Finite Group Databasebeta

← C131×#11043 #45696927

Subgroups — C131×#11043 #45696927

Order 33536.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C131C212yesmaximal
2C2×#386×C131C211yesmaximal, characteristic
3C2×#380×C131C211yesmaximal, characteristic, complemented
4C2×#342×C131C212yesmaximal, complemented
5C22⋊#95×C131C211yesmaximal, characteristic, complemented
6C23×D4×C131C2211yescharacteristic
7C24×C4×C131C2211yescharacteristic
8C22×C4⋊C4×C131—21no—
9C22×C22⋊C4×C131C412yescomplemented
10C22×C22⋊C4×C131C2211yescharacteristic
11C22×C22⋊C4×C131C2212yes—
12C22×C22⋊C4×C131C2212yes—
13C2×#99×C131—24no—
14C2×#99×C131—24no—
15C2×#99×C131—24no—
16#386×C131—21no—
17#386×C131—22no—
18#386×C131—21no—
19#380×C131—24no—
20C2×#95×C131—21no—
21C2×#95×C131—22no—
22C2×#95×C131C412yescomplemented
23#342×C131—24no—
24C25×C131C2×C411yescharacteristic
25C25×C131C2311yescharacteristic
26C22×D4×C131—22no—
27C22×D4×C131—22no—
28C22×D4×C131—21no—
29C22×D4×C131—21no—
30C22×D4×C131—21no—
31C22×D4×C131—21no—
32C22×D4×C131—22no—
33C22×D4×C131—22no—
34C22×D4×C131D412yes—
35C22×D4×C131Q812yes—
36C23×C4×C131—22no—
37C23×C4×C131—22no—
38C23×C4×C131—22no—
39C23×C4×C131—22no—
40C23×C4×C131—44no—
41C23×C4×C131C2×C411yescharacteristic
42C23×C4×C131C2×C412yes—
43C23×C4×C131C2×C412yes—
44C23×C4×C131D411yescharacteristic
45C23×C4×C131D412yes—
46C23×C4×C131D411yescharacteristic
47C2×C4⋊C4×C131—24no—
48C2×C4⋊C4×C131—44no—
49C2×C22⋊C4×C131—22no—
50C2×C22⋊C4×C131—22no—
51C2×C22⋊C4×C131—22no—
52C2×C22⋊C4×C131—22no—
53C2×C22⋊C4×C131—22no—
54C2×C22⋊C4×C131—22no—
55C2×C22⋊C4×C131—22no—
56C2×C22⋊C4×C131—22no—
57C2×C22⋊C4×C131—22no—
58C2×C22⋊C4×C131—22no—
59C2×C22⋊C4×C131—21no—
60C2×C22⋊C4×C131—21no—
61C2×C22⋊C4×C131—22no—
62C2×C22⋊C4×C131—22no—
63C2×C22⋊C4×C131—22no—
64C2×C22⋊C4×C131—22no—
65C2×C22⋊C4×C131—44no—
66C2×C22⋊C4×C131D414yes—
67C2×C22⋊C4×C131D414yes—
68#99×C131—216no—
69#95×C131—24no—
70#95×C131—22no—
71#95×C131—22no—
72#95×C131—44no—
73C24×C131—21no—
74C24×C131—21no—
75C24×C131—22no—
76C24×C131—22no—
77C24×C131—42no—
78C24×C131—42no—
79C24×C131—42no—
80C24×C131—42no—
81C24×C131C4⋊C412yescomplemented
82C24×C131C22×C411yescharacteristic
83C24×C131C2×D411yescharacteristic
84C24×C131C2×D411yescharacteristic
85C24×C131C2×D411yescharacteristic
86C24×C131C2×D412yes—
87C24×C131C2×D412yes—
88C24×C131C2×Q811yescharacteristic
89C24×C131#4111yescharacteristic
90C24×C131#4111yescharacteristic
91C24×C131#4112yes—
92C24×C131#4112yes—
93C2×D4×C131—24no—
94C2×D4×C131—22no—
95C2×D4×C131—22no—
96C2×D4×C131—22no—
97C2×D4×C131—22no—
98C2×D4×C131—24no—
99C2×D4×C131—24no—
100C2×D4×C131—24no—
101C2×D4×C131—41no—
102C2×D4×C131—42no—
103C2×D4×C131—42no—
104C2×D4×C131—42no—
105C2×D4×C131—41no—
106C2×D4×C131—42no—
107C2×D4×C131—42no—
108C2×D4×C131—41no—
109C2×D4×C131—42no—
110C2×D4×C131—41no—
111C22×C4×C131—21no—
112C22×C4×C131—21no—
113C22×C4×C131—24no—
114C22×C4×C131—21no—
115C22×C4×C131—21no—
116C22×C4×C131—24no—
117C22×C4×C131—22no—
118C22×C4×C131—22no—
119C22×C4×C131—21no—
120C22×C4×C131—24no—
121C22×C4×C131—21no—
122C22×C4×C131—24no—
123C22×C4×C131—24no—
124C22×C4×C131—22no—
125C22×C4×C131—24no—
126C22×C4×C131—24no—
127C22×C4×C131—24no—
128C22×C4×C131—42no—
129C22×C4×C131—42no—
130C22×C4×C131—42no—
131C22×C4×C131—48no—
132C22×C4×C131—48no—
133C22×C4×C131—44no—
134C22×C4×C131—44no—
135C22×C4×C131—44no—
136C22×C4×C131—44no—
137C22×C4×C131—42no—
138C22×C4×C131—42no—
139C22×C4×C131—42no—
140C22×C4×C131—42no—
141C22×C4×C131—42no—
142C22×C4×C131—42no—
143C22×C4×C131C22⋊C412yes—
144C22×C4×C131C22⋊C412yes—
145C22×C4×C131C4⋊C412yescomplemented
146C4⋊C4×C131—48no—
147C22⋊C4×C131—24no—
148C22⋊C4×C131—24no—
149C22⋊C4×C131—24no—
150C22⋊C4×C131—24no—
151C22⋊C4×C131—44no—
152C22⋊C4×C131—42no—
153C22⋊C4×C131—42no—
154C22⋊C4×C131—42no—
155C22⋊C4×C131—42no—
156C22⋊C4×C131—41no—
157C22⋊C4×C131—42no—
158C22⋊C4×C131—41no—
159C22⋊C4×C131—44no—
160C23×C131—22no—
161C23×C131—22no—
162C23×C131—22no—
163C23×C131—22no—
164C23×C131—22no—
165C23×C131—22no—
166C23×C131—22no—
167C23×C131—24no—
168C23×C131—42no—
169C23×C131—42no—
170C23×C131—42no—
171C23×C131—42no—
172C23×C131—44no—
173C23×C131—42no—
174C23×C131—42no—
175C23×C131—42no—
176C23×C131—42no—
177C23×C131—44no—
178C23×C131—44no—
179C23×C131—44no—
180C23×C131—41no—
181C23×C131—42no—
182C23×C131—41no—
183C23×C131—42no—
184C23×C131—42no—
185C23×C131—82no—
186C23×C131—82no—
187C23×C131—84no—
188C23×C131C2×C22⋊C411yescharacteristic
189C23×C131C2×C4⋊C411yescharacteristic
190C23×C131#11711yescharacteristic
191C23×C131C4×D412yes—
192C23×C131C4×D412yes—
193C23×C131#12011yescharacteristic
194C23×C131#12012yes—
195C23×C131#12111yescharacteristic
196C23×C131#12111yescharacteristic
197C23×C131#12112yes—
198C23×C131#12112yes—
199C23×C131#12112yes—
200C23×C131C22⋊Q811yescharacteristic
201C23×C131C22⋊Q811yescharacteristic
202C23×C131C22⋊Q812yes—
203C23×C131C22⋊Q812yes—
204C23×C131#12311yescharacteristic
205C23×C131#12312yes—
206C23×C131#12312yes—
207C23×C131#12411yescharacteristic
208C23×C131#12412yes—
209C23×C131#12612yes—
210C23×C131#12711yescharacteristic
211D4×C131—42no—
212D4×C131—42no—
213D4×C131—44no—
214D4×C131—44no—
215D4×C131—42no—
216D4×C131—42no—
217C2×C4×C131—24no—
218C2×C4×C131—24no—
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—22no—
226C2×C4×C131—48no—
227C2×C4×C131—48no—
228C2×C4×C131—42no—
229C2×C4×C131—42no—
230C2×C4×C131—41no—
231C2×C4×C131—42no—
232C2×C4×C131—41no—
233C2×C4×C131—44no—
234C2×C4×C131—44no—
235C2×C4×C131—48no—
236C2×C4×C131—42no—
237C2×C4×C131—44no—
238C2×C4×C131—44no—
239C2×C4×C131—42no—
240C2×C4×C131—42no—
241C2×C4×C131—84no—
242C2×C4×C131—84no—
243C2×C4×C131—82no—
244C2×C4×C131—82no—
245C2×C4×C131—84no—
246C2×C4×C131—84no—
247C2×C4×C131#9914yescomplemented
248C22×C131—22no—
249C22×C131—22no—
250C22×C131—22no—
251C22×C131—22no—
252C22×C131—22no—
253C22×C131—22no—
254C22×C131—21no—
255C22×C131—21no—
256C22×C131—22no—
257C22×C131—22no—
258C22×C131—21no—
259C22×C131—22no—
260C22×C131—22no—
261C22×C131—21no—
262C22×C131—24no—
263C22×C131—22no—
264C22×C131—24no—
265C22×C131—22no—
266C22×C131—42no—
267C22×C131—42no—
268C22×C131—42no—
269C22×C131—42no—
270C22×C131—42no—
271C22×C131—42no—
272C22×C131—42no—
273C22×C131—42no—
274C22×C131—44no—
275C22×C131—42no—
276C22×C131—84no—
277C22×C131—84no—
278C22×C131—81no—
279C22×C131—81no—
280C22×C131—82no—
281C22×C131#38011yescharacteristic
282C22×C131#38512yes—
283C22×C131#38611yescharacteristic
284C22×C131#38812yes—
285C22×C131#39011yescharacteristic
286C22×C131#39211yescharacteristic
287C22×C131#39311yescharacteristic
288C22×C131#39412yes—
289C22×C131#39612yes—
290C22×C131#39711yescharacteristic
291C22×C131#39911yescharacteristic
292C22×C131C2×#9912yes—
293C22×C131#41012yes—
294C4×C131—24no—
295C4×C131—42no—
296C4×C131—42no—
297C4×C131—84no—
298C4×C131—84no—
299C4×C131—82no—
300C2×C131—21no—
301C2×C131—22no—
302C2×C131—22no—
303C2×C131—22no—
304C2×C131—21no—
305C2×C131—22no—
306C2×C131—21no—
307C2×C131—21no—
308C2×C131—82no—
309C2×C131#143911yescharacteristic
310C2×C131#179912yes—
311C2×C131#189811yescharacteristic
312C2×C131#189911yescharacteristic
313C2×C131#196412yes—
314#11043C13111yesmaximal, characteristic, direct product factor, Sylow
315C131#1104311yescharacteristic, direct product factor, Sylow
316C22×#99C2×C13112yes—
317C2×#386C2×C13111yescharacteristic
318C2×#380C2×C13111yescharacteristic, complemented
319C2×#342C2×C13112yescomplemented
320C22⋊#95C2×C13111yescharacteristic, complemented
321C23×D4C22×C13111yescharacteristic
322C24×C4C22×C13111yescharacteristic
323C22×C4⋊C4—21no—
324C22×C22⋊C4C4×C13112yescomplemented
325C22×C22⋊C4C22×C13111yescharacteristic
326C22×C22⋊C4C22×C13112yes—
327C22×C22⋊C4C22×C13112yes—
328C2×#99—24no—
329C2×#99—24no—
330C2×#99—24no—
331#386—21no—
332#386—22no—
333#386—21no—
334#380—24no—
335C2×#95—21no—
336C2×#95—22no—
337C2×#95C4×C13112yescomplemented
338#342—24no—
339C25C2×C4×C13111yescharacteristic
340C25C23×C13111yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4D4×C13112yes—
350C22×D4Q8×C13112yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—44no—
356C23×C4C2×C4×C13111yescharacteristic
357C23×C4C2×C4×C13112yes—
358C23×C4C2×C4×C13112yes—
359C23×C4D4×C13111yescharacteristic
360C23×C4D4×C13112yes—
361C23×C4D4×C13111yescharacteristic
362C2×C4⋊C4—24no—
363C2×C4⋊C4—44no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4D4×C13114yes—
382C2×C22⋊C4D4×C13114yes—
383#99—216no—
384#95—24no—
385#95—22no—
386#95—22no—
387#95—44no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C4⋊C4×C13112yescomplemented
397C24C22×C4×C13111yescharacteristic
398C24C2×D4×C13111yescharacteristic
399C24C2×D4×C13111yescharacteristic
400C24C2×D4×C13111yescharacteristic
401C24C2×D4×C13112yes—
402C24C2×D4×C13112yes—
403C24C2×Q8×C13111yescharacteristic
404C24#41×C13111yescharacteristic
405C24#41×C13111yescharacteristic
406C24#41×C13112yes—
407C24#41×C13112yes—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—41no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—41no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4C22⋊C4×C13112yes—
459C22×C4C22⋊C4×C13112yes—
460C22×C4C4⋊C4×C13112yescomplemented
461C4⋊C4—48no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—44no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—41no—
474C22⋊C4—44no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—44no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—84no—
501C23—82no—
502C23—82no—
503C23C2×C22⋊C4×C13111yescharacteristic
504C23C2×C4⋊C4×C13111yescharacteristic
505C23#117×C13111yescharacteristic
506C23C4×D4×C13112yes—
507C23C4×D4×C13112yes—
508C23#120×C13111yescharacteristic
509C23#120×C13112yes—
510C23#121×C13112yes—
511C23#121×C13111yescharacteristic
512C23#121×C13111yescharacteristic
513C23#121×C13112yes—
514C23#121×C13112yes—
515C23C22⋊Q8×C13111yescharacteristic
516C23C22⋊Q8×C13111yescharacteristic
517C23C22⋊Q8×C13112yes—
518C23C22⋊Q8×C13112yes—
519C23#123×C13111yescharacteristic
520C23#123×C13112yes—
521C23#123×C13112yes—
522C23#124×C13111yescharacteristic
523C23#124×C13112yes—
524C23#126×C13112yes—
525C23#127×C13111yescharacteristic
526D4—42no—
527D4—42no—
528D4—44no—
529D4—44no—
530D4—42no—
531D4—42no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—48no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—84no—
562C2×C4#99×C13114yescomplemented
563C22—24no—
564C22—22no—
565C22—24no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—22no—
577C22—21no—
578C22—22no—
579C22—22no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—42no—
591C22—84no—
592C22—84no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22#380×C13111yescharacteristic
597C22#385×C13112yes—
598C22#386×C13111yescharacteristic
599C22#388×C13112yes—
600C22#390×C13111yescharacteristic
601C22#392×C13111yescharacteristic
602C22#393×C13111yescharacteristic
603C22#394×C13112yes—
604C22#396×C13112yes—
605C22#397×C13111yescharacteristic
606C22#399×C13111yescharacteristic
607C22C2×#99×C13112yes—
608C22#410×C13112yes—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—84no—
613C4—84no—
614C4—82no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2#1439×C13111yescharacteristic
625C2#1799×C13112yes—
626C2#1898×C13111yescharacteristic
627C2#1899×C13111yescharacteristic
628C2#1964×C13112yes—
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC24C22×C4×C131
Frattini, cosocleC25C23×C131
prime radicalC23×D4×C131C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#380×C131C2semidirect
4. C2×#342×C131C2semidirect
5. C22⋊#95×C131C2semidirect
9. C22×C22⋊C4×C131C4semidirect
22. C2×#95×C131C4semidirect
81. C24×C131C4⋊C4semidirect
145. C22×C4×C131C4⋊C4semidirect
247. C2×C4×C131#99semidirect
314. #11043C131direct (N × H)
315. C131#11043direct (N × H)
318. C2×#380C2×C131semidirect
319. C2×#342C2×C131semidirect
320. C22⋊#95C2×C131semidirect
324. C22×C22⋊C4C4×C131semidirect
337. C2×#95C4×C131semidirect
396. C24C4⋊C4×C131semidirect
460. C22×C4C4⋊C4×C131semidirect
562. C2×C4#99×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C1312
C2×#386×C1312
C2×#380×C1312
C2×#342×C1312
C22⋊#95×C1312
#11043131