Finite Group Databasebeta

← C151×#10954 #50315879

Subgroups — C151×#10954 #50315879

Order 38656.

966 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
1C2×#421×C151C211yesmaximal, characteristic
2C2×#417×C151C211yesmaximal, characteristic
3C2×#410×C151C211yesmaximal, characteristic
4#2274×C151C211yesmaximal, characteristic, complemented
5C2×#344×C151C211yesmaximal, characteristic, complemented
6#1736×C151C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C22×M16×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C2×#117×C151C2211yescharacteristic
12C2×#117×C151C2211yescharacteristic
13C2×#117×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15#421×C151—22no—
16#421×C151C414yescomplemented
17C2×#104×C151—22no—
18#417×C151—22no—
19#417×C151—22no—
20C2×#103×C151C412yescomplemented
21C2×#102×C151C412yescomplemented
22#410×C151—22no—
23#410×C151C414yescomplemented
24C2×#99×C151—22no—
25C4×C4⋊C4×C151—22no—
26C4×C4⋊C4×C151—22no—
27C4×C22⋊C4×C151—22no—
28#344×C151—22no—
29#340×C151—22no—
30H(3,ℤ/4)×C151—22no—
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×C151—21no—
41C2×#41×C151C2×C412yes—
42C2×#41×C151C2×C412yes—
43C22×Q8×C151C2×C411yescharacteristic
44C22×D4×C151—21no—
45C22×D4×C151C2×C411yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C23×C4×C151C2311yescharacteristic
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×C151C2×C412yes—
61C22×C8×C151—21no—
62C22×C8×C151C2×C412yes—
63#117×C151—21no—
64#117×C151—21no—
65#117×C151—21no—
66#117×C151—21no—
67#117×C151—21no—
68#117×C151—21no—
69#117×C151—21no—
70#117×C151C2×C412yes—
71#117×C151C2×C412yes—
72#117×C151C2×C412yes—
73#117×C151D412yes—
74#117×C151D412yes—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151C2×C412yes—
82C2×C4⋊C4×C151D412yes—
83C2×C4⋊C4×C151D412yes—
84C2×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151D412yes—
87C2×C42×C151—21no—
88C2×C42×C151—21no—
89C2×C42×C151—24no—
90C2×C42×C151D412yes—
91#104×C151—28no—
92#103×C151—24no—
93#102×C151—24no—
94#99×C151—28no—
95#95×C151—24no—
96C24×C151—21no—
97C24×C151C2×D411yescharacteristic
98#41×C151—22no—
99#41×C151—22no—
100#41×C151—22no—
101#41×C151—22no—
102#41×C151—22no—
103#41×C151—22no—
104#41×C151—22no—
105#41×C151—22no—
106#41×C151—41no—
107#41×C151—41no—
108#41×C151—41no—
109#41×C151—41no—
110#41×C151—41no—
111#41×C151—41no—
112#41×C151—41no—
113#41×C151—41no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151C4212yescomplemented
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151—41no—
128C2×D4×C151—41no—
129C2×D4×C151—41no—
130C2×D4×C151—41no—
131C2×D4×C151C4212yescomplemented
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—41no—
141C22×C4×C151—41no—
142C22×C4×C151—41no—
143C22×C4×C151—41no—
144C22×C4×C151—41no—
145C22×C4×C151—82no—
146C22×C4×C151C22×C411yescharacteristic
147C22×C4×C151C22×C411yescharacteristic
148C22×C4×C151C22×C411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151#4111yescharacteristic
155C22×C4×C151#4111yescharacteristic
156C22×C4×C151#4111yescharacteristic
157C22×C4×C151#4111yescharacteristic
158C22×C4×C151#4111yescharacteristic
159C22×C4×C151#4111yescharacteristic
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—41no—
163M16×C151—41no—
164M16×C151—41no—
165M16×C151—41no—
166M16×C151—41no—
167M16×C151—41no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C2×C8×C151—41no—
173C2×C8×C151—41no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—41no—
183C4⋊C4×C151C22⋊C414yes—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—41no—
189C22⋊C4×C151C22⋊C414yes—
190C42×C151—22no—
191C42×C151—22no—
192C42×C151—22no—
193C42×C151—22no—
194C42×C151—41no—
195C42×C151—84no—
196C42×C151C22⋊C414yes—
197C23×C151—22no—
198C23×C151—41no—
199C23×C151—41no—
200C23×C151—41no—
201C23×C151—41no—
202C23×C151—81no—
203C23×C151—81no—
204C23×C151C2×C22⋊C411yescharacteristic
205C23×C151C4×D411yescharacteristic
206C23×C151C4×D411yescharacteristic
207C23×C151#12011yescharacteristic
208C23×C151#12111yescharacteristic
209C23×C151#12111yescharacteristic
210C23×C151#12311yescharacteristic
211Q8×C151—22no—
212Q8×C151—22no—
213Q8×C151—41no—
214Q8×C151—41no—
215D4×C151—22no—
216D4×C151—22no—
217D4×C151—42no—
218D4×C151—42no—
219D4×C151—42no—
220D4×C151—42no—
221D4×C151—41no—
222D4×C151—41no—
223C2×C4×C151—22no—
224C2×C4×C151—24no—
225C2×C4×C151—24no—
226C2×C4×C151—24no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—44no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—82no—
240C2×C4×C151—82no—
241C2×C4×C151—81no—
242C2×C4×C151—81no—
243C2×C4×C151C2×C4211yescharacteristic
244C2×C4×C151C2×C22⋊C411yescharacteristic
245C2×C4×C151C2×C22⋊C411yescharacteristic
246C2×C4×C151#11711yescharacteristic
247C2×C4×C151#11711yescharacteristic
248C2×C4×C151#11711yescharacteristic
249C2×C4×C151C4×D411yescharacteristic
250C2×C4×C151C4×D411yescharacteristic
251C2×C4×C151C4×D411yescharacteristic
252C2×C4×C151C4×D411yescharacteristic
253C2×C4×C151C4×D411yescharacteristic
254C2×C4×C151C4×D411yescharacteristic
255C2×C4×C151C4×D411yescharacteristic
256C2×C4×C151C4×D411yescharacteristic
257C2×C4×C151C4×D411yescharacteristic
258C2×C4×C151C4×D411yescharacteristic
259C2×C4×C151#12111yescharacteristic
260C2×C4×C151#12111yescharacteristic
261C2×C4×C151#12111yescharacteristic
262C2×C4×C151#12111yescharacteristic
263C2×C4×C151#12311yescharacteristic
264C2×C4×C151#12311yescharacteristic
265C2×C4×C151#12411yescharacteristic
266C2×C4×C151#12411yescharacteristic
267C2×C4×C151#12411yescharacteristic
268C2×C4×C151#12611yescharacteristic
269C2×C4×C151#12611yescharacteristic
270C2×C4×C151#12711yescharacteristic
271C8×C151—42no—
272C8×C151—42no—
273C22×C151—21no—
274C22×C151—21no—
275C22×C151—21no—
276C22×C151—21no—
277C22×C151—21no—
278C22×C151—21no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151—42no—
284C22×C151—82no—
285C22×C151—82no—
286C22×C151—81no—
287C22×C151—81no—
288C22×C151C4×C22⋊C411yescharacteristic
289C22×C151#38611yescharacteristic
290C22×C151#38611yescharacteristic
291C22×C151#38611yescharacteristic
292C22×C151#38811yescharacteristic
293C22×C151#38811yescharacteristic
294C22×C151#39011yescharacteristic
295C4×C151—44no—
296C4×C151—44no—
297C4×C151—44no—
298C4×C151—42no—
299C4×C151—82no—
300C4×C151C4×C22⋊C411yescharacteristic
301C4×C151C4×C22⋊C411yescharacteristic
302C4×C151#38811yescharacteristic
303C4×C151#38811yescharacteristic
304C4×C151#38811yescharacteristic
305C4×C151#38811yescharacteristic
306C4×C151#39011yescharacteristic
307C4×C151#39011yescharacteristic
308C2×C151—21no—
309C2×C151—21no—
310C2×C151—21no—
311C2×C151—21no—
312C2×C151—21no—
313C2×C151—21no—
314C2×C151—82no—
315C2×C151#143711yescharacteristic
316C2×C151#190411yescharacteristic
317C2×C151#190511yescharacteristic
318#10954C15111yesmaximal, characteristic, direct product factor, Sylow
319C151#1095411yescharacteristic, direct product factor, Sylow
320C2×#421C2×C15111yescharacteristic
321C2×#417C2×C15111yescharacteristic
322C2×#410C2×C15111yescharacteristic
323#2274C2×C15111yescharacteristic, complemented
324C2×#344C2×C15111yescharacteristic, complemented
325#1736C2×C15111yescharacteristic, complemented
326C2×H(3,ℤ/4)C2×C15111yescharacteristic, complemented
327C22×#41C22×C15111yescharacteristic
328C22×M16C22×C15111yescharacteristic
329C22×M16C22×C15111yescharacteristic
330C2×#117C22×C15111yescharacteristic
331C2×#117C22×C15111yescharacteristic
332C2×#117C22×C15111yescharacteristic
333C22×C4⋊C4C22×C15111yescharacteristic
334#421—22no—
335#421C4×C15114yescomplemented
336C2×#104—22no—
337#417—22no—
338#417—22no—
339C2×#103C4×C15112yescomplemented
340C2×#102C4×C15112yescomplemented
341#410—22no—
342#410C4×C15114yescomplemented
343C2×#99—22no—
344C4×C4⋊C4—22no—
345C4×C4⋊C4—22no—
346C4×C22⋊C4—22no—
347#344—22no—
348#340—22no—
349H(3,ℤ/4)—22no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41C2×C4×C15112yes—
361C2×#41C2×C4×C15112yes—
362C22×Q8C2×C4×C15111yescharacteristic
363C22×D4—21no—
364C22×D4C2×C4×C15111yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4C23×C15111yescharacteristic
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16C2×C4×C15112yes—
380C22×C8—21no—
381C22×C8C2×C4×C15112yes—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117C2×C4×C15112yes—
390#117C2×C4×C15112yes—
391#117C2×C4×C15112yes—
392#117D4×C15112yes—
393#117D4×C15112yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C2×C4×C15112yes—
401C2×C4⋊C4D4×C15112yes—
402C2×C4⋊C4D4×C15112yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4D4×C15112yes—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—24no—
409C2×C42D4×C15112yes—
410#104—28no—
411#103—24no—
412#102—24no—
413#99—28no—
414#95—24no—
415C24—21no—
416C24C2×D4×C15111yescharacteristic
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—41no—
426#41—41no—
427#41—41no—
428#41—41no—
429#41—41no—
430#41—41no—
431#41—41no—
432#41—41no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C42×C15112yescomplemented
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4C42×C15112yescomplemented
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—82no—
465C22×C4C22×C4×C15111yescharacteristic
466C22×C4C22×C4×C15111yescharacteristic
467C22×C4C22×C4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C2×D4×C15111yescharacteristic
471C22×C4C2×D4×C15111yescharacteristic
472C22×C4C2×D4×C15111yescharacteristic
473C22×C4#41×C15111yescharacteristic
474C22×C4#41×C15111yescharacteristic
475C22×C4#41×C15111yescharacteristic
476C22×C4#41×C15111yescharacteristic
477C22×C4#41×C15111yescharacteristic
478C22×C4#41×C15111yescharacteristic
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—41no—
502C4⋊C4C22⋊C4×C15114yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C22⋊C4C22⋊C4×C15114yes—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—41no—
514C42—84no—
515C42C22⋊C4×C15114yes—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—81no—
522C23—81no—
523C23C2×C22⋊C4×C15111yescharacteristic
524C23C4×D4×C15111yescharacteristic
525C23C4×D4×C15111yescharacteristic
526C23#120×C15111yescharacteristic
527C23#121×C15111yescharacteristic
528C23#121×C15111yescharacteristic
529C23#123×C15111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—41no—
541D4—41no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4C2×C42×C15111yescharacteristic
563C2×C4C2×C22⋊C4×C15111yescharacteristic
564C2×C4C2×C22⋊C4×C15111yescharacteristic
565C2×C4#117×C15111yescharacteristic
566C2×C4#117×C15111yescharacteristic
567C2×C4#117×C15111yescharacteristic
568C2×C4C4×D4×C15111yescharacteristic
569C2×C4C4×D4×C15111yescharacteristic
570C2×C4C4×D4×C15111yescharacteristic
571C2×C4C4×D4×C15111yescharacteristic
572C2×C4C4×D4×C15111yescharacteristic
573C2×C4C4×D4×C15111yescharacteristic
574C2×C4C4×D4×C15111yescharacteristic
575C2×C4C4×D4×C15111yescharacteristic
576C2×C4C4×D4×C15111yescharacteristic
577C2×C4C4×D4×C15111yescharacteristic
578C2×C4#121×C15111yescharacteristic
579C2×C4#121×C15111yescharacteristic
580C2×C4#121×C15111yescharacteristic
581C2×C4#121×C15111yescharacteristic
582C2×C4#123×C15111yescharacteristic
583C2×C4#123×C15111yescharacteristic
584C2×C4#124×C15111yescharacteristic
585C2×C4#124×C15111yescharacteristic
586C2×C4#124×C15111yescharacteristic
587C2×C4#126×C15111yescharacteristic
588C2×C4#126×C15111yescharacteristic
589C2×C4#127×C15111yescharacteristic
590C8—42no—
591C8—42no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—42no—
603C22—82no—
604C22—82no—
605C22—81no—
606C22—81no—
607C22C4×C22⋊C4×C15111yescharacteristic
608C22#386×C15111yescharacteristic
609C22#386×C15111yescharacteristic
610C22#386×C15111yescharacteristic
611C22#388×C15111yescharacteristic
612C22#388×C15111yescharacteristic
613C22#390×C15111yescharacteristic
614C4—44no—
615C4—44no—
616C4—44no—
617C4—42no—
618C4—82no—
619C4C4×C22⋊C4×C15111yescharacteristic
620C4C4×C22⋊C4×C15111yescharacteristic
621C4#388×C15111yescharacteristic
622C4#388×C15111yescharacteristic
623C4#388×C15111yescharacteristic
624C4#388×C15111yescharacteristic
625C4#390×C15111yescharacteristic
626C4#390×C15111yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—82no—
634C2#1437×C15111yescharacteristic
635C2#1904×C15111yescharacteristic
636C2#1905×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC2×C4C2×C42×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC22×#41×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #2274×C151C2semidirect
5. C2×#344×C151C2semidirect
6. #1736×C151C2semidirect
7. C2×H(3,ℤ/4)×C151C2semidirect
16. #421×C151C4semidirect
20. C2×#103×C151C4semidirect
21. C2×#102×C151C4semidirect
23. #410×C151C4semidirect
119. C2×Q8×C151C42semidirect
131. C2×D4×C151C42semidirect
318. #10954C151direct (N × H)
319. C151#10954direct (N × H)
323. #2274C2×C151semidirect
324. C2×#344C2×C151semidirect
325. #1736C2×C151semidirect
326. C2×H(3,ℤ/4)C2×C151semidirect
335. #421C4×C151semidirect
339. C2×#103C4×C151semidirect
340. C2×#102C4×C151semidirect
342. #410C4×C151semidirect
438. C2×Q8C42×C151semidirect
450. C2×D4C42×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#421×C1512
C2×#417×C1512
C2×#410×C1512
#2274×C1512
C2×#344×C1512
#1736×C1512
C2×H(3,ℤ/4)×C1512
#10954151