Finite Group Databasebeta

← C131×#29631 #45715515

Subgroups — C131×#29631 #45715515

Order 33536.

1302 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C131C211yesmaximal, characteristic, complemented
2C2×#449×C131C211yesmaximal, characteristic
3C2×#448×C131C211yesmaximal, characteristic, complemented
4#2624×C131C211yesmaximal, characteristic, complemented
5#2043×C131C212yesmaximal, complemented
6#2042×C131C212yesmaximal, complemented
7#2013×C131C212yesmaximal, complemented
8#2012×C131C212yesmaximal, complemented
9#1818×C131C211yesmaximal, characteristic, complemented
10#1788×C131C211yesmaximal, characteristic, complemented
11#1787×C131C211yesmaximal, characteristic, complemented
12C22×#41×C131C2211yescharacteristic
13C23×Q8×C131C2211yescharacteristic
14C22×SD16×C131C2212yes—
15C22×SD16×C131C2211yescharacteristic
16C22×D8×C131C2211yescharacteristic
17#536×C131—24no—
18#536×C131—24no—
19C2×C4⋊Q8×C131C2212yes—
20C2×#124×C131C2212yes—
21C2×#123×C131—22no—
22C2×C22⋊Q8×C131—21no—
23C2×C22⋊Q8×C131—21no—
24C2×#121×C131C2211yescharacteristic
25C2×#117×C131C2211yescharacteristic
26#449×C131—24no—
27#448×C131—24no—
28C2×#103×C131C2212yes—
29C2×#103×C131C2211yescharacteristic
30C2×#103×C131C2212yes—
31C2×#103×C131C2212yes—
32C2×#103×C131C2212yes—
33C2×#102×C131C2211yescharacteristic
34C2×#102×C131C2212yes—
35C2×C22⋊C8×C131C2211yescharacteristic
36C2×C22⋊C8×C131C2211yescharacteristic
37#399×C131—21no—
38#397×C131—21no—
39#394×C131—22no—
40#390×C131C2212yes—
41#389×C131C2212yes—
42#380×C131C2211yescharacteristic
43#336×C131C2212yes—
44#336×C131C2212yes—
45C2×#41×C131—22no—
46C2×#41×C131—42no—
47C2×#41×C131—42no—
48C2×#41×C131D414yes—
49C22×Q8×C131—21no—
50C22×Q8×C131—22no—
51C22×Q8×C131—42no—
52C22×Q8×C131—42no—
53C22×Q8×C131D414yes—
54C22×Q8×C131C2312yes—
55C22×Q8×C131C2311yescharacteristic
56C22×D4×C131—21no—
57C22×D4×C131—21no—
58C22×D4×C131C2311yescharacteristic
59C22×D4×C131C2311yescharacteristic
60C23×C4×C131—21no—
61C23×C4×C131—21no—
62C23×C4×C131C2311yescharacteristic
63C2×SD16×C131—24no—
64C2×SD16×C131—22no—
65C2×SD16×C131—42no—
66C2×SD16×C131—42no—
67C2×SD16×C131—42no—
68C2×D8×C131—22no—
69C2×D8×C131—42no—
70C22×C8×C131C2311yescharacteristic
71C22×C8×C131C2312yes—
72C22×C8×C131C2311yescharacteristic
73C4⋊Q8×C131—24no—
74C4⋊Q8×C131—24no—
75#124×C131—24no—
76#124×C131—24no—
77#123×C131—216no—
78C22⋊Q8×C131—28no—
79C22⋊Q8×C131—28no—
80#121×C131—22no—
81#121×C131—22no—
82#117×C131—22no—
83#117×C131—22no—
84C2×C4⋊C4×C131—22no—
85C2×C4⋊C4×C131—22no—
86C2×C4⋊C4×C131—22no—
87C2×C4⋊C4×C131D411yescharacteristic
88C2×C4⋊C4×C131D411yescharacteristic
89C2×C4⋊C4×C131C2311yescharacteristic
90C2×C4⋊C4×C131C2312yes—
91C2×C22⋊C4×C131—22no—
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—21no—
94C2×C22⋊C4×C131—21no—
95C2×C22⋊C4×C131—22no—
96C2×C22⋊C4×C131—22no—
97C2×C22⋊C4×C131D412yes—
98C2×C42×C131C2312yes—
99#103×C131—24no—
100#103×C131—22no—
101#103×C131—42no—
102#103×C131—42no—
103#103×C131—42no—
104#102×C131—22no—
105#102×C131—42no—
106C22⋊C8×C131—22no—
107C22⋊C8×C131—22no—
108#95×C131—22no—
109#95×C131—21no—
110C24×C131—21no—
111C24×C131—21no—
112C24×C131C2×D411yescharacteristic
113#41×C131—44no—
114#41×C131—44no—
115#41×C131—48no—
116C2×Q8×C131—24no—
117C2×Q8×C131—22no—
118C2×Q8×C131—21no—
119C2×Q8×C131—22no—
120C2×Q8×C131—22no—
121C2×Q8×C131—22no—
122C2×Q8×C131—22no—
123C2×Q8×C131—22no—
124C2×Q8×C131—22no—
125C2×Q8×C131—48no—
126C2×Q8×C131—44no—
127C2×Q8×C131—44no—
128C2×Q8×C131—44no—
129C2×Q8×C131C2×D414yes—
130C2×Q8×C131C2×D412yes—
131C2×D4×C131—24no—
132C2×D4×C131—21no—
133C2×D4×C131—21no—
134C2×D4×C131—21no—
135C2×D4×C131—22no—
136C2×D4×C131—22no—
137C2×D4×C131—22no—
138C2×D4×C131—22no—
139C2×D4×C131—44no—
140C2×D4×C131—42no—
141C2×D4×C131—82no—
142C2×D4×C131C2×D412yes—
143C22×C4×C131—22no—
144C22×C4×C131—22no—
145C22×C4×C131—24no—
146C22×C4×C131—22no—
147C22×C4×C131—21no—
148C22×C4×C131—24no—
149C22×C4×C131—22no—
150C22×C4×C131—21no—
151C22×C4×C131—44no—
152C22×C4×C131—44no—
153C22×C4×C131C2×D412yes—
154C22×C4×C131C2×D412yes—
155C22×C4×C131C2×D411yescharacteristic
156C22×C4×C131C2×D412yes—
157C22×C4×C131C2×D412yes—
158C22×C4×C131C2411yescharacteristic
159SD16×C131—48no—
160SD16×C131—44no—
161D8×C131—44no—
162C2×C8×C131—21no—
163C2×C8×C131—21no—
164C2×C8×C131—22no—
165C2×C8×C131—22no—
166C2×C8×C131—22no—
167C2×C8×C131—22no—
168C2×C8×C131—22no—
169C4⋊C4×C131—28no—
170C4⋊C4×C131—28no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131—22no—
173C4⋊C4×C131—21no—
174C4⋊C4×C131—21no—
175C4⋊C4×C131—22no—
176C4⋊C4×C131—22no—
177C4⋊C4×C131—82no—
178C22⋊C4×C131—28no—
179C22⋊C4×C131—28no—
180C22⋊C4×C131—24no—
181C22⋊C4×C131—42no—
182C22⋊C4×C131—82no—
183C22⋊C4×C131—82no—
184C22⋊C4×C131—81no—
185C42×C131—22no—
186C42×C131—22no—
187C23×C131—22no—
188C23×C131—21no—
189C23×C131—22no—
190C23×C131—21no—
191C23×C131—22no—
192C23×C131—42no—
193C23×C131—42no—
194C23×C131—41no—
195C23×C131—41no—
196C23×C131—41no—
197C23×C131—42no—
198C23×C131—41no—
199C23×C131—42no—
200C23×C131—41no—
201C23×C131#12012yes—
202C23×C131C22×D411yescharacteristic
203Q8×C131—24no—
204Q8×C131—22no—
205Q8×C131—24no—
206Q8×C131—22no—
207Q8×C131—48no—
208Q8×C131—42no—
209Q8×C131—42no—
210Q8×C131—42no—
211D4×C131—22no—
212D4×C131—22no—
213D4×C131—48no—
214D4×C131—42no—
215D4×C131—41no—
216D4×C131—41no—
217D4×C131—42no—
218D4×C131—84no—
219C2×C4×C131—22no—
220C2×C4×C131—22no—
221C2×C4×C131—22no—
222C2×C4×C131—24no—
223C2×C4×C131—22no—
224C2×C4×C131—22no—
225C2×C4×C131—24no—
226C2×C4×C131—22no—
227C2×C4×C131—22no—
228C2×C4×C131—22no—
229C2×C4×C131—22no—
230C2×C4×C131—22no—
231C2×C4×C131—48no—
232C2×C4×C131—48no—
233C2×C4×C131—42no—
234C2×C4×C131—42no—
235C2×C4×C131—42no—
236C2×C4×C131—41no—
237C2×C4×C131—42no—
238C2×C4×C131—42no—
239C2×C4×C131—42no—
240C2×C4×C131—42no—
241C2×C4×C131#12012yes—
242C2×C4×C131C22×D411yescharacteristic
243C2×C4×C131C22×D411yescharacteristic
244C2×C4×C131H(5,𝔽2)12yes—
245C2×C4×C131H(5,𝔽2)12yes—
246C8×C131—41no—
247C8×C131—41no—
248C8×C131—42no—
249C22×C131—22no—
250C22×C131—22no—
251C22×C131—22no—
252C22×C131—42no—
253C22×C131—42no—
254C22×C131—42no—
255C22×C131—42no—
256C22×C131—42no—
257C22×C131—82no—
258C22×C131—82no—
259C22×C131—81no—
260C22×C131—82no—
261C22×C131—82no—
262C22×C131—81no—
263C22×C131—81no—
264C22×C131C2×#12011yescharacteristic
265C22×C131#53512yes—
266C22×C131#57711yescharacteristic
267C22×C131#57712yes—
268C22×C131#57811yescharacteristic
269C4×C131—22no—
270C4×C131—42no—
271C4×C131—44no—
272C4×C131—42no—
273C4×C131—42no—
274C4×C131—82no—
275C4×C131—81no—
276C4×C131#53411yescharacteristic
277C4×C131#53411yescharacteristic
278C4×C131#53412yes—
279C2×C131—42no—
280C2×C131—82no—
281C2×C131—161no—
282C2×C131#261311yescharacteristic
283C2×C131#301011yescharacteristic
284C2×C131#301311yescharacteristic
285C2×C131#322112yes—
286C2×C131#322512yes—
287#29631C13111yesmaximal, characteristic, direct product factor, Sylow
288C131#2963111yescharacteristic, direct product factor, Sylow
289C2×#536C2×C13111yescharacteristic, complemented
290C2×#449C2×C13111yescharacteristic
291C2×#448C2×C13111yescharacteristic, complemented
292#2624C2×C13111yescharacteristic, complemented
293#2043C2×C13112yescomplemented
294#2042C2×C13112yescomplemented
295#2013C2×C13112yescomplemented
296#2012C2×C13112yescomplemented
297#1818C2×C13111yescharacteristic, complemented
298#1788C2×C13111yescharacteristic, complemented
299#1787C2×C13111yescharacteristic, complemented
300C22×#41C22×C13111yescharacteristic
301C23×Q8C22×C13111yescharacteristic
302C22×SD16C22×C13112yes—
303C22×SD16C22×C13111yescharacteristic
304C22×D8C22×C13111yescharacteristic
305#536—24no—
306#536—24no—
307C2×C4⋊Q8C22×C13112yes—
308C2×#124C22×C13112yes—
309C2×#123—22no—
310C2×C22⋊Q8—21no—
311C2×C22⋊Q8—21no—
312C2×#121C22×C13111yescharacteristic
313C2×#117C22×C13111yescharacteristic
314#449—24no—
315#448—24no—
316C2×#103C22×C13112yes—
317C2×#103C22×C13111yescharacteristic
318C2×#103C22×C13112yes—
319C2×#103C22×C13112yes—
320C2×#103C22×C13112yes—
321C2×#102C22×C13111yescharacteristic
322C2×#102C22×C13112yes—
323C2×C22⋊C8C22×C13111yescharacteristic
324C2×C22⋊C8C22×C13111yescharacteristic
325#399—21no—
326#397—21no—
327#394—22no—
328#390C22×C13112yes—
329#389C22×C13112yes—
330#380C22×C13111yescharacteristic
331#336C22×C13112yes—
332#336C22×C13112yes—
333C2×#41—22no—
334C2×#41—42no—
335C2×#41—42no—
336C2×#41D4×C13114yes—
337C22×Q8—21no—
338C22×Q8—22no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8D4×C13114yes—
342C22×Q8C23×C13112yes—
343C22×Q8C23×C13111yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4C23×C13111yescharacteristic
347C22×D4C23×C13111yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4C23×C13111yescharacteristic
351C2×SD16—24no—
352C2×SD16—22no—
353C2×SD16—42no—
354C2×SD16—42no—
355C2×SD16—42no—
356C2×D8—22no—
357C2×D8—42no—
358C22×C8C23×C13111yescharacteristic
359C22×C8C23×C13111yescharacteristic
360C22×C8C23×C13112yes—
361C4⋊Q8—24no—
362C4⋊Q8—24no—
363#124—24no—
364#124—24no—
365#123—216no—
366C22⋊Q8—28no—
367C22⋊Q8—28no—
368#121—22no—
369#121—22no—
370#117—22no—
371#117—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4D4×C13111yescharacteristic
376C2×C4⋊C4D4×C13111yescharacteristic
377C2×C4⋊C4C23×C13111yescharacteristic
378C2×C4⋊C4C23×C13112yes—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4D4×C13112yes—
386C2×C42C23×C13112yes—
387#103—24no—
388#103—22no—
389#103—42no—
390#103—42no—
391#103—42no—
392#102—22no—
393#102—42no—
394C22⋊C8—22no—
395C22⋊C8—22no—
396#95—21no—
397#95—22no—
398C24—21no—
399C24—21no—
400C24C2×D4×C13111yescharacteristic
401#41—44no—
402#41—44no—
403#41—48no—
404C2×Q8—24no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—48no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8C2×D4×C13114yes—
418C2×Q8C2×D4×C13112yes—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—44no—
428C2×D4—42no—
429C2×D4—82no—
430C2×D4C2×D4×C13112yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4C2×D4×C13112yes—
442C22×C4C2×D4×C13112yes—
443C22×C4C2×D4×C13111yescharacteristic
444C22×C4C2×D4×C13112yes—
445C22×C4C2×D4×C13112yes—
446C22×C4C24×C13111yescharacteristic
447SD16—48no—
448SD16—44no—
449D8—44no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C4⋊C4—28no—
458C4⋊C4—28no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—82no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—24no—
469C22⋊C4—42no—
470C22⋊C4—82no—
471C22⋊C4—82no—
472C22⋊C4—81no—
473C42—22no—
474C42—22no—
475C23—22no—
476C23—21no—
477C23—22no—
478C23—21no—
479C23—22no—
480C23—42no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23#120×C13112yes—
490C23C22×D4×C13111yescharacteristic
491Q8—24no—
492Q8—22no—
493Q8—24no—
494Q8—22no—
495Q8—48no—
496Q8—42no—
497Q8—42no—
498Q8—42no—
499D4—22no—
500D4—22no—
501D4—48no—
502D4—42no—
503D4—41no—
504D4—41no—
505D4—42no—
506D4—84no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—48no—
520C2×C4—48no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4#120×C13112yes—
530C2×C4C22×D4×C13111yescharacteristic
531C2×C4C22×D4×C13111yescharacteristic
532C2×C4H(5,𝔽2)×C13112yes—
533C2×C4H(5,𝔽2)×C13112yes—
534C8—41no—
535C8—41no—
536C8—42no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—82no—
546C22—82no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—82no—
551C22—82no—
552C22C2×#120×C13111yescharacteristic
553C22#535×C13112yes—
554C22#577×C13112yes—
555C22#577×C13111yescharacteristic
556C22#578×C13111yescharacteristic
557C4—22no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—44no—
562C4—81no—
563C4—82no—
564C4#534×C13111yescharacteristic
565C4#534×C13111yescharacteristic
566C4#534×C13112yes—
567C2—42no—
568C2—82no—
569C2—161no—
570C2#2613×C13111yescharacteristic
571C2#3010×C13111yescharacteristic
572C2#3013×C13111yescharacteristic
573C2#3221×C13112yes—
574C2#3225×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#449×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#536×C131C2semidirect
3. C2×#448×C131C2semidirect
4. #2624×C131C2semidirect
5. #2043×C131C2semidirect
6. #2042×C131C2semidirect
7. #2013×C131C2semidirect
8. #2012×C131C2semidirect
9. #1818×C131C2semidirect
10. #1788×C131C2semidirect
11. #1787×C131C2semidirect
287. #29631C131direct (N × H)
288. C131#29631direct (N × H)
289. C2×#536C2×C131semidirect
291. C2×#448C2×C131semidirect
292. #2624C2×C131semidirect
293. #2043C2×C131semidirect
294. #2042C2×C131semidirect
295. #2013C2×C131semidirect
296. #2012C2×C131semidirect
297. #1818C2×C131semidirect
298. #1788C2×C131semidirect
299. #1787C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1312
C2×#449×C1312
C2×#448×C1312
#2624×C1312
#2043×C1312
#2042×C1312
#2013×C1312
#2012×C1312
#1818×C1312
#1788×C1312
#1787×C1312
#29631131