Finite Group Databasebeta

← C151×#23935 #50328860

Subgroups — C151×#23935 #50328860

Order 38656.

1276 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#533×C151C211yesmaximal, characteristic, complemented
2C2×#452×C151C212yesmaximal
3#2297×C151C211yesmaximal, characteristic
4#2024×C151C211yesmaximal, characteristic, complemented
5#2023×C151C211yesmaximal, characteristic, complemented
6#2016×C151C211yesmaximal, characteristic, complemented
7#2013×C151C211yesmaximal, characteristic, complemented
8#1880×C151C212yesmaximal, complemented
9#1878×C151C212yesmaximal, complemented
10#1873×C151C212yesmaximal, complemented
11#1817×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C22×Q16×C151C2212yes—
14C22×SD16×C151C2212yes—
15#533×C151—28no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×#125×C151—21no—
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151C2212yes—
21C2×C4×Q8×C151—21no—
22C2×C4×Q8×C151C2212yes—
23C2×#117×C151—21no—
24C2×#117×C151C2211yescharacteristic
25C22×C42×C151C2211yescharacteristic
26#452×C151—28no—
27C2×#103×C151C2212yes—
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×C22⋊C8×C151C2212yes—
32#391×C151C2211yescharacteristic
33#391×C151C2211yescharacteristic
34#390×C151C2211yescharacteristic
35#390×C151C2211yescharacteristic
36#386×C151—21no—
37#386×C151—21no—
38C4×C22⋊C4×C151—21no—
39C4×C22⋊C4×C151—21no—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43#336×C151C2211yescharacteristic
44#336×C151C2211yescharacteristic
45C2×#41×C151—22no—
46C2×#41×C151—24no—
47C2×#41×C151—22no—
48C2×#41×C151—42no—
49C22×Q8×C151—21no—
50C22×Q8×C151C2312yes—
51C22×Q8×C151C2311yescharacteristic
52C22×D4×C151—21no—
53C22×D4×C151C2311yescharacteristic
54C23×C4×C151—21no—
55C23×C4×C151D411yescharacteristic
56C23×C4×C151D411yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C2×Q16×C151—24no—
59C2×Q16×C151—24no—
60C2×Q16×C151—42no—
61C2×SD16×C151—24no—
62C2×SD16×C151—24no—
63C2×SD16×C151—42no—
64C22×C8×C151C2312yes—
65C22×C8×C151C2312yes—
66C4⋊Q8×C151—24no—
67C4⋊Q8×C151—24no—
68#125×C151—28no—
69C22⋊Q8×C151—28no—
70C22⋊Q8×C151—24no—
71C22⋊Q8×C151D418yes—
72C4×Q8×C151—28no—
73C4×Q8×C151—24no—
74C4×Q8×C151—24no—
75#117×C151—28no—
76#117×C151—42no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C42×C151—24no—
92C2×C42×C151—22no—
93C2×C42×C151—21no—
94C2×C42×C151D411yescharacteristic
95C2×C42×C151D411yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98#103×C151—24no—
99#103×C151—42no—
100#103×C151—42no—
101#102×C151—24no—
102C22⋊C8×C151—24no—
103#95×C151—21no—
104#95×C151—21no—
105#95×C151—21no—
106#95×C151—21no—
107C24×C151—21no—
108C24×C151C2×D411yescharacteristic
109#41×C151—48no—
110#41×C151—48no—
111C2×Q8×C151—24no—
112C2×Q8×C151—22no—
113C2×Q8×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151—22no—
120C2×Q8×C151—42no—
121C2×Q8×C151—42no—
122C2×Q8×C151C2×D414yes—
123C2×Q8×C151#4112yes—
124C2×D4×C151—24no—
125C2×D4×C151—22no—
126C2×D4×C151—21no—
127C2×D4×C151—22no—
128C2×D4×C151—42no—
129C2×D4×C151—42no—
130C2×D4×C151#4112yes—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—22no—
137C22×C4×C151—24no—
138C22×C4×C151—22no—
139C22×C4×C151—21no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—41no—
146C22×C4×C151—42no—
147C22×C4×C151—42no—
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D414yes—
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2411yescharacteristic
155Q16×C151—48no—
156SD16×C151—48no—
157C2×C8×C151—22no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—24no—
165C4⋊C4×C151—28no—
166C4⋊C4×C151—24no—
167C4⋊C4×C151—28no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151C2×D414yes—
172C22⋊C4×C151—28no—
173C22⋊C4×C151—42no—
174C22⋊C4×C151—42no—
175C22⋊C4×C151—42no—
176C22⋊C4×C151—42no—
177C22⋊C4×C151—42no—
178C42×C151—28no—
179C42×C151—22no—
180C42×C151—22no—
181C42×C151—22no—
182C42×C151—22no—
183C42×C151—42no—
184C23×C151—21no—
185C23×C151—21no—
186C23×C151—21no—
187C23×C151—21no—
188C23×C151—21no—
189C23×C151—21no—
190C23×C151—22no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151#12012yes—
198C23×C151C22×D411yescharacteristic
199Q8×C151—24no—
200Q8×C151—24no—
201Q8×C151—24no—
202Q8×C151—48no—
203Q8×C151—42no—
204Q8×C151—42no—
205Q8×C151—42no—
206D4×C151—24no—
207D4×C151—48no—
208D4×C151—42no—
209C2×C4×C151—28no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—24no—
219C2×C4×C151—24no—
220C2×C4×C151—24no—
221C2×C4×C151—24no—
222C2×C4×C151—21no—
223C2×C4×C151—22no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—44no—
227C2×C4×C151—48no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151#12012yes—
241C2×C4×C151#13512yes—
242C2×C4×C151#13712yes—
243C2×C4×C151#13712yes—
244C2×C4×C151C22×D412yes—
245C2×C4×C151C2×#4111yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151H(5,𝔽2)12yes—
248C8×C151—42no—
249C8×C151—42no—
250C22×C151—22no—
251C22×C151—22no—
252C22×C151—22no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151—81no—
264C22×C151C2×#12011yescharacteristic
265C22×C151#52511yescharacteristic
266C22×C151#53511yescharacteristic
267C22×C151C2×#13511yescharacteristic
268C22×C151C2×#13711yescharacteristic
269C22×C151C2×#13711yescharacteristic
270C22×C151#57511yescharacteristic
271C4×C151—22no—
272C4×C151—22no—
273C4×C151—22no—
274C4×C151—22no—
275C4×C151—42no—
276C4×C151—44no—
277C4×C151—41no—
278C4×C151—44no—
279C4×C151—81no—
280C4×C151—81no—
281C4×C151#54612yes—
282C4×C151#54612yes—
283C2×C151—42no—
284C2×C151—82no—
285C2×C151#240411yescharacteristic
286C2×C151#300211yescharacteristic
287C2×C151#300411yescharacteristic
288C2×C151#310711yescharacteristic
289C2×C151#311611yescharacteristic
290C2×C151#321011yescharacteristic
291C2×C151#321611yescharacteristic
292#23935C15111yesmaximal, characteristic, direct product factor, Sylow
293C151#2393511yescharacteristic, direct product factor, Sylow
294C2×#533C2×C15111yescharacteristic, complemented
295C2×#452C2×C15112yes—
296#2297C2×C15111yescharacteristic
297#2024C2×C15111yescharacteristic, complemented
298#2023C2×C15111yescharacteristic, complemented
299#2016C2×C15111yescharacteristic, complemented
300#2013C2×C15111yescharacteristic, complemented
301#1880C2×C15112yescomplemented
302#1878C2×C15112yescomplemented
303#1873C2×C15112yescomplemented
304#1817C2×C15111yescharacteristic, complemented
305C22×#41C22×C15111yescharacteristic
306C22×Q16C22×C15112yes—
307C22×SD16C22×C15112yes—
308#533—28no—
309C2×C4⋊Q8C22×C15111yescharacteristic
310C2×C4⋊Q8C22×C15111yescharacteristic
311C2×#125—21no—
312C2×C22⋊Q8—21no—
313C2×C22⋊Q8C22×C15112yes—
314C2×C4×Q8—21no—
315C2×C4×Q8C22×C15112yes—
316C2×#117—21no—
317C2×#117C22×C15111yescharacteristic
318C22×C42C22×C15111yescharacteristic
319#452—28no—
320C2×#103C22×C15112yes—
321C2×#103C22×C15112yes—
322C2×#103C22×C15112yes—
323C2×#102C22×C15112yes—
324C2×C22⋊C8C22×C15112yes—
325#391C22×C15111yescharacteristic
326#391C22×C15111yescharacteristic
327#390C22×C15111yescharacteristic
328#390C22×C15111yescharacteristic
329#386—21no—
330#386—21no—
331C4×C22⋊C4—21no—
332C4×C22⋊C4—21no—
333#340C22×C15112yes—
334#340C22×C15112yes—
335#336C22×C15112yes—
336#336C22×C15111yescharacteristic
337#336C22×C15111yescharacteristic
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—24no—
341C2×#41—42no—
342C22×Q8—21no—
343C22×Q8C23×C15111yescharacteristic
344C22×Q8C23×C15112yes—
345C22×D4—21no—
346C22×D4C23×C15111yescharacteristic
347C23×C4—21no—
348C23×C4D4×C15111yescharacteristic
349C23×C4D4×C15111yescharacteristic
350C23×C4C23×C15111yescharacteristic
351C2×Q16—24no—
352C2×Q16—24no—
353C2×Q16—42no—
354C2×SD16—24no—
355C2×SD16—24no—
356C2×SD16—42no—
357C22×C8C23×C15112yes—
358C22×C8C23×C15112yes—
359C4⋊Q8—24no—
360C4⋊Q8—24no—
361#125—28no—
362C22⋊Q8—28no—
363C22⋊Q8—24no—
364C22⋊Q8D4×C15118yes—
365C4×Q8—28no—
366C4×Q8—24no—
367C4×Q8—24no—
368#117—28no—
369#117—42no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C4⋊C4C23×C15112yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—21no—
387C2×C42D4×C15111yescharacteristic
388C2×C42D4×C15111yescharacteristic
389C2×C42C23×C15111yescharacteristic
390C2×C42C23×C15111yescharacteristic
391#103—24no—
392#103—42no—
393#103—42no—
394#102—24no—
395C22⋊C8—24no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400C24—21no—
401C24C2×D4×C15111yescharacteristic
402#41—48no—
403#41—48no—
404C2×Q8—24no—
405C2×Q8—22no—
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8C2×D4×C15114yes—
416C2×Q8#41×C15112yes—
417C2×D4—24no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4#41×C15112yes—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—41no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4C2×D4×C15111yescharacteristic
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15114yes—
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C24×C15111yescharacteristic
448Q16—48no—
449SD16—48no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—28no—
459C4⋊C4—24no—
460C4⋊C4—28no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C2×D4×C15114yes—
465C22⋊C4—28no—
466C22⋊C4—42no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C42—28no—
472C42—22no—
473C42—22no—
474C42—22no—
475C42—22no—
476C42—42no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23#120×C15112yes—
491C23C22×D4×C15111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—24no—
495Q8—48no—
496Q8—42no—
497Q8—42no—
498Q8—42no—
499D4—24no—
500D4—48no—
501D4—42no—
502C2×C4—28no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—44no—
520C2×C4—48no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4#120×C15112yes—
534C2×C4#135×C15112yes—
535C2×C4#137×C15112yes—
536C2×C4#137×C15112yes—
537C2×C4C22×D4×C15112yes—
538C2×C4C2×#41×C15111yescharacteristic
539C2×C4C2×#41×C15111yescharacteristic
540C2×C4H(5,𝔽2)×C15112yes—
541C8—42no—
542C8—42no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#120×C15111yescharacteristic
558C22#525×C15111yescharacteristic
559C22#535×C15111yescharacteristic
560C22C2×#135×C15111yescharacteristic
561C22C2×#137×C15111yescharacteristic
562C22C2×#137×C15111yescharacteristic
563C22#575×C15111yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—42no—
569C4—44no—
570C4—41no—
571C4—44no—
572C4—81no—
573C4—81no—
574C4#546×C15112yes—
575C4#546×C15112yes—
576C2—42no—
577C2—82no—
578C2#2404×C15111yescharacteristic
579C2#3002×C15111yescharacteristic
580C2#3004×C15111yescharacteristic
581C2#3107×C15111yescharacteristic
582C2#3116×C15111yescharacteristic
583C2#3210×C15111yescharacteristic
584C2#3216×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#533×C151C2semidirect
4. #2024×C151C2semidirect
5. #2023×C151C2semidirect
6. #2016×C151C2semidirect
7. #2013×C151C2semidirect
8. #1880×C151C2semidirect
9. #1878×C151C2semidirect
10. #1873×C151C2semidirect
11. #1817×C151C2semidirect
292. #23935C151direct (N × H)
293. C151#23935direct (N × H)
294. C2×#533C2×C151semidirect
297. #2024C2×C151semidirect
298. #2023C2×C151semidirect
299. #2016C2×C151semidirect
300. #2013C2×C151semidirect
301. #1880C2×C151semidirect
302. #1878C2×C151semidirect
303. #1873C2×C151semidirect
304. #1817C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#533×C1512
C2×#452×C1512
#2297×C1512
#2024×C1512
#2023×C1512
#2016×C1512
#2013×C1512
#1880×C1512
#1878×C1512
#1873×C1512
#1817×C1512
#23935151