Finite Group Databasebeta

← C31×#18190 #21474949

Subgroups — C31×#18190 #21474949

Order 7936.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3506C211yesmaximal, characteristic, complemented
2C31×#3110C211yesmaximal, characteristic, complemented
3C31×#3109C211yesmaximal, characteristic, complemented
4C31×#2397C211yesmaximal, characteristic, complemented
5C31×#1618C214yesmaximal, complemented
6C31×#1600C214yesmaximal, complemented
7C31×#1506C211yesmaximal, characteristic, complemented
8C31×#1505C211yesmaximal, characteristic, complemented
9C31×#1466C211yesmaximal, characteristic, complemented
10C31×#559—22no—
11C31×#556—21no—
12C31×#555—21no—
13C31×#553—22no—
14C31×#550—21no—
15C31×#547—21no—
16C31×#538C2214yes—
17C31×#535—21no—
18C31×#533C2211yescharacteristic
19C31×#532C2211yescharacteristic
20C31×#525—22no—
21C31×#520—21no—
22C2×C4×D4×C31—22no—
23C2×C4×D4×C31C2211yescharacteristic
24C2×C4×D4×C31C2211yescharacteristic
25C31×#484C2212yes—
26C31×#481C2212yes—
27C31×#476—21no—
28C31×#474—21no—
29C31×#461—21no—
30C31×#459—21no—
31C31×#450C2212yes—
32C31×#447C2212yes—
33C31×#442—22no—
34C31×#440—22no—
35C31×#432C2211yescharacteristic
36C31×#432C2211yescharacteristic
37C31×#399—21no—
38C31×#399C2212yes—
39C31×#392—21no—
40C31×#392C2212yes—
41C31×#376C2211yescharacteristic
42C31×#328C2214yes—
43C31×#327C2214yes—
44C31×#323C2214yes—
45C2×#41×C31—22no—
46C2×#41×C31—21no—
47C22×D4×C31—22no—
48C22×D4×C31D411yescharacteristic
49C22×D4×C31C2311yescharacteristic
50C23×C4×C31—21no—
51C23×C4×C31D412yes—
52C2×SD16×C31—22no—
53C2×D8×C31—22no—
54C31×C4⋊Q8D411yescharacteristic, complemented
55C31×C4⋊Q8D411yescharacteristic, complemented
56C31×C4⋊Q8D411yescharacteristic, complemented
57C31×#127—22no—
58C31×#127D411yescharacteristic, complemented
59C31×#126—24no—
60C31×#125—21no—
61C31×#124—22no—
62C31×#124—24no—
63C31×#124—21no—
64C31×#123—24no—
65C31×#123—24no—
66C31×C22⋊Q8—22no—
67C31×C22⋊Q8—21no—
68C31×C22⋊Q8C2312yes—
69C31×#121—22no—
70C31×#121—22no—
71C31×#121—22no—
72C31×#121—24no—
73C31×#121—21no—
74C31×#121C2312yes—
75C31×#120—24no—
76C4×Q8×C31—22no—
77C4×Q8×C31—21no—
78C4×Q8×C31D412yescomplemented
79C4×D4×C31—22no—
80C4×D4×C31—24no—
81C4×D4×C31—24no—
82C4×D4×C31—21no—
83C4×D4×C31—21no—
84C4×D4×C31—21no—
85C4×D4×C31—21no—
86C4×D4×C31—21no—
87C4×D4×C31—21no—
88C4×D4×C31—21no—
89C4×D4×C31—21no—
90C4×D4×C31—21no—
91C4×D4×C31—48no—
92C4×D4×C31D412yescomplemented
93C31×#117—22no—
94C31×#117—22no—
95C31×#117—21no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31D411yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31C2312yes—
104C2×C42×C31—21no—
105C2×C42×C31C2311yescharacteristic
106C31×#107—22no—
107C31×#106—22no—
108C31×C4⋊C8—21no—
109C31×C4⋊C8—21no—
110C31×#103—22no—
111C31×#102—22no—
112C31×#102—22no—
113C31×#102—22no—
114C31×C22⋊C8C2312yes—
115C31×C22⋊C8C2312yes—
116C31×#97—21no—
117C31×#97—21no—
118C31×#95—21no—
119C31×#95C2312yes—
120C24×C31—21no—
121C24×C31C2×D412yes—
122#41×C31—44no—
123#41×C31—84no—
124C2×Q8×C31—21no—
125C2×Q8×C31—21no—
126C2×Q8×C31C2×D412yes—
127C2×D4×C31—22no—
128C2×D4×C31—24no—
129C2×D4×C31—24no—
130C2×D4×C31—21no—
131C2×D4×C31—21no—
132C2×D4×C31—21no—
133C2×D4×C31—21no—
134C2×D4×C31—21no—
135C2×D4×C31—21no—
136C2×D4×C31—42no—
137C2×D4×C31—44no—
138C2×D4×C31—42no—
139C2×D4×C31—44no—
140C2×D4×C31—44no—
141C2×D4×C31C2×D412yes—
142C22×C4×C31—22no—
143C22×C4×C31—24no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—22no—
147C22×C4×C31—21no—
148C22×C4×C31—44no—
149C22×C4×C31—44no—
150C22×C4×C31—41no—
151C22×C4×C31—41no—
152C22×C4×C31C2×D411yescharacteristic
153C22×C4×C31C2×D411yescharacteristic
154C22×C4×C31C2×D412yes—
155C22×C4×C31C2411yescharacteristic
156SD16×C31—44no—
157D8×C31—44no—
158C2×C8×C31—22no—
159C2×C8×C31—22no—
160C4⋊C4×C31—24no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—21no—
165C4⋊C4×C31—21no—
166C4⋊C4×C31—21no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—22no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—44no—
172C4⋊C4×C31C2×D412yes—
173C4⋊C4×C31C2×D412yes—
174C22⋊C4×C31—24no—
175C22⋊C4×C31—24no—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—22no—
178C22⋊C4×C31—22no—
179C22⋊C4×C31—22no—
180C22⋊C4×C31—22no—
181C22⋊C4×C31—22no—
182C22⋊C4×C31—44no—
183C22⋊C4×C31—44no—
184C22⋊C4×C31—41no—
185C22⋊C4×C31—41no—
186C42×C31—24no—
187C42×C31—24no—
188C42×C31—22no—
189C42×C31C2×D411yescharacteristic
190C42×C31C2×D411yescharacteristic
191C42×C31C2×D411yescharacteristic
192C42×C31C2×D411yescharacteristic
193#18190C3111yesmaximal, characteristic, direct product factor, Sylow
194C23×C31—22no—
195C23×C31—22no—
196C23×C31—22no—
197C23×C31—22no—
198C23×C31—22no—
199C23×C31—42no—
200C23×C31—42no—
201C23×C31—42no—
202C23×C31—41no—
203C23×C31—41no—
204C23×C31—42no—
205C23×C31C22×D411yescharacteristic
206Q8×C31—42no—
207Q8×C31—42no—
208Q8×C31—42no—
209D4×C31—22no—
210D4×C31—22no—
211D4×C31—42no—
212D4×C31—42no—
213D4×C31—42no—
214D4×C31—41no—
215D4×C31—41no—
216D4×C31—42no—
217D4×C31—416no—
218D4×C31—44no—
219D4×C31—42no—
220D4×C31—84no—
221D4×C31—84no—
222C2×C4×C31—22no—
223C2×C4×C31—22no—
224C2×C4×C31—24no—
225C2×C4×C31—22no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—41no—
230C2×C4×C31—44no—
231C2×C4×C31—42no—
232C2×C4×C31—42no—
233C2×C4×C31—44no—
234C2×C4×C31—42no—
235C2×C4×C31—42no—
236C2×C4×C31—41no—
237C2×C4×C31—82no—
238C2×C4×C31—82no—
239C2×C4×C31—84no—
240C2×C4×C31—82no—
241C2×C4×C31#12011yescharacteristic
242C2×C4×C31#12011yescharacteristic
243C2×C4×C31#12011yescharacteristic
244C2×C4×C31#12011yescharacteristic
245C2×C4×C31C22×D411yescharacteristic
246C2×C4×C31C22×D411yescharacteristic
247C8×C31—42no—
248C8×C31—42no—
249#3506C2×C3111yescharacteristic, complemented
250#3110C2×C3111yescharacteristic, complemented
251#3109C2×C3111yescharacteristic, complemented
252#2397C2×C3111yescharacteristic, complemented
253#1618C2×C3114yescomplemented
254#1600C2×C3114yescomplemented
255#1506C2×C3111yescharacteristic, complemented
256#1505C2×C3111yescharacteristic, complemented
257#1466C2×C3111yescharacteristic, complemented
258C22×C31—21no—
259C22×C31—21no—
260C22×C31—44no—
261C22×C31—44no—
262C22×C31—42no—
263C22×C31—42no—
264C22×C31—42no—
265C22×C31—42no—
266C22×C31—42no—
267C22×C31—42no—
268C22×C31—42no—
269C22×C31—82no—
270C22×C31—82no—
271C22×C31—81no—
272C22×C31—81no—
273C22×C31C2×#12011yescharacteristic
274C22×C31#57512yes—
275C4×C31—21no—
276C4×C31—21no—
277C4×C31—21no—
278C4×C31—21no—
279C4×C31—21no—
280C4×C31—44no—
281C4×C31—42no—
282C4×C31—42no—
283C4×C31—42no—
284C4×C31—42no—
285C4×C31—81no—
286C4×C31#45312yes—
287#559—22no—
288#556—21no—
289#555—21no—
290#553—22no—
291#550—21no—
292#547—21no—
293#538C22×C3114yes—
294#535—21no—
295#533C22×C3111yescharacteristic
296#532C22×C3111yescharacteristic
297#525—22no—
298#520—21no—
299C2×C4×D4—22no—
300C2×C4×D4C22×C3111yescharacteristic
301C2×C4×D4C22×C3111yescharacteristic
302#484C22×C3112yes—
303#481C22×C3112yes—
304#476—21no—
305#474—21no—
306#461—21no—
307#459—21no—
308#450C22×C3112yes—
309#447C22×C3112yes—
310#442—22no—
311#440—22no—
312#432C22×C3111yescharacteristic
313#432C22×C3111yescharacteristic
314#399—21no—
315#399C22×C3112yes—
316#392—21no—
317#392C22×C3112yes—
318#376C22×C3111yescharacteristic
319#328C22×C3114yes—
320#327C22×C3114yes—
321#323C22×C3114yes—
322C2×C31—22no—
323C2×C31—82no—
324C2×C31—82no—
325C2×C31—82no—
326C2×C31#300511yescharacteristic
327C2×C31C2×#45311yescharacteristic
328C2×C31#302511yescharacteristic
329C2×#41—22no—
330C2×#41—21no—
331C22×D4—22no—
332C22×D4D4×C3111yescharacteristic
333C22×D4C23×C3111yescharacteristic
334C23×C4—21no—
335C23×C4D4×C3112yes—
336C2×SD16—22no—
337C2×D8—22no—
338C4⋊Q8D4×C3111yescharacteristic, complemented
339C4⋊Q8D4×C3111yescharacteristic, complemented
340C4⋊Q8D4×C3111yescharacteristic, complemented
341#127—22no—
342#127D4×C3111yescharacteristic, complemented
343#126—24no—
344#125—21no—
345#124—22no—
346#124—24no—
347#124—21no—
348#123—24no—
349#123—24no—
350C22⋊Q8—22no—
351C22⋊Q8—21no—
352C22⋊Q8C23×C3112yes—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—24no—
357#121—21no—
358#121C23×C3112yes—
359#120—24no—
360C4×Q8—22no—
361C4×Q8—21no—
362C4×Q8D4×C3112yescomplemented
363C4×D4—22no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—48no—
376C4×D4D4×C3112yescomplemented
377#117—22no—
378#117—22no—
379#117—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4D4×C3111yescharacteristic
383C2×C4⋊C4C23×C3111yescharacteristic
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4C23×C3112yes—
388C2×C42—21no—
389C2×C42C23×C3111yescharacteristic
390#107—22no—
391#106—22no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394#103—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398C22⋊C8C23×C3112yes—
399C22⋊C8C23×C3112yes—
400#97—21no—
401#97—21no—
402#95—21no—
403#95C23×C3112yes—
404C31#1819011yescharacteristic, direct product factor, Sylow
405C24—21no—
406C24C2×D4×C3112yes—
407#41—44no—
408#41—84no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8C2×D4×C3112yes—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—44no—
423C2×D4—42no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4C2×D4×C3112yes—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—44no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4C2×D4×C3111yescharacteristic
438C22×C4C2×D4×C3111yescharacteristic
439C22×C4C2×D4×C3112yes—
440C22×C4C24×C3111yescharacteristic
441SD16—44no—
442D8—44no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—44no—
457C4⋊C4C2×D4×C3112yes—
458C4⋊C4C2×D4×C3112yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—44no—
468C22⋊C4—44no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C42—24no—
472C42—24no—
473C42—22no—
474C42C2×D4×C3111yescharacteristic
475C42C2×D4×C3111yescharacteristic
476C42C2×D4×C3111yescharacteristic
477C42C2×D4×C3111yescharacteristic
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—41no—
487C23—41no—
488C23—42no—
489C23C22×D4×C3111yescharacteristic
490Q8—42no—
491Q8—42no—
492Q8—42no—
493D4—22no—
494D4—22no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—416no—
502D4—44no—
503D4—42no—
504D4—84no—
505D4—84no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—84no—
524C2×C4—82no—
525C2×C4C31×#12011yescharacteristic
526C2×C4C31×#12011yescharacteristic
527C2×C4C31×#12011yescharacteristic
528C2×C4C31×#12011yescharacteristic
529C2×C4C22×D4×C3111yescharacteristic
530C2×C4C22×D4×C3111yescharacteristic
531C8—42no—
532C8—42no—
533C22—21no—
534C22—21no—
535C22—44no—
536C22—44no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22—81no—
547C22—81no—
548C22C2×C31×#12011yescharacteristic
549C22C31×#57512yes—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—81no—
561C4C31×#45312yes—
562C2—22no—
563C2—82no—
564C2—82no—
565C2—82no—
566C2C31×#300511yescharacteristic
567C2C2×C31×#45311yescharacteristic
568C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C31×#3506C2semidirect
2. C31×#3110C2semidirect
3. C31×#3109C2semidirect
4. C31×#2397C2semidirect
5. C31×#1618C2semidirect
6. C31×#1600C2semidirect
7. C31×#1506C2semidirect
8. C31×#1505C2semidirect
9. C31×#1466C2semidirect
54. C31×C4⋊Q8D4semidirect
55. C31×C4⋊Q8D4semidirect
56. C31×C4⋊Q8D4semidirect
58. C31×#127D4semidirect
78. C4×Q8×C31D4semidirect
92. C4×D4×C31D4semidirect
193. #18190C31direct (N × H)
249. #3506C2×C31semidirect
250. #3110C2×C31semidirect
251. #3109C2×C31semidirect
252. #2397C2×C31semidirect
253. #1618C2×C31semidirect
254. #1600C2×C31semidirect
255. #1506C2×C31semidirect
256. #1505C2×C31semidirect
257. #1466C2×C31semidirect
338. C4⋊Q8D4×C31semidirect
339. C4⋊Q8D4×C31semidirect
340. C4⋊Q8D4×C31semidirect
342. #127D4×C31semidirect
362. C4×Q8D4×C31semidirect
376. C4×D4D4×C31semidirect
404. C31#18190direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35062
C31×#31102
C31×#31092
C31×#23972
C31×#16182
C31×#16002
C31×#15062
C31×#15052
C31×#14662
#1819031