Finite Group Databasebeta

← C151×#15134 #50320059

Subgroups — C151×#15134 #50320059

Order 38656.

2006 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C151C214yesmaximal, complemented
2C2×#390×C151C211yesmaximal, characteristic
3C2×#390×C151C211yesmaximal, characteristic
4C2×#390×C151C211yesmaximal, characteristic
5C2×#389×C151C211yesmaximal, characteristic, complemented
6C2×#384×C151C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
8#1439×C151C214yesmaximal, complemented
9C4⋊#95×C151C211yesmaximal, characteristic, complemented
10C23×D4×C151C2211yescharacteristic
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2214yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2214yes—
19C22×C22⋊C4×C151C2214yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C42×C151C2211yescharacteristic
22C22×C42×C151C2211yescharacteristic
23C22×C42×C151C2211yescharacteristic
24#396×C151—216no—
25#390×C151—24no—
26#390×C151—24no—
27#390×C151—24no—
28#389×C151—24no—
29#384×C151—24no—
30C4×C4⋊C4×C151—24no—
31C2×#95×C151C2214yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C25×C151C2312yes—
35C22×D4×C151—22no—
36C22×D4×C151—22no—
37C22×D4×C151—22no—
38C22×D4×C151—22no—
39C22×D4×C151—22no—
40C22×D4×C151—22no—
41C22×D4×C151Q814yes—
42C23×C4×C151C2312yes—
43C23×C4×C151C2312yes—
44C23×C4×C151C2311yescharacteristic
45C23×C4×C151C2312yes—
46C23×C4×C151C2312yes—
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2312yes—
49C23×C4×C151C2311yescharacteristic
50C2×C4⋊C4×C151—24no—
51C2×C4⋊C4×C151—22no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—24no—
54C2×C4⋊C4×C151—28no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—28no—
61C2×C4⋊C4×C151—28no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—44no—
65C2×C4⋊C4×C151D414yes—
66C2×C4⋊C4×C151D418yescomplemented
67C2×C22⋊C4×C151—28no—
68C2×C22⋊C4×C151—24no—
69C2×C22⋊C4×C151—28no—
70C2×C22⋊C4×C151—24no—
71C2×C22⋊C4×C151—28no—
72C2×C22⋊C4×C151—28no—
73C2×C22⋊C4×C151—28no—
74C2×C22⋊C4×C151—28no—
75C2×C22⋊C4×C151—44no—
76C2×C22⋊C4×C151—44no—
77C2×C42×C151—22no—
78C2×C42×C151—22no—
79C2×C42×C151—22no—
80C2×C42×C151—22no—
81C2×C42×C151—22no—
82C2×C42×C151—22no—
83C2×C42×C151—22no—
84C2×C42×C151D414yes—
85C2×C42×C151D414yes—
86#95×C151—24no—
87#95×C151—24no—
88#95×C151—28no—
89C24×C151—24no—
90C24×C151—22no—
91C24×C151—22no—
92C24×C151—22no—
93C24×C151—24no—
94C24×C151—22no—
95C24×C151—22no—
96C24×C151—22no—
97C24×C151—24no—
98C24×C151—24no—
99C24×C151C2×Q814yes—
100C24×C151C2411yescharacteristic
101C2×D4×C151—28no—
102C2×D4×C151—28no—
103C2×D4×C151—28no—
104C2×D4×C151—44no—
105C2×D4×C151—44no—
106C2×D4×C151—44no—
107C2×D4×C151—44no—
108C22×C4×C151—21no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—24no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—24no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—24no—
130C22×C4×C151—24no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—24no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—24no—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D414yes—
141C22×C4×C151C2×D414yes—
142C22×C4×C151C2×D414yes—
143C22×C4×C151C2×D414yes—
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×D414yes—
146C22×C4×C151C2×D412yes—
147C22×C4×C151C2×D412yes—
148C22×C4×C151C2×D412yes—
149C22×C4×C151C2×Q812yes—
150C22×C4×C151#4114yes—
151C22×C4×C151#4112yes—
152C22×C4×C151#4112yes—
153C22×C4×C151#4112yes—
154C4⋊C4×C151—28no—
155C4⋊C4×C151—216no—
156C4⋊C4×C151—416no—
157C4⋊C4×C151—44no—
158C4⋊C4×C151—44no—
159C4⋊C4×C151—48no—
160C22⋊C4×C151—416no—
161C22⋊C4×C151—48no—
162C22⋊C4×C151—416no—
163C22⋊C4×C151—48no—
164C42×C151—28no—
165C42×C151—28no—
166C42×C151—44no—
167C23×C151—24no—
168C23×C151—24no—
169C23×C151—24no—
170C23×C151—28no—
171C23×C151—28no—
172C23×C151—44no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—44no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—44no—
183C23×C151—44no—
184C23×C151—44no—
185C23×C151—44no—
186C23×C151—44no—
187C23×C151—44no—
188C23×C151—44no—
189C23×C151—44no—
190C23×C151C22×D411yescharacteristic
191C23×C151C22×D411yescharacteristic
192C23×C151C22×D411yescharacteristic
193C23×C151C22×D412yes—
194C23×C151C22×Q811yescharacteristic
195C23×C151C2×#4111yescharacteristic
196C23×C151C2×#4111yescharacteristic
197C23×C151C2×#4111yescharacteristic
198C23×C151C2×#4112yes—
199C23×C151H(5,𝔽2)12yes—
200C23×C1512−1+412yes—
201D4×C151—416no—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—22no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—24no—
209C2×C4×C151—24no—
210C2×C4×C151—24no—
211C2×C4×C151—24no—
212C2×C4×C151—22no—
213C2×C4×C151—24no—
214C2×C4×C151—24no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—24no—
218C2×C4×C151—28no—
219C2×C4×C151—24no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—44no—
228C2×C4×C151—42no—
229C2×C4×C151—44no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—44no—
236C2×C4×C151—42no—
237C2×C4×C151—44no—
238C2×C4×C151—44no—
239C2×C4×C151#12118yes—
240C2×C4×C151#12114yes—
241C2×C4×C151#12114yes—
242C2×C4×C151#12114yes—
243C2×C4×C151C22⋊Q814yes—
244C2×C4×C151C22⋊Q814yes—
245C2×C4×C151C22⋊Q814yes—
246C2×C4×C151#12614yes—
247C2×C4×C151#12714yes—
248C22×C151—44no—
249C22×C151—44no—
250C22×C151—48no—
251C22×C151—48no—
252C22×C151—44no—
253C22×C151—82no—
254C22×C151—82no—
255C22×C151—84no—
256C22×C151—84no—
257C22×C151—82no—
258C22×C151—82no—
259C22×C151C2×#12111yescharacteristic
260C22×C151C2×#12112yes—
261C22×C151C2×#12111yescharacteristic
262C22×C151C2×#12111yescharacteristic
263C22×C151C2×C22⋊Q811yescharacteristic
264C22×C151C2×C22⋊Q811yescharacteristic
265C22×C151C2×C22⋊Q811yescharacteristic
266C22×C151C2×#12611yescharacteristic
267C22×C151C2×#12711yescharacteristic
268C22×C151#53211yescharacteristic
269C22×C151#53212yes—
270C22×C151#53511yescharacteristic
271C22×C151#53611yescharacteristic
272C22×C151#53712yes—
273C22×C151#54212yes—
274C22×C151D4212yes—
275C22×C151#54712yes—
276C22×C151#54812yes—
277C22×C151D4×Q812yes—
278C22×C151#55012yes—
279C22×C151#55312yes—
280C22×C151#55412yes—
281C22×C151#55612yes—
282C4×C151—24no—
283C4×C151—28no—
284C4×C151—42no—
285C4×C151—44no—
286C4×C151—44no—
287C4×C151—82no—
288C4×C151—82no—
289C4×C151#39618yescomplemented
290C2×C151—84no—
291C2×C151C2×#39611yescharacteristic
292C2×C151#241612yes—
293C2×C151#245212yes—
294C2×C151#251212yes—
295C2×C151#253812yes—
296C2×C151#254111yescharacteristic
297C2×C151#254211yescharacteristic
298C2×C151#254511yescharacteristic
299C2×C151#256611yescharacteristic
300C2×C151#262011yescharacteristic
301C2×C151#285611yescharacteristic
302#15134C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#1513411yescharacteristic, direct product factor, Sylow
304C2×#396C2×C15114yescomplemented
305C2×#390C2×C15111yescharacteristic
306C2×#390C2×C15111yescharacteristic
307C2×#390C2×C15111yescharacteristic
308C2×#389C2×C15111yescharacteristic, complemented
309C2×#384C2×C15111yescharacteristic, complemented
310C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
311#1439C2×C15114yescomplemented
312C4⋊#95C2×C15111yescharacteristic, complemented
313C23×D4C22×C15111yescharacteristic
314C22×C4⋊C4C22×C15112yes—
315C22×C4⋊C4C22×C15111yescharacteristic
316C22×C4⋊C4C22×C15111yescharacteristic
317C22×C4⋊C4C22×C15114yes—
318C22×C4⋊C4C22×C15111yescharacteristic
319C22×C4⋊C4C22×C15112yes—
320C22×C22⋊C4C22×C15112yes—
321C22×C22⋊C4C22×C15114yes—
322C22×C22⋊C4C22×C15114yes—
323C22×C22⋊C4C22×C15112yes—
324C22×C42C22×C15111yescharacteristic
325C22×C42C22×C15111yescharacteristic
326C22×C42C22×C15111yescharacteristic
327#396—216no—
328#390—24no—
329#390—24no—
330#390—24no—
331#389—24no—
332#384—24no—
333C4×C4⋊C4—24no—
334C2×#95C22×C15114yes—
335C2×#95C22×C15112yes—
336C2×#95C22×C15112yes—
337C25C23×C15112yes—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4Q8×C15114yes—
345C23×C4C23×C15112yes—
346C23×C4C23×C15112yes—
347C23×C4C23×C15112yes—
348C23×C4C23×C15112yes—
349C23×C4C23×C15111yescharacteristic
350C23×C4C23×C15112yes—
351C23×C4C23×C15111yescharacteristic
352C23×C4C23×C15111yescharacteristic
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4D4×C15114yes—
369C2×C4⋊C4D4×C15118yescomplemented
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42D4×C15114yes—
388C2×C42D4×C15114yes—
389#95—24no—
390#95—24no—
391#95—28no—
392C24—24no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24C2×Q8×C15114yes—
403C24C24×C15111yescharacteristic
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—44no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4C2×D4×C15112yes—
443C22×C4C2×D4×C15114yes—
444C22×C4C2×D4×C15114yes—
445C22×C4C2×D4×C15114yes—
446C22×C4C2×D4×C15114yes—
447C22×C4C2×D4×C15112yes—
448C22×C4C2×D4×C15114yes—
449C22×C4C2×D4×C15112yes—
450C22×C4C2×D4×C15112yes—
451C22×C4C2×D4×C15112yes—
452C22×C4C2×Q8×C15112yes—
453C22×C4#41×C15114yes—
454C22×C4#41×C15112yes—
455C22×C4#41×C15112yes—
456C22×C4#41×C15112yes—
457C4⋊C4—28no—
458C4⋊C4—216no—
459C4⋊C4—416no—
460C4⋊C4—44no—
461C4⋊C4—44no—
462C4⋊C4—48no—
463C22⋊C4—416no—
464C22⋊C4—48no—
465C22⋊C4—416no—
466C22⋊C4—48no—
467C42—28no—
468C42—28no—
469C42—44no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—28no—
474C23—28no—
475C23—44no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—44no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—44no—
486C23—44no—
487C23—44no—
488C23—44no—
489C23—44no—
490C23—44no—
491C23—44no—
492C23—44no—
493C23C22×D4×C15111yescharacteristic
494C23C22×D4×C15111yescharacteristic
495C23C22×D4×C15111yescharacteristic
496C23C22×D4×C15112yes—
497C23C22×Q8×C15111yescharacteristic
498C23C2×#41×C15111yescharacteristic
499C23C2×#41×C15111yescharacteristic
500C23C2×#41×C15111yescharacteristic
501C23C2×#41×C15112yes—
502C23H(5,𝔽2)×C15112yes—
503C232−1+4×C15112yes—
504D4—416no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—28no—
522C2×C4—24no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4#121×C15118yes—
543C2×C4#121×C15114yes—
544C2×C4#121×C15114yes—
545C2×C4#121×C15114yes—
546C2×C4C22⋊Q8×C15114yes—
547C2×C4C22⋊Q8×C15114yes—
548C2×C4C22⋊Q8×C15114yes—
549C2×C4#126×C15114yes—
550C2×C4#127×C15114yes—
551C22—44no—
552C22—48no—
553C22—48no—
554C22—44no—
555C22—44no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22—84no—
560C22—82no—
561C22—82no—
562C22C2×#121×C15111yescharacteristic
563C22C2×#121×C15112yes—
564C22C2×#121×C15111yescharacteristic
565C22C2×#121×C15111yescharacteristic
566C22C2×C22⋊Q8×C15111yescharacteristic
567C22C2×C22⋊Q8×C15111yescharacteristic
568C22C2×C22⋊Q8×C15111yescharacteristic
569C22C2×#126×C15111yescharacteristic
570C22C2×#127×C15111yescharacteristic
571C22#532×C15112yes—
572C22#532×C15111yescharacteristic
573C22#535×C15111yescharacteristic
574C22#536×C15111yescharacteristic
575C22#537×C15112yes—
576C22#542×C15112yes—
577C22D42×C15112yes—
578C22#547×C15112yes—
579C22#548×C15112yes—
580C22D4×Q8×C15112yes—
581C22#550×C15112yes—
582C22#553×C15112yes—
583C22#554×C15112yes—
584C22#556×C15112yes—
585C4—24no—
586C4—28no—
587C4—42no—
588C4—44no—
589C4—44no—
590C4—82no—
591C4—82no—
592C4#396×C15118yescomplemented
593C2—84no—
594C2C2×#396×C15111yescharacteristic
595C2#2416×C15112yes—
596C2#2452×C15112yes—
597C2#2512×C15112yes—
598C2#2538×C15112yes—
599C2#2541×C15111yescharacteristic
600C2#2542×C15111yescharacteristic
601C2#2545×C15111yescharacteristic
602C2#2566×C15111yescharacteristic
603C2#2620×C15111yescharacteristic
604C2#2856×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
5. C2×#389×C151C2semidirect
6. C2×#384×C151C2semidirect
7. C2×C4×C4⋊C4×C151C2semidirect
8. #1439×C151C2semidirect
9. C4⋊#95×C151C2semidirect
66. C2×C4⋊C4×C151D4semidirect
289. C4×C151#396semidirect
302. #15134C151direct (N × H)
303. C151#15134direct (N × H)
304. C2×#396C2×C151semidirect
308. C2×#389C2×C151semidirect
309. C2×#384C2×C151semidirect
310. C2×C4×C4⋊C4C2×C151semidirect
311. #1439C2×C151semidirect
312. C4⋊#95C2×C151semidirect
369. C2×C4⋊C4D4×C151semidirect
592. C4#396×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×#390×C1512
C2×#389×C1512
C2×#384×C1512
C2×C4×C4⋊C4×C1512
#1439×C1512
C4⋊#95×C1512
#15134151