Finite Group Databasebeta

← C31×#24069 #21480828

Subgroups — C31×#24069 #21480828

Order 7936.

1130 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#540C211yesmaximal, characteristic
2C2×C31×#481C211yesmaximal, characteristic, complemented
3C2×C31×#480C211yesmaximal, characteristic, complemented
4C31×#2317C211yesmaximal, characteristic, complemented
5C31×#2059C212yesmaximal, complemented
6C31×#2041C212yesmaximal, complemented
7C31×#1875C211yesmaximal, characteristic, complemented
8C31×#1875C211yesmaximal, characteristic, complemented
9C31×#1864C212yesmaximal, complemented
10C31×#1862C212yesmaximal, complemented
11C31×#1818C211yesmaximal, characteristic, complemented
12C31×#540—24no—
13C31×#540—24no—
14C2×C31×#127C2211yescharacteristic
15C2×C31×#125C2211yescharacteristic
16C2×C31×#123—21no—
17C2×C31×#123—21no—
18C2×C31×#121—21no—
19C2×C31×#121—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C2×C31×#117C2211yescharacteristic
25C2×C31×#117C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C31×#481—24no—
28C31×#480—24no—
29C2×C31×#107C2212yes—
30C2×C31×#106C2212yes—
31C2×C31×#102C2212yes—
32C2×C31×#102C2212yes—
33C2×C31×#102C2212yes—
34C2×C31×#102C2212yes—
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C31×#389C2212yes—
38C31×#389C2212yes—
39C31×#385—21no—
40C31×#385—21no—
41C31×#384—21no—
42C31×#382—21no—
43C31×#340C2212yes—
44C31×#340C2212yes—
45C31×#336C2212yes—
46C31×#336C2212yes—
47C22×D4×C31—21no—
48C22×D4×C31—21no—
49C22×D4×C31—21no—
50C22×D4×C31—21no—
51C22×D4×C31C2311yescharacteristic
52C22×D4×C31C2311yescharacteristic
53C23×C4×C31—21no—
54C23×C4×C31—21no—
55C23×C4×C31—21no—
56C23×C4×C31C2311yescharacteristic
57C22×C8×C31C2312yes—
58C22×C8×C31C2312yes—
59C31×#127—22no—
60C31×#127—22no—
61C31×#125—22no—
62C31×#125—22no—
63C31×#123—28no—
64C31×#123—28no—
65C31×#121—28no—
66C31×#121—28no—
67C31×#121—22no—
68C31×#121—22no—
69C31×#121D414yes—
70C31×#121D414yes—
71C4×D4×C31—22no—
72C4×D4×C31—22no—
73C4×D4×C31—22no—
74C4×D4×C31—22no—
75C31×#117—22no—
76C31×#117—22no—
77C31×#117—24no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31—21no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31D411yescharacteristic
86C2×C4⋊C4×C31D411yescharacteristic
87C2×C4⋊C4×C31C2312yes—
88C2×C4⋊C4×C31C2311yescharacteristic
89C2×C4⋊C4×C31C2311yescharacteristic
90C2×C4⋊C4×C31C2312yes—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31—21no—
94C2×C22⋊C4×C31—21no—
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31D411yescharacteristic
97C2×C22⋊C4×C31D411yescharacteristic
98C2×C42×C31—21no—
99C2×C42×C31C2311yescharacteristic
100C2×C42×C31C2311yescharacteristic
101C31×#107—24no—
102C31×#106—24no—
103C31×#102—24no—
104C31×#102—24no—
105C31×#102—24no—
106C31×#102—24no—
107C31×C22⋊C8—22no—
108C31×C22⋊C8—22no—
109C31×#95—22no—
110C31×#95—22no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31C2×D411yescharacteristic
114C2×D4×C31—24no—
115C2×D4×C31—24no—
116C2×D4×C31—24no—
117C2×D4×C31—24no—
118C2×D4×C31—21no—
119C2×D4×C31—21no—
120C2×D4×C31—22no—
121C2×D4×C31—22no—
122C2×D4×C31—22no—
123C2×D4×C31—22no—
124C2×D4×C31—82no—
125C2×D4×C31—82no—
126C2×D4×C31—82no—
127C2×D4×C31—82no—
128C2×D4×C31C2×D412yes—
129C2×D4×C31C2×D412yes—
130C22×C4×C31—22no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—24no—
136C22×C4×C31—24no—
137C22×C4×C31—22no—
138C22×C4×C31—42no—
139C22×C4×C31—82no—
140C22×C4×C31—82no—
141C22×C4×C31—82no—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2×D412yes—
148C22×C4×C31C2×D412yes—
149C22×C4×C31C2411yescharacteristic
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C2×C8×C31—22no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—42no—
166C4⋊C4×C31—82no—
167C4⋊C4×C31—82no—
168C4⋊C4×C31C2×D412yes—
169C4⋊C4×C31C2×D412yes—
170C4⋊C4×C31#4114yes—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—24no—
173C22⋊C4×C31—24no—
174C22⋊C4×C31—22no—
175C22⋊C4×C31—22no—
176C22⋊C4×C31—24no—
177C22⋊C4×C31—24no—
178C42×C31—24no—
179C42×C31—21no—
180C42×C31—21no—
181C42×C31—21no—
182C42×C31—21no—
183#24069C3111yesmaximal, characteristic, direct product factor, Sylow
184C23×C31—21no—
185C23×C31—21no—
186C23×C31—22no—
187C23×C31—22no—
188C23×C31—22no—
189C23×C31—22no—
190C23×C31—41no—
191C23×C31—41no—
192C23×C31—41no—
193C23×C31—41no—
194C23×C31—42no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31—42no—
198C23×C31#12012yes—
199C23×C31C22×D411yescharacteristic
200D4×C31—24no—
201D4×C31—24no—
202D4×C31—42no—
203D4×C31—42no—
204D4×C31—84no—
205D4×C31—84no—
206D4×C31—84no—
207D4×C31—84no—
208C2×C4×C31—21no—
209C2×C4×C31—21no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—21no—
213C2×C4×C31—21no—
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—42no—
226C2×C4×C31—42no—
227C2×C4×C31—42no—
228C2×C4×C31—42no—
229C2×C4×C31—42no—
230C2×C4×C31—84no—
231C2×C4×C31—84no—
232C2×C4×C31—84no—
233C2×C4×C31#12012yes—
234C2×C4×C31C22×D411yescharacteristic
235C2×C4×C31C22×D411yescharacteristic
236C2×C4×C31C2×#4112yes—
237C2×C4×C312−1+412yes—
238C8×C31—42no—
239C8×C31—42no—
240C2×#540C2×C3111yescharacteristic
241C2×#481C2×C3111yescharacteristic, complemented
242C2×#480C2×C3111yescharacteristic, complemented
243#2317C2×C3111yescharacteristic, complemented
244#2059C2×C3112yescomplemented
245#2041C2×C3112yescomplemented
246#1875C2×C3111yescharacteristic, complemented
247#1875C2×C3111yescharacteristic, complemented
248#1864C2×C3112yescomplemented
249#1862C2×C3112yescomplemented
250#1818C2×C3111yescharacteristic, complemented
251C22×C31—22no—
252C22×C31—22no—
253C22×C31—22no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—42no—
262C22×C31—82no—
263C22×C31—82no—
264C22×C31—82no—
265C22×C31—82no—
266C22×C31C2×#12011yescharacteristic
267C22×C31#52511yescharacteristic
268C22×C31#53611yescharacteristic
269C22×C31#57612yes—
270C22×C31#57712yes—
271C4×C31—22no—
272C4×C31—44no—
273C4×C31—41no—
274C4×C31—41no—
275C4×C31—42no—
276C4×C31—41no—
277C4×C31—41no—
278C4×C31—42no—
279C4×C31—82no—
280C4×C31#54712yes—
281C4×C31#54712yes—
282#540—24no—
283#540—24no—
284C2×#127C22×C3111yescharacteristic
285C2×#125C22×C3111yescharacteristic
286C2×#123—21no—
287C2×#123—21no—
288C2×#121—21no—
289C2×#121—21no—
290C2×#121C22×C3111yescharacteristic
291C2×#121C22×C3111yescharacteristic
292C2×C4×D4C22×C3111yescharacteristic
293C2×C4×D4C22×C3111yescharacteristic
294C2×#117C22×C3111yescharacteristic
295C2×#117C22×C3111yescharacteristic
296C22×C4⋊C4C22×C3111yescharacteristic
297#481—24no—
298#480—24no—
299C2×#107C22×C3112yes—
300C2×#106C22×C3112yes—
301C2×#102C22×C3112yes—
302C2×#102C22×C3112yes—
303C2×#102C22×C3112yes—
304C2×#102C22×C3112yes—
305C2×C22⋊C8C22×C3111yescharacteristic
306C2×C22⋊C8C22×C3111yescharacteristic
307#389C22×C3112yes—
308#389C22×C3112yes—
309#385—21no—
310#385—21no—
311#384—21no—
312#382—21no—
313#340C22×C3112yes—
314#340C22×C3112yes—
315#336C22×C3112yes—
316#336C22×C3112yes—
317C2×C31—42no—
318C2×C31—82no—
319C2×C31—82no—
320C2×C31#240611yescharacteristic
321C2×C31#300811yescharacteristic
322C2×C31#300911yescharacteristic
323C2×C31#311912yes—
324C2×C31#324112yes—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4C23×C3111yescharacteristic
330C22×D4C23×C3111yescharacteristic
331C23×C4—21no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4C23×C3111yescharacteristic
335C22×C8C23×C3112yes—
336C22×C8C23×C3112yes—
337#127—22no—
338#127—22no—
339#125—22no—
340#125—22no—
341#123—28no—
342#123—28no—
343#121—28no—
344#121—28no—
345#121—22no—
346#121—22no—
347#121D4×C3114yes—
348#121D4×C3114yes—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353#117—22no—
354#117—22no—
355#117—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4D4×C3111yescharacteristic
364C2×C4⋊C4D4×C3111yescharacteristic
365C2×C4⋊C4C23×C3112yes—
366C2×C4⋊C4C23×C3111yescharacteristic
367C2×C4⋊C4C23×C3111yescharacteristic
368C2×C4⋊C4C23×C3112yes—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4D4×C3111yescharacteristic
375C2×C22⋊C4D4×C3111yescharacteristic
376C2×C42—21no—
377C2×C42C23×C3111yescharacteristic
378C2×C42C23×C3111yescharacteristic
379#107—24no—
380#106—24no—
381#102—24no—
382#102—24no—
383#102—24no—
384#102—24no—
385C22⋊C8—22no—
386C22⋊C8—22no—
387#95—22no—
388#95—22no—
389C31#2406911yescharacteristic, direct product factor, Sylow
390C24—21no—
391C24—21no—
392C24C2×D4×C3111yescharacteristic
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—24no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4C2×D4×C3112yes—
408C2×D4C2×D4×C3112yes—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4—82no—
421C22×C4C2×D4×C3111yescharacteristic
422C22×C4C2×D4×C3111yescharacteristic
423C22×C4C2×D4×C3111yescharacteristic
424C22×C4C2×D4×C3111yescharacteristic
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3112yes—
427C22×C4C2×D4×C3112yes—
428C22×C4C24×C3111yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—82no—
446C4⋊C4—82no—
447C4⋊C4C2×D4×C3112yes—
448C4⋊C4C2×D4×C3112yes—
449C4⋊C4#41×C3114yes—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C42—24no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23C31×#12012yes—
477C23C22×D4×C3111yescharacteristic
478D4—24no—
479D4—24no—
480D4—42no—
481D4—42no—
482D4—84no—
483D4—84no—
484D4—84no—
485D4—84no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4C31×#12012yes—
512C2×C4C22×D4×C3111yescharacteristic
513C2×C4C22×D4×C3111yescharacteristic
514C2×C4C2×#41×C3112yes—
515C2×C4C31×2−1+412yes—
516C8—42no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22C2×C31×#12011yescharacteristic
534C22C31×#52511yescharacteristic
535C22C31×#53611yescharacteristic
536C22C31×#57612yes—
537C22C31×#57712yes—
538C4—22no—
539C4—44no—
540C4—41no—
541C4—41no—
542C4—42no—
543C4—41no—
544C4—41no—
545C4—42no—
546C4—82no—
547C4C31×#54712yes—
548C4C31×#54712yes—
549C2—42no—
550C2—82no—
551C2—82no—
552C2C31×#240611yescharacteristic
553C2C31×#300811yescharacteristic
554C2C31×#300911yescharacteristic
555C2C31×#311912yes—
556C2C31×#324112yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#481C2semidirect
3. C2×C31×#480C2semidirect
4. C31×#2317C2semidirect
5. C31×#2059C2semidirect
6. C31×#2041C2semidirect
7. C31×#1875C2semidirect
8. C31×#1875C2semidirect
9. C31×#1864C2semidirect
10. C31×#1862C2semidirect
11. C31×#1818C2semidirect
183. #24069C31direct (N × H)
241. C2×#481C2×C31semidirect
242. C2×#480C2×C31semidirect
243. #2317C2×C31semidirect
244. #2059C2×C31semidirect
245. #2041C2×C31semidirect
246. #1875C2×C31semidirect
247. #1875C2×C31semidirect
248. #1864C2×C31semidirect
249. #1862C2×C31semidirect
250. #1818C2×C31semidirect
389. C31#24069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5402
C2×C31×#4812
C2×C31×#4802
C31×#23172
C31×#20592
C31×#20412
C31×#18752
C31×#18642
C31×#18622
C31×#18182
#2406931