Finite Group Databasebeta

← C149×#13082 #49192031

Subgroups — C149×#13082 #49192031

Order 38144.

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×C149C211yesmaximal, characteristic, complemented
2#2403×C149C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C149C212yesmaximal, complemented
4#1781×C149C211yesmaximal, characteristic, complemented
5#1390×C149C212yesmaximal, complemented
6C23×D4×C149C411yescharacteristic, complemented
7C23×D4×C149C2211yescharacteristic
8C22×M16×C149—21no—
9C2×#120×C149—21no—
10C2×#120×C149C411yescharacteristic, complemented
11C2×#120×C149C2211yescharacteristic
12C2×#100×C149—21no—
13C2×#100×C149—24no—
14C2×#100×C149C2212yes—
15C2×#99×C149—21no—
16C2×#99×C149C2212yes—
17#392×C149—21no—
18#392×C149—21no—
19#386×C149—21no—
20#386×C149C411yescharacteristic, complemented
21#386×C149C2211yescharacteristic
22#379×C149—21no—
23#379×C149C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C149—24no—
25C25×C149C2×C411yescharacteristic
26C25×C149C2×C411yescharacteristic
27C25×C149D411yescharacteristic
28C22×D4×C149—21no—
29C22×D4×C149—22no—
30C22×D4×C149—22no—
31C22×D4×C149—21no—
32C22×D4×C149—21no—
33C22×D4×C149—21no—
34C22×D4×C149—42no—
35C22×D4×C149—41no—
36C22×D4×C149—41no—
37C22×D4×C149—44no—
38C22×D4×C149—41no—
39C22×D4×C149—41no—
40C22×D4×C149C2×C411yescharacteristic
41C22×D4×C149D411yescharacteristic
42C22×D4×C149D411yescharacteristic
43C22×D4×C149C2311yescharacteristic
44C23×C4×C149C2×C411yescharacteristic
45C23×C4×C149D411yescharacteristic
46C2×M16×C149—24no—
47C2×M16×C149—22no—
48C2×M16×C149—41no—
49C2×M16×C149—42no—
50C22×C8×C149—41no—
51#120×C149—22no—
52#120×C149—22no—
53#120×C149—44no—
54#120×C149—42no—
55C2×C22⋊C4×C149—21no—
56C2×C22⋊C4×C149—21no—
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—21no—
59C2×C22⋊C4×C149—21no—
60C2×C22⋊C4×C149—22no—
61C2×C22⋊C4×C149—21no—
62C2×C22⋊C4×C149—41no—
63C2×C22⋊C4×C149—41no—
64C2×C22⋊C4×C149C2×C411yescharacteristic
65C2×C22⋊C4×C149C2×C411yescharacteristic
66#100×C149—24no—
67#100×C149—22no—
68#100×C149D414yescomplemented
69#99×C149—22no—
70#99×C149—22no—
71#99×C149—42no—
72#95×C149—21no—
73#95×C149—21no—
74C24×C149—21no—
75C24×C149—21no—
76C24×C149—21no—
77C24×C149—21no—
78C24×C149—21no—
79C24×C149—22no—
80C24×C149—22no—
81C24×C149—22no—
82C24×C149—41no—
83C24×C149—41no—
84C24×C149—42no—
85C24×C149—41no—
86C24×C149—42no—
87C24×C149—42no—
88C24×C149—41no—
89C24×C149—81no—
90C24×C149—81no—
91C24×C149—81no—
92C24×C149C22⋊C411yescharacteristic
93C24×C149C22⋊C411yescharacteristic
94C24×C149C22⋊C411yescharacteristic
95C24×C149C22×C411yescharacteristic
96C24×C149C2×D411yescharacteristic
97C2×D4×C149—24no—
98C2×D4×C149—22no—
99C2×D4×C149—22no—
100C2×D4×C149—22no—
101C2×D4×C149—22no—
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149—41no—
105C2×D4×C149—41no—
106C2×D4×C149—41no—
107C2×D4×C149—41no—
108C2×D4×C149—41no—
109C2×D4×C149—41no—
110C2×D4×C149—44no—
111C2×D4×C149—44no—
112C2×D4×C149—44no—
113C2×D4×C149—44no—
114C2×D4×C149—42no—
115C2×D4×C149—42no—
116C2×D4×C149—42no—
117C2×D4×C149—42no—
118C2×D4×C149—44no—
119C2×D4×C149—44no—
120C2×D4×C149—44no—
121C2×D4×C149—41no—
122C2×D4×C149—41no—
123C2×D4×C149—44no—
124C2×D4×C149—42no—
125C2×D4×C149—42no—
126C2×D4×C149—42no—
127C2×D4×C149—42no—
128C2×D4×C149—81no—
129C2×D4×C149—81no—
130C2×D4×C149C2×D412yes—
131C2×D4×C149#4112yes—
132C22×C4×C149—21no—
133C22×C4×C149—21no—
134C22×C4×C149—22no—
135C22×C4×C149—21no—
136C22×C4×C149—21no—
137C22×C4×C149—21no—
138C22×C4×C149—21no—
139C22×C4×C149—21no—
140C22×C4×C149—42no—
141C22×C4×C149—41no—
142C22×C4×C149—42no—
143C22×C4×C149C22⋊C411yescharacteristic
144C22×C4×C149C2×D411yescharacteristic
145M16×C149—24no—
146M16×C149—44no—
147M16×C149—42no—
148C2×C8×C149—44no—
149C2×C8×C149—42no—
150C22⋊C4×C149—22no—
151C22⋊C4×C149—42no—
152C22⋊C4×C149—42no—
153C22⋊C4×C149—42no—
154C22⋊C4×C149—42no—
155C22⋊C4×C149—41no—
156C22⋊C4×C149—41no—
157C22⋊C4×C149—41no—
158C22⋊C4×C149—42no—
159C22⋊C4×C149—42no—
160C22⋊C4×C149—81no—
161C22⋊C4×C149—82no—
162C22⋊C4×C149—82no—
163C23×C149—22no—
164C23×C149—21no—
165C23×C149—21no—
166C23×C149—21no—
167C23×C149—21no—
168C23×C149—21no—
169C23×C149—21no—
170C23×C149—22no—
171C23×C149—21no—
172C23×C149—21no—
173C23×C149—21no—
174C23×C149—21no—
175C23×C149—21no—
176C23×C149—21no—
177C23×C149—41no—
178C23×C149—42no—
179C23×C149—42no—
180C23×C149—42no—
181C23×C149—42no—
182C23×C149—41no—
183C23×C149—41no—
184C23×C149—41no—
185C23×C149—41no—
186C23×C149—41no—
187C23×C149—41no—
188C23×C149—42no—
189C23×C149—41no—
190C23×C149—42no—
191C23×C149—41no—
192C23×C149—41no—
193C23×C149—41no—
194C23×C149—41no—
195C23×C149—42no—
196C23×C149—42no—
197C23×C149—42no—
198C23×C149—42no—
199C23×C149—41no—
200C23×C149—41no—
201C23×C149—41no—
202C23×C149—81no—
203C23×C149—81no—
204C23×C149—81no—
205C23×C149—81no—
206C23×C149—82no—
207C23×C149—84no—
208C23×C149—84no—
209C23×C149—84no—
210C23×C149—84no—
211C23×C149—84no—
212C23×C149—84no—
213C23×C149—82no—
214C23×C149#9911yescharacteristic
215C23×C149#9911yescharacteristic
216C23×C149C2×C22⋊C411yescharacteristic
217C23×C149C4×D412yes—
218C23×C149#12112yes—
219D4×C149—42no—
220D4×C149—42no—
221D4×C149—44no—
222D4×C149—44no—
223D4×C149—42no—
224D4×C149—42no—
225D4×C149—44no—
226D4×C149—48no—
227D4×C149—44no—
228D4×C149—84no—
229D4×C149—84no—
230C2×C4×C149—22no—
231C2×C4×C149—22no—
232C2×C4×C149—22no—
233C2×C4×C149—22no—
234C2×C4×C149—21no—
235C2×C4×C149—21no—
236C2×C4×C149—21no—
237C2×C4×C149—21no—
238C2×C4×C149—22no—
239C2×C4×C149—41no—
240C2×C4×C149—42no—
241C2×C4×C149—41no—
242C2×C4×C149—42no—
243C2×C4×C149—41no—
244C2×C4×C149—41no—
245C2×C4×C149—41no—
246C2×C4×C149—41no—
247C2×C4×C149—41no—
248C2×C4×C149—41no—
249C2×C4×C149—82no—
250C2×C4×C149—82no—
251C2×C4×C149—82no—
252C2×C4×C149#9912yes—
253C2×C4×C149#12011yescharacteristic
254C2×C4×C149#12311yescharacteristic
255C8×C149—44no—
256C22×C149—21no—
257C22×C149—21no—
258C22×C149—21no—
259C22×C149—21no—
260C22×C149—21no—
261C22×C149—21no—
262C22×C149—21no—
263C22×C149—22no—
264C22×C149—22no—
265C22×C149—42no—
266C22×C149—42no—
267C22×C149—42no—
268C22×C149—42no—
269C22×C149—42no—
270C22×C149—42no—
271C22×C149—42no—
272C22×C149—42no—
273C22×C149—41no—
274C22×C149—41no—
275C22×C149—41no—
276C22×C149—41no—
277C22×C149—42no—
278C22×C149—41no—
279C22×C149—41no—
280C22×C149—41no—
281C22×C149—41no—
282C22×C149—41no—
283C22×C149—41no—
284C22×C149—81no—
285C22×C149—84no—
286C22×C149—84no—
287C22×C149—81no—
288C22×C149—81no—
289C22×C149—81no—
290C22×C149—81no—
291C22×C149—81no—
292C22×C149—84no—
293C22×C149—84no—
294C22×C149—84no—
295C22×C149—84no—
296C22×C149—81no—
297C22×C149—81no—
298C22×C149AΣL(1,𝔽16)12yescomplemented
299C22×C149#38611yescharacteristic
300C22×C149C2×#9911yescharacteristic
301C22×C149C2×#9911yescharacteristic
302C4×C149—21no—
303C4×C149—22no—
304C4×C149—21no—
305C4×C149—42no—
306C4×C149—81no—
307C4×C149—81no—
308C4×C149—162no—
309C2×C149—21no—
310C2×C149—21no—
311C2×C149—22no—
312C2×C149—42no—
313C2×C149—41no—
314C2×C149—42no—
315C2×C149—81no—
316C2×C149—82no—
317C2×C149—81no—
318C2×C149#189811yescharacteristic
319C2×C149C2×AΣL(1,𝔽16)11yescharacteristic
320C2×C149#212111yescharacteristic
321#13082C14911yesmaximal, characteristic, direct product factor, Sylow
322C149#1308211yescharacteristic, direct product factor, Sylow
323C22×#100C2×C14911yescharacteristic, complemented
324#2403C2×C14911yescharacteristic
325C2×AΣL(1,𝔽16)C2×C14912yescomplemented
326#1781C2×C14911yescharacteristic, complemented
327#1390C2×C14912yescomplemented
328C23×D4C4×C14911yescharacteristic, complemented
329C23×D4C22×C14911yescharacteristic
330C22×M16—21no—
331C2×#120—21no—
332C2×#120C4×C14911yescharacteristic, complemented
333C2×#120C22×C14911yescharacteristic
334C2×#100—21no—
335C2×#100—24no—
336C2×#100C22×C14912yes—
337C2×#99—21no—
338C2×#99C22×C14912yes—
339#392—21no—
340#392—21no—
341#386—21no—
342#386C4×C14911yescharacteristic, complemented
343#386C22×C14911yescharacteristic
344#379—21no—
345#379C4×C14911yescharacteristic, complemented
346AΣL(1,𝔽16)—24no—
347C25C2×C4×C14911yescharacteristic
348C25C2×C4×C14911yescharacteristic
349C25D4×C14911yescharacteristic
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×C14911yescharacteristic
363C22×D4D4×C14911yescharacteristic
364C22×D4D4×C14911yescharacteristic
365C22×D4C23×C14911yescharacteristic
366C23×C4C2×C4×C14911yescharacteristic
367C23×C4D4×C14911yescharacteristic
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×C14911yescharacteristic
387C2×C22⋊C4C2×C4×C14911yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C14914yescomplemented
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×C14911yescharacteristic
415C24C22⋊C4×C14911yescharacteristic
416C24C22⋊C4×C14911yescharacteristic
417C24C22×C4×C14911yescharacteristic
418C24C2×D4×C14911yescharacteristic
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×C14912yes—
453C2×D4#41×C14912yes—
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×C14911yescharacteristic
466C22×C4C2×D4×C14911yescharacteristic
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×C14911yescharacteristic
537C23#99×C14911yescharacteristic
538C23C2×C22⋊C4×C14911yescharacteristic
539C23C4×D4×C14912yes—
540C23#121×C14912yes—
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×C14912yes—
575C2×C4#120×C14911yescharacteristic
576C2×C4#123×C14911yescharacteristic
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)×C14912yescomplemented
621C22#386×C14911yescharacteristic
622C22C2×#99×C14911yescharacteristic
623C22C2×#99×C14911yescharacteristic
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×C14911yescharacteristic
641C2C2×AΣL(1,𝔽16)×C14911yescharacteristic
642C2#2121×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC24C22×C4×C149
Frattini, cosocleC22×D4C23×C149
prime radical#2403×C149C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C24×C149 ◁ C23×D4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C149C2semidirect
3. C2×AΣL(1,𝔽16)×C149C2semidirect
4. #1781×C149C2semidirect
5. #1390×C149C2semidirect
6. C23×D4×C149C4semidirect
10. C2×#120×C149C4semidirect
20. #386×C149C4semidirect
23. #379×C149C4semidirect
68. #100×C149D4semidirect
298. C22×C149AΣL(1,𝔽16)semidirect
321. #13082C149direct (N × H)
322. C149#13082direct (N × H)
323. C22×#100C2×C149semidirect
325. C2×AΣL(1,𝔽16)C2×C149semidirect
326. #1781C2×C149semidirect
327. #1390C2×C149semidirect
328. C23×D4C4×C149semidirect
332. C2×#120C4×C149semidirect
342. #386C4×C149semidirect
345. #379C4×C149semidirect
390. #100D4×C149semidirect
620. C22AΣL(1,𝔽16)×C149semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1492
#2403×C1492
C2×AΣL(1,𝔽16)×C1492
#1781×C1492
#1390×C1492
#13082149