Finite Group Databasebeta

← C149×#11120 #49190069

Subgroups — C149×#11120 #49190069

Order 38144.

870 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×#430×C149C211yesmaximal, characteristic, complemented
2C2×#421×C149C211yesmaximal, characteristic
3C2×#417×C149C211yesmaximal, characteristic
4C2×#413×C149C211yesmaximal, characteristic
5C2×#344×C149C211yesmaximal, characteristic, complemented
6C2×#343×C149C211yesmaximal, characteristic, complemented
7#1736×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C22×M16×C149C2211yescharacteristic
11C22×M16×C149C2211yescharacteristic
12C22×M16×C149C2211yescharacteristic
13C2×#117×C149C2211yescharacteristic
14C22×C4⋊C4×C149C2211yescharacteristic
15#430×C149—22no—
16#430×C149—22no—
17C2×#108×C149—22no—
18#421×C149—22no—
19#421×C149C414yescomplemented
20C2×#104×C149—22no—
21#417×C149—22no—
22#417×C149—22no—
23C2×#103×C149—21no—
24C2×#102×C149—21no—
25#413×C149—22no—
26#413×C149—22no—
27C2×#101×C149—21no—
28C2×#100×C149—21no—
29#344×C149—22no—
30#343×C149—22no—
31#340×C149—22no—
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×C149C2×C412yes—
43C2×#41×C149Q812yes—
44C22×Q8×C149D411yescharacteristic
45C22×D4×C149—21no—
46C22×D4×C149D411yescharacteristic
47C23×C4×C149—21no—
48C23×C4×C149—21no—
49C23×C4×C149C2311yescharacteristic
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×C149—21no—
60C2×M16×C149—21no—
61C2×M16×C149—21no—
62C2×M16×C149—21no—
63C2×M16×C149—21no—
64C2×M16×C149—21no—
65C2×M16×C149—21no—
66C2×M16×C149—21no—
67C2×M16×C149—21no—
68C2×M16×C149C2×C412yes—
69C2×M16×C149D412yes—
70C2×M16×C149D412yes—
71C2×M16×C149D412yes—
72C2×M16×C149D412yes—
73C2×M16×C149D412yes—
74C22×C8×C149—21no—
75C22×C8×C149—21no—
76C22×C8×C149—21no—
77C22×C8×C149—21no—
78#117×C149—21no—
79#117×C149—21no—
80#117×C149—21no—
81#117×C149C2×C412yes—
82C2×C4⋊C4×C149—21no—
83C2×C4⋊C4×C149—21no—
84C2×C4⋊C4×C149—21no—
85C2×C4⋊C4×C149—21no—
86C2×C4⋊C4×C149—21no—
87C2×C4⋊C4×C149—21no—
88C2×C4⋊C4×C149D412yes—
89C2×C22⋊C4×C149—21no—
90C2×C42×C149—21no—
91#108×C149—28no—
92#104×C149—28no—
93#103×C149—24no—
94#102×C149—24no—
95#101×C149—24no—
96#100×C149—24no—
97C24×C149—21no—
98C24×C149#4111yescharacteristic
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—22no—
106#41×C149—22no—
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—
114#41×C149—41no—
115C2×Q8×C149—21no—
116C2×Q8×C149—21no—
117C2×Q8×C149—21no—
118C2×Q8×C149—21no—
119C2×Q8×C149—21no—
120C2×Q8×C149C4⋊C412yes—
121C2×D4×C149—22no—
122C2×D4×C149—22no—
123C2×D4×C149—21no—
124C2×D4×C149—21no—
125C2×D4×C149—21no—
126C2×D4×C149—21no—
127C2×D4×C149—21no—
128C2×D4×C149—41no—
129C2×D4×C149—41no—
130C2×D4×C149—41no—
131C2×D4×C149—41no—
132C2×D4×C149C4⋊C412yes—
133C22×C4×C149—21no—
134C22×C4×C149—22no—
135C22×C4×C149—22no—
136C22×C4×C149—22no—
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×C149—82no—
145C22×C4×C149C22×C411yescharacteristic
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×D411yescharacteristic
153C22×C4×C149C2×Q811yescharacteristic
154C22×C4×C149#4111yescharacteristic
155C22×C4×C149#4111yescharacteristic
156C22×C4×C149#4111yescharacteristic
157C22×C4×C149#4111yescharacteristic
158C22×C4×C149#4111yescharacteristic
159M16×C149—22no—
160M16×C149—22no—
161M16×C149—22no—
162M16×C149—22no—
163M16×C149—22no—
164M16×C149—22no—
165M16×C149—22no—
166M16×C149—22no—
167M16×C149—22no—
168M16×C149—41no—
169M16×C149—41no—
170M16×C149—41no—
171M16×C149—41no—
172M16×C149—41no—
173M16×C149—41no—
174M16×C149C22⋊C414yes—
175C2×C8×C149—22no—
176C2×C8×C149—22no—
177C2×C8×C149—22no—
178C2×C8×C149—22no—
179C2×C8×C149—22no—
180C2×C8×C149—22no—
181C2×C8×C149—41no—
182C2×C8×C149—41no—
183C2×C8×C149—41no—
184C2×C8×C149—41no—
185C2×C8×C149—41no—
186C2×C8×C149—41no—
187C4⋊C4×C149—22no—
188C4⋊C4×C149—22no—
189C4⋊C4×C149—22no—
190C4⋊C4×C149—41no—
191C4⋊C4×C149—41no—
192C4⋊C4×C149—41no—
193C22⋊C4×C149—22no—
194C22⋊C4×C149—41no—
195C42×C149—22no—
196C42×C149—41no—
197C23×C149—22no—
198C23×C149—41no—
199C23×C149—41no—
200C23×C149—41no—
201C23×C149—41no—
202C23×C149—81no—
203C23×C149—81no—
204C23×C149C4×D411yescharacteristic
205C23×C149#12111yescharacteristic
206C23×C149C22⋊Q811yescharacteristic
207C23×C149#12311yescharacteristic
208C23×C149#12411yescharacteristic
209C23×C149#12411yescharacteristic
210C23×C149#12611yescharacteristic
211Q8×C149—22no—
212Q8×C149—22no—
213Q8×C149—41no—
214Q8×C149—41no—
215D4×C149—22no—
216D4×C149—22no—
217D4×C149—42no—
218D4×C149—42no—
219D4×C149—42no—
220D4×C149—42no—
221D4×C149—41no—
222D4×C149—41no—
223C2×C4×C149—22no—
224C2×C4×C149—41no—
225C2×C4×C149—41no—
226C2×C4×C149—42no—
227C2×C4×C149—42no—
228C2×C4×C149—42no—
229C2×C4×C149—42no—
230C2×C4×C149—42no—
231C2×C4×C149—42no—
232C2×C4×C149—81no—
233C2×C4×C149—81no—
234C2×C4×C149—82no—
235C2×C4×C149—82no—
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#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#12311yescharacteristic
261C2×C4×C149#12311yescharacteristic
262C2×C4×C149#12411yescharacteristic
263C2×C4×C149#12611yescharacteristic
264C2×C4×C149#12711yescharacteristic
265C8×C149—24no—
266C8×C149—42no—
267C8×C149—42no—
268C8×C149—42no—
269C22×C149—21no—
270C22×C149—21no—
271C22×C149—21no—
272C22×C149—21no—
273C22×C149—21no—
274C22×C149—21no—
275C22×C149—41no—
276C22×C149—41no—
277C22×C149—41no—
278C22×C149—41no—
279C22×C149—42no—
280C22×C149—82no—
281C22×C149—82no—
282C22×C149—81no—
283C22×C149—81no—
284C22×C149#38511yescharacteristic
285C22×C149#38811yescharacteristic
286C22×C149#39011yescharacteristic
287C22×C149#39311yescharacteristic
288C22×C149#39411yescharacteristic
289C22×C149#39611yescharacteristic
290C22×C149#39711yescharacteristic
291C4×C149—42no—
292C4×C149—82no—
293C4×C149—82no—
294C4×C149#38011yescharacteristic
295C4×C149#38511yescharacteristic
296C4×C149#38611yescharacteristic
297C4×C149#38811yescharacteristic
298C4×C149#39211yescharacteristic
299C4×C149#39411yescharacteristic
300C4×C149#39611yescharacteristic
301C4×C149#39911yescharacteristic
302C2×C149—21no—
303C2×C149—21no—
304C2×C149—21no—
305C2×C149—21no—
306C2×C149—21no—
307C2×C149—21no—
308C2×C149—82no—
309C2×C149#143911yescharacteristic
310C2×C149#204811yescharacteristic
311C2×C149#204911yescharacteristic
312#11120C14911yesmaximal, characteristic, direct product factor, Sylow
313C149#1112011yescharacteristic, direct product factor, Sylow
314C2×#430C2×C14911yescharacteristic, complemented
315C2×#421C2×C14911yescharacteristic
316C2×#417C2×C14911yescharacteristic
317C2×#413C2×C14911yescharacteristic
318C2×#344C2×C14911yescharacteristic, complemented
319C2×#343C2×C14911yescharacteristic, complemented
320#1736C2×C14911yescharacteristic, complemented
321C22×#41C22×C14911yescharacteristic
322C22×M16C22×C14911yescharacteristic
323C22×M16C22×C14911yescharacteristic
324C22×M16C22×C14911yescharacteristic
325C22×M16C22×C14911yescharacteristic
326C2×#117C22×C14911yescharacteristic
327C22×C4⋊C4C22×C14911yescharacteristic
328#430—22no—
329#430—22no—
330C2×#108—22no—
331#421—22no—
332#421C4×C14914yescomplemented
333C2×#104—22no—
334#417—22no—
335#417—22no—
336C2×#103—21no—
337C2×#102—21no—
338#413—22no—
339#413—22no—
340C2×#101—21no—
341C2×#100—21no—
342#344—22no—
343#343—22no—
344#340—22no—
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×#41—21no—
355C2×#41C2×C4×C14912yes—
356C2×#41Q8×C14912yes—
357C22×Q8D4×C14911yescharacteristic
358C22×D4—21no—
359C22×D4D4×C14911yescharacteristic
360C23×C4—21no—
361C23×C4—21no—
362C23×C4C23×C14911yescharacteristic
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×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16C2×C4×C14912yes—
382C2×M16D4×C14912yes—
383C2×M16D4×C14912yes—
384C2×M16D4×C14912yes—
385C2×M16D4×C14912yes—
386C2×M16D4×C14912yes—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390C22×C8—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117C2×C4×C14912yes—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4D4×C14912yes—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404#108—28no—
405#104—28no—
406#103—24no—
407#102—24no—
408#101—24no—
409#100—24no—
410C24—21no—
411C24#41×C14911yescharacteristic
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C4⋊C4×C14912yes—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4C4⋊C4×C14912yes—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—82no—
458C22×C4C22×C4×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×D4×C14911yescharacteristic
466C22×C4C2×Q8×C14911yescharacteristic
467C22×C4#41×C14911yescharacteristic
468C22×C4#41×C14911yescharacteristic
469C22×C4#41×C14911yescharacteristic
470C22×C4#41×C14911yescharacteristic
471C22×C4#41×C14911yescharacteristic
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16C22⋊C4×C14914yes—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C42—22no—
509C42—41no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—81no—
516C23—81no—
517C23C4×D4×C14911yescharacteristic
518C23#121×C14911yescharacteristic
519C23C22⋊Q8×C14911yescharacteristic
520C23#123×C14911yescharacteristic
521C23#124×C14911yescharacteristic
522C23#124×C14911yescharacteristic
523C23#126×C14911yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—41no—
535D4—41no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—82no—
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#123×C14911yescharacteristic
574C2×C4#123×C14911yescharacteristic
575C2×C4#124×C14911yescharacteristic
576C2×C4#126×C14911yescharacteristic
577C2×C4#127×C14911yescharacteristic
578C8—24no—
579C8—42no—
580C8—42no—
581C8—42no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—81no—
596C22—81no—
597C22#385×C14911yescharacteristic
598C22#388×C14911yescharacteristic
599C22#390×C14911yescharacteristic
600C22#393×C14911yescharacteristic
601C22#394×C14911yescharacteristic
602C22#396×C14911yescharacteristic
603C22#397×C14911yescharacteristic
604C4—42no—
605C4—82no—
606C4—82no—
607C4#380×C14911yescharacteristic
608C4#385×C14911yescharacteristic
609C4#386×C14911yescharacteristic
610C4#388×C14911yescharacteristic
611C4#392×C14911yescharacteristic
612C4#394×C14911yescharacteristic
613C4#396×C14911yescharacteristic
614C4#399×C14911yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—82no—
622C2#1439×C14911yescharacteristic
623C2#2048×C14911yescharacteristic
624C2#2049×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#394
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radicalC22×#41×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#430×C149C2semidirect
5. C2×#344×C149C2semidirect
6. C2×#343×C149C2semidirect
7. #1736×C149C2semidirect
19. #421×C149C4semidirect
312. #11120C149direct (N × H)
313. C149#11120direct (N × H)
314. C2×#430C2×C149semidirect
318. C2×#344C2×C149semidirect
319. C2×#343C2×C149semidirect
320. #1736C2×C149semidirect
332. #421C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#430×C1492
C2×#421×C1492
C2×#417×C1492
C2×#413×C1492
C2×#344×C1492
C2×#343×C1492
#1736×C1492
#11120149