Finite Group Databasebeta

← C151×#14444 #50319369

Subgroups — C151×#14444 #50319369

Order 38656.

1658 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×#390×C151C211yesmaximal, characteristic
2C2×#388×C151C212yesmaximal, complemented
3#1440×C151C212yesmaximal, complemented
4#1439×C151C212yesmaximal, complemented
5#1438×C151C212yesmaximal
6#1437×C151C212yesmaximal, complemented
7#1436×C151C212yesmaximal, complemented
8C4⋊#95×C151C211yesmaximal, characteristic, complemented
9#1434×C151C211yesmaximal, characteristic, complemented
10C23×D4×C151C2211yescharacteristic
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C22⋊C4×C151C2212yes—
14C22×C22⋊C4×C151C2212yes—
15C22×C22⋊C4×C151C2212yes—
16C22×C22⋊C4×C151C2212yes—
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C42×C151C2212yes—
20C22×C42×C151C2211yescharacteristic
21#390×C151C418yescomplemented
22#388×C151—28no—
23C2×#95×C151C2212yes—
24C2×#95×C151C2211yescharacteristic
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2211yescharacteristic
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2211yescharacteristic
33C25×C151C2312yes—
34C22×D4×C151—22no—
35C22×D4×C151—22no—
36C22×D4×C151—42no—
37C22×D4×C151—42no—
38C22×D4×C151C2×C414yes—
39C23×C4×C151C2312yes—
40C23×C4×C151C2312yes—
41C23×C4×C151C2311yescharacteristic
42C23×C4×C151C2312yes—
43C23×C4×C151C2312yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2311yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C2×C4⋊C4×C151—24no—
48C2×C4⋊C4×C151—24no—
49C2×C4⋊C4×C151—42no—
50C2×C4⋊C4×C151—42no—
51C2×C4⋊C4×C151C2×C414yes—
52C2×C22⋊C4×C151—24no—
53C2×C22⋊C4×C151—24no—
54C2×C22⋊C4×C151—24no—
55C2×C22⋊C4×C151—24no—
56C2×C22⋊C4×C151—24no—
57C2×C22⋊C4×C151—24no—
58C2×C22⋊C4×C151—42no—
59C2×C22⋊C4×C151—42no—
60C2×C22⋊C4×C151—42no—
61C2×C22⋊C4×C151—42no—
62C2×C22⋊C4×C151—42no—
63C2×C22⋊C4×C151—42no—
64C2×C22⋊C4×C151—42no—
65C2×C22⋊C4×C151—42no—
66C2×C22⋊C4×C151—42no—
67C2×C22⋊C4×C151—42no—
68C2×C22⋊C4×C151C2×C418yes—
69C2×C22⋊C4×C151C2×C418yes—
70C2×C42×C151—24no—
71C2×C42×C151—42no—
72C2×C42×C151—42no—
73C2×C42×C151—42no—
74C2×C42×C151C2×C414yes—
75#95×C151—24no—
76#95×C151—24no—
77#95×C151—24no—
78#95×C151—22no—
79#95×C151—41no—
80#95×C151—41no—
81#95×C151—42no—
82#95×C151—42no—
83#95×C151—42no—
84#95×C151D414yescomplemented
85C24×C151—22no—
86C24×C151—22no—
87C24×C151—22no—
88C24×C151—22no—
89C24×C151—22no—
90C24×C151—22no—
91C24×C151—22no—
92C24×C151—22no—
93C24×C151—22no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—22no—
97C24×C151—22no—
98C24×C151—22no—
99C24×C151C22×C414yes—
100C24×C151C2411yescharacteristic
101C2×D4×C151—28no—
102C2×D4×C151—44no—
103C2×D4×C151—44no—
104C2×D4×C151—48no—
105C2×D4×C151—48no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—21no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
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—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151C22×C412yes—
147C22×C4×C151C22×C414yes—
148C22×C4×C151C22×C412yes—
149C22×C4×C151C22×C412yes—
150C22×C4×C151C2×D414yes—
151C22×C4×C151C2×D412yes—
152C22×C4×C151#4114yes—
153C22×C4×C151#4112yes—
154C22×C4×C151#4112yes—
155C22×C4×C151#4112yes—
156C4⋊C4×C151—44no—
157C4⋊C4×C151—48no—
158C22⋊C4×C151—216no—
159C22⋊C4×C151—48no—
160C22⋊C4×C151—48no—
161C22⋊C4×C151—48no—
162C22⋊C4×C151—48no—
163C22⋊C4×C151—48no—
164C42×C151—44no—
165C42×C151—48no—
166C23×C151—24no—
167C23×C151—24no—
168C23×C151—24no—
169C23×C151—24no—
170C23×C151—24no—
171C23×C151—24no—
172C23×C151—24no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151C23×C411yescharacteristic
202C23×C151C22×D411yescharacteristic
203C23×C151C2×#4111yescharacteristic
204C23×C151C2×#4111yescharacteristic
205C23×C151C2×#4111yescharacteristic
206C23×C151C2×#4112yes—
207C23×C151H(5,𝔽2)12yes—
208C23×C151H(5,𝔽2)12yes—
209C23×C151H(5,𝔽2)12yes—
210C23×C151H(5,𝔽2)11yescharacteristic
211C23×C1512−1+411yescharacteristic
212D4×C151—416no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—24no—
218C2×C4×C151—24no—
219C2×C4×C151—24no—
220C2×C4×C151—24no—
221C2×C4×C151—24no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—24no—
225C2×C4×C151—24no—
226C2×C4×C151—22no—
227C2×C4×C151—24no—
228C2×C4×C151—24no—
229C2×C4×C151—24no—
230C2×C4×C151—24no—
231C2×C4×C151—24no—
232C2×C4×C151—24no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—42no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151—42no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—42no—
260C2×C4×C151—42no—
261C2×C4×C151#11714yes—
262C2×C4×C151C4×D414yes—
263C22×C151—44no—
264C22×C151—44no—
265C22×C151—44no—
266C22×C151—44no—
267C22×C151—44no—
268C22×C151—44no—
269C22×C151—44no—
270C22×C151—82no—
271C22×C151—82no—
272C22×C151—82no—
273C22×C151—82no—
274C22×C151—82no—
275C22×C151—82no—
276C22×C151—82no—
277C22×C151—82no—
278C22×C151C2×#11711yescharacteristic
279C22×C151C2×C4×D411yescharacteristic
280C22×C151C4×#4111yescharacteristic
281C22×C151#51811yescharacteristic
282C22×C151#51811yescharacteristic
283C22×C151#51811yescharacteristic
284C22×C151#52011yescharacteristic
285C22×C151#53512yes—
286C22×C151#53812yes—
287C22×C151#53812yes—
288C22×C151#53812yes—
289C22×C151#54012yes—
290C22×C151#54212yes—
291C22×C151#54612yes—
292C22×C151#54711yescharacteristic
293C22×C151#55011yescharacteristic
294C22×C151#55312yes—
295C22×C151#55312yes—
296C22×C151#55511yescharacteristic
297C22×C151#55611yescharacteristic
298C22×C151#55912yes—
299C22×C151#56012yes—
300C22×C151#56212yes—
301C4×C151—24no—
302C4×C151—24no—
303C4×C151—44no—
304C4×C151—42no—
305C4×C151—44no—
306C4×C151—44no—
307C4×C151—82no—
308C4×C151—82no—
309C2×C151—84no—
310C2×C151#231211yescharacteristic
311C2×C151#232811yescharacteristic
312C2×C151#233711yescharacteristic
313C2×C151#235411yescharacteristic
314C2×C151#235711yescharacteristic
315C2×C151#236411yescharacteristic
316C2×C151#237711yescharacteristic
317C2×C151#271012yes—
318C2×C151#271412yes—
319C2×C151#280012yes—
320C2×C151#280312yes—
321#14444C15111yesmaximal, characteristic, direct product factor, Sylow
322C151#1444411yescharacteristic, direct product factor, Sylow
323C2×#390C2×C15111yescharacteristic
324C2×#388C2×C15112yescomplemented
325#1440C2×C15112yescomplemented
326#1439C2×C15112yescomplemented
327#1438C2×C15112yes—
328#1437C2×C15112yescomplemented
329#1436C2×C15112yescomplemented
330C4⋊#95C2×C15111yescharacteristic, complemented
331#1434C2×C15111yescharacteristic, complemented
332C23×D4C22×C15111yescharacteristic
333C22×C4⋊C4C22×C15112yes—
334C22×C4⋊C4C22×C15111yescharacteristic
335C22×C22⋊C4C22×C15112yes—
336C22×C22⋊C4C22×C15112yes—
337C22×C22⋊C4C22×C15112yes—
338C22×C22⋊C4C22×C15112yes—
339C22×C22⋊C4C22×C15112yes—
340C22×C22⋊C4C22×C15112yes—
341C22×C42C22×C15112yes—
342C22×C42C22×C15111yescharacteristic
343#390C4×C15118yescomplemented
344#388—28no—
345C2×#95C22×C15112yes—
346C2×#95C22×C15111yescharacteristic
347C2×#95C22×C15112yes—
348C2×#95C22×C15112yes—
349C2×#95C22×C15112yes—
350C2×#95C22×C15111yescharacteristic
351C2×#95C22×C15111yescharacteristic
352C2×#95C22×C15112yes—
353C2×#95C22×C15112yes—
354C2×#95C22×C15111yescharacteristic
355C25C23×C15112yes—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4C2×C4×C15114yes—
361C23×C4C23×C15112yes—
362C23×C4C23×C15112yes—
363C23×C4C23×C15112yes—
364C23×C4C23×C15112yes—
365C23×C4C23×C15111yescharacteristic
366C23×C4C23×C15112yes—
367C23×C4C23×C15111yescharacteristic
368C23×C4C23×C15111yescharacteristic
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4C2×C4×C15114yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4C2×C4×C15118yes—
391C2×C22⋊C4C2×C4×C15118yes—
392C2×C42—24no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42C2×C4×C15114yes—
397#95—24no—
398#95—24no—
399#95—22no—
400#95—24no—
401#95—41no—
402#95—41no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95D4×C15114yescomplemented
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24C22×C4×C15114yes—
422C24C24×C15111yescharacteristic
423C2×D4—28no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—48no—
427C2×D4—48no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4C22×C4×C15112yes—
469C22×C4C22×C4×C15114yes—
470C22×C4C22×C4×C15112yes—
471C22×C4C22×C4×C15112yes—
472C22×C4C2×D4×C15114yes—
473C22×C4C2×D4×C15112yes—
474C22×C4#41×C15114yes—
475C22×C4#41×C15112yes—
476C22×C4#41×C15112yes—
477C22×C4#41×C15112yes—
478C4⋊C4—44no—
479C4⋊C4—48no—
480C22⋊C4—216no—
481C22⋊C4—48no—
482C22⋊C4—48no—
483C22⋊C4—48no—
484C22⋊C4—48no—
485C22⋊C4—48no—
486C42—44no—
487C42—48no—
488C23—24no—
489C23—24no—
490C23—24no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23C23×C4×C15111yescharacteristic
524C23C22×D4×C15111yescharacteristic
525C23C2×#41×C15111yescharacteristic
526C23C2×#41×C15111yescharacteristic
527C23C2×#41×C15111yescharacteristic
528C23C2×#41×C15112yes—
529C23H(5,𝔽2)×C15112yes—
530C23H(5,𝔽2)×C15112yes—
531C23H(5,𝔽2)×C15112yes—
532C23H(5,𝔽2)×C15111yescharacteristic
533C232−1+4×C15111yescharacteristic
534D4—416no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4#117×C15114yes—
584C2×C4C4×D4×C15114yes—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—82no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22C2×#117×C15111yescharacteristic
601C22C2×C4×D4×C15111yescharacteristic
602C22C4×#41×C15111yescharacteristic
603C22#518×C15111yescharacteristic
604C22#518×C15111yescharacteristic
605C22#518×C15111yescharacteristic
606C22#520×C15111yescharacteristic
607C22#535×C15112yes—
608C22#538×C15112yes—
609C22#538×C15112yes—
610C22#538×C15112yes—
611C22#540×C15112yes—
612C22#542×C15112yes—
613C22#546×C15112yes—
614C22#547×C15111yescharacteristic
615C22#550×C15111yescharacteristic
616C22#553×C15112yes—
617C22#553×C15112yes—
618C22#555×C15111yescharacteristic
619C22#556×C15111yescharacteristic
620C22#559×C15112yes—
621C22#560×C15112yes—
622C22#562×C15112yes—
623C4—24no—
624C4—24no—
625C4—42no—
626C4—44no—
627C4—44no—
628C4—44no—
629C4—82no—
630C4—82no—
631C2—84no—
632C2#2312×C15111yescharacteristic
633C2#2328×C15111yescharacteristic
634C2#2337×C15111yescharacteristic
635C2#2354×C15111yescharacteristic
636C2#2357×C15111yescharacteristic
637C2#2364×C15111yescharacteristic
638C2#2377×C15111yescharacteristic
639C2#2710×C15112yes—
640C2#2714×C15112yes—
641C2#2800×C15112yes—
642C2#2803×C15112yes—
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C151C2semidirect
3. #1440×C151C2semidirect
4. #1439×C151C2semidirect
6. #1437×C151C2semidirect
7. #1436×C151C2semidirect
8. C4⋊#95×C151C2semidirect
9. #1434×C151C2semidirect
21. #390×C151C4semidirect
84. #95×C151D4semidirect
321. #14444C151direct (N × H)
322. C151#14444direct (N × H)
324. C2×#388C2×C151semidirect
325. #1440C2×C151semidirect
326. #1439C2×C151semidirect
328. #1437C2×C151semidirect
329. #1436C2×C151semidirect
330. C4⋊#95C2×C151semidirect
331. #1434C2×C151semidirect
343. #390C4×C151semidirect
406. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#390×C1512
C2×#388×C1512
#1440×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#1436×C1512
C4⋊#95×C1512
#1434×C1512
#14444151