Finite Group Databasebeta

← C137×#13082 #46862468

Subgroups — C137×#13082 #46862468

Order 35072.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C137C211yesmaximal, characteristic, complemented
2#2403×C137C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C137C212yesmaximal, complemented
4#1781×C137C211yesmaximal, characteristic, complemented
5#1390×C137C212yesmaximal, complemented
6C23×D4×C137C411yescharacteristic, complemented
7C23×D4×C137C2211yescharacteristic
8C22×M16×C137—21no—
9C2×#120×C137—21no—
10C2×#120×C137C411yescharacteristic, complemented
11C2×#120×C137C2211yescharacteristic
12C2×#100×C137—21no—
13C2×#100×C137—24no—
14C2×#100×C137C2212yes—
15C2×#99×C137—21no—
16C2×#99×C137C2212yes—
17#392×C137—21no—
18#392×C137—21no—
19#386×C137—21no—
20#386×C137C411yescharacteristic, complemented
21#386×C137C2211yescharacteristic
22#379×C137—21no—
23#379×C137C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C137—24no—
25C25×C137C2×C411yescharacteristic
26C25×C137C2×C411yescharacteristic
27C25×C137D411yescharacteristic
28C22×D4×C137—21no—
29C22×D4×C137—22no—
30C22×D4×C137—22no—
31C22×D4×C137—21no—
32C22×D4×C137—21no—
33C22×D4×C137—21no—
34C22×D4×C137—42no—
35C22×D4×C137—41no—
36C22×D4×C137—41no—
37C22×D4×C137—44no—
38C22×D4×C137—41no—
39C22×D4×C137—41no—
40C22×D4×C137C2×C411yescharacteristic
41C22×D4×C137D411yescharacteristic
42C22×D4×C137D411yescharacteristic
43C22×D4×C137C2311yescharacteristic
44C23×C4×C137C2×C411yescharacteristic
45C23×C4×C137D411yescharacteristic
46C2×M16×C137—24no—
47C2×M16×C137—22no—
48C2×M16×C137—41no—
49C2×M16×C137—42no—
50C22×C8×C137—41no—
51#120×C137—22no—
52#120×C137—22no—
53#120×C137—44no—
54#120×C137—42no—
55C2×C22⋊C4×C137—21no—
56C2×C22⋊C4×C137—21no—
57C2×C22⋊C4×C137—21no—
58C2×C22⋊C4×C137—21no—
59C2×C22⋊C4×C137—21no—
60C2×C22⋊C4×C137—22no—
61C2×C22⋊C4×C137—21no—
62C2×C22⋊C4×C137—41no—
63C2×C22⋊C4×C137—41no—
64C2×C22⋊C4×C137C2×C411yescharacteristic
65C2×C22⋊C4×C137C2×C411yescharacteristic
66#100×C137—24no—
67#100×C137—22no—
68#100×C137D414yescomplemented
69#99×C137—22no—
70#99×C137—22no—
71#99×C137—42no—
72#95×C137—21no—
73#95×C137—21no—
74C24×C137—21no—
75C24×C137—21no—
76C24×C137—21no—
77C24×C137—21no—
78C24×C137—21no—
79C24×C137—22no—
80C24×C137—22no—
81C24×C137—22no—
82C24×C137—41no—
83C24×C137—41no—
84C24×C137—42no—
85C24×C137—41no—
86C24×C137—42no—
87C24×C137—42no—
88C24×C137—41no—
89C24×C137—81no—
90C24×C137—81no—
91C24×C137—81no—
92C24×C137C22⋊C411yescharacteristic
93C24×C137C22⋊C411yescharacteristic
94C24×C137C22⋊C411yescharacteristic
95C24×C137C22×C411yescharacteristic
96C24×C137C2×D411yescharacteristic
97C2×D4×C137—24no—
98C2×D4×C137—22no—
99C2×D4×C137—22no—
100C2×D4×C137—22no—
101C2×D4×C137—22no—
102C2×D4×C137—21no—
103C2×D4×C137—21no—
104C2×D4×C137—41no—
105C2×D4×C137—41no—
106C2×D4×C137—41no—
107C2×D4×C137—41no—
108C2×D4×C137—41no—
109C2×D4×C137—41no—
110C2×D4×C137—44no—
111C2×D4×C137—44no—
112C2×D4×C137—44no—
113C2×D4×C137—44no—
114C2×D4×C137—42no—
115C2×D4×C137—42no—
116C2×D4×C137—42no—
117C2×D4×C137—42no—
118C2×D4×C137—44no—
119C2×D4×C137—44no—
120C2×D4×C137—44no—
121C2×D4×C137—41no—
122C2×D4×C137—41no—
123C2×D4×C137—44no—
124C2×D4×C137—42no—
125C2×D4×C137—42no—
126C2×D4×C137—42no—
127C2×D4×C137—42no—
128C2×D4×C137—81no—
129C2×D4×C137—81no—
130C2×D4×C137C2×D412yes—
131C2×D4×C137#4112yes—
132C22×C4×C137—21no—
133C22×C4×C137—21no—
134C22×C4×C137—22no—
135C22×C4×C137—21no—
136C22×C4×C137—21no—
137C22×C4×C137—21no—
138C22×C4×C137—21no—
139C22×C4×C137—21no—
140C22×C4×C137—42no—
141C22×C4×C137—41no—
142C22×C4×C137—42no—
143C22×C4×C137C22⋊C411yescharacteristic
144C22×C4×C137C2×D411yescharacteristic
145M16×C137—24no—
146M16×C137—44no—
147M16×C137—42no—
148C2×C8×C137—44no—
149C2×C8×C137—42no—
150C22⋊C4×C137—22no—
151C22⋊C4×C137—42no—
152C22⋊C4×C137—42no—
153C22⋊C4×C137—42no—
154C22⋊C4×C137—42no—
155C22⋊C4×C137—41no—
156C22⋊C4×C137—41no—
157C22⋊C4×C137—41no—
158C22⋊C4×C137—42no—
159C22⋊C4×C137—42no—
160C22⋊C4×C137—81no—
161C22⋊C4×C137—82no—
162C22⋊C4×C137—82no—
163C23×C137—22no—
164C23×C137—21no—
165C23×C137—21no—
166C23×C137—21no—
167C23×C137—21no—
168C23×C137—21no—
169C23×C137—21no—
170C23×C137—22no—
171C23×C137—21no—
172C23×C137—21no—
173C23×C137—21no—
174C23×C137—21no—
175C23×C137—21no—
176C23×C137—21no—
177C23×C137—41no—
178C23×C137—42no—
179C23×C137—42no—
180C23×C137—42no—
181C23×C137—42no—
182C23×C137—41no—
183C23×C137—41no—
184C23×C137—41no—
185C23×C137—41no—
186C23×C137—41no—
187C23×C137—41no—
188C23×C137—42no—
189C23×C137—41no—
190C23×C137—42no—
191C23×C137—41no—
192C23×C137—41no—
193C23×C137—41no—
194C23×C137—41no—
195C23×C137—42no—
196C23×C137—42no—
197C23×C137—42no—
198C23×C137—42no—
199C23×C137—41no—
200C23×C137—41no—
201C23×C137—41no—
202C23×C137—81no—
203C23×C137—81no—
204C23×C137—81no—
205C23×C137—81no—
206C23×C137—82no—
207C23×C137—84no—
208C23×C137—84no—
209C23×C137—84no—
210C23×C137—84no—
211C23×C137—84no—
212C23×C137—84no—
213C23×C137—82no—
214C23×C137#9911yescharacteristic
215C23×C137#9911yescharacteristic
216C23×C137C2×C22⋊C411yescharacteristic
217C23×C137C4×D412yes—
218C23×C137#12112yes—
219D4×C137—42no—
220D4×C137—42no—
221D4×C137—44no—
222D4×C137—44no—
223D4×C137—42no—
224D4×C137—42no—
225D4×C137—44no—
226D4×C137—48no—
227D4×C137—44no—
228D4×C137—84no—
229D4×C137—84no—
230C2×C4×C137—22no—
231C2×C4×C137—22no—
232C2×C4×C137—22no—
233C2×C4×C137—22no—
234C2×C4×C137—21no—
235C2×C4×C137—21no—
236C2×C4×C137—21no—
237C2×C4×C137—21no—
238C2×C4×C137—22no—
239C2×C4×C137—41no—
240C2×C4×C137—42no—
241C2×C4×C137—41no—
242C2×C4×C137—42no—
243C2×C4×C137—41no—
244C2×C4×C137—41no—
245C2×C4×C137—41no—
246C2×C4×C137—41no—
247C2×C4×C137—41no—
248C2×C4×C137—41no—
249C2×C4×C137—82no—
250C2×C4×C137—82no—
251C2×C4×C137—82no—
252C2×C4×C137#9912yes—
253C2×C4×C137#12011yescharacteristic
254C2×C4×C137#12311yescharacteristic
255C8×C137—44no—
256C22×C137—21no—
257C22×C137—21no—
258C22×C137—21no—
259C22×C137—21no—
260C22×C137—21no—
261C22×C137—21no—
262C22×C137—21no—
263C22×C137—22no—
264C22×C137—22no—
265C22×C137—42no—
266C22×C137—42no—
267C22×C137—42no—
268C22×C137—42no—
269C22×C137—42no—
270C22×C137—42no—
271C22×C137—42no—
272C22×C137—42no—
273C22×C137—41no—
274C22×C137—41no—
275C22×C137—41no—
276C22×C137—41no—
277C22×C137—42no—
278C22×C137—41no—
279C22×C137—41no—
280C22×C137—41no—
281C22×C137—41no—
282C22×C137—41no—
283C22×C137—41no—
284C22×C137—81no—
285C22×C137—84no—
286C22×C137—84no—
287C22×C137—81no—
288C22×C137—81no—
289C22×C137—81no—
290C22×C137—81no—
291C22×C137—81no—
292C22×C137—84no—
293C22×C137—84no—
294C22×C137—84no—
295C22×C137—84no—
296C22×C137—81no—
297C22×C137—81no—
298C22×C137AΣL(1,𝔽16)12yescomplemented
299C22×C137#38611yescharacteristic
300C22×C137C2×#9911yescharacteristic
301C22×C137C2×#9911yescharacteristic
302C4×C137—21no—
303C4×C137—22no—
304C4×C137—21no—
305C4×C137—42no—
306C4×C137—81no—
307C4×C137—81no—
308C4×C137—162no—
309C2×C137—21no—
310C2×C137—21no—
311C2×C137—22no—
312C2×C137—42no—
313C2×C137—41no—
314C2×C137—42no—
315C2×C137—81no—
316C2×C137—82no—
317C2×C137—81no—
318C2×C137#189811yescharacteristic
319C2×C137C2×AΣL(1,𝔽16)11yescharacteristic
320C2×C137#212111yescharacteristic
321#13082C13711yesmaximal, characteristic, direct product factor, Sylow
322C137#1308211yescharacteristic, direct product factor, Sylow
323C22×#100C2×C13711yescharacteristic, complemented
324#2403C2×C13711yescharacteristic
325C2×AΣL(1,𝔽16)C2×C13712yescomplemented
326#1781C2×C13711yescharacteristic, complemented
327#1390C2×C13712yescomplemented
328C23×D4C4×C13711yescharacteristic, complemented
329C23×D4C22×C13711yescharacteristic
330C22×M16—21no—
331C2×#120—21no—
332C2×#120C4×C13711yescharacteristic, complemented
333C2×#120C22×C13711yescharacteristic
334C2×#100—21no—
335C2×#100—24no—
336C2×#100C22×C13712yes—
337C2×#99—21no—
338C2×#99C22×C13712yes—
339#392—21no—
340#392—21no—
341#386—21no—
342#386C4×C13711yescharacteristic, complemented
343#386C22×C13711yescharacteristic
344#379—21no—
345#379C4×C13711yescharacteristic, complemented
346AΣL(1,𝔽16)—24no—
347C25C2×C4×C13711yescharacteristic
348C25C2×C4×C13711yescharacteristic
349C25D4×C13711yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—44no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C13711yescharacteristic
363C22×D4D4×C13711yescharacteristic
364C22×D4D4×C13711yescharacteristic
365C22×D4C23×C13711yescharacteristic
366C23×C4C2×C4×C13711yescharacteristic
367C23×C4D4×C13711yescharacteristic
368C2×M16—24no—
369C2×M16—22no—
370C2×M16—41no—
371C2×M16—42no—
372C22×C8—41no—
373#120—22no—
374#120—22no—
375#120—44no—
376#120—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4C2×C4×C13711yescharacteristic
387C2×C22⋊C4C2×C4×C13711yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C13714yescomplemented
391#99—22no—
392#99—22no—
393#99—42no—
394#95—21no—
395#95—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—41no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C13711yescharacteristic
415C24C22⋊C4×C13711yescharacteristic
416C24C22⋊C4×C13711yescharacteristic
417C24C22×C4×C13711yescharacteristic
418C24C2×D4×C13711yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C13712yes—
453C2×D4#41×C13712yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C13711yescharacteristic
466C22×C4C2×D4×C13711yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—42no—
523C23—42no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23#99×C13711yescharacteristic
537C23#99×C13711yescharacteristic
538C23C2×C22⋊C4×C13711yescharacteristic
539C23C4×D4×C13712yes—
540C23#121×C13712yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#99×C13712yes—
575C2×C4#120×C13711yescharacteristic
576C2×C4#123×C13711yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22AΣL(1,𝔽16)×C13712yescomplemented
621C22#386×C13711yescharacteristic
622C22C2×#99×C13711yescharacteristic
623C22C2×#99×C13711yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2#1898×C13711yescharacteristic
641C2C2×AΣL(1,𝔽16)×C13711yescharacteristic
642C2#2121×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#99
commutatorC24C22×C4×C137
Frattini, cosocleC22×D4C23×C137
prime radical#2403×C137C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C24×C137 ◁ C23×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C137C2semidirect
3. C2×AΣL(1,𝔽16)×C137C2semidirect
4. #1781×C137C2semidirect
5. #1390×C137C2semidirect
6. C23×D4×C137C4semidirect
10. C2×#120×C137C4semidirect
20. #386×C137C4semidirect
23. #379×C137C4semidirect
68. #100×C137D4semidirect
298. C22×C137AΣL(1,𝔽16)semidirect
321. #13082C137direct (N × H)
322. C137#13082direct (N × H)
323. C22×#100C2×C137semidirect
325. C2×AΣL(1,𝔽16)C2×C137semidirect
326. #1781C2×C137semidirect
327. #1390C2×C137semidirect
328. C23×D4C4×C137semidirect
332. C2×#120C4×C137semidirect
342. #386C4×C137semidirect
345. #379C4×C137semidirect
390. #100D4×C137semidirect
620. C22AΣL(1,𝔽16)×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1372
#2403×C1372
C2×AΣL(1,𝔽16)×C1372
#1781×C1372
#1390×C1372
#13082137