Finite Group Databasebeta

← C151×#23689 #50328614

Subgroups — C151×#23689 #50328614

Order 38656.

844 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2327×C151C211yesmaximal, characteristic, complemented
4#2319×C151C211yesmaximal, characteristic
5#2085×C151C211yesmaximal, characteristic, complemented
6#2073×C151C211yesmaximal, characteristic
7#2068×C151C211yesmaximal, characteristic, complemented
8#2066×C151C211yesmaximal, characteristic, complemented
9#2055×C151C211yesmaximal, characteristic
10#2055×C151C211yesmaximal, characteristic
11#2043×C151C211yesmaximal, characteristic, complemented
12#2013×C151C211yesmaximal, characteristic
13#1768×C151C211yesmaximal, characteristic, complemented
14#1763×C151C211yesmaximal, characteristic, complemented
15C4×#103×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22#440×C151—24no—
23C4×SD16×C151—24no—
24C2×#107×C151C2211yescharacteristic
25C2×#106×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊C8×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#97×C151C2211yescharacteristic
37C2×C4×C8×C151C2211yescharacteristic
38#391×C151C2211yescharacteristic
39#391×C151C2211yescharacteristic
40#390×C151C2211yescharacteristic
41#390×C151C2211yescharacteristic
42#389×C151C2211yescharacteristic
43#389×C151C2211yescharacteristic
44#388×C151—21no—
45#388×C151—21no—
46#387×C151—21no—
47#387×C151—21no—
48#387×C151—21no—
49#387×C151—21no—
50#382×C151C2211yescharacteristic
51#381×C151—21no—
52#380×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic
54#376×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151C2311yescharacteristic
64C23×C4×C151—21no—
65C2×SD16×C151—22no—
66C2×SD16×C151—22no—
67C2×SD16×C151—22no—
68C2×SD16×C151—22no—
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C4⋊Q8×C151—22no—
76C4⋊Q8×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151—22no—
79C4×Q8×C151—22no—
80C4×Q8×C151—22no—
81C4×D4×C151—22no—
82C4×D4×C151D414yes—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C42×C151—21no—
100C2×C42×C151—21no—
101C2×C42×C151—21no—
102C2×C42×C151C2311yescharacteristic
103C2×C42×C151C2311yescharacteristic
104C2×C42×C151C2311yescharacteristic
105#107×C151—22no—
106#106×C151—22no—
107C4⋊C8×C151—22no—
108C4⋊C8×C151—22no—
109#103×C151—22no—
110#103×C151—22no—
111#103×C151—22no—
112#103×C151—22no—
113#103×C151—22no—
114#103×C151—22no—
115#102×C151—22no—
116#102×C151—22no—
117#97×C151—22no—
118C4×C8×C151—22no—
119#95×C151—21no—
120#95×C151—21no—
121#95×C151—21no—
122#95×C151—21no—
123#95×C151—21no—
124#95×C151—21no—
125#95×C151—21no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151D411yescharacteristic
129#95×C151D411yescharacteristic
130#95×C151D411yescharacteristic
131#95×C151D411yescharacteristic
132C24×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151—21no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151#4112yes—
144C2×Q8×C151#4112yes—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151C2×D412yes—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—24no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—81no—
160C22×C4×C151—81no—
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2411yescharacteristic
168SD16×C151—28no—
169SD16×C151—28no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151#4112yes—
181C2×C8×C151#4112yes—
182C4⋊C4×C151—24no—
183C4⋊C4×C151—24no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—42no—
194C4⋊C4×C151—42no—
195C4⋊C4×C151—81no—
196C4⋊C4×C151—81no—
197C4⋊C4×C151C2×D412yes—
198C22⋊C4×C151—24no—
199C22⋊C4×C151—81no—
200C22⋊C4×C151—81no—
201C22⋊C4×C151—81no—
202C22⋊C4×C151—81no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151—42no—
208C42×C151—42no—
209C42×C151—81no—
210C42×C151C2×D412yes—
211C42×C151#4112yes—
212C23×C151—22no—
213C23×C151—41no—
214C23×C151—41no—
215C23×C151—41no—
216C23×C151—41no—
217C23×C151—41no—
218C23×C151—41no—
219C23×C151C22×D411yescharacteristic
220Q8×C151—22no—
221Q8×C151—22no—
222Q8×C151—22no—
223Q8×C151—22no—
224Q8×C151—41no—
225Q8×C151—41no—
226Q8×C151—41no—
227Q8×C151—41no—
228D4×C151—22no—
229D4×C151—22no—
230D4×C151—41no—
231D4×C151—41no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—22no—
237C2×C4×C151—22no—
238C2×C4×C151—22no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—41no—
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—41no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—84no—
270C2×C4×C151#12112yes—
271C2×C4×C151#12112yes—
272C2×C4×C151C22×D411yescharacteristic
273C2×C4×C151C2×#4111yescharacteristic
274C2×C4×C151C2×#4111yescharacteristic
275C2×C4×C151C2×#4111yescharacteristic
276C2×C4×C151C2×#4111yescharacteristic
277C2×C4×C151C2×#4111yescharacteristic
278C8×C151—22no—
279C8×C151—22no—
280C8×C151—41no—
281C8×C151—41no—
282C22×C151—42no—
283C22×C151—42no—
284C22×C151—42no—
285C22×C151—81no—
286C22×C151—81no—
287C22×C151—81no—
288C22×C151—81no—
289C22×C151C2×#12111yescharacteristic
290C22×C151#52511yescharacteristic
291C22×C151#53211yescharacteristic
292C22×C151#57711yescharacteristic
293C22×C151#57711yescharacteristic
294C22×C151#57711yescharacteristic
295C22×C151#57811yescharacteristic
296C4×C151—22no—
297C4×C151—22no—
298C4×C151—41no—
299C4×C151—41no—
300C4×C151—42no—
301C4×C151—42no—
302C4×C151—41no—
303C4×C151—41no—
304C4×C151—42no—
305C4×C151—81no—
306C4×C151—81no—
307C4×C151—81no—
308C4×C151—81no—
309C4×C151#52511yescharacteristic
310C4×C151#52511yescharacteristic
311C4×C151#52911yescharacteristic
312C4×C151#52911yescharacteristic
313C2×C151—82no—
314C2×C151#239211yescharacteristic
315C2×C151#304211yescharacteristic
316C2×C151#304611yescharacteristic
317C2×C151#312111yescharacteristic
318C2×C151#312611yescharacteristic
319C2×C151#317411yescharacteristic
320C2×C151#317811yescharacteristic
321#23689C15111yesmaximal, characteristic, direct product factor, Sylow
322C151#2368911yescharacteristic, direct product factor, Sylow
323C2×#440C2×C15111yescharacteristic
324C2×C4×SD16C2×C15111yescharacteristic
325#2327C2×C15111yescharacteristic, complemented
326#2319C2×C15111yescharacteristic
327#2085C2×C15111yescharacteristic, complemented
328#2073C2×C15111yescharacteristic
329#2068C2×C15111yescharacteristic, complemented
330#2066C2×C15111yescharacteristic, complemented
331#2055C2×C15111yescharacteristic
332#2055C2×C15111yescharacteristic
333#2043C2×C15111yescharacteristic, complemented
334#2013C2×C15111yescharacteristic
335#1768C2×C15111yescharacteristic, complemented
336#1763C2×C15111yescharacteristic, complemented
337C4×#103C2×C15111yescharacteristic, complemented
338C22×SD16C22×C15111yescharacteristic
339C22×SD16C22×C15111yescharacteristic
340C2×C4⋊Q8C22×C15111yescharacteristic
341C2×C4×Q8C22×C15111yescharacteristic
342C2×C4×Q8C22×C15111yescharacteristic
343C2×C4×D4C22×C15111yescharacteristic
344#440—24no—
345C4×SD16—24no—
346C2×#107C22×C15111yescharacteristic
347C2×#106C22×C15111yescharacteristic
348C2×C4⋊C8C22×C15111yescharacteristic
349C2×C4⋊C8C22×C15111yescharacteristic
350C2×#103C22×C15111yescharacteristic
351C2×#103C22×C15111yescharacteristic
352C2×#103C22×C15111yescharacteristic
353C2×#103C22×C15111yescharacteristic
354C2×#103C22×C15111yescharacteristic
355C2×#103C22×C15111yescharacteristic
356C2×#102C22×C15111yescharacteristic
357C2×#102C22×C15111yescharacteristic
358C2×#97C22×C15111yescharacteristic
359C2×C4×C8C22×C15111yescharacteristic
360#391C22×C15111yescharacteristic
361#391C22×C15111yescharacteristic
362#390C22×C15111yescharacteristic
363#390C22×C15111yescharacteristic
364#389C22×C15111yescharacteristic
365#389C22×C15111yescharacteristic
366#388—21no—
367#388—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#382C22×C15111yescharacteristic
373#381—21no—
374#380—21no—
375C4×C4⋊C4C22×C15111yescharacteristic
376#376C22×C15111yescharacteristic
377#340C22×C15111yescharacteristic
378#340C22×C15111yescharacteristic
379#340C22×C15111yescharacteristic
380#340C22×C15111yescharacteristic
381#336C22×C15111yescharacteristic
382#336C22×C15111yescharacteristic
383C22×Q8C23×C15111yescharacteristic
384C22×Q8C23×C15111yescharacteristic
385C22×D4C23×C15111yescharacteristic
386C23×C4—21no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—22no—
393C22×C8C23×C15111yescharacteristic
394C22×C8C23×C15111yescharacteristic
395C22×C8C23×C15111yescharacteristic
396C22×C8C23×C15111yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399C4×Q8—22no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×D4—22no—
404C4×D4D4×C15114yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4C23×C15111yescharacteristic
412C2×C4⋊C4C23×C15111yescharacteristic
413C2×C4⋊C4C23×C15111yescharacteristic
414C2×C4⋊C4C23×C15111yescharacteristic
415C2×C4⋊C4C23×C15111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C42—21no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42C23×C15111yescharacteristic
425C2×C42C23×C15111yescharacteristic
426C2×C42C23×C15111yescharacteristic
427#107—22no—
428#106—22no—
429C4⋊C8—22no—
430C4⋊C8—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—22no—
436#103—22no—
437#102—22no—
438#102—22no—
439#97—22no—
440C4×C8—22no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95D4×C15111yescharacteristic
451#95D4×C15111yescharacteristic
452#95D4×C15111yescharacteristic
453#95D4×C15111yescharacteristic
454C24—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8#41×C15112yes—
466C2×Q8#41×C15112yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C2×D4×C15112yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4C2×D4×C15111yescharacteristic
484C22×C4C2×D4×C15111yescharacteristic
485C22×C4C2×D4×C15111yescharacteristic
486C22×C4C2×D4×C15111yescharacteristic
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4C24×C15111yescharacteristic
490SD16—28no—
491SD16—28no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8#41×C15112yes—
503C2×C8#41×C15112yes—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—81no—
518C4⋊C4—81no—
519C4⋊C4C2×D4×C15112yes—
520C22⋊C4—24no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—42no—
531C42—81no—
532C42C2×D4×C15112yes—
533C42#41×C15112yes—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×D4×C15111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—22no—
545Q8—22no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—84no—
592C2×C4#121×C15112yes—
593C2×C4#121×C15112yes—
594C2×C4C22×D4×C15111yescharacteristic
595C2×C4C2×#41×C15111yescharacteristic
596C2×C4C2×#41×C15111yescharacteristic
597C2×C4C2×#41×C15111yescharacteristic
598C2×C4C2×#41×C15111yescharacteristic
599C2×C4C2×#41×C15111yescharacteristic
600C8—22no—
601C8—22no—
602C8—41no—
603C8—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×#121×C15111yescharacteristic
612C22#525×C15111yescharacteristic
613C22#532×C15111yescharacteristic
614C22#577×C15111yescharacteristic
615C22#577×C15111yescharacteristic
616C22#577×C15111yescharacteristic
617C22#578×C15111yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—42no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4#525×C15111yescharacteristic
632C4#525×C15111yescharacteristic
633C4#529×C15111yescharacteristic
634C4#529×C15111yescharacteristic
635C2—82no—
636C2#2392×C15111yescharacteristic
637C2#3042×C15111yescharacteristic
638C2#3046×C15111yescharacteristic
639C2#3121×C15111yescharacteristic
640C2#3126×C15111yescharacteristic
641C2#3174×C15111yescharacteristic
642C2#3178×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ #376×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2327×C151C2semidirect
5. #2085×C151C2semidirect
7. #2068×C151C2semidirect
8. #2066×C151C2semidirect
11. #2043×C151C2semidirect
13. #1768×C151C2semidirect
14. #1763×C151C2semidirect
15. C4×#103×C151C2semidirect
321. #23689C151direct (N × H)
322. C151#23689direct (N × H)
325. #2327C2×C151semidirect
327. #2085C2×C151semidirect
329. #2068C2×C151semidirect
330. #2066C2×C151semidirect
333. #2043C2×C151semidirect
335. #1768C2×C151semidirect
336. #1763C2×C151semidirect
337. C4×#103C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#440×C1512
C2×C4×SD16×C1512
#2327×C1512
#2319×C1512
#2085×C1512
#2073×C1512
#2068×C1512
#2066×C1512
#2055×C1512
#2043×C1512
#2013×C1512
#1768×C1512
#1763×C1512
C4×#103×C1512
#23689151