Finite Group Databasebeta

← C31×#25947 #21482706

Subgroups — C31×#25947 #21482706

Order 7936.

1490 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3501C211yesmaximal, characteristic, complemented
2C31×#2435C212yesmaximal, complemented
3C31×#2408C211yesmaximal, characteristic
4C31×#2029C214yesmaximal, complemented
5C31×#1996C212yesmaximal, complemented
6C31×#1889C214yesmaximal, complemented
7C4×C31×#99C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C31×#554—22no—
10C31×#554—24no—
11D4×Q8×C31—22no—
12C31×#544—21no—
13C31×#543—21no—
14C31×#543C2212yes—
15C31×#533—21no—
16C2×C31×#124—22no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×#121—21no—
20C2×C31×#120C2212yes—
21C31×#518C2212yes—
22C2×C4×D4×C31C2211yescharacteristic
23C2×C31×#99C2212yes—
24C31×#394—21no—
25C31×#394—24no—
26C31×#392—21no—
27C31×#390—22no—
28C31×#390—21no—
29C31×#380C2211yescharacteristic
30C31×#379C2218yes—
31C31×#379C2212yes—
32C4×C22⋊C4×C31C2212yes—
33C31×#342C2218yes—
34C31×#342C2212yes—
35C25×C31C2312yes—
36C22×Q8×C31—21no—
37C22×Q8×C31D412yescomplemented
38C22×D4×C31—22no—
39C22×D4×C31—21no—
40C22×D4×C31—22no—
41C22×D4×C31—21no—
42C22×D4×C31—22no—
43C22×D4×C31—44no—
44C22×D4×C31C2311yescharacteristic
45C23×C4×C31D411yescharacteristic
46C23×C4×C31C2311yescharacteristic
47C31×C4⋊Q8—21no—
48C31×C4⋊Q8—21no—
49C31×C4⋊Q8—24no—
50C31×#125—22no—
51C31×#125—24no—
52C31×#124—48no—
53C31×C22⋊Q8—22no—
54C31×C22⋊Q8—22no—
55C31×C22⋊Q8—24no—
56C31×C22⋊Q8—24no—
57C31×C22⋊Q8—22no—
58C31×C22⋊Q8—22no—
59C31×C22⋊Q8—22no—
60C31×C22⋊Q8—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—24no—
64C31×C22⋊Q8—24no—
65C31×#121—44no—
66C31×#120—28no—
67C4×Q8×C31—22no—
68C4×Q8×C31—22no—
69C4×D4×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31—24no—
72C4×D4×C31—24no—
73C31×#117—22no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31D411yescharacteristic
78C2×C4⋊C4×C31D412yescomplemented
79C2×C4⋊C4×C31D414yescomplemented
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—22no—
83C2×C22⋊C4×C31—28no—
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—28no—
86C2×C22⋊C4×C31D411yescharacteristic
87C2×C22⋊C4×C31C2314yes—
88C2×C22⋊C4×C31C2312yes—
89C2×C22⋊C4×C31C2311yescharacteristic
90C2×C22⋊C4×C31C2314yes—
91C2×C42×C31—22no—
92C2×C42×C31D411yescharacteristic
93C31×#99—24no—
94C31×#95—22no—
95C31×#95—21no—
96C24×C31—24no—
97C24×C31—22no—
98C24×C31—24no—
99C24×C31—24no—
100C24×C31—44no—
101C24×C31—82no—
102C24×C31C2×D411yescharacteristic
103C24×C31C2411yescharacteristic
104C2×Q8×C31—22no—
105C2×Q8×C31—22no—
106C2×Q8×C31—22no—
107C2×Q8×C31—22no—
108C2×Q8×C31—44no—
109C2×Q8×C31—82no—
110C2×D4×C31—22no—
111C2×D4×C31—22no—
112C2×D4×C31—24no—
113C2×D4×C31—28no—
114C2×D4×C31—44no—
115C2×D4×C31—42no—
116C2×D4×C31—48no—
117C2×D4×C31—44no—
118C2×D4×C31—44no—
119C2×D4×C31—44no—
120C2×D4×C31—41no—
121C2×D4×C31—42no—
122C2×D4×C31—41no—
123C2×D4×C31—82no—
124C2×D4×C31#4114yes—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—24no—
130C22×C4×C31—22no—
131C22×C4×C31—42no—
132C22×C4×C31—42no—
133C22×C4×C31C2×D412yes—
134C22×C4×C31C2×D411yescharacteristic
135C22×C4×C31C2×D411yescharacteristic
136C22×C4×C31C2×D411yescharacteristic
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D414yes—
139C22×C4×C31C2×D414yes—
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2×D412yes—
142C4⋊C4×C31—22no—
143C4⋊C4×C31—24no—
144C4⋊C4×C31—22no—
145C4⋊C4×C31—22no—
146C4⋊C4×C31—24no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—24no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—22no—
151C4⋊C4×C31—22no—
152C4⋊C4×C31—24no—
153C4⋊C4×C31—42no—
154C22⋊C4×C31—24no—
155C22⋊C4×C31—24no—
156C22⋊C4×C31—22no—
157C22⋊C4×C31—24no—
158C22⋊C4×C31—22no—
159C22⋊C4×C31—24no—
160C22⋊C4×C31—24no—
161C22⋊C4×C31—24no—
162C22⋊C4×C31—44no—
163C22⋊C4×C31—416no—
164C22⋊C4×C31—44no—
165C22⋊C4×C31—88no—
166C22⋊C4×C31—82no—
167C42×C31—24no—
168C42×C31—21no—
169C42×C31—21no—
170C42×C31—44no—
171#25947C3111yesmaximal, characteristic, direct product factor, Sylow
172C23×C31—21no—
173C23×C31—21no—
174C23×C31—28no—
175C23×C31—24no—
176C23×C31—41no—
177C23×C31—41no—
178C23×C31—41no—
179C23×C31—41no—
180C23×C31—48no—
181C23×C31—42no—
182C23×C31—44no—
183C23×C31—42no—
184C23×C31—42no—
185C23×C31—42no—
186C23×C31—42no—
187C23×C31—42no—
188C23×C31—48no—
189C23×C31—88no—
190C23×C31—88no—
191C23×C31#12412yescomplemented
192C23×C31C22×D411yescharacteristic
193C23×C31C22×D412yes—
194C23×C31C2×#4112yes—
195C23×C312−1+412yes—
196Q8×C31—44no—
197Q8×C31—82no—
198Q8×C31—82no—
199Q8×C31—82no—
200D4×C31—28no—
201D4×C31—44no—
202D4×C31—48no—
203D4×C31—44no—
204D4×C31—88no—
205C2×C4×C31—21no—
206C2×C4×C31—21no—
207C2×C4×C31—24no—
208C2×C4×C31—22no—
209C2×C4×C31—21no—
210C2×C4×C31—24no—
211C2×C4×C31—24no—
212C2×C4×C31—21no—
213C2×C4×C31—42no—
214C2×C4×C31—41no—
215C2×C4×C31—42no—
216C2×C4×C31—41no—
217C2×C4×C31—44no—
218C2×C4×C31—44no—
219C2×C4×C31—41no—
220C2×C4×C31—44no—
221C2×C4×C31—42no—
222C2×C4×C31—44no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—44no—
226C2×C4×C31—81no—
227C2×C4×C31—82no—
228C2×C4×C31—82no—
229C2×C4×C31#12011yescharacteristic
230C2×C4×C31#12012yes—
231C2×C4×C31#12011yescharacteristic
232C2×C4×C31#12412yescomplemented
233#3501C2×C3111yescharacteristic, complemented
234#2435C2×C3112yescomplemented
235#2408C2×C3111yescharacteristic
236#2029C2×C3114yescomplemented
237#1996C2×C3112yescomplemented
238#1889C2×C3114yescomplemented
239C4×#99C2×C3111yescharacteristic, complemented
240C22×C31—22no—
241C22×C31—21no—
242C22×C31—22no—
243C22×C31—21no—
244C22×C31—22no—
245C22×C31—42no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31—44no—
249C22×C31—416no—
250C22×C31—44no—
251C22×C31—41no—
252C22×C31—41no—
253C22×C31—44no—
254C22×C31—81no—
255C22×C31—82no—
256C22×C31—88no—
257C22×C31—82no—
258C22×C31—82no—
259C22×C31—82no—
260C22×C31C2×#12011yescharacteristic
261C22×C31C2×#12411yescharacteristic
262C22×C31#53611yescharacteristic
263C22×C31#54814yes—
264C4×C31—22no—
265C4×C31—21no—
266C4×C31—22no—
267C4×C31—41no—
268C4×C31—44no—
269C4×C31—44no—
270C4×C31—41no—
271C4×C31—84no—
272C4×C31—82no—
273C4×C31B(4,𝔽2)12yes—
274C23×D4C22×C3111yescharacteristic
275#554—22no—
276#554—24no—
277D4×Q8—22no—
278#544—21no—
279#543—21no—
280#543C22×C3112yes—
281#533—21no—
282C2×#124—22no—
283C2×C22⋊Q8—21no—
284C2×C22⋊Q8C22×C3112yes—
285C2×#121—21no—
286C2×#120C22×C3112yes—
287#518C22×C3112yes—
288C2×C4×D4C22×C3111yescharacteristic
289C2×#99C22×C3112yes—
290#394—21no—
291#394—24no—
292#392—21no—
293#390—22no—
294#390—21no—
295#380C22×C3111yescharacteristic
296#379C22×C3118yes—
297#379C22×C3112yes—
298C4×C22⋊C4C22×C3112yes—
299#342C22×C3118yes—
300#342C22×C3112yes—
301C2×C31—21no—
302C2×C31—24no—
303C2×C31—21no—
304C2×C31—42no—
305C2×C31—84no—
306C2×C31#243611yescharacteristic
307C2×C31C2×B(4,𝔽2)11yescharacteristic
308C2×C31#302711yescharacteristic
309C25C23×C3112yes—
310C22×Q8—21no—
311C22×Q8D4×C3112yescomplemented
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—22no—
317C22×D4—44no—
318C22×D4C23×C3111yescharacteristic
319C23×C4D4×C3111yescharacteristic
320C23×C4C23×C3111yescharacteristic
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—24no—
324#125—22no—
325#125—24no—
326#124—48no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—24no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—24no—
338C22⋊Q8—24no—
339#121—44no—
340#120—28no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—24no—
346C4×D4—24no—
347#117—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4D4×C3111yescharacteristic
352C2×C4⋊C4D4×C3112yescomplemented
353C2×C4⋊C4D4×C3114yescomplemented
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4D4×C3111yescharacteristic
361C2×C22⋊C4C23×C3112yes—
362C2×C22⋊C4C23×C3114yes—
363C2×C22⋊C4C23×C3111yescharacteristic
364C2×C22⋊C4C23×C3114yes—
365C2×C42—22no—
366C2×C42D4×C3111yescharacteristic
367#99—24no—
368#95—22no—
369#95—21no—
370C31#2594711yescharacteristic, direct product factor, Sylow
371C24—24no—
372C24—22no—
373C24—24no—
374C24—24no—
375C24—44no—
376C24—82no—
377C24C2×D4×C3111yescharacteristic
378C24C24×C3111yescharacteristic
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—44no—
384C2×Q8—82no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—28no—
389C2×D4—44no—
390C2×D4—42no—
391C2×D4—48no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—82no—
399C2×D4#41×C3114yes—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4C2×D4×C3112yes—
409C22×C4C2×D4×C3111yescharacteristic
410C22×C4C2×D4×C3111yescharacteristic
411C22×C4C2×D4×C3111yescharacteristic
412C22×C4C2×D4×C3111yescharacteristic
413C22×C4C2×D4×C3114yes—
414C22×C4C2×D4×C3114yes—
415C22×C4C2×D4×C3111yescharacteristic
416C22×C4C2×D4×C3112yes—
417C4⋊C4—22no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—24no—
422C4⋊C4—22no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—24no—
428C4⋊C4—42no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—22no—
432C22⋊C4—24no—
433C22⋊C4—22no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—44no—
438C22⋊C4—416no—
439C22⋊C4—44no—
440C22⋊C4—88no—
441C22⋊C4—82no—
442C42—24no—
443C42—21no—
444C42—21no—
445C42—44no—
446C23—21no—
447C23—21no—
448C23—28no—
449C23—24no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—48no—
455C23—42no—
456C23—44no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—48no—
463C23—88no—
464C23—88no—
465C23C31×#12412yescomplemented
466C23C22×D4×C3111yescharacteristic
467C23C22×D4×C3112yes—
468C23C2×#41×C3112yes—
469C23C31×2−1+412yes—
470Q8—44no—
471Q8—82no—
472Q8—82no—
473Q8—82no—
474D4—28no—
475D4—44no—
476D4—48no—
477D4—44no—
478D4—88no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—21no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4C31×#12011yescharacteristic
504C2×C4C31×#12012yes—
505C2×C4C31×#12011yescharacteristic
506C2×C4C31×#12412yescomplemented
507C22—22no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—22no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—44no—
516C22—416no—
517C22—44no—
518C22—41no—
519C22—41no—
520C22—44no—
521C22—81no—
522C22—82no—
523C22—88no—
524C22—82no—
525C22—82no—
526C22—82no—
527C22C2×C31×#12011yescharacteristic
528C22C2×C31×#12411yescharacteristic
529C22C31×#53611yescharacteristic
530C22C31×#54814yes—
531C4—22no—
532C4—21no—
533C4—22no—
534C4—41no—
535C4—44no—
536C4—44no—
537C4—41no—
538C4—82no—
539C4—84no—
540C4C31×B(4,𝔽2)12yes—
541C2—21no—
542C2—24no—
543C2—21no—
544C2—42no—
545C2—84no—
546C2C31×#243611yescharacteristic
547C2C2×C31×B(4,𝔽2)11yescharacteristic
548C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#2408C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3501C2semidirect
2. C31×#2435C2semidirect
4. C31×#2029C2semidirect
5. C31×#1996C2semidirect
6. C31×#1889C2semidirect
7. C4×C31×#99C2semidirect
37. C22×Q8×C31D4semidirect
78. C2×C4⋊C4×C31D4semidirect
79. C2×C4⋊C4×C31D4semidirect
171. #25947C31direct (N × H)
191. C23×C31#124semidirect
232. C2×C4×C31#124semidirect
233. #3501C2×C31semidirect
234. #2435C2×C31semidirect
236. #2029C2×C31semidirect
237. #1996C2×C31semidirect
238. #1889C2×C31semidirect
239. C4×#99C2×C31semidirect
311. C22×Q8D4×C31semidirect
352. C2×C4⋊C4D4×C31semidirect
353. C2×C4⋊C4D4×C31semidirect
370. C31#25947direct (N × H)
465. C23C31×#124semidirect
506. C2×C4C31×#124semidirect

Maximal subgroups

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

subgroupindex
C31×#35012
C31×#24352
C31×#24082
C31×#20292
C31×#19962
C31×#18892
C4×C31×#992
#2594731