C3111yescharacteristic
471C4⋊C4C2×D4×C3111yescharacteristic
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C22⋊C4—22no—
484C42—24no—
485C42—22no—
486C42—21no—
487C42C2×D4×C3111yescharacteristic
488C42C2×D4×C3111yescharacteristic
489C42C2×D4×C3111yescharacteristic
490C42C2×D4×C3111yescharacteristic
491C23—21no—
492C23—22no—
493C23C22×D4×C3111yescharacteristic
494Q8—41no—
495Q8—44no—
496Q8—42no—
497Q8—42no—
498Q8—81no—
499Q8—82no—
500D4—42no—
501D4—41no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—81no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C31×#12011yescharacteristic
530C2×C4C31×#12011yescharacteristic
531C2×C4C31×#12011yescharacteristic
532C2×C4C31×#12011yescharacteristic
533C2×C4C22×D4×C3111yescharacteristic
534C2×C4C22×D4×C3111yescharacteristic
535C8—42no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—41no—
545C22C2×C31×#12011yescharacteristic
546C22C31×#57712yes—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—41no—
556C4—41no—
557C4—42no—
558C4—41no—
559C4—82no—
560C4C31×#45612yes—
561C2—22no—
562C2—81no—
563C2—82no—
564C2C31×#300911yescharacteristic
565C2C2×C31×#45611yescharacteristic
566C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3559C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3218C2semidirect
3. C31×#3206C2semidirect
4. C31×#2660C2semidirect
5. C31×#1604C2semidirect
6. C31×#1603C2semidirect
7. C31×#1505C2semidirect
8. C31×#1500C2semidirect
9. C31×#1470C2semidirect
207. #18431C31direct (N × H)
255. #3218C2×C31semidirect
256. #3206C2×C31semidirect
257. #2660C2×C31semidirect
258. #1604C2×C31semidirect
259. #1603C2×C31semidirect
260. #1505C2×C31semidirect
261. #1500C2×C31semidirect
262. #1470C2×C31semidirect
413. C31#18431direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35592
C31×#32182
C31×#32062
C31×#26602
C31×#16042
C31×#16032
C31×#15052
C31×#15002
C31×#14702
#1843131