Finite Group Databasebeta

← C149×#13041 #49191990

Subgroups — C149×#13041 #49191990

Order 38144.

964 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
1C2×B(4,𝔽2)×C149C211yesmaximal, characteristic
2#2358×C149C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C149C211yesmaximal, characteristic, complemented
4#1792×C149C211yesmaximal, characteristic, complemented
5#1790×C149C211yesmaximal, characteristic, complemented
6#1393×C149C211yesmaximal, characteristic, complemented
7#1390×C149C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C149C2211yescharacteristic
9C2×#120×C149—21no—
10C2×#120×C149C2211yescharacteristic
11C2×C4×D4×C149—21no—
12C22×C22⋊C4×C149—21no—
13B(4,𝔽2)×C149—22no—
14B(4,𝔽2)×C149C414yescomplemented
15C2×#104×C149—21no—
16#417×C149—21no—
17C2×#100×C149C2211yescharacteristic
18C2×#99×C149—21no—
19C2×#99×C149—21no—
20C2×#99×C149C2211yescharacteristic
21C2×#99×C149C2211yescharacteristic
22#390×C149C2211yescharacteristic
23#388×C149—21no—
24#386×C149—21no—
25#386×C149—21no—
26#386×C149C2211yescharacteristic
27#385×C149—21no—
28C4×C22⋊C4×C149—21no—
29AΣL(1,𝔽16)×C149—22no—
30C25×C149D411yescharacteristic
31H(5,𝔽2)×C149—21no—
32H(5,𝔽2)×C149—21no—
33H(5,𝔽2)×C149—21no—
34H(5,𝔽2)×C149—42no—
35H(5,𝔽2)×C149C2×C412yescomplemented
36C2×#41×C149—21no—
37C2×#41×C149—41no—
38C22×D4×C149—21no—
39C22×D4×C149—21no—
40C22×D4×C149—21no—
41C22×D4×C149—41no—
42C22×D4×C149—41no—
43C22×D4×C149C2311yescharacteristic
44C23×C4×C149—21no—
45C23×C4×C149—21no—
46C23×C4×C149D411yescharacteristic, complemented
47C2×M16×C149—21no—
48#120×C149—21no—
49#120×C149—21no—
50#120×C149—24no—
51#120×C149—42no—
52#120×C149C2×C412yes—
53#120×C149D412yes—
54C4×D4×C149—44no—
55C2×C4⋊C4×C149—21no—
56C2×C4⋊C4×C149D411yescharacteristic, complemented
57C2×C22⋊C4×C149—21no—
58C2×C22⋊C4×C149—21no—
59C2×C22⋊C4×C149—21no—
60C2×C22⋊C4×C149—21no—
61C2×C22⋊C4×C149—21no—
62C2×C22⋊C4×C149—21no—
63C2×C22⋊C4×C149—21no—
64C2×C22⋊C4×C149—21no—
65C2×C22⋊C4×C149—44no—
66C2×C22⋊C4×C149—41no—
67C2×C22⋊C4×C149—41no—
68C2×C22⋊C4×C149D411yescharacteristic
69C2×C22⋊C4×C149D411yescharacteristic, complemented
70C2×C42×C149—21no—
71C2×C42×C149D411yescharacteristic, complemented
72#104×C149—42no—
73#103×C149—41no—
74#102×C149—41no—
75#100×C149—21no—
76#100×C149—21no—
77#99×C149—21no—
78#99×C149—24no—
79#99×C149—21no—
80#99×C149—21no—
81#99×C149—42no—
82#99×C149C2×C412yescomplemented
83#95×C149—21no—
84#95×C149—21no—
85#95×C149—21no—
86#95×C149—41no—
87C24×C149—21no—
88C24×C149—21no—
89C24×C149—21no—
90C24×C149—21no—
91C24×C149—42no—
92C24×C149—41no—
93C24×C149—42no—
94C24×C149—41no—
95C24×C149C22⋊C412yescomplemented
96C24×C149C2×D411yescharacteristic
97C24×C149C2×D411yescharacteristic
98#41×C149—22no—
99#41×C149—22no—
100#41×C149—42no—
101#41×C149—41no—
102#41×C149—42no—
103#41×C149—42no—
104#41×C149—42no—
105#41×C149—41no—
106C2×Q8×C149—21no—
107C2×D4×C149—21no—
108C2×D4×C149—22no—
109C2×D4×C149—22no—
110C2×D4×C149—22no—
111C2×D4×C149—22no—
112C2×D4×C149—22no—
113C2×D4×C149—22no—
114C2×D4×C149—41no—
115C2×D4×C149—41no—
116C2×D4×C149—42no—
117C2×D4×C149—42no—
118C2×D4×C149—42no—
119C2×D4×C149—42no—
120C2×D4×C149—41no—
121C2×D4×C149—41no—
122C2×D4×C149—41no—
123C2×D4×C149—41no—
124C2×D4×C149—42no—
125C2×D4×C149—42no—
126C2×D4×C149—41no—
127C2×D4×C149—41no—
128C2×D4×C149—41no—
129C2×D4×C149—44no—
130C2×D4×C149—82no—
131C2×D4×C149—82no—
132C2×D4×C149C22×C411yescharacteristic
133C2×D4×C149C2×D411yescharacteristic
134C2×D4×C149#4111yescharacteristic
135C2×D4×C149#4111yescharacteristic
136C22×C4×C149—21no—
137C22×C4×C149—21no—
138C22×C4×C149—21no—
139C22×C4×C149—21no—
140C22×C4×C149—21no—
141C22×C4×C149—21no—
142C22×C4×C149—21no—
143C22×C4×C149—41no—
144C22×C4×C149—42no—
145C22×C4×C149—42no—
146C22×C4×C149—42no—
147C22×C4×C149—41no—
148C22×C4×C149—41no—
149C22×C4×C149—42no—
150C22×C4×C149—42no—
151C22×C4×C149—41no—
152C22×C4×C149—81no—
153C22×C4×C149—81no—
154C22×C4×C149C2×D411yescharacteristic
155M16×C149—41no—
156M16×C149—41no—
157C2×C8×C149—41no—
158C4⋊C4×C149—42no—
159C4⋊C4×C149—41no—
160C22⋊C4×C149—24no—
161C22⋊C4×C149—21no—
162C22⋊C4×C149—22no—
163C22⋊C4×C149—22no—
164C22⋊C4×C149—22no—
165C22⋊C4×C149—42no—
166C22⋊C4×C149—42no—
167C22⋊C4×C149—42no—
168C22⋊C4×C149—44no—
169C22⋊C4×C149—42no—
170C22⋊C4×C149—41no—
171C22⋊C4×C149—41no—
172C22⋊C4×C149—41no—
173C22⋊C4×C149—41no—
174C22⋊C4×C149—82no—
175C22⋊C4×C149C22⋊C412yescomplemented
176C42×C149—42no—
177C42×C149—41no—
178C23×C149—22no—
179C23×C149—22no—
180C23×C149—22no—
181C23×C149—21no—
182C23×C149—21no—
183C23×C149—21no—
184C23×C149—21no—
185C23×C149—22no—
186C23×C149—22no—
187C23×C149—41no—
188C23×C149—41no—
189C23×C149—41no—
190C23×C149—41no—
191C23×C149—42no—
192C23×C149—41no—
193C23×C149—44no—
194C23×C149—41no—
195C23×C149—44no—
196C23×C149—41no—
197C23×C149—41no—
198C23×C149—41no—
199C23×C149—41no—
200C23×C149—42no—
201C23×C149—42no—
202C23×C149—41no—
203C23×C149—81no—
204C23×C149—84no—
205C23×C149—81no—
206C23×C149—81no—
207C23×C149—81no—
208C23×C149—81no—
209C23×C149—81no—
210C23×C149—81no—
211C23×C149C2×C22⋊C411yescharacteristic
212C23×C149C4×D411yescharacteristic
213C23×C149#12011yescharacteristic
214C23×C149#12111yescharacteristic
215C23×C149#12311yescharacteristic
216Q8×C149—22no—
217Q8×C149—41no—
218D4×C149—22no—
219D4×C149—41no—
220D4×C149—41no—
221D4×C149—41no—
222D4×C149—41no—
223D4×C149—41no—
224D4×C149—44no—
225D4×C149—44no—
226D4×C149—42no—
227D4×C149—42no—
228D4×C149—42no—
229D4×C149—42no—
230D4×C149—42no—
231D4×C149—42no—
232D4×C149—88no—
233C2×C4×C149—21no—
234C2×C4×C149—21no—
235C2×C4×C149—22no—
236C2×C4×C149—22no—
237C2×C4×C149—22no—
238C2×C4×C149—22no—
239C2×C4×C149—22no—
240C2×C4×C149—42no—
241C2×C4×C149—42no—
242C2×C4×C149—41no—
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—41no—
250C2×C4×C149—41no—
251C2×C4×C149—42no—
252C2×C4×C149—42no—
253C2×C4×C149—41no—
254C2×C4×C149—41no—
255C2×C4×C149—41no—
256C2×C4×C149—41no—
257C2×C4×C149—41no—
258C2×C4×C149—41no—
259C2×C4×C149—81no—
260C2×C4×C149—84no—
261C2×C4×C149—84no—
262C2×C4×C149—81no—
263C2×C4×C149—81no—
264C2×C4×C149—81no—
265C2×C4×C149—81no—
266C2×C4×C149—81no—
267C2×C4×C149C4×D411yescharacteristic
268C2×C4×C149#12111yescharacteristic
269C8×C149—81no—
270C22×C149—21no—
271C22×C149—21no—
272C22×C149—24no—
273C22×C149—21no—
274C22×C149—21no—
275C22×C149—21no—
276C22×C149—21no—
277C22×C149—41no—
278C22×C149—41no—
279C22×C149—41no—
280C22×C149—41no—
281C22×C149—42no—
282C22×C149—42no—
283C22×C149—42no—
284C22×C149—44no—
285C22×C149—42no—
286C22×C149—41no—
287C22×C149—42no—
288C22×C149—41no—
289C22×C149—41no—
290C22×C149—41no—
291C22×C149—42no—
292C22×C149—42no—
293C22×C149—81no—
294C22×C149—81no—
295C22×C149—82no—
296C22×C149—82no—
297C22×C149—82no—
298C22×C149—82no—
299C22×C149—82no—
300C22×C149—81no—
301C22×C149—81no—
302C22×C149—161no—
303C22×C149—161no—
304C22×C149#38611yescharacteristic
305C22×C149B(4,𝔽2)11yescharacteristic
306C22×C149B(4,𝔽2)11yescharacteristic
307C4×C149—21no—
308C4×C149—21no—
309C4×C149—42no—
310C4×C149—42no—
311C4×C149—42no—
312C4×C149—42no—
313C4×C149—81no—
314C4×C149—82no—
315C4×C149—81no—
316C4×C149—161no—
317C2×C149—21no—
318C2×C149—21no—
319C2×C149—41no—
320C2×C149—41no—
321C2×C149—44no—
322C2×C149—41no—
323C2×C149—41no—
324C2×C149—82no—
325C2×C149#188911yescharacteristic
326C2×C149#219611yescharacteristic
327C2×C149#219711yescharacteristic
328#13041C14911yesmaximal, characteristic, direct product factor, Sylow
329C149#1304111yescharacteristic, direct product factor, Sylow
330C2×B(4,𝔽2)C2×C14911yescharacteristic
331#2358C2×C14911yescharacteristic, complemented
332C2×AΣL(1,𝔽16)C2×C14911yescharacteristic, complemented
333#1792C2×C14911yescharacteristic, complemented
334#1790C2×C14911yescharacteristic, complemented
335#1393C2×C14911yescharacteristic, complemented
336#1390C2×C14911yescharacteristic, complemented
337C2×H(5,𝔽2)C22×C14911yescharacteristic
338C2×#120—21no—
339C2×#120C22×C14911yescharacteristic
340C2×C4×D4—21no—
341C22×C22⋊C4—21no—
342B(4,𝔽2)—22no—
343B(4,𝔽2)C4×C14914yescomplemented
344C2×#104—21no—
345#417—21no—
346C2×#100C22×C14911yescharacteristic
347C2×#99—21no—
348C2×#99—21no—
349C2×#99C22×C14911yescharacteristic
350C2×#99C22×C14911yescharacteristic
351#390C22×C14911yescharacteristic
352#388—21no—
353#386—21no—
354#386—21no—
355#386C22×C14911yescharacteristic
356#385—21no—
357C4×C22⋊C4—21no—
358AΣL(1,𝔽16)—22no—
359C25D4×C14911yescharacteristic
360H(5,𝔽2)—21no—
361H(5,𝔽2)—21no—
362H(5,𝔽2)—21no—
363H(5,𝔽2)—42no—
364H(5,𝔽2)C2×C4×C14912yescomplemented
365C2×#41—21no—
366C2×#41—41no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—41no—
371C22×D4—41no—
372C22×D4C23×C14911yescharacteristic
373C23×C4—21no—
374C23×C4—21no—
375C23×C4D4×C14911yescharacteristic, complemented
376C2×M16—21no—
377#120—21no—
378#120—21no—
379#120—24no—
380#120—42no—
381#120C2×C4×C14912yes—
382#120D4×C14912yes—
383C4×D4—44no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C14911yescharacteristic, complemented
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4D4×C14911yescharacteristic
398C2×C22⋊C4D4×C14911yescharacteristic, complemented
399C2×C42—21no—
400C2×C42D4×C14911yescharacteristic, complemented
401#104—42no—
402#103—41no—
403#102—41no—
404#100—21no—
405#100—21no—
406#99—21no—
407#99—24no—
408#99—21no—
409#99—21no—
410#99—42no—
411#99C2×C4×C14912yescomplemented
412#95—21no—
413#95—21no—
414#95—21no—
415#95—41no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—42no—
421C24—41no—
422C24—42no—
423C24—41no—
424C24C22⋊C4×C14912yescomplemented
425C24C2×D4×C14911yescharacteristic
426C24C2×D4×C14911yescharacteristic
427#41—22no—
428#41—22no—
429#41—42no—
430#41—41no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41—41no—
435C2×Q8—21no—
436C2×D4—21no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—44no—
459C2×D4—82no—
460C2×D4—82no—
461C2×D4C22×C4×C14911yescharacteristic
462C2×D4C2×D4×C14911yescharacteristic
463C2×D4#41×C14911yescharacteristic
464C2×D4#41×C14911yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4C2×D4×C14911yescharacteristic
484M16—41no—
485M16—41no—
486C2×C8—41no—
487C4⋊C4—41no—
488C4⋊C4—42no—
489C22⋊C4—24no—
490C22⋊C4—21no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—44no—
498C22⋊C4—42no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—82no—
504C22⋊C4C22⋊C4×C14912yescomplemented
505C42—41no—
506C42—42no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—44no—
523C23—41no—
524C23—44no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—81no—
533C23—84no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23C2×C22⋊C4×C14911yescharacteristic
541C23C4×D4×C14911yescharacteristic
542C23#120×C14911yescharacteristic
543C23#121×C14911yescharacteristic
544C23#123×C14911yescharacteristic
545Q8—22no—
546Q8—41no—
547D4—22no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—44no—
554D4—44no—
555D4—42no—
556D4—42no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—88no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—81no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4C4×D4×C14911yescharacteristic
597C2×C4#121×C14911yescharacteristic
598C8—81no—
599C22—21no—
600C22—21no—
601C22—24no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—41no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—81no—
623C22—81no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—81no—
630C22—81no—
631C22—161no—
632C22—161no—
633C22#386×C14911yescharacteristic
634C22B(4,𝔽2)×C14911yescharacteristic
635C22B(4,𝔽2)×C14911yescharacteristic
636C4—21no—
637C4—21no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—82no—
644C4—81no—
645C4—161no—
646C2—21no—
647C2—21no—
648C2—41no—
649C2—41no—
650C2—44no—
651C2—41no—
652C2—41no—
653C2—82no—
654C2#1889×C14911yescharacteristic
655C2#2196×C14911yescharacteristic
656C2#2197×C14911yescharacteristic
subgroupG/H
center, socleC22×C149B(4,𝔽2)
commutatorC2×D4C22×C4×C149
Frattini, cosocleC22×D4C23×C149
prime radicalC2×B(4,𝔽2)×C149C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C22×D4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2358×C149C2semidirect
3. C2×AΣL(1,𝔽16)×C149C2semidirect
4. #1792×C149C2semidirect
5. #1790×C149C2semidirect
6. #1393×C149C2semidirect
7. #1390×C149C2semidirect
14. B(4,𝔽2)×C149C4semidirect
35. H(5,𝔽2)×C149C2×C4semidirect
46. C23×C4×C149D4semidirect
56. C2×C4⋊C4×C149D4semidirect
69. C2×C22⋊C4×C149D4semidirect
71. C2×C42×C149D4semidirect
82. #99×C149C2×C4semidirect
95. C24×C149C22⋊C4semidirect
175. C22⋊C4×C149C22⋊C4semidirect
328. #13041C149direct (N × H)
329. C149#13041direct (N × H)
331. #2358C2×C149semidirect
332. C2×AΣL(1,𝔽16)C2×C149semidirect
333. #1792C2×C149semidirect
334. #1790C2×C149semidirect
335. #1393C2×C149semidirect
336. #1390C2×C149semidirect
343. B(4,𝔽2)C4×C149semidirect
364. H(5,𝔽2)C2×C4×C149semidirect
375. C23×C4D4×C149semidirect
385. C2×C4⋊C4D4×C149semidirect
398. C2×C22⋊C4D4×C149semidirect
400. C2×C42D4×C149semidirect
411. #99C2×C4×C149semidirect
424. C24C22⋊C4×C149semidirect
504. C22⋊C4C22⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C1492
#2358×C1492
C2×AΣL(1,𝔽16)×C1492
#1792×C1492
#1790×C1492
#1393×C1492
#1390×C1492
#13041149