Finite Group Databasebeta

← C149×#19014 #49197963

Subgroups — C149×#19014 #49197963

Order 38144.

1140 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558×C149C211yesmaximal, characteristic, complemented
2#3217×C149C211yesmaximal, characteristic, complemented
3#3151×C149C211yesmaximal, characteristic, complemented
4C2×#496×C149C211yesmaximal, characteristic, complemented
5#1656×C149C214yesmaximal, complemented
6#1655×C149C214yesmaximal, complemented
7#1530×C149C211yesmaximal, characteristic, complemented
8#1527×C149C211yesmaximal, characteristic, complemented
9#1524×C149C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C149—22no—
11C22×SD16×C149—21no—
12C22×D8×C149—21no—
13#562×C149C2212yescomplemented
14H(3,𝔽4)×C149C2212yescomplemented
15#559×C149—21no—
16#548×C149—21no—
17#546×C149—22no—
18#546×C149—21no—
19D42×C149—21no—
20#542×C149—21no—
21#538×C149—22no—
22#538×C149—21no—
23#535×C149—21no—
24#534×C149—21no—
25#532×C149C2211yescharacteristic
26C2×#127×C149C2211yescharacteristic, complemented
27#529×C149C2211yescharacteristic
28C2×#124×C149C2211yescharacteristic
29#496×C149—22no—
30#496×C149C2212yescomplemented
31#496×C149C2214yescomplemented
32#496×C149C2214yescomplemented
33#493×C149—21no—
34#492×C149—21no—
35#490×C149C2212yescomplemented
36#460×C149—21no—
37#459×C149—21no—
38#450×C149—21no—
39#447×C149—21no—
40#432×C149C2211yescharacteristic, complemented
41C4×M16×C149C2211yescharacteristic, complemented
42C2×#97×C149C2211yescharacteristic, complemented
43#330×C149C2212yescomplemented
44#329×C149C2212yescomplemented
45#329×C149C2214yescomplemented
46#329×C149C2214yescomplemented
47C2×#41×C149—21no—
48C2×#41×C149D412yes—
49C22×Q8×C149D411yescharacteristic
50C22×D4×C149—22no—
51C22×D4×C149—21no—
52C22×D4×C149—21no—
53C22×D4×C149—21no—
54C22×D4×C149—21no—
55C22×D4×C149D411yescharacteristic
56AGL(1,ℤ/8)×C149—48no—
57C2×SD16×C149—24no—
58C2×SD16×C149—24no—
59C2×SD16×C149—22no—
60C2×SD16×C149—44no—
61C2×D8×C149—24no—
62C2×D8×C149—24no—
63C2×D8×C149—22no—
64C2×D8×C149—44no—
65C2×M16×C149—21no—
66C22×C8×C149—21no—
67C4⋊Q8×C149D411yescharacteristic
68#127×C149—21no—
69#127×C149—21no—
70#127×C149—21no—
71#127×C149—21no—
72#127×C149D411yescharacteristic
73#127×C149C2312yes—
74#126×C149—22no—
75#126×C149—21no—
76#125×C149C2311yescharacteristic
77#124×C149—21no—
78#124×C149—22no—
79#124×C149—22no—
80#124×C149—22no—
81#124×C149—21no—
82#124×C149—21no—
83#124×C149D412yes—
84#124×C149C2312yes—
85#124×C149C2311yescharacteristic
86#124×C149C2312yes—
87#123×C149—22no—
88#123×C149—22no—
89#123×C149—21no—
90#123×C149—22no—
91#123×C149—22no—
92C22⋊Q8×C149—21no—
93C22⋊Q8×C149—22no—
94C22⋊Q8×C149—22no—
95C22⋊Q8×C149D411yescharacteristic
96#121×C149—22no—
97#121×C149—22no—
98#121×C149—22no—
99#121×C149—21no—
100#121×C149—22no—
101#121×C149—22no—
102#121×C149—21no—
103#121×C149—21no—
104#121×C149D411yescharacteristic
105#120×C149—22no—
106#120×C149—22no—
107#120×C149—22no—
108#120×C149—22no—
109#120×C149—22no—
110C4×Q8×C149—21no—
111C4×Q8×C149D411yescharacteristic
112C4×D4×C149—22no—
113C4×D4×C149—22no—
114C4×D4×C149—21no—
115C4×D4×C149—21no—
116C4×D4×C149—21no—
117C4×D4×C149—21no—
118C4×D4×C149D411yescharacteristic
119#117×C149—21no—
120C2×C22⋊C4×C149—22no—
121C2×C22⋊C4×C149—21no—
122C2×C22⋊C4×C149—21no—
123C2×C42×C149C2311yescharacteristic
124C4⋊C8×C149—21no—
125#102×C149—22no—
126#102×C149—22no—
127C22⋊C8×C149—21no—
128#97×C149—21no—
129#97×C149C2312yes—
130#97×C149C2312yes—
131#97×C149C2312yes—
132C4×C8×C149—21no—
133C24×C149—22no—
134C24×C149—21no—
135C24×C149—41no—
136#41×C149—44no—
137#41×C149—82no—
138C2×Q8×C149—21no—
139C2×Q8×C149—42no—
140C2×Q8×C149C2×D411yescharacteristic
141C2×Q8×C149C2×D412yes—
142C2×Q8×C149C2×D412yes—
143C2×D4×C149—22no—
144C2×D4×C149—21no—
145C2×D4×C149—22no—
146C2×D4×C149—22no—
147C2×D4×C149—22no—
148C2×D4×C149—22no—
149C2×D4×C149—22no—
150C2×D4×C149—21no—
151C2×D4×C149—21no—
152C2×D4×C149—21no—
153C2×D4×C149—22no—
154C2×D4×C149—22no—
155C2×D4×C149—22no—
156C2×D4×C149—42no—
157C2×D4×C149—42no—
158C2×D4×C149—42no—
159C2×D4×C149—44no—
160C2×D4×C149—41no—
161C2×D4×C149—41no—
162C2×D4×C149—41no—
163C2×D4×C149—82no—
164C2×D4×C149—82no—
165C2×D4×C149—84no—
166C2×D4×C149C2×D411yescharacteristic
167C2×D4×C149C2×D412yes—
168C2×D4×C149C2×D412yes—
169C22×C4×C149—22no—
170C22×C4×C149—22no—
171C22×C4×C149—21no—
172C22×C4×C149—21no—
173C22×C4×C149—22no—
174C22×C4×C149C2×D411yescharacteristic
175C22×C4×C149C2×D411yescharacteristic
176C22×C4×C149C2×D411yescharacteristic
177SD16×C149—48no—
178SD16×C149—48no—
179SD16×C149—82no—
180D8×C149—48no—
181D8×C149—48no—
182D8×C149—82no—
183M16×C149—24no—
184C2×C8×C149—24no—
185C2×C8×C149—22no—
186C2×C8×C149—22no—
187C2×C8×C149—22no—
188C4⋊C4×C149—22no—
189C4⋊C4×C149—22no—
190C4⋊C4×C149—21no—
191C4⋊C4×C149—21no—
192C4⋊C4×C149—21no—
193C4⋊C4×C149—21no—
194C4⋊C4×C149—21no—
195C4⋊C4×C149—21no—
196C4⋊C4×C149C2×D411yescharacteristic
197C4⋊C4×C149C2×D411yescharacteristic
198C22⋊C4×C149—22no—
199C22⋊C4×C149—22no—
200C22⋊C4×C149—22no—
201C22⋊C4×C149—22no—
202C22⋊C4×C149—22no—
203C22⋊C4×C149—21no—
204C22⋊C4×C149—22no—
205C22⋊C4×C149—21no—
206C22⋊C4×C149—22no—
207C22⋊C4×C149—21no—
208C22⋊C4×C149—22no—
209C22⋊C4×C149—22no—
210C22⋊C4×C149—21no—
211C22⋊C4×C149—21no—
212C22⋊C4×C149—22no—
213C22⋊C4×C149—22no—
214C42×C149—22no—
215C42×C149—21no—
216C42×C149C2×D411yescharacteristic
217C42×C149C2×D411yescharacteristic
218C42×C149C2×D411yescharacteristic
219C42×C149C2411yescharacteristic
220C23×C149—21no—
221C23×C149—22no—
222C23×C149—22no—
223C23×C149—42no—
224C23×C149—42no—
225C23×C149—81no—
226C23×C149—81no—
227C23×C149—82no—
228C23×C149—82no—
229C23×C149—82no—
230C23×C149—82no—
231C23×C149—82no—
232C23×C149—82no—
233C23×C149#12011yescharacteristic
234Q8×C149—42no—
235Q8×C149—42no—
236Q8×C149—41no—
237Q8×C149—42no—
238D4×C149—42no—
239D4×C149—42no—
240D4×C149—41no—
241D4×C149—42no—
242D4×C149—44no—
243D4×C149—42no—
244D4×C149—42no—
245D4×C149—42no—
246D4×C149—42no—
247D4×C149—44no—
248D4×C149—42no—
249D4×C149—42no—
250D4×C149—81no—
251D4×C149—82no—
252D4×C149—82no—
253D4×C149—82no—
254D4×C149—82no—
255D4×C149—82no—
256D4×C149—82no—
257D4×C149—82no—
258D4×C149—82no—
259C2×C4×C149—22no—
260C2×C4×C149—22no—
261C2×C4×C149—21no—
262C2×C4×C149—22no—
263C2×C4×C149—22no—
264C2×C4×C149—21no—
265C2×C4×C149—21no—
266C2×C4×C149—41no—
267C2×C4×C149—42no—
268C2×C4×C149—82no—
269C2×C4×C149—81no—
270C2×C4×C149—82no—
271C2×C4×C149—82no—
272C2×C4×C149#12011yescharacteristic
273C2×C4×C149#12011yescharacteristic
274C2×C4×C149#12011yescharacteristic
275C2×C4×C149C22×D411yescharacteristic
276C2×C4×C149C22×D411yescharacteristic
277C2×C4×C149C22×D411yescharacteristic
278C8×C149—24no—
279C8×C149—24no—
280C8×C149—42no—
281C22×C149—21no—
282C22×C149—21no—
283C22×C149—41no—
284C22×C149—42no—
285C22×C149—42no—
286C22×C149—42no—
287C22×C149—42no—
288C22×C149—41no—
289C22×C149—41no—
290C22×C149—42no—
291C22×C149—42no—
292C22×C149—82no—
293C22×C149—82no—
294C22×C149—82no—
295C22×C149—162no—
296C22×C149—164no—
297C22×C149—164no—
298C22×C149#45312yes—
299C22×C149C2×#12011yescharacteristic
300C4×C149—21no—
301C4×C149—21no—
302C4×C149—21no—
303C4×C149—21no—
304C4×C149—21no—
305C4×C149—41no—
306C4×C149—41no—
307C4×C149—42no—
308C4×C149—42no—
309C4×C149—41no—
310C4×C149#45312yes—
311C2×C149—22no—
312C2×C149—82no—
313C2×C149—81no—
314C2×C149—82no—
315C2×C149—162no—
316C2×C149C2×#45311yescharacteristic
317C2×C149C2×#45311yescharacteristic
318C2×C149#302111yescharacteristic
319#19014C14911yesmaximal, characteristic, direct product factor, Sylow
320C149#1901411yescharacteristic, direct product factor, Sylow
321#3558C2×C14911yescharacteristic, complemented
322#3217C2×C14911yescharacteristic, complemented
323#3151C2×C14911yescharacteristic, complemented
324C2×#496C2×C14911yescharacteristic, complemented
325#1656C2×C14914yescomplemented
326#1655C2×C14914yescomplemented
327#1530C2×C14911yescharacteristic, complemented
328#1527C2×C14911yescharacteristic, complemented
329#1524C2×C14911yescharacteristic, complemented
330C2×AGL(1,ℤ/8)—22no—
331C22×SD16—21no—
332C22×D8—21no—
333#562C22×C14912yescomplemented
334H(3,𝔽4)C22×C14912yescomplemented
335#559—21no—
336#548—21no—
337#546—22no—
338#546—21no—
339D42—21no—
340#542—21no—
341#538—22no—
342#538—21no—
343#535—21no—
344#534—21no—
345#532C22×C14911yescharacteristic
346C2×#127C22×C14911yescharacteristic, complemented
347#529C22×C14911yescharacteristic
348C2×#124C22×C14911yescharacteristic
349#496—22no—
350#496C22×C14914yescomplemented
351#496C22×C14914yescomplemented
352#496C22×C14912yescomplemented
353#493—21no—
354#492—21no—
355#490C22×C14912yescomplemented
356#460—21no—
357#459—21no—
358#450—21no—
359#447—21no—
360#432C22×C14911yescharacteristic, complemented
361C4×M16C22×C14911yescharacteristic, complemented
362C2×#97C22×C14911yescharacteristic, complemented
363#330C22×C14912yescomplemented
364#329C22×C14912yescomplemented
365#329C22×C14914yescomplemented
366#329C22×C14914yescomplemented
367C2×#41—21no—
368C2×#41D4×C14912yes—
369C22×Q8D4×C14911yescharacteristic
370C22×D4—22no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C22×D4D4×C14911yescharacteristic
376AGL(1,ℤ/8)—48no—
377C2×SD16—24no—
378C2×SD16—24no—
379C2×SD16—22no—
380C2×SD16—44no—
381C2×D8—24no—
382C2×D8—24no—
383C2×D8—22no—
384C2×D8—44no—
385C2×M16—21no—
386C22×C8—21no—
387C4⋊Q8D4×C14911yescharacteristic
388#127—21no—
389#127—21no—
390#127—21no—
391#127—21no—
392#127D4×C14911yescharacteristic
393#127C23×C14912yes—
394#126—22no—
395#126—21no—
396#125C23×C14911yescharacteristic
397#124—21no—
398#124—22no—
399#124—22no—
400#124—22no—
401#124—21no—
402#124—21no—
403#124D4×C14912yes—
404#124C23×C14912yes—
405#124C23×C14911yescharacteristic
406#124C23×C14912yes—
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411#123—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8D4×C14911yescharacteristic
416#121—22no—
417#121—22no—
418#121—22no—
419#121—21no—
420#121—22no—
421#121—22no—
422#121—21no—
423#121—21no—
424#121D4×C14911yescharacteristic
425#120—22no—
426#120—22no—
427#120—22no—
428#120—22no—
429#120—22no—
430C4×Q8—21no—
431C4×Q8D4×C14911yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4D4×C14911yescharacteristic
439#117—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C42C23×C14911yescharacteristic
444C4⋊C8—21no—
445#102—22no—
446#102—22no—
447C22⋊C8—21no—
448#97—21no—
449#97C23×C14912yes—
450#97C23×C14912yes—
451#97C23×C14912yes—
452C4×C8—21no—
453C24—22no—
454C24—21no—
455C24—41no—
456#41—44no—
457#41—82no—
458C2×Q8—21no—
459C2×Q8—42no—
460C2×Q8C2×D4×C14911yescharacteristic
461C2×Q8C2×D4×C14912yes—
462C2×Q8C2×D4×C14912yes—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—82no—
484C2×D4—82no—
485C2×D4—84no—
486C2×D4C2×D4×C14911yescharacteristic
487C2×D4C2×D4×C14912yes—
488C2×D4C2×D4×C14912yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4C2×D4×C14911yescharacteristic
495C22×C4C2×D4×C14911yescharacteristic
496C22×C4C2×D4×C14911yescharacteristic
497SD16—48no—
498SD16—48no—
499SD16—82no—
500D8—48no—
501D8—48no—
502D8—82no—
503M16—24no—
504C2×C8—24no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4C2×D4×C14911yescharacteristic
517C4⋊C4C2×D4×C14911yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C42—22no—
535C42—21no—
536C42C2×D4×C14911yescharacteristic
537C42C2×D4×C14911yescharacteristic
538C42C2×D4×C14911yescharacteristic
539C42C24×C14911yescharacteristic
540C23—21no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—81no—
546C23—81no—
547C23—82no—
548C23—82no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23—82no—
553C23#120×C14911yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—41no—
557Q8—42no—
558D4—42no—
559D4—42no—
560D4—41no—
561D4—42no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—44no—
568D4—42no—
569D4—42no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—82no—
589C2×C4—81no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4#120×C14911yescharacteristic
593C2×C4#120×C14911yescharacteristic
594C2×C4#120×C14911yescharacteristic
595C2×C4C22×D4×C14911yescharacteristic
596C2×C4C22×D4×C14911yescharacteristic
597C2×C4C22×D4×C14911yescharacteristic
598C8—24no—
599C8—24no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—162no—
616C22—164no—
617C22—164no—
618C22#453×C14912yes—
619C22C2×#120×C14911yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—42no—
629C4—41no—
630C4#453×C14912yes—
631C2—22no—
632C2—81no—
633C2—82no—
634C2—82no—
635C2—162no—
636C2C2×#453×C14911yescharacteristic
637C2C2×#453×C14911yescharacteristic
638C2#3021×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3558×C149C2semidirect
2. #3217×C149C2semidirect
3. #3151×C149C2semidirect
4. C2×#496×C149C2semidirect
5. #1656×C149C2semidirect
6. #1655×C149C2semidirect
7. #1530×C149C2semidirect
8. #1527×C149C2semidirect
9. #1524×C149C2semidirect
13. #562×C149C22semidirect
14. H(3,𝔽4)×C149C22semidirect
26. C2×#127×C149C22semidirect
30. #496×C149C22semidirect
31. #496×C149C22semidirect
32. #496×C149C22semidirect
35. #490×C149C22semidirect
40. #432×C149C22semidirect
41. C4×M16×C149C22semidirect
42. C2×#97×C149C22semidirect
43. #330×C149C22semidirect
44. #329×C149C22semidirect
45. #329×C149C22semidirect
46. #329×C149C22semidirect
319. #19014C149direct (N × H)
320. C149#19014direct (N × H)
321. #3558C2×C149semidirect
322. #3217C2×C149semidirect
323. #3151C2×C149semidirect
324. C2×#496C2×C149semidirect
325. #1656C2×C149semidirect
326. #1655C2×C149semidirect
327. #1530C2×C149semidirect
328. #1527C2×C149semidirect
329. #1524C2×C149semidirect
333. #562C22×C149semidirect
334. H(3,𝔽4)C22×C149semidirect
346. C2×#127C22×C149semidirect
350. #496C22×C149semidirect
351. #496C22×C149semidirect
352. #496C22×C149semidirect
355. #490C22×C149semidirect
360. #432C22×C149semidirect
361. C4×M16C22×C149semidirect
362. C2×#97C22×C149semidirect
363. #330C22×C149semidirect
364. #329C22×C149semidirect
365. #329C22×C149semidirect
366. #329C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3558×C1492
#3217×C1492
#3151×C1492
C2×#496×C1492
#1656×C1492
#1655×C1492
#1530×C1492
#1527×C1492
#1524×C1492
#19014149