Finite Group Databasebeta

← C131×#13422 #45699306

Subgroups — C131×#13422 #45699306

Order 33536.

734 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 90 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#2669×C131C211yesmaximal, characteristic
2C2×#353×C131C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C131C211yesmaximal, characteristic, complemented
4#1889×C131C211yesmaximal, characteristic, complemented
5#1887×C131C211yesmaximal, characteristic, complemented
6#1867×C131C211yesmaximal, characteristic, complemented
7#1390×C131C211yesmaximal, characteristic, complemented
8C2×#127×C131C2211yescharacteristic
9C2×#121×C131—21no—
10C2×#120×C131—21no—
11C2×#120×C131C2211yescharacteristic
12#518×C131C2211yescharacteristic
13#418×C131—21no—
14C2×#100×C131C2211yescharacteristic
15C2×#99×C131C2211yescharacteristic
16C2×#99×C131C2211yescharacteristic
17#394×C131—21no—
18#392×C131—21no—
19#392×C131—21no—
20#388×C131—21no—
21#386×C131C2211yescharacteristic
22#385×C131—21no—
23#379×C131—21no—
24#353×C131—22no—
25AΣL(1,𝔽16)×C131—22no—
26#342×C131—21no—
27#342×C131—21no—
28#339×C131—21no—
29C25×C131D411yescharacteristic
30C22×D4×C131—21no—
31C22×D4×C131—21no—
32C22×D4×C131—21no—
33C22×D4×C131—21no—
34C22×D4×C131—21no—
35C22×D4×C131D411yescharacteristic
36C22×D4×C131C2311yescharacteristic
37C23×C4×C131D411yescharacteristic
38C2×M16×C131—21no—
39#127×C131—21no—
40#127×C131—21no—
41#127×C131—21no—
42#127×C131—21no—
43#121×C131—44no—
44#120×C131—21no—
45#120×C131—21no—
46#120×C131—21no—
47#120×C131—21no—
48#120×C131—44no—
49C4×D4×C131—41no—
50C4×D4×C131—41no—
51#117×C131—21no—
52C2×C4⋊C4×C131—21no—
53C2×C4⋊C4×C131—41no—
54C2×C22⋊C4×C131—21no—
55C2×C22⋊C4×C131—21no—
56C2×C22⋊C4×C131—21no—
57C2×C22⋊C4×C131—21no—
58C2×C22⋊C4×C131—21no—
59C2×C22⋊C4×C131—21no—
60C2×C22⋊C4×C131—21no—
61C2×C22⋊C4×C131—21no—
62C2×C22⋊C4×C131—21no—
63C2×C22⋊C4×C131—21no—
64C2×C22⋊C4×C131—41no—
65C2×C22⋊C4×C131—41no—
66C2×C22⋊C4×C131D411yescharacteristic
67C2×C22⋊C4×C131D411yescharacteristic
68C2×C42×C131D411yescharacteristic
69#102×C131—41no—
70#102×C131—41no—
71#100×C131—21no—
72#100×C131—21no—
73#99×C131—21no—
74#99×C131—21no—
75#99×C131—21no—
76#99×C131D412yescomplemented
77#95×C131—21no—
78#95×C131—21no—
79#95×C131—41no—
80C24×C131—21no—
81C24×C131—21no—
82C24×C131—21no—
83C24×C131—21no—
84C24×C131—41no—
85C24×C131—42no—
86C24×C131—41no—
87C24×C131—81no—
88C24×C131C2×D411yescharacteristic
89C24×C131C2×D411yescharacteristic
90C2×D4×C131—21no—
91C2×D4×C131—21no—
92C2×D4×C131—41no—
93C2×D4×C131—41no—
94C2×D4×C131—41no—
95C2×D4×C131—41no—
96C2×D4×C131—42no—
97C2×D4×C131—42no—
98C2×D4×C131—42no—
99C2×D4×C131—42no—
100C2×D4×C131—42no—
101C2×D4×C131—42no—
102C2×D4×C131—41no—
103C2×D4×C131—41no—
104C2×D4×C131—41no—
105C2×D4×C131—41no—
106C2×D4×C131—41no—
107C2×D4×C131—41no—
108C2×D4×C131—81no—
109C2×D4×C131—81no—
110C2×D4×C131—81no—
111C2×D4×C131—81no—
112C2×D4×C131—81no—
113C2×D4×C131—81no—
114C2×D4×C131C2×D411yescharacteristic
115C2×D4×C131#4111yescharacteristic
116C2×D4×C131#4111yescharacteristic
117C2×D4×C131#4111yescharacteristic
118C22×C4×C131—21no—
119C22×C4×C131—21no—
120C22×C4×C131—21no—
121C22×C4×C131—21no—
122C22×C4×C131—21no—
123C22×C4×C131—21no—
124C22×C4×C131—21no—
125C22×C4×C131—21no—
126C22×C4×C131—42no—
127C22×C4×C131—41no—
128C22×C4×C131—41no—
129C22×C4×C131—41no—
130C22×C4×C131C2×D411yescharacteristic
131M16×C131—41no—
132M16×C131—41no—
133C2×C8×C131—41no—
134C4⋊C4×C131—21no—
135C4⋊C4×C131—21no—
136C4⋊C4×C131—42no—
137C4⋊C4×C131—82no—
138C22⋊C4×C131—24no—
139C22⋊C4×C131—22no—
140C22⋊C4×C131—21no—
141C22⋊C4×C131—21no—
142C22⋊C4×C131—42no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—42no—
145C22⋊C4×C131—41no—
146C22⋊C4×C131—41no—
147C22⋊C4×C131—41no—
148C22⋊C4×C131—41no—
149C22⋊C4×C131—41no—
150C22⋊C4×C131—41no—
151C22⋊C4×C131—41no—
152C22⋊C4×C131—41no—
153C22⋊C4×C131—41no—
154C22⋊C4×C131—81no—
155C22⋊C4×C131—82no—
156C22⋊C4×C131—82no—
157C42×C131—21no—
158C42×C131—21no—
159C42×C131—41no—
160C23×C131—21no—
161C23×C131—21no—
162C23×C131—21no—
163C23×C131—21no—
164C23×C131—22no—
165C23×C131—41no—
166C23×C131—41no—
167C23×C131—41no—
168C23×C131—41no—
169C23×C131—41no—
170C23×C131—41no—
171C23×C131—41no—
172C23×C131—42no—
173C23×C131—41no—
174C23×C131—41no—
175C23×C131—41no—
176C23×C131—41no—
177C23×C131—42no—
178C23×C131—42no—
179C23×C131—41no—
180C23×C131—41no—
181C23×C131—41no—
182C23×C131—41no—
183C23×C131—41no—
184C23×C131—41no—
185C23×C131—81no—
186C23×C131—82no—
187C23×C131—81no—
188C23×C131—82no—
189C23×C131—84no—
190C23×C131—81no—
191C23×C131#12011yescharacteristic
192C23×C131#12111yescharacteristic
193C23×C131#12111yescharacteristic
194C23×C131#12311yescharacteristic
195C23×C131#12411yescharacteristic
196D4×C131—41no—
197D4×C131—41no—
198D4×C131—41no—
199D4×C131—41no—
200D4×C131—42no—
201D4×C131—81no—
202D4×C131—82no—
203D4×C131—82no—
204D4×C131—82no—
205D4×C131—82no—
206D4×C131—84no—
207D4×C131—82no—
208D4×C131—82no—
209D4×C131—84no—
210C2×C4×C131—21no—
211C2×C4×C131—21no—
212C2×C4×C131—22no—
213C2×C4×C131—22no—
214C2×C4×C131—41no—
215C2×C4×C131—41no—
216C2×C4×C131—41no—
217C2×C4×C131—41no—
218C2×C4×C131—42no—
219C2×C4×C131—42no—
220C2×C4×C131—41no—
221C2×C4×C131—41no—
222C2×C4×C131—41no—
223C2×C4×C131—41no—
224C2×C4×C131—41no—
225C2×C4×C131—41no—
226C2×C4×C131—41no—
227C2×C4×C131—41no—
228C2×C4×C131—81no—
229C2×C4×C131—81no—
230C2×C4×C131—81no—
231C2×C4×C131—81no—
232C2×C4×C131—81no—
233C2×C4×C131—81no—
234C2×C4×C131—81no—
235C2×C4×C131—81no—
236C2×C4×C131—81no—
237C2×C4×C131—81no—
238C2×C4×C131#12111yescharacteristic
239C2×C4×C131#12311yescharacteristic
240C8×C131—81no—
241C22×C131—21no—
242C22×C131—21no—
243C22×C131—21no—
244C22×C131—21no—
245C22×C131—21no—
246C22×C131—21no—
247C22×C131—41no—
248C22×C131—41no—
249C22×C131—41no—
250C22×C131—41no—
251C22×C131—42no—
252C22×C131—42no—
253C22×C131—41no—
254C22×C131—41no—
255C22×C131—41no—
256C22×C131—41no—
257C22×C131—44no—
258C22×C131—42no—
259C22×C131—81no—
260C22×C131—81no—
261C22×C131—81no—
262C22×C131—81no—
263C22×C131—81no—
264C22×C131—81no—
265C22×C131—81no—
266C22×C131—81no—
267C22×C131—82no—
268C22×C131—82no—
269C22×C131—82no—
270C22×C131—81no—
271C22×C131—81no—
272C22×C131—81no—
273C22×C131—81no—
274C22×C131—81no—
275C22×C131#39411yescharacteristic
276C22×C131B(4,𝔽2)11yescharacteristic
277C22×C131#45811yescharacteristic
278C4×C131—21no—
279C4×C131—21no—
280C4×C131—42no—
281C4×C131—42no—
282C4×C131—81no—
283C4×C131—81no—
284C4×C131—82no—
285C4×C131—81no—
286C4×C131—81no—
287C4×C131—161no—
288C2×C131—21no—
289C2×C131—21no—
290C2×C131—41no—
291C2×C131—41no—
292C2×C131—41no—
293C2×C131—41no—
294C2×C131—82no—
295C2×C131—161no—
296C2×C131#204411yescharacteristic
297C2×C131#219611yescharacteristic
298C2×C131#220011yescharacteristic
299#13422C13111yesmaximal, characteristic, direct product factor, Sylow
300C131#1342211yescharacteristic, direct product factor, Sylow
301#2669C2×C13111yescharacteristic
302C2×#353C2×C13111yescharacteristic, complemented
303C2×AΣL(1,𝔽16)C2×C13111yescharacteristic, complemented
304#1889C2×C13111yescharacteristic, complemented
305#1887C2×C13111yescharacteristic, complemented
306#1867C2×C13111yescharacteristic, complemented
307#1390C2×C13111yescharacteristic, complemented
308C2×#127C22×C13111yescharacteristic
309C2×#121—21no—
310C2×#120—21no—
311C2×#120C22×C13111yescharacteristic
312#518C22×C13111yescharacteristic
313#418—21no—
314C2×#100C22×C13111yescharacteristic
315C2×#99C22×C13111yescharacteristic
316C2×#99C22×C13111yescharacteristic
317#394—21no—
318#392—21no—
319#392—21no—
320#388—21no—
321#386C22×C13111yescharacteristic
322#385—21no—
323#379—21no—
324#353—22no—
325AΣL(1,𝔽16)—22no—
326#342—21no—
327#342—21no—
328#339—21no—
329C25D4×C13111yescharacteristic
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4D4×C13111yescharacteristic
336C22×D4C23×C13111yescharacteristic
337C23×C4D4×C13111yescharacteristic
338C2×M16—21no—
339#127—21no—
340#127—21no—
341#127—21no—
342#127—21no—
343#121—44no—
344#120—21no—
345#120—21no—
346#120—21no—
347#120—21no—
348#120—44no—
349C4×D4—41no—
350C4×D4—41no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—41no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4D4×C13111yescharacteristic
367C2×C22⋊C4D4×C13111yescharacteristic
368C2×C42D4×C13111yescharacteristic
369#102—41no—
370#102—41no—
371#100—21no—
372#100—21no—
373#99—21no—
374#99—21no—
375#99—21no—
376#99D4×C13112yescomplemented
377#95—21no—
378#95—21no—
379#95—41no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—41no—
385C24—42no—
386C24—41no—
387C24—81no—
388C24C2×D4×C13111yescharacteristic
389C24C2×D4×C13111yescharacteristic
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—81no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—81no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4C2×D4×C13111yescharacteristic
415C2×D4#41×C13111yescharacteristic
416C2×D4#41×C13111yescharacteristic
417C2×D4#41×C13111yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4C2×D4×C13111yescharacteristic
431M16—41no—
432M16—41no—
433C2×C8—41no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—42no—
437C4⋊C4—82no—
438C22⋊C4—24no—
439C22⋊C4—22no—
440C22⋊C4—21no—
441C22⋊C4—21no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—81no—
455C22⋊C4—82no—
456C22⋊C4—82no—
457C42—21no—
458C42—21no—
459C42—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—81no—
486C23—82no—
487C23—81no—
488C23—82no—
489C23—84no—
490C23—81no—
491C23#120×C13111yescharacteristic
492C23#121×C13111yescharacteristic
493C23#121×C13111yescharacteristic
494C23#123×C13111yescharacteristic
495C23#124×C13111yescharacteristic
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—42no—
501D4—81no—
502D4—82no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—84no—
507D4—82no—
508D4—82no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4#121×C13111yescharacteristic
539C2×C4#123×C13111yescharacteristic
540C8—81no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—44no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—82no—
568C22—82no—
569C22—82no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#394×C13111yescharacteristic
576C22B(4,𝔽2)×C13111yescharacteristic
577C22#458×C13111yescharacteristic
578C4—21no—
579C4—21no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—82no—
585C4—81no—
586C4—81no—
587C4—161no—
588C2—21no—
589C2—21no—
590C2—41no—
591C2—41no—
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2#2044×C13111yescharacteristic
597C2#2196×C13111yescharacteristic
598C2#2200×C13111yescharacteristic
subgroupG/H
center, socleC22×C131B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C23×C131
prime radical#2669×C131C2
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#353×C131C2semidirect
3. C2×AΣL(1,𝔽16)×C131C2semidirect
4. #1889×C131C2semidirect
5. #1887×C131C2semidirect
6. #1867×C131C2semidirect
7. #1390×C131C2semidirect
76. #99×C131D4semidirect
299. #13422C131direct (N × H)
300. C131#13422direct (N × H)
302. C2×#353C2×C131semidirect
303. C2×AΣL(1,𝔽16)C2×C131semidirect
304. #1889C2×C131semidirect
305. #1887C2×C131semidirect
306. #1867C2×C131semidirect
307. #1390C2×C131semidirect
376. #99D4×C131semidirect

Maximal subgroups

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

subgroupindex
#2669×C1312
C2×#353×C1312
C2×AΣL(1,𝔽16)×C1312
#1889×C1312
#1887×C1312
#1867×C1312
#1390×C1312
#13422131