Finite Group Databasebeta

← C149×#18690 #49197639

Subgroups — C149×#18690 #49197639

Order 38144.

878 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#3544×C149C211yesmaximal, characteristic
2#3239×C149C211yesmaximal, characteristic, complemented
3#3218×C149C211yesmaximal, characteristic, complemented
4C2×#487×C149C211yesmaximal, characteristic, complemented
5#1646×C149C212yesmaximal, complemented
6#1645×C149C212yesmaximal, complemented
7#1644×C149C212yesmaximal, complemented
8#1643×C149C212yesmaximal, complemented
9#1558×C149C211yesmaximal, characteristic, complemented
10#1494×C149C211yesmaximal, characteristic, complemented
11#1494×C149C211yesmaximal, characteristic, complemented
12#563×C149—22no—
13Q82×C149C2211yescharacteristic
14#555×C149C2211yescharacteristic
15#554×C149C2211yescharacteristic
16#554×C149C2211yescharacteristic
17#552×C149—21no—
18#552×C149—21no—
19#547×C149—21no—
20#547×C149—21no—
21#544×C149—21no—
22#544×C149—21no—
23#542×C149—21no—
24#542×C149—21no—
25#536×C149—22no—
26C2×C4⋊Q8×C149C2211yescharacteristic
27C2×C4⋊Q8×C149C2211yescharacteristic
28#529×C149C2211yescharacteristic
29#529×C149C2211yescharacteristic
30#501×C149—21no—
31#497×C149—21no—
32#491×C149—21no—
33#489×C149—21no—
34#487×C149—22no—
35#487×C149C2212yes—
36#487×C149C2212yes—
37#484×C149—21no—
38#481×C149—21no—
39#475×C149C2212yes—
40#474×C149C2212yes—
41#462×C149C2212yes—
42#461×C149C2212yes—
43#451×C149—21no—
44#448×C149—21no—
45#432×C149C2211yescharacteristic
46#432×C149C2211yescharacteristic
47C2×#103×C149—22no—
48C2×C4×C8×C149C2211yescharacteristic
49#333×C149C2212yes—
50#333×C149C2212yes—
51Q8⋊C8×C149C2212yes—
52Q8⋊C8×C149C2212yes—
53D4⋊C8×C149C2212yes—
54D4⋊C8×C149C2212yes—
55C2×#41×C149—22no—
56C22×Q8×C149—21no—
57C22×Q8×C149D412yes—
58C2×Q16×C149—22no—
59C2×SD16×C149—22no—
60C22×C8×C149—21no—
61C4⋊Q8×C149—22no—
62C4⋊Q8×C149—22no—
63C4⋊Q8×C149—21no—
64C4⋊Q8×C149—21no—
65C4⋊Q8×C149—21no—
66C4⋊Q8×C149—21no—
67C4⋊Q8×C149—21no—
68C4⋊Q8×C149—21no—
69C4⋊Q8×C149—21no—
70C4⋊Q8×C149D412yes—
71C4⋊Q8×C149C2312yes—
72C4⋊Q8×C149C2311yescharacteristic
73C4⋊Q8×C149C2311yescharacteristic
74#126×C149—22no—
75#126×C149—22no—
76#126×C149—21no—
77#126×C149—21no—
78#125×C149—22no—
79#125×C149—22no—
80#125×C149—21no—
81#125×C149—21no—
82#125×C149D411yescharacteristic
83#125×C149D411yescharacteristic
84#124×C149—22no—
85#124×C149—22no—
86#124×C149D411yescharacteristic
87#124×C149D411yescharacteristic
88#123×C149—22no—
89#123×C149—22no—
90#123×C149—22no—
91#123×C149—22no—
92#123×C149—21no—
93#123×C149—21no—
94C22⋊Q8×C149—22no—
95C22⋊Q8×C149—22no—
96C22⋊Q8×C149—22no—
97C22⋊Q8×C149—22no—
98C22⋊Q8×C149—22no—
99C22⋊Q8×C149—22no—
100C22⋊Q8×C149—21no—
101C22⋊Q8×C149—21no—
102C22⋊Q8×C149D411yescharacteristic
103C22⋊Q8×C149D411yescharacteristic
104#121×C149—21no—
105#121×C149—21no—
106#121×C149D411yescharacteristic
107#121×C149D411yescharacteristic
108C4×Q8×C149—21no—
109C4×Q8×C149—21no—
110C4×Q8×C149C2311yescharacteristic
111C4×Q8×C149C2311yescharacteristic
112C4×D4×C149—21no—
113C4×D4×C149—21no—
114C4×D4×C149—21no—
115C4×D4×C149—21no—
116C4×D4×C149C2311yescharacteristic
117C4×D4×C149C2311yescharacteristic
118#117×C149—22no—
119#117×C149—21no—
120#117×C149—21no—
121#117×C149—21no—
122#117×C149—21no—
123C2×C4⋊C4×C149—21no—
124C2×C4⋊C4×C149—21no—
125C2×C4⋊C4×C149—21no—
126C2×C4⋊C4×C149—21no—
127C2×C4⋊C4×C149—21no—
128C2×C4⋊C4×C149—21no—
129C2×C42×C149C2311yescharacteristic
130#107×C149—22no—
131#106×C149—22no—
132C4⋊C8×C149C2312yes—
133C4⋊C8×C149C2312yes—
134#103×C149—24no—
135#103×C149—24no—
136#103×C149—22no—
137#103×C149—22no—
138#103×C149—22no—
139#102×C149—22no—
140C22⋊C8×C149—21no—
141C22⋊C8×C149—21no—
142#97×C149—21no—
143#97×C149—21no—
144C4×C8×C149—21no—
145C4×C8×C149C2312yes—
146#41×C149—84no—
147C2×Q8×C149—22no—
148C2×Q8×C149—22no—
149C2×Q8×C149—22no—
150C2×Q8×C149—44no—
151C2×Q8×C149—41no—
152C2×Q8×C149—82no—
153C2×Q8×C149C2×D411yescharacteristic
154C2×Q8×C149C2×D411yescharacteristic
155C2×Q8×C149C2×D412yes—
156C2×Q8×C149C2×D412yes—
157C2×D4×C149—21no—
158C2×D4×C149—21no—
159C2×D4×C149—22no—
160C2×D4×C149C2×D411yescharacteristic
161C2×D4×C149C2×D411yescharacteristic
162C22×C4×C149—22no—
163C22×C4×C149—22no—
164C22×C4×C149—22no—
165C22×C4×C149—21no—
166C22×C4×C149—21no—
167C22×C4×C149—41no—
168C22×C4×C149C2×D411yescharacteristic
169C22×C4×C149C2×D411yescharacteristic
170C22×C4×C149C2×D411yescharacteristic
171Q16×C149—82no—
172SD16×C149—82no—
173C2×C8×C149—22no—
174C2×C8×C149—22no—
175C2×C8×C149—22no—
176C2×C8×C149—42no—
177C4⋊C4×C149—22no—
178C4⋊C4×C149—22no—
179C4⋊C4×C149—22no—
180C4⋊C4×C149—22no—
181C4⋊C4×C149—22no—
182C4⋊C4×C149—22no—
183C4⋊C4×C149—22no—
184C4⋊C4×C149—22no—
185C4⋊C4×C149—21no—
186C4⋊C4×C149—21no—
187C4⋊C4×C149—21no—
188C4⋊C4×C149—21no—
189C4⋊C4×C149—21no—
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×C149—21no—
197C4⋊C4×C149—22no—
198C4⋊C4×C149—22no—
199C4⋊C4×C149—41no—
200C4⋊C4×C149—41no—
201C4⋊C4×C149C2×D411yescharacteristic
202C4⋊C4×C149C2×D411yescharacteristic
203C4⋊C4×C149C2×D411yescharacteristic
204C4⋊C4×C149C2×D411yescharacteristic
205C22⋊C4×C149—22no—
206C22⋊C4×C149—22no—
207C22⋊C4×C149—22no—
208C22⋊C4×C149—22no—
209C22⋊C4×C149—21no—
210C22⋊C4×C149—21no—
211C22⋊C4×C149—21no—
212C22⋊C4×C149—21no—
213C22⋊C4×C149—21no—
214C22⋊C4×C149—21no—
215C22⋊C4×C149—21no—
216C22⋊C4×C149—21no—
217C22⋊C4×C149—21no—
218C22⋊C4×C149—21no—
219C42×C149—22no—
220C42×C149—22no—
221C42×C149—21no—
222C42×C149—21no—
223C42×C149C2×D411yescharacteristic
224C42×C149C2×D411yescharacteristic
225C42×C149C2×D411yescharacteristic
226C42×C149C2411yescharacteristic
227C23×C149—21no—
228C23×C149—21no—
229C23×C149#12011yescharacteristic
230Q8×C149—22no—
231Q8×C149—22no—
232Q8×C149—42no—
233Q8×C149—42no—
234Q8×C149—42no—
235Q8×C149—42no—
236Q8×C149—82no—
237Q8×C149—82no—
238Q8×C149—82no—
239D4×C149—22no—
240D4×C149—22no—
241D4×C149—42no—
242D4×C149—42no—
243D4×C149—82no—
244C2×C4×C149—22no—
245C2×C4×C149—22no—
246C2×C4×C149—22no—
247C2×C4×C149—21no—
248C2×C4×C149—21no—
249C2×C4×C149—21no—
250C2×C4×C149—21no—
251C2×C4×C149—22no—
252C2×C4×C149—21no—
253C2×C4×C149—21no—
254C2×C4×C149—22no—
255C2×C4×C149—44no—
256C2×C4×C149—42no—
257C2×C4×C149—42no—
258C2×C4×C149—42no—
259C2×C4×C149—82no—
260C2×C4×C149—82no—
261C2×C4×C149—82no—
262C2×C4×C149#12011yescharacteristic
263C2×C4×C149#12011yescharacteristic
264C2×C4×C149#12011yescharacteristic
265C2×C4×C149C22×D411yescharacteristic
266C2×C4×C149C22×D411yescharacteristic
267C2×C4×C149C22×D411yescharacteristic
268C8×C149—42no—
269C8×C149—42no—
270C8×C149—42no—
271C22×C149—21no—
272C22×C149—21no—
273C22×C149—41no—
274C22×C149—41no—
275C22×C149—41no—
276C22×C149—41no—
277C22×C149—41no—
278C22×C149—41no—
279C22×C149#45512yes—
280C22×C149C2×#12011yescharacteristic
281C4×C149—21no—
282C4×C149—21no—
283C4×C149—21no—
284C4×C149—21no—
285C4×C149—41no—
286C4×C149—41no—
287C4×C149—41no—
288C4×C149—41no—
289C4×C149—42no—
290C4×C149—42no—
291C4×C149—41no—
292C4×C149—41no—
293C4×C149—82no—
294C4×C149#57712yes—
295C4×C149#57812yes—
296C2×C149—22no—
297C2×C149—81no—
298C2×C149—81no—
299C2×C149#301011yescharacteristic
300C2×C149#301111yescharacteristic
301C2×C149C2×#45511yescharacteristic
302#18690C14911yesmaximal, characteristic, direct product factor, Sylow
303C149#1869011yescharacteristic, direct product factor, Sylow
304#3544C2×C14911yescharacteristic
305#3239C2×C14911yescharacteristic, complemented
306#3218C2×C14911yescharacteristic, complemented
307C2×#487C2×C14911yescharacteristic, complemented
308#1646C2×C14912yescomplemented
309#1645C2×C14912yescomplemented
310#1644C2×C14912yescomplemented
311#1643C2×C14912yescomplemented
312#1558C2×C14911yescharacteristic, complemented
313#1494C2×C14911yescharacteristic, complemented
314#1494C2×C14911yescharacteristic, complemented
315#563—22no—
316Q82C22×C14911yescharacteristic
317#555C22×C14911yescharacteristic
318#554C22×C14911yescharacteristic
319#554C22×C14911yescharacteristic
320#552—21no—
321#552—21no—
322#547—21no—
323#547—21no—
324#544—21no—
325#544—21no—
326#542—21no—
327#542—21no—
328#536—22no—
329C2×C4⋊Q8C22×C14911yescharacteristic
330C2×C4⋊Q8C22×C14911yescharacteristic
331#529C22×C14911yescharacteristic
332#529C22×C14911yescharacteristic
333#501—21no—
334#497—21no—
335#491—21no—
336#489—21no—
337#487—22no—
338#487C22×C14912yes—
339#487C22×C14912yes—
340#484—21no—
341#481—21no—
342#475C22×C14912yes—
343#474C22×C14912yes—
344#462C22×C14912yes—
345#461C22×C14912yes—
346#451—21no—
347#448—21no—
348#432C22×C14911yescharacteristic
349#432C22×C14911yescharacteristic
350C2×#103—22no—
351C2×C4×C8C22×C14911yescharacteristic
352#333C22×C14912yes—
353#333C22×C14912yes—
354Q8⋊C8C22×C14912yes—
355Q8⋊C8C22×C14912yes—
356D4⋊C8C22×C14912yes—
357D4⋊C8C22×C14912yes—
358C2×#41—22no—
359C22×Q8—21no—
360C22×Q8D4×C14912yes—
361C2×Q16—22no—
362C2×SD16—22no—
363C22×C8—21no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—21no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8D4×C14912yes—
374C4⋊Q8C23×C14912yes—
375C4⋊Q8C23×C14911yescharacteristic
376C4⋊Q8C23×C14911yescharacteristic
377#126—22no—
378#126—22no—
379#126—21no—
380#126—21no—
381#125—22no—
382#125—22no—
383#125—21no—
384#125—21no—
385#125D4×C14911yescharacteristic
386#125D4×C14911yescharacteristic
387#124—22no—
388#124—22no—
389#124D4×C14911yescharacteristic
390#124D4×C14911yescharacteristic
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—21no—
396#123—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8D4×C14911yescharacteristic
406C22⋊Q8D4×C14911yescharacteristic
407#121—21no—
408#121—21no—
409#121D4×C14911yescharacteristic
410#121D4×C14911yescharacteristic
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C23×C14911yescharacteristic
414C4×Q8C23×C14911yescharacteristic
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4C23×C14911yescharacteristic
420C4×D4C23×C14911yescharacteristic
421#117—22no—
422#117—21no—
423#117—21no—
424#117—21no—
425#117—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C42C23×C14911yescharacteristic
433#107—22no—
434#106—22no—
435C4⋊C8C23×C14912yes—
436C4⋊C8C23×C14912yes—
437#103—24no—
438#103—24no—
439#103—22no—
440#103—22no—
441#103—22no—
442#102—22no—
443C22⋊C8—21no—
444C22⋊C8—21no—
445#97—21no—
446#97—21no—
447C4×C8—21no—
448C4×C8C23×C14912yes—
449#41—84no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—44no—
454C2×Q8—41no—
455C2×Q8—82no—
456C2×Q8C2×D4×C14911yescharacteristic
457C2×Q8C2×D4×C14911yescharacteristic
458C2×Q8C2×D4×C14912yes—
459C2×Q8C2×D4×C14912yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4C2×D4×C14911yescharacteristic
464C2×D4C2×D4×C14911yescharacteristic
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4C2×D4×C14911yescharacteristic
472C22×C4C2×D4×C14911yescharacteristic
473C22×C4C2×D4×C14911yescharacteristic
474Q16—82no—
475SD16—82no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—42no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C14911yescharacteristic
505C4⋊C4C2×D4×C14911yescharacteristic
506C4⋊C4C2×D4×C14911yescharacteristic
507C4⋊C4C2×D4×C14911yescharacteristic
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C42—22no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42C2×D4×C14911yescharacteristic
527C42C2×D4×C14911yescharacteristic
528C42C2×D4×C14911yescharacteristic
529C42C24×C14911yescharacteristic
530C23—21no—
531C23—21no—
532C23#120×C14911yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—42no—
537Q8—42no—
538Q8—42no—
539Q8—82no—
540Q8—82no—
541Q8—82no—
542D4—22no—
543D4—22no—
544D4—42no—
545D4—42no—
546D4—82no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—44no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4#120×C14911yescharacteristic
566C2×C4#120×C14911yescharacteristic
567C2×C4#120×C14911yescharacteristic
568C2×C4C22×D4×C14911yescharacteristic
569C2×C4C22×D4×C14911yescharacteristic
570C2×C4C22×D4×C14911yescharacteristic
571C8—42no—
572C8—42no—
573C8—42no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22#455×C14912yes—
583C22C2×#120×C14911yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—82no—
597C4#577×C14912yes—
598C4#578×C14912yes—
599C2—22no—
600C2—81no—
601C2—81no—
602C2#3010×C14911yescharacteristic
603C2#3011×C14911yescharacteristic
604C2C2×#455×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#3544×C149C2
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
2. #3239×C149C2semidirect
3. #3218×C149C2semidirect
4. C2×#487×C149C2semidirect
5. #1646×C149C2semidirect
6. #1645×C149C2semidirect
7. #1644×C149C2semidirect
8. #1643×C149C2semidirect
9. #1558×C149C2semidirect
10. #1494×C149C2semidirect
11. #1494×C149C2semidirect
302. #18690C149direct (N × H)
303. C149#18690direct (N × H)
305. #3239C2×C149semidirect
306. #3218C2×C149semidirect
307. C2×#487C2×C149semidirect
308. #1646C2×C149semidirect
309. #1645C2×C149semidirect
310. #1644C2×C149semidirect
311. #1643C2×C149semidirect
312. #1558C2×C149semidirect
313. #1494C2×C149semidirect
314. #1494C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3544×C1492
#3239×C1492
#3218×C1492
C2×#487×C1492
#1646×C1492
#1645×C1492
#1644×C1492
#1643×C1492
#1558×C1492
#1494×C1492
#18690149