Finite Group Databasebeta

← C151×#23721 #50328646

Subgroups — C151×#23721 #50328646

Order 38656.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#137×C151C211yesmaximal, characteristic, complemented
2C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic
3C2×#440×C151C211yesmaximal, characteristic, complemented
4#2923×C151C211yesmaximal, characteristic, complemented
5#2089×C151C211yesmaximal, characteristic, complemented
6#2078×C151C211yesmaximal, characteristic, complemented
7#2064×C151C211yesmaximal, characteristic, complemented
8#2063×C151C211yesmaximal, characteristic, complemented
9#2052×C151C211yesmaximal, characteristic, complemented
10#2051×C151C211yesmaximal, characteristic
11#2046×C151C211yesmaximal, characteristic, complemented
12#2019×C151C211yesmaximal, characteristic
13#1778×C151C211yesmaximal, characteristic, complemented
14C4×#101×C151C211yesmaximal, characteristic, complemented
15C4×#100×C151C211yesmaximal, characteristic, complemented
16C2×#137×C151C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C4×#41×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22#442×C151—21no—
23#441×C151—21no—
24#440×C151—21no—
25#440×C151—21no—
26#440×C151—22no—
27#440×C151—22no—
28C4×Q16×C151—21no—
29C4×SD16×C151—21no—
30C4×SD16×C151—21no—
31C4×D8×C151—21no—
32#433×C151—22no—
33#432×C151—22no—
34C2×#108×C151C2211yescharacteristic
35C2×#108×C151C2211yescharacteristic
36#428×C151C2211yescharacteristic
37#428×C151C2211yescharacteristic
38C2×#107×C151C2211yescharacteristic
39#424×C151C2211yescharacteristic
40#424×C151C2211yescharacteristic
41#419×C151C2211yescharacteristic
42#418×C151C2211yescharacteristic
43#417×C151C2211yescharacteristic
44#417×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#101×C151C2211yescharacteristic
48C2×#101×C151C2211yescharacteristic
49C2×#100×C151C2211yescharacteristic
50C2×#100×C151C2211yescharacteristic
51#408×C151C2211yescharacteristic
52#408×C151C2211yescharacteristic
53C4×M16×C151C2211yescharacteristic
54C4×M16×C151C2211yescharacteristic
55C4×M16×C151C2211yescharacteristic
56C2×#97×C151C2211yescharacteristic
57#343×C151C2211yescharacteristic
58#343×C151C2211yescharacteristic
59#343×C151C2211yescharacteristic
60#343×C151C2211yescharacteristic
61#341×C151C2211yescharacteristic
62#341×C151C2211yescharacteristic
63C2×#41×C151C2311yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×D4×C151C2311yescharacteristic
66C23×C4×C151—21no—
67#137×C151—22no—
68#137×C151—22no—
69AGL(1,ℤ/8)×C151—22no—
70AGL(1,ℤ/8)×C151—22no—
71C2×Q16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—21no—
76C2×SD16×C151—22no—
77C2×D8×C151—21no—
78C2×M16×C151C2311yescharacteristic
79C2×M16×C151C2311yescharacteristic
80C2×M16×C151C2311yescharacteristic
81C2×M16×C151C2311yescharacteristic
82C2×M16×C151C2311yescharacteristic
83C2×M16×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C4×Q8×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151D411yescharacteristic
91C4×Q8×C151D411yescharacteristic
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151D411yescharacteristic
99C4×D4×C151D411yescharacteristic
100#117×C151—21no—
101#117×C151C2311yescharacteristic
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C22⋊C4×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151—21no—
108C2×C42×C151C2311yescharacteristic
109#108×C151—22no—
110#108×C151—22no—
111#107×C151—22no—
112#107×C151—21no—
113#107×C151—21no—
114#106×C151—21no—
115#106×C151—21no—
116C4⋊C8×C151—22no—
117C4⋊C8×C151—22no—
118#103×C151—22no—
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#102×C151—21no—
124#102×C151—21no—
125#102×C151—22no—
126#102×C151—21no—
127#102×C151—21no—
128#101×C151—22no—
129#101×C151—22no—
130#100×C151—22no—
131#100×C151—22no—
132C22⋊C8×C151—22no—
133C22⋊C8×C151—22no—
134#97×C151—21no—
135#97×C151—21no—
136#97×C151—21no—
137#97×C151D412yes—
138#97×C151D412yes—
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C24×C151—21no—
143#41×C151—21no—
144#41×C151—21no—
145#41×C151—21no—
146#41×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151C2×D411yescharacteristic
153C2×Q8×C151#4112yes—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151C2×D411yescharacteristic
161C2×D4×C151#4112yes—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—41no—
169C22×C4×C151—41no—
170C22×C4×C151—82no—
171C22×C4×C151#4111yescharacteristic
172C22×C4×C151#4111yescharacteristic
173C22×C4×C151C2411yescharacteristic
174Q16×C151—24no—
175SD16×C151—28no—
176SD16×C151—24no—
177SD16×C151—24no—
178D8×C151—24no—
179M16×C151—21no—
180M16×C151—21no—
181M16×C151—21no—
182M16×C151—21no—
183M16×C151—21no—
184M16×C151—21no—
185M16×C151—21no—
186M16×C151—21no—
187M16×C151—21no—
188M16×C151—21no—
189M16×C151#4112yes—
190M16×C151#4112yes—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151C2×D412yes—
202C2×C8×C151C2×D412yes—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—21no—
209C4⋊C4×C151—41no—
210C4⋊C4×C151—41no—
211C4⋊C4×C151C2×D411yescharacteristic
212C4⋊C4×C151C2×D411yescharacteristic
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—41no—
217C22⋊C4×C151—41no—
218C42×C151—21no—
219C42×C151—21no—
220C42×C151—21no—
221C42×C151—41no—
222C42×C151—41no—
223C42×C151C2×D411yescharacteristic
224C42×C151C2×D411yescharacteristic
225C42×C151C2×D411yescharacteristic
226C42×C151C2×D411yescharacteristic
227C23×C151—21no—
228C23×C151—22no—
229C23×C151—41no—
230C23×C151—41no—
231C23×C151—81no—
232C23×C151—81no—
233C23×C151C2×#4111yescharacteristic
234Q8×C151—22no—
235Q8×C151—22no—
236Q8×C151—21no—
237Q8×C151—21no—
238Q8×C151—41no—
239Q8×C151—41no—
240D4×C151—21no—
241D4×C151—21no—
242D4×C151—22no—
243D4×C151—22no—
244D4×C151—41no—
245D4×C151—41no—
246D4×C151—41no—
247D4×C151—41no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—22no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—81no—
261C2×C4×C151—81no—
262C2×C4×C151—82no—
263C2×C4×C151—82no—
264C2×C4×C151—81no—
265C2×C4×C151—81no—
266C2×C4×C151#12111yescharacteristic
267C2×C4×C151#12111yescharacteristic
268C2×C4×C151#12111yescharacteristic
269C2×C4×C151#12111yescharacteristic
270C2×C4×C151C22×D411yescharacteristic
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C2×#4111yescharacteristic
273C2×C4×C151C2×#4111yescharacteristic
274C2×C4×C151C2×#4111yescharacteristic
275C2×C4×C151C2×#4111yescharacteristic
276C8×C151—22no—
277C8×C151—22no—
278C8×C151—22no—
279C8×C151—22no—
280C8×C151—41no—
281C8×C151—41no—
282C8×C151—41no—
283C8×C151—41no—
284C22×C151—21no—
285C22×C151—21no—
286C22×C151—41no—
287C22×C151—42no—
288C22×C151—41no—
289C22×C151—41no—
290C22×C151—82no—
291C22×C151—82no—
292C22×C151—81no—
293C22×C151—81no—
294C22×C151C2×#12111yescharacteristic
295C22×C151#52911yescharacteristic
296C22×C151#52911yescharacteristic
297C4×C151—21no—
298C4×C151—21no—
299C4×C151—21no—
300C4×C151—21no—
301C4×C151—41no—
302C4×C151—42no—
303C4×C151—41no—
304C4×C151—41no—
305C4×C151—81no—
306C4×C151—81no—
307C4×C151#52511yescharacteristic
308C4×C151#52511yescharacteristic
309C4×C151#52511yescharacteristic
310C4×C151#53211yescharacteristic
311C2×C151—21no—
312C2×C151—21no—
313C2×C151—81no—
314C2×C151—82no—
315C2×C151#239211yescharacteristic
316C2×C151#306811yescharacteristic
317C2×C151#306911yescharacteristic
318#23721C15111yesmaximal, characteristic, direct product factor, Sylow
319C151#2372111yescharacteristic, direct product factor, Sylow
320C4×#137C2×C15111yescharacteristic, complemented
321C4×AGL(1,ℤ/8)C2×C15111yescharacteristic
322C2×#440C2×C15111yescharacteristic, complemented
323#2923C2×C15111yescharacteristic, complemented
324#2089C2×C15111yescharacteristic, complemented
325#2078C2×C15111yescharacteristic, complemented
326#2064C2×C15111yescharacteristic, complemented
327#2063C2×C15111yescharacteristic, complemented
328#2052C2×C15111yescharacteristic, complemented
329#2051C2×C15111yescharacteristic
330#2046C2×C15111yescharacteristic, complemented
331#2019C2×C15111yescharacteristic
332#1778C2×C15111yescharacteristic, complemented
333C4×#101C2×C15111yescharacteristic, complemented
334C4×#100C2×C15111yescharacteristic, complemented
335C2×#137C22×C15111yescharacteristic
336C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
337C22×SD16C22×C15111yescharacteristic
338C4×#41C22×C15111yescharacteristic
339C2×C4×Q8C22×C15111yescharacteristic
340C2×C4×D4C22×C15111yescharacteristic
341#442—21no—
342#441—21no—
343#440—21no—
344#440—21no—
345#440—22no—
346#440—22no—
347C4×Q16—21no—
348C4×SD16—21no—
349C4×SD16—21no—
350C4×D8—21no—
351#433—22no—
352#432—22no—
353C2×#108C22×C15111yescharacteristic
354C2×#108C22×C15111yescharacteristic
355#428C22×C15111yescharacteristic
356#428C22×C15111yescharacteristic
357C2×#107C22×C15111yescharacteristic
358#424C22×C15111yescharacteristic
359#424C22×C15111yescharacteristic
360#419C22×C15111yescharacteristic
361#418C22×C15111yescharacteristic
362#417C22×C15111yescharacteristic
363#417C22×C15111yescharacteristic
364C2×#103C22×C15111yescharacteristic
365C2×#102C22×C15111yescharacteristic
366C2×#101C22×C15111yescharacteristic
367C2×#101C22×C15111yescharacteristic
368C2×#100C22×C15111yescharacteristic
369C2×#100C22×C15111yescharacteristic
370#408C22×C15111yescharacteristic
371#408C22×C15111yescharacteristic
372C4×M16C22×C15111yescharacteristic
373C4×M16C22×C15111yescharacteristic
374C4×M16C22×C15111yescharacteristic
375C2×#97C22×C15111yescharacteristic
376#343C22×C15111yescharacteristic
377#343C22×C15111yescharacteristic
378#343C22×C15111yescharacteristic
379#343C22×C15111yescharacteristic
380#341C22×C15111yescharacteristic
381#341C22×C15111yescharacteristic
382C2×#41C23×C15111yescharacteristic
383C22×Q8C23×C15111yescharacteristic
384C22×D4C23×C15111yescharacteristic
385C23×C4—21no—
386#137—22no—
387#137—22no—
388AGL(1,ℤ/8)—22no—
389AGL(1,ℤ/8)—22no—
390C2×Q16—21no—
391C2×SD16—22no—
392C2×SD16—21no—
393C2×SD16—22no—
394C2×SD16—21no—
395C2×SD16—22no—
396C2×D8—21no—
397C2×M16C23×C15111yescharacteristic
398C2×M16C23×C15111yescharacteristic
399C2×M16C23×C15111yescharacteristic
400C2×M16C23×C15111yescharacteristic
401C2×M16C23×C15111yescharacteristic
402C2×M16C23×C15111yescharacteristic
403C22×C8C23×C15111yescharacteristic
404C22×C8C23×C15111yescharacteristic
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8D4×C15111yescharacteristic
410C4×Q8D4×C15111yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4D4×C15111yescharacteristic
418C4×D4D4×C15111yescharacteristic
419#117—21no—
420#117C23×C15111yescharacteristic
421C2×C4⋊C4—21no—
422C2×C4⋊C4C23×C15111yescharacteristic
423C2×C4⋊C4C23×C15111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C23×C15111yescharacteristic
428#108—22no—
429#108—22no—
430#107—22no—
431#107—21no—
432#107—21no—
433#106—21no—
434#106—21no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437#103—21no—
438#103—21no—
439#103—22no—
440#103—21no—
441#103—21no—
442#102—21no—
443#102—21no—
444#102—22no—
445#102—21no—
446#102—21no—
447#101—22no—
448#101—22no—
449#100—22no—
450#100—22no—
451C22⋊C8—22no—
452C22⋊C8—22no—
453#97—21no—
454#97—21no—
455#97—21no—
456#97D4×C15112yes—
457#97D4×C15112yes—
458C4×C8—21no—
459C4×C8—21no—
460C4×C8—21no—
461C24—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8C2×D4×C15111yescharacteristic
472C2×Q8#41×C15112yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4C2×D4×C15111yescharacteristic
480C2×D4#41×C15112yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—82no—
490C22×C4#41×C15111yescharacteristic
491C22×C4#41×C15111yescharacteristic
492C22×C4C24×C15111yescharacteristic
493Q16—24no—
494SD16—28no—
495SD16—24no—
496SD16—24no—
497D8—24no—
498M16—21no—
499M16—21no—
500M16—21no—
501M16—21no—
502M16—21no—
503M16—21no—
504M16—21no—
505M16—21no—
506M16—21no—
507M16—21no—
508M16#41×C15112yes—
509M16#41×C15112yes—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×D4×C15112yes—
521C2×C8C2×D4×C15112yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C15111yescharacteristic
531C4⋊C4C2×D4×C15111yescharacteristic
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—41no—
541C42—41no—
542C42C2×D4×C15111yescharacteristic
543C42C2×D4×C15111yescharacteristic
544C42C2×D4×C15111yescharacteristic
545C42C2×D4×C15111yescharacteristic
546C23—21no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—81no—
551C23—81no—
552C23C2×#41×C15111yescharacteristic
553Q8—22no—
554Q8—21no—
555Q8—22no—
556Q8—21no—
557Q8—41no—
558Q8—41no—
559D4—21no—
560D4—22no—
561D4—22no—
562D4—21no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—81no—
584C2×C4—81no—
585C2×C4#121×C15111yescharacteristic
586C2×C4#121×C15111yescharacteristic
587C2×C4#121×C15111yescharacteristic
588C2×C4#121×C15111yescharacteristic
589C2×C4C22×D4×C15111yescharacteristic
590C2×C4C22×D4×C15111yescharacteristic
591C2×C4C2×#41×C15111yescharacteristic
592C2×C4C2×#41×C15111yescharacteristic
593C2×C4C2×#41×C15111yescharacteristic
594C2×C4C2×#41×C15111yescharacteristic
595C8—22no—
596C8—22no—
597C8—22no—
598C8—22no—
599C8—41no—
600C8—41no—
601C8—41no—
602C8—41no—
603C22—21no—
604C22—21no—
605C22—41no—
606C22—42no—
607C22—41no—
608C22—41no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22C2×#121×C15111yescharacteristic
614C22#529×C15111yescharacteristic
615C22#529×C15111yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4#525×C15111yescharacteristic
627C4#525×C15111yescharacteristic
628C4#525×C15111yescharacteristic
629C4#532×C15111yescharacteristic
630C2—21no—
631C2—21no—
632C2—81no—
633C2—82no—
634C2#2392×C15111yescharacteristic
635C2#3068×C15111yescharacteristic
636C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×AGL(1,ℤ/8)×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C4×#137×C151C2semidirect
3. C2×#440×C151C2semidirect
4. #2923×C151C2semidirect
5. #2089×C151C2semidirect
6. #2078×C151C2semidirect
7. #2064×C151C2semidirect
8. #2063×C151C2semidirect
9. #2052×C151C2semidirect
11. #2046×C151C2semidirect
13. #1778×C151C2semidirect
14. C4×#101×C151C2semidirect
15. C4×#100×C151C2semidirect
318. #23721C151direct (N × H)
319. C151#23721direct (N × H)
320. C4×#137C2×C151semidirect
322. C2×#440C2×C151semidirect
323. #2923C2×C151semidirect
324. #2089C2×C151semidirect
325. #2078C2×C151semidirect
326. #2064C2×C151semidirect
327. #2063C2×C151semidirect
328. #2052C2×C151semidirect
330. #2046C2×C151semidirect
332. #1778C2×C151semidirect
333. C4×#101C2×C151semidirect
334. C4×#100C2×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#137×C1512
C4×AGL(1,ℤ/8)×C1512
C2×#440×C1512
#2923×C1512
#2089×C1512
#2078×C1512
#2064×C1512
#2063×C1512
#2052×C1512
#2051×C1512
#2046×C1512
#2019×C1512
#1778×C1512
C4×#101×C1512
C4×#100×C1512
#23721151