Finite Group Databasebeta

← C131×#29605 #45715489

Subgroups — C131×#29605 #45715489

Order 33536.

1268 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C131C211yesmaximal, characteristic
2C2×#485×C131C211yesmaximal, characteristic, complemented
3C2×#451×C131C211yesmaximal, characteristic, complemented
4#2616×C131C211yesmaximal, characteristic
5#2036×C131C212yesmaximal, complemented
6#2035×C131C212yesmaximal, complemented
7#2001×C131C212yesmaximal, complemented
8#2001×C131C212yesmaximal, complemented
9#1825×C131C211yesmaximal, characteristic, complemented
10#1787×C131C211yesmaximal, characteristic, complemented
11#1780×C131C211yesmaximal, characteristic
12C22×#41×C131C2211yescharacteristic
13C23×Q8×C131C2211yescharacteristic
14C22×Q16×C131C2212yes—
15#536×C131—24no—
16#536×C131—24no—
17C2×C4⋊Q8×C131—21no—
18C2×#124×C131—21no—
19C2×#123×C131—22no—
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×C22⋊Q8×C131C2212yes—
22C2×C22⋊Q8×C131C2212yes—
23C2×C22⋊Q8×C131C2212yes—
24C2×#117×C131C2211yescharacteristic
25#485×C131—24no—
26#451×C131—24no—
27C2×#107×C131C2211yescharacteristic
28C2×#106×C131C2211yescharacteristic
29C2×#103×C131C2212yes—
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2212yes—
33C2×#103×C131C2212yes—
34C2×C22⋊C8×C131C2211yescharacteristic
35C2×C22⋊C8×C131C2211yescharacteristic
36C2×C22⋊C8×C131C2212yes—
37C2×C22⋊C8×C131C2212yes—
38#395×C131—21no—
39#394×C131—22no—
40#394×C131—21no—
41#380×C131C2212yes—
42#380×C131C2211yescharacteristic
43#340×C131C2212yes—
44#340×C131C2212yes—
45C2×#41×C131—22no—
46C2×#41×C131—22no—
47C2×#41×C131—42no—
48C2×#41×C131—42no—
49C22×Q8×C131—21no—
50C22×Q8×C131—22no—
51C22×Q8×C131—42no—
52C22×Q8×C131—42no—
53C22×Q8×C131D414yes—
54C22×Q8×C131D411yescharacteristic
55C22×Q8×C131C2311yescharacteristic
56C22×Q8×C131C2312yes—
57C22×D4×C131D412yes—
58C22×D4×C131D411yescharacteristic
59C23×C4×C131—21no—
60C23×C4×C131C2312yes—
61C23×C4×C131C2311yescharacteristic
62C2×Q16×C131—24no—
63C2×Q16×C131—42no—
64C2×Q16×C131—42no—
65C22×C8×C131C2311yescharacteristic
66C22×C8×C131C2311yescharacteristic
67C22×C8×C131C2312yes—
68C4⋊Q8×C131—28no—
69#124×C131—28no—
70#123×C131—216no—
71C22⋊Q8×C131—24no—
72C22⋊Q8×C131—24no—
73C22⋊Q8×C131—24no—
74C22⋊Q8×C131—24no—
75C22⋊Q8×C131—22no—
76C22⋊Q8×C131—22no—
77C22⋊Q8×C131—42no—
78C22⋊Q8×C131—42no—
79#117×C131—22no—
80#117×C131D414yes—
81C2×C4⋊C4×C131—22no—
82C2×C4⋊C4×C131—22no—
83C2×C4⋊C4×C131—22no—
84C2×C4⋊C4×C131—21no—
85C2×C4⋊C4×C131C2311yescharacteristic
86C2×C4⋊C4×C131C2312yes—
87C2×C4⋊C4×C131C2311yescharacteristic
88C2×C4⋊C4×C131C2311yescharacteristic
89C2×C22⋊C4×C131—21no—
90C2×C22⋊C4×C131—22no—
91C2×C22⋊C4×C131—22no—
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—21no—
94C2×C22⋊C4×C131—22no—
95C2×C22⋊C4×C131—21no—
96C2×C42×C131—21no—
97#107×C131—22no—
98#106×C131—22no—
99#103×C131—24no—
100#103×C131—22no—
101#103×C131—22no—
102#103×C131—42no—
103#103×C131—42no—
104C22⋊C8×C131—22no—
105C22⋊C8×C131—22no—
106C22⋊C8×C131—42no—
107C22⋊C8×C131—42no—
108#95×C131—22no—
109#95×C131—21no—
110C24×C131C2×D412yes—
111C24×C131C2×D411yescharacteristic
112#41×C131—48no—
113#41×C131—44no—
114#41×C131—44no—
115C2×Q8×C131—24no—
116C2×Q8×C131—22no—
117C2×Q8×C131—22no—
118C2×Q8×C131—21no—
119C2×Q8×C131—21no—
120C2×Q8×C131—22no—
121C2×Q8×C131—22no—
122C2×Q8×C131—22no—
123C2×Q8×C131—22no—
124C2×Q8×C131—22no—
125C2×Q8×C131—22no—
126C2×Q8×C131—42no—
127C2×Q8×C131—48no—
128C2×Q8×C131—44no—
129C2×Q8×C131—44no—
130C2×Q8×C131—44no—
131C2×Q8×C131C2×D414yes—
132C2×D4×C131—24no—
133C2×D4×C131—22no—
134C2×D4×C131—42no—
135C2×D4×C131—42no—
136C2×D4×C131—42no—
137C22×C4×C131—22no—
138C22×C4×C131—22no—
139C22×C4×C131—24no—
140C22×C4×C131—21no—
141C22×C4×C131—21no—
142C22×C4×C131—22no—
143C22×C4×C131—22no—
144C22×C4×C131—22no—
145C22×C4×C131—22no—
146C22×C4×C131—22no—
147C22×C4×C131—22no—
148C22×C4×C131—22no—
149C22×C4×C131—21no—
150C22×C4×C131—22no—
151C22×C4×C131—21no—
152C22×C4×C131—44no—
153C22×C4×C131C2×D412yes—
154C22×C4×C131C2×D411yescharacteristic
155C22×C4×C131C2×D412yes—
156C22×C4×C131C2×D412yes—
157C22×C4×C131C2411yescharacteristic
158Q16×C131—48no—
159C2×C8×C131—21no—
160C2×C8×C131—21no—
161C2×C8×C131—22no—
162C2×C8×C131—22no—
163C2×C8×C131—22no—
164C2×C8×C131—22no—
165C2×C8×C131—22no—
166C4⋊C4×C131—28no—
167C4⋊C4×C131—28no—
168C4⋊C4×C131—21no—
169C4⋊C4×C131—21no—
170C4⋊C4×C131—21no—
171C4⋊C4×C131—21no—
172C4⋊C4×C131—22no—
173C4⋊C4×C131—22no—
174C4⋊C4×C131—44no—
175C4⋊C4×C131—42no—
176C4⋊C4×C131C2×D412yes—
177C4⋊C4×C131C2×D412yes—
178C22⋊C4×C131—28no—
179C22⋊C4×C131—28no—
180C22⋊C4×C131—24no—
181C22⋊C4×C131—44no—
182C22⋊C4×C131—42no—
183C22⋊C4×C131—81no—
184C22⋊C4×C131—82no—
185C42×C131—24no—
186C23×C131—22no—
187C23×C131—21no—
188C23×C131—22no—
189C23×C131—21no—
190C23×C131—22no—
191C23×C131—22no—
192C23×C131—22no—
193C23×C131—22no—
194C23×C131—22no—
195C23×C131—22no—
196C23×C131—22no—
197C23×C131#12012yes—
198C23×C131C22×D411yescharacteristic
199Q8×C131—24no—
200Q8×C131—24no—
201Q8×C131—48no—
202Q8×C131—44no—
203Q8×C131—42no—
204Q8×C131—42no—
205Q8×C131—42no—
206Q8×C131—41no—
207Q8×C131—41no—
208D4×C131—44no—
209D4×C131—48no—
210C2×C4×C131—22no—
211C2×C4×C131—24no—
212C2×C4×C131—22no—
213C2×C4×C131—22no—
214C2×C4×C131—22no—
215C2×C4×C131—22no—
216C2×C4×C131—24no—
217C2×C4×C131—22no—
218C2×C4×C131—22no—
219C2×C4×C131—22no—
220C2×C4×C131—48no—
221C2×C4×C131—42no—
222C2×C4×C131—42no—
223C2×C4×C131—41no—
224C2×C4×C131—42no—
225C2×C4×C131—41no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—41no—
231C2×C4×C131—41no—
232C2×C4×C131—42no—
233C2×C4×C131—42no—
234C2×C4×C131—42no—
235C2×C4×C131—41no—
236C2×C4×C131—42no—
237C2×C4×C131—41no—
238C2×C4×C131#12012yes—
239C2×C4×C131C22×D411yescharacteristic
240C2×C4×C131C22×D411yescharacteristic
241C2×C4×C131H(5,𝔽2)12yes—
242C2×C4×C131H(5,𝔽2)12yes—
243C8×C131—42no—
244C8×C131—41no—
245C8×C131—41no—
246C22×C131—22no—
247C22×C131—22no—
248C22×C131—22no—
249C22×C131—42no—
250C22×C131—42no—
251C22×C131—42no—
252C22×C131—42no—
253C22×C131—42no—
254C22×C131—42no—
255C22×C131—42no—
256C22×C131—42no—
257C22×C131—42no—
258C22×C131C2×#12011yescharacteristic
259C22×C131#53412yes—
260C22×C131#57711yescharacteristic
261C22×C131#57812yes—
262C22×C131#57811yescharacteristic
263C4×C131—22no—
264C4×C131—42no—
265C4×C131—44no—
266C4×C131—42no—
267C4×C131—42no—
268C4×C131—81no—
269C4×C131—82no—
270C4×C131—81no—
271C4×C131#53412yes—
272C4×C131#53511yescharacteristic
273C4×C131#53511yescharacteristic
274C2×C131—42no—
275C2×C131—82no—
276C2×C131#261311yescharacteristic
277C2×C131#301111yescharacteristic
278C2×C131#301311yescharacteristic
279C2×C131#320112yes—
280C2×C131#320212yes—
281#29605C13111yesmaximal, characteristic, direct product factor, Sylow
282C131#2960511yescharacteristic, direct product factor, Sylow
283C2×#536C2×C13111yescharacteristic
284C2×#485C2×C13111yescharacteristic, complemented
285C2×#451C2×C13111yescharacteristic, complemented
286#2616C2×C13111yescharacteristic
287#2036C2×C13112yescomplemented
288#2035C2×C13112yescomplemented
289#2001C2×C13112yescomplemented
290#2001C2×C13112yescomplemented
291#1825C2×C13111yescharacteristic, complemented
292#1787C2×C13111yescharacteristic, complemented
293#1780C2×C13111yescharacteristic
294C22×#41C22×C13111yescharacteristic
295C23×Q8C22×C13111yescharacteristic
296C22×Q16C22×C13112yes—
297#536—24no—
298#536—24no—
299C2×C4⋊Q8—21no—
300C2×#124—21no—
301C2×#123—22no—
302C2×C22⋊Q8C22×C13111yescharacteristic
303C2×C22⋊Q8C22×C13112yes—
304C2×C22⋊Q8C22×C13112yes—
305C2×C22⋊Q8C22×C13112yes—
306C2×#117C22×C13111yescharacteristic
307#485—24no—
308#451—24no—
309C2×#107C22×C13111yescharacteristic
310C2×#106C22×C13111yescharacteristic
311C2×#103C22×C13111yescharacteristic
312C2×#103C22×C13111yescharacteristic
313C2×#103C22×C13112yes—
314C2×#103C22×C13112yes—
315C2×#103C22×C13112yes—
316C2×C22⋊C8C22×C13111yescharacteristic
317C2×C22⋊C8C22×C13111yescharacteristic
318C2×C22⋊C8C22×C13112yes—
319C2×C22⋊C8C22×C13112yes—
320#395—21no—
321#394—22no—
322#394—21no—
323#380C22×C13111yescharacteristic
324#380C22×C13112yes—
325#340C22×C13112yes—
326#340C22×C13112yes—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—42no—
330C2×#41—42no—
331C22×Q8—21no—
332C22×Q8—22no—
333C22×Q8—42no—
334C22×Q8—42no—
335C22×Q8D4×C13114yes—
336C22×Q8D4×C13111yescharacteristic
337C22×Q8C23×C13111yescharacteristic
338C22×Q8C23×C13112yes—
339C22×D4D4×C13112yes—
340C22×D4D4×C13111yescharacteristic
341C23×C4—21no—
342C23×C4C23×C13112yes—
343C23×C4C23×C13111yescharacteristic
344C2×Q16—24no—
345C2×Q16—42no—
346C2×Q16—42no—
347C22×C8C23×C13112yes—
348C22×C8C23×C13111yescharacteristic
349C22×C8C23×C13111yescharacteristic
350C4⋊Q8—28no—
351#124—28no—
352#123—216no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—24no—
356C22⋊Q8—24no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—42no—
360C22⋊Q8—42no—
361#117—22no—
362#117D4×C13114yes—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C13112yes—
368C2×C4⋊C4C23×C13111yescharacteristic
369C2×C4⋊C4C23×C13111yescharacteristic
370C2×C4⋊C4C23×C13111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C42—21no—
379#107—22no—
380#106—22no—
381#103—24no—
382#103—22no—
383#103—22no—
384#103—42no—
385#103—42no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388C22⋊C8—42no—
389C22⋊C8—42no—
390#95—22no—
391#95—21no—
392C24C2×D4×C13112yes—
393C24C2×D4×C13111yescharacteristic
394#41—48no—
395#41—44no—
396#41—44no—
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—42no—
409C2×Q8—48no—
410C2×Q8—44no—
411C2×Q8—44no—
412C2×Q8—44no—
413C2×Q8C2×D4×C13114yes—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—42no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—44no—
435C22×C4C2×D4×C13112yes—
436C22×C4C2×D4×C13111yescharacteristic
437C22×C4C2×D4×C13112yes—
438C22×C4C2×D4×C13112yes—
439C22×C4C24×C13111yescharacteristic
440Q16—48no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—22no—
448C4⋊C4—28no—
449C4⋊C4—28no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—44no—
457C4⋊C4—42no—
458C4⋊C4C2×D4×C13112yes—
459C4⋊C4C2×D4×C13112yes—
460C22⋊C4—28no—
461C22⋊C4—28no—
462C22⋊C4—24no—
463C22⋊C4—44no—
464C22⋊C4—42no—
465C22⋊C4—81no—
466C22⋊C4—82no—
467C42—24no—
468C23—22no—
469C23—21no—
470C23—22no—
471C23—21no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23#120×C13112yes—
480C23C22×D4×C13111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—48no—
484Q8—44no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488Q8—41no—
489Q8—41no—
490D4—44no—
491D4—48no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—48no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4#120×C13112yes—
521C2×C4C22×D4×C13111yescharacteristic
522C2×C4C22×D4×C13111yescharacteristic
523C2×C4H(5,𝔽2)×C13112yes—
524C2×C4H(5,𝔽2)×C13112yes—
525C8—42no—
526C8—41no—
527C8—41no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22C2×#120×C13111yescharacteristic
541C22#534×C13112yes—
542C22#577×C13111yescharacteristic
543C22#578×C13112yes—
544C22#578×C13111yescharacteristic
545C4—22no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—44no—
550C4—81no—
551C4—81no—
552C4—82no—
553C4#534×C13112yes—
554C4#535×C13111yescharacteristic
555C4#535×C13111yescharacteristic
556C2—42no—
557C2—82no—
558C2#2613×C13111yescharacteristic
559C2#3011×C13111yescharacteristic
560C2#3013×C13111yescharacteristic
561C2#3201×C13112yes—
562C2#3202×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC22×#41×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C131C2semidirect
3. C2×#451×C131C2semidirect
5. #2036×C131C2semidirect
6. #2035×C131C2semidirect
7. #2001×C131C2semidirect
8. #2001×C131C2semidirect
9. #1825×C131C2semidirect
10. #1787×C131C2semidirect
281. #29605C131direct (N × H)
282. C131#29605direct (N × H)
284. C2×#485C2×C131semidirect
285. C2×#451C2×C131semidirect
287. #2036C2×C131semidirect
288. #2035C2×C131semidirect
289. #2001C2×C131semidirect
290. #2001C2×C131semidirect
291. #1825C2×C131semidirect
292. #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×#485×C1312
C2×#451×C1312
#2616×C1312
#2036×C1312
#2035×C1312
#2001×C1312
#1825×C1312
#1787×C1312
#1780×C1312
#29605131