Finite Group Databasebeta

← C149×#19026 #49197975

Subgroups — C149×#19026 #49197975

Order 38144.

1012 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3561×C149C211yesmaximal, characteristic, complemented
2#3217×C149C211yesmaximal, characteristic, complemented
3C2×#496×C149C211yesmaximal, characteristic, complemented
4#3138×C149C211yesmaximal, characteristic, complemented
5#1657×C149C214yesmaximal, complemented
6#1656×C149C214yesmaximal, complemented
7#1531×C149C211yesmaximal, characteristic, complemented
8#1527×C149C211yesmaximal, characteristic, complemented
9#1524×C149C211yesmaximal, characteristic, complemented
10C22×SD16×C149—21no—
11C22×D8×C149—21no—
12#563×C149C2212yescomplemented
13#562×C149C2212yescomplemented
14#556×C149—21no—
15#551×C149—22no—
16D4×Q8×C149—21no—
17#548×C149—21no—
18#546×C149—21no—
19#543×C149—21no—
20#542×C149—21no—
21#542×C149—22no—
22#538×C149—21no—
23#536×C149—21no—
24#533×C149C2211yescharacteristic
25C2×#127×C149C2211yescharacteristic
26#529×C149C2211yescharacteristic
27C2×#124×C149C2211yescharacteristic
28#496×C149—22no—
29#496×C149C2214yes—
30#496×C149C2212yescomplemented
31#490×C149C2212yescomplemented
32#490×C149C2214yescomplemented
33#486×C149—21no—
34#486×C149—21no—
35#460×C149—21no—
36#459×C149—21no—
37#450×C149—21no—
38#447×C149—21no—
39#432×C149C2211yescharacteristic
40#418×C149—22no—
41C4×M16×C149C2211yescharacteristic
42C2×#97×C149C2211yescharacteristic
43#330×C149C2212yescomplemented
44#330×C149C2214yescomplemented
45#329×C149C2212yescomplemented
46#329×C149C2214yescomplemented
47C2×#41×C149—21no—
48C22×Q8×C149—21no—
49C22×Q8×C149D411yescharacteristic
50C22×D4×C149—21no—
51C22×D4×C149—21no—
52C22×D4×C149—21no—
53C22×D4×C149D411yescharacteristic
54C2×SD16×C149—24no—
55C2×SD16×C149—22no—
56C2×SD16×C149—44no—
57C2×D8×C149—24no—
58C2×D8×C149—22no—
59C2×D8×C149—44no—
60C2×M16×C149—21no—
61C22×C8×C149—21no—
62C4⋊Q8×C149—21no—
63C4⋊Q8×C149—22no—
64C4⋊Q8×C149D411yescharacteristic
65C4⋊Q8×C149D411yescharacteristic
66#127×C149—21no—
67#127×C149—21no—
68#127×C149—21no—
69#127×C149C2312yes—
70#126×C149—22no—
71#126×C149—22no—
72#126×C149—22no—
73#126×C149—21no—
74#125×C149C2311yescharacteristic
75#125×C149C2312yes—
76#124×C149—21no—
77#124×C149—22no—
78#124×C149—22no—
79#124×C149—21no—
80#124×C149—21no—
81#124×C149D412yes—
82#124×C149C2312yes—
83#124×C149C2311yescharacteristic
84#123×C149—22no—
85#123×C149—22no—
86#123×C149—21no—
87#123×C149—22no—
88#123×C149—22no—
89C22⋊Q8×C149—22no—
90C22⋊Q8×C149—22no—
91C22⋊Q8×C149—21no—
92C22⋊Q8×C149—22no—
93C22⋊Q8×C149—22no—
94C22⋊Q8×C149—22no—
95C22⋊Q8×C149—21no—
96C22⋊Q8×C149—21no—
97C22⋊Q8×C149—22no—
98C22⋊Q8×C149—22no—
99C22⋊Q8×C149D411yescharacteristic
100#121×C149—21no—
101#121×C149—22no—
102#121×C149—22no—
103#121×C149D411yescharacteristic
104#120×C149—22no—
105C4×Q8×C149—21no—
106C4×Q8×C149—21no—
107C4×Q8×C149—21no—
108C4×Q8×C149D411yescharacteristic
109C4×D4×C149—22no—
110C4×D4×C149—21no—
111C4×D4×C149—22no—
112C4×D4×C149—21no—
113C4×D4×C149D411yescharacteristic
114#117×C149—22no—
115#117×C149—21no—
116#117×C149D412yes—
117C2×C22⋊C4×C149—22no—
118C2×C22⋊C4×C149—21no—
119C2×C22⋊C4×C149—21no—
120C2×C42×C149C2311yescharacteristic
121C4⋊C8×C149—21no—
122#102×C149—24no—
123#102×C149—24no—
124#102×C149—22no—
125#102×C149—22no—
126C22⋊C8×C149—21no—
127#97×C149—21no—
128#97×C149C2312yes—
129#97×C149C2312yes—
130#97×C149C2312yes—
131C4×C8×C149—21no—
132C24×C149—21no—
133C24×C149—41no—
134#41×C149—82no—
135C2×Q8×C149—22no—
136C2×Q8×C149—21no—
137C2×Q8×C149—21no—
138C2×Q8×C149—21no—
139C2×Q8×C149—42no—
140C2×Q8×C149—82no—
141C2×Q8×C149C2×D411yescharacteristic
142C2×Q8×C149C2×D412yes—
143C2×D4×C149—21no—
144C2×D4×C149—22no—
145C2×D4×C149—22no—
146C2×D4×C149—21no—
147C2×D4×C149—22no—
148C2×D4×C149—22no—
149C2×D4×C149—22no—
150C2×D4×C149—42no—
151C2×D4×C149—42no—
152C2×D4×C149—42no—
153C2×D4×C149—44no—
154C2×D4×C149—41no—
155C2×D4×C149—41no—
156C2×D4×C149—41no—
157C2×D4×C149—82no—
158C2×D4×C149C2×D411yescharacteristic
159C2×D4×C149C2×D412yes—
160C22×C4×C149—22no—
161C22×C4×C149—22no—
162C22×C4×C149—22no—
163C22×C4×C149—21no—
164C22×C4×C149—21no—
165C22×C4×C149C2×D411yescharacteristic
166C22×C4×C149C2×D411yescharacteristic
167C22×C4×C149C2×D411yescharacteristic
168SD16×C149—48no—
169SD16×C149—82no—
170D8×C149—48no—
171D8×C149—82no—
172M16×C149—42no—
173C2×C8×C149—24no—
174C2×C8×C149—22no—
175C2×C8×C149—22no—
176C2×C8×C149—22no—
177C4⋊C4×C149—22no—
178C4⋊C4×C149—22no—
179C4⋊C4×C149—22no—
180C4⋊C4×C149—22no—
181C4⋊C4×C149—21no—
182C4⋊C4×C149—21no—
183C4⋊C4×C149—21no—
184C4⋊C4×C149—21no—
185C4⋊C4×C149—21no—
186C4⋊C4×C149—21no—
187C4⋊C4×C149—22no—
188C4⋊C4×C149—22no—
189C4⋊C4×C149C2×D412yes—
190C4⋊C4×C149C2×D412yes—
191C4⋊C4×C149C2×D411yescharacteristic
192C4⋊C4×C149C2×D411yescharacteristic
193C22⋊C4×C149—22no—
194C22⋊C4×C149—22no—
195C22⋊C4×C149—22no—
196C22⋊C4×C149—22no—
197C22⋊C4×C149—22no—
198C22⋊C4×C149—21no—
199C22⋊C4×C149—22no—
200C22⋊C4×C149—22no—
201C22⋊C4×C149—22no—
202C22⋊C4×C149—21no—
203C22⋊C4×C149—21no—
204C22⋊C4×C149—22no—
205C22⋊C4×C149—22no—
206C22⋊C4×C149—21no—
207C22⋊C4×C149—21no—
208C42×C149—22no—
209C42×C149—22no—
210C42×C149—21no—
211C42×C149C2×D411yescharacteristic
212C42×C149C2×D411yescharacteristic
213C42×C149C2×D411yescharacteristic
214C42×C149C2411yescharacteristic
215C23×C149—22no—
216C23×C149—21no—
217C23×C149—42no—
218C23×C149—42no—
219C23×C149—81no—
220C23×C149—81no—
221C23×C149—82no—
222C23×C149—82no—
223C23×C149—82no—
224C23×C149#12011yescharacteristic
225Q8×C149—42no—
226Q8×C149—41no—
227Q8×C149—42no—
228Q8×C149—42no—
229Q8×C149—81no—
230Q8×C149—82no—
231D4×C149—42no—
232D4×C149—41no—
233D4×C149—42no—
234D4×C149—42no—
235D4×C149—42no—
236D4×C149—42no—
237D4×C149—44no—
238D4×C149—42no—
239D4×C149—42no—
240D4×C149—82no—
241D4×C149—82no—
242D4×C149—82no—
243D4×C149—82no—
244D4×C149—82no—
245C2×C4×C149—22no—
246C2×C4×C149—22no—
247C2×C4×C149—21no—
248C2×C4×C149—22no—
249C2×C4×C149—21no—
250C2×C4×C149—22no—
251C2×C4×C149—22no—
252C2×C4×C149—21no—
253C2×C4×C149—41no—
254C2×C4×C149—42no—
255C2×C4×C149—81no—
256C2×C4×C149—82no—
257C2×C4×C149—82no—
258C2×C4×C149—82no—
259C2×C4×C149#12011yescharacteristic
260C2×C4×C149#12011yescharacteristic
261C2×C4×C149#12011yescharacteristic
262C2×C4×C149C22×D411yescharacteristic
263C2×C4×C149C22×D411yescharacteristic
264C2×C4×C149C22×D411yescharacteristic
265C8×C149—24no—
266C8×C149—42no—
267C8×C149—42no—
268C22×C149—21no—
269C22×C149—21no—
270C22×C149—41no—
271C22×C149—42no—
272C22×C149—41no—
273C22×C149—42no—
274C22×C149—42no—
275C22×C149—41no—
276C22×C149—82no—
277C22×C149—82no—
278C22×C149—82no—
279C22×C149—162no—
280C22×C149—164no—
281C22×C149#45412yes—
282C22×C149C2×#12011yescharacteristic
283C4×C149—21no—
284C4×C149—21no—
285C4×C149—21no—
286C4×C149—21no—
287C4×C149—21no—
288C4×C149—41no—
289C4×C149—42no—
290C4×C149—42no—
291C4×C149—41no—
292C4×C149—41no—
293C4×C149—42no—
294C4×C149#45312yes—
295C2×C149—22no—
296C2×C149—81no—
297C2×C149—82no—
298C2×C149—162no—
299C2×C149C2×#45311yescharacteristic
300C2×C149C2×#45411yescharacteristic
301C2×C149#302111yescharacteristic
302#19026C14911yesmaximal, characteristic, direct product factor, Sylow
303C149#1902611yescharacteristic, direct product factor, Sylow
304#3561C2×C14911yescharacteristic, complemented
305#3217C2×C14911yescharacteristic, complemented
306C2×#496C2×C14911yescharacteristic, complemented
307#3138C2×C14911yescharacteristic, complemented
308#1657C2×C14914yescomplemented
309#1656C2×C14914yescomplemented
310#1531C2×C14911yescharacteristic, complemented
311#1527C2×C14911yescharacteristic, complemented
312#1524C2×C14911yescharacteristic, complemented
313C22×SD16—21no—
314C22×D8—21no—
315#563C22×C14912yescomplemented
316#562C22×C14912yescomplemented
317#556—21no—
318#551—22no—
319D4×Q8—21no—
320#548—21no—
321#546—21no—
322#543—21no—
323#542—21no—
324#542—22no—
325#538—21no—
326#536—21no—
327#533C22×C14911yescharacteristic
328C2×#127C22×C14911yescharacteristic
329#529C22×C14911yescharacteristic
330C2×#124C22×C14911yescharacteristic
331#496—22no—
332#496C22×C14914yes—
333#496C22×C14912yescomplemented
334#490C22×C14914yescomplemented
335#490C22×C14912yescomplemented
336#486—21no—
337#486—21no—
338#460—21no—
339#459—21no—
340#450—21no—
341#447—21no—
342#432C22×C14911yescharacteristic
343#418—22no—
344C4×M16C22×C14911yescharacteristic
345C2×#97C22×C14911yescharacteristic
346#330C22×C14914yescomplemented
347#330C22×C14912yescomplemented
348#329C22×C14912yescomplemented
349#329C22×C14914yescomplemented
350C2×#41—21no—
351C22×Q8—21no—
352C22×Q8D4×C14911yescharacteristic
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4D4×C14911yescharacteristic
357C2×SD16—24no—
358C2×SD16—22no—
359C2×SD16—44no—
360C2×D8—24no—
361C2×D8—22no—
362C2×D8—44no—
363C2×M16—21no—
364C22×C8—21no—
365C4⋊Q8—21no—
366C4⋊Q8—22no—
367C4⋊Q8D4×C14911yescharacteristic
368C4⋊Q8D4×C14911yescharacteristic
369#127—21no—
370#127—21no—
371#127—21no—
372#127C23×C14912yes—
373#126—22no—
374#126—22no—
375#126—22no—
376#126—21no—
377#125C23×C14911yescharacteristic
378#125C23×C14912yes—
379#124—21no—
380#124—22no—
381#124—22no—
382#124—21no—
383#124—21no—
384#124D4×C14912yes—
385#124C23×C14912yes—
386#124C23×C14911yescharacteristic
387#123—22no—
388#123—22no—
389#123—21no—
390#123—22no—
391#123—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8D4×C14911yescharacteristic
403#121—21no—
404#121—22no—
405#121—22no—
406#121D4×C14911yescharacteristic
407#120—22no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8D4×C14911yescharacteristic
412C4×D4—22no—
413C4×D4—21no—
414C4×D4—22no—
415C4×D4—21no—
416C4×D4D4×C14911yescharacteristic
417#117—22no—
418#117—21no—
419#117D4×C14912yes—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42C23×C14911yescharacteristic
424C4⋊C8—21no—
425#102—24no—
426#102—24no—
427#102—22no—
428#102—22no—
429C22⋊C8—21no—
430#97—21no—
431#97C23×C14912yes—
432#97C23×C14912yes—
433#97C23×C14912yes—
434C4×C8—21no—
435C24—21no—
436C24—41no—
437#41—82no—
438C2×Q8—22no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—42no—
443C2×Q8—82no—
444C2×Q8C2×D4×C14911yescharacteristic
445C2×Q8C2×D4×C14912yes—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—44no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—82no—
461C2×D4C2×D4×C14911yescharacteristic
462C2×D4C2×D4×C14912yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4C2×D4×C14911yescharacteristic
469C22×C4C2×D4×C14911yescharacteristic
470C22×C4C2×D4×C14911yescharacteristic
471SD16—48no—
472SD16—82no—
473D8—48no—
474D8—82no—
475M16—42no—
476C2×C8—24no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4C2×D4×C14912yes—
493C4⋊C4C2×D4×C14912yes—
494C4⋊C4C2×D4×C14911yescharacteristic
495C4⋊C4C2×D4×C14911yescharacteristic
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—21no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42C2×D4×C14911yescharacteristic
515C42C2×D4×C14911yescharacteristic
516C42C2×D4×C14911yescharacteristic
517C42C24×C14911yescharacteristic
518C23—22no—
519C23—21no—
520C23—42no—
521C23—42no—
522C23—81no—
523C23—81no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23#120×C14911yescharacteristic
528Q8—42no—
529Q8—41no—
530Q8—42no—
531Q8—42no—
532Q8—81no—
533Q8—82no—
534D4—42no—
535D4—41no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—44no—
541D4—42no—
542D4—42no—
543D4—82no—
544D4—82no—
545D4—82no—
546D4—82no—
547D4—82no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4#120×C14911yescharacteristic
563C2×C4#120×C14911yescharacteristic
564C2×C4#120×C14911yescharacteristic
565C2×C4C22×D4×C14911yescharacteristic
566C2×C4C22×D4×C14911yescharacteristic
567C2×C4C22×D4×C14911yescharacteristic
568C8—24no—
569C8—42no—
570C8—42no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—42no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22—162no—
583C22—164no—
584C22#454×C14912yes—
585C22C2×#120×C14911yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4#453×C14912yes—
598C2—22no—
599C2—82no—
600C2—81no—
601C2—162no—
602C2C2×#453×C14911yescharacteristic
603C2C2×#454×C14911yescharacteristic
604C2#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. #3561×C149C2semidirect
2. #3217×C149C2semidirect
3. C2×#496×C149C2semidirect
4. #3138×C149C2semidirect
5. #1657×C149C2semidirect
6. #1656×C149C2semidirect
7. #1531×C149C2semidirect
8. #1527×C149C2semidirect
9. #1524×C149C2semidirect
12. #563×C149C22semidirect
13. #562×C149C22semidirect
30. #496×C149C22semidirect
31. #490×C149C22semidirect
32. #490×C149C22semidirect
43. #330×C149C22semidirect
44. #330×C149C22semidirect
45. #329×C149C22semidirect
46. #329×C149C22semidirect
302. #19026C149direct (N × H)
303. C149#19026direct (N × H)
304. #3561C2×C149semidirect
305. #3217C2×C149semidirect
306. C2×#496C2×C149semidirect
307. #3138C2×C149semidirect
308. #1657C2×C149semidirect
309. #1656C2×C149semidirect
310. #1531C2×C149semidirect
311. #1527C2×C149semidirect
312. #1524C2×C149semidirect
315. #563C22×C149semidirect
316. #562C22×C149semidirect
333. #496C22×C149semidirect
334. #490C22×C149semidirect
335. #490C22×C149semidirect
346. #330C22×C149semidirect
347. #330C22×C149semidirect
348. #329C22×C149semidirect
349. #329C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3561×C1492
#3217×C1492
C2×#496×C1492
#3138×C1492
#1657×C1492
#1656×C1492
#1531×C1492
#1527×C1492
#1524×C1492
#19026149