Finite Group Databasebeta

← C149×#18593 #49197542

Subgroups — C149×#18593 #49197542

Order 38144.

916 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C149C211yesmaximal, characteristic
2#3254×C149C211yesmaximal, characteristic, complemented
3#3165×C149C211yesmaximal, characteristic, complemented
4#3107×C149C211yesmaximal, characteristic, complemented
5#1654×C149C212yesmaximal, complemented
6#1652×C149C212yesmaximal, complemented
7#1650×C149C212yesmaximal, complemented
8#1647×C149C212yesmaximal, complemented
9#1546×C149C211yesmaximal, characteristic, complemented
10#1489×C149C211yesmaximal, characteristic, complemented
11#1484×C149C211yesmaximal, characteristic, complemented
12#556×C149C2212yes—
13#555×C149—21no—
14#554×C149—21no—
15#553×C149—22no—
16#548×C149—22no—
17#547×C149C2212yes—
18#542×C149—22no—
19#537×C149—21no—
20#533×C149—21no—
21#533×C149C2211yescharacteristic
22#532×C149—21no—
23#532×C149C2211yescharacteristic
24C2×C4⋊Q8×C149C2211yescharacteristic
25#520×C149—21no—
26C4×#41×C149C2211yescharacteristic
27#501×C149—22no—
28#500×C149C2212yes—
29#498×C149C2212yes—
30#485×C149—21no—
31#477×C149—21no—
32#475×C149C2211yescharacteristic
33#474×C149C2212yes—
34#474×C149C2211yescharacteristic
35#468×C149—22no—
36#462×C149C2211yescharacteristic
37#461×C149C2212yes—
38#461×C149C2211yescharacteristic
39#460×C149—21no—
40#452×C149—21no—
41C4×Q16×C149—21no—
42C4×SD16×C149—21no—
43#431×C149C2211yescharacteristic
44#428×C149—22no—
45#423×C149C2211yescharacteristic
46C4×M16×C149C2211yescharacteristic
47#332×C149C2212yes—
48#332×C149C2212yes—
49Q8⋊C8×C149C2212yes—
50D4⋊C8×C149C2212yes—
51D4⋊C8×C149C2212yes—
52D4⋊C8×C149C2212yes—
53C2×#41×C149—22no—
54C2×#41×C149—21no—
55C2×#41×C149D411yescharacteristic
56C22×Q8×C149—21no—
57C2×Q16×C149—21no—
58C2×SD16×C149—21no—
59C2×SD16×C149—22no—
60C2×M16×C149—21no—
61C2×M16×C149—21no—
62C4⋊Q8×C149—21no—
63C4⋊Q8×C149—21no—
64C4⋊Q8×C149D411yescharacteristic
65C4⋊Q8×C149D412yes—
66C4⋊Q8×C149C2311yescharacteristic
67C4⋊Q8×C149C2311yescharacteristic
68C4⋊Q8×C149C2312yes—
69#127×C149D411yescharacteristic
70#126×C149—24no—
71#125×C149—22no—
72#125×C149—21no—
73#124×C149—24no—
74#124×C149—22no—
75#124×C149—21no—
76#123×C149—24no—
77C22⋊Q8×C149—22no—
78C22⋊Q8×C149—24no—
79C22⋊Q8×C149—22no—
80C22⋊Q8×C149—22no—
81C22⋊Q8×C149—21no—
82C22⋊Q8×C149—21no—
83#121×C149—22no—
84#121×C149—22no—
85#121×C149—24no—
86#121×C149—22no—
87#121×C149—21no—
88#121×C149D412yes—
89C4×Q8×C149—22no—
90C4×Q8×C149—22no—
91C4×Q8×C149—21no—
92C4×Q8×C149—21no—
93C4×Q8×C149D411yescharacteristic
94C4×Q8×C149C2311yescharacteristic
95C4×D4×C149—22no—
96C4×D4×C149—24no—
97C4×D4×C149—22no—
98C4×D4×C149—21no—
99C4×D4×C149—21no—
100C4×D4×C149—21no—
101C4×D4×C149D411yescharacteristic
102C4×D4×C149C2311yescharacteristic
103C4×D4×C149C2312yes—
104#117×C149—22no—
105#117×C149—22no—
106#117×C149—21no—
107#117×C149—21no—
108#117×C149D411yescharacteristic
109C2×C4⋊C4×C149—21no—
110C2×C4⋊C4×C149—22no—
111C2×C4⋊C4×C149D412yes—
112C2×C42×C149—21no—
113C2×C42×C149C2311yescharacteristic
114#107×C149—24no—
115#107×C149—21no—
116#107×C149—22no—
117#106×C149—24no—
118#106×C149—21no—
119C4⋊C8×C149—21no—
120C4⋊C8×C149C2312yes—
121C4⋊C8×C149C2311yescharacteristic
122C4⋊C8×C149C2311yescharacteristic
123#103×C149—21no—
124#103×C149—21no—
125#103×C149—21no—
126#103×C149—22no—
127#102×C149—21no—
128#102×C149—22no—
129C22⋊C8×C149—21no—
130#97×C149—21no—
131C4×C8×C149—21no—
132C4×C8×C149C2312yes—
133#41×C149—41no—
134#41×C149—41no—
135#41×C149—42no—
136#41×C149—42no—
137#41×C149—82no—
138#41×C149—82no—
139C2×Q8×C149—21no—
140C2×Q8×C149—22no—
141C2×Q8×C149—22no—
142C2×Q8×C149—21no—
143C2×Q8×C149—21no—
144C2×Q8×C149—81no—
145C2×Q8×C149—81no—
146C2×Q8×C149C2×D411yescharacteristic
147C2×D4×C149—21no—
148C2×D4×C149—22no—
149C2×D4×C149—24no—
150C2×D4×C149—21no—
151C2×D4×C149—21no—
152C2×D4×C149C2×D411yescharacteristic
153C2×D4×C149C2×D412yes—
154C22×C4×C149—24no—
155C22×C4×C149—22no—
156C22×C4×C149—21no—
157C22×C4×C149—21no—
158C22×C4×C149—21no—
159C22×C4×C149—22no—
160C22×C4×C149C2×D411yescharacteristic
161C22×C4×C149C2×D411yescharacteristic
162C22×C4×C149C2×D411yescharacteristic
163Q16×C149—42no—
164SD16×C149—42no—
165SD16×C149—82no—
166M16×C149—24no—
167M16×C149—81no—
168C2×C8×C149—22no—
169C2×C8×C149—21no—
170C2×C8×C149—21no—
171C2×C8×C149—22no—
172C4⋊C4×C149—24no—
173C4⋊C4×C149—24no—
174C4⋊C4×C149—22no—
175C4⋊C4×C149—22no—
176C4⋊C4×C149—21no—
177C4⋊C4×C149—21no—
178C4⋊C4×C149—22no—
179C4⋊C4×C149—21no—
180C4⋊C4×C149—21no—
181C4⋊C4×C149—21no—
182C4⋊C4×C149—21no—
183C4⋊C4×C149—21no—
184C4⋊C4×C149—41no—
185C4⋊C4×C149—41no—
186C4⋊C4×C149C2×D411yescharacteristic
187C4⋊C4×C149C2×D411yescharacteristic
188C4⋊C4×C149C2×D412yes—
189C4⋊C4×C149C2×D414yes—
190C22⋊C4×C149—24no—
191C22⋊C4×C149—24no—
192C22⋊C4×C149—24no—
193C22⋊C4×C149—21no—
194C22⋊C4×C149—21no—
195C22⋊C4×C149—22no—
196C22⋊C4×C149—21no—
197C22⋊C4×C149—22no—
198C22⋊C4×C149—41no—
199C42×C149—24no—
200C42×C149—21no—
201C42×C149—21no—
202C42×C149—21no—
203C42×C149—41no—
204C42×C149C2×D411yescharacteristic
205C42×C149C2×D411yescharacteristic
206C42×C149C2×D411yescharacteristic
207C42×C149C2411yescharacteristic
208C23×C149—21no—
209C23×C149—22no—
210C23×C149#12011yescharacteristic
211Q8×C149—21no—
212Q8×C149—21no—
213Q8×C149—42no—
214Q8×C149—42no—
215Q8×C149—42no—
216Q8×C149—41no—
217Q8×C149—41no—
218Q8×C149—41no—
219Q8×C149—41no—
220Q8×C149—82no—
221D4×C149—21no—
222D4×C149—21no—
223D4×C149—22no—
224D4×C149—22no—
225D4×C149—42no—
226D4×C149—42no—
227D4×C149—44no—
228D4×C149—42no—
229D4×C149—84no—
230C2×C4×C149—21no—
231C2×C4×C149—21no—
232C2×C4×C149—21no—
233C2×C4×C149—21no—
234C2×C4×C149—22no—
235C2×C4×C149—21no—
236C2×C4×C149—21no—
237C2×C4×C149—22no—
238C2×C4×C149—21no—
239C2×C4×C149—24no—
240C2×C4×C149—42no—
241C2×C4×C149—42no—
242C2×C4×C149—42no—
243C2×C4×C149—41no—
244C2×C4×C149—41no—
245C2×C4×C149—42no—
246C2×C4×C149—41no—
247C2×C4×C149—41no—
248C2×C4×C149—82no—
249C2×C4×C149—84no—
250C2×C4×C149#12011yescharacteristic
251C2×C4×C149#12011yescharacteristic
252C2×C4×C149#12011yescharacteristic
253C2×C4×C149C22×D411yescharacteristic
254C2×C4×C149C22×D411yescharacteristic
255C2×C4×C149C22×D411yescharacteristic
256C8×C149—24no—
257C8×C149—41no—
258C8×C149—41no—
259C8×C149—42no—
260C22×C149—21no—
261C22×C149—21no—
262C22×C149—21no—
263C22×C149—41no—
264C22×C149—42no—
265C22×C149—41no—
266C22×C149—42no—
267C22×C149—41no—
268C22×C149—42no—
269C22×C149C2×#12011yescharacteristic
270C4×C149—21no—
271C4×C149—21no—
272C4×C149—21no—
273C4×C149—41no—
274C4×C149—42no—
275C4×C149—41no—
276C4×C149—44no—
277C4×C149—41no—
278C4×C149—81no—
279C4×C149—81no—
280C4×C149#45612yes—
281C4×C149#57511yescharacteristic
282C4×C149#57511yescharacteristic
283C4×C149#57611yescharacteristic
284C4×C149#57711yescharacteristic
285C2×C149—41no—
286C2×C149—81no—
287C2×C149—82no—
288C2×C149#300511yescharacteristic
289C2×C149#301211yescharacteristic
290C2×C149C2×#45611yescharacteristic
291#18593C14911yesmaximal, characteristic, direct product factor, Sylow
292C149#1859311yescharacteristic, direct product factor, Sylow
293#3511C2×C14911yescharacteristic
294#3254C2×C14911yescharacteristic, complemented
295#3165C2×C14911yescharacteristic, complemented
296#3107C2×C14911yescharacteristic, complemented
297#1654C2×C14912yescomplemented
298#1652C2×C14912yescomplemented
299#1650C2×C14912yescomplemented
300#1647C2×C14912yescomplemented
301#1546C2×C14911yescharacteristic, complemented
302#1489C2×C14911yescharacteristic, complemented
303#1484C2×C14911yescharacteristic, complemented
304#556C22×C14912yes—
305#555—21no—
306#554—21no—
307#553—22no—
308#548—22no—
309#547C22×C14912yes—
310#542—22no—
311#537—21no—
312#533—21no—
313#533C22×C14911yescharacteristic
314#532—21no—
315#532C22×C14911yescharacteristic
316C2×C4⋊Q8C22×C14911yescharacteristic
317#520—21no—
318C4×#41C22×C14911yescharacteristic
319#501—22no—
320#500C22×C14912yes—
321#498C22×C14912yes—
322#485—21no—
323#477—21no—
324#475C22×C14911yescharacteristic
325#474C22×C14911yescharacteristic
326#474C22×C14912yes—
327#468—22no—
328#462C22×C14911yescharacteristic
329#461C22×C14911yescharacteristic
330#461C22×C14912yes—
331#460—21no—
332#452—21no—
333C4×Q16—21no—
334C4×SD16—21no—
335#431C22×C14911yescharacteristic
336#428—22no—
337#423C22×C14911yescharacteristic
338C4×M16C22×C14911yescharacteristic
339#332C22×C14912yes—
340#332C22×C14912yes—
341Q8⋊C8C22×C14912yes—
342D4⋊C8C22×C14912yes—
343D4⋊C8C22×C14912yes—
344D4⋊C8C22×C14912yes—
345C2×#41—22no—
346C2×#41—21no—
347C2×#41D4×C14911yescharacteristic
348C22×Q8—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—22no—
352C2×M16—21no—
353C2×M16—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8D4×C14912yes—
357C4⋊Q8D4×C14911yescharacteristic
358C4⋊Q8C23×C14911yescharacteristic
359C4⋊Q8C23×C14911yescharacteristic
360C4⋊Q8C23×C14912yes—
361#127D4×C14911yescharacteristic
362#126—24no—
363#125—22no—
364#125—21no—
365#124—24no—
366#124—22no—
367#124—21no—
368#123—24no—
369C22⋊Q8—22no—
370C22⋊Q8—24no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375#121—22no—
376#121—22no—
377#121—24no—
378#121—22no—
379#121—21no—
380#121D4×C14912yes—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8D4×C14911yescharacteristic
386C4×Q8C23×C14911yescharacteristic
387C4×D4—22no—
388C4×D4—24no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4D4×C14911yescharacteristic
394C4×D4C23×C14911yescharacteristic
395C4×D4C23×C14912yes—
396#117—22no—
397#117—22no—
398#117—21no—
399#117—21no—
400#117D4×C14911yescharacteristic
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4D4×C14912yes—
404C2×C42—21no—
405C2×C42C23×C14911yescharacteristic
406#107—24no—
407#107—21no—
408#107—22no—
409#106—24no—
410#106—21no—
411C4⋊C8—21no—
412C4⋊C8C23×C14911yescharacteristic
413C4⋊C8C23×C14911yescharacteristic
414C4⋊C8C23×C14912yes—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—22no—
419#102—21no—
420#102—22no—
421C22⋊C8—21no—
422#97—21no—
423C4×C8—21no—
424C4×C8C23×C14912yes—
425#41—41no—
426#41—41no—
427#41—42no—
428#41—42no—
429#41—82no—
430#41—82no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—81no—
437C2×Q8—81no—
438C2×Q8C2×D4×C14911yescharacteristic
439C2×D4—21no—
440C2×D4—22no—
441C2×D4—24no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×D4×C14911yescharacteristic
445C2×D4C2×D4×C14912yes—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4C2×D4×C14911yescharacteristic
453C22×C4C2×D4×C14911yescharacteristic
454C22×C4C2×D4×C14911yescharacteristic
455Q16—42no—
456SD16—42no—
457SD16—82no—
458M16—24no—
459M16—81no—
460C2×C8—22no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—22no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C14911yescharacteristic
479C4⋊C4C2×D4×C14911yescharacteristic
480C4⋊C4C2×D4×C14912yes—
481C4⋊C4C2×D4×C14914yes—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—41no—
491C42—24no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42C2×D4×C14911yescharacteristic
497C42C2×D4×C14911yescharacteristic
498C42C2×D4×C14911yescharacteristic
499C42C24×C14911yescharacteristic
500C23—21no—
501C23—22no—
502C23#120×C14911yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—82no—
513D4—21no—
514D4—21no—
515D4—22no—
516D4—22no—
517D4—42no—
518D4—42no—
519D4—44no—
520D4—42no—
521D4—84no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—84no—
542C2×C4#120×C14911yescharacteristic
543C2×C4#120×C14911yescharacteristic
544C2×C4#120×C14911yescharacteristic
545C2×C4C22×D4×C14911yescharacteristic
546C2×C4C22×D4×C14911yescharacteristic
547C2×C4C22×D4×C14911yescharacteristic
548C8—24no—
549C8—41no—
550C8—41no—
551C8—42no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—42no—
557C22—41no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22C2×#120×C14911yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—44no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4#456×C14912yes—
573C4#575×C14911yescharacteristic
574C4#575×C14911yescharacteristic
575C4#576×C14911yescharacteristic
576C4#577×C14911yescharacteristic
577C2—41no—
578C2—81no—
579C2—82no—
580C2#3005×C14911yescharacteristic
581C2#3012×C14911yescharacteristic
582C2C2×#456×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#3511×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. #3254×C149C2semidirect
3. #3165×C149C2semidirect
4. #3107×C149C2semidirect
5. #1654×C149C2semidirect
6. #1652×C149C2semidirect
7. #1650×C149C2semidirect
8. #1647×C149C2semidirect
9. #1546×C149C2semidirect
10. #1489×C149C2semidirect
11. #1484×C149C2semidirect
291. #18593C149direct (N × H)
292. C149#18593direct (N × H)
294. #3254C2×C149semidirect
295. #3165C2×C149semidirect
296. #3107C2×C149semidirect
297. #1654C2×C149semidirect
298. #1652C2×C149semidirect
299. #1650C2×C149semidirect
300. #1647C2×C149semidirect
301. #1546C2×C149semidirect
302. #1489C2×C149semidirect
303. #1484C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3511×C1492
#3254×C1492
#3165×C1492
#3107×C1492
#1654×C1492
#1652×C1492
#1650×C1492
#1647×C1492
#1546×C1492
#1489×C1492
#1484×C1492
#18593149