Finite Group Databasebeta

← C2×#2034×C151 #50328402

Subgroups — C2×#2034×C151 #50328402

Order 38656.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic
2C22×#106×C151C211yesmaximal, characteristic, complemented
3C22×#102×C151C211yesmaximal, characteristic, complemented
4C22×#102×C151C211yesmaximal, characteristic, complemented
5C22×C22⋊C8×C151C211yesmaximal, characteristic, complemented
6C2×#380×C151C211yesmaximal, characteristic, complemented
7#2034×C151C218yesmaximal, direct product factor
8C2×#340×C151C211yesmaximal, characteristic, complemented
9C23×D4×C151—21no—
10C23×D4×C151C2211yescharacteristic
11C24×C4×C151C2211yescharacteristic
12C23×C8×C151C2211yescharacteristic
13C23×C8×C151C2211yescharacteristic
14C2×#121×C151—24no—
15C2×#121×C151—22no—
16C2×#121×C151—24no—
17C2×#121×C151C2214yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C22⋊C4×C151—21no—
22C22×C22⋊C4×C151—21no—
23C2×#106×C151—24no—
24C2×#106×C151C2214yescomplemented
25C2×#102×C151—24no—
26C2×#102×C151—24no—
27C2×#102×C151C2214yescomplemented
28C2×#102×C151C2214yescomplemented
29C2×C22⋊C8×C151—24no—
30C2×C22⋊C8×C151C2214yescomplemented
31#380×C151—22no—
32#380×C151C2214yescomplemented
33C2×#95×C151—21no—
34#340×C151C2214yescomplemented
35C25×C151—21no—
36C25×C151D411yescharacteristic
37C22×D4×C151—28no—
38C22×D4×C151—22no—
39C22×D4×C151—21no—
40C22×D4×C151—24no—
41C22×D4×C151—22no—
42C22×D4×C151—22no—
43C22×D4×C151—22no—
44C22×D4×C151—22no—
45C22×D4×C151—44no—
46C22×D4×C151—44no—
47C22×D4×C151D414yes—
48C22×D4×C151C2312yes—
49C23×C4×C151—22no—
50C23×C4×C151—22no—
51C23×C4×C151—22no—
52C23×C4×C151—22no—
53C23×C4×C151—22no—
54C23×C4×C151—22no—
55C23×C4×C151—21no—
56C23×C4×C151—21no—
57C23×C4×C151—21no—
58C23×C4×C151D412yes—
59C23×C4×C151D411yescharacteristic
60C23×C4×C151C2312yes—
61C23×C4×C151C2311yescharacteristic
62C22×C8×C151—22no—
63C22×C8×C151—22no—
64C22×C8×C151—22no—
65C22×C8×C151—22no—
66C22×C8×C151—22no—
67C22×C8×C151D414yescomplemented
68C22×C8×C151C2312yes—
69C22×C8×C151C2312yes—
70#121×C151—216no—
71#121×C151—28no—
72#121×C151—28no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151D414yes—
82C2×C4⋊C4×C151C2312yes—
83C2×C4⋊C4×C151C2312yes—
84C2×C4⋊C4×C151C2312yes—
85C2×C22⋊C4×C151—28no—
86C2×C22⋊C4×C151—24no—
87C2×C22⋊C4×C151—24no—
88C2×C22⋊C4×C151—44no—
89#106×C151—28no—
90#102×C151—28no—
91#102×C151—28no—
92C22⋊C8×C151—28no—
93#95×C151—24no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—22no—
97C24×C151—22no—
98C24×C151—22no—
99C24×C151—22no—
100C24×C151—24no—
101C24×C151—22no—
102C24×C151—42no—
103C24×C151—42no—
104C24×C151—42no—
105C24×C151—42no—
106C24×C151—42no—
107C24×C151—42no—
108C24×C151SD1614yes—
109C24×C151C2×D412yes—
110C24×C151C2×D411yescharacteristic
111C2×D4×C151—216no—
112C2×D4×C151—24no—
113C2×D4×C151—28no—
114C2×D4×C151—28no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—22no—
120C2×D4×C151—48no—
121C2×D4×C151—432no—
122C2×D4×C151—48no—
123C2×D4×C151—44no—
124C2×D4×C151—42no—
125C2×D4×C151—42no—
126C2×D4×C151—44no—
127C2×D4×C151C2×D414yes—
128C22×C4×C151—22no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—24no—
134C22×C4×C151—24no—
135C22×C4×C151—24no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—42no—
145C22×C4×C151—42no—
146C22×C4×C151—44no—
147C22×C4×C151—44no—
148C22×C4×C151—44no—
149C22×C4×C151—44no—
150C22×C4×C151—42no—
151C22×C4×C151—42no—
152C22×C4×C151—42no—
153C22×C4×C151—42no—
154C22×C4×C151—42no—
155C22×C4×C151—42no—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2×D412yes—
161C22×C4×C151#4112yes—
162C22×C4×C151#4112yes—
163C22×C4×C151#4112yes—
164C22×C4×C151C2411yescharacteristic
165C2×C8×C151—28no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—44no—
172C2×C8×C151C2×D414yescomplemented
173C4⋊C4×C151—24no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—42no—
180C4⋊C4×C151—42no—
181C4⋊C4×C151C2×D414yes—
182C22⋊C4×C151—216no—
183C22⋊C4×C151—48no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—28no—
191C23×C151—28no—
192C23×C151—28no—
193C23×C151—24no—
194C23×C151—44no—
195C23×C151—44no—
196C23×C151—44no—
197C23×C151—44no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—48no—
205C23×C151—48no—
206C23×C151—48no—
207C23×C151—84no—
208C23×C151—84no—
209C23×C151—84no—
210C23×C151—84no—
211C23×C151#12012yes—
212C23×C151#12112yes—
213C23×C151#12312yes—
214C23×C151C2×SD1614yes—
215C23×C151C2×SD1612yes—
216C23×C151#13512yes—
217C23×C151AGL(1,ℤ/8)12yes—
218C23×C151AGL(1,ℤ/8)12yes—
219C23×C151C22×D411yescharacteristic
220D4×C151—24no—
221D4×C151—24no—
222D4×C151—432no—
223D4×C151—42no—
224D4×C151—42no—
225D4×C151—48no—
226C2×C4×C151—22no—
227C2×C4×C151—24no—
228C2×C4×C151—22no—
229C2×C4×C151—22no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—44no—
233C2×C4×C151—48no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—48no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—42no—
245C2×C4×C151—84no—
246C2×C4×C151—84no—
247C2×C4×C151#12012yes—
248C2×C4×C151#12114yes—
249C2×C4×C151#12114yes—
250C2×C4×C151#12112yes—
251C2×C4×C151#12314yes—
252C2×C4×C151#12312yes—
253C2×C4×C151#12414yes—
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151C22×D411yescharacteristic
256C2×C4×C151C22×D411yescharacteristic
257C2×C4×C151C2×#4111yescharacteristic
258C2×C4×C151C2×#4111yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C8×C151—24no—
261C8×C151—42no—
262C22×C151—24no—
263C22×C151—24no—
264C22×C151—24no—
265C22×C151—42no—
266C22×C151—42no—
267C22×C151—42no—
268C22×C151—42no—
269C22×C151—416no—
270C22×C151—44no—
271C22×C151—44no—
272C22×C151—44no—
273C22×C151—82no—
274C22×C151—82no—
275C22×C151—82no—
276C22×C151—82no—
277C22×C151—816no—
278C22×C151#39414yes—
279C22×C151#44914yes—
280C22×C151#45014yes—
281C22×C151#46514yes—
282C22×C151#46914yes—
283C22×C151#48114yes—
284C22×C151#48214yes—
285C22×C151C2×#12011yescharacteristic
286C22×C151C2×#12111yescharacteristic
287C22×C151C2×#12311yescharacteristic
288C22×C151C22×SD1611yescharacteristic
289C22×C151C2×#13511yescharacteristic
290C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C151—42no—
293C4×C151—44no—
294C4×C151—82no—
295C4×C151—82no—
296C4×C151#39414yes—
297C4×C151C2×#12111yescharacteristic
298C4×C151C2×#12111yescharacteristic
299C4×C151C2×#12311yescharacteristic
300C4×C151C2×#12411yescharacteristic
301C2×C151—44no—
302C2×C151—84no—
303C2×C151#203418yesdirect product factor
304C2×C151C2×#39411yescharacteristic
305C2×C151C2×#45011yescharacteristic
306C2×C151C2×#44911yescharacteristic
307C2×C151C2×#46511yescharacteristic
308C2×C151C2×#46911yescharacteristic
309C2×C151C2×#48211yescharacteristic
310C2×C151C2×#48111yescharacteristic
311C2×#2034C15111yesmaximal, characteristic, direct product factor, Sylow
312C151C2×#203411yescharacteristic, direct product factor, Sylow
313C22×#121C2×C15111yescharacteristic
314C22×#106C2×C15111yescharacteristic, complemented
315C22×#102C2×C15111yescharacteristic, complemented
316C22×#102C2×C15111yescharacteristic, complemented
317C22×C22⋊C8C2×C15111yescharacteristic, complemented
318C2×#380C2×C15111yescharacteristic, complemented
319#2034C2×C15118yesdirect product factor
320C2×#340C2×C15111yescharacteristic, complemented
321C23×D4—21no—
322C23×D4C22×C15111yescharacteristic
323C24×C4C22×C15111yescharacteristic
324C23×C8C22×C15111yescharacteristic
325C23×C8C22×C15111yescharacteristic
326C2×#121—24no—
327C2×#121—22no—
328C2×#121—24no—
329C2×#121C22×C15114yes—
330C22×C4⋊C4C22×C15111yescharacteristic
331C22×C4⋊C4C22×C15111yescharacteristic
332C22×C4⋊C4C22×C15111yescharacteristic
333C22×C22⋊C4—21no—
334C22×C22⋊C4—21no—
335C2×#106—24no—
336C2×#106C22×C15114yescomplemented
337C2×#102—24no—
338C2×#102—24no—
339C2×#102C22×C15114yescomplemented
340C2×#102C22×C15114yescomplemented
341C2×C22⋊C8—24no—
342C2×C22⋊C8C22×C15114yescomplemented
343#380—22no—
344#380C22×C15114yescomplemented
345C2×#95—21no—
346#340C22×C15114yescomplemented
347C25—21no—
348C25D4×C15111yescharacteristic
349C22×D4—28no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—22no—
357C22×D4—44no—
358C22×D4—44no—
359C22×D4D4×C15114yes—
360C22×D4C23×C15112yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4D4×C15111yescharacteristic
371C23×C4D4×C15112yes—
372C23×C4C23×C15112yes—
373C23×C4C23×C15111yescharacteristic
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—22no—
379C22×C8D4×C15114yescomplemented
380C22×C8C23×C15112yes—
381C22×C8C23×C15112yes—
382#121—216no—
383#121—28no—
384#121—28no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4D4×C15114yes—
394C2×C4⋊C4C23×C15112yes—
395C2×C4⋊C4C23×C15112yes—
396C2×C4⋊C4C23×C15112yes—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—44no—
401#106—28no—
402#102—28no—
403#102—28no—
404C22⋊C8—28no—
405#95—24no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24SD16×C15114yes—
421C24C2×D4×C15112yes—
422C24C2×D4×C15111yescharacteristic
423C2×D4—216no—
424C2×D4—24no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—432no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—42no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4—44no—
439C2×D4C2×D4×C15114yes—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4C2×D4×C15112yes—
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C2×D4×C15112yes—
471C22×C4C2×D4×C15112yes—
472C22×C4C2×D4×C15112yes—
473C22×C4#41×C15112yes—
474C22×C4#41×C15112yes—
475C22×C4#41×C15112yes—
476C22×C4C24×C15111yescharacteristic
477C2×C8—28no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—44no—
484C2×C8C2×D4×C15114yescomplemented
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4C2×D4×C15114yes—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C23—28no—
497C23—28no—
498C23—28no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—48no—
511C23—48no—
512C23—48no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—84no—
523C23#120×C15112yes—
524C23#121×C15112yes—
525C23#123×C15112yes—
526C23C2×SD16×C15114yes—
527C23C2×SD16×C15112yes—
528C23#135×C15112yes—
529C23AGL(1,ℤ/8)×C15112yes—
530C23AGL(1,ℤ/8)×C15112yes—
531C23C22×D4×C15111yescharacteristic
532D4—24no—
533D4—24no—
534D4—432no—
535D4—48no—
536D4—42no—
537D4—42no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—44no—
543C2×C4—48no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4#120×C15112yes—
560C2×C4#121×C15112yes—
561C2×C4#121×C15114yes—
562C2×C4#121×C15114yes—
563C2×C4#123×C15112yes—
564C2×C4#123×C15114yes—
565C2×C4#124×C15114yes—
566C2×C4C22×D4×C15111yescharacteristic
567C2×C4C22×D4×C15111yescharacteristic
568C2×C4C22×D4×C15111yescharacteristic
569C2×C4C2×#41×C15111yescharacteristic
570C2×C4C2×#41×C15111yescharacteristic
571C2×C4C2×#41×C15111yescharacteristic
572C8—24no—
573C8—42no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—416no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—816no—
588C22—82no—
589C22—82no—
590C22#394×C15114yes—
591C22#449×C15114yes—
592C22#450×C15114yes—
593C22#465×C15114yes—
594C22#469×C15114yes—
595C22#481×C15114yes—
596C22#482×C15114yes—
597C22C2×#120×C15111yescharacteristic
598C22C2×#121×C15111yescharacteristic
599C22C2×#123×C15111yescharacteristic
600C22C22×SD16×C15111yescharacteristic
601C22C2×#135×C15111yescharacteristic
602C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
603C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
604C4—42no—
605C4—44no—
606C4—82no—
607C4—82no—
608C4#394×C15114yes—
609C4C2×#121×C15111yescharacteristic
610C4C2×#121×C15111yescharacteristic
611C4C2×#123×C15111yescharacteristic
612C4C2×#124×C15111yescharacteristic
613C2—44no—
614C2—84no—
615C2#2034×C15118yesdirect product factor
616C2C2×#394×C15111yescharacteristic
617C2C2×#450×C15111yescharacteristic
618C2C2×#449×C15111yescharacteristic
619C2C2×#465×C15111yescharacteristic
620C2C2×#469×C15111yescharacteristic
621C2C2×#482×C15111yescharacteristic
622C2C2×#481×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#121×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#106×C151C2semidirect
3. C22×#102×C151C2semidirect
4. C22×#102×C151C2semidirect
5. C22×C22⋊C8×C151C2semidirect
6. C2×#380×C151C2semidirect
7. #2034×C151C2direct (N × H)
8. C2×#340×C151C2semidirect
24. C2×#106×C151C22semidirect
27. C2×#102×C151C22semidirect
28. C2×#102×C151C22semidirect
30. C2×C22⋊C8×C151C22semidirect
32. #380×C151C22semidirect
34. #340×C151C22semidirect
67. C22×C8×C151D4semidirect
172. C2×C8×C151C2×D4semidirect
303. C2×C151#2034direct (N × H)
311. C2×#2034C151direct (N × H)
312. C151C2×#2034direct (N × H)
314. C22×#106C2×C151semidirect
315. C22×#102C2×C151semidirect
316. C22×#102C2×C151semidirect
317. C22×C22⋊C8C2×C151semidirect
318. C2×#380C2×C151semidirect
319. #2034C2×C151direct (N × H)
320. C2×#340C2×C151semidirect
336. C2×#106C22×C151semidirect
339. C2×#102C22×C151semidirect
340. C2×#102C22×C151semidirect
342. C2×C22⋊C8C22×C151semidirect
344. #380C22×C151semidirect
346. #340C22×C151semidirect
379. C22×C8D4×C151semidirect
484. C2×C8C2×D4×C151semidirect
615. C2#2034×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#121×C1512
C22×#106×C1512
C22×#102×C1512
C22×C22⋊C8×C1512
C2×#380×C1512
#2034×C1512
C2×#340×C1512
C2×#2034151