Finite Group Databasebeta

← C149×#18756 #49197705

Subgroups — C149×#18756 #49197705

Order 38144.

1224 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C149C211yesmaximal, characteristic, complemented
2#3226×C149C211yesmaximal, characteristic, complemented
3#3100×C149C211yesmaximal, characteristic, complemented
4#3036×C149C211yesmaximal, characteristic, complemented
5#1647×C149C214yesmaximal, complemented
6#1625×C149C214yesmaximal, complemented
7#1546×C149C211yesmaximal, characteristic, complemented
8#1486×C149C211yesmaximal, characteristic, complemented
9#1478×C149C211yesmaximal, characteristic, complemented
10C22×#41×C149—21no—
11C2×AGL(1,ℤ/8)×C149—21no—
12#547×C149—22no—
13#547×C149—22no—
14#547×C149—22no—
15#547×C149C2214yes—
16#532×C149C2211yescharacteristic
17C2×C4⋊Q8×C149C2211yescharacteristic
18C2×#123×C149—22no—
19C2×C22⋊Q8×C149—21no—
20C2×#121×C149—21no—
21C2×C4×D4×C149C2211yescharacteristic
22C2×C4×D4×C149C2211yescharacteristic
23C22×C4⋊C4×C149—21no—
24#500×C149C2212yescomplemented
25#486×C149C2212yescomplemented
26#480×C149—22no—
27#480×C149—21no—
28#474×C149—22no—
29#474×C149C2212yescomplemented
30#463×C149—22no—
31#461×C149C2212yescomplemented
32#459×C149C2212yescomplemented
33#459×C149C2212yescomplemented
34#447×C149—21no—
35C4×D8×C149—22no—
36#431×C149C2211yescharacteristic
37#431×C149C2211yescharacteristic
38#423×C149C2211yescharacteristic
39#417×C149—21no—
40#332×C149C2214yescomplemented
41D4⋊C8×C149C2214yescomplemented
42D4⋊C8×C149C2214yescomplemented
43C2×#41×C149—24no—
44C2×#41×C149—24no—
45C2×#41×C149—21no—
46C2×#41×C149—44no—
47C2×#41×C149—44no—
48C22×Q8×C149—21no—
49C22×D4×C149—22no—
50C22×D4×C149D411yescharacteristic
51C22×D4×C149D411yescharacteristic
52C23×C4×C149—22no—
53C23×C4×C149—21no—
54C23×C4×C149—21no—
55AGL(1,ℤ/8)×C149—44no—
56C2×SD16×C149—22no—
57C2×D8×C149—22no—
58C2×D8×C149—22no—
59C2×M16×C149—21no—
60C4⋊Q8×C149—21no—
61C4⋊Q8×C149—21no—
62C4⋊Q8×C149D412yes—
63C4⋊Q8×C149C2311yescharacteristic
64C4⋊Q8×C149C2312yes—
65#127×C149C2311yescharacteristic
66#124×C149—21no—
67#123×C149—28no—
68#123×C149—28no—
69C22⋊Q8×C149—24no—
70C22⋊Q8×C149—24no—
71#121×C149—24no—
72#121×C149—24no—
73#121×C149—21no—
74#121×C149—21no—
75C4×D4×C149—21no—
76C4×D4×C149—21no—
77C4×D4×C149—21no—
78C4×D4×C149—21no—
79C4×D4×C149—21no—
80C4×D4×C149—21no—
81C4×D4×C149D412yes—
82C4×D4×C149D412yes—
83C4×D4×C149C2312yes—
84C4×D4×C149C2312yes—
85C2×C4⋊C4×C149—22no—
86C2×C4⋊C4×C149—24no—
87C2×C4⋊C4×C149—21no—
88C2×C4⋊C4×C149—24no—
89C2×C4⋊C4×C149D411yescharacteristic
90C2×C4⋊C4×C149D411yescharacteristic
91C2×C4⋊C4×C149D412yes—
92C2×C22⋊C4×C149—22no—
93C2×C22⋊C4×C149—21no—
94C2×C22⋊C4×C149—21no—
95C2×C42×C149C2311yescharacteristic
96#107×C149—22no—
97#107×C149—24no—
98C4⋊C8×C149—21no—
99C4⋊C8×C149—21no—
100C4⋊C8×C149C2312yes—
101C4⋊C8×C149C2312yes—
102#103×C149—22no—
103#102×C149—22no—
104#102×C149—22no—
105#102×C149—22no—
106#102×C149—24no—
107C22⋊C8×C149—21no—
108C22⋊C8×C149—21no—
109C4×C8×C149—21no—
110C4×C8×C149C2312yes—
111C24×C149—21no—
112C24×C149—21no—
113#41×C149—48no—
114#41×C149—416no—
115#41×C149—48no—
116#41×C149—42no—
117#41×C149—42no—
118C2×Q8×C149—22no—
119C2×Q8×C149—22no—
120C2×Q8×C149—21no—
121C2×Q8×C149—42no—
122C2×Q8×C149—42no—
123C2×D4×C149—28no—
124C2×D4×C149—21no—
125C2×D4×C149—21no—
126C2×D4×C149—22no—
127C2×D4×C149—21no—
128C2×D4×C149—21no—
129C2×D4×C149—21no—
130C2×D4×C149—42no—
131C2×D4×C149—48no—
132C2×D4×C149—41no—
133C2×D4×C149D814yescomplemented
134C2×D4×C149C2×D412yes—
135C2×D4×C149C2×D412yes—
136C22×C4×C149—28no—
137C22×C4×C149—21no—
138C22×C4×C149—21no—
139C22×C4×C149—22no—
140C22×C4×C149—22no—
141C22×C4×C149—22no—
142C22×C4×C149—22no—
143C22×C4×C149—22no—
144C22×C4×C149—44no—
145C22×C4×C149—48no—
146C22×C4×C149—42no—
147C22×C4×C149—42no—
148C22×C4×C149—41no—
149C22×C4×C149C2×D411yescharacteristic
150C22×C4×C149C2×D411yescharacteristic
151C22×C4×C149C2×D411yescharacteristic
152SD16×C149—44no—
153D8×C149—44no—
154D8×C149—44no—
155M16×C149—42no—
156C2×C8×C149—22no—
157C2×C8×C149—22no—
158C2×C8×C149—22no—
159C4⋊C4×C149—28no—
160C4⋊C4×C149—21no—
161C4⋊C4×C149—22no—
162C4⋊C4×C149—21no—
163C4⋊C4×C149—22no—
164C4⋊C4×C149—22no—
165C4⋊C4×C149—21no—
166C4⋊C4×C149—21no—
167C4⋊C4×C149C2×D412yes—
168C4⋊C4×C149C2×D412yes—
169C4⋊C4×C149C2×D414yes—
170C22⋊C4×C149—28no—
171C22⋊C4×C149—22no—
172C22⋊C4×C149—22no—
173C22⋊C4×C149—22no—
174C22⋊C4×C149—22no—
175C22⋊C4×C149—41no—
176C22⋊C4×C149—41no—
177C42×C149C2×D411yescharacteristic
178C42×C149C2×D411yescharacteristic
179C42×C149C2×D411yescharacteristic
180C42×C149C2411yescharacteristic
181C23×C149—22no—
182C23×C149—24no—
183C23×C149—22no—
184C23×C149—42no—
185C23×C149—42no—
186C23×C149—42no—
187C23×C149—42no—
188C23×C149—42no—
189C23×C149—41no—
190C23×C149#12011yescharacteristic
191Q8×C149—42no—
192Q8×C149—42no—
193Q8×C149—44no—
194Q8×C149—41no—
195Q8×C149—41no—
196D4×C149—22no—
197D4×C149—22no—
198D4×C149—22no—
199D4×C149—24no—
200D4×C149—42no—
201D4×C149—42no—
202D4×C149—416no—
203D4×C149—41no—
204D4×C149—41no—
205D4×C149—42no—
206D4×C149—82no—
207D4×C149C2×D814yes—
208C2×C4×C149—22no—
209C2×C4×C149—22no—
210C2×C4×C149—22no—
211C2×C4×C149—24no—
212C2×C4×C149—41no—
213C2×C4×C149—44no—
214C2×C4×C149—42no—
215C2×C4×C149—416no—
216C2×C4×C149—42no—
217C2×C4×C149—44no—
218C2×C4×C149—42no—
219C2×C4×C149—42no—
220C2×C4×C149—44no—
221C2×C4×C149—44no—
222C2×C4×C149—41no—
223C2×C4×C149—82no—
224C2×C4×C149#12011yescharacteristic
225C2×C4×C149#12011yescharacteristic
226C2×C4×C149#12011yescharacteristic
227C2×C4×C149C2×D812yes—
228C2×C4×C149AGL(1,ℤ/8)12yes—
229C2×C4×C149C22×D411yescharacteristic
230C2×C4×C149C22×D411yescharacteristic
231C2×C4×C149C22×D411yescharacteristic
232C8×C149—42no—
233C8×C149—42no—
234C8×C149—42no—
235C22×C149—21no—
236C22×C149—21no—
237C22×C149—24no—
238C22×C149—48no—
239C22×C149—42no—
240C22×C149—42no—
241C22×C149—42no—
242C22×C149—42no—
243C22×C149—42no—
244C22×C149—84no—
245C22×C149—81no—
246C22×C149—81no—
247C22×C149—81no—
248C22×C149#44712yes—
249C22×C149C2×#12011yescharacteristic
250C4×C149—21no—
251C4×C149—21no—
252C4×C149—21no—
253C4×C149—42no—
254C4×C149—44no—
255C4×C149—42no—
256C4×C149—81no—
257C4×C149#44712yes—
258C4×C149C22×D811yescharacteristic
259C4×C149C2×AGL(1,ℤ/8)11yescharacteristic
260C4×C149#57512yes—
261C2×C149—22no—
262C2×C149—44no—
263C2×C149—82no—
264C2×C149—161no—
265C2×C149C2×#44711yescharacteristic
266C2×C149#300511yescharacteristic
267C2×C149#302011yescharacteristic
268#18756C14911yesmaximal, characteristic, direct product factor, Sylow
269C149#1875611yescharacteristic, direct product factor, Sylow
270C2×#547C2×C14911yescharacteristic, complemented
271#3226C2×C14911yescharacteristic, complemented
272#3100C2×C14911yescharacteristic, complemented
273#3036C2×C14911yescharacteristic, complemented
274#1647C2×C14914yescomplemented
275#1625C2×C14914yescomplemented
276#1546C2×C14911yescharacteristic, complemented
277#1486C2×C14911yescharacteristic, complemented
278#1478C2×C14911yescharacteristic, complemented
279C22×#41—21no—
280C2×AGL(1,ℤ/8)—21no—
281#547—22no—
282#547—22no—
283#547—22no—
284#547C22×C14914yes—
285#532C22×C14911yescharacteristic
286C2×C4⋊Q8C22×C14911yescharacteristic
287C2×#123—22no—
288C2×C22⋊Q8—21no—
289C2×#121—21no—
290C2×C4×D4C22×C14911yescharacteristic
291C2×C4×D4C22×C14911yescharacteristic
292C22×C4⋊C4—21no—
293#500C22×C14912yescomplemented
294#486C22×C14912yescomplemented
295#480—21no—
296#480—22no—
297#474—22no—
298#474C22×C14912yescomplemented
299#463—22no—
300#461C22×C14912yescomplemented
301#459C22×C14912yescomplemented
302#459C22×C14912yescomplemented
303#447—21no—
304C4×D8—22no—
305#431C22×C14911yescharacteristic
306#431C22×C14911yescharacteristic
307#423C22×C14911yescharacteristic
308#417—21no—
309#332C22×C14914yescomplemented
310D4⋊C8C22×C14914yescomplemented
311D4⋊C8C22×C14914yescomplemented
312C2×#41—24no—
313C2×#41—24no—
314C2×#41—21no—
315C2×#41—44no—
316C2×#41—44no—
317C22×Q8—21no—
318C22×D4—22no—
319C22×D4D4×C14911yescharacteristic
320C22×D4D4×C14911yescharacteristic
321C23×C4—22no—
322C23×C4—21no—
323C23×C4—21no—
324AGL(1,ℤ/8)—44no—
325C2×SD16—22no—
326C2×D8—22no—
327C2×D8—22no—
328C2×M16—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8D4×C14912yes—
332C4⋊Q8C23×C14911yescharacteristic
333C4⋊Q8C23×C14912yes—
334#127C23×C14911yescharacteristic
335#124—21no—
336#123—28no—
337#123—28no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340#121—24no—
341#121—24no—
342#121—21no—
343#121—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—21no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4D4×C14912yes—
351C4×D4D4×C14912yes—
352C4×D4C23×C14912yes—
353C4×D4C23×C14912yes—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4D4×C14911yescharacteristic
359C2×C4⋊C4D4×C14911yescharacteristic
360C2×C4⋊C4D4×C14912yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42C23×C14911yescharacteristic
365#107—22no—
366#107—24no—
367C4⋊C8—21no—
368C4⋊C8—21no—
369C4⋊C8C23×C14912yes—
370C4⋊C8C23×C14912yes—
371#103—22no—
372#102—22no—
373#102—22no—
374#102—22no—
375#102—24no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C4×C8—21no—
379C4×C8C23×C14912yes—
380C24—21no—
381C24—21no—
382#41—416no—
383#41—48no—
384#41—48no—
385#41—42no—
386#41—42no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×D4—28no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4—42no—
400C2×D4—48no—
401C2×D4—41no—
402C2×D4D8×C14914yescomplemented
403C2×D4C2×D4×C14912yes—
404C2×D4C2×D4×C14912yes—
405C22×C4—28no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—44no—
414C22×C4—48no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—41no—
418C22×C4C2×D4×C14911yescharacteristic
419C22×C4C2×D4×C14911yescharacteristic
420C22×C4C2×D4×C14911yescharacteristic
421SD16—44no—
422D8—44no—
423D8—44no—
424M16—42no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C4⋊C4—28no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4C2×D4×C14912yes—
437C4⋊C4C2×D4×C14912yes—
438C4⋊C4C2×D4×C14914yes—
439C22⋊C4—28no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C42C2×D4×C14911yescharacteristic
447C42C2×D4×C14911yescharacteristic
448C42C2×D4×C14911yescharacteristic
449C42C24×C14911yescharacteristic
450C23—24no—
451C23—22no—
452C23—22no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—41no—
459C23#120×C14911yescharacteristic
460Q8—44no—
461Q8—42no—
462Q8—42no—
463Q8—41no—
464Q8—41no—
465D4—24no—
466D4—22no—
467D4—22no—
468D4—22no—
469D4—42no—
470D4—42no—
471D4—416no—
472D4—41no—
473D4—41no—
474D4—42no—
475D4—82no—
476D4C2×D8×C14914yes—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—41no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—416no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—41no—
492C2×C4—82no—
493C2×C4#120×C14911yescharacteristic
494C2×C4#120×C14911yescharacteristic
495C2×C4#120×C14911yescharacteristic
496C2×C4C2×D8×C14912yes—
497C2×C4AGL(1,ℤ/8)×C14912yes—
498C2×C4C22×D4×C14911yescharacteristic
499C2×C4C22×D4×C14911yescharacteristic
500C2×C4C22×D4×C14911yescharacteristic
501C8—42no—
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—24no—
507C22—48no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—84no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22#447×C14912yes—
518C22C2×#120×C14911yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—44no—
524C4—42no—
525C4—81no—
526C4#447×C14912yes—
527C4C22×D8×C14911yescharacteristic
528C4C2×AGL(1,ℤ/8)×C14911yescharacteristic
529C4#575×C14912yes—
530C2—22no—
531C2—44no—
532C2—82no—
533C2—161no—
534C2C2×#447×C14911yescharacteristic
535C2#3005×C14911yescharacteristic
536C2#3020×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. C2×#547×C149C2semidirect
2. #3226×C149C2semidirect
3. #3100×C149C2semidirect
4. #3036×C149C2semidirect
5. #1647×C149C2semidirect
6. #1625×C149C2semidirect
7. #1546×C149C2semidirect
8. #1486×C149C2semidirect
9. #1478×C149C2semidirect
24. #500×C149C22semidirect
25. #486×C149C22semidirect
29. #474×C149C22semidirect
31. #461×C149C22semidirect
32. #459×C149C22semidirect
33. #459×C149C22semidirect
40. #332×C149C22semidirect
41. D4⋊C8×C149C22semidirect
42. D4⋊C8×C149C22semidirect
133. C2×D4×C149D8semidirect
268. #18756C149direct (N × H)
269. C149#18756direct (N × H)
270. C2×#547C2×C149semidirect
271. #3226C2×C149semidirect
272. #3100C2×C149semidirect
273. #3036C2×C149semidirect
274. #1647C2×C149semidirect
275. #1625C2×C149semidirect
276. #1546C2×C149semidirect
277. #1486C2×C149semidirect
278. #1478C2×C149semidirect
293. #500C22×C149semidirect
294. #486C22×C149semidirect
298. #474C22×C149semidirect
300. #461C22×C149semidirect
301. #459C22×C149semidirect
302. #459C22×C149semidirect
309. #332C22×C149semidirect
310. D4⋊C8C22×C149semidirect
311. D4⋊C8C22×C149semidirect
402. C2×D4D8×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1492
#3226×C1492
#3100×C1492
#3036×C1492
#1647×C1492
#1625×C1492
#1546×C1492
#1486×C1492
#1478×C1492
#18756149