Finite Group Databasebeta

← C151×#15429 #50320354

Subgroups — C151×#15429 #50320354

Order 38656.

2090 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C151C212yesmaximal, complemented
2C2×#386×C151C212yesmaximal
3C2×#385×C151C212yesmaximal, complemented
4C2×#380×C151C212yesmaximal, complemented
5#1444×C151C211yesmaximal, characteristic, complemented
6#1442×C151C211yesmaximal, characteristic, complemented
7#1441×C151C212yesmaximal, complemented
8#1439×C151C212yesmaximal, complemented
9#1438×C151C211yesmaximal, characteristic
10C23×D4×C151C2211yescharacteristic
11C24×C4×C151C2212yes—
12C22×C4⋊C4×C151C2212yes—
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2212yes—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22#396×C151—28no—
23#386×C151—28no—
24#385×C151—28no—
25#380×C151—28no—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2211yescharacteristic
35C25×C151C2312yes—
36C22×D4×C151—24no—
37C22×D4×C151—24no—
38C22×D4×C151—41no—
39C22×D4×C151—41no—
40C22×D4×C151Q814yes—
41C23×C4×C151—24no—
42C23×C4×C151—24no—
43C23×C4×C151—24no—
44C23×C4×C151—24no—
45C23×C4×C151—24no—
46C23×C4×C151—42no—
47C23×C4×C151—42no—
48C23×C4×C151C2312yes—
49C23×C4×C151C2312yes—
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2312yes—
52C23×C4×C151C2312yes—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C23×C4×C151C2312yes—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—24no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—24no—
62C2×C4⋊C4×C151—24no—
63C2×C4⋊C4×C151—24no—
64C2×C4⋊C4×C151—42no—
65C2×C4⋊C4×C151—42no—
66C2×C4⋊C4×C151—41no—
67C2×C4⋊C4×C151—41no—
68C2×C4⋊C4×C151—42no—
69C2×C22⋊C4×C151—24no—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—24no—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—24no—
76C2×C22⋊C4×C151—24no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—24no—
79C2×C22⋊C4×C151—42no—
80C2×C22⋊C4×C151—42no—
81C2×C22⋊C4×C151—42no—
82C2×C22⋊C4×C151—42no—
83C2×C22⋊C4×C151D418yes—
84#95×C151—24no—
85#95×C151—24no—
86#95×C151—24no—
87#95×C151—24no—
88#95×C151—24no—
89#95×C151—41no—
90#95×C151—41no—
91#95×C151D414yescomplemented
92#95×C151D414yescomplemented
93C24×C151—22no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—22no—
97C24×C151—22no—
98C24×C151—22no—
99C24×C151—22no—
100C24×C151—22no—
101C24×C151—22no—
102C24×C151—22no—
103C24×C151—22no—
104C24×C151—22no—
105C24×C151C2×D414yes—
106C24×C151C2×Q814yes—
107C24×C151#4114yes—
108C24×C151C2411yescharacteristic
109C2×D4×C151—216no—
110C2×D4×C151—44no—
111C2×D4×C151—44no—
112C2×D4×C151—48no—
113C2×D4×C151—44no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—216no—
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—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
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—22no—
156C22×C4×C151—22no—
157C22×C4×C151—48no—
158C22×C4×C151—48no—
159C22×C4×C151—48no—
160C22×C4×C151—48no—
161C22×C4×C151—48no—
162C22×C4×C151—48no—
163C22×C4×C151C2×D412yes—
164C22×C4×C151C2×D414yes—
165C22×C4×C151C2×D414yes—
166C22×C4×C151C2×D412yes—
167C22×C4×C151C2×D414yes—
168C22×C4×C151C2×D414yes—
169C22×C4×C151C2×Q812yes—
170C22×C4×C151#4114yes—
171C4⋊C4×C151—48no—
172C4⋊C4×C151—48no—
173C4⋊C4×C151—44no—
174C4⋊C4×C151—44no—
175C4⋊C4×C151—48no—
176C22⋊C4×C151—216no—
177C22⋊C4×C151—48no—
178C22⋊C4×C151—48no—
179C22⋊C4×C151—48no—
180C22⋊C4×C151—48no—
181C23×C151—24no—
182C23×C151—24no—
183C23×C151—24no—
184C23×C151—24no—
185C23×C151—24no—
186C23×C151—24no—
187C23×C151—24no—
188C23×C151—24no—
189C23×C151—24no—
190C23×C151—24no—
191C23×C151—24no—
192C23×C151—24no—
193C23×C151—24no—
194C23×C151—24no—
195C23×C151—24no—
196C23×C151—24no—
197C23×C151—24no—
198C23×C151—24no—
199C23×C151—42no—
200C23×C151—42no—
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—42no—
212C23×C151—42no—
213C23×C151—42no—
214C23×C151—42no—
215C23×C151C22⋊Q818yes—
216C23×C151C22×D411yescharacteristic
217C23×C151C22×D412yes—
218C23×C151C22×D411yescharacteristic
219C23×C151C22×Q811yescharacteristic
220C23×C151C2×#4112yes—
221C23×C151C2×#4112yes—
222C23×C151H(5,𝔽2)11yescharacteristic
223C23×C151H(5,𝔽2)12yes—
224C23×C151H(5,𝔽2)11yescharacteristic
225C23×C1512−1+411yescharacteristic
226C23×C1512−1+411yescharacteristic
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—24no—
236C2×C4×C151—24no—
237C2×C4×C151—22no—
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—432no—
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—41no—
254C2×C4×C151—41no—
255C2×C4×C151—42no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—42no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—42no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
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×C151—42no—
276C2×C4×C151—42no—
277C2×C4×C151—42no—
278C2×C4×C151#12118yes—
279C22×C151—28no—
280C22×C151—28no—
281C22×C151—28no—
282C22×C151—44no—
283C22×C151—44no—
284C22×C151—44no—
285C22×C151—44no—
286C22×C151—44no—
287C22×C151—44no—
288C22×C151—44no—
289C22×C151—44no—
290C22×C151—44no—
291C22×C151—44no—
292C22×C151—44no—
293C22×C151—44no—
294C22×C151C2×#12112yes—
295C22×C151C2×C22⋊Q812yes—
296C22×C151#52512yes—
297C22×C151#53711yescharacteristic
298C22×C151#53712yes—
299C22×C151#53711yescharacteristic
300C22×C151#53812yes—
301C22×C151#53912yes—
302C22×C151#54311yescharacteristic
303C22×C151D4212yes—
304C22×C151D4211yescharacteristic
305C22×C151D4211yescharacteristic
306C22×C151#54612yes—
307C22×C151#54612yes—
308C22×C151#54712yes—
309C22×C151D4×Q811yescharacteristic
310C22×C151D4×Q811yescharacteristic
311C22×C151#55111yescharacteristic
312C22×C151#55212yes—
313C22×C151#55412yes—
314C22×C151#55511yescharacteristic
315C22×C151#56011yescharacteristic
316C22×C151#56311yescharacteristic
317C4×C151—28no—
318C4×C151—42no—
319C4×C151—44no—
320C4×C151—42no—
321C4×C151—42no—
322C4×C151—44no—
323C4×C151—82no—
324C4×C151—82no—
325C2×C151—48no—
326C2×C151#241712yes—
327C2×C151#242412yes—
328C2×C151#243711yescharacteristic
329C2×C151#244912yes—
330C2×C151#253711yescharacteristic
331C2×C151#260911yescharacteristic
332C2×C151#267511yescharacteristic
333C2×C151#268311yescharacteristic
334C2×C151#269311yescharacteristic
335C2×C151#269512yes—
336C2×C151#278411yescharacteristic
337#15429C15111yesmaximal, characteristic, direct product factor, Sylow
338C151#1542911yescharacteristic, direct product factor, Sylow
339C2×#396C2×C15112yescomplemented
340C2×#386C2×C15112yes—
341C2×#385C2×C15112yescomplemented
342C2×#380C2×C15112yescomplemented
343#1444C2×C15111yescharacteristic, complemented
344#1442C2×C15111yescharacteristic, complemented
345#1441C2×C15112yescomplemented
346#1439C2×C15112yescomplemented
347#1438C2×C15111yescharacteristic
348C23×D4C22×C15111yescharacteristic
349C24×C4C22×C15112yes—
350C22×C4⋊C4C22×C15112yes—
351C22×C4⋊C4C22×C15111yescharacteristic
352C22×C4⋊C4C22×C15112yes—
353C22×C4⋊C4C22×C15112yes—
354C22×C4⋊C4C22×C15111yescharacteristic
355C22×C22⋊C4C22×C15112yes—
356C22×C22⋊C4C22×C15112yes—
357C22×C22⋊C4C22×C15112yes—
358C22×C22⋊C4C22×C15112yes—
359C22×C22⋊C4C22×C15112yes—
360#396—28no—
361#386—28no—
362#385—28no—
363#380—28no—
364C2×#95C22×C15112yes—
365C2×#95C22×C15112yes—
366C2×#95C22×C15112yes—
367C2×#95C22×C15112yes—
368C2×#95C22×C15112yes—
369C2×#95C22×C15111yescharacteristic
370C2×#95C22×C15111yescharacteristic
371C2×#95C22×C15111yescharacteristic
372C2×#95C22×C15111yescharacteristic
373C25C23×C15112yes—
374C22×D4—24no—
375C22×D4—24no—
376C22×D4—41no—
377C22×D4—41no—
378C22×D4Q8×C15114yes—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4C23×C15112yes—
387C23×C4C23×C15112yes—
388C23×C4C23×C15111yescharacteristic
389C23×C4C23×C15111yescharacteristic
390C23×C4C23×C15112yes—
391C23×C4C23×C15111yescharacteristic
392C23×C4C23×C15112yes—
393C23×C4C23×C15112yes—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—24no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—24no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—42no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4D4×C15118yes—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—41no—
428#95—41no—
429#95D4×C15114yescomplemented
430#95D4×C15114yescomplemented
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24C2×D4×C15114yes—
444C24C2×Q8×C15114yes—
445C24#41×C15114yes—
446C24C24×C15111yescharacteristic
447C2×D4—216no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—44no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—216no—
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—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
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—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4C2×D4×C15112yes—
502C22×C4C2×D4×C15114yes—
503C22×C4C2×D4×C15114yes—
504C22×C4C2×D4×C15112yes—
505C22×C4C2×D4×C15114yes—
506C22×C4C2×D4×C15114yes—
507C22×C4C2×Q8×C15112yes—
508C22×C4#41×C15114yes—
509C4⋊C4—48no—
510C4⋊C4—48no—
511C4⋊C4—44no—
512C4⋊C4—44no—
513C4⋊C4—48no—
514C22⋊C4—216no—
515C22⋊C4—48no—
516C22⋊C4—48no—
517C22⋊C4—48no—
518C22⋊C4—48no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—24no—
529C23—24no—
530C23—24no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23C22⋊Q8×C15118yes—
554C23C22×D4×C15111yescharacteristic
555C23C22×D4×C15112yes—
556C23C22×D4×C15111yescharacteristic
557C23C22×Q8×C15111yescharacteristic
558C23C2×#41×C15112yes—
559C23C2×#41×C15112yes—
560C23H(5,𝔽2)×C15111yescharacteristic
561C23H(5,𝔽2)×C15112yes—
562C23H(5,𝔽2)×C15111yescharacteristic
563C232−1+4×C15111yescharacteristic
564C232−1+4×C15111yescharacteristic
565D4—416no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—432no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4#121×C15118yes—
617C22—28no—
618C22—28no—
619C22—28no—
620C22—44no—
621C22—44no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22C2×#121×C15112yes—
633C22C2×C22⋊Q8×C15112yes—
634C22#525×C15112yes—
635C22#537×C15111yescharacteristic
636C22#537×C15112yes—
637C22#537×C15111yescharacteristic
638C22#538×C15112yes—
639C22#539×C15112yes—
640C22#543×C15111yescharacteristic
641C22D42×C15112yes—
642C22D42×C15111yescharacteristic
643C22D42×C15111yescharacteristic
644C22#546×C15112yes—
645C22#546×C15112yes—
646C22#547×C15112yes—
647C22D4×Q8×C15111yescharacteristic
648C22D4×Q8×C15111yescharacteristic
649C22#551×C15111yescharacteristic
650C22#552×C15112yes—
651C22#554×C15112yes—
652C22#555×C15111yescharacteristic
653C22#560×C15111yescharacteristic
654C22#563×C15111yescharacteristic
655C4—28no—
656C4—42no—
657C4—44no—
658C4—42no—
659C4—42no—
660C4—44no—
661C4—82no—
662C4—82no—
663C2—48no—
664C2#2417×C15112yes—
665C2#2424×C15112yes—
666C2#2437×C15111yescharacteristic
667C2#2449×C15112yes—
668C2#2537×C15111yescharacteristic
669C2#2609×C15111yescharacteristic
670C2#2675×C15111yescharacteristic
671C2#2683×C15111yescharacteristic
672C2#2693×C15111yescharacteristic
673C2#2695×C15112yes—
674C2#2784×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#396×C151C2semidirect
3. C2×#385×C151C2semidirect
4. C2×#380×C151C2semidirect
5. #1444×C151C2semidirect
6. #1442×C151C2semidirect
7. #1441×C151C2semidirect
8. #1439×C151C2semidirect
91. #95×C151D4semidirect
92. #95×C151D4semidirect
337. #15429C151direct (N × H)
338. C151#15429direct (N × H)
339. C2×#396C2×C151semidirect
341. C2×#385C2×C151semidirect
342. C2×#380C2×C151semidirect
343. #1444C2×C151semidirect
344. #1442C2×C151semidirect
345. #1441C2×C151semidirect
346. #1439C2×C151semidirect
429. #95D4×C151semidirect
430. #95D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1512
C2×#386×C1512
C2×#385×C1512
C2×#380×C1512
#1444×C1512
#1442×C1512
#1441×C1512
#1439×C1512
#1438×C1512
#15429151