Finite Group Databasebeta

← C149×#11138 #49190087

Subgroups — C149×#11138 #49190087

Order 38144.

864 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2911×C149C211yesmaximal, characteristic, complemented
2C2×#413×C149C211yesmaximal, characteristic
3C2×#410×C149C211yesmaximal, characteristic
4C2×#410×C149C211yesmaximal, characteristic
5#1733×C149C211yesmaximal, characteristic, complemented
6#1733×C149C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C22×M16×C149C2211yescharacteristic
11C2×#117×C149C2211yescharacteristic
12C2×#117×C149C2211yescharacteristic
13C2×#117×C149C2211yescharacteristic
14C2×#117×C149C2211yescharacteristic
15#428×C149—22no—
16#428×C149—22no—
17#427×C149—22no—
18#413×C149—22no—
19#413×C149—22no—
20C2×#101×C149C412yescomplemented
21C2×#100×C149C412yescomplemented
22#410×C149—22no—
23#410×C149—22no—
24#410×C149—22no—
25#410×C149—22no—
26C2×#99×C149—22no—
27C2×#99×C149—22no—
28#339×C149—22no—
29#339×C149—22no—
30H(3,ℤ/4)×C149—22no—
31C2×#41×C149—21no—
32C2×#41×C149—21no—
33C2×#41×C149—21no—
34C2×#41×C149—21no—
35C2×#41×C149—21no—
36C2×#41×C149—21no—
37C2×#41×C149—21no—
38C2×#41×C149—21no—
39C2×#41×C149—21no—
40C2×#41×C149—21no—
41C2×#41×C149—21no—
42C2×#41×C149—21no—
43C22×Q8×C149C2×C411yescharacteristic
44C22×D4×C149C2×C411yescharacteristic
45C22×D4×C149D412yes—
46C23×C4×C149Q812yes—
47C23×C4×C149C2311yescharacteristic
48C2×M16×C149—21no—
49C2×M16×C149—21no—
50C2×M16×C149—21no—
51C2×M16×C149—21no—
52C2×M16×C149—21no—
53C2×M16×C149—21no—
54C2×M16×C149—21no—
55C2×M16×C149—21no—
56C2×M16×C149C2×C412yes—
57C2×M16×C149C2×C412yes—
58C2×M16×C149D412yes—
59C2×M16×C149D412yes—
60C22×C8×C149—21no—
61C22×C8×C149—21no—
62#117×C149—21no—
63#117×C149—21no—
64#117×C149—21no—
65#117×C149—21no—
66#117×C149—21no—
67#117×C149—21no—
68#117×C149—21no—
69#117×C149—21no—
70#117×C149—21no—
71#117×C149—21no—
72#117×C149—21no—
73#117×C149—21no—
74#117×C149D412yes—
75#117×C149D412yes—
76#117×C149D412yes—
77#117×C149D412yes—
78C2×C4⋊C4×C149—21no—
79C2×C4⋊C4×C149—21no—
80C2×C4⋊C4×C149—21no—
81C2×C4⋊C4×C149—21no—
82C2×C22⋊C4×C149—21no—
83C2×C22⋊C4×C149—21no—
84C2×C22⋊C4×C149—21no—
85C2×C22⋊C4×C149—21no—
86C2×C42×C149—21no—
87C2×C42×C149—21no—
88C2×C42×C149—21no—
89C2×C42×C149—21no—
90#107×C149—24no—
91#106×C149—24no—
92#101×C149—24no—
93#100×C149—24no—
94#99×C149—28no—
95#99×C149—28no—
96C24×C149C4⋊C412yes—
97C24×C149C2×D411yescharacteristic
98#41×C149—41no—
99#41×C149—41no—
100#41×C149—41no—
101#41×C149—41no—
102#41×C149—41no—
103#41×C149—41no—
104#41×C149—41no—
105#41×C149—41no—
106#41×C149—41no—
107#41×C149—41no—
108#41×C149—41no—
109#41×C149—41no—
110#41×C149—41no—
111#41×C149—41no—
112#41×C149—41no—
113#41×C149—41no—
114C2×Q8×C149—21no—
115C2×Q8×C149—21no—
116C2×Q8×C149—21no—
117C2×Q8×C149—21no—
118C2×Q8×C149—21no—
119C2×Q8×C149—21no—
120C2×D4×C149—22no—
121C2×D4×C149—22no—
122C2×D4×C149—22no—
123C2×D4×C149—22no—
124C2×D4×C149—22no—
125C2×D4×C149—22no—
126C2×D4×C149—21no—
127C2×D4×C149—21no—
128C2×D4×C149—21no—
129C2×D4×C149—21no—
130C2×D4×C149—21no—
131C2×D4×C149—21no—
132C22×C4×C149—22no—
133C22×C4×C149—22no—
134C22×C4×C149—22no—
135C22×C4×C149—22no—
136C22×C4×C149—22no—
137C22×C4×C149—22no—
138C22×C4×C149—41no—
139C22×C4×C149—41no—
140C22×C4×C149—41no—
141C22×C4×C149—41no—
142C22×C4×C149C4⋊C412yes—
143C22×C4×C149C22×C411yescharacteristic
144C22×C4×C149C2×D411yescharacteristic
145C22×C4×C149C2×D411yescharacteristic
146C22×C4×C149C2×D411yescharacteristic
147C22×C4×C149C2×D411yescharacteristic
148C22×C4×C149C2×D411yescharacteristic
149C22×C4×C149C2×D411yescharacteristic
150C22×C4×C149C2×Q811yescharacteristic
151C22×C4×C149#4111yescharacteristic
152C22×C4×C149#4111yescharacteristic
153C22×C4×C149#4111yescharacteristic
154C22×C4×C149#4111yescharacteristic
155C22×C4×C149#4111yescharacteristic
156C22×C4×C149#4111yescharacteristic
157M16×C149—22no—
158M16×C149—22no—
159M16×C149—22no—
160M16×C149—22no—
161M16×C149—22no—
162M16×C149—41no—
163M16×C149—41no—
164M16×C149C22⋊C414yes—
165C2×C8×C149—22no—
166C2×C8×C149—22no—
167C2×C8×C149—22no—
168C2×C8×C149—22no—
169C2×C8×C149—41no—
170C2×C8×C149—41no—
171C4⋊C4×C149—22no—
172C4⋊C4×C149—22no—
173C4⋊C4×C149—22no—
174C4⋊C4×C149—22no—
175C4⋊C4×C149—41no—
176C4⋊C4×C149—41no—
177C4⋊C4×C149—41no—
178C4⋊C4×C149—41no—
179C22⋊C4×C149—22no—
180C22⋊C4×C149—22no—
181C22⋊C4×C149—22no—
182C22⋊C4×C149—22no—
183C22⋊C4×C149—41no—
184C22⋊C4×C149—41no—
185C22⋊C4×C149—41no—
186C22⋊C4×C149—41no—
187C42×C149—22no—
188C42×C149—22no—
189C42×C149—22no—
190C42×C149—22no—
191C42×C149—41no—
192C42×C149—41no—
193C42×C149—41no—
194C42×C149—41no—
195C23×C149—22no—
196C23×C149—22no—
197C23×C149—22no—
198C23×C149—81no—
199C23×C149—82no—
200C23×C149C2×C4⋊C411yescharacteristic
201C23×C149#12011yescharacteristic
202C23×C149#12011yescharacteristic
203C23×C149#12111yescharacteristic
204C23×C149#12111yescharacteristic
205C23×C149#12311yescharacteristic
206C23×C149#12311yescharacteristic
207Q8×C149—41no—
208Q8×C149—41no—
209Q8×C149—41no—
210Q8×C149—41no—
211D4×C149—42no—
212D4×C149—42no—
213D4×C149—42no—
214D4×C149—42no—
215D4×C149—41no—
216D4×C149—41no—
217D4×C149—41no—
218D4×C149—41no—
219C2×C4×C149—22no—
220C2×C4×C149—22no—
221C2×C4×C149—22no—
222C2×C4×C149—42no—
223C2×C4×C149—42no—
224C2×C4×C149—42no—
225C2×C4×C149—42no—
226C2×C4×C149—42no—
227C2×C4×C149—42no—
228C2×C4×C149—42no—
229C2×C4×C149—42no—
230C2×C4×C149—82no—
231C2×C4×C149—82no—
232C2×C4×C149—82no—
233C2×C4×C149—82no—
234C2×C4×C149C2×C22⋊C411yescharacteristic
235C2×C4×C149#11711yescharacteristic
236C2×C4×C149C4×D411yescharacteristic
237C2×C4×C149C4×D411yescharacteristic
238C2×C4×C149C4×D411yescharacteristic
239C2×C4×C149C4×D411yescharacteristic
240C2×C4×C149#12011yescharacteristic
241C2×C4×C149#12111yescharacteristic
242C2×C4×C149#12111yescharacteristic
243C2×C4×C149#12111yescharacteristic
244C2×C4×C149#12111yescharacteristic
245C2×C4×C149#12111yescharacteristic
246C2×C4×C149#12111yescharacteristic
247C2×C4×C149C22⋊Q811yescharacteristic
248C2×C4×C149C22⋊Q811yescharacteristic
249C2×C4×C149C22⋊Q811yescharacteristic
250C2×C4×C149C22⋊Q811yescharacteristic
251C2×C4×C149C22⋊Q811yescharacteristic
252C2×C4×C149C22⋊Q811yescharacteristic
253C2×C4×C149#12311yescharacteristic
254C2×C4×C149#12311yescharacteristic
255C2×C4×C149#12311yescharacteristic
256C2×C4×C149#12411yescharacteristic
257C2×C4×C149#12411yescharacteristic
258C2×C4×C149#12411yescharacteristic
259C2×C4×C149#12611yescharacteristic
260C2×C4×C149#12611yescharacteristic
261C2×C4×C149#12711yescharacteristic
262C8×C149—24no—
263C8×C149—42no—
264C22×C149—41no—
265C22×C149—41no—
266C22×C149—41no—
267C22×C149—41no—
268C22×C149—41no—
269C22×C149—41no—
270C22×C149—41no—
271C22×C149—42no—
272C22×C149—82no—
273C22×C149—82no—
274C22×C149—82no—
275C22×C149#38011yescharacteristic
276C22×C149#38511yescharacteristic
277C22×C149#38511yescharacteristic
278C22×C149#39211yescharacteristic
279C22×C149#39411yescharacteristic
280C22×C149#39411yescharacteristic
281C22×C149#39711yescharacteristic
282C4×C149—42no—
283C4×C149—82no—
284C4×C149—82no—
285C4×C149—82no—
286C4×C149—82no—
287C4×C149#38611yescharacteristic
288C4×C149#38811yescharacteristic
289C4×C149#38811yescharacteristic
290C4×C149#39011yescharacteristic
291C4×C149#39311yescharacteristic
292C4×C149#39611yescharacteristic
293C4×C149#39611yescharacteristic
294C4×C149#39911yescharacteristic
295C2×C149—21no—
296C2×C149—21no—
297C2×C149—21no—
298C2×C149—21no—
299C2×C149—21no—
300C2×C149—21no—
301C2×C149—21no—
302C2×C149—82no—
303C2×C149#143911yescharacteristic
304#11138C14911yesmaximal, characteristic, direct product factor, Sylow
305C149#1113811yescharacteristic, direct product factor, Sylow
306#2911C2×C14911yescharacteristic, complemented
307C2×#413C2×C14911yescharacteristic
308C2×#410C2×C14911yescharacteristic
309C2×#410C2×C14911yescharacteristic
310#1733C2×C14911yescharacteristic, complemented
311#1733C2×C14911yescharacteristic, complemented
312C2×H(3,ℤ/4)C2×C14911yescharacteristic, complemented
313C22×#41C22×C14911yescharacteristic
314C22×M16C22×C14911yescharacteristic
315C22×M16C22×C14911yescharacteristic
316C2×#117C22×C14911yescharacteristic
317C2×#117C22×C14911yescharacteristic
318C2×#117C22×C14911yescharacteristic
319C2×#117C22×C14911yescharacteristic
320#428—22no—
321#428—22no—
322#427—22no—
323#413—22no—
324#413—22no—
325C2×#101C4×C14912yescomplemented
326C2×#100C4×C14912yescomplemented
327#410—22no—
328#410—22no—
329#410—22no—
330#410—22no—
331C2×#99—22no—
332C2×#99—22no—
333#339—22no—
334#339—22no—
335H(3,ℤ/4)—22no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C22×Q8C2×C4×C14911yescharacteristic
349C22×D4C2×C4×C14911yescharacteristic
350C22×D4D4×C14912yes—
351C23×C4Q8×C14912yes—
352C23×C4C23×C14911yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16C2×C4×C14912yes—
362C2×M16C2×C4×C14912yes—
363C2×M16D4×C14912yes—
364C2×M16D4×C14912yes—
365C22×C8—21no—
366C22×C8—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117D4×C14912yes—
380#117D4×C14912yes—
381#117D4×C14912yes—
382#117D4×C14912yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395#107—24no—
396#106—24no—
397#101—24no—
398#100—24no—
399#99—28no—
400#99—28no—
401C24C4⋊C4×C14912yes—
402C24C2×D4×C14911yescharacteristic
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4C4⋊C4×C14912yes—
448C22×C4C22×C4×C14911yescharacteristic
449C22×C4C2×D4×C14911yescharacteristic
450C22×C4C2×D4×C14911yescharacteristic
451C22×C4C2×D4×C14911yescharacteristic
452C22×C4C2×D4×C14911yescharacteristic
453C22×C4C2×D4×C14911yescharacteristic
454C22×C4C2×D4×C14911yescharacteristic
455C22×C4C2×Q8×C14911yescharacteristic
456C22×C4#41×C14911yescharacteristic
457C22×C4#41×C14911yescharacteristic
458C22×C4#41×C14911yescharacteristic
459C22×C4#41×C14911yescharacteristic
460C22×C4#41×C14911yescharacteristic
461C22×C4#41×C14911yescharacteristic
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467M16—41no—
468M16—41no—
469M16C22⋊C4×C14914yes—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—41no—
475C2×C8—41no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C42—22no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42—41no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—81no—
504C23—82no—
505C23C2×C4⋊C4×C14911yescharacteristic
506C23#120×C14911yescharacteristic
507C23#120×C14911yescharacteristic
508C23#121×C14911yescharacteristic
509C23#121×C14911yescharacteristic
510C23#123×C14911yescharacteristic
511C23#123×C14911yescharacteristic
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4C2×C22⋊C4×C14911yescharacteristic
540C2×C4#117×C14911yescharacteristic
541C2×C4C4×D4×C14911yescharacteristic
542C2×C4C4×D4×C14911yescharacteristic
543C2×C4C4×D4×C14911yescharacteristic
544C2×C4C4×D4×C14911yescharacteristic
545C2×C4#120×C14911yescharacteristic
546C2×C4#121×C14911yescharacteristic
547C2×C4#121×C14911yescharacteristic
548C2×C4#121×C14911yescharacteristic
549C2×C4#121×C14911yescharacteristic
550C2×C4#121×C14911yescharacteristic
551C2×C4#121×C14911yescharacteristic
552C2×C4C22⋊Q8×C14911yescharacteristic
553C2×C4C22⋊Q8×C14911yescharacteristic
554C2×C4C22⋊Q8×C14911yescharacteristic
555C2×C4C22⋊Q8×C14911yescharacteristic
556C2×C4C22⋊Q8×C14911yescharacteristic
557C2×C4C22⋊Q8×C14911yescharacteristic
558C2×C4#123×C14911yescharacteristic
559C2×C4#123×C14911yescharacteristic
560C2×C4#123×C14911yescharacteristic
561C2×C4#124×C14911yescharacteristic
562C2×C4#124×C14911yescharacteristic
563C2×C4#124×C14911yescharacteristic
564C2×C4#126×C14911yescharacteristic
565C2×C4#126×C14911yescharacteristic
566C2×C4#127×C14911yescharacteristic
567C8—24no—
568C8—42no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22#380×C14911yescharacteristic
581C22#385×C14911yescharacteristic
582C22#385×C14911yescharacteristic
583C22#392×C14911yescharacteristic
584C22#394×C14911yescharacteristic
585C22#394×C14911yescharacteristic
586C22#397×C14911yescharacteristic
587C4—42no—
588C4—82no—
589C4—82no—
590C4—82no—
591C4—82no—
592C4#386×C14911yescharacteristic
593C4#388×C14911yescharacteristic
594C4#388×C14911yescharacteristic
595C4#390×C14911yescharacteristic
596C4#393×C14911yescharacteristic
597C4#396×C14911yescharacteristic
598C4#396×C14911yescharacteristic
599C4#399×C14911yescharacteristic
600C2—21no—
601C2—21no—
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—82no—
608C2#1439×C14911yescharacteristic
subgroupG/H
centerC4×C149#396
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
socleC2×C149#1439
prime radicalC22×#41×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2911×C149C2semidirect
5. #1733×C149C2semidirect
6. #1733×C149C2semidirect
7. C2×H(3,ℤ/4)×C149C2semidirect
20. C2×#101×C149C4semidirect
21. C2×#100×C149C4semidirect
304. #11138C149direct (N × H)
305. C149#11138direct (N × H)
306. #2911C2×C149semidirect
310. #1733C2×C149semidirect
311. #1733C2×C149semidirect
312. C2×H(3,ℤ/4)C2×C149semidirect
325. C2×#101C4×C149semidirect
326. C2×#100C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2911×C1492
C2×#413×C1492
C2×#410×C1492
#1733×C1492
C2×H(3,ℤ/4)×C1492
#11138149