Finite Group Databasebeta

← C149×#19030 #49197979

Subgroups — C149×#19030 #49197979

Order 38144.

902 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3559×C149C211yesmaximal, characteristic, complemented
2#3214×C149C211yesmaximal, characteristic, complemented
3#3171×C149C211yesmaximal, characteristic, complemented
4#3142×C149C211yesmaximal, characteristic, complemented
5#1664×C149C212yesmaximal, complemented
6#1662×C149C212yesmaximal, complemented
7#1657×C149C212yesmaximal, complemented
8#1656×C149C212yesmaximal, complemented
9#1529×C149C211yesmaximal, characteristic, complemented
10#1528×C149C211yesmaximal, characteristic, complemented
11#1525×C149C211yesmaximal, characteristic, complemented
12#563×C149C2212yes—
13#562×C149C2212yes—
14#554×C149—21no—
15#553×C149—21no—
16#553×C149—21no—
17#547×C149—22no—
18#547×C149—21no—
19#544×C149—21no—
20#540×C149—21no—
21#539×C149—22no—
22#539×C149—21no—
23#537×C149—21no—
24#532×C149C2211yescharacteristic
25#532×C149C2211yescharacteristic
26#529×C149C2211yescharacteristic
27C2×#125×C149C2211yescharacteristic
28#501×C149C2211yescharacteristic
29#496×C149C2212yes—
30#496×C149C2211yescharacteristic
31#491×C149C2212yes—
32#490×C149C2212yes—
33#490×C149C2211yescharacteristic
34#489×C149C2212yes—
35#489×C149C2211yescharacteristic
36#488×C149—22no—
37#469×C149—21no—
38#468×C149—21no—
39#461×C149—21no—
40#459×C149—21no—
41#449×C149—22no—
42C4×SD16×C149—21no—
43C4×D8×C149—21no—
44#432×C149C2211yescharacteristic
45#417×C149—21no—
46#417×C149—21no—
47C4×M16×C149C2211yescharacteristic
48C4×M16×C149C2211yescharacteristic
49#330×C149C2212yes—
50#330×C149C2212yes—
51#330×C149C2212yes—
52#329×C149C2212yes—
53#329×C149C2212yes—
54#329×C149C2212yes—
55C2×#41×C149—22no—
56C2×#41×C149—21no—
57C2×#41×C149D412yes—
58C2×SD16×C149—21no—
59C2×SD16×C149—22no—
60C2×D8×C149—21no—
61C2×D8×C149—22no—
62C2×M16×C149—21no—
63C2×M16×C149—21no—
64C4⋊Q8×C149—21no—
65C4⋊Q8×C149—22no—
66C4⋊Q8×C149D411yescharacteristic
67C4⋊Q8×C149C2311yescharacteristic
68#127×C149D411yescharacteristic
69#127×C149C2311yescharacteristic
70#126×C149—22no—
71#126×C149—22no—
72#126×C149—21no—
73#125×C149—22no—
74#125×C149—21no—
75#125×C149—21no—
76#125×C149—21no—
77#125×C149D412yes—
78#125×C149C2312yes—
79#125×C149C2311yescharacteristic
80#124×C149—21no—
81#124×C149C2311yescharacteristic
82#124×C149C2312yes—
83#123×C149—22no—
84#123×C149—22no—
85#123×C149—22no—
86#123×C149—22no—
87#123×C149—21no—
88#123×C149—22no—
89#123×C149—22no—
90C22⋊Q8×C149—22no—
91C22⋊Q8×C149—22no—
92C22⋊Q8×C149—22no—
93C22⋊Q8×C149—22no—
94C22⋊Q8×C149—22no—
95C22⋊Q8×C149—22no—
96C22⋊Q8×C149D411yescharacteristic
97#121×C149—22no—
98#121×C149—22no—
99#121×C149—21no—
100#121×C149—21no—
101#121×C149—22no—
102#121×C149—22no—
103#121×C149—21no—
104#121×C149—21no—
105#121×C149—21no—
106#121×C149—21no—
107#121×C149D411yescharacteristic
108C4×Q8×C149D411yescharacteristic
109C4×D4×C149—22no—
110C4×D4×C149—22no—
111C4×D4×C149—21no—
112C4×D4×C149—21no—
113C4×D4×C149—21no—
114C4×D4×C149—21no—
115C4×D4×C149—21no—
116C4×D4×C149—21no—
117C4×D4×C149—21no—
118C4×D4×C149D411yescharacteristic
119#117×C149—21no—
120#117×C149—21no—
121C2×C4⋊C4×C149—22no—
122C2×C4⋊C4×C149—21no—
123C2×C4⋊C4×C149—21no—
124C2×C4⋊C4×C149—21no—
125C2×C4⋊C4×C149D411yescharacteristic
126C2×C4⋊C4×C149D411yescharacteristic
127C2×C42×C149C2311yescharacteristic
128#107×C149—21no—
129#106×C149—21no—
130C4⋊C8×C149—21no—
131#103×C149—21no—
132#103×C149—22no—
133#103×C149—22no—
134#103×C149—22no—
135#102×C149—21no—
136#102×C149—22no—
137#102×C149—22no—
138#102×C149—22no—
139#102×C149—21no—
140#102×C149—21no—
141C22⋊C8×C149—21no—
142#97×C149C2311yescharacteristic
143#97×C149C2312yes—
144#97×C149C2311yescharacteristic
145#97×C149C2312yes—
146C4×C8×C149—21no—
147C4×C8×C149—21no—
148#41×C149—44no—
149#41×C149—84no—
150#41×C149—82no—
151C2×Q8×C149—22no—
152C2×Q8×C149—21no—
153C2×Q8×C149C2×D411yescharacteristic
154C2×Q8×C149C2×D412yes—
155C2×D4×C149—22no—
156C2×D4×C149—21no—
157C2×D4×C149—22no—
158C2×D4×C149—22no—
159C2×D4×C149—21no—
160C2×D4×C149—21no—
161C2×D4×C149—21no—
162C2×D4×C149—21no—
163C2×D4×C149—21no—
164C2×D4×C149—41no—
165C2×D4×C149C2×D411yescharacteristic
166C2×D4×C149C2×D412yes—
167C22×C4×C149—21no—
168C22×C4×C149—22no—
169C22×C4×C149—22no—
170C22×C4×C149—22no—
171C22×C4×C149—21no—
172C22×C4×C149—21no—
173C22×C4×C149—22no—
174C22×C4×C149—41no—
175C22×C4×C149C2×D411yescharacteristic
176C22×C4×C149C2×D411yescharacteristic
177C22×C4×C149C2×D411yescharacteristic
178SD16×C149—42no—
179SD16×C149—82no—
180D8×C149—42no—
181D8×C149—82no—
182M16×C149—42no—
183M16×C149—42no—
184C2×C8×C149—21no—
185C2×C8×C149—21no—
186C2×C8×C149—22no—
187C2×C8×C149—22no—
188C4⋊C4×C149—22no—
189C4⋊C4×C149—22no—
190C4⋊C4×C149—22no—
191C4⋊C4×C149—22no—
192C4⋊C4×C149—22no—
193C4⋊C4×C149—21no—
194C4⋊C4×C149—21no—
195C4⋊C4×C149—21no—
196C4⋊C4×C149—22no—
197C4⋊C4×C149—21no—
198C4⋊C4×C149—21no—
199C4⋊C4×C149—21no—
200C4⋊C4×C149—22no—
201C4⋊C4×C149—22no—
202C4⋊C4×C149—21no—
203C4⋊C4×C149—21no—
204C4⋊C4×C149—21no—
205C4⋊C4×C149—21no—
206C4⋊C4×C149C2×D412yes—
207C4⋊C4×C149C2×D412yes—
208C4⋊C4×C149C2×D411yescharacteristic
209C4⋊C4×C149C2×D411yescharacteristic
210C22⋊C4×C149—22no—
211C22⋊C4×C149—22no—
212C22⋊C4×C149—22no—
213C22⋊C4×C149—22no—
214C22⋊C4×C149—22no—
215C22⋊C4×C149—21no—
216C22⋊C4×C149—21no—
217C22⋊C4×C149—21no—
218C22⋊C4×C149—21no—
219C22⋊C4×C149—22no—
220C22⋊C4×C149—22no—
221C22⋊C4×C149—21no—
222C22⋊C4×C149—41no—
223C22⋊C4×C149—41no—
224C42×C149—22no—
225C42×C149—21no—
226C42×C149C2×D411yescharacteristic
227C42×C149C2×D411yescharacteristic
228C42×C149C2×D411yescharacteristic
229C42×C149C2411yescharacteristic
230C23×C149—21no—
231C23×C149—22no—
232C23×C149—41no—
233C23×C149#12011yescharacteristic
234Q8×C149—41no—
235Q8×C149—42no—
236Q8×C149—42no—
237Q8×C149—82no—
238D4×C149—41no—
239D4×C149—42no—
240D4×C149—41no—
241D4×C149—41no—
242D4×C149—41no—
243D4×C149—41no—
244D4×C149—42no—
245D4×C149—44no—
246D4×C149—42no—
247D4×C149—42no—
248D4×C149—81no—
249D4×C149—82no—
250D4×C149—82no—
251D4×C149—82no—
252C2×C4×C149—22no—
253C2×C4×C149—21no—
254C2×C4×C149—21no—
255C2×C4×C149—22no—
256C2×C4×C149—22no—
257C2×C4×C149—21no—
258C2×C4×C149—22no—
259C2×C4×C149—41no—
260C2×C4×C149—41no—
261C2×C4×C149—42no—
262C2×C4×C149—42no—
263C2×C4×C149—41no—
264C2×C4×C149—82no—
265C2×C4×C149—81no—
266C2×C4×C149—82no—
267C2×C4×C149—82no—
268C2×C4×C149—82no—
269C2×C4×C149—82no—
270C2×C4×C149#12011yescharacteristic
271C2×C4×C149#12011yescharacteristic
272C2×C4×C149#12011yescharacteristic
273C2×C4×C149C22×D411yescharacteristic
274C2×C4×C149C22×D411yescharacteristic
275C2×C4×C149C22×D411yescharacteristic
276C8×C149—22no—
277C8×C149—42no—
278C8×C149—41no—
279C8×C149—42no—
280C22×C149—21no—
281C22×C149—21no—
282C22×C149—21no—
283C22×C149—41no—
284C22×C149—42no—
285C22×C149—42no—
286C22×C149—41no—
287C22×C149—42no—
288C22×C149—41no—
289C22×C149—81no—
290C22×C149—81no—
291C22×C149—81no—
292C22×C149C2×#12011yescharacteristic
293C4×C149—21no—
294C4×C149—21no—
295C4×C149—21no—
296C4×C149—21no—
297C4×C149—21no—
298C4×C149—41no—
299C4×C149—42no—
300C4×C149—41no—
301C4×C149—42no—
302C4×C149—42no—
303C4×C149—41no—
304C4×C149—81no—
305C4×C149#45412yes—
306C2×C149—41no—
307C2×C149—81no—
308C2×C149—82no—
309C2×C149—161no—
310C2×C149C2×#45411yescharacteristic
311C2×C149#301811yescharacteristic
312C2×C149#301911yescharacteristic
313#19030C14911yesmaximal, characteristic, direct product factor, Sylow
314C149#1903011yescharacteristic, direct product factor, Sylow
315#3559C2×C14911yescharacteristic, complemented
316#3214C2×C14911yescharacteristic, complemented
317#3171C2×C14911yescharacteristic, complemented
318#3142C2×C14911yescharacteristic, complemented
319#1664C2×C14912yescomplemented
320#1662C2×C14912yescomplemented
321#1657C2×C14912yescomplemented
322#1656C2×C14912yescomplemented
323#1529C2×C14911yescharacteristic, complemented
324#1528C2×C14911yescharacteristic, complemented
325#1525C2×C14911yescharacteristic, complemented
326#563C22×C14912yes—
327#562C22×C14912yes—
328#554—21no—
329#553—21no—
330#553—21no—
331#547—22no—
332#547—21no—
333#544—21no—
334#540—21no—
335#539—22no—
336#539—21no—
337#537—21no—
338#532C22×C14911yescharacteristic
339#532C22×C14911yescharacteristic
340#529C22×C14911yescharacteristic
341C2×#125C22×C14911yescharacteristic
342#501C22×C14911yescharacteristic
343#496C22×C14911yescharacteristic
344#496C22×C14912yes—
345#491C22×C14912yes—
346#490C22×C14912yes—
347#490C22×C14911yescharacteristic
348#489C22×C14911yescharacteristic
349#489C22×C14912yes—
350#488—22no—
351#469—21no—
352#468—21no—
353#461—21no—
354#459—21no—
355#449—22no—
356C4×SD16—21no—
357C4×D8—21no—
358#432C22×C14911yescharacteristic
359#417—21no—
360#417—21no—
361C4×M16C22×C14911yescharacteristic
362C4×M16C22×C14911yescharacteristic
363#330C22×C14912yes—
364#330C22×C14912yes—
365#330C22×C14912yes—
366#329C22×C14912yes—
367#329C22×C14912yes—
368#329C22×C14912yes—
369C2×#41—22no—
370C2×#41—21no—
371C2×#41D4×C14912yes—
372C2×SD16—21no—
373C2×SD16—22no—
374C2×D8—21no—
375C2×D8—22no—
376C2×M16—21no—
377C2×M16—21no—
378C4⋊Q8—21no—
379C4⋊Q8—22no—
380C4⋊Q8D4×C14911yescharacteristic
381C4⋊Q8C23×C14911yescharacteristic
382#127D4×C14911yescharacteristic
383#127C23×C14911yescharacteristic
384#126—22no—
385#126—22no—
386#126—21no—
387#125—22no—
388#125—21no—
389#125—21no—
390#125—21no—
391#125D4×C14912yes—
392#125C23×C14912yes—
393#125C23×C14911yescharacteristic
394#124—21no—
395#124C23×C14911yescharacteristic
396#124C23×C14912yes—
397#123—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8D4×C14911yescharacteristic
411#121—22no—
412#121—22no—
413#121—21no—
414#121—21no—
415#121—22no—
416#121—22no—
417#121—21no—
418#121—21no—
419#121—21no—
420#121—21no—
421#121D4×C14911yescharacteristic
422C4×Q8D4×C14911yescharacteristic
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4D4×C14911yescharacteristic
433#117—21no—
434#117—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4D4×C14911yescharacteristic
440C2×C4⋊C4D4×C14911yescharacteristic
441C2×C42C23×C14911yescharacteristic
442#107—21no—
443#106—21no—
444C4⋊C8—21no—
445#103—21no—
446#103—22no—
447#103—22no—
448#103—22no—
449#102—21no—
450#102—22no—
451#102—22no—
452#102—22no—
453#102—21no—
454#102—21no—
455C22⋊C8—21no—
456#97C23×C14912yes—
457#97C23×C14911yescharacteristic
458#97C23×C14911yescharacteristic
459#97C23×C14912yes—
460C4×C8—21no—
461C4×C8—21no—
462#41—44no—
463#41—84no—
464#41—82no—
465C2×Q8—22no—
466C2×Q8—21no—
467C2×Q8C2×D4×C14911yescharacteristic
468C2×Q8C2×D4×C14912yes—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4C2×D4×C14911yescharacteristic
480C2×D4C2×D4×C14912yes—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—41no—
489C22×C4C2×D4×C14911yescharacteristic
490C22×C4C2×D4×C14911yescharacteristic
491C22×C4C2×D4×C14911yescharacteristic
492SD16—42no—
493SD16—82no—
494D8—42no—
495D8—82no—
496M16—42no—
497M16—42no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—22no—
501C2×C8—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4C2×D4×C14912yes—
521C4⋊C4C2×D4×C14912yes—
522C4⋊C4C2×D4×C14911yescharacteristic
523C4⋊C4C2×D4×C14911yescharacteristic
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C42—22no—
539C42—21no—
540C42C2×D4×C14911yescharacteristic
541C42C2×D4×C14911yescharacteristic
542C42C2×D4×C14911yescharacteristic
543C42C24×C14911yescharacteristic
544C23—21no—
545C23—22no—
546C23—41no—
547C23#120×C14911yescharacteristic
548Q8—41no—
549Q8—42no—
550Q8—42no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—81no—
563D4—82no—
564D4—82no—
565D4—82no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—81no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4#120×C14911yescharacteristic
585C2×C4#120×C14911yescharacteristic
586C2×C4#120×C14911yescharacteristic
587C2×C4C22×D4×C14911yescharacteristic
588C2×C4C22×D4×C14911yescharacteristic
589C2×C4C22×D4×C14911yescharacteristic
590C8—22no—
591C8—42no—
592C8—41no—
593C8—42no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—42no—
599C22—42no—
600C22—41no—
601C22—42no—
602C22—41no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22C2×#120×C14911yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—21no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—41no—
618C4—81no—
619C4#454×C14912yes—
620C2—41no—
621C2—81no—
622C2—82no—
623C2—161no—
624C2C2×#454×C14911yescharacteristic
625C2#3018×C14911yescharacteristic
626C2#3019×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. #3559×C149C2semidirect
2. #3214×C149C2semidirect
3. #3171×C149C2semidirect
4. #3142×C149C2semidirect
5. #1664×C149C2semidirect
6. #1662×C149C2semidirect
7. #1657×C149C2semidirect
8. #1656×C149C2semidirect
9. #1529×C149C2semidirect
10. #1528×C149C2semidirect
11. #1525×C149C2semidirect
313. #19030C149direct (N × H)
314. C149#19030direct (N × H)
315. #3559C2×C149semidirect
316. #3214C2×C149semidirect
317. #3171C2×C149semidirect
318. #3142C2×C149semidirect
319. #1664C2×C149semidirect
320. #1662C2×C149semidirect
321. #1657C2×C149semidirect
322. #1656C2×C149semidirect
323. #1529C2×C149semidirect
324. #1528C2×C149semidirect
325. #1525C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3559×C1492
#3214×C1492
#3171×C1492
#3142×C1492
#1664×C1492
#1662×C1492
#1657×C1492
#1656×C1492
#1529×C1492
#1528×C1492
#1525×C1492
#19030149