Finite Group Databasebeta

← C149×#11085 #49190034

Subgroups — C149×#11085 #49190034

Order 38144.

938 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#421×C149C211yesmaximal, characteristic
2C22×#104×C149C211yesmaximal, characteristic
3C2×#410×C149C211yesmaximal, characteristic
4#2296×C149C211yesmaximal, characteristic, complemented
5C2×#344×C149C211yesmaximal, characteristic, complemented
6C2×#339×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
14C22×C42×C149C2211yescharacteristic
15#421×C149—22no—
16#421×C149C414yescomplemented
17C2×#104×C149—22no—
18C2×#104×C149—22no—
19C2×#104×C149—22no—
20C2×#104×C149—22no—
21#410×C149—22no—
22#410×C149—22no—
23C2×#99×C149—22no—
24#389×C149—22no—
25#385×C149—22no—
26C4×C4⋊C4×C149—22no—
27#344×C149—22no—
28#339×C149—22no—
29H(3,ℤ/4)×C149—22no—
30C2×#41×C149—21no—
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×C149C2×C412yes—
41C2×#41×C149D412yes—
42C22×Q8×C149Q811yescharacteristic
43C22×D4×C149—21no—
44C22×D4×C149Q811yescharacteristic
45C23×C4×C149—21no—
46C23×C4×C149—21no—
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×C149—21no—
57C2×M16×C149—21no—
58C2×M16×C149C2×C412yes—
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×C149C2×C412yes—
72#117×C149D412yes—
73#117×C149D412yes—
74C2×C4⋊C4×C149—21no—
75C2×C4⋊C4×C149—21no—
76C2×C4⋊C4×C149—24no—
77C2×C4⋊C4×C149—21no—
78C2×C22⋊C4×C149—21no—
79C2×C22⋊C4×C149—21no—
80C2×C22⋊C4×C149D412yes—
81C2×C42×C149—21no—
82C2×C42×C149—21no—
83C2×C42×C149—21no—
84C2×C42×C149—21no—
85C2×C42×C149—21no—
86C2×C42×C149—21no—
87C2×C42×C149—21no—
88C2×C42×C149D412yes—
89C2×C42×C149D412yes—
90#104×C149—28no—
91#104×C149—28no—
92#99×C149—28no—
93#95×C149—24no—
94C24×C149—21no—
95C24×C149C2×D411yescharacteristic
96#41×C149—22no—
97#41×C149—22no—
98#41×C149—22no—
99#41×C149—22no—
100#41×C149—22no—
101#41×C149—22no—
102#41×C149—22no—
103#41×C149—22no—
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—
112C2×Q8×C149—21no—
113C2×Q8×C149—21no—
114C2×Q8×C149—21no—
115C2×Q8×C149—21no—
116C2×Q8×C149—21no—
117C2×Q8×C149C4⋊C412yescomplemented
118C2×D4×C149—22no—
119C2×D4×C149—22no—
120C2×D4×C149—21no—
121C2×D4×C149—21no—
122C2×D4×C149—21no—
123C2×D4×C149—21no—
124C2×D4×C149—21no—
125C2×D4×C149—41no—
126C2×D4×C149—41no—
127C2×D4×C149—41no—
128C2×D4×C149—41no—
129C2×D4×C149C4⋊C412yescomplemented
130C22×C4×C149—22no—
131C22×C4×C149—22no—
132C22×C4×C149—21no—
133C22×C4×C149—22no—
134C22×C4×C149—22no—
135C22×C4×C149—22no—
136C22×C4×C149—44no—
137C22×C4×C149—41no—
138C22×C4×C149—41no—
139C22×C4×C149—41no—
140C22×C4×C149—41no—
141C22×C4×C149—41no—
142C22×C4×C149—41no—
143C22×C4×C149—41no—
144C22×C4×C149C22×C411yescharacteristic
145C22×C4×C149C2×D411yescharacteristic
146C22×C4×C149C2×D411yescharacteristic
147C22×C4×C149C2×D411yescharacteristic
148C22×C4×C149C2×D411yescharacteristic
149C22×C4×C149C2×D411yescharacteristic
150C22×C4×C149C2×D411yescharacteristic
151C22×C4×C149C2×Q811yescharacteristic
152C22×C4×C149#4111yescharacteristic
153C22×C4×C149#4111yescharacteristic
154C22×C4×C149#4111yescharacteristic
155C22×C4×C149#4111yescharacteristic
156C22×C4×C149#4111yescharacteristic
157C22×C4×C149#4111yescharacteristic
158M16×C149—22no—
159M16×C149—22no—
160M16×C149—22no—
161M16×C149—22no—
162M16×C149—41no—
163M16×C149—41no—
164M16×C149—41no—
165M16×C149—41no—
166C2×C8×C149—22no—
167C2×C8×C149—22no—
168C2×C8×C149—41no—
169C2×C8×C149—41no—
170C2×C8×C149—41no—
171C2×C8×C149—41no—
172C4⋊C4×C149—22no—
173C4⋊C4×C149—22no—
174C4⋊C4×C149—22no—
175C4⋊C4×C149—48no—
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—22no—
184C22⋊C4×C149—41no—
185C42×C149—22no—
186C42×C149—22no—
187C42×C149—22no—
188C42×C149—22no—
189C42×C149—41no—
190C42×C149—41no—
191C42×C149—41no—
192C42×C149—41no—
193C42×C149—41no—
194C42×C149C22⋊C414yes—
195C23×C149—22no—
196C23×C149—42no—
197C23×C149—41no—
198C23×C149—41no—
199C23×C149—82no—
200C23×C149C4×D411yescharacteristic
201C23×C149#12011yescharacteristic
202C23×C149#12011yescharacteristic
203C23×C149#12111yescharacteristic
204C23×C149#12111yescharacteristic
205C23×C149C22⋊Q811yescharacteristic
206C23×C149#12411yescharacteristic
207Q8×C149—22no—
208Q8×C149—22no—
209Q8×C149—41no—
210Q8×C149—41no—
211D4×C149—22no—
212D4×C149—22no—
213D4×C149—42no—
214D4×C149—42no—
215D4×C149—42no—
216D4×C149—42no—
217D4×C149—41no—
218D4×C149—41no—
219C2×C4×C149—24no—
220C2×C4×C149—22no—
221C2×C4×C149—24no—
222C2×C4×C149—44no—
223C2×C4×C149—42no—
224C2×C4×C149—44no—
225C2×C4×C149—44no—
226C2×C4×C149—42no—
227C2×C4×C149—41no—
228C2×C4×C149—41no—
229C2×C4×C149—42no—
230C2×C4×C149—42no—
231C2×C4×C149—42no—
232C2×C4×C149—42no—
233C2×C4×C149—44no—
234C2×C4×C149—42no—
235C2×C4×C149—42no—
236C2×C4×C149—82no—
237C2×C4×C149C2×C22⋊C411yescharacteristic
238C2×C4×C149C2×C4⋊C411yescharacteristic
239C2×C4×C149#11711yescharacteristic
240C2×C4×C149C4×D411yescharacteristic
241C2×C4×C149C4×D411yescharacteristic
242C2×C4×C149C4×D411yescharacteristic
243C2×C4×C149#12011yescharacteristic
244C2×C4×C149#12111yescharacteristic
245C2×C4×C149#12111yescharacteristic
246C2×C4×C149#12111yescharacteristic
247C2×C4×C149#12111yescharacteristic
248C2×C4×C149#12111yescharacteristic
249C2×C4×C149#12111yescharacteristic
250C2×C4×C149C22⋊Q811yescharacteristic
251C2×C4×C149C22⋊Q811yescharacteristic
252C2×C4×C149C22⋊Q811yescharacteristic
253C2×C4×C149C22⋊Q811yescharacteristic
254C2×C4×C149C22⋊Q811yescharacteristic
255C2×C4×C149#12311yescharacteristic
256C2×C4×C149#12311yescharacteristic
257C2×C4×C149#12311yescharacteristic
258C2×C4×C149#12311yescharacteristic
259C2×C4×C149#12311yescharacteristic
260C2×C4×C149#12411yescharacteristic
261C2×C4×C149#12411yescharacteristic
262C2×C4×C149#12611yescharacteristic
263C2×C4×C149#12611yescharacteristic
264C2×C4×C149#12711yescharacteristic
265C8×C149—42no—
266C8×C149—42no—
267C22×C149—22no—
268C22×C149—22no—
269C22×C149—22no—
270C22×C149—41no—
271C22×C149—41no—
272C22×C149—41no—
273C22×C149—41no—
274C22×C149—42no—
275C22×C149—82no—
276C22×C149—82no—
277C22×C149—82no—
278C22×C149#38511yescharacteristic
279C22×C149#38611yescharacteristic
280C22×C149#38811yescharacteristic
281C22×C149#39211yescharacteristic
282C22×C149#39311yescharacteristic
283C22×C149#39411yescharacteristic
284C22×C149#39611yescharacteristic
285C4×C149—44no—
286C4×C149—44no—
287C4×C149—42no—
288C4×C149—82no—
289C4×C149—82no—
290C4×C149#38011yescharacteristic
291C4×C149#38511yescharacteristic
292C4×C149#38811yescharacteristic
293C4×C149#39011yescharacteristic
294C4×C149#39411yescharacteristic
295C4×C149#39611yescharacteristic
296C4×C149#39711yescharacteristic
297C4×C149#39911yescharacteristic
298C2×C149—21no—
299C2×C149—21no—
300C2×C149—21no—
301C2×C149—21no—
302C2×C149—21no—
303C2×C149—21no—
304C2×C149—82no—
305C2×C149#143911yescharacteristic
306C2×C149#203112yes—
307#11085C14911yesmaximal, characteristic, direct product factor, Sylow
308C149#1108511yescharacteristic, direct product factor, Sylow
309C2×#421C2×C14911yescharacteristic
310C22×#104C2×C14911yescharacteristic
311C2×#410C2×C14911yescharacteristic
312#2296C2×C14911yescharacteristic, complemented
313C2×#344C2×C14911yescharacteristic, complemented
314C2×#339C2×C14911yescharacteristic, complemented
315C2×H(3,ℤ/4)C2×C14911yescharacteristic, complemented
316C22×#41C22×C14911yescharacteristic
317C22×M16C22×C14911yescharacteristic
318C22×M16C22×C14911yescharacteristic
319C2×#117C22×C14911yescharacteristic
320C2×#117C22×C14911yescharacteristic
321C2×#117C22×C14911yescharacteristic
322C22×C42C22×C14911yescharacteristic
323#421—22no—
324#421C4×C14914yescomplemented
325C2×#104—22no—
326C2×#104—22no—
327C2×#104—22no—
328C2×#104—22no—
329#410—22no—
330#410—22no—
331C2×#99—22no—
332#389—22no—
333#385—22no—
334C4×C4⋊C4—22no—
335#344—22no—
336#339—22no—
337H(3,ℤ/4)—22no—
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—
348C2×#41C2×C4×C14912yes—
349C2×#41D4×C14912yes—
350C22×Q8Q8×C14911yescharacteristic
351C22×D4—21no—
352C22×D4Q8×C14911yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C23×C14911yescharacteristic
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16C2×C4×C14912yes—
367C2×M16D4×C14912yes—
368C22×C8—21no—
369C22×C8—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#117C2×C4×C14912yes—
380#117D4×C14912yes—
381#117D4×C14912yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4D4×C14912yes—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42D4×C14912yes—
397C2×C42D4×C14912yes—
398#104—28no—
399#104—28no—
400#99—28no—
401#95—24no—
402C24—21no—
403C24C2×D4×C14911yescharacteristic
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8C4⋊C4×C14912yescomplemented
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4C4⋊C4×C14912yescomplemented
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—44no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C22×C4×C14911yescharacteristic
453C22×C4C2×D4×C14911yescharacteristic
454C22×C4C2×D4×C14911yescharacteristic
455C22×C4C2×D4×C14911yescharacteristic
456C22×C4C2×D4×C14911yescharacteristic
457C22×C4C2×D4×C14911yescharacteristic
458C22×C4C2×D4×C14911yescharacteristic
459C22×C4C2×Q8×C14911yescharacteristic
460C22×C4#41×C14911yescharacteristic
461C22×C4#41×C14911yescharacteristic
462C22×C4#41×C14911yescharacteristic
463C22×C4#41×C14911yescharacteristic
464C22×C4#41×C14911yescharacteristic
465C22×C4#41×C14911yescharacteristic
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—48no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—41no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—41no—
498C42—41no—
499C42—41no—
500C42—41no—
501C42—41no—
502C42C22⋊C4×C14914yes—
503C23—22no—
504C23—42no—
505C23—41no—
506C23—41no—
507C23—82no—
508C23C4×D4×C14911yescharacteristic
509C23#120×C14911yescharacteristic
510C23#120×C14911yescharacteristic
511C23#121×C14911yescharacteristic
512C23#121×C14911yescharacteristic
513C23C22⋊Q8×C14911yescharacteristic
514C23#124×C14911yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—41no—
518Q8—41no—
519D4—22no—
520D4—22no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—41no—
526D4—41no—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—82no—
545C2×C4C2×C22⋊C4×C14911yescharacteristic
546C2×C4C2×C4⋊C4×C14911yescharacteristic
547C2×C4#117×C14911yescharacteristic
548C2×C4C4×D4×C14911yescharacteristic
549C2×C4C4×D4×C14911yescharacteristic
550C2×C4C4×D4×C14911yescharacteristic
551C2×C4#120×C14911yescharacteristic
552C2×C4#121×C14911yescharacteristic
553C2×C4#121×C14911yescharacteristic
554C2×C4#121×C14911yescharacteristic
555C2×C4#121×C14911yescharacteristic
556C2×C4#121×C14911yescharacteristic
557C2×C4#121×C14911yescharacteristic
558C2×C4C22⋊Q8×C14911yescharacteristic
559C2×C4C22⋊Q8×C14911yescharacteristic
560C2×C4C22⋊Q8×C14911yescharacteristic
561C2×C4C22⋊Q8×C14911yescharacteristic
562C2×C4C22⋊Q8×C14911yescharacteristic
563C2×C4#123×C14911yescharacteristic
564C2×C4#123×C14911yescharacteristic
565C2×C4#123×C14911yescharacteristic
566C2×C4#123×C14911yescharacteristic
567C2×C4#123×C14911yescharacteristic
568C2×C4#124×C14911yescharacteristic
569C2×C4#124×C14911yescharacteristic
570C2×C4#126×C14911yescharacteristic
571C2×C4#126×C14911yescharacteristic
572C2×C4#127×C14911yescharacteristic
573C8—42no—
574C8—42no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22#385×C14911yescharacteristic
587C22#386×C14911yescharacteristic
588C22#388×C14911yescharacteristic
589C22#392×C14911yescharacteristic
590C22#393×C14911yescharacteristic
591C22#394×C14911yescharacteristic
592C22#396×C14911yescharacteristic
593C4—44no—
594C4—44no—
595C4—42no—
596C4—82no—
597C4—82no—
598C4#380×C14911yescharacteristic
599C4#385×C14911yescharacteristic
600C4#388×C14911yescharacteristic
601C4#390×C14911yescharacteristic
602C4#394×C14911yescharacteristic
603C4#396×C14911yescharacteristic
604C4#397×C14911yescharacteristic
605C4#399×C14911yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—82no—
613C2#1439×C14911yescharacteristic
614C2#2031×C14912yes—
subgroupG/H
centerC2×C4×C149#124
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
socleC22×C149#393
prime radicalC22×#41×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
4. #2296×C149C2semidirect
5. C2×#344×C149C2semidirect
6. C2×#339×C149C2semidirect
7. C2×H(3,ℤ/4)×C149C2semidirect
16. #421×C149C4semidirect
117. C2×Q8×C149C4⋊C4semidirect
129. C2×D4×C149C4⋊C4semidirect
307. #11085C149direct (N × H)
308. C149#11085direct (N × H)
312. #2296C2×C149semidirect
313. C2×#344C2×C149semidirect
314. C2×#339C2×C149semidirect
315. C2×H(3,ℤ/4)C2×C149semidirect
324. #421C4×C149semidirect
425. C2×Q8C4⋊C4×C149semidirect
437. C2×D4C4⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#421×C1492
C22×#104×C1492
C2×#410×C1492
#2296×C1492
C2×#344×C1492
C2×#339×C1492
C2×H(3,ℤ/4)×C1492
#11085149