Finite Group Databasebeta

← C149×#19090 #49198039

Subgroups — C149×#19090 #49198039

Order 38144.

888 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#3561×C149C211yesmaximal, characteristic, complemented
2#3235×C149C211yesmaximal, characteristic, complemented
3#3219×C149C211yesmaximal, characteristic, complemented
4#3213×C149C211yesmaximal, characteristic, complemented
5#1664×C149C212yesmaximal, complemented
6#1661×C149C212yesmaximal, complemented
7#1657×C149C212yesmaximal, complemented
8#1656×C149C212yesmaximal, complemented
9#1537×C149C211yesmaximal, characteristic, complemented
10#1535×C149C211yesmaximal, characteristic, complemented
11#1533×C149C211yesmaximal, characteristic, complemented
12#563×C149C2212yes—
13#562×C149C2212yes—
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
25#532×C149C2211yescharacteristic
26#529×C149C2211yescharacteristic
27C2×#124×C149C2211yescharacteristic
28#501×C149C2212yescomplemented
29#497×C149C2211yescharacteristic, complemented
30#496×C149C2212yes—
31#496×C149C2211yescharacteristic, complemented
32#491×C149C2211yescharacteristic, complemented
33#490×C149C2211yescharacteristic, complemented
34#490×C149C2212yescomplemented
35#489×C149C2212yes—
36#482×C149—22no—
37#476×C149—21no—
38#474×C149—21no—
39#464×C149—21no—
40#463×C149—22no—
41#463×C149—21no—
42#452×C149—21no—
43#449×C149—21no—
44#448×C149—21no—
45#447×C149—21no—
46#432×C149C2211yescharacteristic
47#432×C149C2211yescharacteristic
48#432×C149C2211yescharacteristic
49#330×C149C2212yescomplemented
50#330×C149C2212yescomplemented
51#330×C149C2212yescomplemented
52#329×C149C2212yes—
53#329×C149C2212yes—
54#329×C149C2212yescomplemented
55C2×#41×C149—21no—
56C2×#41×C149—21no—
57C22×Q8×C149—21no—
58C22×Q8×C149D411yescharacteristic
59C22×D4×C149D411yescharacteristic
60C2×Q16×C149—21no—
61C2×SD16×C149—22no—
62C2×SD16×C149—21no—
63C2×SD16×C149—21no—
64C2×D8×C149—22no—
65C2×D8×C149—21no—
66C4⋊Q8×C149—21no—
67C4⋊Q8×C149—22no—
68C4⋊Q8×C149D411yescharacteristic
69C4⋊Q8×C149D411yescharacteristic
70C4⋊Q8×C149C2311yescharacteristic
71#127×C149C2311yescharacteristic
72#126×C149—22no—
73#126×C149—22no—
74#126×C149—22no—
75#126×C149—21no—
76#125×C149C2311yescharacteristic
77#125×C149C2312yes—
78#124×C149—21no—
79#124×C149—22no—
80#124×C149—22no—
81#124×C149—21no—
82#124×C149—21no—
83#124×C149—21no—
84#124×C149D412yes—
85#124×C149C2312yes—
86#124×C149C2311yescharacteristic
87#123×C149—22no—
88#123×C149—22no—
89#123×C149—21no—
90#123×C149—22no—
91#123×C149—22no—
92C22⋊Q8×C149—22no—
93C22⋊Q8×C149—22no—
94C22⋊Q8×C149—21no—
95C22⋊Q8×C149—22no—
96C22⋊Q8×C149—22no—
97C22⋊Q8×C149—22no—
98C22⋊Q8×C149—21no—
99C22⋊Q8×C149—21no—
100C22⋊Q8×C149—22no—
101C22⋊Q8×C149—22no—
102C22⋊Q8×C149D411yescharacteristic
103#121×C149—21no—
104#121×C149—22no—
105#121×C149—22no—
106#121×C149—21no—
107#121×C149—21no—
108#121×C149D411yescharacteristic
109#120×C149—22no—
110C4×Q8×C149—21no—
111C4×Q8×C149—21no—
112C4×Q8×C149—21no—
113C4×Q8×C149D411yescharacteristic
114C4×D4×C149—22no—
115C4×D4×C149—21no—
116C4×D4×C149—22no—
117C4×D4×C149—21no—
118C4×D4×C149—21no—
119C4×D4×C149—21no—
120C4×D4×C149D411yescharacteristic
121#117×C149—22no—
122#117×C149—21no—
123#117×C149D412yes—
124C2×C22⋊C4×C149—22no—
125C2×C22⋊C4×C149—21no—
126C2×C22⋊C4×C149—21no—
127C2×C42×C149C2311yescharacteristic
128#107×C149—22no—
129#106×C149—22no—
130C4⋊C8×C149—21no—
131C4⋊C8×C149—21no—
132C4⋊C8×C149—21no—
133#103×C149—22no—
134#103×C149—21no—
135#103×C149—21no—
136#102×C149—22no—
137#102×C149—21no—
138#102×C149—21no—
139#102×C149—22no—
140#102×C149—22no—
141C22⋊C8×C149—21no—
142C22⋊C8×C149—21no—
143C22⋊C8×C149—21no—
144#97×C149C2312yes—
145#97×C149C2311yescharacteristic
146#97×C149C2312yes—
147#97×C149C2311yescharacteristic
148C24×C149—21no—
149#41×C149—81no—
150#41×C149—81no—
151#41×C149—82no—
152C2×Q8×C149—22no—
153C2×Q8×C149—21no—
154C2×Q8×C149—21no—
155C2×Q8×C149—21no—
156C2×Q8×C149—21no—
157C2×Q8×C149—82no—
158C2×Q8×C149—81no—
159C2×Q8×C149C2×D412yes—
160C2×Q8×C149C2×D411yescharacteristic
161C2×D4×C149—21no—
162C2×D4×C149—22no—
163C2×D4×C149—22no—
164C2×D4×C149—21no—
165C2×D4×C149—21no—
166C2×D4×C149—21no—
167C2×D4×C149—21no—
168C2×D4×C149—41no—
169C2×D4×C149—81no—
170C2×D4×C149C2×D412yes—
171C2×D4×C149C2×D411yescharacteristic
172C22×C4×C149—22no—
173C22×C4×C149—22no—
174C22×C4×C149—22no—
175C22×C4×C149—21no—
176C22×C4×C149—21no—
177C22×C4×C149—41no—
178C22×C4×C149C2×D411yescharacteristic
179C22×C4×C149C2×D411yescharacteristic
180C22×C4×C149C2×D411yescharacteristic
181Q16×C149—81no—
182SD16×C149—82no—
183SD16×C149—81no—
184SD16×C149—81no—
185D8×C149—81no—
186D8×C149—82no—
187C2×C8×C149—22no—
188C2×C8×C149—21no—
189C2×C8×C149—22no—
190C2×C8×C149—21no—
191C4⋊C4×C149—22no—
192C4⋊C4×C149—22no—
193C4⋊C4×C149—22no—
194C4⋊C4×C149—22no—
195C4⋊C4×C149—21no—
196C4⋊C4×C149—21no—
197C4⋊C4×C149—21no—
198C4⋊C4×C149—21no—
199C4⋊C4×C149—21no—
200C4⋊C4×C149—21no—
201C4⋊C4×C149—22no—
202C4⋊C4×C149—22no—
203C4⋊C4×C149—21no—
204C4⋊C4×C149—21no—
205C4⋊C4×C149C2×D411yescharacteristic
206C4⋊C4×C149C2×D411yescharacteristic
207C4⋊C4×C149C2×D412yes—
208C4⋊C4×C149C2×D412yes—
209C22⋊C4×C149—22no—
210C22⋊C4×C149—22no—
211C22⋊C4×C149—22no—
212C22⋊C4×C149—22no—
213C22⋊C4×C149—22no—
214C22⋊C4×C149—21no—
215C22⋊C4×C149—22no—
216C22⋊C4×C149—22no—
217C22⋊C4×C149—22no—
218C22⋊C4×C149—21no—
219C22⋊C4×C149—21no—
220C22⋊C4×C149—22no—
221C22⋊C4×C149—22no—
222C22⋊C4×C149—21no—
223C22⋊C4×C149—21no—
224C22⋊C4×C149—41no—
225C22⋊C4×C149—41no—
226C42×C149—22no—
227C42×C149—22no—
228C42×C149—21no—
229C42×C149C2×D411yescharacteristic
230C42×C149C2×D411yescharacteristic
231C42×C149C2×D411yescharacteristic
232C42×C149C2411yescharacteristic
233C23×C149—22no—
234C23×C149—21no—
235C23×C149—42no—
236C23×C149—41no—
237C23×C149—81no—
238C23×C149—81no—
239C23×C149#12011yescharacteristic
240Q8×C149—41no—
241Q8×C149—42no—
242Q8×C149—42no—
243Q8×C149—42no—
244Q8×C149—41no—
245Q8×C149—41no—
246Q8×C149—81no—
247Q8×C149—82no—
248D4×C149—41no—
249D4×C149—42no—
250D4×C149—42no—
251D4×C149—42no—
252D4×C149—41no—
253D4×C149—41no—
254D4×C149—42no—
255D4×C149—42no—
256D4×C149—82no—
257D4×C149—82no—
258D4×C149—82no—
259C2×C4×C149—21no—
260C2×C4×C149—22no—
261C2×C4×C149—21no—
262C2×C4×C149—22no—
263C2×C4×C149—22no—
264C2×C4×C149—21no—
265C2×C4×C149—41no—
266C2×C4×C149—41no—
267C2×C4×C149—41no—
268C2×C4×C149—42no—
269C2×C4×C149—41no—
270C2×C4×C149—82no—
271C2×C4×C149—81no—
272C2×C4×C149—82no—
273C2×C4×C149—82no—
274C2×C4×C149—82no—
275C2×C4×C149#12011yescharacteristic
276C2×C4×C149#12011yescharacteristic
277C2×C4×C149#12011yescharacteristic
278C2×C4×C149C22×D411yescharacteristic
279C2×C4×C149C22×D411yescharacteristic
280C2×C4×C149C22×D411yescharacteristic
281C8×C149—42no—
282C8×C149—42no—
283C8×C149—41no—
284C8×C149—41no—
285C22×C149—21no—
286C22×C149—21no—
287C22×C149—21no—
288C22×C149—41no—
289C22×C149—42no—
290C22×C149—41no—
291C22×C149—42no—
292C22×C149—42no—
293C22×C149—41no—
294C22×C149—81no—
295C22×C149—81no—
296C22×C149—81no—
297C22×C149—162no—
298C22×C149C2×#12011yescharacteristic
299C4×C149—21no—
300C4×C149—21no—
301C4×C149—21no—
302C4×C149—21no—
303C4×C149—21no—
304C4×C149—21no—
305C4×C149—41no—
306C4×C149—42no—
307C4×C149—42no—
308C4×C149—41no—
309C4×C149—41no—
310C4×C149—42no—
311C4×C149—81no—
312C2×C149—41no—
313C2×C149—81no—
314C2×C149—82no—
315C2×C149—161no—
316C2×C149#301911yescharacteristic
317C2×C149#302011yescharacteristic
318C2×C149#302111yescharacteristic
319#19090C14911yesmaximal, characteristic, direct product factor, Sylow
320C149#1909011yescharacteristic, direct product factor, Sylow
321#3561C2×C14911yescharacteristic, complemented
322#3235C2×C14911yescharacteristic, complemented
323#3219C2×C14911yescharacteristic, complemented
324#3213C2×C14911yescharacteristic, complemented
325#1664C2×C14912yescomplemented
326#1661C2×C14912yescomplemented
327#1657C2×C14912yescomplemented
328#1656C2×C14912yescomplemented
329#1537C2×C14911yescharacteristic, complemented
330#1535C2×C14911yescharacteristic, complemented
331#1533C2×C14911yescharacteristic, complemented
332#563C22×C14912yes—
333#562C22×C14912yes—
334#556—21no—
335#551—22no—
336D4×Q8—21no—
337#548—21no—
338#546—21no—
339#543—21no—
340#542—21no—
341#542—22no—
342#538—21no—
343#536—21no—
344#533C22×C14911yescharacteristic
345#532C22×C14911yescharacteristic
346#529C22×C14911yescharacteristic
347C2×#124C22×C14911yescharacteristic
348#501C22×C14912yescomplemented
349#497C22×C14911yescharacteristic, complemented
350#496C22×C14912yes—
351#496C22×C14911yescharacteristic, complemented
352#491C22×C14911yescharacteristic, complemented
353#490C22×C14912yescomplemented
354#490C22×C14911yescharacteristic, complemented
355#489C22×C14912yes—
356#482—22no—
357#476—21no—
358#474—21no—
359#464—21no—
360#463—22no—
361#463—21no—
362#452—21no—
363#449—21no—
364#448—21no—
365#447—21no—
366#432C22×C14911yescharacteristic
367#432C22×C14911yescharacteristic
368#432C22×C14911yescharacteristic
369#330C22×C14912yescomplemented
370#330C22×C14912yescomplemented
371#330C22×C14912yescomplemented
372#329C22×C14912yes—
373#329C22×C14912yes—
374#329C22×C14912yescomplemented
375C2×#41—21no—
376C2×#41—21no—
377C22×Q8—21no—
378C22×Q8D4×C14911yescharacteristic
379C22×D4D4×C14911yescharacteristic
380C2×Q16—21no—
381C2×SD16—22no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×D8—22no—
385C2×D8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—22no—
388C4⋊Q8D4×C14911yescharacteristic
389C4⋊Q8D4×C14911yescharacteristic
390C4⋊Q8C23×C14911yescharacteristic
391#127C23×C14911yescharacteristic
392#126—22no—
393#126—22no—
394#126—22no—
395#126—21no—
396#125C23×C14911yescharacteristic
397#125C23×C14912yes—
398#124—21no—
399#124—22no—
400#124—22no—
401#124—21no—
402#124—21no—
403#124—21no—
404#124D4×C14912yes—
405#124C23×C14912yes—
406#124C23×C14911yescharacteristic
407#123—22no—
408#123—22no—
409#123—21no—
410#123—22no—
411#123—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8D4×C14911yescharacteristic
423#121—21no—
424#121—22no—
425#121—22no—
426#121—21no—
427#121—21no—
428#121D4×C14911yescharacteristic
429#120—22no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8D4×C14911yescharacteristic
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4D4×C14911yescharacteristic
441#117—22no—
442#117—21no—
443#117D4×C14912yes—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42C23×C14911yescharacteristic
448#107—22no—
449#106—22no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453#103—22no—
454#103—21no—
455#103—21no—
456#102—22no—
457#102—21no—
458#102—21no—
459#102—22no—
460#102—22no—
461C22⋊C8—21no—
462C22⋊C8—21no—
463C22⋊C8—21no—
464#97C23×C14912yes—
465#97C23×C14911yescharacteristic
466#97C23×C14911yescharacteristic
467#97C23×C14912yes—
468C24—21no—
469#41—81no—
470#41—81no—
471#41—82no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—82no—
478C2×Q8—81no—
479C2×Q8C2×D4×C14912yes—
480C2×Q8C2×D4×C14911yescharacteristic
481C2×D4—21no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—41no—
489C2×D4—81no—
490C2×D4C2×D4×C14912yes—
491C2×D4C2×D4×C14911yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—41no—
498C22×C4C2×D4×C14911yescharacteristic
499C22×C4C2×D4×C14911yescharacteristic
500C22×C4C2×D4×C14911yescharacteristic
501Q16—81no—
502SD16—82no—
503SD16—81no—
504SD16—81no—
505D8—81no—
506D8—82no—
507C2×C8—22no—
508C2×C8—21no—
509C2×C8—22no—
510C2×C8—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4C2×D4×C14911yescharacteristic
526C4⋊C4C2×D4×C14911yescharacteristic
527C4⋊C4C2×D4×C14912yes—
528C4⋊C4C2×D4×C14912yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C42—22no—
547C42—22no—
548C42—21no—
549C42C2×D4×C14911yescharacteristic
550C42C2×D4×C14911yescharacteristic
551C42C2×D4×C14911yescharacteristic
552C42C24×C14911yescharacteristic
553C23—22no—
554C23—21no—
555C23—42no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23#120×C14911yescharacteristic
560Q8—41no—
561Q8—42no—
562Q8—42no—
563Q8—42no—
564Q8—41no—
565Q8—41no—
566Q8—81no—
567Q8—82no—
568D4—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—42no—
575D4—42no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—82no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4#120×C14911yescharacteristic
596C2×C4#120×C14911yescharacteristic
597C2×C4#120×C14911yescharacteristic
598C2×C4C22×D4×C14911yescharacteristic
599C2×C4C22×D4×C14911yescharacteristic
600C2×C4C22×D4×C14911yescharacteristic
601C8—42no—
602C8—42no—
603C8—41no—
604C8—41no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—42no—
612C22—42no—
613C22—41no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—162no—
618C22C2×#120×C14911yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—42no—
631C4—81no—
632C2—41no—
633C2—82no—
634C2—81no—
635C2—161no—
636C2#3019×C14911yescharacteristic
637C2#3020×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. #3561×C149C2semidirect
2. #3235×C149C2semidirect
3. #3219×C149C2semidirect
4. #3213×C149C2semidirect
5. #1664×C149C2semidirect
6. #1661×C149C2semidirect
7. #1657×C149C2semidirect
8. #1656×C149C2semidirect
9. #1537×C149C2semidirect
10. #1535×C149C2semidirect
11. #1533×C149C2semidirect
28. #501×C149C22semidirect
29. #497×C149C22semidirect
31. #496×C149C22semidirect
32. #491×C149C22semidirect
33. #490×C149C22semidirect
34. #490×C149C22semidirect
49. #330×C149C22semidirect
50. #330×C149C22semidirect
51. #330×C149C22semidirect
54. #329×C149C22semidirect
319. #19090C149direct (N × H)
320. C149#19090direct (N × H)
321. #3561C2×C149semidirect
322. #3235C2×C149semidirect
323. #3219C2×C149semidirect
324. #3213C2×C149semidirect
325. #1664C2×C149semidirect
326. #1661C2×C149semidirect
327. #1657C2×C149semidirect
328. #1656C2×C149semidirect
329. #1537C2×C149semidirect
330. #1535C2×C149semidirect
331. #1533C2×C149semidirect
348. #501C22×C149semidirect
349. #497C22×C149semidirect
351. #496C22×C149semidirect
352. #491C22×C149semidirect
353. #490C22×C149semidirect
354. #490C22×C149semidirect
369. #330C22×C149semidirect
370. #330C22×C149semidirect
371. #330C22×C149semidirect
374. #329C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3561×C1492
#3235×C1492
#3219×C1492
#3213×C1492
#1664×C1492
#1661×C1492
#1657×C1492
#1656×C1492
#1537×C1492
#1535×C1492
#1533×C1492
#19090149