Finite Group Databasebeta

← C149×#13086 #49192035

Subgroups — C149×#13086 #49192035

Order 38144.

1118 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C149C211yesmaximal, characteristic, complemented
2#2403×C149C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C149C212yesmaximal, complemented
4#1783×C149C211yesmaximal, characteristic, complemented
5#1390×C149C212yesmaximal, complemented
6C23×D4×C149C411yescharacteristic, complemented
7C23×D4×C149C2211yescharacteristic
8C2×#120×C149—21no—
9C2×#120×C149C411yescharacteristic, complemented
10C2×#120×C149C2211yescharacteristic
11C22×C22⋊C4×C149—21no—
12C2×#100×C149—21no—
13C2×#100×C149C2212yes—
14C2×#99×C149—21no—
15C2×#99×C149—24no—
16C2×#99×C149C2212yes—
17#407×C149—21no—
18#392×C149—21no—
19#392×C149—21no—
20#386×C149—21no—
21#386×C149C411yescharacteristic, complemented
22#386×C149C2211yescharacteristic
23#379×C149C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C149—24no—
25C25×C149C2×C411yescharacteristic
26C25×C149C2×C411yescharacteristic, complemented
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—41no—
35C22×D4×C149—41no—
36C22×D4×C149—42no—
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×C149—41no—
45C23×C4×C149C2×C411yescharacteristic, complemented
46C23×C4×C149D411yescharacteristic
47C2×M16×C149—22no—
48#120×C149—22no—
49#120×C149—22no—
50#120×C149—44no—
51#120×C149—42no—
52C2×C22⋊C4×C149—24no—
53C2×C22⋊C4×C149—22no—
54C2×C22⋊C4×C149—21no—
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—41no—
61C2×C22⋊C4×C149—42no—
62C2×C22⋊C4×C149C2×C411yescharacteristic, complemented
63C2×C22⋊C4×C149C2×C411yescharacteristic, complemented
64#100×C149—22no—
65#100×C149—22no—
66#100×C149—42no—
67#99×C149—24no—
68#99×C149—22no—
69#99×C149D414yescomplemented
70C22⋊C8×C149—41no—
71C22⋊C8×C149—41no—
72#95×C149—21no—
73#95×C149—21no—
74C24×C149—21no—
75C24×C149—22no—
76C24×C149—21no—
77C24×C149—21no—
78C24×C149—21no—
79C24×C149—21no—
80C24×C149—21no—
81C24×C149—21no—
82C24×C149—22no—
83C24×C149—22no—
84C24×C149—41no—
85C24×C149—42no—
86C24×C149—41no—
87C24×C149—42no—
88C24×C149—42no—
89C24×C149—41no—
90C24×C149—81no—
91C24×C149—81no—
92C24×C149—81no—
93C24×C149C22⋊C411yescharacteristic
94C24×C149C22⋊C411yescharacteristic
95C24×C149C22⋊C411yescharacteristic
96C24×C149C22×C411yescharacteristic
97C24×C149C2×D411yescharacteristic
98C2×D4×C149—24no—
99C2×D4×C149—22no—
100C2×D4×C149—22no—
101C2×D4×C149—22no—
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149—22no—
105C2×D4×C149—41no—
106C2×D4×C149—41no—
107C2×D4×C149—41no—
108C2×D4×C149—41no—
109C2×D4×C149—41no—
110C2×D4×C149—41no—
111C2×D4×C149—42no—
112C2×D4×C149—44no—
113C2×D4×C149—44no—
114C2×D4×C149—44no—
115C2×D4×C149—44no—
116C2×D4×C149—42no—
117C2×D4×C149—42no—
118C2×D4×C149—42no—
119C2×D4×C149—44no—
120C2×D4×C149—44no—
121C2×D4×C149—44no—
122C2×D4×C149—41no—
123C2×D4×C149—41no—
124C2×D4×C149—44no—
125C2×D4×C149—42no—
126C2×D4×C149—42no—
127C2×D4×C149—42no—
128C2×D4×C149—41no—
129C2×D4×C149—41no—
130C2×D4×C149—81no—
131C2×D4×C149—81no—
132C2×D4×C149C2×D412yes—
133C2×D4×C149#4112yes—
134C22×C4×C149—21no—
135C22×C4×C149—21no—
136C22×C4×C149—21no—
137C22×C4×C149—22no—
138C22×C4×C149—21no—
139C22×C4×C149—21no—
140C22×C4×C149—41no—
141C22×C4×C149—42no—
142C22×C4×C149—41no—
143C22×C4×C149—44no—
144C22×C4×C149—42no—
145C22×C4×C149—82no—
146C22×C4×C149—82no—
147C22×C4×C149C22⋊C411yescharacteristic
148C22×C4×C149C2×D411yescharacteristic
149M16×C149—42no—
150M16×C149—42no—
151C2×C8×C149—42no—
152C22⋊C4×C149—22no—
153C22⋊C4×C149—24no—
154C22⋊C4×C149—42no—
155C22⋊C4×C149—42no—
156C22⋊C4×C149—42no—
157C22⋊C4×C149—44no—
158C22⋊C4×C149—42no—
159C22⋊C4×C149—42no—
160C22⋊C4×C149—42no—
161C22⋊C4×C149—41no—
162C22⋊C4×C149—81no—
163C23×C149—22no—
164C23×C149—22no—
165C23×C149—22no—
166C23×C149—22no—
167C23×C149—22no—
168C23×C149—21no—
169C23×C149—21no—
170C23×C149—21no—
171C23×C149—21no—
172C23×C149—21no—
173C23×C149—21no—
174C23×C149—21no—
175C23×C149—21no—
176C23×C149—22no—
177C23×C149—21no—
178C23×C149—21no—
179C23×C149—21no—
180C23×C149—41no—
181C23×C149—42no—
182C23×C149—42no—
183C23×C149—41no—
184C23×C149—41no—
185C23×C149—42no—
186C23×C149—41no—
187C23×C149—41no—
188C23×C149—41no—
189C23×C149—41no—
190C23×C149—41no—
191C23×C149—42no—
192C23×C149—41no—
193C23×C149—41no—
194C23×C149—41no—
195C23×C149—41no—
196C23×C149—42no—
197C23×C149—42no—
198C23×C149—42no—
199C23×C149—42no—
200C23×C149—41no—
201C23×C149—41no—
202C23×C149—41no—
203C23×C149—81no—
204C23×C149—81no—
205C23×C149—81no—
206C23×C149—81no—
207C23×C149—82no—
208C23×C149—84no—
209C23×C149—82no—
210C23×C149—82no—
211C23×C149—84no—
212C23×C149—84no—
213C23×C149—84no—
214C23×C149—84no—
215C23×C149—82no—
216C23×C149#9911yescharacteristic
217C23×C149#9911yescharacteristic
218C23×C149#9912yes—
219C23×C149C2×C22⋊C411yescharacteristic
220C23×C149C4×D412yes—
221C23×C149#12011yescharacteristic
222C23×C149#12311yescharacteristic
223D4×C149—42no—
224D4×C149—42no—
225D4×C149—44no—
226D4×C149—44no—
227D4×C149—44no—
228D4×C149—42no—
229D4×C149—42no—
230D4×C149—48no—
231D4×C149—44no—
232D4×C149—84no—
233D4×C149—82no—
234D4×C149—82no—
235C2×C4×C149—21no—
236C2×C4×C149—21no—
237C2×C4×C149—22no—
238C2×C4×C149—21no—
239C2×C4×C149—21no—
240C2×C4×C149—21no—
241C2×C4×C149—42no—
242C2×C4×C149—42no—
243C2×C4×C149—41no—
244C2×C4×C149—42no—
245C2×C4×C149—41no—
246C2×C4×C149—42no—
247C2×C4×C149—44no—
248C2×C4×C149—41no—
249C2×C4×C149—41no—
250C2×C4×C149—41no—
251C2×C4×C149—41no—
252C2×C4×C149—41no—
253C2×C4×C149—41no—
254C2×C4×C149—88no—
255C2×C4×C149—82no—
256C2×C4×C149—82no—
257C2×C4×C149#12112yes—
258C8×C149—82no—
259C22×C149—21no—
260C22×C149—21no—
261C22×C149—21no—
262C22×C149—21no—
263C22×C149—21no—
264C22×C149—21no—
265C22×C149—21no—
266C22×C149—21no—
267C22×C149—22no—
268C22×C149—21no—
269C22×C149—22no—
270C22×C149—42no—
271C22×C149—42no—
272C22×C149—42no—
273C22×C149—41no—
274C22×C149—41no—
275C22×C149—42no—
276C22×C149—44no—
277C22×C149—44no—
278C22×C149—42no—
279C22×C149—42no—
280C22×C149—42no—
281C22×C149—41no—
282C22×C149—41no—
283C22×C149—41no—
284C22×C149—41no—
285C22×C149—41no—
286C22×C149—41no—
287C22×C149—42no—
288C22×C149—41no—
289C22×C149—41no—
290C22×C149—41no—
291C22×C149—81no—
292C22×C149—81no—
293C22×C149—84no—
294C22×C149—81no—
295C22×C149—81no—
296C22×C149—81no—
297C22×C149—81no—
298C22×C149—82no—
299C22×C149—82no—
300C22×C149—84no—
301C22×C149—84no—
302C22×C149—84no—
303C22×C149—81no—
304C22×C149—81no—
305C22×C149AΣL(1,𝔽16)12yescomplemented
306C22×C149#38611yescharacteristic
307C22×C149C2×#9911yescharacteristic
308C22×C149C2×#9911yescharacteristic
309C4×C149—22no—
310C4×C149—42no—
311C4×C149—41no—
312C4×C149—81no—
313C4×C149—81no—
314C4×C149—84no—
315C2×C149—21no—
316C2×C149—21no—
317C2×C149—22no—
318C2×C149—41no—
319C2×C149—41no—
320C2×C149—42no—
321C2×C149—41no—
322C2×C149—42no—
323C2×C149—82no—
324C2×C149—81no—
325C2×C149#189811yescharacteristic
326C2×C149C2×AΣL(1,𝔽16)11yescharacteristic
327C2×C149#212111yescharacteristic
328#13086C14911yesmaximal, characteristic, direct product factor, Sylow
329C149#1308611yescharacteristic, direct product factor, Sylow
330C22×#99C2×C14911yescharacteristic, complemented
331#2403C2×C14911yescharacteristic
332C2×AΣL(1,𝔽16)C2×C14912yescomplemented
333#1783C2×C14911yescharacteristic, complemented
334#1390C2×C14912yescomplemented
335C23×D4C4×C14911yescharacteristic, complemented
336C23×D4C22×C14911yescharacteristic
337C2×#120—21no—
338C2×#120C4×C14911yescharacteristic, complemented
339C2×#120C22×C14911yescharacteristic
340C22×C22⋊C4—21no—
341C2×#100—21no—
342C2×#100C22×C14912yes—
343C2×#99—21no—
344C2×#99—24no—
345C2×#99C22×C14912yes—
346#407—21no—
347#392—21no—
348#392—21no—
349#386—21no—
350#386C4×C14911yescharacteristic, complemented
351#386C22×C14911yescharacteristic
352#379C4×C14911yescharacteristic, complemented
353AΣL(1,𝔽16)—24no—
354C25C2×C4×C14911yescharacteristic
355C25C2×C4×C14911yescharacteristic, complemented
356C25D4×C14911yescharacteristic
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4—42no—
366C22×D4—44no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4C2×C4×C14911yescharacteristic
370C22×D4D4×C14911yescharacteristic
371C22×D4D4×C14911yescharacteristic
372C22×D4C23×C14911yescharacteristic
373C23×C4—41no—
374C23×C4C2×C4×C14911yescharacteristic, complemented
375C23×C4D4×C14911yescharacteristic
376C2×M16—22no—
377#120—22no—
378#120—22no—
379#120—44no—
380#120—42no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4C2×C4×C14911yescharacteristic, complemented
392C2×C22⋊C4C2×C4×C14911yescharacteristic, complemented
393#100—22no—
394#100—22no—
395#100—42no—
396#99—24no—
397#99—22no—
398#99D4×C14914yescomplemented
399C22⋊C8—41no—
400C22⋊C8—41no—
401#95—21no—
402#95—21no—
403C24—21no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—22no—
413C24—41no—
414C24—42no—
415C24—41no—
416C24—42no—
417C24—42no—
418C24—41no—
419C24—81no—
420C24—81no—
421C24—81no—
422C24C22⋊C4×C14911yescharacteristic
423C24C22⋊C4×C14911yescharacteristic
424C24C22⋊C4×C14911yescharacteristic
425C24C22×C4×C14911yescharacteristic
426C24C2×D4×C14911yescharacteristic
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—44no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4C2×D4×C14912yes—
462C2×D4#41×C14912yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—44no—
473C22×C4—42no—
474C22×C4—82no—
475C22×C4—82no—
476C22×C4C22⋊C4×C14911yescharacteristic
477C22×C4C2×D4×C14911yescharacteristic
478M16—42no—
479M16—42no—
480C2×C8—42no—
481C22⋊C4—22no—
482C22⋊C4—24no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—44no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—41no—
491C22⋊C4—81no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—22no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—82no—
537C23—84no—
538C23—82no—
539C23—82no—
540C23—84no—
541C23—84no—
542C23—84no—
543C23—84no—
544C23—82no—
545C23#99×C14911yescharacteristic
546C23#99×C14911yescharacteristic
547C23#99×C14912yes—
548C23C2×C22⋊C4×C14911yescharacteristic
549C23C4×D4×C14912yes—
550C23#120×C14911yescharacteristic
551C23#123×C14911yescharacteristic
552D4—42no—
553D4—42no—
554D4—44no—
555D4—44no—
556D4—44no—
557D4—42no—
558D4—42no—
559D4—48no—
560D4—44no—
561D4—84no—
562D4—82no—
563D4—82no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—88no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4#121×C14912yes—
587C8—82no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—22no—
597C22—21no—
598C22—22no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—42no—
605C22—44no—
606C22—42no—
607C22—44no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—81no—
621C22—81no—
622C22—84no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—82no—
628C22—82no—
629C22—84no—
630C22—84no—
631C22—84no—
632C22—81no—
633C22—81no—
634C22AΣL(1,𝔽16)×C14912yescomplemented
635C22#386×C14911yescharacteristic
636C22C2×#99×C14911yescharacteristic
637C22C2×#99×C14911yescharacteristic
638C4—22no—
639C4—42no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4—84no—
644C2—21no—
645C2—21no—
646C2—22no—
647C2—41no—
648C2—41no—
649C2—42no—
650C2—41no—
651C2—42no—
652C2—82no—
653C2—81no—
654C2#1898×C14911yescharacteristic
655C2C2×AΣL(1,𝔽16)×C14911yescharacteristic
656C2#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×#99×C149C2semidirect
3. C2×AΣL(1,𝔽16)×C149C2semidirect
4. #1783×C149C2semidirect
5. #1390×C149C2semidirect
6. C23×D4×C149C4semidirect
9. C2×#120×C149C4semidirect
21. #386×C149C4semidirect
23. #379×C149C4semidirect
26. C25×C149C2×C4semidirect
45. C23×C4×C149C2×C4semidirect
62. C2×C22⋊C4×C149C2×C4semidirect
63. C2×C22⋊C4×C149C2×C4semidirect
69. #99×C149D4semidirect
305. C22×C149AΣL(1,𝔽16)semidirect
328. #13086C149direct (N × H)
329. C149#13086direct (N × H)
330. C22×#99C2×C149semidirect
332. C2×AΣL(1,𝔽16)C2×C149semidirect
333. #1783C2×C149semidirect
334. #1390C2×C149semidirect
335. C23×D4C4×C149semidirect
338. C2×#120C4×C149semidirect
350. #386C4×C149semidirect
352. #379C4×C149semidirect
355. C25C2×C4×C149semidirect
374. C23×C4C2×C4×C149semidirect
391. C2×C22⋊C4C2×C4×C149semidirect
392. C2×C22⋊C4C2×C4×C149semidirect
398. #99D4×C149semidirect
634. 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×#99×C1492
#2403×C1492
C2×AΣL(1,𝔽16)×C1492
#1783×C1492
#1390×C1492
#13086149