Finite Group Databasebeta

← C149×#10745 #49189694

Subgroups — C149×#10745 #49189694

Order 38144.

1794 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C149C211yesmaximal, characteristic
2C22×#99×C149C211yesmaximal, characteristic
3C2×#386×C149C211yesmaximal, characteristic
4C2×#342×C149C212yesmaximal, complemented
5C22⋊#95×C149C212yesmaximal, complemented
6C23×D4×C149C2211yescharacteristic
7C24×C4×C149C2211yescharacteristic
8#518×C149—22no—
9#518×C149—24no—
10#518×C149C414yescomplemented
11C2×C4×D4×C149—24no—
12C2×#117×C149—21no—
13C22×C22⋊C4×C149—21no—
14C22×C22⋊C4×C149—21no—
15C22×C22⋊C4×C149C2212yes—
16C22×C22⋊C4×C149C2211yescharacteristic
17C22×C22⋊C4×C149C2212yes—
18C2×#99×C149—22no—
19C2×#99×C149—22no—
20C2×#99×C149C414yescomplemented
21#386×C149—22no—
22#386×C149C414yescomplemented
23C2×#95×C149—21no—
24C2×#95×C149—24no—
25#342×C149—24no—
26C25×C149D411yescharacteristic
27C25×C149C2311yescharacteristic
28C22×D4×C149—22no—
29C22×D4×C149—22no—
30C22×D4×C149—22no—
31C22×D4×C149—22no—
32C22×D4×C149C2×C412yes—
33C22×D4×C149C2×C412yes—
34C22×D4×C149C2×C412yes—
35C22×D4×C149D412yes—
36C22×D4×C149D412yes—
37C22×D4×C149Q812yes—
38C23×C4×C149—22no—
39C23×C4×C149—21no—
40C23×C4×C149—22no—
41C23×C4×C149—22no—
42C23×C4×C149—21no—
43C23×C4×C149—21no—
44C23×C4×C149—22no—
45C23×C4×C149—44no—
46C23×C4×C149C2×C412yescomplemented
47C23×C4×C149D411yescharacteristic
48C23×C4×C149D414yes—
49C4×D4×C149—216no—
50C4×D4×C149—216no—
51#117×C149—24no—
52#117×C149—24no—
53C2×C4⋊C4×C149—22no—
54C2×C22⋊C4×C149—22no—
55C2×C22⋊C4×C149—24no—
56C2×C22⋊C4×C149—24no—
57C2×C22⋊C4×C149—22no—
58C2×C22⋊C4×C149—22no—
59C2×C22⋊C4×C149—22no—
60C2×C22⋊C4×C149—22no—
61C2×C22⋊C4×C149—22no—
62C2×C22⋊C4×C149—22no—
63C2×C22⋊C4×C149—22no—
64C2×C22⋊C4×C149—22no—
65C2×C22⋊C4×C149—22no—
66C2×C22⋊C4×C149—22no—
67C2×C22⋊C4×C149—24no—
68C2×C22⋊C4×C149—21no—
69C2×C22⋊C4×C149—22no—
70C2×C22⋊C4×C149—44no—
71C2×C22⋊C4×C149C2×C414yes—
72C2×C22⋊C4×C149C2×C412yescomplemented
73C2×C22⋊C4×C149C2×C414yescomplemented
74C2×C22⋊C4×C149D414yes—
75C2×C42×C149—22no—
76#99×C149—28no—
77#95×C149—24no—
78#95×C149—48no—
79C24×C149—21no—
80C24×C149—21no—
81C24×C149—21no—
82C24×C149—21no—
83C24×C149—42no—
84C24×C149—42no—
85C24×C149—42no—
86C24×C149—42no—
87C24×C149C22⋊C412yes—
88C24×C149C22⋊C412yes—
89C24×C149C4⋊C412yes—
90C24×C149C22×C411yescharacteristic
91C24×C149C22×C411yescharacteristic
92C24×C149C22×C411yescharacteristic
93C24×C149C2×D411yescharacteristic
94C24×C149C2×D412yes—
95C24×C149C2×D411yescharacteristic
96C24×C149C2×D411yescharacteristic
97C24×C149C2×D412yes—
98C24×C149C2×Q811yescharacteristic
99C24×C149#4112yes—
100C24×C149#4112yes—
101C2×D4×C149—24no—
102C2×D4×C149—24no—
103C2×D4×C149—24no—
104C2×D4×C149—24no—
105C2×D4×C149—24no—
106C2×D4×C149—24no—
107C2×D4×C149—24no—
108C2×D4×C149—24no—
109C2×D4×C149—24no—
110C2×D4×C149—24no—
111C2×D4×C149—24no—
112C2×D4×C149—24no—
113C2×D4×C149C4214yes—
114C2×D4×C149C22⋊C414yes—
115C2×D4×C149C4⋊C414yes—
116C2×D4×C149C4⋊C414yes—
117C22×C4×C149—21no—
118C22×C4×C149—21no—
119C22×C4×C149—21no—
120C22×C4×C149—21no—
121C22×C4×C149—28no—
122C22×C4×C149—24no—
123C22×C4×C149—22no—
124C22×C4×C149—24no—
125C22×C4×C149—24no—
126C22×C4×C149—28no—
127C22×C4×C149—24no—
128C22×C4×C149—22no—
129C22×C4×C149—24no—
130C22×C4×C149—44no—
131C22×C4×C149—44no—
132C22×C4×C149—48no—
133C22×C4×C149—44no—
134C22×C4×C149—42no—
135C22×C4×C149—41no—
136C22×C4×C149—42no—
137C22×C4×C149—41no—
138C22×C4×C149—44no—
139C22×C4×C149—44no—
140C22×C4×C149—44no—
141C22×C4×C149—42no—
142C22×C4×C149—44no—
143C22×C4×C149—42no—
144C22×C4×C149—41no—
145C22×C4×C149—42no—
146C22×C4×C149—42no—
147C22×C4×C149—41no—
148C22×C4×C149—82no—
149C22×C4×C149—82no—
150C22×C4×C149C22⋊C412yes—
151C22×C4×C149C22⋊C412yes—
152C22×C4×C149C22⋊C418yescomplemented
153C22×C4×C149C4⋊C412yes—
154C4⋊C4×C149—28no—
155C22⋊C4×C149—28no—
156C22⋊C4×C149—24no—
157C22⋊C4×C149—24no—
158C22⋊C4×C149—24no—
159C22⋊C4×C149—24no—
160C22⋊C4×C149—24no—
161C22⋊C4×C149—24no—
162C22⋊C4×C149—24no—
163C22⋊C4×C149—48no—
164C22⋊C4×C149—42no—
165C22⋊C4×C149—42no—
166C22⋊C4×C149—42no—
167C42×C149—28no—
168C23×C149—24no—
169C23×C149—22no—
170C23×C149—24no—
171C23×C149—22no—
172C23×C149—22no—
173C23×C149—22no—
174C23×C149—22no—
175C23×C149—22no—
176C23×C149—22no—
177C23×C149—22no—
178C23×C149—41no—
179C23×C149—41no—
180C23×C149—42no—
181C23×C149—42no—
182C23×C149—41no—
183C23×C149—42no—
184C23×C149—41no—
185C23×C149—44no—
186C23×C149—42no—
187C23×C149—42no—
188C23×C149—44no—
189C23×C149—42no—
190C23×C149—42no—
191C23×C149—42no—
192C23×C149—44no—
193C23×C149—44no—
194C23×C149—42no—
195C23×C149—42no—
196C23×C149—82no—
197C23×C149—81no—
198C23×C149—81no—
199C23×C149—82no—
200C23×C149#9514yescomplemented
201C23×C149C2×C4211yescharacteristic
202C23×C149C2×C22⋊C411yescharacteristic
203C23×C149C2×C22⋊C411yescharacteristic
204C23×C149C2×C22⋊C412yes—
205C23×C149C2×C22⋊C411yescharacteristic
206C23×C149C2×C4⋊C411yescharacteristic
207C23×C149C2×C4⋊C411yescharacteristic
208C23×C149C2×C4⋊C411yescharacteristic
209C23×C149#11712yes—
210C23×C149C4×D412yes—
211C23×C149C4×D412yes—
212C23×C149C4×D412yes—
213C23×C149C4×D412yes—
214C23×C149#12011yescharacteristic
215C23×C149#12012yes—
216C23×C149#12011yescharacteristic
217C23×C149#12112yes—
218C23×C149#12112yes—
219C23×C149C22⋊Q812yes—
220C23×C149C22⋊Q812yes—
221C23×C149#12311yescharacteristic
222C23×C149#12311yescharacteristic
223C23×C149#12312yes—
224D4×C149—28no—
225D4×C149—28no—
226D4×C149—28no—
227D4×C149—28no—
228C2×C4×C149—22no—
229C2×C4×C149—22no—
230C2×C4×C149—22no—
231C2×C4×C149—22no—
232C2×C4×C149—22no—
233C2×C4×C149—22no—
234C2×C4×C149—24no—
235C2×C4×C149—28no—
236C2×C4×C149—28no—
237C2×C4×C149—42no—
238C2×C4×C149—44no—
239C2×C4×C149—48no—
240C2×C4×C149—44no—
241C2×C4×C149—42no—
242C2×C4×C149—44no—
243C2×C4×C149—44no—
244C2×C4×C149—44no—
245C2×C4×C149—48no—
246C2×C4×C149—42no—
247C2×C4×C149—48no—
248C2×C4×C149—42no—
249C2×C4×C149—42no—
250C2×C4×C149—44no—
251C2×C4×C149—84no—
252C2×C4×C149—88no—
253C2×C4×C149—82no—
254C2×C4×C149—82no—
255C2×C4×C149—82no—
256C2×C4×C149—84no—
257C2×C4×C149—82no—
258C2×C4×C149#9514yescomplemented
259C22×C149—24no—
260C22×C149—22no—
261C22×C149—22no—
262C22×C149—24no—
263C22×C149—21no—
264C22×C149—22no—
265C22×C149—22no—
266C22×C149—21no—
267C22×C149—21no—
268C22×C149—22no—
269C22×C149—21no—
270C22×C149—22no—
271C22×C149—24no—
272C22×C149—24no—
273C22×C149—22no—
274C22×C149—22no—
275C22×C149—24no—
276C22×C149—41no—
277C22×C149—41no—
278C22×C149—41no—
279C22×C149—41no—
280C22×C149—42no—
281C22×C149—42no—
282C22×C149—42no—
283C22×C149—42no—
284C22×C149—42no—
285C22×C149—42no—
286C22×C149—44no—
287C22×C149—44no—
288C22×C149—42no—
289C22×C149—42no—
290C22×C149—44no—
291C22×C149—82no—
292C22×C149—82no—
293C22×C149—82no—
294C22×C149C2×#9511yescharacteristic
295C22×C149C4×C22⋊C412yes—
296C22×C149#37911yescharacteristic
297C22×C149#38012yes—
298C22×C149#38111yescharacteristic
299C22×C149#38511yescharacteristic
300C22×C149#38512yes—
301C22×C149#38511yescharacteristic
302C22×C149#38611yescharacteristic
303C22×C149#38612yes—
304C22×C149#38611yescharacteristic
305C22×C149B(4,𝔽2)12yes—
306C22×C149#45812yes—
307C4×C149—24no—
308C4×C149—44no—
309C4×C149—48no—
310C4×C149—82no—
311C4×C149—84no—
312C2×C149—21no—
313C2×C149—22no—
314C2×C149—21no—
315C2×C149—21no—
316C2×C149—21no—
317C2×C149—22no—
318C2×C149—22no—
319C2×C149—22no—
320C2×C149—44no—
321C2×C149C22⋊#9511yescharacteristic
322C2×C149#179012yes—
323C2×C149#186712yes—
324C2×C149#188911yescharacteristic
325C2×C149#189011yescharacteristic
326#10745C14911yesmaximal, characteristic, direct product factor, Sylow
327C149#1074511yescharacteristic, direct product factor, Sylow
328C2×#518C2×C14911yescharacteristic
329C22×#99C2×C14911yescharacteristic
330C2×#386C2×C14911yescharacteristic
331C2×#342C2×C14912yescomplemented
332C22⋊#95C2×C14912yescomplemented
333C23×D4C22×C14911yescharacteristic
334C24×C4C22×C14911yescharacteristic
335#518—22no—
336#518—24no—
337#518C4×C14914yescomplemented
338C2×C4×D4—24no—
339C2×#117—21no—
340C22×C22⋊C4—21no—
341C22×C22⋊C4—21no—
342C22×C22⋊C4C22×C14912yes—
343C22×C22⋊C4C22×C14911yescharacteristic
344C22×C22⋊C4C22×C14912yes—
345C2×#99—22no—
346C2×#99—22no—
347C2×#99C4×C14914yescomplemented
348#386—22no—
349#386C4×C14914yescomplemented
350C2×#95—21no—
351C2×#95—24no—
352#342—24no—
353C25D4×C14911yescharacteristic
354C25C23×C14911yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C2×C4×C14912yes—
360C22×D4C2×C4×C14912yes—
361C22×D4C2×C4×C14912yes—
362C22×D4D4×C14912yes—
363C22×D4D4×C14912yes—
364C22×D4Q8×C14912yes—
365C23×C4—21no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—22no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—44no—
373C23×C4C2×C4×C14912yescomplemented
374C23×C4D4×C14911yescharacteristic
375C23×C4D4×C14914yes—
376C4×D4—216no—
377C4×D4—216no—
378#117—24no—
379#117—24no—
380C2×C4⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×C4×C14914yes—
399C2×C22⋊C4C2×C4×C14912yescomplemented
400C2×C22⋊C4C2×C4×C14914yescomplemented
401C2×C22⋊C4D4×C14914yes—
402C2×C42—22no—
403#99—28no—
404#95—24no—
405#95—48no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24C22⋊C4×C14912yes—
415C24C22⋊C4×C14912yes—
416C24C4⋊C4×C14912yes—
417C24C22×C4×C14911yescharacteristic
418C24C22×C4×C14911yescharacteristic
419C24C22×C4×C14911yescharacteristic
420C24C2×D4×C14911yescharacteristic
421C24C2×D4×C14912yes—
422C24C2×D4×C14911yescharacteristic
423C24C2×D4×C14911yescharacteristic
424C24C2×D4×C14912yes—
425C24C2×Q8×C14911yescharacteristic
426C24#41×C14912yes—
427C24#41×C14912yes—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C42×C14914yes—
441C2×D4C22⋊C4×C14914yes—
442C2×D4C4⋊C4×C14914yes—
443C2×D4C4⋊C4×C14914yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4C22⋊C4×C14912yes—
478C22×C4C22⋊C4×C14912yes—
479C22×C4C22⋊C4×C14918yescomplemented
480C22×C4C4⋊C4×C14912yes—
481C4⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—48no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—44no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—44no—
519C23—42no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—82no—
524C23—82no—
525C23—81no—
526C23—81no—
527C23#95×C14914yescomplemented
528C23C2×C42×C14911yescharacteristic
529C23C2×C22⋊C4×C14911yescharacteristic
530C23C2×C22⋊C4×C14911yescharacteristic
531C23C2×C22⋊C4×C14912yes—
532C23C2×C22⋊C4×C14911yescharacteristic
533C23C2×C4⋊C4×C14911yescharacteristic
534C23C2×C4⋊C4×C14911yescharacteristic
535C23C2×C4⋊C4×C14911yescharacteristic
536C23#117×C14912yes—
537C23C4×D4×C14912yes—
538C23C4×D4×C14912yes—
539C23C4×D4×C14912yes—
540C23C4×D4×C14912yes—
541C23#120×C14911yescharacteristic
542C23#120×C14912yes—
543C23#120×C14911yescharacteristic
544C23#121×C14912yes—
545C23#121×C14912yes—
546C23C22⋊Q8×C14912yes—
547C23C22⋊Q8×C14912yes—
548C23#123×C14911yescharacteristic
549C23#123×C14911yescharacteristic
550C23#123×C14912yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—84no—
579C2×C4—88no—
580C2×C4—84no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4#95×C14914yescomplemented
586C22—24no—
587C22—24no—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—22no—
592C22—22no—
593C22—24no—
594C22—21no—
595C22—22no—
596C22—22no—
597C22—21no—
598C22—21no—
599C22—22no—
600C22—21no—
601C22—22no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×#95×C14911yescharacteristic
622C22C4×C22⋊C4×C14912yes—
623C22#379×C14911yescharacteristic
624C22#380×C14912yes—
625C22#381×C14911yescharacteristic
626C22#385×C14911yescharacteristic
627C22#385×C14912yes—
628C22#385×C14911yescharacteristic
629C22#386×C14911yescharacteristic
630C22#386×C14912yes—
631C22#386×C14911yescharacteristic
632C22B(4,𝔽2)×C14912yes—
633C22#458×C14912yes—
634C4—24no—
635C4—48no—
636C4—44no—
637C4—82no—
638C4—84no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2C22⋊#95×C14911yescharacteristic
649C2#1790×C14912yes—
650C2#1867×C14912yes—
651C2#1889×C14911yescharacteristic
652C2#1890×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#120
commutatorC23C2×C42×C149
Frattini, cosocleC25C23×C149
prime radicalC23×D4×C149C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C149 ◁ C25×C149 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#342×C149C2semidirect
5. C22⋊#95×C149C2semidirect
10. #518×C149C4semidirect
20. C2×#99×C149C4semidirect
22. #386×C149C4semidirect
46. C23×C4×C149C2×C4semidirect
72. C2×C22⋊C4×C149C2×C4semidirect
73. C2×C22⋊C4×C149C2×C4semidirect
152. C22×C4×C149C22⋊C4semidirect
200. C23×C149#95semidirect
258. C2×C4×C149#95semidirect
326. #10745C149direct (N × H)
327. C149#10745direct (N × H)
331. C2×#342C2×C149semidirect
332. C22⋊#95C2×C149semidirect
337. #518C4×C149semidirect
347. C2×#99C4×C149semidirect
349. #386C4×C149semidirect
373. C23×C4C2×C4×C149semidirect
399. C2×C22⋊C4C2×C4×C149semidirect
400. C2×C22⋊C4C2×C4×C149semidirect
479. C22×C4C22⋊C4×C149semidirect
527. C23#95×C149semidirect
585. C2×C4#95×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1492
C22×#99×C1492
C2×#386×C1492
C2×#342×C1492
C22⋊#95×C1492
#10745149