Finite Group Databasebeta

← C131×#12687 #45698571

Subgroups — C131×#12687 #45698571

Order 33536.

2508 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 2508 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C131C211yesmaximal, characteristic
2C2×AΣL(1,𝔽16)×C131C214yesmaximal, complemented
3#1783×C131C211yesmaximal, characteristic, complemented
4#1781×C131C211yesmaximal, characteristic, complemented
5C26×C131C411yescharacteristic, complemented
6C23×D4×C131—21no—
7C23×D4×C131C2211yescharacteristic
8C2×#120×C131—21no—
9C2×#120×C131—21no—
10C2×#120×C131—28no—
11C2×#120×C131C412yescomplemented
12C2×#120×C131C2212yes—
13C22×C22⋊C4×C131—21no—
14C22×C22⋊C4×C131C411yescharacteristic, complemented
15C2×#100×C131—21no—
16C2×#100×C131C2212yescomplemented
17C2×#99×C131—21no—
18C2×#99×C131C2212yescomplemented
19#407×C131—21no—
20#379×C131—21no—
21AΣL(1,𝔽16)×C131—28no—
22C25×C131—21no—
23C25×C131—21no—
24C25×C131—24no—
25C25×C131—48no—
26C25×C131—42no—
27C25×C131—42no—
28C25×C131C2×C411yescharacteristic
29C25×C131C2×C412yes—
30C25×C131D411yescharacteristic
31C22×D4×C131—28no—
32C22×D4×C131—22no—
33C22×D4×C131—22no—
34C22×D4×C131—24no—
35C22×D4×C131—42no—
36C22×D4×C131—42no—
37C22×D4×C131—48no—
38C22×D4×C131C2×C411yescharacteristic
39C22×D4×C131D411yescharacteristic
40C22×D4×C131D411yescharacteristic
41C22×D4×C131C2311yescharacteristic
42C23×C4×C131—21no—
43C23×C4×C131D411yescharacteristic
44C2×M16×C131—22no—
45#120×C131—28no—
46#120×C131—28no—
47#120×C131—24no—
48#120×C131—24no—
49#120×C131—24no—
50#120×C131D418yes—
51C2×C22⋊C4×C131—28no—
52C2×C22⋊C4×C131—21no—
53C2×C22⋊C4×C131—22no—
54C2×C22⋊C4×C131—22no—
55C2×C22⋊C4×C131—24no—
56C2×C22⋊C4×C131—22no—
57C2×C22⋊C4×C131—42no—
58C2×C22⋊C4×C131C2×C412yes—
59#100×C131—24no—
60#100×C131—42no—
61#99×C131—24no—
62#99×C131—42no—
63C22⋊C8×C131—42no—
64C24×C131—24no—
65C24×C131—28no—
66C24×C131—22no—
67C24×C131—22no—
68C24×C131—22no—
69C24×C131—22no—
70C24×C131—24no—
71C24×C131—22no—
72C24×C131—22no—
73C24×C131—22no—
74C24×C131—41no—
75C24×C131—44no—
76C24×C131—48no—
77C24×C131—42no—
78C24×C131—42no—
79C24×C131—44no—
80C24×C131—42no—
81C24×C131—48no—
82C24×C131—432no—
83C24×C131—416no—
84C24×C131—42no—
85C24×C131—44no—
86C24×C131—48no—
87C24×C131—416no—
88C24×C131—432no—
89C24×C131—48no—
90C24×C131—42no—
91C24×C131—42no—
92C24×C131C22⋊C411yescharacteristic
93C24×C131C22⋊C411yescharacteristic
94C24×C131C22⋊C411yescharacteristic
95C24×C131C22⋊C414yescomplemented
96C24×C131C22×C411yescharacteristic
97C24×C131C2×D411yescharacteristic
98C2×D4×C131—28no—
99C2×D4×C131—22no—
100C2×D4×C131—22no—
101C2×D4×C131—22no—
102C2×D4×C131—22no—
103C2×D4×C131—28no—
104C2×D4×C131—22no—
105C2×D4×C131—41no—
106C2×D4×C131—41no—
107C2×D4×C131—41no—
108C2×D4×C131—41no—
109C2×D4×C131—41no—
110C2×D4×C131—41no—
111C2×D4×C131—416no—
112C2×D4×C131—48no—
113C2×D4×C131—48no—
114C2×D4×C131—432no—
115C2×D4×C131C2×D414yes—
116C22×C4×C131—24no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—22no—
120C22×C4×C131—41no—
121C22×C4×C131—44no—
122C22×C4×C131—42no—
123C22×C4×C131C22⋊C411yescharacteristic
124C22×C4×C131C2×D411yescharacteristic
125M16×C131—42no—
126M16×C131—42no—
127C2×C8×C131—42no—
128C22⋊C4×C131—28no—
129C22⋊C4×C131—24no—
130C22⋊C4×C131—22no—
131C22⋊C4×C131—28no—
132C22⋊C4×C131—42no—
133C22⋊C4×C131—42no—
134C22⋊C4×C131—84no—
135C22⋊C4×C131C22⋊C414yescomplemented
136C23×C131—24no—
137C23×C131—21no—
138C23×C131—21no—
139C23×C131—216no—
140C23×C131—28no—
141C23×C131—28no—
142C23×C131—21no—
143C23×C131—24no—
144C23×C131—21no—
145C23×C131—21no—
146C23×C131—21no—
147C23×C131—21no—
148C23×C131—21no—
149C23×C131—21no—
150C23×C131—21no—
151C23×C131—21no—
152C23×C131—44no—
153C23×C131—42no—
154C23×C131—48no—
155C23×C131—44no—
156C23×C131—42no—
157C23×C131—48no—
158C23×C131—48no—
159C23×C131—48no—
160C23×C131—416no—
161C23×C131—44no—
162C23×C131—48no—
163C23×C131—44no—
164C23×C131—48no—
165C23×C131—48no—
166C23×C131—416no—
167C23×C131—48no—
168C23×C131—44no—
169C23×C131—42no—
170C23×C131—42no—
171C23×C131—48no—
172C23×C131—48no—
173C23×C131—416no—
174C23×C131—416no—
175C23×C131—464no—
176C23×C131—464no—
177C23×C131—48no—
178C23×C131—416no—
179C23×C131—48no—
180C23×C131—44no—
181C23×C131—42no—
182C23×C131—42no—
183C23×C131—44no—
184C23×C131—82no—
185C23×C131—84no—
186C23×C131#9912yes—
187C23×C131#9912yes—
188C23×C131C2×C22⋊C411yescharacteristic
189C23×C131C2×C22⋊C412yes—
190C23×C131#12012yes—
191D4×C131—44no—
192D4×C131—44no—
193D4×C131—44no—
194D4×C131—416no—
195D4×C131—416no—
196D4×C131—44no—
197C2×C4×C131—21no—
198C2×C4×C131—21no—
199C2×C4×C131—21no—
200C2×C4×C131—24no—
201C2×C4×C131—21no—
202C2×C4×C131—21no—
203C2×C4×C131—44no—
204C2×C4×C131—48no—
205C2×C4×C131—44no—
206C2×C4×C131—82no—
207C2×C4×C131—84no—
208C2×C4×C131#12012yes—
209C8×C131—82no—
210C22×C131—24no—
211C22×C131—24no—
212C22×C131—22no—
213C22×C131—22no—
214C22×C131—22no—
215C22×C131—28no—
216C22×C131—22no—
217C22×C131—22no—
218C22×C131—22no—
219C22×C131—42no—
220C22×C131—42no—
221C22×C131—42no—
222C22×C131—42no—
223C22×C131—44no—
224C22×C131—432no—
225C22×C131—416no—
226C22×C131—48no—
227C22×C131—42no—
228C22×C131—42no—
229C22×C131—48no—
230C22×C131—48no—
231C22×C131—416no—
232C22×C131—432no—
233C22×C131—42no—
234C22×C131—48no—
235C22×C131—42no—
236C22×C131—42no—
237C22×C131—44no—
238C22×C131—42no—
239C22×C131—41no—
240C22×C131—81no—
241C22×C131—88no—
242C22×C131—81no—
243C22×C131AΣL(1,𝔽16)14yescomplemented
244C22×C131#37911yescharacteristic
245C22×C131C2×#9911yescharacteristic
246C22×C131C2×#9911yescharacteristic
247C4×C131—22no—
248C4×C131—44no—
249C4×C131—41no—
250C4×C131—162no—
251C2×C131—21no—
252C2×C131—24no—
253C2×C131—21no—
254C2×C131—42no—
255C2×C131—48no—
256C2×C131—42no—
257C2×C131—42no—
258C2×C131—81no—
259C2×C131#178111yescharacteristic
260C2×C131C2×AΣL(1,𝔽16)12yes—
261#12687C13111yesmaximal, characteristic, direct product factor, Sylow
262C131#1268711yescharacteristic, direct product factor, Sylow
263C22×#120C2×C13111yescharacteristic
264C2×AΣL(1,𝔽16)C2×C13114yescomplemented
265#1783C2×C13111yescharacteristic, complemented
266#1781C2×C13111yescharacteristic, complemented
267C26C4×C13111yescharacteristic, complemented
268C23×D4—21no—
269C23×D4C22×C13111yescharacteristic
270C2×#120—21no—
271C2×#120—21no—
272C2×#120—28no—
273C2×#120C4×C13112yescomplemented
274C2×#120C22×C13112yes—
275C22×C22⋊C4—21no—
276C22×C22⋊C4C4×C13111yescharacteristic, complemented
277C2×#100—21no—
278C2×#100C22×C13112yescomplemented
279C2×#99—21no—
280C2×#99C22×C13112yescomplemented
281#407—21no—
282#379—21no—
283AΣL(1,𝔽16)—28no—
284C25—21no—
285C25—21no—
286C25—24no—
287C25—48no—
288C25—42no—
289C25—42no—
290C25C2×C4×C13111yescharacteristic
291C25C2×C4×C13112yes—
292C25D4×C13111yescharacteristic
293C22×D4—28no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—24no—
297C22×D4—42no—
298C22×D4—42no—
299C22×D4—48no—
300C22×D4C2×C4×C13111yescharacteristic
301C22×D4D4×C13111yescharacteristic
302C22×D4D4×C13111yescharacteristic
303C22×D4C23×C13111yescharacteristic
304C23×C4—21no—
305C23×C4D4×C13111yescharacteristic
306C2×M16—22no—
307#120—28no—
308#120—28no—
309#120—24no—
310#120—24no—
311#120—24no—
312#120D4×C13118yes—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4C2×C4×C13112yes—
321#100—24no—
322#100—42no—
323#99—24no—
324#99—42no—
325C22⋊C8—42no—
326C24—24no—
327C24—28no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—22no—
332C24—24no—
333C24—22no—
334C24—22no—
335C24—22no—
336C24—41no—
337C24—44no—
338C24—48no—
339C24—42no—
340C24—42no—
341C24—42no—
342C24—44no—
343C24—48no—
344C24—432no—
345C24—416no—
346C24—42no—
347C24—44no—
348C24—48no—
349C24—416no—
350C24—432no—
351C24—48no—
352C24—42no—
353C24—42no—
354C24C22⋊C4×C13111yescharacteristic
355C24C22⋊C4×C13111yescharacteristic
356C24C22⋊C4×C13111yescharacteristic
357C24C22⋊C4×C13114yescomplemented
358C24C22×C4×C13111yescharacteristic
359C24C2×D4×C13111yescharacteristic
360C2×D4—28no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—416no—
374C2×D4—48no—
375C2×D4—48no—
376C2×D4—432no—
377C2×D4C2×D4×C13114yes—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—44no—
384C22×C4—42no—
385C22×C4C22⋊C4×C13111yescharacteristic
386C22×C4C2×D4×C13111yescharacteristic
387M16—42no—
388M16—42no—
389C2×C8—42no—
390C22⋊C4—28no—
391C22⋊C4—24no—
392C22⋊C4—22no—
393C22⋊C4—28no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—84no—
397C22⋊C4C22⋊C4×C13114yescomplemented
398C23—21no—
399C23—24no—
400C23—21no—
401C23—216no—
402C23—28no—
403C23—28no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—24no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—44no—
415C23—42no—
416C23—48no—
417C23—44no—
418C23—42no—
419C23—48no—
420C23—48no—
421C23—48no—
422C23—416no—
423C23—48no—
424C23—44no—
425C23—48no—
426C23—44no—
427C23—48no—
428C23—416no—
429C23—48no—
430C23—44no—
431C23—42no—
432C23—42no—
433C23—48no—
434C23—48no—
435C23—416no—
436C23—416no—
437C23—464no—
438C23—464no—
439C23—48no—
440C23—416no—
441C23—42no—
442C23—42no—
443C23—48no—
444C23—44no—
445C23—44no—
446C23—82no—
447C23—84no—
448C23#99×C13112yes—
449C23#99×C13112yes—
450C23C2×C22⋊C4×C13111yescharacteristic
451C23C2×C22⋊C4×C13112yes—
452C23#120×C13112yes—
453D4—44no—
454D4—44no—
455D4—44no—
456D4—416no—
457D4—416no—
458D4—44no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—48no—
467C2×C4—44no—
468C2×C4—82no—
469C2×C4—84no—
470C2×C4#120×C13112yes—
471C8—82no—
472C22—24no—
473C22—24no—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—28no—
478C22—22no—
479C22—22no—
480C22—22no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—44no—
486C22—48no—
487C22—42no—
488C22—432no—
489C22—416no—
490C22—42no—
491C22—48no—
492C22—48no—
493C22—416no—
494C22—432no—
495C22—44no—
496C22—42no—
497C22—48no—
498C22—42no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—81no—
503C22—88no—
504C22—81no—
505C22AΣL(1,𝔽16)×C13114yescomplemented
506C22#379×C13111yescharacteristic
507C22C2×#99×C13111yescharacteristic
508C22C2×#99×C13111yescharacteristic
509C4—22no—
510C4—44no—
511C4—41no—
512C4—162no—
513C2—21no—
514C2—21no—
515C2—24no—
516C2—42no—
517C2—48no—
518C2—42no—
519C2—42no—
520C2—81no—
521C2#1781×C13111yescharacteristic
522C2C2×AΣL(1,𝔽16)×C13112yes—
subgroupG/H
center, socleC22×C131C2×#99
commutatorC24C22×C4×C131
Frattini, cosocleC22×D4C23×C131
prime radicalC22×#120×C131C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C24×C131 ◁ C23×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×AΣL(1,𝔽16)×C131C2semidirect
3. #1783×C131C2semidirect
4. #1781×C131C2semidirect
5. C26×C131C4semidirect
11. C2×#120×C131C4semidirect
14. C22×C22⋊C4×C131C4semidirect
16. C2×#100×C131C22semidirect
18. C2×#99×C131C22semidirect
95. C24×C131C22⋊C4semidirect
135. C22⋊C4×C131C22⋊C4semidirect
243. C22×C131AΣL(1,𝔽16)semidirect
261. #12687C131direct (N × H)
262. C131#12687direct (N × H)
264. C2×AΣL(1,𝔽16)C2×C131semidirect
265. #1783C2×C131semidirect
266. #1781C2×C131semidirect
267. C26C4×C131semidirect
273. C2×#120C4×C131semidirect
276. C22×C22⋊C4C4×C131semidirect
278. C2×#100C22×C131semidirect
280. C2×#99C22×C131semidirect
357. C24C22⋊C4×C131semidirect
397. C22⋊C4C22⋊C4×C131semidirect
505. C22AΣL(1,𝔽16)×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1312
C2×AΣL(1,𝔽16)×C1312
#1783×C1312
#1781×C1312
#12687131