Finite Group Databasebeta

← C149×#19028 #49197977

Subgroups — C149×#19028 #49197977

Order 38144.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3563×C149C211yesmaximal, characteristic, complemented
2#3217×C149C211yesmaximal, characteristic
3#3138×C149C211yesmaximal, characteristic, complemented
4C2×#490×C149C211yesmaximal, characteristic, complemented
5#1658×C149C214yesmaximal, complemented
6#1657×C149C214yesmaximal, complemented
7#1531×C149C211yesmaximal, characteristic, complemented
8#1528×C149C211yesmaximal, characteristic, complemented
9#1524×C149C211yesmaximal, characteristic, complemented
10#564×C149C2212yescomplemented
11#563×C149C2212yescomplemented
12#557×C149—21no—
13#554×C149—21no—
14#552×C149—21no—
15#552×C149—22no—
16#552×C149—21no—
17#544×C149—21no—
18#544×C149—21no—
19#541×C149—21no—
20#541×C149—22no—
21#539×C149—21no—
22#533×C149C2211yescharacteristic
23C2×#127×C149C2211yescharacteristic
24#529×C149C2211yescharacteristic
25C2×#125×C149C2211yescharacteristic
26#496×C149C2212yes—
27#490×C149—22no—
28#490×C149C2212yes—
29#490×C149C2214yes—
30#490×C149C2214yes—
31#486×C149—21no—
32#486×C149—21no—
33#460×C149—21no—
34#459×C149—21no—
35#450×C149—21no—
36#447×C149—21no—
37#432×C149C2211yescharacteristic
38#418×C149—22no—
39C2×#102×C149—21no—
40C2×#102×C149—21no—
41C4×M16×C149C2211yescharacteristic
42C2×#97×C149C2211yescharacteristic
43#330×C149C2212yescomplemented
44#330×C149C2214yescomplemented
45#330×C149C2214yescomplemented
46#329×C149C2212yescomplemented
47C22×D4×C149—21no—
48C22×D4×C149—21no—
49C22×D4×C149—21no—
50C2×SD16×C149—22no—
51C2×D8×C149—22no—
52C2×M16×C149—21no—
53C22×C8×C149—21no—
54C4⋊Q8×C149—22no—
55C4⋊Q8×C149—21no—
56C4⋊Q8×C149—22no—
57C4⋊Q8×C149D411yescharacteristic
58C4⋊Q8×C149D411yescharacteristic
59#127×C149—21no—
60#127×C149—21no—
61#127×C149—21no—
62#127×C149C2312yes—
63#126×C149—22no—
64#126×C149—22no—
65#126×C149—22no—
66#126×C149—22no—
67#126×C149—21no—
68#125×C149—22no—
69#125×C149—22no—
70#125×C149—21no—
71#125×C149—22no—
72#125×C149—22no—
73#125×C149—22no—
74#125×C149—22no—
75#125×C149—22no—
76#125×C149—22no—
77#125×C149—21no—
78#125×C149—21no—
79#125×C149D412yes—
80#125×C149C2312yes—
81#125×C149C2311yescharacteristic
82#125×C149C2312yes—
83#124×C149C2311yescharacteristic
84#123×C149—22no—
85#123×C149—22no—
86#123×C149—21no—
87C22⋊Q8×C149—22no—
88C22⋊Q8×C149—21no—
89C22⋊Q8×C149—21no—
90C22⋊Q8×C149—22no—
91C22⋊Q8×C149—21no—
92C22⋊Q8×C149—21no—
93C22⋊Q8×C149—22no—
94C22⋊Q8×C149—22no—
95C22⋊Q8×C149D411yescharacteristic
96#121×C149D411yescharacteristic
97C4×Q8×C149—21no—
98C4×Q8×C149—22no—
99C4×Q8×C149—21no—
100C4×Q8×C149—21no—
101C4×Q8×C149—21no—
102C4×Q8×C149D411yescharacteristic
103C4×D4×C149—22no—
104C4×D4×C149—21no—
105C4×D4×C149D411yescharacteristic
106#117×C149—22no—
107#117×C149—21no—
108#117×C149—22no—
109#117×C149—21no—
110#117×C149D412yes—
111C2×C4⋊C4×C149—21no—
112C2×C4⋊C4×C149—21no—
113C2×C4⋊C4×C149—21no—
114C2×C4⋊C4×C149D411yescharacteristic
115C2×C4⋊C4×C149D411yescharacteristic
116C2×C42×C149C2311yescharacteristic
117C4⋊C8×C149—21no—
118#102×C149—24no—
119#102×C149—24no—
120#102×C149—24no—
121#102×C149—24no—
122#102×C149—22no—
123#102×C149—22no—
124C22⋊C8×C149—21no—
125#97×C149—21no—
126#97×C149C2312yes—
127#97×C149C2312yes—
128#97×C149C2312yes—
129C4×C8×C149—21no—
130C24×C149—41no—
131C2×Q8×C149—22no—
132C2×Q8×C149—21no—
133C2×Q8×C149—21no—
134C2×Q8×C149C2×D411yescharacteristic
135C2×D4×C149—21no—
136C2×D4×C149—22no—
137C2×D4×C149—22no—
138C2×D4×C149—22no—
139C2×D4×C149—44no—
140C2×D4×C149—44no—
141C2×D4×C149—41no—
142C2×D4×C149—41no—
143C2×D4×C149—41no—
144C2×D4×C149—82no—
145C2×D4×C149C2×D411yescharacteristic
146C22×C4×C149—21no—
147C22×C4×C149—22no—
148C22×C4×C149—21no—
149C22×C4×C149—21no—
150C22×C4×C149C2×D411yescharacteristic
151C22×C4×C149C2×D411yescharacteristic
152C22×C4×C149C2×D411yescharacteristic
153SD16×C149—82no—
154D8×C149—82no—
155M16×C149—42no—
156C2×C8×C149—22no—
157C2×C8×C149—22no—
158C2×C8×C149—22no—
159C2×C8×C149—42no—
160C4⋊C4×C149—22no—
161C4⋊C4×C149—22no—
162C4⋊C4×C149—22no—
163C4⋊C4×C149—22no—
164C4⋊C4×C149—22no—
165C4⋊C4×C149—22no—
166C4⋊C4×C149—22no—
167C4⋊C4×C149—22no—
168C4⋊C4×C149—21no—
169C4⋊C4×C149—21no—
170C4⋊C4×C149—22no—
171C4⋊C4×C149—22no—
172C4⋊C4×C149—21no—
173C4⋊C4×C149—21no—
174C4⋊C4×C149—21no—
175C4⋊C4×C149—21no—
176C4⋊C4×C149—22no—
177C4⋊C4×C149—22no—
178C4⋊C4×C149—21no—
179C4⋊C4×C149—21no—
180C4⋊C4×C149—22no—
181C4⋊C4×C149—22no—
182C4⋊C4×C149C2×D412yes—
183C4⋊C4×C149C2×D412yes—
184C4⋊C4×C149C2×D412yes—
185C4⋊C4×C149C2×D412yes—
186C4⋊C4×C149C2×D411yescharacteristic
187C4⋊C4×C149C2×D411yescharacteristic
188C22⋊C4×C149—22no—
189C22⋊C4×C149—22no—
190C22⋊C4×C149—22no—
191C22⋊C4×C149—21no—
192C22⋊C4×C149—22no—
193C22⋊C4×C149—21no—
194C22⋊C4×C149—21no—
195C22⋊C4×C149—21no—
196C22⋊C4×C149—21no—
197C42×C149—22no—
198C42×C149—22no—
199C42×C149—22no—
200C42×C149—22no—
201C42×C149—21no—
202C42×C149C2×D411yescharacteristic
203C42×C149C2×D411yescharacteristic
204C42×C149C2×D411yescharacteristic
205C42×C149C2411yescharacteristic
206C23×C149—21no—
207C23×C149—42no—
208C23×C149—82no—
209C23×C149—82no—
210C23×C149—82no—
211C23×C149#12011yescharacteristic
212Q8×C149—41no—
213Q8×C149—42no—
214Q8×C149—81no—
215Q8×C149—82no—
216D4×C149—41no—
217D4×C149—42no—
218D4×C149—42no—
219D4×C149—44no—
220D4×C149—44no—
221D4×C149—42no—
222D4×C149—82no—
223D4×C149—82no—
224D4×C149—82no—
225C2×C4×C149—22no—
226C2×C4×C149—22no—
227C2×C4×C149—22no—
228C2×C4×C149—21no—
229C2×C4×C149—21no—
230C2×C4×C149—21no—
231C2×C4×C149—22no—
232C2×C4×C149—22no—
233C2×C4×C149—22no—
234C2×C4×C149—41no—
235C2×C4×C149—42no—
236C2×C4×C149—42no—
237C2×C4×C149—81no—
238C2×C4×C149—82no—
239C2×C4×C149#12011yescharacteristic
240C2×C4×C149#12011yescharacteristic
241C2×C4×C149#12011yescharacteristic
242C2×C4×C149C22×D411yescharacteristic
243C2×C4×C149C22×D411yescharacteristic
244C2×C4×C149C22×D411yescharacteristic
245C8×C149—42no—
246C8×C149—42no—
247C8×C149—42no—
248C22×C149—21no—
249C22×C149—21no—
250C22×C149—41no—
251C22×C149—41no—
252C22×C149—41no—
253C22×C149—82no—
254C22×C149—82no—
255C22×C149—82no—
256C22×C149—164no—
257C22×C149#45412yes—
258C22×C149C2×#12011yescharacteristic
259C4×C149—21no—
260C4×C149—21no—
261C4×C149—21no—
262C4×C149—21no—
263C4×C149—21no—
264C4×C149—42no—
265C4×C149—41no—
266C4×C149—41no—
267C4×C149—42no—
268C4×C149—42no—
269C4×C149—42no—
270C4×C149—41no—
271C4×C149#45412yes—
272C2×C149—22no—
273C2×C149—81no—
274C2×C149—162no—
275C2×C149C2×#45411yescharacteristic
276C2×C149C2×#45411yescharacteristic
277C2×C149#302111yescharacteristic
278#19028C14911yesmaximal, characteristic, direct product factor, Sylow
279C149#1902811yescharacteristic, direct product factor, Sylow
280#3563C2×C14911yescharacteristic, complemented
281#3217C2×C14911yescharacteristic
282#3138C2×C14911yescharacteristic, complemented
283C2×#490C2×C14911yescharacteristic, complemented
284#1658C2×C14914yescomplemented
285#1657C2×C14914yescomplemented
286#1531C2×C14911yescharacteristic, complemented
287#1528C2×C14911yescharacteristic, complemented
288#1524C2×C14911yescharacteristic, complemented
289#564C22×C14912yescomplemented
290#563C22×C14912yescomplemented
291#557—21no—
292#554—21no—
293#552—21no—
294#552—22no—
295#552—21no—
296#544—21no—
297#544—21no—
298#541—21no—
299#541—22no—
300#539—21no—
301#533C22×C14911yescharacteristic
302C2×#127C22×C14911yescharacteristic
303#529C22×C14911yescharacteristic
304C2×#125C22×C14911yescharacteristic
305#496C22×C14912yes—
306#490—22no—
307#490C22×C14914yes—
308#490C22×C14914yes—
309#490C22×C14912yes—
310#486—21no—
311#486—21no—
312#460—21no—
313#459—21no—
314#450—21no—
315#447—21no—
316#432C22×C14911yescharacteristic
317#418—22no—
318C2×#102—21no—
319C2×#102—21no—
320C4×M16C22×C14911yescharacteristic
321C2×#97C22×C14911yescharacteristic
322#330C22×C14914yescomplemented
323#330C22×C14914yescomplemented
324#330C22×C14912yescomplemented
325#329C22×C14912yescomplemented
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C2×SD16—22no—
330C2×D8—22no—
331C2×M16—21no—
332C22×C8—21no—
333C4⋊Q8—22no—
334C4⋊Q8—21no—
335C4⋊Q8—22no—
336C4⋊Q8D4×C14911yescharacteristic
337C4⋊Q8D4×C14911yescharacteristic
338#127—21no—
339#127—21no—
340#127—21no—
341#127C23×C14912yes—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—22no—
346#126—21no—
347#125—22no—
348#125—22no—
349#125—21no—
350#125—22no—
351#125—22no—
352#125—22no—
353#125—22no—
354#125—22no—
355#125—22no—
356#125—21no—
357#125—21no—
358#125D4×C14912yes—
359#125C23×C14912yes—
360#125C23×C14911yescharacteristic
361#125C23×C14912yes—
362#124C23×C14911yescharacteristic
363#123—22no—
364#123—22no—
365#123—21no—
366C22⋊Q8—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8—22no—
374C22⋊Q8D4×C14911yescharacteristic
375#121D4×C14911yescharacteristic
376C4×Q8—21no—
377C4×Q8—22no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8D4×C14911yescharacteristic
382C4×D4—22no—
383C4×D4—21no—
384C4×D4D4×C14911yescharacteristic
385#117—22no—
386#117—21no—
387#117—22no—
388#117—21no—
389#117D4×C14912yes—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4D4×C14911yescharacteristic
394C2×C4⋊C4D4×C14911yescharacteristic
395C2×C42C23×C14911yescharacteristic
396C4⋊C8—21no—
397#102—24no—
398#102—24no—
399#102—24no—
400#102—24no—
401#102—22no—
402#102—22no—
403C22⋊C8—21no—
404#97—21no—
405#97C23×C14912yes—
406#97C23×C14912yes—
407#97C23×C14912yes—
408C4×C8—21no—
409C24—41no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8C2×D4×C14911yescharacteristic
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—82no—
424C2×D4C2×D4×C14911yescharacteristic
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4C2×D4×C14911yescharacteristic
430C22×C4C2×D4×C14911yescharacteristic
431C22×C4C2×D4×C14911yescharacteristic
432SD16—82no—
433D8—82no—
434M16—42no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—42no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4C2×D4×C14912yes—
462C4⋊C4C2×D4×C14912yes—
463C4⋊C4C2×D4×C14912yes—
464C4⋊C4C2×D4×C14912yes—
465C4⋊C4C2×D4×C14911yescharacteristic
466C4⋊C4C2×D4×C14911yescharacteristic
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42C2×D4×C14911yescharacteristic
482C42C2×D4×C14911yescharacteristic
483C42C2×D4×C14911yescharacteristic
484C42C24×C14911yescharacteristic
485C23—21no—
486C23—42no—
487C23—82no—
488C23—82no—
489C23—82no—
490C23#120×C14911yescharacteristic
491Q8—41no—
492Q8—42no—
493Q8—81no—
494Q8—82no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—44no—
500D4—42no—
501D4—82no—
502D4—82no—
503D4—82no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4#120×C14911yescharacteristic
519C2×C4#120×C14911yescharacteristic
520C2×C4#120×C14911yescharacteristic
521C2×C4C22×D4×C14911yescharacteristic
522C2×C4C22×D4×C14911yescharacteristic
523C2×C4C22×D4×C14911yescharacteristic
524C8—42no—
525C8—42no—
526C8—42no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—164no—
536C22#454×C14912yes—
537C22C2×#120×C14911yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—42no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—41no—
550C4#454×C14912yes—
551C2—22no—
552C2—81no—
553C2—162no—
554C2C2×#454×C14911yescharacteristic
555C2C2×#454×C14911yescharacteristic
556C2#3021×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#120
commutator, Frattini, cosocleC42C24×C149
prime radical#3217×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
1. #3563×C149C2semidirect
3. #3138×C149C2semidirect
4. C2×#490×C149C2semidirect
5. #1658×C149C2semidirect
6. #1657×C149C2semidirect
7. #1531×C149C2semidirect
8. #1528×C149C2semidirect
9. #1524×C149C2semidirect
10. #564×C149C22semidirect
11. #563×C149C22semidirect
43. #330×C149C22semidirect
44. #330×C149C22semidirect
45. #330×C149C22semidirect
46. #329×C149C22semidirect
278. #19028C149direct (N × H)
279. C149#19028direct (N × H)
280. #3563C2×C149semidirect
282. #3138C2×C149semidirect
283. C2×#490C2×C149semidirect
284. #1658C2×C149semidirect
285. #1657C2×C149semidirect
286. #1531C2×C149semidirect
287. #1528C2×C149semidirect
288. #1524C2×C149semidirect
289. #564C22×C149semidirect
290. #563C22×C149semidirect
322. #330C22×C149semidirect
323. #330C22×C149semidirect
324. #330C22×C149semidirect
325. #329C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3563×C1492
#3217×C1492
#3138×C1492
C2×#490×C1492
#1658×C1492
#1657×C1492
#1531×C1492
#1528×C1492
#1524×C1492
#19028149