Finite Group Databasebeta

← C149×#10322 #49189271

Subgroups — C149×#10322 #49189271

Order 38144.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3187×C149C211yesmaximal, characteristic, complemented
2#2848×C149C211yesmaximal, characteristic, complemented
3#2847×C149C211yesmaximal, characteristic
4#1779×C149C211yesmaximal, characteristic, complemented
5#1520×C149C211yesmaximal, characteristic, complemented
6#1519×C149C211yesmaximal, characteristic, complemented
7#1289×C149C211yesmaximal, characteristic, complemented
8C24×C4×C149C2211yescharacteristic
9C2×C22⋊Q8×C149—21no—
10C2×C22⋊Q8×C149C2211yescharacteristic
11C2×#121×C149—21no—
12C2×#121×C149C2211yescharacteristic
13C2×#120×C149—21no—
14#483×C149—21no—
15#481×C149—21no—
16#465×C149—22no—
17#450×C149—21no—
18#448×C149—21no—
19C2×C22⋊C8×C149—22no—
20C2×C22⋊C8×C149C2211yescharacteristic
21C2×C22⋊C8×C149C2211yescharacteristic
22#386×C149—21no—
23#386×C149—22no—
24#385×C149—21no—
25#385×C149—22no—
26#380×C149—21no—
27#380×C149—21no—
28#380×C149C2211yescharacteristic
29#380×C149C2211yescharacteristic
30#379×C149—21no—
31#328×C149—22no—
32#327×C149—22no—
33C25×C149D411yescharacteristic
34C22×Q8×C149D411yescharacteristic, complemented
35C22×D4×C149—22no—
36C22×D4×C149—21no—
37C22×D4×C149D411yescharacteristic
38C23×C4×C149—21no—
39C23×C4×C149—21no—
40C23×C4×C149—21no—
41C23×C4×C149—21no—
42C23×C4×C149—21no—
43C23×C4×C149—21no—
44C23×C4×C149—44no—
45C23×C4×C149D411yescharacteristic
46C23×C4×C149C2311yescharacteristic
47C2×SD16×C149—22no—
48C22×C8×C149—21no—
49C22×C8×C149D412yescomplemented
50C22⋊Q8×C149—21no—
51C22⋊Q8×C149—21no—
52C22⋊Q8×C149—21no—
53C22⋊Q8×C149—21no—
54C22⋊Q8×C149—44no—
55#121×C149—21no—
56#121×C149—21no—
57#121×C149—21no—
58#121×C149—21no—
59#121×C149—44no—
60#120×C149—42no—
61#120×C149—42no—
62C2×C4⋊C4×C149—22no—
63C2×C4⋊C4×C149—21no—
64C2×C4⋊C4×C149—21no—
65C2×C4⋊C4×C149—21no—
66C2×C4⋊C4×C149D411yescharacteristic
67C2×C4⋊C4×C149D411yescharacteristic, complemented
68C2×C22⋊C4×C149—22no—
69C2×C22⋊C4×C149—22no—
70C2×C22⋊C4×C149—22no—
71C2×C22⋊C4×C149—22no—
72C2×C22⋊C4×C149—21no—
73C2×C22⋊C4×C149—21no—
74C2×C22⋊C4×C149—21no—
75C2×C22⋊C4×C149—21no—
76#106×C149—22no—
77#103×C149—22no—
78#102×C149—22no—
79C22⋊C8×C149—21no—
80C22⋊C8×C149—21no—
81C22⋊C8×C149—21no—
82C22⋊C8×C149—21no—
83C22⋊C8×C149—44no—
84#95×C149—22no—
85#95×C149—22no—
86#95×C149D412yes—
87#95×C149D412yescomplemented
88C24×C149—21no—
89C24×C149—21no—
90C24×C149—21no—
91C24×C149—21no—
92C24×C149—21no—
93C24×C149—21no—
94C24×C149—21no—
95C24×C149—42no—
96C24×C149—42no—
97C24×C149SD1612yescomplemented
98C24×C149C2×D411yescharacteristic
99C2×Q8×C149—21no—
100C2×Q8×C149—21no—
101C2×Q8×C149—42no—
102C2×D4×C149—21no—
103C2×D4×C149—21no—
104C2×D4×C149—42no—
105C2×D4×C149—44no—
106C2×D4×C149—44no—
107C2×D4×C149—44no—
108C2×D4×C149—41no—
109C2×D4×C149—41no—
110C2×D4×C149—41no—
111C2×D4×C149—41no—
112C2×D4×C149—41no—
113C2×D4×C149—41no—
114C22×C4×C149—24no—
115C22×C4×C149—24no—
116C22×C4×C149—24no—
117C22×C4×C149—21no—
118C22×C4×C149—21no—
119C22×C4×C149—21no—
120C22×C4×C149—21no—
121C22×C4×C149—21no—
122C22×C4×C149—22no—
123C22×C4×C149—22no—
124C22×C4×C149—21no—
125C22×C4×C149—42no—
126C22×C4×C149—42no—
127C22×C4×C149—42no—
128C22×C4×C149—42no—
129C22×C4×C149—42no—
130C22×C4×C149—42no—
131C22×C4×C149—42no—
132C22×C4×C149—42no—
133C22×C4×C149—42no—
134C22×C4×C149—42no—
135C22×C4×C149—42no—
136C22×C4×C149—41no—
137C22×C4×C149—41no—
138C22×C4×C149—41no—
139C22×C4×C149—41no—
140C22×C4×C149C2×D411yescharacteristic
141C22×C4×C149C2×D411yescharacteristic
142C22×C4×C149C2×D411yescharacteristic
143C22×C4×C149C2×D411yescharacteristic
144C22×C4×C149C2×D411yescharacteristic
145C22×C4×C149#4111yescharacteristic
146SD16×C149—82no—
147C2×C8×C149—22no—
148C2×C8×C149—42no—
149C2×C8×C149—42no—
150C2×C8×C149—41no—
151C4⋊C4×C149—21no—
152C4⋊C4×C149—21no—
153C4⋊C4×C149—21no—
154C4⋊C4×C149—21no—
155C4⋊C4×C149—42no—
156C4⋊C4×C149—42no—
157C4⋊C4×C149—44no—
158C4⋊C4×C149—41no—
159C4⋊C4×C149—41no—
160C22⋊C4×C149—44no—
161C22⋊C4×C149—44no—
162C22⋊C4×C149—44no—
163C22⋊C4×C149—44no—
164C22⋊C4×C149—41no—
165C22⋊C4×C149—41no—
166C22⋊C4×C149—41no—
167C22⋊C4×C149—41no—
168C22⋊C4×C149—41no—
169C22⋊C4×C149—41no—
170C22⋊C4×C149—41no—
171C22⋊C4×C149—41no—
172C23×C149—22no—
173C23×C149—22no—
174C23×C149—22no—
175C23×C149—22no—
176C23×C149—22no—
177C23×C149—22no—
178C23×C149—22no—
179C23×C149—22no—
180C23×C149—22no—
181C23×C149—41no—
182C23×C149—44no—
183C23×C149—41no—
184C23×C149—41no—
185C23×C149—41no—
186C23×C149—41no—
187C23×C149—41no—
188C23×C149—41no—
189C23×C149—41no—
190C23×C149—44no—
191C23×C149—44no—
192C23×C149—44no—
193C23×C149—42no—
194C23×C149—42no—
195C23×C149—41no—
196C23×C149—41no—
197C23×C149—41no—
198C23×C149—41no—
199C23×C149—41no—
200C23×C149—41no—
201C23×C149—41no—
202C23×C149#12011yescharacteristic
203C23×C149#12011yescharacteristic
204C23×C149#12111yescharacteristic
205C23×C149C2×SD1611yescharacteristic
206C23×C149#13511yescharacteristic
207C23×C149AGL(1,ℤ/8)11yescharacteristic
208C23×C149#13711yescharacteristic
209Q8×C149—42no—
210Q8×C149—81no—
211D4×C149—42no—
212D4×C149—81no—
213D4×C149—88no—
214D4×C149—81no—
215D4×C149—81no—
216D4×C149—81no—
217D4×C149—81no—
218C2×C4×C149—22no—
219C2×C4×C149—22no—
220C2×C4×C149—22no—
221C2×C4×C149—22no—
222C2×C4×C149—22no—
223C2×C4×C149—22no—
224C2×C4×C149—41no—
225C2×C4×C149—41no—
226C2×C4×C149—41no—
227C2×C4×C149—44no—
228C2×C4×C149—44no—
229C2×C4×C149—44no—
230C2×C4×C149—41no—
231C2×C4×C149—41no—
232C2×C4×C149—41no—
233C2×C4×C149—41no—
234C2×C4×C149—44no—
235C2×C4×C149—42no—
236C2×C4×C149—42no—
237C2×C4×C149—42no—
238C2×C4×C149—42no—
239C2×C4×C149—42no—
240C2×C4×C149—42no—
241C2×C4×C149—41no—
242C2×C4×C149—41no—
243C2×C4×C149—41no—
244C2×C4×C149—42no—
245C2×C4×C149—42no—
246C2×C4×C149—41no—
247C2×C4×C149—41no—
248C2×C4×C149#12011yescharacteristic
249C2×C4×C149#12111yescharacteristic
250C2×C4×C149#12111yescharacteristic
251C2×C4×C149#12711yescharacteristic
252C8×C149—42no—
253C8×C149—81no—
254C22×C149—21no—
255C22×C149—21no—
256C22×C149—21no—
257C22×C149—21no—
258C22×C149—21no—
259C22×C149—21no—
260C22×C149—24no—
261C22×C149—24no—
262C22×C149—24no—
263C22×C149—41no—
264C22×C149—41no—
265C22×C149—41no—
266C22×C149—41no—
267C22×C149—42no—
268C22×C149—42no—
269C22×C149—42no—
270C22×C149—42no—
271C22×C149—42no—
272C22×C149—42no—
273C22×C149—42no—
274C22×C149—42no—
275C22×C149—42no—
276C22×C149—42no—
277C22×C149—42no—
278C22×C149—42no—
279C22×C149—82no—
280C22×C149—82no—
281C22×C149—81no—
282C22×C149—81no—
283C22×C149—81no—
284C22×C149#39211yescharacteristic
285C22×C149#44811yescharacteristic
286C22×C149#44911yescharacteristic
287C22×C149#45011yescharacteristic
288C22×C149#45211yescharacteristic
289C22×C149#46511yescharacteristic
290C22×C149#46811yescharacteristic
291C4×C149—21no—
292C4×C149—21no—
293C4×C149—21no—
294C4×C149—42no—
295C4×C149—82no—
296C4×C149—82no—
297C4×C149—81no—
298C4×C149—81no—
299C4×C149—81no—
300C4×C149B(4,𝔽2)12yes—
301C2×C149—21no—
302C2×C149—21no—
303C2×C149—21no—
304C2×C149—21no—
305C2×C149—21no—
306C2×C149—21no—
307C2×C149—44no—
308C2×C149—161no—
309C2×C149#200011yescharacteristic
310C2×C149#201011yescharacteristic
311C2×C149#202111yescharacteristic
312#10322C14911yesmaximal, characteristic, direct product factor, Sylow
313C149#1032211yescharacteristic, direct product factor, Sylow
314#3187C2×C14911yescharacteristic, complemented
315#2848C2×C14911yescharacteristic, complemented
316#2847C2×C14911yescharacteristic
317#1779C2×C14911yescharacteristic, complemented
318#1520C2×C14911yescharacteristic, complemented
319#1519C2×C14911yescharacteristic, complemented
320#1289C2×C14911yescharacteristic, complemented
321C24×C4C22×C14911yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8C22×C14911yescharacteristic
324C2×#121—21no—
325C2×#121C22×C14911yescharacteristic
326C2×#120—21no—
327#483—21no—
328#481—21no—
329#465—22no—
330#450—21no—
331#448—21no—
332C2×C22⋊C8—22no—
333C2×C22⋊C8C22×C14911yescharacteristic
334C2×C22⋊C8C22×C14911yescharacteristic
335#386—21no—
336#386—22no—
337#385—21no—
338#385—22no—
339#380—21no—
340#380—21no—
341#380C22×C14911yescharacteristic
342#380C22×C14911yescharacteristic
343#379—21no—
344#328—22no—
345#327—22no—
346C25D4×C14911yescharacteristic
347C22×Q8D4×C14911yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C14911yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C14911yescharacteristic
359C23×C4C23×C14911yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C14912yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C14911yescharacteristic
380C2×C4⋊C4D4×C14911yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C14912yes—
400#95D4×C14912yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C14912yescomplemented
411C24C2×D4×C14911yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C14911yescharacteristic
454C22×C4C2×D4×C14911yescharacteristic
455C22×C4C2×D4×C14911yescharacteristic
456C22×C4C2×D4×C14911yescharacteristic
457C22×C4C2×D4×C14911yescharacteristic
458C22×C4#41×C14911yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C14911yescharacteristic
516C23#120×C14911yescharacteristic
517C23#121×C14911yescharacteristic
518C23C2×SD16×C14911yescharacteristic
519C23#135×C14911yescharacteristic
520C23AGL(1,ℤ/8)×C14911yescharacteristic
521C23#137×C14911yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C14911yescharacteristic
562C2×C4#121×C14911yescharacteristic
563C2×C4#121×C14911yescharacteristic
564C2×C4#127×C14911yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#392×C14911yescharacteristic
598C22#448×C14911yescharacteristic
599C22#449×C14911yescharacteristic
600C22#450×C14911yescharacteristic
601C22#452×C14911yescharacteristic
602C22#465×C14911yescharacteristic
603C22#468×C14911yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4B(4,𝔽2)×C14912yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2#2000×C14911yescharacteristic
623C2#2010×C14911yescharacteristic
624C2#2021×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC23×C4C23×C149
prime radical#2847×C149C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3187×C149C2semidirect
2. #2848×C149C2semidirect
4. #1779×C149C2semidirect
5. #1520×C149C2semidirect
6. #1519×C149C2semidirect
7. #1289×C149C2semidirect
34. C22×Q8×C149D4semidirect
49. C22×C8×C149D4semidirect
67. C2×C4⋊C4×C149D4semidirect
87. #95×C149D4semidirect
97. C24×C149SD16semidirect
312. #10322C149direct (N × H)
313. C149#10322direct (N × H)
314. #3187C2×C149semidirect
315. #2848C2×C149semidirect
317. #1779C2×C149semidirect
318. #1520C2×C149semidirect
319. #1519C2×C149semidirect
320. #1289C2×C149semidirect
347. C22×Q8D4×C149semidirect
362. C22×C8D4×C149semidirect
380. C2×C4⋊C4D4×C149semidirect
400. #95D4×C149semidirect
410. C24SD16×C149semidirect

Maximal subgroups

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

subgroupindex
#3187×C1492
#2848×C1492
#2847×C1492
#1779×C1492
#1520×C1492
#1519×C1492
#1289×C1492
#10322149