Finite Group Databasebeta

← C149×#11068 #49190017

Subgroups — C149×#11068 #49190017

Order 38144.

934 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
1C2×#424×C149C211yesmaximal, characteristic, complemented
2C22×#104×C149C211yesmaximal, characteristic
3C2×#416×C149C211yesmaximal, characteristic
4C2×#408×C149C211yesmaximal, characteristic
5C2×#341×C149C211yesmaximal, characteristic, complemented
6C2×#339×C149C211yesmaximal, characteristic, complemented
7C2×#336×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C22×M16×C149C2211yescharacteristic
11C23×C8×C149C2211yescharacteristic
12C23×C8×C149C2211yescharacteristic
13C2×#117×C149C2211yescharacteristic
14C22×C42×C149C2211yescharacteristic
15#424×C149—22no—
16#424×C149—22no—
17C2×C4⋊C8×C149—22no—
18C2×#104×C149—22no—
19C2×#104×C149—22no—
20C2×#104×C149—22no—
21#416×C149—22no—
22#416×C149—22no—
23C2×#103×C149C412yescomplemented
24C2×#102×C149C412yescomplemented
25#408×C149—22no—
26#408×C149—22no—
27C2×C22⋊C8×C149—22no—
28#341×C149—22no—
29#339×C149—22no—
30#336×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×C149D412yes—
42C2×#41×C149Q812yes—
43C22×Q8×C149C2×C411yescharacteristic
44C22×D4×C149—21no—
45C22×D4×C149C2×C411yescharacteristic
46C23×C4×C149—21no—
47C23×C4×C149—21no—
48C23×C4×C149C2311yescharacteristic
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×C149—21no—
59C2×M16×C149D412yes—
60C2×M16×C149D412yes—
61C22×C8×C149—21no—
62C22×C8×C149—21no—
63C22×C8×C149—21no—
64C22×C8×C149—21no—
65C22×C8×C149—21no—
66C22×C8×C149—21no—
67C22×C8×C149—21no—
68C22×C8×C149—21no—
69C22×C8×C149—21no—
70C22×C8×C149—21no—
71C22×C8×C149—21no—
72C22×C8×C149—21no—
73C22×C8×C149—21no—
74C22×C8×C149—21no—
75C22×C8×C149C2×C412yes—
76C22×C8×C149D412yes—
77#117×C149—21no—
78#117×C149—21no—
79#117×C149D412yes—
80#117×C149D412yes—
81C2×C4⋊C4×C149C2×C412yes—
82C2×C22⋊C4×C149—21no—
83C2×C42×C149—21no—
84C2×C42×C149—21no—
85C2×C42×C149—21no—
86C2×C42×C149—21no—
87C2×C42×C149—21no—
88C2×C42×C149—21no—
89C2×C42×C149D412yes—
90C4⋊C8×C149—28no—
91#104×C149—28no—
92#103×C149—24no—
93#102×C149—24no—
94C22⋊C8×C149—28no—
95C24×C149—21no—
96C24×C149#4111yescharacteristic
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—22no—
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—
113C2×Q8×C149—21no—
114C2×Q8×C149—21no—
115C2×Q8×C149—21no—
116C2×Q8×C149—21no—
117C2×Q8×C149—21no—
118C2×Q8×C149C4⋊C412yes—
119C2×D4×C149—22no—
120C2×D4×C149—22no—
121C2×D4×C149—21no—
122C2×D4×C149—21no—
123C2×D4×C149—21no—
124C2×D4×C149—21no—
125C2×D4×C149—21no—
126C2×D4×C149—41no—
127C2×D4×C149—41no—
128C2×D4×C149—41no—
129C2×D4×C149—41no—
130C2×D4×C149C4⋊C412yes—
131C22×C4×C149—24no—
132C22×C4×C149—22no—
133C22×C4×C149—21no—
134C22×C4×C149—22no—
135C22×C4×C149—22no—
136C22×C4×C149—22no—
137C22×C4×C149—42no—
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×D411yescharacteristic
152C22×C4×C149C2×Q811yescharacteristic
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—22no—
169C2×C8×C149—22no—
170C2×C8×C149—22no—
171C2×C8×C149—22no—
172C2×C8×C149—22no—
173C2×C8×C149—22no—
174C2×C8×C149—41no—
175C2×C8×C149—41no—
176C2×C8×C149—41no—
177C2×C8×C149—41no—
178C2×C8×C149—41no—
179C2×C8×C149—41no—
180C2×C8×C149—41no—
181C2×C8×C149—41no—
182C2×C8×C149—41no—
183C2×C8×C149—41no—
184C2×C8×C149—41no—
185C2×C8×C149—41no—
186C4⋊C4×C149—22no—
187C4⋊C4×C149C22⋊C414yes—
188C22⋊C4×C149—22no—
189C22⋊C4×C149—22no—
190C42×C149—22no—
191C42×C149—22no—
192C42×C149—22no—
193C42×C149—22no—
194C42×C149—41no—
195C42×C149—41no—
196C23×C149—22no—
197C23×C149—22no—
198C23×C149—22no—
199C23×C149—41no—
200C23×C149—41no—
201C23×C149—42no—
202C23×C149—42no—
203C23×C149C4×D411yescharacteristic
204C23×C149#12111yescharacteristic
205C23×C149C22⋊Q811yescharacteristic
206C23×C149#12311yescharacteristic
207C23×C149#12311yescharacteristic
208C23×C149#12311yescharacteristic
209C23×C149#12611yescharacteristic
210Q8×C149—22no—
211Q8×C149—22no—
212Q8×C149—41no—
213Q8×C149—41no—
214D4×C149—22no—
215D4×C149—22no—
216D4×C149—42no—
217D4×C149—42no—
218D4×C149—42no—
219D4×C149—42no—
220D4×C149—41no—
221D4×C149—41no—
222C2×C4×C149—24no—
223C2×C4×C149—22no—
224C2×C4×C149—24no—
225C2×C4×C149—44no—
226C2×C4×C149—44no—
227C2×C4×C149—42no—
228C2×C4×C149—41no—
229C2×C4×C149—41no—
230C2×C4×C149—42no—
231C2×C4×C149—42no—
232C2×C4×C149—42no—
233C2×C4×C149—42no—
234C2×C4×C149—42no—
235C2×C4×C149—42no—
236C2×C4×C149—42no—
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#12011yescharacteristic
245C2×C4×C149#12011yescharacteristic
246C2×C4×C149#12111yescharacteristic
247C2×C4×C149#12111yescharacteristic
248C2×C4×C149#12111yescharacteristic
249C2×C4×C149#12111yescharacteristic
250C2×C4×C149#12111yescharacteristic
251C2×C4×C149#12111yescharacteristic
252C2×C4×C149#12111yescharacteristic
253C2×C4×C149C22⋊Q811yescharacteristic
254C2×C4×C149C22⋊Q811yescharacteristic
255C2×C4×C149C22⋊Q811yescharacteristic
256C2×C4×C149C22⋊Q811yescharacteristic
257C2×C4×C149C22⋊Q811yescharacteristic
258C2×C4×C149#12311yescharacteristic
259C2×C4×C149#12311yescharacteristic
260C2×C4×C149#12411yescharacteristic
261C2×C4×C149#12411yescharacteristic
262C2×C4×C149#12411yescharacteristic
263C2×C4×C149#12611yescharacteristic
264C2×C4×C149#12711yescharacteristic
265C8×C149—42no—
266C8×C149—42no—
267C8×C149—42no—
268C8×C149—42no—
269C22×C149—22no—
270C22×C149—22no—
271C22×C149—22no—
272C22×C149—22no—
273C22×C149—21no—
274C22×C149—21no—
275C22×C149—21no—
276C22×C149—21no—
277C22×C149—44no—
278C22×C149—42no—
279C22×C149—82no—
280C22×C149—81no—
281C22×C149—81no—
282C22×C149#38511yescharacteristic
283C22×C149#38611yescharacteristic
284C22×C149#38811yescharacteristic
285C22×C149#39411yescharacteristic
286C22×C149#39611yescharacteristic
287C22×C149#39711yescharacteristic
288C22×C149#39911yescharacteristic
289C22×C149#44312yes—
290C22×C149#44412yes—
291C4×C149—44no—
292C4×C149—44no—
293C4×C149—42no—
294C4×C149#38011yescharacteristic
295C4×C149#38511yescharacteristic
296C4×C149#38811yescharacteristic
297C4×C149#39011yescharacteristic
298C4×C149#39211yescharacteristic
299C4×C149#39311yescharacteristic
300C4×C149#39411yescharacteristic
301C4×C149#39611yescharacteristic
302C2×C149—21no—
303C2×C149—21no—
304C2×C149—21no—
305C2×C149—21no—
306C2×C149—82no—
307C2×C149#143911yescharacteristic
308C2×C149#186612yes—
309C2×C149#187612yes—
310C2×C149#193711yescharacteristic
311C2×C149#193811yescharacteristic
312#11068C14911yesmaximal, characteristic, direct product factor, Sylow
313C149#1106811yescharacteristic, direct product factor, Sylow
314C2×#424C2×C14911yescharacteristic, complemented
315C22×#104C2×C14911yescharacteristic
316C2×#416C2×C14911yescharacteristic
317C2×#408C2×C14911yescharacteristic
318C2×#341C2×C14911yescharacteristic, complemented
319C2×#339C2×C14911yescharacteristic, complemented
320C2×#336C2×C14911yescharacteristic, complemented
321C22×#41C22×C14911yescharacteristic
322C22×M16C22×C14911yescharacteristic
323C22×M16C22×C14911yescharacteristic
324C23×C8C22×C14911yescharacteristic
325C23×C8C22×C14911yescharacteristic
326C2×#117C22×C14911yescharacteristic
327C22×C42C22×C14911yescharacteristic
328#424—22no—
329#424—22no—
330C2×C4⋊C8—22no—
331C2×#104—22no—
332C2×#104—22no—
333C2×#104—22no—
334#416—22no—
335#416—22no—
336C2×#103C4×C14912yescomplemented
337C2×#102C4×C14912yescomplemented
338#408—22no—
339#408—22no—
340C2×C22⋊C8—22no—
341#341—22no—
342#339—22no—
343#336—22no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41D4×C14912yes—
355C2×#41Q8×C14912yes—
356C22×Q8C2×C4×C14911yescharacteristic
357C22×D4—21no—
358C22×D4C2×C4×C14911yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C23×C14911yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16D4×C14912yes—
373C2×M16D4×C14912yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8C2×C4×C14912yes—
389C22×C8D4×C14912yes—
390#117—21no—
391#117—21no—
392#117D4×C14912yes—
393#117D4×C14912yes—
394C2×C4⋊C4C2×C4×C14912yes—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42D4×C14912yes—
403C4⋊C8—28no—
404#104—28no—
405#103—24no—
406#102—24no—
407C22⋊C8—28no—
408C24—21no—
409C24#41×C14911yescharacteristic
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8C4⋊C4×C14912yes—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4C4⋊C4×C14912yes—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—42no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4C22×C4×C14911yescharacteristic
458C22×C4C2×D4×C14911yescharacteristic
459C22×C4C2×D4×C14911yescharacteristic
460C22×C4C2×D4×C14911yescharacteristic
461C22×C4C2×D4×C14911yescharacteristic
462C22×C4C2×D4×C14911yescharacteristic
463C22×C4C2×D4×C14911yescharacteristic
464C22×C4C2×D4×C14911yescharacteristic
465C22×C4C2×Q8×C14911yescharacteristic
466C22×C4#41×C14911yescharacteristic
467C22×C4#41×C14911yescharacteristic
468C22×C4#41×C14911yescharacteristic
469C22×C4#41×C14911yescharacteristic
470C22×C4#41×C14911yescharacteristic
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C4⋊C4—22no—
500C4⋊C4C22⋊C4×C14914yes—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—41no—
508C42—41no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—41no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23C4×D4×C14911yescharacteristic
517C23#121×C14911yescharacteristic
518C23C22⋊Q8×C14911yescharacteristic
519C23#123×C14911yescharacteristic
520C23#123×C14911yescharacteristic
521C23#123×C14911yescharacteristic
522C23#126×C14911yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527D4—22no—
528D4—22no—
529D4—42no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—41no—
534D4—41no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4C2×C22⋊C4×C14911yescharacteristic
551C2×C4C2×C4⋊C4×C14911yescharacteristic
552C2×C4#117×C14911yescharacteristic
553C2×C4C4×D4×C14911yescharacteristic
554C2×C4C4×D4×C14911yescharacteristic
555C2×C4C4×D4×C14911yescharacteristic
556C2×C4#120×C14911yescharacteristic
557C2×C4#120×C14911yescharacteristic
558C2×C4#120×C14911yescharacteristic
559C2×C4#121×C14911yescharacteristic
560C2×C4#121×C14911yescharacteristic
561C2×C4#121×C14911yescharacteristic
562C2×C4#121×C14911yescharacteristic
563C2×C4#121×C14911yescharacteristic
564C2×C4#121×C14911yescharacteristic
565C2×C4#121×C14911yescharacteristic
566C2×C4C22⋊Q8×C14911yescharacteristic
567C2×C4C22⋊Q8×C14911yescharacteristic
568C2×C4C22⋊Q8×C14911yescharacteristic
569C2×C4C22⋊Q8×C14911yescharacteristic
570C2×C4C22⋊Q8×C14911yescharacteristic
571C2×C4#123×C14911yescharacteristic
572C2×C4#123×C14911yescharacteristic
573C2×C4#124×C14911yescharacteristic
574C2×C4#124×C14911yescharacteristic
575C2×C4#124×C14911yescharacteristic
576C2×C4#126×C14911yescharacteristic
577C2×C4#127×C14911yescharacteristic
578C8—42no—
579C8—42no—
580C8—42no—
581C8—42no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—22no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—42no—
591C22—44no—
592C22—81no—
593C22—81no—
594C22—82no—
595C22#385×C14911yescharacteristic
596C22#386×C14911yescharacteristic
597C22#388×C14911yescharacteristic
598C22#394×C14911yescharacteristic
599C22#396×C14911yescharacteristic
600C22#397×C14911yescharacteristic
601C22#399×C14911yescharacteristic
602C22#443×C14912yes—
603C22#444×C14912yes—
604C4—44no—
605C4—42no—
606C4—44no—
607C4#380×C14911yescharacteristic
608C4#385×C14911yescharacteristic
609C4#388×C14911yescharacteristic
610C4#390×C14911yescharacteristic
611C4#392×C14911yescharacteristic
612C4#393×C14911yescharacteristic
613C4#394×C14911yescharacteristic
614C4#396×C14911yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—82no—
620C2#1439×C14911yescharacteristic
621C2#1866×C14912yes—
622C2#1876×C14912yes—
623C2#1937×C14911yescharacteristic
624C2#1938×C14911yescharacteristic
subgroupG/H
centerC22×C4×C149C2×D4
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
socleC23×C149C4×D4
prime radicalC22×#41×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C149 ◁ C23×C8×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#424×C149C2semidirect
5. C2×#341×C149C2semidirect
6. C2×#339×C149C2semidirect
7. C2×#336×C149C2semidirect
23. C2×#103×C149C4semidirect
24. C2×#102×C149C4semidirect
312. #11068C149direct (N × H)
313. C149#11068direct (N × H)
314. C2×#424C2×C149semidirect
318. C2×#341C2×C149semidirect
319. C2×#339C2×C149semidirect
320. C2×#336C2×C149semidirect
336. C2×#103C4×C149semidirect
337. C2×#102C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#424×C1492
C22×#104×C1492
C2×#416×C1492
C2×#408×C1492
C2×#341×C1492
C2×#339×C1492
C2×#336×C1492
#11068149