Finite Group Databasebeta

← C149×#11092 #49190041

Subgroups — C149×#11092 #49190041

Order 38144.

882 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#424×C149C211yesmaximal, characteristic, complemented
2#2896×C149C211yesmaximal, characteristic
3C2×#416×C149C211yesmaximal, characteristic
4C2×#410×C149C211yesmaximal, characteristic
5#1740×C149C211yesmaximal, characteristic, complemented
6#1735×C149C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C149C211yesmaximal, characteristic, complemented
8C22×#41×C149C2211yescharacteristic
9C22×M16×C149C2211yescharacteristic
10C23×C8×C149C2211yescharacteristic
11C2×#117×C149C2211yescharacteristic
12C2×#117×C149C2211yescharacteristic
13C2×#117×C149C2211yescharacteristic
14C2×#117×C149C2211yescharacteristic
15#424×C149—22no—
16#424×C149—22no—
17C2×C4⋊C8×C149—22no—
18#419×C149—21no—
19#418×C149—21no—
20#417×C149—22no—
21#416×C149—22no—
22#416×C149—22no—
23#416×C149—22no—
24C2×#103×C149—21no—
25C2×#102×C149—21no—
26#410×C149—22no—
27#410×C149C414yescomplemented
28C2×#99×C149—22no—
29#342×C149—22no—
30#340×C149—22no—
31H(3,ℤ/4)×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×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—
55C22×C8×C149—21no—
56C22×C8×C149—21no—
57C22×C8×C149—21no—
58C22×C8×C149—21no—
59C22×C8×C149—21no—
60C22×C8×C149—21no—
61C22×C8×C149D412yes—
62C22×C8×C149D412yes—
63#117×C149—21no—
64#117×C149—21no—
65#117×C149—21no—
66#117×C149—21no—
67#117×C149—21no—
68#117×C149—21no—
69#117×C149—21no—
70#117×C149—21no—
71#117×C149—21no—
72#117×C149—21no—
73#117×C149—21no—
74#117×C149—21no—
75#117×C149C2×C412yes—
76#117×C149C2×C412yes—
77#117×C149D412yes—
78#117×C149D412yes—
79C2×C4⋊C4×C149—21no—
80C2×C4⋊C4×C149—21no—
81C2×C4⋊C4×C149—21no—
82C2×C4⋊C4×C149D412yes—
83C2×C22⋊C4×C149—21no—
84C2×C22⋊C4×C149—21no—
85C2×C22⋊C4×C149—21no—
86C2×C22⋊C4×C149D412yes—
87C2×C42×C149—21no—
88C2×C42×C149—21no—
89C2×C42×C149—21no—
90C2×C42×C149—21no—
91C4⋊C8×C149—28no—
92#103×C149—24no—
93#103×C149—24no—
94#102×C149—24no—
95#102×C149—24no—
96#99×C149—28no—
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—21no—
135C22×C4×C149—22no—
136C22×C4×C149—22no—
137C22×C4×C149—22no—
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×Q811yescharacteristic
152C22×C4×C149#4111yescharacteristic
153C22×C4×C149#4111yescharacteristic
154C22×C4×C149#4111yescharacteristic
155C22×C4×C149#4111yescharacteristic
156C22×C4×C149#4111yescharacteristic
157C22×C4×C149#4111yescharacteristic
158M16×C149—41no—
159M16×C149—41no—
160M16×C149—41no—
161M16×C149—41no—
162C2×C8×C149—22no—
163C2×C8×C149—22no—
164C2×C8×C149—22no—
165C2×C8×C149—22no—
166C2×C8×C149—22no—
167C2×C8×C149—22no—
168C2×C8×C149—41no—
169C2×C8×C149—41no—
170C2×C8×C149—41no—
171C2×C8×C149—41no—
172C4⋊C4×C149—22no—
173C4⋊C4×C149—22no—
174C4⋊C4×C149—22no—
175C4⋊C4×C149—22no—
176C4⋊C4×C149—22no—
177C4⋊C4×C149—22no—
178C4⋊C4×C149—41no—
179C4⋊C4×C149—41no—
180C22⋊C4×C149—22no—
181C22⋊C4×C149—22no—
182C22⋊C4×C149—22no—
183C22⋊C4×C149—41no—
184C22⋊C4×C149—41no—
185C22⋊C4×C149—41no—
186C22⋊C4×C149—41no—
187C22⋊C4×C149C22⋊C414yes—
188C42×C149—22no—
189C42×C149—22no—
190C42×C149—22no—
191C42×C149—22no—
192C42×C149—41no—
193C42×C149—41no—
194C42×C149—41no—
195C42×C149—41no—
196C23×C149—22no—
197C23×C149—42no—
198C23×C149—41no—
199C23×C149—41no—
200C23×C149—82no—
201C23×C149C2×C22⋊C411yescharacteristic
202C23×C149#12111yescharacteristic
203C23×C149#12111yescharacteristic
204C23×C149#12111yescharacteristic
205C23×C149#12111yescharacteristic
206C23×C149#12111yescharacteristic
207C23×C149C22⋊Q811yescharacteristic
208Q8×C149—22no—
209Q8×C149—22no—
210Q8×C149—41no—
211Q8×C149—41no—
212D4×C149—22no—
213D4×C149—22no—
214D4×C149—42no—
215D4×C149—42no—
216D4×C149—42no—
217D4×C149—42no—
218D4×C149—41no—
219D4×C149—41no—
220C2×C4×C149—22no—
221C2×C4×C149—24no—
222C2×C4×C149—44no—
223C2×C4×C149—41no—
224C2×C4×C149—41no—
225C2×C4×C149—42no—
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—82no—
233C2×C4×C149—82no—
234C2×C4×C149—82no—
235C2×C4×C149C2×C4⋊C411yescharacteristic
236C2×C4×C149#11711yescharacteristic
237C2×C4×C149C4×D411yescharacteristic
238C2×C4×C149C4×D411yescharacteristic
239C2×C4×C149C4×D411yescharacteristic
240C2×C4×C149C4×D411yescharacteristic
241C2×C4×C149#12011yescharacteristic
242C2×C4×C149#12011yescharacteristic
243C2×C4×C149#12011yescharacteristic
244C2×C4×C149#12111yescharacteristic
245C2×C4×C149#12111yescharacteristic
246C2×C4×C149#12111yescharacteristic
247C2×C4×C149C22⋊Q811yescharacteristic
248C2×C4×C149C22⋊Q811yescharacteristic
249C2×C4×C149C22⋊Q811yescharacteristic
250C2×C4×C149C22⋊Q811yescharacteristic
251C2×C4×C149C22⋊Q811yescharacteristic
252C2×C4×C149#12311yescharacteristic
253C2×C4×C149#12311yescharacteristic
254C2×C4×C149#12311yescharacteristic
255C2×C4×C149#12311yescharacteristic
256C2×C4×C149#12311yescharacteristic
257C2×C4×C149#12411yescharacteristic
258C2×C4×C149#12411yescharacteristic
259C2×C4×C149#12411yescharacteristic
260C2×C4×C149#12611yescharacteristic
261C2×C4×C149#12611yescharacteristic
262C2×C4×C149#12711yescharacteristic
263C8×C149—42no—
264C8×C149—42no—
265C22×C149—22no—
266C22×C149—22no—
267C22×C149—22no—
268C22×C149—41no—
269C22×C149—41no—
270C22×C149—41no—
271C22×C149—41no—
272C22×C149—42no—
273C22×C149—82no—
274C22×C149—82no—
275C22×C149—82no—
276C22×C149#38011yescharacteristic
277C22×C149#38611yescharacteristic
278C22×C149#39011yescharacteristic
279C22×C149#39411yescharacteristic
280C22×C149#39411yescharacteristic
281C22×C149#39611yescharacteristic
282C22×C149#39611yescharacteristic
283C4×C149—44no—
284C4×C149—42no—
285C4×C149—82no—
286C4×C149—82no—
287C4×C149—82no—
288C4×C149#38511yescharacteristic
289C4×C149#38511yescharacteristic
290C4×C149#38811yescharacteristic
291C4×C149#38811yescharacteristic
292C4×C149#39211yescharacteristic
293C4×C149#39311yescharacteristic
294C4×C149#39711yescharacteristic
295C4×C149#39911yescharacteristic
296C2×C149—21no—
297C2×C149—21no—
298C2×C149—21no—
299C2×C149—21no—
300C2×C149—21no—
301C2×C149—21no—
302C2×C149—82no—
303C2×C149#143911yescharacteristic
304C2×C149#205312yes—
305#11092C14911yesmaximal, characteristic, direct product factor, Sylow
306C149#1109211yescharacteristic, direct product factor, Sylow
307C2×#424C2×C14911yescharacteristic, complemented
308#2896C2×C14911yescharacteristic
309C2×#416C2×C14911yescharacteristic
310C2×#410C2×C14911yescharacteristic
311#1740C2×C14911yescharacteristic, complemented
312#1735C2×C14911yescharacteristic, complemented
313C2×H(3,ℤ/4)C2×C14911yescharacteristic, complemented
314C22×#41C22×C14911yescharacteristic
315C22×M16C22×C14911yescharacteristic
316C23×C8C22×C14911yescharacteristic
317C2×#117C22×C14911yescharacteristic
318C2×#117C22×C14911yescharacteristic
319C2×#117C22×C14911yescharacteristic
320C2×#117C22×C14911yescharacteristic
321#424—22no—
322#424—22no—
323C2×C4⋊C8—22no—
324#419—21no—
325#418—21no—
326#417—22no—
327#416—22no—
328#416—22no—
329#416—22no—
330C2×#103—21no—
331C2×#102—21no—
332#410—22no—
333#410C4×C14914yescomplemented
334C2×#99—22no—
335#342—22no—
336#340—22no—
337H(3,ℤ/4)—22no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41C2×C4×C14912yes—
349C2×#41Q8×C14912yes—
350C22×Q8D4×C14911yescharacteristic
351C22×D4—21no—
352C22×D4D4×C14911yescharacteristic
353C23×C4—21no—
354C23×C4C23×C14911yescharacteristic
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8D4×C14912yes—
368C22×C8D4×C14912yes—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117C2×C4×C14912yes—
382#117C2×C4×C14912yes—
383#117D4×C14912yes—
384#117D4×C14912yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C14912yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4D4×C14912yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C4⋊C8—28no—
398#103—24no—
399#103—24no—
400#102—24no—
401#102—24no—
402#99—28no—
403C24—21no—
404C24C2×D4×C14911yescharacteristic
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C4⋊C4×C14912yes—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4C4⋊C4×C14912yes—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C22×C4×C14911yescharacteristic
451C22×C4C2×D4×C14911yescharacteristic
452C22×C4C2×D4×C14911yescharacteristic
453C22×C4C2×D4×C14911yescharacteristic
454C22×C4C2×D4×C14911yescharacteristic
455C22×C4C2×D4×C14911yescharacteristic
456C22×C4C2×D4×C14911yescharacteristic
457C22×C4C2×Q8×C14911yescharacteristic
458C22×C4#41×C14911yescharacteristic
459C22×C4#41×C14911yescharacteristic
460C22×C4#41×C14911yescharacteristic
461C22×C4#41×C14911yescharacteristic
462C22×C4#41×C14911yescharacteristic
463C22×C4#41×C14911yescharacteristic
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4C22⋊C4×C14914yes—
494C42—22no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—41no—
499C42—41no—
500C42—41no—
501C42—41no—
502C23—22no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—82no—
507C23C2×C22⋊C4×C14911yescharacteristic
508C23#121×C14911yescharacteristic
509C23#121×C14911yescharacteristic
510C23#121×C14911yescharacteristic
511C23#121×C14911yescharacteristic
512C23#121×C14911yescharacteristic
513C23C22⋊Q8×C14911yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—41no—
517Q8—41no—
518D4—22no—
519D4—22no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—41no—
525D4—41no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4C2×C4⋊C4×C14911yescharacteristic
542C2×C4#117×C14911yescharacteristic
543C2×C4C4×D4×C14911yescharacteristic
544C2×C4C4×D4×C14911yescharacteristic
545C2×C4C4×D4×C14911yescharacteristic
546C2×C4C4×D4×C14911yescharacteristic
547C2×C4#120×C14911yescharacteristic
548C2×C4#120×C14911yescharacteristic
549C2×C4#120×C14911yescharacteristic
550C2×C4#121×C14911yescharacteristic
551C2×C4#121×C14911yescharacteristic
552C2×C4#121×C14911yescharacteristic
553C2×C4C22⋊Q8×C14911yescharacteristic
554C2×C4C22⋊Q8×C14911yescharacteristic
555C2×C4C22⋊Q8×C14911yescharacteristic
556C2×C4C22⋊Q8×C14911yescharacteristic
557C2×C4C22⋊Q8×C14911yescharacteristic
558C2×C4#123×C14911yescharacteristic
559C2×C4#123×C14911yescharacteristic
560C2×C4#123×C14911yescharacteristic
561C2×C4#123×C14911yescharacteristic
562C2×C4#123×C14911yescharacteristic
563C2×C4#124×C14911yescharacteristic
564C2×C4#124×C14911yescharacteristic
565C2×C4#124×C14911yescharacteristic
566C2×C4#126×C14911yescharacteristic
567C2×C4#126×C14911yescharacteristic
568C2×C4#127×C14911yescharacteristic
569C8—42no—
570C8—42no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—82no—
580C22—82no—
581C22—82no—
582C22#380×C14911yescharacteristic
583C22#386×C14911yescharacteristic
584C22#390×C14911yescharacteristic
585C22#394×C14911yescharacteristic
586C22#394×C14911yescharacteristic
587C22#396×C14911yescharacteristic
588C22#396×C14911yescharacteristic
589C4—44no—
590C4—42no—
591C4—82no—
592C4—82no—
593C4—82no—
594C4#385×C14911yescharacteristic
595C4#385×C14911yescharacteristic
596C4#388×C14911yescharacteristic
597C4#388×C14911yescharacteristic
598C4#392×C14911yescharacteristic
599C4#393×C14911yescharacteristic
600C4#397×C14911yescharacteristic
601C4#399×C14911yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—82no—
609C2#1439×C14911yescharacteristic
610C2#2053×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×#424×C149C2semidirect
5. #1740×C149C2semidirect
6. #1735×C149C2semidirect
7. C2×H(3,ℤ/4)×C149C2semidirect
27. #410×C149C4semidirect
305. #11092C149direct (N × H)
306. C149#11092direct (N × H)
307. C2×#424C2×C149semidirect
311. #1740C2×C149semidirect
312. #1735C2×C149semidirect
313. C2×H(3,ℤ/4)C2×C149semidirect
333. #410C4×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#424×C1492
#2896×C1492
C2×#416×C1492
C2×#410×C1492
#1740×C1492
#1735×C1492
C2×H(3,ℤ/4)×C1492
#11092149