Finite Group Databasebeta

← C31×#24062 #21480821

Subgroups — C31×#24062 #21480821

Order 7936.

1352 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
1C2×C31×#532C211yesmaximal, characteristic
2C2×C31×#482C212yesmaximal, complemented
3C31×#2296C211yesmaximal, characteristic, complemented
4C31×#2058C211yesmaximal, characteristic, complemented
5C31×#2057C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#1875C212yesmaximal, complemented
9C31×#1864C212yesmaximal, complemented
10C31×#1862C212yesmaximal, complemented
11C31×#1817C211yesmaximal, characteristic, complemented
12C22×#41×C31—21no—
13C31×#532—28no—
14C2×C31×C4⋊Q8C2211yescharacteristic
15C2×C31×#127C2211yescharacteristic
16C2×C31×#124—21no—
17C2×C31×#121—21no—
18C2×C31×#121C2212yes—
19C2×C4×D4×C31—21no—
20C2×C4×D4×C31C2212yes—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C42×C31C2211yescharacteristic
24C31×#482—28no—
25C2×C31×#107C2212yes—
26C2×C31×#106C2212yes—
27C2×C31×#102C2212yes—
28C2×C31×#102C2212yes—
29C2×C31×#102C2212yes—
30C2×C31×#102C2212yes—
31C2×C31×C22⋊C8C2212yes—
32C31×#389C2211yescharacteristic
33C31×#389C2211yescharacteristic
34C31×#389C2211yescharacteristic
35C31×#389C2211yescharacteristic
36C31×#385—21no—
37C31×#385—21no—
38C4×C4⋊C4×C31—21no—
39C4×C4⋊C4×C31—21no—
40C31×#340C2212yes—
41C31×#340C2212yes—
42C31×#336C2211yescharacteristic
43C31×#336C2211yescharacteristic
44C31×#336C2212yes—
45C2×#41×C31—28no—
46C2×#41×C31—44no—
47C2×#41×C31—44no—
48C22×Q8×C31—21no—
49C22×D4×C31—22no—
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31C2312yes—
53C23×C4×C31—22no—
54C23×C4×C31D411yescharacteristic
55C23×C4×C31D411yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C22×C8×C31C2312yes—
58C22×C8×C31C2312yes—
59C31×C4⋊Q8—24no—
60C31×#127—24no—
61C31×#124—28no—
62C31×#121—28no—
63C31×#121—24no—
64C31×#121D418yes—
65C4×D4×C31—28no—
66C4×D4×C31—24no—
67C4×D4×C31—24no—
68C31×#117—22no—
69C31×#117—22no—
70C31×#117—24no—
71C2×C4⋊C4×C31—21no—
72C2×C4⋊C4×C31—21no—
73C2×C4⋊C4×C31—21no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—21no—
76C2×C4⋊C4×C31C2311yescharacteristic
77C2×C4⋊C4×C31C2311yescharacteristic
78C2×C4⋊C4×C31C2312yes—
79C2×C4⋊C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C22⋊C4×C31—21no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—22no—
84C2×C22⋊C4×C31—21no—
85C2×C42×C31—24no—
86C2×C42×C31—21no—
87C2×C42×C31—21no—
88C2×C42×C31D411yescharacteristic
89C2×C42×C31D411yescharacteristic
90C2×C42×C31C2311yescharacteristic
91C2×C42×C31C2311yescharacteristic
92C31×#107—24no—
93C31×#106—24no—
94C31×#102—24no—
95C31×#102—24no—
96C31×#102—24no—
97C31×#102—24no—
98C31×C22⋊C8—24no—
99C31×#95—21no—
100C31×#95—21no—
101C31×#95—21no—
102C31×#95—21no—
103C24×C31—22no—
104C24×C31C2×D411yescharacteristic
105#41×C31—432no—
106C2×Q8×C31—24no—
107C2×Q8×C31—42no—
108C2×Q8×C31—42no—
109C2×D4×C31—24no—
110C2×D4×C31—24no—
111C2×D4×C31—28no—
112C2×D4×C31—22no—
113C2×D4×C31—22no—
114C2×D4×C31—22no—
115C2×D4×C31—22no—
116C2×D4×C31—22no—
117C2×D4×C31—42no—
118C2×D4×C31—42no—
119C2×D4×C31—44no—
120C2×D4×C31—44no—
121C2×D4×C31—42no—
122C2×D4×C31—42no—
123C2×D4×C31C2×D414yes—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—22no—
130C22×C4×C31—28no—
131C22×C4×C31—22no—
132C22×C4×C31—21no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—41no—
139C22×C4×C31—44no—
140C22×C4×C31—44no—
141C22×C4×C31C2×D411yescharacteristic
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D414yes—
144C22×C4×C31C2×D411yescharacteristic
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2411yescharacteristic
148C2×C8×C31—22no—
149C2×C8×C31—22no—
150C2×C8×C31—22no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C4⋊C4×C31—24no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—21no—
157C4⋊C4×C31—21no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—42no—
161C4⋊C4×C31—42no—
162C4⋊C4×C31—42no—
163C4⋊C4×C31—42no—
164C4⋊C4×C31C2×D414yes—
165C4⋊C4×C31#4112yescomplemented
166C4⋊C4×C31#4112yescomplemented
167C22⋊C4×C31—24no—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—28no—
170C22⋊C4×C31—42no—
171C42×C31—24no—
172C42×C31—22no—
173C42×C31—22no—
174C42×C31—22no—
175C42×C31—22no—
176C42×C31—42no—
177#24062C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—21no—
179C23×C31—21no—
180C23×C31—21no—
181C23×C31—21no—
182C23×C31—21no—
183C23×C31—21no—
184C23×C31—24no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—42no—
189C23×C31—42no—
190C23×C31—42no—
191C23×C31#12012yes—
192C23×C31C22×D411yescharacteristic
193Q8×C31—48no—
194D4×C31—24no—
195D4×C31—24no—
196D4×C31—48no—
197D4×C31—48no—
198D4×C31—416no—
199D4×C31—42no—
200D4×C31—42no—
201C2×C4×C31—28no—
202C2×C4×C31—21no—
203C2×C4×C31—21no—
204C2×C4×C31—21no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—21no—
208C2×C4×C31—21no—
209C2×C4×C31—21no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—21no—
213C2×C4×C31—24no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—44no—
219C2×C4×C31—416no—
220C2×C4×C31—41no—
221C2×C4×C31—41no—
222C2×C4×C31—41no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—41no—
226C2×C4×C31—41no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—41no—
230C2×C4×C31—41no—
231C2×C4×C31—41no—
232C2×C4×C31#12012yes—
233C2×C4×C31#13512yes—
234C2×C4×C31AGL(1,ℤ/8)12yes—
235C2×C4×C31AGL(1,ℤ/8)12yes—
236C2×C4×C31C22×D412yes—
237C2×C4×C31C2×#4111yescharacteristic
238C2×C4×C31C2×#4111yescharacteristic
239C2×C4×C312−1+412yes—
240C8×C31—42no—
241C8×C31—42no—
242C2×#532C2×C3111yescharacteristic
243C2×#482C2×C3112yescomplemented
244#2296C2×C3111yescharacteristic, complemented
245#2058C2×C3111yescharacteristic, complemented
246#2057C2×C3111yescharacteristic, complemented
247#2041C2×C3111yescharacteristic, complemented
248#2041C2×C3111yescharacteristic, complemented
249#1875C2×C3112yescomplemented
250#1864C2×C3112yescomplemented
251#1862C2×C3112yescomplemented
252#1817C2×C3111yescharacteristic, complemented
253C22×C31—22no—
254C22×C31—22no—
255C22×C31—22no—
256C22×C31—41no—
257C22×C31—41no—
258C22×C31—41no—
259C22×C31—41no—
260C22×C31—44no—
261C22×C31—44no—
262C22×C31—44no—
263C22×C31—82no—
264C22×C31—82no—
265C22×C31—82no—
266C22×C31—82no—
267C22×C31C2×#12011yescharacteristic
268C22×C31#52511yescharacteristic
269C22×C31#53611yescharacteristic
270C22×C31C2×#13511yescharacteristic
271C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C31#57511yescharacteristic
274C4×C31—22no—
275C4×C31—22no—
276C4×C31—22no—
277C4×C31—22no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—41no—
281C4×C31—44no—
282C4×C31—81no—
283C4×C31—81no—
284C4×C31#54712yes—
285C4×C31#54712yes—
286C22×#41—21no—
287#532—28no—
288C2×C4⋊Q8C22×C3111yescharacteristic
289C2×#127C22×C3111yescharacteristic
290C2×#124—21no—
291C2×#121—21no—
292C2×#121C22×C3112yes—
293C2×C4×D4—21no—
294C2×C4×D4C22×C3112yes—
295C2×#117C22×C3111yescharacteristic
296C2×#117C22×C3111yescharacteristic
297C22×C42C22×C3111yescharacteristic
298#482—28no—
299C2×#107C22×C3112yes—
300C2×#106C22×C3112yes—
301C2×#102C22×C3112yes—
302C2×#102C22×C3112yes—
303C2×#102C22×C3112yes—
304C2×#102C22×C3112yes—
305C2×C22⋊C8C22×C3112yes—
306#389C22×C3111yescharacteristic
307#389C22×C3111yescharacteristic
308#389C22×C3111yescharacteristic
309#389C22×C3111yescharacteristic
310#385—21no—
311#385—21no—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—21no—
314#340C22×C3112yes—
315#340C22×C3112yes—
316#336C22×C3111yescharacteristic
317#336C22×C3111yescharacteristic
318#336C22×C3112yes—
319C2×C31—42no—
320C2×C31—84no—
321C2×C31#240611yescharacteristic
322C2×C31#300211yescharacteristic
323C2×C31#300311yescharacteristic
324C2×C31#310611yescharacteristic
325C2×C31#311511yescharacteristic
326C2×C31#322811yescharacteristic
327C2×C31#323511yescharacteristic
328C2×#41—28no—
329C2×#41—44no—
330C2×#41—44no—
331C22×Q8—21no—
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4C23×C3112yes—
336C23×C4—22no—
337C23×C4D4×C3111yescharacteristic
338C23×C4D4×C3111yescharacteristic
339C23×C4C23×C3111yescharacteristic
340C22×C8C23×C3112yes—
341C22×C8C23×C3112yes—
342C4⋊Q8—24no—
343#127—24no—
344#124—28no—
345#121—28no—
346#121—24no—
347#121D4×C3118yes—
348C4×D4—28no—
349C4×D4—24no—
350C4×D4—24no—
351#117—22no—
352#117—22no—
353#117—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4C23×C3111yescharacteristic
360C2×C4⋊C4C23×C3111yescharacteristic
361C2×C4⋊C4C23×C3112yes—
362C2×C4⋊C4C23×C3111yescharacteristic
363C2×C4⋊C4C23×C3111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369C2×C42—24no—
370C2×C42—21no—
371C2×C42D4×C3111yescharacteristic
372C2×C42D4×C3111yescharacteristic
373C2×C42C23×C3111yescharacteristic
374C2×C42C23×C3111yescharacteristic
375#107—24no—
376#106—24no—
377#102—24no—
378#102—24no—
379#102—24no—
380#102—24no—
381C22⋊C8—24no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386C31#2406211yescharacteristic, direct product factor, Sylow
387C24—22no—
388C24C2×D4×C3111yescharacteristic
389#41—432no—
390C2×Q8—24no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—28no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—44no—
404C2×D4—44no—
405C2×D4—42no—
406C2×D4—42no—
407C2×D4C2×D4×C3114yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—28no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—41no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4C2×D4×C3111yescharacteristic
426C22×C4C2×D4×C3111yescharacteristic
427C22×C4C2×D4×C3114yes—
428C22×C4C2×D4×C3111yescharacteristic
429C22×C4C2×D4×C3111yescharacteristic
430C22×C4C2×D4×C3111yescharacteristic
431C22×C4C24×C3111yescharacteristic
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4C2×D4×C3114yes—
449C4⋊C4#41×C3112yescomplemented
450C4⋊C4#41×C3112yescomplemented
451C22⋊C4—24no—
452C22⋊C4—28no—
453C22⋊C4—28no—
454C22⋊C4—42no—
455C42—24no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—42no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—24no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23C31×#12012yes—
475C23C22×D4×C3111yescharacteristic
476Q8—48no—
477D4—24no—
478D4—24no—
479D4—48no—
480D4—48no—
481D4—416no—
482D4—42no—
483D4—42no—
484C2×C4—28no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—44no—
502C2×C4—416no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4C31×#12012yes—
516C2×C4C31×#13512yes—
517C2×C4C31×AGL(1,ℤ/8)12yes—
518C2×C4C31×AGL(1,ℤ/8)12yes—
519C2×C4C22×D4×C3112yes—
520C2×C4C2×#41×C3111yescharacteristic
521C2×C4C2×#41×C3111yescharacteristic
522C2×C4C31×2−1+412yes—
523C8—42no—
524C8—42no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—44no—
534C22—44no—
535C22—82no—
536C22—82no—
537C22—82no—
538C22—82no—
539C22C2×C31×#12011yescharacteristic
540C22C31×#52511yescharacteristic
541C22C31×#53611yescharacteristic
542C22C2×C31×#13511yescharacteristic
543C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
544C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
545C22C31×#57511yescharacteristic
546C4—22no—
547C4—22no—
548C4—22no—
549C4—22no—
550C4—42no—
551C4—42no—
552C4—41no—
553C4—44no—
554C4—81no—
555C4—81no—
556C4C31×#54712yes—
557C4C31×#54712yes—
558C2—42no—
559C2—84no—
560C2C31×#240611yescharacteristic
561C2C31×#300211yescharacteristic
562C2C31×#300311yescharacteristic
563C2C31×#310611yescharacteristic
564C2C31×#311511yescharacteristic
565C2C31×#322811yescharacteristic
566C2C31×#323511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#532C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#482C2semidirect
3. C31×#2296C2semidirect
4. C31×#2058C2semidirect
5. C31×#2057C2semidirect
6. C31×#2041C2semidirect
7. C31×#2041C2semidirect
8. C31×#1875C2semidirect
9. C31×#1864C2semidirect
10. C31×#1862C2semidirect
11. C31×#1817C2semidirect
165. C4⋊C4×C31#41semidirect
166. C4⋊C4×C31#41semidirect
177. #24062C31direct (N × H)
243. C2×#482C2×C31semidirect
244. #2296C2×C31semidirect
245. #2058C2×C31semidirect
246. #2057C2×C31semidirect
247. #2041C2×C31semidirect
248. #2041C2×C31semidirect
249. #1875C2×C31semidirect
250. #1864C2×C31semidirect
251. #1862C2×C31semidirect
252. #1817C2×C31semidirect
386. C31#24062direct (N × H)
449. C4⋊C4#41×C31semidirect
450. C4⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5322
C2×C31×#4822
C31×#22962
C31×#20582
C31×#20572
C31×#20412
C31×#18752
C31×#18642
C31×#18622
C31×#18172
#2406231