Finite Group Databasebeta

← C2×#1877×C151 #50325845

Subgroups — C2×#1877×C151 #50325845

Order 38656.

2254 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C151C211yesmaximal, characteristic
2C22×C4×D4×C151C211yesmaximal, characteristic
3C22×#103×C151C211yesmaximal, characteristic, complemented
4C22×#102×C151C211yesmaximal, characteristic
5C2×#391×C151C211yesmaximal, characteristic, complemented
6#1877×C151C218yesmaximal, direct product factor
7C2×#340×C151C211yesmaximal, characteristic, complemented
8C2×#336×C151C211yesmaximal, characteristic, complemented
9C23×Q8×C151C2211yescharacteristic
10C23×D4×C151C2211yescharacteristic
11C24×C4×C151—21no—
12C22×SD16×C151—24no—
13C22×SD16×C151—24no—
14C22×SD16×C151C418yescomplemented
15C22×SD16×C151C2214yes—
16C23×C8×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×C4×D4×C151—24no—
19C2×C4×D4×C151—24no—
20C2×C4×D4×C151—22no—
21C2×C4×D4×C151C2214yes—
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24C22×C22⋊C4×C151—21no—
25C22×C42×C151C2211yescharacteristic
26C2×#103×C151—24no—
27C2×#103×C151C2214yescomplemented
28C2×#102×C151—24no—
29C2×#102×C151C2214yes—
30#391×C151—22no—
31#391×C151C2214yescomplemented
32C2×#95×C151—21no—
33C2×#95×C151—21no—
34#340×C151C2214yescomplemented
35#336×C151C2214yescomplemented
36C25×C151—21no—
37C22×Q8×C151—22no—
38C22×Q8×C151—22no—
39C22×Q8×C151—22no—
40C22×Q8×C151—22no—
41C22×Q8×C151—21no—
42C22×Q8×C151—22no—
43C22×Q8×C151C2×C414yescomplemented
44C22×Q8×C151C2312yes—
45C22×D4×C151—22no—
46C22×D4×C151—21no—
47C22×D4×C151—22no—
48C22×D4×C151—22no—
49C22×D4×C151C2×C414yes—
50C22×D4×C151D414yes—
51C22×D4×C151D414yes—
52C22×D4×C151C2312yes—
53C23×C4×C151—28no—
54C23×C4×C151—24no—
55C23×C4×C151—21no—
56C23×C4×C151—21no—
57C23×C4×C151—21no—
58C23×C4×C151—44no—
59C23×C4×C151—44no—
60C23×C4×C151D411yescharacteristic
61C23×C4×C151D411yescharacteristic
62C23×C4×C151C2311yescharacteristic
63C2×SD16×C151—232no—
64C2×SD16×C151—28no—
65C2×SD16×C151—28no—
66C2×SD16×C151C2×C4116yescomplemented
67C22×C8×C151—22no—
68C22×C8×C151—22no—
69C22×C8×C151—22no—
70C22×C8×C151—22no—
71C22×C8×C151—22no—
72C22×C8×C151C2×C414yescomplemented
73C22×C8×C151C2312yes—
74C22×C8×C151C2312yes—
75C4×D4×C151—216no—
76C4×D4×C151—28no—
77C4×D4×C151—28no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151D414yes—
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2312yes—
86C2×C22⋊C4×C151—28no—
87C2×C22⋊C4×C151—24no—
88C2×C42×C151—22no—
89C2×C42×C151—22no—
90C2×C42×C151D412yes—
91C2×C42×C151C2312yes—
92#103×C151—28no—
93#102×C151—28no—
94#95×C151—24no—
95#95×C151—24no—
96C24×C151—24no—
97C24×C151—24no—
98C24×C151—24no—
99C24×C151—22no—
100C24×C151—42no—
101C24×C151—42no—
102C24×C151—42no—
103C24×C151—42no—
104C24×C151C2×D411yescharacteristic
105C2×Q8×C151—24no—
106C2×Q8×C151—22no—
107C2×Q8×C151—28no—
108C2×Q8×C151—28no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—42no—
114C2×Q8×C151—42no—
115C2×Q8×C151—44no—
116C2×Q8×C151—44no—
117C2×Q8×C151C22×C414yescomplemented
118C2×D4×C151—28no—
119C2×D4×C151—24no—
120C2×D4×C151—24no—
121C2×D4×C151—28no—
122C2×D4×C151—24no—
123C2×D4×C151—28no—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151C22⋊C4116yes—
128C2×D4×C151C22×C414yes—
129C2×D4×C151C2×D414yes—
130C2×D4×C151C2×D414yes—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—216no—
134C22×C4×C151—24no—
135C22×C4×C151—22no—
136C22×C4×C151—24no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—48no—
143C22×C4×C151—432no—
144C22×C4×C151—42no—
145C22×C4×C151—42no—
146C22×C4×C151—42no—
147C22×C4×C151—42no—
148C22×C4×C151—48no—
149C22×C4×C151—42no—
150C22×C4×C151—42no—
151C22×C4×C151—42no—
152C22×C4×C151SD1614yescomplemented
153C22×C4×C151C22×C412yes—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D412yes—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D412yes—
160C22×C4×C151#4112yes—
161C22×C4×C151#4112yes—
162C22×C4×C151C2411yescharacteristic
163SD16×C151—232no—
164C2×C8×C151—28no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—44no—
171C2×C8×C151C22×C414yescomplemented
172C4⋊C4×C151—24no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—42no—
177C4⋊C4×C151C2×D414yes—
178C22⋊C4×C151—216no—
179C42×C151—24no—
180C42×C151—22no—
181C42×C151—22no—
182C23×C151—24no—
183C23×C151—24no—
184C23×C151—24no—
185C23×C151—216no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—48no—
191C23×C151—48no—
192C23×C151—48no—
193C23×C151—48no—
194C23×C151—48no—
195C23×C151—48no—
196C23×C151C4×D412yes—
197C23×C151#12012yes—
198C23×C151#12112yes—
199C23×C151C2×SD1612yes—
200C23×C151#13512yes—
201C23×C151AGL(1,ℤ/8)12yes—
202C23×C151#13712yes—
203C23×C151C22×D411yescharacteristic
204Q8×C151—24no—
205Q8×C151—24no—
206Q8×C151—42no—
207Q8×C151—42no—
208Q8×C151—48no—
209D4×C151—24no—
210D4×C151—24no—
211D4×C151—24no—
212D4×C151—216no—
213D4×C151C2×C22⋊C418yes—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—28no—
217C2×C4×C151—24no—
218C2×C4×C151—22no—
219C2×C4×C151—24no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—432no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—48no—
228C2×C4×C151—48no—
229C2×C4×C151—44no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—84no—
234C2×C4×C151C2×C22⋊C414yes—
235C2×C4×C151C4×D414yes—
236C2×C4×C151C4×D412yes—
237C2×C4×C151#12012yes—
238C2×C4×C151#12114yes—
239C2×C4×C151#12112yes—
240C2×C4×C151#12314yes—
241C2×C4×C151C2×SD1614yescomplemented
242C2×C4×C151C23×C411yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151C2×#4111yescharacteristic
248C8×C151—24no—
249C8×C151—42no—
250C22×C151—28no—
251C22×C151—432no—
252C22×C151—44no—
253C22×C151—44no—
254C22×C151—44no—
255C22×C151—44no—
256C22×C151—44no—
257C22×C151—44no—
258C22×C151#38614yes—
259C22×C151C4×SD1614yes—
260C22×C151#44014yes—
261C22×C151#45014yes—
262C22×C151#45214yes—
263C22×C151#46114yes—
264C22×C151#46314yes—
265C22×C151C2×C4×D411yescharacteristic
266C22×C151C2×#12011yescharacteristic
267C22×C151C2×#12111yescharacteristic
268C22×C151C22×SD1611yescharacteristic
269C22×C151C2×#13511yescharacteristic
270C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C151C2×#13711yescharacteristic
272C4×C151—24no—
273C4×C151—44no—
274C4×C151—42no—
275C4×C151—44no—
276C4×C151—82no—
277C4×C151#38614yes—
278C4×C151C22×C22⋊C411yescharacteristic
279C4×C151C2×C4×D411yescharacteristic
280C4×C151C2×#12111yescharacteristic
281C4×C151C2×#12311yescharacteristic
282C2×C151—48no—
283C2×C151#187718yesdirect product factor
284C2×C151C2×#38611yescharacteristic
285C2×C151C2×C4×SD1611yescharacteristic
286C2×C151C2×#44011yescharacteristic
287C2×C151C2×#45011yescharacteristic
288C2×C151C2×#45211yescharacteristic
289C2×C151C2×#46111yescharacteristic
290C2×C151C2×#46311yescharacteristic
291C2×#1877C15111yesmaximal, characteristic, direct product factor, Sylow
292C151C2×#187711yescharacteristic, direct product factor, Sylow
293C23×SD16C2×C15111yescharacteristic
294C22×C4×D4C2×C15111yescharacteristic
295C22×#103C2×C15111yescharacteristic, complemented
296C22×#102C2×C15111yescharacteristic
297C2×#391C2×C15111yescharacteristic, complemented
298#1877C2×C15118yesdirect product factor
299C2×#340C2×C15111yescharacteristic, complemented
300C2×#336C2×C15111yescharacteristic, complemented
301C23×Q8C22×C15111yescharacteristic
302C23×D4C22×C15111yescharacteristic
303C24×C4—21no—
304C22×SD16—24no—
305C22×SD16—24no—
306C22×SD16C4×C15118yescomplemented
307C22×SD16C22×C15114yes—
308C23×C8C22×C15111yescharacteristic
309C23×C8C22×C15111yescharacteristic
310C2×C4×D4—24no—
311C2×C4×D4—24no—
312C2×C4×D4—22no—
313C2×C4×D4C22×C15114yes—
314C22×C4⋊C4C22×C15111yescharacteristic
315C22×C4⋊C4C22×C15111yescharacteristic
316C22×C22⋊C4—21no—
317C22×C42C22×C15111yescharacteristic
318C2×#103—24no—
319C2×#103C22×C15114yescomplemented
320C2×#102—24no—
321C2×#102C22×C15114yes—
322#391—22no—
323#391C22×C15114yescomplemented
324C2×#95—21no—
325C2×#95—21no—
326#340C22×C15114yescomplemented
327#336C22×C15114yescomplemented
328C25—21no—
329C22×Q8—22no—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8C2×C4×C15114yescomplemented
336C22×Q8C23×C15112yes—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4C2×C4×C15114yes—
342C22×D4D4×C15114yes—
343C22×D4D4×C15114yes—
344C22×D4C23×C15112yes—
345C23×C4—28no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—24no—
349C23×C4—21no—
350C23×C4—44no—
351C23×C4—44no—
352C23×C4D4×C15111yescharacteristic
353C23×C4D4×C15111yescharacteristic
354C23×C4C23×C15111yescharacteristic
355C2×SD16—232no—
356C2×SD16—28no—
357C2×SD16—28no—
358C2×SD16C2×C4×C151116yescomplemented
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8C2×C4×C15114yescomplemented
365C22×C8C23×C15112yes—
366C22×C8C23×C15112yes—
367C4×D4—216no—
368C4×D4—28no—
369C4×D4—28no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C15114yes—
376C2×C4⋊C4C23×C15112yes—
377C2×C4⋊C4C23×C15112yes—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42D4×C15112yes—
383C2×C42C23×C15112yes—
384#103—28no—
385#102—28no—
386#95—24no—
387#95—24no—
388C24—24no—
389C24—24no—
390C24—24no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C2×D4×C15111yescharacteristic
397C2×Q8—24no—
398C2×Q8—22no—
399C2×Q8—28no—
400C2×Q8—28no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—42no—
406C2×Q8—44no—
407C2×Q8—42no—
408C2×Q8—44no—
409C2×Q8C22×C4×C15114yescomplemented
410C2×D4—24no—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4C22⋊C4×C151116yes—
420C2×D4C22×C4×C15114yes—
421C2×D4C2×D4×C15114yes—
422C2×D4C2×D4×C15114yes—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—216no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—432no—
435C22×C4—48no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—48no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4SD16×C15114yescomplemented
445C22×C4C22×C4×C15112yes—
446C22×C4C2×D4×C15112yes—
447C22×C4C2×D4×C15112yes—
448C22×C4C2×D4×C15112yes—
449C22×C4C2×D4×C15112yes—
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15112yes—
452C22×C4#41×C15112yes—
453C22×C4#41×C15112yes—
454C22×C4C24×C15111yescharacteristic
455SD16—232no—
456C2×C8—28no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—44no—
463C2×C8C22×C4×C15114yescomplemented
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—42no—
469C4⋊C4C2×D4×C15114yes—
470C22⋊C4—216no—
471C42—24no—
472C42—22no—
473C42—22no—
474C23—216no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—48no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—48no—
483C23—48no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23C4×D4×C15112yes—
489C23#120×C15112yes—
490C23#121×C15112yes—
491C23C2×SD16×C15112yes—
492C23#135×C15112yes—
493C23AGL(1,ℤ/8)×C15112yes—
494C23#137×C15112yes—
495C23C22×D4×C15111yescharacteristic
496Q8—24no—
497Q8—24no—
498Q8—48no—
499Q8—42no—
500Q8—42no—
501D4—216no—
502D4—24no—
503D4—24no—
504D4—24no—
505D4C2×C22⋊C4×C15118yes—
506C2×C4—28no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—432no—
515C2×C4—48no—
516C2×C4—48no—
517C2×C4—44no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—84no—
526C2×C4C2×C22⋊C4×C15114yes—
527C2×C4C4×D4×C15112yes—
528C2×C4C4×D4×C15114yes—
529C2×C4#120×C15112yes—
530C2×C4#121×C15112yes—
531C2×C4#121×C15114yes—
532C2×C4#123×C15114yes—
533C2×C4C2×SD16×C15114yescomplemented
534C2×C4C23×C4×C15111yescharacteristic
535C2×C4C22×D4×C15111yescharacteristic
536C2×C4C22×D4×C15111yescharacteristic
537C2×C4C22×D4×C15111yescharacteristic
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15111yescharacteristic
540C8—24no—
541C8—42no—
542C22—28no—
543C22—432no—
544C22—44no—
545C22—44no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22#386×C15114yes—
551C22C4×SD16×C15114yes—
552C22#440×C15114yes—
553C22#450×C15114yes—
554C22#452×C15114yes—
555C22#461×C15114yes—
556C22#463×C15114yes—
557C22C2×C4×D4×C15111yescharacteristic
558C22C2×#120×C15111yescharacteristic
559C22C2×#121×C15111yescharacteristic
560C22C22×SD16×C15111yescharacteristic
561C22C2×#135×C15111yescharacteristic
562C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
563C22C2×#137×C15111yescharacteristic
564C4—24no—
565C4—44no—
566C4—42no—
567C4—44no—
568C4—82no—
569C4#386×C15114yes—
570C4C22×C22⋊C4×C15111yescharacteristic
571C4C2×C4×D4×C15111yescharacteristic
572C4C2×#121×C15111yescharacteristic
573C4C2×#123×C15111yescharacteristic
574C2—48no—
575C2#1877×C15118yesdirect product factor
576C2C2×#386×C15111yescharacteristic
577C2C2×C4×SD16×C15111yescharacteristic
578C2C2×#440×C15111yescharacteristic
579C2C2×#450×C15111yescharacteristic
580C2C2×#452×C15111yescharacteristic
581C2C2×#461×C15111yescharacteristic
582C2C2×#463×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C2×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×#103×C151C2semidirect
5. C2×#391×C151C2semidirect
6. #1877×C151C2direct (N × H)
7. C2×#340×C151C2semidirect
8. C2×#336×C151C2semidirect
14. C22×SD16×C151C4semidirect
27. C2×#103×C151C22semidirect
31. #391×C151C22semidirect
34. #340×C151C22semidirect
35. #336×C151C22semidirect
43. C22×Q8×C151C2×C4semidirect
66. C2×SD16×C151C2×C4semidirect
72. C22×C8×C151C2×C4semidirect
117. C2×Q8×C151C22×C4semidirect
152. C22×C4×C151SD16semidirect
171. C2×C8×C151C22×C4semidirect
241. C2×C4×C151C2×SD16semidirect
283. C2×C151#1877direct (N × H)
291. C2×#1877C151direct (N × H)
292. C151C2×#1877direct (N × H)
295. C22×#103C2×C151semidirect
297. C2×#391C2×C151semidirect
298. #1877C2×C151direct (N × H)
299. C2×#340C2×C151semidirect
300. C2×#336C2×C151semidirect
306. C22×SD16C4×C151semidirect
319. C2×#103C22×C151semidirect
323. #391C22×C151semidirect
326. #340C22×C151semidirect
327. #336C22×C151semidirect
335. C22×Q8C2×C4×C151semidirect
358. C2×SD16C2×C4×C151semidirect
364. C22×C8C2×C4×C151semidirect
409. C2×Q8C22×C4×C151semidirect
444. C22×C4SD16×C151semidirect
463. C2×C8C22×C4×C151semidirect
533. C2×C4C2×SD16×C151semidirect
575. C2#1877×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C23×SD16×C1512
C22×C4×D4×C1512
C22×#103×C1512
C22×#102×C1512
C2×#391×C1512
#1877×C1512
C2×#340×C1512
C2×#336×C1512
C2×#1877151