Finite Group Databasebeta

← C149×#11079 #49190028

Subgroups — C149×#11079 #49190028

Order 38144.

990 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#104×C149C211yesmaximal, characteristic
2C2×#417×C149C211yesmaximal, characteristic
3#2311×C149C211yesmaximal, characteristic
4C2×#382×C149C211yesmaximal, characteristic, complemented
5C2×#343×C149C211yesmaximal, characteristic, complemented
6#1736×C149C211yesmaximal, characteristic, complemented
7C2×#339×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C22×M16×C149C2211yescharacteristic
11C2×#117×C149C2211yescharacteristic
12C22×C4⋊C4×C149C2211yescharacteristic
13C22×C4⋊C4×C149C2211yescharacteristic
14C22×C42×C149C2211yescharacteristic
15C2×#104×C149—22no—
16C2×#104×C149—22no—
17C2×#104×C149C414yescomplemented
18#417×C149—22no—
19#417×C149—22no—
20C2×#103×C149—21no—
21C2×#102×C149—21no—
22#391×C149—21no—
23#390×C149—21no—
24#386×C149—22no—
25#382×C149—22no—
26#382×C149—22no—
27#380×C149—22no—
28C2×#95×C149—22no—
29#343×C149—22no—
30#340×C149—22no—
31#339×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×C149—21no—
50C23×C4×C149D412yes—
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×C149C2×C412yes—
63C2×M16×C149D412yes—
64C22×C8×C149—21no—
65C22×C8×C149—21no—
66#117×C149—21no—
67#117×C149—21no—
68#117×C149—21no—
69#117×C149—21no—
70C2×C4⋊C4×C149—21no—
71C2×C4⋊C4×C149—21no—
72C2×C4⋊C4×C149—21no—
73C2×C4⋊C4×C149—21no—
74C2×C4⋊C4×C149—21no—
75C2×C4⋊C4×C149—21no—
76C2×C4⋊C4×C149—21no—
77C2×C4⋊C4×C149—21no—
78C2×C4⋊C4×C149—21no—
79C2×C4⋊C4×C149—21no—
80C2×C4⋊C4×C149—21no—
81C2×C4⋊C4×C149D412yes—
82C2×C4⋊C4×C149D412yes—
83C2×C22⋊C4×C149—21no—
84C2×C22⋊C4×C149—24no—
85C2×C42×C149—21no—
86C2×C42×C149—21no—
87C2×C42×C149—21no—
88C2×C42×C149—21no—
89C2×C42×C149C2×C412yes—
90C2×C42×C149D412yes—
91C2×C42×C149D412yes—
92#104×C149—28no—
93#103×C149—24no—
94#102×C149—24no—
95#95×C149—28no—
96#95×C149—24no—
97C24×C149—21no—
98C24×C149C2×D411yescharacteristic
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—22no—
134C22×C4×C149—22no—
135C22×C4×C149—21no—
136C22×C4×C149—22no—
137C22×C4×C149—22no—
138C22×C4×C149—22no—
139C22×C4×C149—22no—
140C22×C4×C149—22no—
141C22×C4×C149—22no—
142C22×C4×C149—22no—
143C22×C4×C149—22no—
144C22×C4×C149—42no—
145C22×C4×C149—42no—
146C22×C4×C149—41no—
147C22×C4×C149—41no—
148C22×C4×C149—41no—
149C22×C4×C149—41no—
150C22×C4×C149—44no—
151C22×C4×C149—44no—
152C22×C4×C149—41no—
153C22×C4×C149—41no—
154C22×C4×C149C22×C411yescharacteristic
155C22×C4×C149C2×D411yescharacteristic
156C22×C4×C149C2×D411yescharacteristic
157C22×C4×C149C2×D411yescharacteristic
158C22×C4×C149C2×D411yescharacteristic
159C22×C4×C149C2×D411yescharacteristic
160C22×C4×C149C2×D411yescharacteristic
161C22×C4×C149C2×Q811yescharacteristic
162C22×C4×C149#4111yescharacteristic
163C22×C4×C149#4111yescharacteristic
164C22×C4×C149#4111yescharacteristic
165C22×C4×C149#4111yescharacteristic
166C22×C4×C149#4111yescharacteristic
167C22×C4×C149#4111yescharacteristic
168M16×C149—22no—
169M16×C149—22no—
170M16×C149—22no—
171M16×C149—22no—
172M16×C149—41no—
173M16×C149—41no—
174M16×C149—41no—
175M16×C149—41no—
176C2×C8×C149—22no—
177C2×C8×C149—22no—
178C2×C8×C149—41no—
179C2×C8×C149—41no—
180C2×C8×C149—41no—
181C2×C8×C149—41no—
182C4⋊C4×C149—22no—
183C4⋊C4×C149—22no—
184C4⋊C4×C149—22no—
185C4⋊C4×C149—22no—
186C4⋊C4×C149—41no—
187C4⋊C4×C149—41no—
188C4⋊C4×C149—41no—
189C4⋊C4×C149—41no—
190C4⋊C4×C149—41no—
191C4⋊C4×C149—41no—
192C22⋊C4×C149—41no—
193C22⋊C4×C149—41no—
194C22⋊C4×C149—84no—
195C42×C149—22no—
196C42×C149—22no—
197C42×C149—22no—
198C42×C149—41no—
199C42×C149—41no—
200C42×C149C22⋊C414yescomplemented
201C23×C149—22no—
202C23×C149—22no—
203C23×C149—22no—
204C23×C149—41no—
205C23×C149—41no—
206C23×C149—42no—
207C23×C149—42no—
208C23×C149C4×D411yescharacteristic
209C23×C149#12011yescharacteristic
210C23×C149#12011yescharacteristic
211C23×C149#12111yescharacteristic
212C23×C149#12111yescharacteristic
213C23×C149C22⋊Q811yescharacteristic
214C23×C149#12411yescharacteristic
215Q8×C149—22no—
216Q8×C149—22no—
217Q8×C149—41no—
218Q8×C149—41no—
219D4×C149—22no—
220D4×C149—22no—
221D4×C149—42no—
222D4×C149—42no—
223D4×C149—42no—
224D4×C149—42no—
225D4×C149—41no—
226D4×C149—41no—
227C2×C4×C149—22no—
228C2×C4×C149—24no—
229C2×C4×C149—44no—
230C2×C4×C149—42no—
231C2×C4×C149—42no—
232C2×C4×C149—44no—
233C2×C4×C149—41no—
234C2×C4×C149—41no—
235C2×C4×C149—42no—
236C2×C4×C149—42no—
237C2×C4×C149—42no—
238C2×C4×C149—42no—
239C2×C4×C149—44no—
240C2×C4×C149—44no—
241C2×C4×C149—42no—
242C2×C4×C149—42no—
243C2×C4×C149—42no—
244C2×C4×C149—42no—
245C2×C4×C149—42no—
246C2×C4×C149—44no—
247C2×C4×C149—82no—
248C2×C4×C149—82no—
249C2×C4×C149—82no—
250C2×C4×C149C2×C22⋊C411yescharacteristic
251C2×C4×C149C2×C4⋊C411yescharacteristic
252C2×C4×C149#11711yescharacteristic
253C2×C4×C149C4×D411yescharacteristic
254C2×C4×C149C4×D411yescharacteristic
255C2×C4×C149C4×D411yescharacteristic
256C2×C4×C149#12011yescharacteristic
257C2×C4×C149#12111yescharacteristic
258C2×C4×C149#12111yescharacteristic
259C2×C4×C149#12111yescharacteristic
260C2×C4×C149#12111yescharacteristic
261C2×C4×C149#12111yescharacteristic
262C2×C4×C149#12111yescharacteristic
263C2×C4×C149C22⋊Q811yescharacteristic
264C2×C4×C149C22⋊Q811yescharacteristic
265C2×C4×C149C22⋊Q811yescharacteristic
266C2×C4×C149C22⋊Q811yescharacteristic
267C2×C4×C149C22⋊Q811yescharacteristic
268C2×C4×C149#12311yescharacteristic
269C2×C4×C149#12311yescharacteristic
270C2×C4×C149#12311yescharacteristic
271C2×C4×C149#12311yescharacteristic
272C2×C4×C149#12311yescharacteristic
273C2×C4×C149#12411yescharacteristic
274C2×C4×C149#12411yescharacteristic
275C2×C4×C149#12611yescharacteristic
276C2×C4×C149#12611yescharacteristic
277C2×C4×C149#12711yescharacteristic
278C8×C149—42no—
279C8×C149—42no—
280C22×C149—22no—
281C22×C149—22no—
282C22×C149—21no—
283C22×C149—21no—
284C22×C149—21no—
285C22×C149—21no—
286C22×C149—22no—
287C22×C149—22no—
288C22×C149—44no—
289C22×C149—42no—
290C22×C149—81no—
291C22×C149—81no—
292C22×C149—82no—
293C22×C149#38511yescharacteristic
294C22×C149#38611yescharacteristic
295C22×C149#38811yescharacteristic
296C22×C149#39211yescharacteristic
297C22×C149#39311yescharacteristic
298C22×C149#39411yescharacteristic
299C22×C149#39611yescharacteristic
300C22×C149#45412yes—
301C22×C149#45512yes—
302C4×C149—44no—
303C4×C149—42no—
304C4×C149—82no—
305C4×C149—82no—
306C4×C149—82no—
307C4×C149#38011yescharacteristic
308C4×C149#38511yescharacteristic
309C4×C149#38811yescharacteristic
310C4×C149#39011yescharacteristic
311C4×C149#39411yescharacteristic
312C4×C149#39611yescharacteristic
313C4×C149#39711yescharacteristic
314C4×C149#39911yescharacteristic
315C2×C149—21no—
316C2×C149—21no—
317C2×C149—21no—
318C2×C149—21no—
319C2×C149—82no—
320C2×C149#143911yescharacteristic
321C2×C149#186012yes—
322C2×C149#200311yescharacteristic
323C2×C149#200411yescharacteristic
324C2×C149#204012yes—
325#11079C14911yesmaximal, characteristic, direct product factor, Sylow
326C149#1107911yescharacteristic, direct product factor, Sylow
327C22×#104C2×C14911yescharacteristic
328C2×#417C2×C14911yescharacteristic
329#2311C2×C14911yescharacteristic
330C2×#382C2×C14911yescharacteristic, complemented
331C2×#343C2×C14911yescharacteristic, complemented
332#1736C2×C14911yescharacteristic, complemented
333C2×#339C2×C14911yescharacteristic, complemented
334C22×#41C22×C14911yescharacteristic
335C22×M16C22×C14911yescharacteristic
336C22×M16C22×C14911yescharacteristic
337C2×#117C22×C14911yescharacteristic
338C22×C4⋊C4C22×C14911yescharacteristic
339C22×C4⋊C4C22×C14911yescharacteristic
340C22×C42C22×C14911yescharacteristic
341C2×#104—22no—
342C2×#104—22no—
343C2×#104C4×C14914yescomplemented
344#417—22no—
345#417—22no—
346C2×#103—21no—
347C2×#102—21no—
348#391—21no—
349#390—21no—
350#386—22no—
351#382—22no—
352#382—22no—
353#380—22no—
354C2×#95—22no—
355#343—22no—
356#340—22no—
357#339—22no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41C2×C4×C14912yes—
369C2×#41Q8×C14912yes—
370C22×Q8D4×C14911yescharacteristic
371C22×D4—21no—
372C22×D4D4×C14911yescharacteristic
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—21no—
376C23×C4D4×C14912yes—
377C23×C4C23×C14911yescharacteristic
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—
390C22×C8—21no—
391C22×C8—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C14912yes—
408C2×C4⋊C4D4×C14912yes—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—24no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C2×C4×C14912yes—
416C2×C42D4×C14912yes—
417C2×C42D4×C14912yes—
418#104—28no—
419#103—24no—
420#102—24no—
421#95—28no—
422#95—24no—
423C24—21no—
424C24C2×D4×C14911yescharacteristic
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C4⋊C4×C14912yes—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C4⋊C4×C14912yes—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4C22×C4×C14911yescharacteristic
481C22×C4C2×D4×C14911yescharacteristic
482C22×C4C2×D4×C14911yescharacteristic
483C22×C4C2×D4×C14911yescharacteristic
484C22×C4C2×D4×C14911yescharacteristic
485C22×C4C2×D4×C14911yescharacteristic
486C22×C4C2×D4×C14911yescharacteristic
487C22×C4C2×Q8×C14911yescharacteristic
488C22×C4#41×C14911yescharacteristic
489C22×C4#41×C14911yescharacteristic
490C22×C4#41×C14911yescharacteristic
491C22×C4#41×C14911yescharacteristic
492C22×C4#41×C14911yescharacteristic
493C22×C4#41×C14911yescharacteristic
494M16—22no—
495M16—22no—
496M16—22no—
497M16—22no—
498M16—41no—
499M16—41no—
500M16—41no—
501M16—41no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—84no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C42C22⋊C4×C14914yescomplemented
527C23—22no—
528C23—22no—
529C23—22no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23C4×D4×C14911yescharacteristic
535C23#120×C14911yescharacteristic
536C23#120×C14911yescharacteristic
537C23#121×C14911yescharacteristic
538C23#121×C14911yescharacteristic
539C23C22⋊Q8×C14911yescharacteristic
540C23#124×C14911yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545D4—22no—
546D4—22no—
547D4—42no—
548D4—42no—
549D4—42no—
550D4—42no—
551D4—41no—
552D4—41no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—44no—
558C2×C4—44no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—44no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—82no—
576C2×C4C2×C22⋊C4×C14911yescharacteristic
577C2×C4C2×C4⋊C4×C14911yescharacteristic
578C2×C4#117×C14911yescharacteristic
579C2×C4C4×D4×C14911yescharacteristic
580C2×C4C4×D4×C14911yescharacteristic
581C2×C4C4×D4×C14911yescharacteristic
582C2×C4#120×C14911yescharacteristic
583C2×C4#121×C14911yescharacteristic
584C2×C4#121×C14911yescharacteristic
585C2×C4#121×C14911yescharacteristic
586C2×C4#121×C14911yescharacteristic
587C2×C4#121×C14911yescharacteristic
588C2×C4#121×C14911yescharacteristic
589C2×C4C22⋊Q8×C14911yescharacteristic
590C2×C4C22⋊Q8×C14911yescharacteristic
591C2×C4C22⋊Q8×C14911yescharacteristic
592C2×C4C22⋊Q8×C14911yescharacteristic
593C2×C4C22⋊Q8×C14911yescharacteristic
594C2×C4#123×C14911yescharacteristic
595C2×C4#123×C14911yescharacteristic
596C2×C4#123×C14911yescharacteristic
597C2×C4#123×C14911yescharacteristic
598C2×C4#123×C14911yescharacteristic
599C2×C4#124×C14911yescharacteristic
600C2×C4#124×C14911yescharacteristic
601C2×C4#126×C14911yescharacteristic
602C2×C4#126×C14911yescharacteristic
603C2×C4#127×C14911yescharacteristic
604C8—42no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—42no—
615C22—44no—
616C22—81no—
617C22—81no—
618C22—82no—
619C22#385×C14911yescharacteristic
620C22#386×C14911yescharacteristic
621C22#388×C14911yescharacteristic
622C22#392×C14911yescharacteristic
623C22#393×C14911yescharacteristic
624C22#394×C14911yescharacteristic
625C22#396×C14911yescharacteristic
626C22#454×C14912yes—
627C22#455×C14912yes—
628C4—44no—
629C4—42no—
630C4—82no—
631C4—82no—
632C4—82no—
633C4#380×C14911yescharacteristic
634C4#385×C14911yescharacteristic
635C4#388×C14911yescharacteristic
636C4#390×C14911yescharacteristic
637C4#394×C14911yescharacteristic
638C4#396×C14911yescharacteristic
639C4#397×C14911yescharacteristic
640C4#399×C14911yescharacteristic
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—82no—
646C2#1439×C14911yescharacteristic
647C2#1860×C14912yes—
648C2#2003×C14911yescharacteristic
649C2#2004×C14911yescharacteristic
650C2#2040×C14912yes—
subgroupG/H
center, socleC23×C149#120
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radicalC22×#41×C149C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C149 ◁ C23×C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#382×C149C2semidirect
5. C2×#343×C149C2semidirect
6. #1736×C149C2semidirect
7. C2×#339×C149C2semidirect
17. C2×#104×C149C4semidirect
200. C42×C149C22⋊C4semidirect
325. #11079C149direct (N × H)
326. C149#11079direct (N × H)
330. C2×#382C2×C149semidirect
331. C2×#343C2×C149semidirect
332. #1736C2×C149semidirect
333. C2×#339C2×C149semidirect
343. C2×#104C4×C149semidirect
526. C42C22⋊C4×C149semidirect

Maximal subgroups

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

subgroupindex
C22×#104×C1492
C2×#417×C1492
#2311×C1492
C2×#382×C1492
C2×#343×C1492
#1736×C1492
C2×#339×C1492
#11079149