Finite Group Databasebeta

← C31×#25892 #21482651

Subgroups — C31×#25892 #21482651

Order 7936.

1292 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#547C211yesmaximal, characteristic
2C2×C31×#491C211yesmaximal, characteristic, complemented
3C2×C31×#478C211yesmaximal, characteristic, complemented
4C31×#2562C211yesmaximal, characteristic, complemented
5C31×#2036C212yesmaximal, complemented
6C31×#2035C212yesmaximal, complemented
7C31×#1981C211yesmaximal, characteristic, complemented
8C31×#1955C211yesmaximal, characteristic, complemented
9C31×#1788C212yesmaximal, complemented
10C31×#1788C212yesmaximal, complemented
11C31×#1762C211yesmaximal, characteristic, complemented
12C22×#41×C31C2212yes—
13C31×#547—24no—
14C31×#547—24no—
15C2×C31×C4⋊Q8C2211yescharacteristic
16C2×C31×#125C2211yescharacteristic
17C2×C31×#123—22no—
18C2×C31×C22⋊Q8C2212yes—
19C2×C31×#121—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C22×C4⋊C4×C31—21no—
23C31×#491—24no—
24C31×#478—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#106C2211yescharacteristic
27C2×C31×C4⋊C8C2211yescharacteristic
28C2×C31×#103C2212yes—
29C2×C31×#103C2212yes—
30C2×C31×#103C2212yes—
31C2×C31×#103C2212yes—
32C2×C31×#102C2212yes—
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×C22⋊C8C2212yes—
36C2×C31×C22⋊C8C2212yes—
37C2×C31×#97C2211yescharacteristic
38C31×#400—21no—
39C31×#394—21no—
40C31×#388—22no—
41C31×#380C2212yes—
42C31×#380C2212yes—
43C4×C4⋊C4×C31C2211yescharacteristic
44C31×#340C2212yes—
45C2×#41×C31—24no—
46C2×#41×C31—24no—
47C2×#41×C31—24no—
48C2×#41×C31—24no—
49C2×#41×C31—42no—
50C2×#41×C31—42no—
51C22×Q8×C31C2312yes—
52C22×D4×C31—22no—
53C22×D4×C31D411yescharacteristic
54C22×D4×C31C2311yescharacteristic
55C23×C4×C31—21no—
56C23×C4×C31—22no—
57C23×C4×C31C2312yes—
58C22×C8×C31C2312yes—
59C22×C8×C31C2311yescharacteristic
60C22×C8×C31C2311yescharacteristic
61C31×C4⋊Q8—22no—
62C31×C4⋊Q8D414yes—
63C31×#125—22no—
64C31×#125—22no—
65C31×#123—216no—
66C31×C22⋊Q8—24no—
67C31×C22⋊Q8—24no—
68C31×#121—28no—
69C4×D4×C31—22no—
70C4×D4×C31—22no—
71C4×D4×C31—22no—
72C4×D4×C31D414yes—
73C2×C4⋊C4×C31—28no—
74C2×C4⋊C4×C31—21no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—21no—
77C2×C4⋊C4×C31—21no—
78C2×C4⋊C4×C31—21no—
79C2×C4⋊C4×C31D411yescharacteristic
80C2×C4⋊C4×C31C2311yescharacteristic
81C2×C4⋊C4×C31C2311yescharacteristic
82C2×C4⋊C4×C31C2312yes—
83C2×C4⋊C4×C31C2311yescharacteristic
84C2×C22⋊C4×C31—22no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31D412yes—
89C2×C42×C31—21no—
90C2×C42×C31C2311yescharacteristic
91C31×#107—22no—
92C31×#106—22no—
93C31×C4⋊C8—22no—
94C31×#103—24no—
95C31×#103—24no—
96C31×#103—42no—
97C31×#103—42no—
98C31×#102—22no—
99C31×#102—22no—
100C31×#102—24no—
101C31×C22⋊C8—42no—
102C31×C22⋊C8—42no—
103C31×#97—22no—
104C31×#95—21no—
105C31×#95—22no—
106C31×#95—22no—
107C24×C31—21no—
108C24×C31C2×D412yes—
109#41×C31—48no—
110#41×C31—48no—
111#41×C31—48no—
112#41×C31—48no—
113C2×Q8×C31—22no—
114C2×Q8×C31—22no—
115C2×Q8×C31—22no—
116C2×Q8×C31—22no—
117C2×Q8×C31—22no—
118C2×Q8×C31C2×D414yes—
119C2×D4×C31—28no—
120C2×D4×C31—22no—
121C2×D4×C31—21no—
122C2×D4×C31—22no—
123C2×D4×C31—42no—
124C2×D4×C31—44no—
125C2×D4×C31—44no—
126C2×D4×C31C2×D412yes—
127C2×D4×C31#4114yes—
128C22×C4×C31—28no—
129C22×C4×C31—21no—
130C22×C4×C31—22no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—22no—
134C22×C4×C31—22no—
135C22×C4×C31—22no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—44no—
142C22×C4×C31—44no—
143C22×C4×C31—44no—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2×D411yescharacteristic
146C22×C4×C31C2×D411yescharacteristic
147C22×C4×C31C2411yescharacteristic
148C2×C8×C31—22no—
149C2×C8×C31—21no—
150C2×C8×C31—21no—
151C2×C8×C31—22no—
152C2×C8×C31—22no—
153C2×C8×C31—22no—
154C2×C8×C31—22no—
155C4⋊C4×C31—28no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—24no—
158C4⋊C4×C31—24no—
159C4⋊C4×C31—21no—
160C4⋊C4×C31—21no—
161C4⋊C4×C31—21no—
162C4⋊C4×C31—21no—
163C4⋊C4×C31—21no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—42no—
167C4⋊C4×C31—42no—
168C4⋊C4×C31C2×D412yes—
169C22⋊C4×C31—28no—
170C22⋊C4×C31—24no—
171C22⋊C4×C31—24no—
172C22⋊C4×C31—44no—
173C22⋊C4×C31—82no—
174C42×C31—81no—
175C42×C31C2×D412yes—
176C42×C31C2×D412yes—
177#25892C3111yesmaximal, characteristic, direct product factor, Sylow
178C23×C31—22no—
179C23×C31—24no—
180C23×C31—22no—
181C23×C31—22no—
182C23×C31—22no—
183C23×C31—22no—
184C23×C31—22no—
185C23×C31—22no—
186C23×C31—22no—
187C23×C31—42no—
188C23×C31—41no—
189C23×C31—41no—
190C23×C31C22×D411yescharacteristic
191Q8×C31—24no—
192Q8×C31—24no—
193Q8×C31—42no—
194Q8×C31—42no—
195D4×C31—22no—
196D4×C31—24no—
197D4×C31—44no—
198D4×C31—416no—
199D4×C31#12414yes—
200C2×C4×C31—22no—
201C2×C4×C31—21no—
202C2×C4×C31—21no—
203C2×C4×C31—22no—
204C2×C4×C31—22no—
205C2×C4×C31—24no—
206C2×C4×C31—22no—
207C2×C4×C31—22no—
208C2×C4×C31—48no—
209C2×C4×C31—416no—
210C2×C4×C31—42no—
211C2×C4×C31—42no—
212C2×C4×C31—42no—
213C2×C4×C31—42no—
214C2×C4×C31—42no—
215C2×C4×C31—42no—
216C2×C4×C31—42no—
217C2×C4×C31—41no—
218C2×C4×C31—41no—
219C2×C4×C31—42no—
220C2×C4×C31—42no—
221C2×C4×C31—42no—
222C2×C4×C31—42no—
223C2×C4×C31—41no—
224C2×C4×C31—41no—
225C2×C4×C31#12012yes—
226C2×C4×C31#12012yes—
227C2×C4×C31C22×D411yescharacteristic
228C2×C4×C31C22×D411yescharacteristic
229C2×C4×C31C2×#4112yes—
230C2×C4×C31H(5,𝔽2)12yes—
231C8×C31—41no—
232C8×C31—41no—
233C8×C31—42no—
234C2×#547C2×C3111yescharacteristic
235C2×#491C2×C3111yescharacteristic, complemented
236C2×#478C2×C3111yescharacteristic, complemented
237#2562C2×C3111yescharacteristic, complemented
238#2036C2×C3112yescomplemented
239#2035C2×C3112yescomplemented
240#1981C2×C3111yescharacteristic, complemented
241#1955C2×C3111yescharacteristic, complemented
242#1788C2×C3112yescomplemented
243#1788C2×C3112yescomplemented
244#1762C2×C3111yescharacteristic, complemented
245C22×C31—24no—
246C22×C31—42no—
247C22×C31—42no—
248C22×C31—44no—
249C22×C31—44no—
250C22×C31—42no—
251C22×C31—42no—
252C22×C31—42no—
253C22×C31—42no—
254C22×C31—42no—
255C22×C31—42no—
256C22×C31—42no—
257C22×C31C2×#12011yescharacteristic
258C22×C31#54612yes—
259C22×C31#57512yes—
260C22×C31#57711yescharacteristic
261C22×C31#57811yescharacteristic
262C4×C31—22no—
263C4×C31—22no—
264C4×C31—42no—
265C4×C31—44no—
266C4×C31—42no—
267C4×C31—81no—
268C4×C31—81no—
269C4×C31—82no—
270C4×C31C2×#12411yescharacteristic
271C4×C31#53511yescharacteristic
272C4×C31#54612yes—
273C22×#41C22×C3112yes—
274#547—24no—
275#547—24no—
276C2×C4⋊Q8C22×C3111yescharacteristic
277C2×#125C22×C3111yescharacteristic
278C2×#123—22no—
279C2×C22⋊Q8C22×C3112yes—
280C2×#121—21no—
281C2×C4×D4C22×C3111yescharacteristic
282C2×C4×D4C22×C3111yescharacteristic
283C22×C4⋊C4—21no—
284#491—24no—
285#478—24no—
286C2×#107C22×C3111yescharacteristic
287C2×#106C22×C3111yescharacteristic
288C2×C4⋊C8C22×C3111yescharacteristic
289C2×#103C22×C3112yes—
290C2×#103C22×C3112yes—
291C2×#103C22×C3112yes—
292C2×#103C22×C3112yes—
293C2×#102C22×C3111yescharacteristic
294C2×#102C22×C3111yescharacteristic
295C2×#102C22×C3112yes—
296C2×C22⋊C8C22×C3112yes—
297C2×C22⋊C8C22×C3112yes—
298C2×#97C22×C3111yescharacteristic
299#400—21no—
300#394—21no—
301#388—22no—
302#380C22×C3112yes—
303#380C22×C3112yes—
304C4×C4⋊C4C22×C3111yescharacteristic
305#340C22×C3112yes—
306C2×C31—44no—
307C2×C31—82no—
308C2×C31#243511yescharacteristic
309C2×C31#300511yescharacteristic
310C2×C31#301311yescharacteristic
311C2×C31#330712yes—
312C2×C31#331512yes—
313C2×#41—24no—
314C2×#41—24no—
315C2×#41—24no—
316C2×#41—24no—
317C2×#41—42no—
318C2×#41—42no—
319C22×Q8C23×C3112yes—
320C22×D4—22no—
321C22×D4D4×C3111yescharacteristic
322C22×D4C23×C3111yescharacteristic
323C23×C4—21no—
324C23×C4—22no—
325C23×C4C23×C3112yes—
326C22×C8C23×C3112yes—
327C22×C8C23×C3111yescharacteristic
328C22×C8C23×C3111yescharacteristic
329C4⋊Q8—22no—
330C4⋊Q8D4×C3114yes—
331#125—22no—
332#125—22no—
333#123—216no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336#121—28no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4D4×C3114yes—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4D4×C3111yescharacteristic
348C2×C4⋊C4C23×C3111yescharacteristic
349C2×C4⋊C4C23×C3111yescharacteristic
350C2×C4⋊C4C23×C3112yes—
351C2×C4⋊C4C23×C3111yescharacteristic
352C2×C22⋊C4—22no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4D4×C3112yes—
357C2×C42—21no—
358C2×C42C23×C3111yescharacteristic
359#107—22no—
360#106—22no—
361C4⋊C8—22no—
362#103—24no—
363#103—24no—
364#103—42no—
365#103—42no—
366#102—22no—
367#102—22no—
368#102—24no—
369C22⋊C8—42no—
370C22⋊C8—42no—
371#97—22no—
372#95—21no—
373#95—22no—
374#95—22no—
375C31#2589211yescharacteristic, direct product factor, Sylow
376C24—21no—
377C24C2×D4×C3112yes—
378#41—48no—
379#41—48no—
380#41—48no—
381#41—48no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8C2×D4×C3114yes—
388C2×D4—28no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—22no—
392C2×D4—42no—
393C2×D4—44no—
394C2×D4—44no—
395C2×D4C2×D4×C3112yes—
396C2×D4#41×C3114yes—
397C22×C4—28no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—44no—
411C22×C4—44no—
412C22×C4—44no—
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3111yescharacteristic
415C22×C4C2×D4×C3111yescharacteristic
416C22×C4C24×C3111yescharacteristic
417C2×C8—22no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C4⋊C4—28no—
425C4⋊C4—22no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—42no—
437C4⋊C4C2×D4×C3112yes—
438C22⋊C4—28no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—44no—
442C22⋊C4—82no—
443C42—81no—
444C42C2×D4×C3112yes—
445C42C2×D4×C3112yes—
446C23—22no—
447C23—24no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—42no—
456C23—41no—
457C23—41no—
458C23C22×D4×C3111yescharacteristic
459Q8—24no—
460Q8—24no—
461Q8—42no—
462Q8—42no—
463D4—22no—
464D4—24no—
465D4—44no—
466D4—416no—
467D4C31×#12414yes—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—48no—
477C2×C4—416no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4C31×#12012yes—
494C2×C4C31×#12012yes—
495C2×C4C22×D4×C3111yescharacteristic
496C2×C4C22×D4×C3111yescharacteristic
497C2×C4C2×#41×C3112yes—
498C2×C4C31×H(5,𝔽2)12yes—
499C8—41no—
500C8—41no—
501C8—42no—
502C22—24no—
503C22—42no—
504C22—42no—
505C22—44no—
506C22—44no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22C2×C31×#12011yescharacteristic
515C22C31×#54612yes—
516C22C31×#57512yes—
517C22C31×#57711yescharacteristic
518C22C31×#57811yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—81no—
525C4—81no—
526C4—82no—
527C4C2×C31×#12411yescharacteristic
528C4C31×#53511yescharacteristic
529C4C31×#54612yes—
530C2—44no—
531C2—82no—
532C2C31×#243511yescharacteristic
533C2C31×#300511yescharacteristic
534C2C31×#301311yescharacteristic
535C2C31×#330712yes—
536C2C31×#331512yes—
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#547C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#491C2semidirect
3. C2×C31×#478C2semidirect
4. C31×#2562C2semidirect
5. C31×#2036C2semidirect
6. C31×#2035C2semidirect
7. C31×#1981C2semidirect
8. C31×#1955C2semidirect
9. C31×#1788C2semidirect
10. C31×#1788C2semidirect
11. C31×#1762C2semidirect
177. #25892C31direct (N × H)
235. C2×#491C2×C31semidirect
236. C2×#478C2×C31semidirect
237. #2562C2×C31semidirect
238. #2036C2×C31semidirect
239. #2035C2×C31semidirect
240. #1981C2×C31semidirect
241. #1955C2×C31semidirect
242. #1788C2×C31semidirect
243. #1788C2×C31semidirect
244. #1762C2×C31semidirect
375. C31#25892direct (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
C2×C31×#4912
C2×C31×#4782
C31×#25622
C31×#20362
C31×#20352
C31×#19812
C31×#19552
C31×#17882
C31×#17622
#2589231