Finite Group Databasebeta

← C131×#8534 #45694418

Subgroups — C131×#8534 #45694418

Order 33536.

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 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
1#3484×C131C211yesmaximal, characteristic
2#1898×C131C214yesmaximal, complemented
3#1781×C131C211yesmaximal, characteristic, complemented
4#1438×C131C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C131C411yescharacteristic, complemented
6C23×D4×C131C2211yescharacteristic
7#546×C131—24no—
8D42×C131—24no—
9#535×C131—21no—
10#534×C131—21no—
11#534×C131C412yescomplemented
12#525×C131—21no—
13C2×#120×C131—21no—
14C2×#120×C131C2212yes—
15#518×C131C411yescharacteristic, complemented
16C22×C22⋊C4×C131—21no—
17C22×C22⋊C4×C131C2212yescomplemented
18C2×#99×C131—21no—
19C2×#99×C131—21no—
20C2×#99×C131—24no—
21#379×C131C2212yescomplemented
22C2×#95×C131—21no—
23#342×C131—24no—
24C25×C131D411yescharacteristic
25C25×C131C2311yescharacteristic
26H(5,𝔽2)×C131—42no—
27H(5,𝔽2)×C131—42no—
28C2×#41×C131—21no—
29C2×#41×C131—22no—
30C22×D4×C131—21no—
31C22×D4×C131—22no—
32C22×D4×C131—24no—
33C22×D4×C131—22no—
34C22×D4×C131—42no—
35C22×D4×C131—42no—
36C22×D4×C131C2×C411yescharacteristic
37C22×D4×C131C2×C411yescharacteristic
38C22×D4×C131C2×C412yes—
39C22×D4×C131D411yescharacteristic
40C22×D4×C131D411yescharacteristic
41C22×D4×C131D414yes—
42C23×C4×C131—22no—
43C23×C4×C131D411yescharacteristic
44#127×C131—22no—
45#124×C131—22no—
46#123×C131—22no—
47#123×C131—22no—
48#123×C131—22no—
49C22⋊Q8×C131—22no—
50#121×C131—22no—
51#121×C131—24no—
52#121×C131—24no—
53#121×C131—24no—
54#120×C131—24no—
55#120×C131—22no—
56#120×C131—22no—
57#120×C131—22no—
58#120×C131—22no—
59#120×C131—22no—
60#120×C131—24no—
61C4×D4×C131—24no—
62C4×D4×C131—24no—
63#117×C131—21no—
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131—21no—
66C2×C22⋊C4×C131—24no—
67C2×C22⋊C4×C131—22no—
68C2×C22⋊C4×C131—24no—
69C2×C22⋊C4×C131—44no—
70C2×C22⋊C4×C131—44no—
71C2×C22⋊C4×C131—42no—
72C2×C22⋊C4×C131C2×C412yes—
73C2×C22⋊C4×C131D414yes—
74#99×C131—48no—
75#99×C131—42no—
76#99×C131—42no—
77#95×C131—42no—
78C24×C131—21no—
79C24×C131—22no—
80C24×C131—22no—
81C24×C131—42no—
82C24×C131—41no—
83C24×C131—41no—
84C24×C131—41no—
85C24×C131—42no—
86C24×C131—42no—
87C24×C131—42no—
88C24×C131C22⋊C411yescharacteristic
89C24×C131C22⋊C411yescharacteristic
90C24×C131C22⋊C412yescomplemented
91C24×C131C22×C411yescharacteristic
92C24×C131C2×D411yescharacteristic
93C24×C131C2×D414yes—
94C24×C131C2×D411yescharacteristic
95#41×C131—42no—
96#41×C131—48no—
97#41×C131—42no—
98C2×Q8×C131—21no—
99C2×D4×C131—22no—
100C2×D4×C131—22no—
101C2×D4×C131—22no—
102C2×D4×C131—21no—
103C2×D4×C131—22no—
104C2×D4×C131—22no—
105C2×D4×C131—22no—
106C2×D4×C131—22no—
107C2×D4×C131—24no—
108C2×D4×C131—22no—
109C2×D4×C131—22no—
110C2×D4×C131—24no—
111C2×D4×C131—24no—
112C2×D4×C131—22no—
113C2×D4×C131—22no—
114C2×D4×C131—41no—
115C2×D4×C131—41no—
116C2×D4×C131—41no—
117C2×D4×C131—41no—
118C2×D4×C131—416no—
119C2×D4×C131—48no—
120C2×D4×C131—42no—
121C2×D4×C131—42no—
122C2×D4×C131—42no—
123C2×D4×C131—42no—
124C2×D4×C131—44no—
125C2×D4×C131—44no—
126C2×D4×C131—82no—
127C2×D4×C131—82no—
128C22×C4×C131—21no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—22no—
132C22×C4×C131—22no—
133C22×C4×C131—24no—
134C22×C4×C131—41no—
135C22×C4×C131—42no—
136C22×C4×C131—42no—
137C22×C4×C131—42no—
138C22×C4×C131—42no—
139C22×C4×C131—42no—
140C22×C4×C131—42no—
141C22×C4×C131—42no—
142C22×C4×C131C22⋊C411yescharacteristic
143C22×C4×C131C22⋊C411yescharacteristic
144C22×C4×C131C22⋊C414yescomplemented
145C22×C4×C131C22⋊C412yescomplemented
146C4⋊C4×C131—22no—
147C4⋊C4×C131—24no—
148C22⋊C4×C131—22no—
149C22⋊C4×C131—24no—
150C22⋊C4×C131—24no—
151C22⋊C4×C131—22no—
152C22⋊C4×C131—22no—
153C22⋊C4×C131—24no—
154C22⋊C4×C131—24no—
155C22⋊C4×C131—28no—
156C22⋊C4×C131—44no—
157C22⋊C4×C131—48no—
158C22⋊C4×C131—42no—
159C22⋊C4×C131—42no—
160C22⋊C4×C131—44no—
161C22⋊C4×C131—44no—
162C42×C131—22no—
163C23×C131—21no—
164C23×C131—21no—
165C23×C131—22no—
166C23×C131—22no—
167C23×C131—21no—
168C23×C131—21no—
169C23×C131—21no—
170C23×C131—21no—
171C23×C131—21no—
172C23×C131—21no—
173C23×C131—24no—
174C23×C131—24no—
175C23×C131—21no—
176C23×C131—22no—
177C23×C131—21no—
178C23×C131—21no—
179C23×C131—44no—
180C23×C131—42no—
181C23×C131—44no—
182C23×C131—42no—
183C23×C131—44no—
184C23×C131—42no—
185C23×C131—42no—
186C23×C131—42no—
187C23×C131—44no—
188C23×C131—42no—
189C23×C131—42no—
190C23×C131—42no—
191C23×C131—44no—
192C23×C131—42no—
193C23×C131—42no—
194C23×C131—82no—
195C23×C131—81no—
196C23×C131—82no—
197C23×C131—82no—
198C23×C131—81no—
199C23×C131—81no—
200C23×C131—82no—
201C23×C131—81no—
202C23×C131—81no—
203C23×C131—81no—
204C23×C131—82no—
205C23×C131#9912yescomplemented
206C23×C131C2×C22⋊C412yes—
207C23×C131C2×C22⋊C411yescharacteristic
208C23×C131#12012yes—
209C23×C131#12012yes—
210Q8×C131—42no—
211D4×C131—28no—
212D4×C131—44no—
213D4×C131—42no—
214D4×C131—44no—
215D4×C131—44no—
216D4×C131—44no—
217D4×C131—44no—
218D4×C131—42no—
219D4×C131—42no—
220D4×C131—44no—
221D4×C131—44no—
222D4×C131—84no—
223D4×C131—84no—
224C2×C4×C131—21no—
225C2×C4×C131—21no—
226C2×C4×C131—24no—
227C2×C4×C131—22no—
228C2×C4×C131—21no—
229C2×C4×C131—21no—
230C2×C4×C131—21no—
231C2×C4×C131—44no—
232C2×C4×C131—44no—
233C2×C4×C131—42no—
234C2×C4×C131—44no—
235C2×C4×C131—42no—
236C2×C4×C131—44no—
237C2×C4×C131—44no—
238C2×C4×C131—44no—
239C2×C4×C131—82no—
240C2×C4×C131—82no—
241C2×C4×C131—82no—
242C2×C4×C131—82no—
243C2×C4×C131—82no—
244C2×C4×C131—82no—
245C2×C4×C131—84no—
246C2×C4×C131#9912yescomplemented
247C22×C131—21no—
248C22×C131—22no—
249C22×C131—21no—
250C22×C131—22no—
251C22×C131—21no—
252C22×C131—21no—
253C22×C131—22no—
254C22×C131—22no—
255C22×C131—22no—
256C22×C131—22no—
257C22×C131—22no—
258C22×C131—22no—
259C22×C131—24no—
260C22×C131—24no—
261C22×C131—42no—
262C22×C131—42no—
263C22×C131—42no—
264C22×C131—42no—
265C22×C131—41no—
266C22×C131—44no—
267C22×C131—42no—
268C22×C131—84no—
269C22×C131—81no—
270C22×C131—81no—
271C22×C131—81no—
272C22×C131—81no—
273C22×C131—81no—
274C22×C131—84no—
275C22×C131—84no—
276C22×C131—84no—
277C22×C131—81no—
278C22×C131—162no—
279C22×C131—162no—
280C22×C131#37911yescharacteristic
281C22×C131C2×#9911yescharacteristic
282C22×C131C2×#9911yescharacteristic
283C22×C131B(4,𝔽2)12yes—
284C22×C131#45812yes—
285C4×C131—22no—
286C4×C131—41no—
287C4×C131—42no—
288C4×C131—44no—
289C4×C131—84no—
290C4×C131—162no—
291C2×C131—22no—
292C2×C131—21no—
293C2×C131—21no—
294C2×C131—22no—
295C2×C131—42no—
296C2×C131—42no—
297C2×C131—42no—
298C2×C131—81no—
299C2×C131—82no—
300C2×C131#178111yescharacteristic
301C2×C131#179012yes—
302#8534C13111yesmaximal, characteristic, direct product factor, Sylow
303C131#853411yescharacteristic, direct product factor, Sylow
304#3484C2×C13111yescharacteristic
305#1898C2×C13114yescomplemented
306#1781C2×C13111yescharacteristic, complemented
307#1438C2×C13111yescharacteristic, complemented
308C2×H(5,𝔽2)C4×C13111yescharacteristic, complemented
309C23×D4C22×C13111yescharacteristic
310#546—24no—
311D42—24no—
312#535—21no—
313#534—21no—
314#534C4×C13112yescomplemented
315#525—21no—
316C2×#120—21no—
317C2×#120C22×C13112yes—
318#518C4×C13111yescharacteristic, complemented
319C22×C22⋊C4—21no—
320C22×C22⋊C4C22×C13112yescomplemented
321C2×#99—24no—
322C2×#99—21no—
323C2×#99—21no—
324#379C22×C13112yescomplemented
325C2×#95—21no—
326#342—24no—
327C25D4×C13111yescharacteristic
328C25C23×C13111yescharacteristic
329H(5,𝔽2)—42no—
330H(5,𝔽2)—42no—
331C2×#41—21no—
332C2×#41—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4C2×C4×C13111yescharacteristic
340C22×D4C2×C4×C13111yescharacteristic
341C22×D4C2×C4×C13112yes—
342C22×D4D4×C13111yescharacteristic
343C22×D4D4×C13111yescharacteristic
344C22×D4D4×C13114yes—
345C23×C4—22no—
346C23×C4D4×C13111yescharacteristic
347#127—22no—
348#124—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352C22⋊Q8—22no—
353#121—22no—
354#121—24no—
355#121—24no—
356#121—24no—
357#120—24no—
358#120—22no—
359#120—22no—
360#120—22no—
361#120—22no—
362#120—22no—
363#120—24no—
364C4×D4—24no—
365C4×D4—24no—
366#117—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C2×C4×C13112yes—
376C2×C22⋊C4D4×C13114yes—
377#99—48no—
378#99—42no—
379#99—42no—
380#95—42no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—42no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24C22⋊C4×C13111yescharacteristic
392C24C22⋊C4×C13111yescharacteristic
393C24C22⋊C4×C13112yescomplemented
394C24C22×C4×C13111yescharacteristic
395C24C2×D4×C13111yescharacteristic
396C24C2×D4×C13114yes—
397C24C2×D4×C13111yescharacteristic
398#41—42no—
399#41—48no—
400#41—42no—
401C2×Q8—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—416no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C22⋊C4×C13111yescharacteristic
446C22×C4C22⋊C4×C13111yescharacteristic
447C22×C4C22⋊C4×C13114yescomplemented
448C22×C4C22⋊C4×C13112yescomplemented
449C4⋊C4—22no—
450C4⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—28no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C42—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—24no—
477C23—24no—
478C23—21no—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—44no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—82no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23—81no—
502C23—81no—
503C23—82no—
504C23—81no—
505C23—81no—
506C23—81no—
507C23—82no—
508C23#99×C13112yescomplemented
509C23C2×C22⋊C4×C13112yes—
510C23C2×C22⋊C4×C13111yescharacteristic
511C23#120×C13112yes—
512C23#120×C13112yes—
513Q8—42no—
514D4—28no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—42no—
522D4—42no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—84no—
549C2×C4#99×C13112yescomplemented
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—84no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—84no—
578C22—84no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22—162no—
583C22#379×C13111yescharacteristic
584C22C2×#99×C13111yescharacteristic
585C22C2×#99×C13111yescharacteristic
586C22B(4,𝔽2)×C13112yes—
587C22#458×C13112yes—
588C4—22no—
589C4—41no—
590C4—42no—
591C4—44no—
592C4—84no—
593C4—162no—
594C2—22no—
595C2—21no—
596C2—21no—
597C2—22no—
598C2—42no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2—82no—
603C2#1781×C13111yescharacteristic
604C2#1790×C13112yes—
subgroupG/H
center, socleC22×C131#379
commutatorC24C22×C4×C131
Frattini, cosocleC25C23×C131
prime radical#3484×C131C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C25×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1898×C131C2semidirect
3. #1781×C131C2semidirect
4. #1438×C131C2semidirect
5. C2×H(5,𝔽2)×C131C4semidirect
11. #534×C131C4semidirect
15. #518×C131C4semidirect
17. C22×C22⋊C4×C131C22semidirect
21. #379×C131C22semidirect
90. C24×C131C22⋊C4semidirect
144. C22×C4×C131C22⋊C4semidirect
145. C22×C4×C131C22⋊C4semidirect
205. C23×C131#99semidirect
246. C2×C4×C131#99semidirect
302. #8534C131direct (N × H)
303. C131#8534direct (N × H)
305. #1898C2×C131semidirect
306. #1781C2×C131semidirect
307. #1438C2×C131semidirect
308. C2×H(5,𝔽2)C4×C131semidirect
314. #534C4×C131semidirect
318. #518C4×C131semidirect
320. C22×C22⋊C4C22×C131semidirect
324. #379C22×C131semidirect
393. C24C22⋊C4×C131semidirect
447. C22×C4C22⋊C4×C131semidirect
448. C22×C4C22⋊C4×C131semidirect
508. C23#99×C131semidirect
549. C2×C4#99×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
#1898×C1312
#1781×C1312
#1438×C1312
#8534131