Finite Group Databasebeta

← C149×#11082 #49190031

Subgroups — C149×#11082 #49190031

Order 38144.

898 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#423×C149C211yesmaximal, characteristic, complemented
2C22×#104×C149C211yesmaximal, characteristic
3#2896×C149C211yesmaximal, characteristic
4C2×#413×C149C211yesmaximal, characteristic
5#1742×C149C211yesmaximal, characteristic, complemented
6C2×#339×C149C211yesmaximal, characteristic, complemented
7C2×#338×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C22×M16×C149C2211yescharacteristic
11C22×M16×C149C2211yescharacteristic
12C22×M16×C149C2211yescharacteristic
13C2×#117×C149C2211yescharacteristic
14C22×C42×C149C2211yescharacteristic
15#423×C149—22no—
16#423×C149—22no—
17C2×C4⋊C8×C149—22no—
18C2×#104×C149—22no—
19C2×#104×C149—21no—
20C2×#104×C149—21no—
21C2×#104×C149C414yescomplemented
22#419×C149—21no—
23#418×C149—21no—
24#417×C149—22no—
25#416×C149—22no—
26#413×C149—22no—
27#413×C149—22no—
28C2×#101×C149—21no—
29C2×#100×C149—21no—
30#343×C149—22no—
31#339×C149—21no—
32#339×C149—21no—
33#338×C149—22no—
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—
43C2×#41×C149—21no—
44C2×#41×C149C2×C412yes—
45C2×#41×C149Q812yes—
46C22×Q8×C149D411yescharacteristic
47C22×D4×C149—21no—
48C22×D4×C149D411yescharacteristic
49C23×C4×C149—21no—
50C23×C4×C149—21no—
51C23×C4×C149C2311yescharacteristic
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×C149—21no—
69C2×M16×C149—21no—
70C2×M16×C149—21no—
71C2×M16×C149—21no—
72C2×M16×C149—21no—
73C2×M16×C149C2×C412yes—
74C2×M16×C149D412yes—
75C2×M16×C149D412yes—
76C22×C8×C149—21no—
77C22×C8×C149—21no—
78C22×C8×C149—21no—
79C22×C8×C149D412yes—
80#117×C149—21no—
81#117×C149—21no—
82#117×C149—21no—
83#117×C149—21no—
84C2×C4⋊C4×C149D412yes—
85C2×C22⋊C4×C149—21no—
86C2×C42×C149—21no—
87C2×C42×C149—21no—
88C2×C42×C149—21no—
89C2×C42×C149—21no—
90C2×C42×C149C2×C412yes—
91C2×C42×C149D412yes—
92C2×C42×C149D411yescharacteristic
93C2×C42×C149D411yescharacteristic
94C4⋊C8×C149—28no—
95#104×C149—24no—
96#104×C149—24no—
97#103×C149—24no—
98#102×C149—24no—
99#101×C149—24no—
100#100×C149—24no—
101C24×C149—21no—
102C24×C149#4111yescharacteristic
103#41×C149—22no—
104#41×C149—22no—
105#41×C149—22no—
106#41×C149—22no—
107#41×C149—22no—
108#41×C149—22no—
109#41×C149—22no—
110#41×C149—22no—
111#41×C149—41no—
112#41×C149—41no—
113#41×C149—41no—
114#41×C149—41no—
115#41×C149—41no—
116#41×C149—41no—
117#41×C149—41no—
118#41×C149—41no—
119C2×Q8×C149—21no—
120C2×Q8×C149—21no—
121C2×Q8×C149—21no—
122C2×Q8×C149—21no—
123C2×Q8×C149—21no—
124C2×Q8×C149C4⋊C412yes—
125C2×D4×C149—22no—
126C2×D4×C149—22no—
127C2×D4×C149—21no—
128C2×D4×C149—21no—
129C2×D4×C149—21no—
130C2×D4×C149—21no—
131C2×D4×C149—21no—
132C2×D4×C149—41no—
133C2×D4×C149—41no—
134C2×D4×C149—41no—
135C2×D4×C149—41no—
136C2×D4×C149C4⋊C412yes—
137C22×C4×C149—21no—
138C22×C4×C149—22no—
139C22×C4×C149—21no—
140C22×C4×C149—22no—
141C22×C4×C149—21no—
142C22×C4×C149—22no—
143C22×C4×C149—22no—
144C22×C4×C149—22no—
145C22×C4×C149—44no—
146C22×C4×C149—41no—
147C22×C4×C149—41no—
148C22×C4×C149—41no—
149C22×C4×C149—41no—
150C22×C4×C149C22×C411yescharacteristic
151C22×C4×C149C2×D411yescharacteristic
152C22×C4×C149C2×D411yescharacteristic
153C22×C4×C149C2×D411yescharacteristic
154C22×C4×C149C2×D411yescharacteristic
155C22×C4×C149C2×D411yescharacteristic
156C22×C4×C149C2×D411yescharacteristic
157C22×C4×C149C2×D411yescharacteristic
158C22×C4×C149C2×Q811yescharacteristic
159C22×C4×C149#4111yescharacteristic
160C22×C4×C149#4111yescharacteristic
161C22×C4×C149#4111yescharacteristic
162C22×C4×C149#4111yescharacteristic
163C22×C4×C149#4111yescharacteristic
164M16×C149—22no—
165M16×C149—22no—
166M16×C149—22no—
167M16×C149—22no—
168M16×C149—22no—
169M16×C149—22no—
170M16×C149—41no—
171M16×C149—41no—
172M16×C149—41no—
173M16×C149—41no—
174M16×C149—41no—
175M16×C149—41no—
176M16×C149—41no—
177M16×C149—41no—
178M16×C149—41no—
179M16×C149—41no—
180C2×C8×C149—22no—
181C2×C8×C149—22no—
182C2×C8×C149—22no—
183C2×C8×C149—22no—
184C2×C8×C149—22no—
185C2×C8×C149—22no—
186C2×C8×C149—41no—
187C2×C8×C149—41no—
188C2×C8×C149—41no—
189C2×C8×C149—41no—
190C2×C8×C149—41no—
191C2×C8×C149—41no—
192C4⋊C4×C149—22no—
193C4⋊C4×C149—22no—
194C22⋊C4×C149—41no—
195C22⋊C4×C149—41no—
196C42×C149—22no—
197C42×C149—22no—
198C42×C149—21no—
199C42×C149—21no—
200C42×C149—41no—
201C42×C149—41no—
202C42×C149C22⋊C412yes—
203C42×C149C22⋊C412yes—
204C23×C149—22no—
205C23×C149—42no—
206C23×C149—41no—
207C23×C149—41no—
208C23×C149—82no—
209C23×C149C4×D411yescharacteristic
210C23×C149#12111yescharacteristic
211C23×C149C22⋊Q811yescharacteristic
212C23×C149#12311yescharacteristic
213C23×C149#12311yescharacteristic
214C23×C149#12311yescharacteristic
215C23×C149#12611yescharacteristic
216Q8×C149—22no—
217Q8×C149—22no—
218Q8×C149—41no—
219Q8×C149—41no—
220D4×C149—22no—
221D4×C149—22no—
222D4×C149—42no—
223D4×C149—42no—
224D4×C149—42no—
225D4×C149—42no—
226D4×C149—41no—
227D4×C149—41no—
228C2×C4×C149—24no—
229C2×C4×C149—22no—
230C2×C4×C149—22no—
231C2×C4×C149—22no—
232C2×C4×C149—44no—
233C2×C4×C149—44no—
234C2×C4×C149—42no—
235C2×C4×C149—41no—
236C2×C4×C149—41no—
237C2×C4×C149—42no—
238C2×C4×C149—42no—
239C2×C4×C149—42no—
240C2×C4×C149—42no—
241C2×C4×C149—42no—
242C2×C4×C149—82no—
243C2×C4×C149C2×C22⋊C411yescharacteristic
244C2×C4×C149C2×C4⋊C411yescharacteristic
245C2×C4×C149#11711yescharacteristic
246C2×C4×C149C4×D411yescharacteristic
247C2×C4×C149C4×D411yescharacteristic
248C2×C4×C149C4×D411yescharacteristic
249C2×C4×C149#12011yescharacteristic
250C2×C4×C149#12011yescharacteristic
251C2×C4×C149#12011yescharacteristic
252C2×C4×C149#12111yescharacteristic
253C2×C4×C149#12111yescharacteristic
254C2×C4×C149#12111yescharacteristic
255C2×C4×C149#12111yescharacteristic
256C2×C4×C149#12111yescharacteristic
257C2×C4×C149#12111yescharacteristic
258C2×C4×C149#12111yescharacteristic
259C2×C4×C149C22⋊Q811yescharacteristic
260C2×C4×C149C22⋊Q811yescharacteristic
261C2×C4×C149C22⋊Q811yescharacteristic
262C2×C4×C149C22⋊Q811yescharacteristic
263C2×C4×C149C22⋊Q811yescharacteristic
264C2×C4×C149#12311yescharacteristic
265C2×C4×C149#12311yescharacteristic
266C2×C4×C149#12411yescharacteristic
267C2×C4×C149#12411yescharacteristic
268C2×C4×C149#12411yescharacteristic
269C2×C4×C149#12611yescharacteristic
270C2×C4×C149#12711yescharacteristic
271C8×C149—42no—
272C8×C149—42no—
273C8×C149—42no—
274C8×C149—42no—
275C22×C149—22no—
276C22×C149—22no—
277C22×C149—22no—
278C22×C149—41no—
279C22×C149—41no—
280C22×C149—41no—
281C22×C149—41no—
282C22×C149—42no—
283C22×C149—82no—
284C22×C149—82no—
285C22×C149—82no—
286C22×C149#38511yescharacteristic
287C22×C149#38611yescharacteristic
288C22×C149#38811yescharacteristic
289C22×C149#39411yescharacteristic
290C22×C149#39611yescharacteristic
291C22×C149#39711yescharacteristic
292C22×C149#39911yescharacteristic
293C4×C149—24no—
294C4×C149—42no—
295C4×C149—42no—
296C4×C149—82no—
297C4×C149#38011yescharacteristic
298C4×C149#38511yescharacteristic
299C4×C149#38811yescharacteristic
300C4×C149#39011yescharacteristic
301C4×C149#39211yescharacteristic
302C4×C149#39311yescharacteristic
303C4×C149#39411yescharacteristic
304C4×C149#39611yescharacteristic
305C2×C149—21no—
306C2×C149—21no—
307C2×C149—21no—
308C2×C149—21no—
309C2×C149—21no—
310C2×C149—21no—
311C2×C149—82no—
312C2×C149#143911yescharacteristic
313C2×C149#205012yes—
314#11082C14911yesmaximal, characteristic, direct product factor, Sylow
315C149#1108211yescharacteristic, direct product factor, Sylow
316C2×#423C2×C14911yescharacteristic, complemented
317C22×#104C2×C14911yescharacteristic
318#2896C2×C14911yescharacteristic
319C2×#413C2×C14911yescharacteristic
320#1742C2×C14911yescharacteristic, complemented
321C2×#339C2×C14911yescharacteristic, complemented
322C2×#338C2×C14911yescharacteristic, complemented
323C22×#41C22×C14911yescharacteristic
324C22×M16C22×C14911yescharacteristic
325C22×M16C22×C14911yescharacteristic
326C22×M16C22×C14911yescharacteristic
327C22×M16C22×C14911yescharacteristic
328C2×#117C22×C14911yescharacteristic
329C22×C42C22×C14911yescharacteristic
330#423—22no—
331#423—22no—
332C2×C4⋊C8—22no—
333C2×#104—21no—
334C2×#104—21no—
335C2×#104—22no—
336C2×#104C4×C14914yescomplemented
337#419—21no—
338#418—21no—
339#417—22no—
340#416—22no—
341#413—22no—
342#413—22no—
343C2×#101—21no—
344C2×#100—21no—
345#343—22no—
346#339—21no—
347#339—21no—
348#338—22no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41C2×C4×C14912yes—
360C2×#41Q8×C14912yes—
361C22×Q8D4×C14911yescharacteristic
362C22×D4—21no—
363C22×D4D4×C14911yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4C23×C14911yescharacteristic
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×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16C2×C4×C14912yes—
389C2×M16D4×C14912yes—
390C2×M16D4×C14912yes—
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C22×C8D4×C14912yes—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399C2×C4⋊C4D4×C14912yes—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C2×C4×C14912yes—
406C2×C42D4×C14911yescharacteristic
407C2×C42D4×C14911yescharacteristic
408C2×C42D4×C14912yes—
409C4⋊C8—28no—
410#104—24no—
411#104—24no—
412#103—24no—
413#102—24no—
414#101—24no—
415#100—24no—
416C24—21no—
417C24#41×C14911yescharacteristic
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—22no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432#41—41no—
433#41—41no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C4⋊C4×C14912yes—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4C4⋊C4×C14912yes—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—44no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4C22×C4×C14911yescharacteristic
466C22×C4C2×D4×C14911yescharacteristic
467C22×C4C2×D4×C14911yescharacteristic
468C22×C4C2×D4×C14911yescharacteristic
469C22×C4C2×D4×C14911yescharacteristic
470C22×C4C2×D4×C14911yescharacteristic
471C22×C4C2×D4×C14911yescharacteristic
472C22×C4C2×D4×C14911yescharacteristic
473C22×C4C2×Q8×C14911yescharacteristic
474C22×C4#41×C14911yescharacteristic
475C22×C4#41×C14911yescharacteristic
476C22×C4#41×C14911yescharacteristic
477C22×C4#41×C14911yescharacteristic
478C22×C4#41×C14911yescharacteristic
479M16—22no—
480M16—22no—
481M16—22no—
482M16—22no—
483M16—22no—
484M16—22no—
485M16—41no—
486M16—41no—
487M16—41no—
488M16—41no—
489M16—41no—
490M16—41no—
491M16—41no—
492M16—41no—
493M16—41no—
494M16—41no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42—41no—
517C42C22⋊C4×C14912yes—
518C42C22⋊C4×C14912yes—
519C23—22no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23C4×D4×C14911yescharacteristic
525C23#121×C14911yescharacteristic
526C23C22⋊Q8×C14911yescharacteristic
527C23#123×C14911yescharacteristic
528C23#123×C14911yescharacteristic
529C23#123×C14911yescharacteristic
530C23#126×C14911yescharacteristic
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535D4—22no—
536D4—22no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—42no—
541D4—41no—
542D4—41no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—82no—
558C2×C4C2×C22⋊C4×C14911yescharacteristic
559C2×C4C2×C4⋊C4×C14911yescharacteristic
560C2×C4#117×C14911yescharacteristic
561C2×C4C4×D4×C14911yescharacteristic
562C2×C4C4×D4×C14911yescharacteristic
563C2×C4C4×D4×C14911yescharacteristic
564C2×C4#120×C14911yescharacteristic
565C2×C4#120×C14911yescharacteristic
566C2×C4#120×C14911yescharacteristic
567C2×C4#121×C14911yescharacteristic
568C2×C4#121×C14911yescharacteristic
569C2×C4#121×C14911yescharacteristic
570C2×C4#121×C14911yescharacteristic
571C2×C4#121×C14911yescharacteristic
572C2×C4#121×C14911yescharacteristic
573C2×C4#121×C14911yescharacteristic
574C2×C4C22⋊Q8×C14911yescharacteristic
575C2×C4C22⋊Q8×C14911yescharacteristic
576C2×C4C22⋊Q8×C14911yescharacteristic
577C2×C4C22⋊Q8×C14911yescharacteristic
578C2×C4C22⋊Q8×C14911yescharacteristic
579C2×C4#123×C14911yescharacteristic
580C2×C4#123×C14911yescharacteristic
581C2×C4#124×C14911yescharacteristic
582C2×C4#124×C14911yescharacteristic
583C2×C4#124×C14911yescharacteristic
584C2×C4#126×C14911yescharacteristic
585C2×C4#127×C14911yescharacteristic
586C8—42no—
587C8—42no—
588C8—42no—
589C8—42no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—42no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22#385×C14911yescharacteristic
602C22#386×C14911yescharacteristic
603C22#388×C14911yescharacteristic
604C22#394×C14911yescharacteristic
605C22#396×C14911yescharacteristic
606C22#397×C14911yescharacteristic
607C22#399×C14911yescharacteristic
608C4—24no—
609C4—42no—
610C4—42no—
611C4—82no—
612C4#380×C14911yescharacteristic
613C4#385×C14911yescharacteristic
614C4#388×C14911yescharacteristic
615C4#390×C14911yescharacteristic
616C4#392×C14911yescharacteristic
617C4#393×C14911yescharacteristic
618C4#394×C14911yescharacteristic
619C4#396×C14911yescharacteristic
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—82no—
627C2#1439×C14911yescharacteristic
628C2#2050×C14912yes—
subgroupG/H
centerC2×C4×C149#124
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
socleC22×C149#394
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
1. C2×#423×C149C2semidirect
5. #1742×C149C2semidirect
6. C2×#339×C149C2semidirect
7. C2×#338×C149C2semidirect
21. C2×#104×C149C4semidirect
314. #11082C149direct (N × H)
315. C149#11082direct (N × H)
316. C2×#423C2×C149semidirect
320. #1742C2×C149semidirect
321. C2×#339C2×C149semidirect
322. C2×#338C2×C149semidirect
336. C2×#104C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#423×C1492
C22×#104×C1492
#2896×C1492
C2×#413×C1492
#1742×C1492
C2×#339×C1492
C2×#338×C1492
#11082149