Finite Group Databasebeta

← C151×#11114 #50316039

Subgroups — C151×#11114 #50316039

Order 38656.

898 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#430×C151C211yesmaximal, characteristic, complemented
2C2×#421×C151C211yesmaximal, characteristic
3C22×#104×C151C211yesmaximal, characteristic
4#2879×C151C211yesmaximal, characteristic
5C2×#344×C151C211yesmaximal, characteristic, complemented
6C2×#339×C151C211yesmaximal, characteristic, complemented
7#1728×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C22×M16×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C22×M16×C151C2211yescharacteristic
12C22×M16×C151C2211yescharacteristic
13C2×#117×C151C2211yescharacteristic
14C22×C42×C151C2211yescharacteristic
15#430×C151—22no—
16#430×C151—22no—
17C2×#108×C151—22no—
18#421×C151—22no—
19#421×C151—22no—
20C2×#104×C151—22no—
21C2×#104×C151—22no—
22C2×#104×C151—22no—
23C2×#104×C151C414yescomplemented
24#408×C151—22no—
25#408×C151—22no—
26#407×C151—22no—
27#344×C151—22no—
28#339×C151—22no—
29#336×C151—22no—
30C2×#41×C151—21no—
31C2×#41×C151—21no—
32C2×#41×C151—21no—
33C2×#41×C151—21no—
34C2×#41×C151—21no—
35C2×#41×C151—21no—
36C2×#41×C151—21no—
37C2×#41×C151—21no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151C2×C412yes—
41C2×#41×C151D412yes—
42C22×Q8×C151Q811yescharacteristic
43C22×D4×C151—21no—
44C22×D4×C151Q811yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151—21no—
47C23×C4×C151C2311yescharacteristic
48C2×M16×C151—21no—
49C2×M16×C151—21no—
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C2×M16×C151—21no—
53C2×M16×C151—21no—
54C2×M16×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151—21no—
63C2×M16×C151—21no—
64C2×M16×C151—21no—
65C2×M16×C151—21no—
66C2×M16×C151—21no—
67C2×M16×C151C2×C412yes—
68C2×M16×C151D412yes—
69C2×M16×C151D412yes—
70C2×M16×C151D412yes—
71C2×M16×C151D412yes—
72C22×C8×C151—21no—
73C22×C8×C151—21no—
74C22×C8×C151—21no—
75C22×C8×C151D412yes—
76#117×C151—21no—
77#117×C151—21no—
78#117×C151—21no—
79#117×C151D412yes—
80C2×C4⋊C4×C151—21no—
81C2×C22⋊C4×C151—21no—
82C2×C42×C151—21no—
83C2×C42×C151—21no—
84C2×C42×C151—21no—
85C2×C42×C151—21no—
86C2×C42×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151C2×C412yes—
89#108×C151—28no—
90#104×C151—28no—
91#104×C151—28no—
92C22⋊C8×C151—28no—
93C24×C151—21no—
94C24×C151#4111yescharacteristic
95#41×C151—22no—
96#41×C151—22no—
97#41×C151—22no—
98#41×C151—22no—
99#41×C151—22no—
100#41×C151—22no—
101#41×C151—22no—
102#41×C151—22no—
103#41×C151—41no—
104#41×C151—41no—
105#41×C151—41no—
106#41×C151—41no—
107#41×C151—41no—
108#41×C151—41no—
109#41×C151—41no—
110#41×C151—41no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151C4⋊C412yes—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—41no—
125C2×D4×C151—41no—
126C2×D4×C151—41no—
127C2×D4×C151—41no—
128C2×D4×C151C4⋊C412yes—
129C22×C4×C151—22no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—44no—
134C22×C4×C151—41no—
135C22×C4×C151—41no—
136C22×C4×C151—41no—
137C22×C4×C151—41no—
138C22×C4×C151—41no—
139C22×C4×C151—41no—
140C22×C4×C151—41no—
141C22×C4×C151C22×C411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×Q811yescharacteristic
150C22×C4×C151#4111yescharacteristic
151C22×C4×C151#4111yescharacteristic
152C22×C4×C151#4111yescharacteristic
153C22×C4×C151#4111yescharacteristic
154C22×C4×C151#4111yescharacteristic
155M16×C151—22no—
156M16×C151—22no—
157M16×C151—22no—
158M16×C151—22no—
159M16×C151—22no—
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—41no—
163M16×C151—41no—
164M16×C151—41no—
165M16×C151—41no—
166M16×C151—41no—
167M16×C151—41no—
168M16×C151—41no—
169M16×C151—41no—
170M16×C151C22⋊C414yes—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C2×C8×C151—22no—
174C2×C8×C151—22no—
175C2×C8×C151—22no—
176C2×C8×C151—22no—
177C2×C8×C151—22no—
178C2×C8×C151—22no—
179C2×C8×C151—41no—
180C2×C8×C151—41no—
181C2×C8×C151—41no—
182C2×C8×C151—41no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—41no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—41no—
187C42×C151—22no—
188C42×C151—22no—
189C42×C151—22no—
190C42×C151—41no—
191C42×C151—41no—
192C42×C151—41no—
193C23×C151—22no—
194C23×C151—42no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—82no—
198C23×C151C4×D411yescharacteristic
199C23×C151#12111yescharacteristic
200C23×C151C22⋊Q811yescharacteristic
201C23×C151#12311yescharacteristic
202C23×C151#12411yescharacteristic
203C23×C151#12411yescharacteristic
204C23×C151#12611yescharacteristic
205Q8×C151—22no—
206Q8×C151—22no—
207Q8×C151—41no—
208Q8×C151—41no—
209D4×C151—22no—
210D4×C151—22no—
211D4×C151—42no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—41no—
216D4×C151—41no—
217C2×C4×C151—24no—
218C2×C4×C151—22no—
219C2×C4×C151—42no—
220C2×C4×C151—44no—
221C2×C4×C151—44no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—82no—
231C2×C4×C151C2×C22⋊C411yescharacteristic
232C2×C4×C151C2×C4⋊C411yescharacteristic
233C2×C4×C151#11711yescharacteristic
234C2×C4×C151C4×D411yescharacteristic
235C2×C4×C151C4×D411yescharacteristic
236C2×C4×C151C4×D411yescharacteristic
237C2×C4×C151#12011yescharacteristic
238C2×C4×C151#12011yescharacteristic
239C2×C4×C151#12011yescharacteristic
240C2×C4×C151#12111yescharacteristic
241C2×C4×C151#12111yescharacteristic
242C2×C4×C151#12111yescharacteristic
243C2×C4×C151#12111yescharacteristic
244C2×C4×C151#12111yescharacteristic
245C2×C4×C151#12111yescharacteristic
246C2×C4×C151#12111yescharacteristic
247C2×C4×C151C22⋊Q811yescharacteristic
248C2×C4×C151C22⋊Q811yescharacteristic
249C2×C4×C151C22⋊Q811yescharacteristic
250C2×C4×C151C22⋊Q811yescharacteristic
251C2×C4×C151C22⋊Q811yescharacteristic
252C2×C4×C151#12311yescharacteristic
253C2×C4×C151#12311yescharacteristic
254C2×C4×C151#12311yescharacteristic
255C2×C4×C151#12311yescharacteristic
256C2×C4×C151#12411yescharacteristic
257C2×C4×C151#12611yescharacteristic
258C2×C4×C151#12711yescharacteristic
259C8×C151—24no—
260C8×C151—42no—
261C8×C151—42no—
262C8×C151—42no—
263C22×C151—22no—
264C22×C151—22no—
265C22×C151—22no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—41no—
270C22×C151—44no—
271C22×C151—42no—
272C22×C151—82no—
273C22×C151—82no—
274C22×C151#38511yescharacteristic
275C22×C151#38811yescharacteristic
276C22×C151#39011yescharacteristic
277C22×C151#39311yescharacteristic
278C22×C151#39411yescharacteristic
279C22×C151#39611yescharacteristic
280C22×C151#39711yescharacteristic
281C4×C151—44no—
282C4×C151—42no—
283C4×C151—82no—
284C4×C151#38011yescharacteristic
285C4×C151#38511yescharacteristic
286C4×C151#38611yescharacteristic
287C4×C151#38811yescharacteristic
288C4×C151#39211yescharacteristic
289C4×C151#39411yescharacteristic
290C4×C151#39611yescharacteristic
291C4×C151#39911yescharacteristic
292C2×C151—21no—
293C2×C151—21no—
294C2×C151—21no—
295C2×C151—21no—
296C2×C151—21no—
297C2×C151—21no—
298C2×C151—82no—
299C2×C151#143911yescharacteristic
300C2×C151#186112yes—
301#11114C15111yesmaximal, characteristic, direct product factor, Sylow
302C151#1111411yescharacteristic, direct product factor, Sylow
303C2×#430C2×C15111yescharacteristic, complemented
304C2×#421C2×C15111yescharacteristic
305C22×#104C2×C15111yescharacteristic
306#2879C2×C15111yescharacteristic
307C2×#344C2×C15111yescharacteristic, complemented
308C2×#339C2×C15111yescharacteristic, complemented
309#1728C2×C15111yescharacteristic, complemented
310C22×#41C22×C15111yescharacteristic
311C22×M16C22×C15111yescharacteristic
312C22×M16C22×C15111yescharacteristic
313C22×M16C22×C15111yescharacteristic
314C22×M16C22×C15111yescharacteristic
315C2×#117C22×C15111yescharacteristic
316C22×C42C22×C15111yescharacteristic
317#430—22no—
318#430—22no—
319C2×#108—22no—
320#421—22no—
321#421—22no—
322C2×#104—22no—
323C2×#104—22no—
324C2×#104—22no—
325C2×#104C4×C15114yescomplemented
326#408—22no—
327#408—22no—
328#407—22no—
329#344—22no—
330#339—22no—
331#336—22no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41C2×C4×C15112yes—
343C2×#41D4×C15112yes—
344C22×Q8Q8×C15111yescharacteristic
345C22×D4—21no—
346C22×D4Q8×C15111yescharacteristic
347C23×C4—21no—
348C23×C4—21no—
349C23×C4C23×C15111yescharacteristic
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16C2×C4×C15112yes—
370C2×M16D4×C15112yes—
371C2×M16D4×C15112yes—
372C2×M16D4×C15112yes—
373C2×M16D4×C15112yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8D4×C15112yes—
378#117—21no—
379#117—21no—
380#117—21no—
381#117D4×C15112yes—
382C2×C4⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C2×C4×C15112yes—
391#108—28no—
392#104—28no—
393#104—28no—
394C22⋊C8—28no—
395C24—21no—
396C24#41×C15111yescharacteristic
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8C4⋊C4×C15112yes—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4C4⋊C4×C15112yes—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—44no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4C22×C4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×Q8×C15111yescharacteristic
452C22×C4#41×C15111yescharacteristic
453C22×C4#41×C15111yescharacteristic
454C22×C4#41×C15111yescharacteristic
455C22×C4#41×C15111yescharacteristic
456C22×C4#41×C15111yescharacteristic
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16C22⋊C4×C15114yes—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C22⋊C4—22no—
488C22⋊C4—41no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—41no—
493C42—41no—
494C42—41no—
495C23—22no—
496C23—42no—
497C23—41no—
498C23—41no—
499C23—82no—
500C23C4×D4×C15111yescharacteristic
501C23#121×C15111yescharacteristic
502C23C22⋊Q8×C15111yescharacteristic
503C23#123×C15111yescharacteristic
504C23#124×C15111yescharacteristic
505C23#124×C15111yescharacteristic
506C23#126×C15111yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511D4—22no—
512D4—22no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4C2×C22⋊C4×C15111yescharacteristic
534C2×C4C2×C4⋊C4×C15111yescharacteristic
535C2×C4#117×C15111yescharacteristic
536C2×C4C4×D4×C15111yescharacteristic
537C2×C4C4×D4×C15111yescharacteristic
538C2×C4C4×D4×C15111yescharacteristic
539C2×C4#120×C15111yescharacteristic
540C2×C4#120×C15111yescharacteristic
541C2×C4#120×C15111yescharacteristic
542C2×C4#121×C15111yescharacteristic
543C2×C4#121×C15111yescharacteristic
544C2×C4#121×C15111yescharacteristic
545C2×C4#121×C15111yescharacteristic
546C2×C4#121×C15111yescharacteristic
547C2×C4#121×C15111yescharacteristic
548C2×C4#121×C15111yescharacteristic
549C2×C4C22⋊Q8×C15111yescharacteristic
550C2×C4C22⋊Q8×C15111yescharacteristic
551C2×C4C22⋊Q8×C15111yescharacteristic
552C2×C4C22⋊Q8×C15111yescharacteristic
553C2×C4C22⋊Q8×C15111yescharacteristic
554C2×C4#123×C15111yescharacteristic
555C2×C4#123×C15111yescharacteristic
556C2×C4#123×C15111yescharacteristic
557C2×C4#123×C15111yescharacteristic
558C2×C4#124×C15111yescharacteristic
559C2×C4#126×C15111yescharacteristic
560C2×C4#127×C15111yescharacteristic
561C8—24no—
562C8—42no—
563C8—42no—
564C8—42no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—82no—
576C22#385×C15111yescharacteristic
577C22#388×C15111yescharacteristic
578C22#390×C15111yescharacteristic
579C22#393×C15111yescharacteristic
580C22#394×C15111yescharacteristic
581C22#396×C15111yescharacteristic
582C22#397×C15111yescharacteristic
583C4—44no—
584C4—42no—
585C4—82no—
586C4#380×C15111yescharacteristic
587C4#385×C15111yescharacteristic
588C4#386×C15111yescharacteristic
589C4#388×C15111yescharacteristic
590C4#392×C15111yescharacteristic
591C4#394×C15111yescharacteristic
592C4#396×C15111yescharacteristic
593C4#399×C15111yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—82no—
601C2#1439×C15111yescharacteristic
602C2#1861×C15112yes—
subgroupG/H
centerC2×C4×C151#120
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
socleC22×C151#385
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#430×C151C2semidirect
5. C2×#344×C151C2semidirect
6. C2×#339×C151C2semidirect
7. #1728×C151C2semidirect
23. C2×#104×C151C4semidirect
301. #11114C151direct (N × H)
302. C151#11114direct (N × H)
303. C2×#430C2×C151semidirect
307. C2×#344C2×C151semidirect
308. C2×#339C2×C151semidirect
309. #1728C2×C151semidirect
325. C2×#104C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#430×C1512
C2×#421×C1512
C22×#104×C1512
#2879×C1512
C2×#344×C1512
C2×#339×C1512
#1728×C1512
#11114151