Finite Group Databasebeta

← C31×#15083 #21471842

Subgroups — C31×#15083 #21471842

Order 7936.

1282 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#387C212yesmaximal
2C2×C31×#387C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
4C31×#1445C211yesmaximal, characteristic
5C31×#1445C211yesmaximal, characteristic
6C31×#1444C211yesmaximal, characteristic
7C31×#1442C211yesmaximal, characteristic
8C31×#1441C212yesmaximal
9C31×#1441C212yesmaximal
10C31×C4⋊#95C211yesmaximal, characteristic
11C31×#1434C212yesmaximal
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2212yes—
14C22×C4⋊C4×C31C2211yescharacteristic
15C22×C4⋊C4×C31C2212yes—
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C42×C31C2212yes—
19C22×C42×C31C2211yescharacteristic
20C31×#387—28no—
21C31×#387—24no—
22C4×C4⋊C4×C31—24no—
23C2×C31×#95C2211yescharacteristic
24C2×C31×#95C2212yes—
25C2×C31×#95C2212yes—
26C2×C31×#95C2212yes—
27C2×C31×#95C2211yescharacteristic
28C2×C31×#95C2211yescharacteristic
29C2×C31×#95C2212yes—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C23×C4×C31C2312yes—
39C23×C4×C31C2311yescharacteristic
40C23×C4×C31C2311yescharacteristic
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2311yescharacteristic
43C23×C4×C31C2312yes—
44C23×C4×C31C2312yes—
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C2×C4⋊C4×C31—22no—
50C2×C4⋊C4×C31—22no—
51C2×C4⋊C4×C31—24no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—24no—
54C2×C4⋊C4×C31—24no—
55C2×C4⋊C4×C31—24no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—24no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—42no—
63C2×C4⋊C4×C31D414yes—
64C2×C4⋊C4×C31Q814yes—
65C2×C42×C31—24no—
66C2×C42×C31—24no—
67C2×C42×C31—24no—
68C2×C42×C31—24no—
69C2×C42×C31D414yes—
70C31×#95—24no—
71C31×#95—24no—
72C31×#95—24no—
73C31×#95—24no—
74C31×#95—22no—
75C31×#95—22no—
76C31×#95—24no—
77C31×#95—22no—
78C31×#95—22no—
79C31×#95—22no—
80C31×#95—24no—
81C31×#95—24no—
82C31×#95—22no—
83C31×#95—42no—
84C31×#95—42no—
85C24×C31C2411yescharacteristic
86C22×C4×C31—22no—
87C22×C4×C31—22no—
88C22×C4×C31—22no—
89C22×C4×C31—22no—
90C22×C4×C31—21no—
91C22×C4×C31—22no—
92C22×C4×C31—21no—
93C22×C4×C31—22no—
94C22×C4×C31—21no—
95C22×C4×C31—22no—
96C22×C4×C31—22no—
97C22×C4×C31—22no—
98C22×C4×C31—22no—
99C22×C4×C31—21no—
100C22×C4×C31—22no—
101C22×C4×C31—22no—
102C22×C4×C31—22no—
103C22×C4×C31—22no—
104C22×C4×C31—21no—
105C22×C4×C31—21no—
106C22×C4×C31—22no—
107C22×C4×C31—22no—
108C22×C4×C31—22no—
109C22×C4×C31—22no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—22no—
113C22×C4×C31—22no—
114C22×C4×C31—22no—
115C22×C4×C31—22no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—22no—
119C22×C4×C31—21no—
120C22×C4×C31—22no—
121C22×C4×C31—21no—
122C22×C4×C31—22no—
123C22×C4×C31—22no—
124C22×C4×C31—22no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—22no—
136C22×C4×C31C2×D412yes—
137C22×C4×C31C2×D412yes—
138C22×C4×C31C2×D412yes—
139C22×C4×C31C2×D412yes—
140C22×C4×C31C2×D412yes—
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×Q814yes—
143C22×C4×C31C2×Q812yes—
144C22×C4×C31#4114yes—
145C22×C4×C31#4114yes—
146C22×C4×C31#4112yes—
147C22×C4×C31#4112yes—
148C22×C4×C31#4114yes—
149C4⋊C4×C31—28no—
150C4⋊C4×C31—216no—
151C4⋊C4×C31—28no—
152C4⋊C4×C31—28no—
153C4⋊C4×C31—48no—
154C4⋊C4×C31—44no—
155C42×C31—28no—
156C42×C31—48no—
157#15083C3111yesmaximal, characteristic, direct product factor, Sylow
158C23×C31C22×D411yescharacteristic
159C23×C31C22×D411yescharacteristic
160C23×C31C22×Q811yescharacteristic
161C23×C31C2×#4111yescharacteristic
162C23×C31C2×#4111yescharacteristic
163C23×C31C2×#4112yes—
164C23×C31C2×#4112yes—
165C23×C31C2×#4112yes—
166C23×C31H(5,𝔽2)11yescharacteristic
167C23×C312−1+412yes—
168C23×C312−1+411yescharacteristic
169C2×C4×C31—22no—
170C2×C4×C31—22no—
171C2×C4×C31—22no—
172C2×C4×C31—24no—
173C2×C4×C31—22no—
174C2×C4×C31—24no—
175C2×C4×C31—22no—
176C2×C4×C31—22no—
177C2×C4×C31—24no—
178C2×C4×C31—24no—
179C2×C4×C31—24no—
180C2×C4×C31—24no—
181C2×C4×C31—22no—
182C2×C4×C31—22no—
183C2×C4×C31—24no—
184C2×C4×C31—24no—
185C2×C4×C31—24no—
186C2×C4×C31—24no—
187C2×C4×C31—24no—
188C2×C4×C31—24no—
189C2×C4×C31—24no—
190C2×C4×C31—24no—
191C2×C4×C31—24no—
192C2×C4×C31—24no—
193C2×C4×C31—24no—
194C2×C4×C31—42no—
195C2×C4×C31—42no—
196C2×C4×C31—41no—
197C2×C4×C31—41no—
198C2×C4×C31—42no—
199C2×C4×C31—42no—
200C2×C4×C31—42no—
201C2×C4×C31—42no—
202C2×C4×C31—41no—
203C2×C4×C31—42no—
204C2×C4×C31—41no—
205C2×C4×C31—42no—
206C2×C4×C31—42no—
207C2×C4×C31—42no—
208C2×C4×C31—42no—
209C2×C4×C31—42no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—41no—
213C2×C4×C31—41no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—41no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—41no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
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#12114yes—
230C2×C4×C31C22⋊Q814yes—
231C2×C4×C31#12314yes—
232C2×#387C2×C3111yescharacteristic
233C2×#387C2×C3112yes—
234C2×C4×C4⋊C4C2×C3111yescharacteristic
235#1445C2×C3111yescharacteristic
236#1445C2×C3111yescharacteristic
237#1444C2×C3111yescharacteristic
238#1442C2×C3111yescharacteristic
239#1441C2×C3112yes—
240#1441C2×C3112yes—
241C4⋊#95C2×C3111yescharacteristic
242#1434C2×C3112yes—
243C22×C31C2×#12111yescharacteristic
244C22×C31C2×C22⋊Q811yescharacteristic
245C22×C31C2×#12311yescharacteristic
246C22×C31#52511yescharacteristic
247C22×C31#52512yes—
248C22×C31#52912yes—
249C22×C31#52912yes—
250C22×C31#53211yescharacteristic
251C22×C31#53312yes—
252C22×C31#53611yescharacteristic
253C22×C31#53711yescharacteristic
254C22×C31#54112yes—
255C22×C31#54212yes—
256C22×C31#54712yes—
257C22×C31D4×Q811yescharacteristic
258C22×C31#55011yescharacteristic
259C22×C31#55112yes—
260C22×C31#55212yes—
261C22×C31#55212yes—
262C22×C31#55212yes—
263C22×C31#55411yescharacteristic
264C22×C31#55611yescharacteristic
265C22×C31#55712yes—
266C4×C31—24no—
267C4×C31—24no—
268C4×C31—24no—
269C4×C31—42no—
270C4×C31—44no—
271C4×C31—44no—
272C4×C31—42no—
273C4×C31—44no—
274C4×C31—81no—
275C4×C31—82no—
276C4×C31—81no—
277C22×C4⋊C4C22×C3111yescharacteristic
278C22×C4⋊C4C22×C3112yes—
279C22×C4⋊C4C22×C3111yescharacteristic
280C22×C4⋊C4C22×C3112yes—
281C22×C4⋊C4C22×C3111yescharacteristic
282C22×C4⋊C4C22×C3111yescharacteristic
283C22×C42C22×C3112yes—
284C22×C42C22×C3111yescharacteristic
285#387—28no—
286#387—24no—
287C4×C4⋊C4—24no—
288C2×#95C22×C3111yescharacteristic
289C2×#95C22×C3112yes—
290C2×#95C22×C3112yes—
291C2×#95C22×C3112yes—
292C2×#95C22×C3111yescharacteristic
293C2×#95C22×C3111yescharacteristic
294C2×#95C22×C3112yes—
295C2×#95C22×C3111yescharacteristic
296C2×#95C22×C3112yes—
297C2×#95C22×C3112yes—
298C2×#95C22×C3112yes—
299C2×#95C22×C3111yescharacteristic
300C2×#95C22×C3111yescharacteristic
301C2×#95C22×C3112yes—
302C2×#95C22×C3112yes—
303C2×C31#239211yescharacteristic
304C2×C31#246212yes—
305C2×C31#247912yes—
306C2×C31#248611yescharacteristic
307C2×C31#249811yescharacteristic
308C2×C31#252012yes—
309C2×C31#253312yes—
310C2×C31#253811yescharacteristic
311C2×C31#256511yescharacteristic
312C2×C31#263711yescharacteristic
313C2×C31#285511yescharacteristic
314C23×C4C23×C3112yes—
315C23×C4C23×C3111yescharacteristic
316C23×C4C23×C3111yescharacteristic
317C23×C4C23×C3111yescharacteristic
318C23×C4C23×C3111yescharacteristic
319C23×C4C23×C3112yes—
320C23×C4C23×C3112yes—
321C23×C4C23×C3112yes—
322C23×C4C23×C3111yescharacteristic
323C23×C4C23×C3111yescharacteristic
324C23×C4C23×C3111yescharacteristic
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4D4×C3114yes—
340C2×C4⋊C4Q8×C3114yes—
341C2×C42—24no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42D4×C3114yes—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—22no—
351#95—22no—
352#95—24no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—24no—
357#95—24no—
358#95—22no—
359#95—42no—
360#95—42no—
361C31#1508311yescharacteristic, direct product factor, Sylow
362C24C24×C3111yescharacteristic
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3112yes—
415C22×C4C2×D4×C3112yes—
416C22×C4C2×D4×C3112yes—
417C22×C4C2×D4×C3112yes—
418C22×C4C2×D4×C3112yes—
419C22×C4C2×Q8×C3114yes—
420C22×C4C2×Q8×C3112yes—
421C22×C4#41×C3114yes—
422C22×C4#41×C3114yes—
423C22×C4#41×C3112yes—
424C22×C4#41×C3112yes—
425C22×C4#41×C3114yes—
426C4⋊C4—28no—
427C4⋊C4—216no—
428C4⋊C4—28no—
429C4⋊C4—28no—
430C4⋊C4—48no—
431C4⋊C4—44no—
432C42—28no—
433C42—48no—
434C23C22×D4×C3111yescharacteristic
435C23C22×D4×C3111yescharacteristic
436C23C22×Q8×C3111yescharacteristic
437C23C2×#41×C3111yescharacteristic
438C23C2×#41×C3111yescharacteristic
439C23C2×#41×C3112yes—
440C23C2×#41×C3112yes—
441C23C2×#41×C3112yes—
442C23C31×H(5,𝔽2)11yescharacteristic
443C23C31×2−1+412yes—
444C23C31×2−1+411yescharacteristic
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4C31×#12114yes—
506C2×C4C31×C22⋊Q814yes—
507C2×C4C31×#12314yes—
508C22C2×C31×#12111yescharacteristic
509C22C2×C31×C22⋊Q811yescharacteristic
510C22C2×C31×#12311yescharacteristic
511C22C31×#52511yescharacteristic
512C22C31×#52512yes—
513C22C31×#52912yes—
514C22C31×#52912yes—
515C22C31×#53211yescharacteristic
516C22C31×#53312yes—
517C22C31×#53611yescharacteristic
518C22C31×#53711yescharacteristic
519C22C31×#54112yes—
520C22C31×#54212yes—
521C22C31×#54712yes—
522C22D4×Q8×C3111yescharacteristic
523C22C31×#55011yescharacteristic
524C22C31×#55112yes—
525C22C31×#55212yes—
526C22C31×#55212yes—
527C22C31×#55212yes—
528C22C31×#55411yescharacteristic
529C22C31×#55611yescharacteristic
530C22C31×#55712yes—
531C4—24no—
532C4—24no—
533C4—24no—
534C4—42no—
535C4—44no—
536C4—44no—
537C4—42no—
538C4—44no—
539C4—81no—
540C4—82no—
541C4—81no—
542C2C31×#239211yescharacteristic
543C2C31×#246212yes—
544C2C31×#247912yes—
545C2C31×#248611yescharacteristic
546C2C31×#249811yescharacteristic
547C2C31×#252012yes—
548C2C31×#253312yes—
549C2C31×#253811yescharacteristic
550C2C31×#256511yescharacteristic
551C2C31×#263711yescharacteristic
552C2C31×#285511yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
157. #15083C31direct (N × H)
361. C31#15083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C2×C4×C4⋊C4×C312
C31×#14452
C31×#14442
C31×#14422
C31×#14412
C31×C4⋊#952
C31×#14342
#1508331