Finite Group Databasebeta

← C151×#14506 #50319431

Subgroups — C151×#14506 #50319431

Order 38656.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C151C211yesmaximal, characteristic
2C2×#388×C151C212yesmaximal, complemented
3#1445×C151C212yesmaximal, complemented
4#1439×C151C212yesmaximal, complemented
5#1438×C151C211yesmaximal, characteristic
6#1438×C151C211yesmaximal, characteristic
7#1437×C151C212yesmaximal, complemented
8C4⋊#95×C151C212yesmaximal, complemented
9C22⋊#95×C151C212yesmaximal, complemented
10C23×D4×C151C2211yescharacteristic
11C24×C4×C151C2211yescharacteristic
12C2×#123×C151—28no—
13C2×#123×C151C418yescomplemented
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2212yes—
16C22×C22⋊C4×C151C2212yes—
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2211yescharacteristic
23C22×C42×C151C2212yes—
24#388×C151—28no—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2212yes—
33C2×#95×C151C2211yescharacteristic
34C25×C151C2311yescharacteristic
35C25×C151C2311yescharacteristic
36C22×D4×C151—24no—
37C22×D4×C151—42no—
38C22×D4×C151—41no—
39C22×D4×C151—41no—
40C22×D4×C151C2×C414yes—
41C23×C4×C151—24no—
42C23×C4×C151—42no—
43C23×C4×C151—41no—
44C23×C4×C151—41no—
45C23×C4×C151C2×C414yes—
46C23×C4×C151C2312yes—
47C23×C4×C151C2312yes—
48C23×C4×C151C2312yes—
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2312yes—
52C23×C4×C151C2312yes—
53#123×C151—232no—
54C2×C4⋊C4×C151—24no—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—42no—
59C2×C4⋊C4×C151C2×C418yes—
60C2×C22⋊C4×C151—24no—
61C2×C22⋊C4×C151—24no—
62C2×C22⋊C4×C151—24no—
63C2×C22⋊C4×C151—24no—
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—24no—
66C2×C22⋊C4×C151—24no—
67C2×C22⋊C4×C151—24no—
68C2×C22⋊C4×C151—42no—
69C2×C22⋊C4×C151—42no—
70C2×C22⋊C4×C151—42no—
71C2×C22⋊C4×C151—42no—
72C2×C22⋊C4×C151—41no—
73C2×C22⋊C4×C151—42no—
74C2×C22⋊C4×C151—41no—
75C2×C22⋊C4×C151C2×C418yes—
76C2×C22⋊C4×C151C2×C414yes—
77C2×C22⋊C4×C151D418yes—
78C2×C42×C151—24no—
79C2×C42×C151—24no—
80C2×C42×C151—42no—
81#95×C151—24no—
82#95×C151—24no—
83#95×C151—41no—
84#95×C151—42no—
85#95×C151—42no—
86#95×C151—42no—
87#95×C151—42no—
88#95×C151—42no—
89#95×C151—41no—
90C24×C151—22no—
91C24×C151—22no—
92C24×C151—22no—
93C24×C151—22no—
94C24×C151—21no—
95C24×C151—21no—
96C24×C151—22no—
97C24×C151—22no—
98C24×C151—22no—
99C24×C151—22no—
100C24×C151—22no—
101C24×C151—22no—
102C24×C151—21no—
103C24×C151—21no—
104C24×C151—22no—
105C24×C151C22×C412yes—
106C24×C151C22×C412yes—
107C24×C151C2×D414yes—
108C24×C151C2411yescharacteristic
109C2×D4×C151—28no—
110C2×D4×C151—44no—
111C2×D4×C151—44no—
112C2×D4×C151—48no—
113C2×D4×C151—48no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—28no—
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—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
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×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—44no—
156C22×C4×C151—44no—
157C22×C4×C151—48no—
158C22×C4×C151—48no—
159C22×C4×C151C22×C414yes—
160C22×C4×C151C22×C412yes—
161C22×C4×C151C22×C414yes—
162C22×C4×C151C2×D414yes—
163C22×C4×C151C2×D414yes—
164C22×C4×C151#4114yes—
165C22×C4×C151#4114yes—
166C4⋊C4×C151—216no—
167C4⋊C4×C151—48no—
168C22⋊C4×C151—216no—
169C22⋊C4×C151—44no—
170C22⋊C4×C151—48no—
171C22⋊C4×C151—48no—
172C22⋊C4×C151—48no—
173C22⋊C4×C151—44no—
174C22⋊C4×C151C22⋊C4116yescomplemented
175C42×C151—48no—
176C23×C151—24no—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151—24no—
180C23×C151—24no—
181C23×C151—24no—
182C23×C151—24no—
183C23×C151—24no—
184C23×C151—24no—
185C23×C151—24no—
186C23×C151—22no—
187C23×C151—24no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—24no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151—41no—
196C23×C151—42no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—42no—
200C23×C151—41no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—42no—
205C23×C151—42no—
206C23×C151—42no—
207C23×C151—42no—
208C23×C151—42no—
209C23×C151—42no—
210C23×C151—42no—
211C23×C151—41no—
212C23×C151—42no—
213C23×C151—41no—
214C23×C151—41no—
215C23×C151—42no—
216C23×C151—41no—
217C23×C151C2×C22⋊C414yes—
218C23×C151C23×C411yescharacteristic
219C23×C151C22×D412yes—
220C23×C151C2×#4112yes—
221C23×C151C2×#4112yes—
222C23×C151H(5,𝔽2)12yes—
223C23×C151H(5,𝔽2)11yescharacteristic
224C23×C151H(5,𝔽2)11yescharacteristic
225C23×C151H(5,𝔽2)12yes—
226C23×C1512−1+412yes—
227D4×C151—416no—
228C2×C4×C151—24no—
229C2×C4×C151—24no—
230C2×C4×C151—24no—
231C2×C4×C151—24no—
232C2×C4×C151—24no—
233C2×C4×C151—24no—
234C2×C4×C151—24no—
235C2×C4×C151—22no—
236C2×C4×C151—24no—
237C2×C4×C151—24no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
240C2×C4×C151—24no—
241C2×C4×C151—24no—
242C2×C4×C151—24no—
243C2×C4×C151—24no—
244C2×C4×C151—24no—
245C2×C4×C151—24no—
246C2×C4×C151—416no—
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—42no—
262C2×C4×C151—42no—
263C2×C4×C151—42no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151—42no—
267C2×C4×C151—42no—
268C2×C4×C151—42no—
269C2×C4×C151—42no—
270C2×C4×C151—42no—
271C2×C4×C151—42no—
272C2×C4×C151—42no—
273C2×C4×C151—42no—
274C2×C4×C151—42no—
275C2×C4×C151C2×C22⋊C418yes—
276C22×C151—24no—
277C22×C151—28no—
278C22×C151—44no—
279C22×C151—42no—
280C22×C151—42no—
281C22×C151—44no—
282C22×C151—44no—
283C22×C151—44no—
284C22×C151—44no—
285C22×C151—42no—
286C22×C151—44no—
287C22×C151—44no—
288C22×C151—42no—
289C22×C151—42no—
290C22×C151—82no—
291C22×C151—82no—
292C22×C151—82no—
293C22×C151—82no—
294C22×C151C22×C22⋊C411yescharacteristic
295C22×C151C4×#4112yes—
296C22×C151#51811yescharacteristic
297C22×C151#51811yescharacteristic
298C22×C151#52012yes—
299C22×C151#53512yes—
300C22×C151#53512yes—
301C22×C151#53812yes—
302C22×C151#53912yes—
303C22×C151#54012yes—
304C22×C151#54212yes—
305C22×C151#54612yes—
306C22×C151#54612yes—
307C22×C151#54712yes—
308C22×C151#54712yes—
309C22×C151#55111yescharacteristic
310C22×C151#55312yes—
311C22×C151#55911yescharacteristic
312C22×C151#56011yescharacteristic
313C22×C151#56212yes—
314C22×C151#56311yescharacteristic
315C4×C151—28no—
316C4×C151—44no—
317C4×C151—42no—
318C4×C151—44no—
319C4×C151—44no—
320C4×C151—82no—
321C4×C151—82no—
322C2×C151—44no—
323C2×C151—82no—
324C2×C151#230911yescharacteristic
325C2×C151#233512yes—
326C2×C151#233912yes—
327C2×C151#237411yescharacteristic
328C2×C151#237611yescharacteristic
329C2×C151#270312yes—
330C2×C151#270612yes—
331C2×C151#271012yes—
332C2×C151#271812yes—
333#14506C15111yesmaximal, characteristic, direct product factor, Sylow
334C151#1450611yescharacteristic, direct product factor, Sylow
335C22×#123C2×C15111yescharacteristic
336C2×#388C2×C15112yescomplemented
337#1445C2×C15112yescomplemented
338#1439C2×C15112yescomplemented
339#1438C2×C15111yescharacteristic
340#1438C2×C15111yescharacteristic
341#1437C2×C15112yescomplemented
342C4⋊#95C2×C15112yescomplemented
343C22⋊#95C2×C15112yescomplemented
344C23×D4C22×C15111yescharacteristic
345C24×C4C22×C15111yescharacteristic
346C2×#123—28no—
347C2×#123C4×C15118yescomplemented
348C22×C4⋊C4C22×C15112yes—
349C22×C4⋊C4C22×C15112yes—
350C22×C22⋊C4C22×C15112yes—
351C22×C22⋊C4C22×C15112yes—
352C22×C22⋊C4C22×C15111yescharacteristic
353C22×C22⋊C4C22×C15112yes—
354C22×C22⋊C4C22×C15112yes—
355C22×C22⋊C4C22×C15111yescharacteristic
356C22×C22⋊C4C22×C15111yescharacteristic
357C22×C42C22×C15112yes—
358#388—28no—
359C2×#95C22×C15112yes—
360C2×#95C22×C15112yes—
361C2×#95C22×C15112yes—
362C2×#95C22×C15112yes—
363C2×#95C22×C15112yes—
364C2×#95C22×C15112yes—
365C2×#95C22×C15111yescharacteristic
366C2×#95C22×C15112yes—
367C2×#95C22×C15111yescharacteristic
368C25C23×C15111yescharacteristic
369C25C23×C15111yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C15114yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C15114yes—
380C23×C4C23×C15112yes—
381C23×C4C23×C15112yes—
382C23×C4C23×C15112yes—
383C23×C4C23×C15112yes—
384C23×C4C23×C15112yes—
385C23×C4C23×C15111yescharacteristic
386C23×C4C23×C15112yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C15118yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C15118yes—
410C2×C22⋊C4C2×C4×C15114yes—
411C2×C22⋊C4D4×C15118yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C15112yes—
440C24C22×C4×C15112yes—
441C24C2×D4×C15114yes—
442C24C24×C15111yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
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×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C15114yes—
494C22×C4C22×C4×C15112yes—
495C22×C4C22×C4×C15114yes—
496C22×C4C2×D4×C15114yes—
497C22×C4C2×D4×C15114yes—
498C22×C4#41×C15114yes—
499C22×C4#41×C15114yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C151116yescomplemented
509C42—48no—
510C23—24no—
511C23—22no—
512C23—22no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—22no—
521C23—24no—
522C23—22no—
523C23—22no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C15114yes—
552C23C23×C4×C15111yescharacteristic
553C23C22×D4×C15112yes—
554C23C2×#41×C15112yes—
555C23C2×#41×C15112yes—
556C23H(5,𝔽2)×C15112yes—
557C23H(5,𝔽2)×C15111yescharacteristic
558C23H(5,𝔽2)×C15111yescharacteristic
559C23H(5,𝔽2)×C15112yes—
560C232−1+4×C15112yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C15118yes—
610C22—28no—
611C22—24no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C15111yescharacteristic
629C22C4×#41×C15112yes—
630C22#518×C15111yescharacteristic
631C22#518×C15111yescharacteristic
632C22#520×C15112yes—
633C22#535×C15112yes—
634C22#535×C15112yes—
635C22#538×C15112yes—
636C22#539×C15112yes—
637C22#540×C15112yes—
638C22#542×C15112yes—
639C22#546×C15112yes—
640C22#546×C15112yes—
641C22#547×C15112yes—
642C22#547×C15112yes—
643C22#551×C15111yescharacteristic
644C22#553×C15112yes—
645C22#559×C15111yescharacteristic
646C22#560×C15111yescharacteristic
647C22#562×C15112yes—
648C22#563×C15111yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2#2309×C15111yescharacteristic
659C2#2335×C15112yes—
660C2#2339×C15112yes—
661C2#2374×C15111yescharacteristic
662C2#2376×C15111yescharacteristic
663C2#2703×C15112yes—
664C2#2706×C15112yes—
665C2#2710×C15112yes—
666C2#2718×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. #1445×C151C2semidirect
4. #1439×C151C2semidirect
7. #1437×C151C2semidirect
8. C4⋊#95×C151C2semidirect
9. C22⋊#95×C151C2semidirect
13. C2×#123×C151C4semidirect
174. C22⋊C4×C151C22⋊C4semidirect
333. #14506C151direct (N × H)
334. C151#14506direct (N × H)
336. C2×#388C2×C151semidirect
337. #1445C2×C151semidirect
338. #1439C2×C151semidirect
341. #1437C2×C151semidirect
342. C4⋊#95C2×C151semidirect
343. C22⋊#95C2×C151semidirect
347. C2×#123C4×C151semidirect
508. C22⋊C4C22⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1512
C2×#388×C1512
#1445×C1512
#1439×C1512
#1438×C1512
#1437×C1512
C4⋊#95×C1512
C22⋊#95×C1512
#14506151