Finite Group Databasebeta

← C31×#18783 #21475542

Subgroups — C31×#18783 #21475542

Order 7936.

1170 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#547C211yesmaximal, characteristic
2C31×#3230C211yesmaximal, characteristic, complemented
3C31×#3101C211yesmaximal, characteristic, complemented
4C31×#3077C211yesmaximal, characteristic, complemented
5C31×#1647C214yesmaximal, complemented
6C31×#1635C214yesmaximal, complemented
7C31×#1549C211yesmaximal, characteristic, complemented
8C31×#1486C211yesmaximal, characteristic, complemented
9C31×#1478C211yesmaximal, characteristic, complemented
10C22×#41×C31—21no—
11C31×#547—22no—
12C31×#547—22no—
13C31×#547—22no—
14C31×#547C2214yes—
15C31×#533C2211yescharacteristic
16C2×C31×C4⋊Q8C2211yescharacteristic
17C2×C31×#123—22no—
18C2×C31×C22⋊Q8—21no—
19C2×C31×#121—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31—21no—
23C31×#500C2212yescomplemented
24C31×#487C2212yescomplemented
25C31×#484—22no—
26C31×#483—21no—
27C31×#478—22no—
28C31×#477—22no—
29C31×#476C2212yescomplemented
30C31×#476C2212yescomplemented
31C31×#474C2212yescomplemented
32C31×#461C2212yescomplemented
33C31×#450—21no—
34C4×SD16×C31—22no—
35C31×#431C2211yescharacteristic
36C31×#431C2211yescharacteristic
37C31×#428—21no—
38C31×#423C2211yescharacteristic
39C31×#418—21no—
40C31×#332C2214yescomplemented
41C31×D4⋊C8C2214yescomplemented
42C31×D4⋊C8C2214yescomplemented
43C2×#41×C31—24no—
44C2×#41×C31—24no—
45C2×#41×C31—48no—
46C22×Q8×C31—21no—
47C22×D4×C31—22no—
48C22×D4×C31D411yescharacteristic
49C22×D4×C31D411yescharacteristic
50C23×C4×C31—22no—
51C23×C4×C31—21no—
52C23×C4×C31—21no—
53C2×SD16×C31—22no—
54C2×M16×C31—21no—
55C31×C4⋊Q8—21no—
56C31×C4⋊Q8—21no—
57C31×C4⋊Q8D412yes—
58C31×C4⋊Q8C2311yescharacteristic
59C31×C4⋊Q8C2311yescharacteristic
60C31×C4⋊Q8C2312yes—
61C31×#125—21no—
62C31×#123—28no—
63C31×#123—28no—
64C31×C22⋊Q8—24no—
65C31×C22⋊Q8—24no—
66C31×C22⋊Q8—21no—
67C31×C22⋊Q8—21no—
68C31×#121—24no—
69C31×#121—24no—
70C4×Q8×C31—21no—
71C4×Q8×C31—21no—
72C4×D4×C31—21no—
73C4×D4×C31—21no—
74C4×D4×C31—21no—
75C4×D4×C31—21no—
76C4×D4×C31D412yes—
77C4×D4×C31D412yes—
78C4×D4×C31C2312yes—
79C4×D4×C31C2312yes—
80C31×#117—21no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—24no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31D411yescharacteristic
86C2×C4⋊C4×C31D411yescharacteristic
87C2×C4⋊C4×C31D412yes—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C42×C31C2311yescharacteristic
92C31×#107—22no—
93C31×#107—24no—
94C31×#106—22no—
95C31×#106—22no—
96C31×C4⋊C8—21no—
97C31×C4⋊C8—21no—
98C31×C4⋊C8C2312yes—
99C31×C4⋊C8C2312yes—
100C31×#103—22no—
101C31×#103—24no—
102C31×#102—22no—
103C31×#102—22no—
104C31×#102—22no—
105C31×C22⋊C8—21no—
106C31×C22⋊C8—21no—
107C4×C8×C31—21no—
108C4×C8×C31C2312yes—
109C24×C31—21no—
110C24×C31—21no—
111#41×C31—416no—
112#41×C31—48no—
113#41×C31—48no—
114C2×Q8×C31—22no—
115C2×Q8×C31—22no—
116C2×Q8×C31—21no—
117C2×Q8×C31—21no—
118C2×Q8×C31—44no—
119C2×D4×C31—24no—
120C2×D4×C31—28no—
121C2×D4×C31—21no—
122C2×D4×C31—21no—
123C2×D4×C31—22no—
124C2×D4×C31—22no—
125C2×D4×C31—48no—
126C2×D4×C31C2×D412yes—
127C2×D4×C31C2×D412yes—
128C22×C4×C31—28no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—44no—
137C22×C4×C31—48no—
138C22×C4×C31—42no—
139C22×C4×C31—42no—
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143SD16×C31—44no—
144M16×C31—42no—
145C2×C8×C31—22no—
146C2×C8×C31—22no—
147C2×C8×C31—22no—
148C4⋊C4×C31—28no—
149C4⋊C4×C31—21no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—21no—
155C4⋊C4×C31—21no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—41no—
159C4⋊C4×C31—41no—
160C4⋊C4×C31C2×D412yes—
161C4⋊C4×C31C2×D414yes—
162C4⋊C4×C31C2×D412yes—
163C22⋊C4×C31—28no—
164C22⋊C4×C31—22no—
165C22⋊C4×C31—22no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—41no—
169C42×C31—41no—
170C42×C31C2×D411yescharacteristic
171C42×C31C2×D411yescharacteristic
172C42×C31C2×D411yescharacteristic
173C42×C31C2411yescharacteristic
174#18783C3111yesmaximal, characteristic, direct product factor, Sylow
175C23×C31—24no—
176C23×C31—22no—
177C23×C31—22no—
178C23×C31—42no—
179C23×C31—42no—
180C23×C31—42no—
181C23×C31—42no—
182C23×C31—42no—
183C23×C31#12011yescharacteristic
184Q8×C31—44no—
185Q8×C31—42no—
186Q8×C31—44no—
187Q8×C31—42no—
188D4×C31—24no—
189D4×C31—22no—
190D4×C31—22no—
191D4×C31—22no—
192D4×C31—416no—
193D4×C31—42no—
194D4×C31AGL(1,ℤ/8)14yes—
195C2×C4×C31—22no—
196C2×C4×C31—22no—
197C2×C4×C31—22no—
198C2×C4×C31—24no—
199C2×C4×C31—41no—
200C2×C4×C31—44no—
201C2×C4×C31—42no—
202C2×C4×C31—44no—
203C2×C4×C31—416no—
204C2×C4×C31—42no—
205C2×C4×C31—42no—
206C2×C4×C31—44no—
207C2×C4×C31—42no—
208C2×C4×C31—44no—
209C2×C4×C31—41no—
210C2×C4×C31—41no—
211C2×C4×C31#12011yescharacteristic
212C2×C4×C31#12011yescharacteristic
213C2×C4×C31#12011yescharacteristic
214C2×C4×C31#13512yes—
215C2×C4×C31#13712yes—
216C2×C4×C31C22×D411yescharacteristic
217C2×C4×C31C22×D411yescharacteristic
218C2×C4×C31C22×D411yescharacteristic
219C8×C31—42no—
220C8×C31—42no—
221C8×C31—42no—
222C2×#547C2×C3111yescharacteristic
223#3230C2×C3111yescharacteristic, complemented
224#3101C2×C3111yescharacteristic, complemented
225#3077C2×C3111yescharacteristic, complemented
226#1647C2×C3114yescomplemented
227#1635C2×C3114yescomplemented
228#1549C2×C3111yescharacteristic, complemented
229#1486C2×C3111yescharacteristic, complemented
230#1478C2×C3111yescharacteristic, complemented
231C22×C31—21no—
232C22×C31—21no—
233C22×C31—24no—
234C22×C31—48no—
235C22×C31—42no—
236C22×C31—42no—
237C22×C31—42no—
238C22×C31—42no—
239C22×C31—42no—
240C22×C31—84no—
241C22×C31#45212yes—
242C22×C31C2×#12011yescharacteristic
243C4×C31—21no—
244C4×C31—21no—
245C4×C31—21no—
246C4×C31—42no—
247C4×C31—42no—
248C4×C31—44no—
249C4×C31—81no—
250C4×C31—81no—
251C4×C31#45212yes—
252C4×C31C2×#13511yescharacteristic
253C4×C31C2×AGL(1,ℤ/8)12yes—
254C4×C31C2×#13711yescharacteristic
255C22×#41—21no—
256#547—22no—
257#547—22no—
258#547—22no—
259#547C22×C3114yes—
260#533C22×C3111yescharacteristic
261C2×C4⋊Q8C22×C3111yescharacteristic
262C2×#123—22no—
263C2×C22⋊Q8—21no—
264C2×#121—21no—
265C2×C4×D4C22×C3111yescharacteristic
266C2×C4×D4C22×C3111yescharacteristic
267C22×C4⋊C4—21no—
268#500C22×C3112yescomplemented
269#487C22×C3112yescomplemented
270#484—22no—
271#483—21no—
272#478—22no—
273#477—22no—
274#476C22×C3112yescomplemented
275#476C22×C3112yescomplemented
276#474C22×C3112yescomplemented
277#461C22×C3112yescomplemented
278#450—21no—
279C4×SD16—22no—
280#431C22×C3111yescharacteristic
281#431C22×C3111yescharacteristic
282#428—21no—
283#423C22×C3111yescharacteristic
284#418—21no—
285#332C22×C3114yescomplemented
286D4⋊C8C22×C3114yescomplemented
287D4⋊C8C22×C3114yescomplemented
288C2×C31—22no—
289C2×C31—44no—
290C2×C31—82no—
291C2×C31C2×#45211yescharacteristic
292C2×C31#300311yescharacteristic
293C2×C31#302011yescharacteristic
294C2×#41—24no—
295C2×#41—24no—
296C2×#41—48no—
297C22×Q8—21no—
298C22×D4—22no—
299C22×D4D4×C3111yescharacteristic
300C22×D4D4×C3111yescharacteristic
301C23×C4—22no—
302C23×C4—21no—
303C23×C4—21no—
304C2×SD16—22no—
305C2×M16—21no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8D4×C3112yes—
309C4⋊Q8C23×C3111yescharacteristic
310C4⋊Q8C23×C3111yescharacteristic
311C4⋊Q8C23×C3112yes—
312#125—21no—
313#123—28no—
314#123—28no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319#121—24no—
320#121—24no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4D4×C3112yes—
328C4×D4D4×C3112yes—
329C4×D4C23×C3112yes—
330C4×D4C23×C3112yes—
331#117—21no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4D4×C3111yescharacteristic
337C2×C4⋊C4D4×C3111yescharacteristic
338C2×C4⋊C4D4×C3112yes—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C42C23×C3111yescharacteristic
343#107—22no—
344#107—24no—
345#106—22no—
346#106—22no—
347C4⋊C8—21no—
348C4⋊C8—21no—
349C4⋊C8C23×C3112yes—
350C4⋊C8C23×C3112yes—
351#103—22no—
352#103—24no—
353#102—22no—
354#102—22no—
355#102—22no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C4×C8—21no—
359C4×C8C23×C3112yes—
360C31#1878311yescharacteristic, direct product factor, Sylow
361C24—21no—
362C24—21no—
363#41—416no—
364#41—48no—
365#41—48no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—44no—
371C2×D4—24no—
372C2×D4—28no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—48no—
378C2×D4C2×D4×C3112yes—
379C2×D4C2×D4×C3112yes—
380C22×C4—28no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—44no—
389C22×C4—48no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4C2×D4×C3111yescharacteristic
393C22×C4C2×D4×C3111yescharacteristic
394C22×C4C2×D4×C3111yescharacteristic
395SD16—44no—
396M16—42no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C4⋊C4—28no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4C2×D4×C3112yes—
413C4⋊C4C2×D4×C3114yes—
414C4⋊C4C2×D4×C3112yes—
415C22⋊C4—28no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—41no—
421C42—41no—
422C42C2×D4×C3111yescharacteristic
423C42C2×D4×C3111yescharacteristic
424C42C2×D4×C3111yescharacteristic
425C42C24×C3111yescharacteristic
426C23—24no—
427C23—22no—
428C23—22no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23C31×#12011yescharacteristic
435Q8—44no—
436Q8—42no—
437Q8—44no—
438Q8—42no—
439D4—24no—
440D4—22no—
441D4—22no—
442D4—22no—
443D4—416no—
444D4—42no—
445D4C31×AGL(1,ℤ/8)14yes—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—416no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4C31×#12011yescharacteristic
463C2×C4C31×#12011yescharacteristic
464C2×C4C31×#12011yescharacteristic
465C2×C4C31×#13512yes—
466C2×C4C31×#13712yes—
467C2×C4C22×D4×C3111yescharacteristic
468C2×C4C22×D4×C3111yescharacteristic
469C2×C4C22×D4×C3111yescharacteristic
470C8—42no—
471C8—42no—
472C8—42no—
473C22—21no—
474C22—21no—
475C22—24no—
476C22—48no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—84no—
483C22C31×#45212yes—
484C22C2×C31×#12011yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—44no—
491C4—81no—
492C4—81no—
493C4C31×#45212yes—
494C4C2×C31×#13511yescharacteristic
495C4C2×C31×AGL(1,ℤ/8)12yes—
496C4C2×C31×#13711yescharacteristic
497C2—22no—
498C2—44no—
499C2—82no—
500C2C2×C31×#45211yescharacteristic
501C2C31×#300311yescharacteristic
502C2C31×#302011yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC2×C31×#547C2
LCSG ▷ C42 ▷ 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×#3230C2semidirect
3. C31×#3101C2semidirect
4. C31×#3077C2semidirect
5. C31×#1647C2semidirect
6. C31×#1635C2semidirect
7. C31×#1549C2semidirect
8. C31×#1486C2semidirect
9. C31×#1478C2semidirect
23. C31×#500C22semidirect
24. C31×#487C22semidirect
29. C31×#476C22semidirect
30. C31×#476C22semidirect
31. C31×#474C22semidirect
32. C31×#461C22semidirect
40. C31×#332C22semidirect
41. C31×D4⋊C8C22semidirect
42. C31×D4⋊C8C22semidirect
174. #18783C31direct (N × H)
223. #3230C2×C31semidirect
224. #3101C2×C31semidirect
225. #3077C2×C31semidirect
226. #1647C2×C31semidirect
227. #1635C2×C31semidirect
228. #1549C2×C31semidirect
229. #1486C2×C31semidirect
230. #1478C2×C31semidirect
268. #500C22×C31semidirect
269. #487C22×C31semidirect
274. #476C22×C31semidirect
275. #476C22×C31semidirect
276. #474C22×C31semidirect
277. #461C22×C31semidirect
285. #332C22×C31semidirect
286. D4⋊C8C22×C31semidirect
287. D4⋊C8C22×C31semidirect
360. C31#18783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5472
C31×#32302
C31×#31012
C31×#30772
C31×#16472
C31×#16352
C31×#15492
C31×#14862
C31×#14782
#1878331