Finite Group Databasebeta

← C151×#14441 #50319366

Subgroups — C151×#14441 #50319366

Order 38656.

1390 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C151C212yesmaximal
2C2×#389×C151C211yesmaximal, characteristic
3C2×#387×C151C212yesmaximal
4#1444×C151C212yesmaximal
5#1441×C151C212yesmaximal
6#1441×C151C212yesmaximal
7#1436×C151C212yesmaximal
8C4⋊#95×C151C211yesmaximal, characteristic
9C4⋊#95×C151C211yesmaximal, characteristic
10C22×C4⋊C4×C151C2212yes—
11C22×C4⋊C4×C151C2212yes—
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C42×C151C2212yes—
20C22×C42×C151C2211yescharacteristic
21#389×C151—28no—
22#389×C151C418yescomplemented
23#387×C151—28no—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2212yes—
31C2×#95×C151C2212yes—
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C23×C4×C151C2312yes—
35C23×C4×C151C2312yes—
36C23×C4×C151C2312yes—
37C23×C4×C151C2312yes—
38C23×C4×C151C2312yes—
39C23×C4×C151C2311yescharacteristic
40C23×C4×C151C2312yes—
41C23×C4×C151C2311yescharacteristic
42C23×C4×C151C2311yescharacteristic
43C2×C4⋊C4×C151—24no—
44C2×C4⋊C4×C151—24no—
45C2×C4⋊C4×C151—24no—
46C2×C4⋊C4×C151—24no—
47C2×C4⋊C4×C151—24no—
48C2×C4⋊C4×C151—22no—
49C2×C4⋊C4×C151—22no—
50C2×C4⋊C4×C151—41no—
51C2×C4⋊C4×C151—41no—
52C2×C4⋊C4×C151—41no—
53C2×C4⋊C4×C151—41no—
54C2×C4⋊C4×C151—41no—
55C2×C4⋊C4×C151—41no—
56C2×C4⋊C4×C151—42no—
57C2×C4⋊C4×C151—41no—
58C2×C4⋊C4×C151—41no—
59C2×C4⋊C4×C151—41no—
60C2×C4⋊C4×C151—41no—
61C2×C4⋊C4×C151—42no—
62C2×C4⋊C4×C151—42no—
63C2×C4⋊C4×C151C2×C418yes—
64C2×C4⋊C4×C151C2×C414yes—
65C2×C4⋊C4×C151C2×C414yes—
66C2×C4⋊C4×C151D414yes—
67C2×C4⋊C4×C151D414yes—
68C2×C4⋊C4×C151Q814yes—
69C2×C4⋊C4×C151Q814yes—
70C2×C42×C151—24no—
71C2×C42×C151—24no—
72C2×C42×C151—41no—
73C2×C42×C151—41no—
74C2×C42×C151—42no—
75C2×C42×C151C2×C414yes—
76#95×C151—24no—
77#95×C151—24no—
78#95×C151—24no—
79#95×C151—24no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—24no—
83#95×C151—42no—
84#95×C151—42no—
85#95×C151C2×C418yes—
86C24×C151C2411yescharacteristic
87C22×C4×C151—22no—
88C22×C4×C151—22no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—22no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
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—22no—
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—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151C22×C414yes—
136C22×C4×C151C22×C414yes—
137C22×C4×C151C22×C412yes—
138C22×C4×C151C22×C412yes—
139C22×C4×C151C22×C412yes—
140C22×C4×C151C2×D414yes—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D414yes—
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×Q814yes—
145C22×C4×C151C2×Q812yes—
146C22×C4×C151C2×Q814yes—
147C22×C4×C151C2×Q812yes—
148C22×C4×C151#4112yes—
149C22×C4×C151#4112yes—
150C4⋊C4×C151—216no—
151C4⋊C4×C151—44no—
152C4⋊C4×C151—44no—
153C4⋊C4×C151—44no—
154C4⋊C4×C151—48no—
155C4⋊C4×C151—44no—
156C4⋊C4×C151—44no—
157C4⋊C4×C151—48no—
158C4⋊C4×C151C4⋊C4116yescomplemented
159C42×C151—44no—
160C42×C151—48no—
161C23×C151C23×C411yescharacteristic
162C23×C151C22×D411yescharacteristic
163C23×C151C22×D411yescharacteristic
164C23×C151C22×Q811yescharacteristic
165C23×C151C22×Q811yescharacteristic
166C23×C151C2×#4111yescharacteristic
167C23×C151C2×#4111yescharacteristic
168C23×C151H(5,𝔽2)11yescharacteristic
169C23×C151H(5,𝔽2)11yescharacteristic
170C23×C151H(5,𝔽2)11yescharacteristic
171C23×C151H(5,𝔽2)11yescharacteristic
172C23×C1512−1+411yescharacteristic
173C23×C1512−1+411yescharacteristic
174C23×C1512−1+411yescharacteristic
175C23×C1512−1+411yescharacteristic
176C2×C4×C151—24no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—24no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—24no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—24no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—24no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
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—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151C2×C4⋊C414yes—
236C2×C4×C151C2×C4⋊C418yes—
237C2×C4×C151C4×D414yes—
238C2×C4×C151C4×Q814yes—
239C22×C151C22×C4⋊C411yescharacteristic
240C22×C151C2×C4×D411yescharacteristic
241C22×C151C2×C4×Q811yescharacteristic
242C22×C151#51811yescharacteristic
243C22×C151#51911yescharacteristic
244C22×C151#52011yescharacteristic
245C22×C151#52011yescharacteristic
246C22×C151#53411yescharacteristic
247C22×C151#53711yescharacteristic
248C22×C151#53711yescharacteristic
249C22×C151#53711yescharacteristic
250C22×C151#53811yescharacteristic
251C22×C151#53811yescharacteristic
252C22×C151#53911yescharacteristic
253C22×C151#53911yescharacteristic
254C22×C151#54311yescharacteristic
255C22×C151#54411yescharacteristic
256C22×C151#54411yescharacteristic
257C22×C151#54411yescharacteristic
258C22×C151D4211yescharacteristic
259C22×C151#54711yescharacteristic
260C22×C151#54711yescharacteristic
261C22×C151D4×Q811yescharacteristic
262C22×C151D4×Q811yescharacteristic
263C22×C151D4×Q811yescharacteristic
264C22×C151#55011yescharacteristic
265C22×C151#55411yescharacteristic
266C22×C151#55611yescharacteristic
267C22×C151#55711yescharacteristic
268C22×C151#55711yescharacteristic
269C22×C151Q8211yescharacteristic
270C22×C151#56211yescharacteristic
271C22×C151#56311yescharacteristic
272C22×C151#56311yescharacteristic
273C22×C151#56411yescharacteristic
274C4×C151—24no—
275C4×C151—24no—
276C4×C151—24no—
277C4×C151—28no—
278C4×C151—44no—
279C4×C151—44no—
280C4×C151—44no—
281C4×C151—82no—
282C4×C151—82no—
283C2×C151#231611yescharacteristic
284C2×C151#232511yescharacteristic
285C2×C151#232911yescharacteristic
286C2×C151D4×C4⋊C411yescharacteristic
287C2×C151Q8×C4⋊C411yescharacteristic
288C2×C151#236511yescharacteristic
289C2×C151#238211yescharacteristic
290C2×C151#268211yescharacteristic
291C2×C151#268311yescharacteristic
292C2×C151#272611yescharacteristic
293C2×C151#272611yescharacteristic
294C2×C151#272711yescharacteristic
295C2×C151#273411yescharacteristic
296C2×C151#280511yescharacteristic
297C2×C151#280611yescharacteristic
298#14441C15111yesmaximal, characteristic, direct product factor, Sylow
299C151#1444111yescharacteristic, direct product factor, Sylow
300C2×#389C2×C15112yes—
301C2×#389C2×C15111yescharacteristic
302C2×#387C2×C15112yes—
303#1444C2×C15112yes—
304#1441C2×C15112yes—
305#1441C2×C15112yes—
306#1436C2×C15112yes—
307C4⋊#95C2×C15111yescharacteristic
308C4⋊#95C2×C15111yescharacteristic
309C22×C4⋊C4C22×C15112yes—
310C22×C4⋊C4C22×C15112yes—
311C22×C4⋊C4C22×C15111yescharacteristic
312C22×C4⋊C4C22×C15111yescharacteristic
313C22×C4⋊C4C22×C15112yes—
314C22×C4⋊C4C22×C15111yescharacteristic
315C22×C4⋊C4C22×C15111yescharacteristic
316C22×C4⋊C4C22×C15111yescharacteristic
317C22×C4⋊C4C22×C15111yescharacteristic
318C22×C42C22×C15112yes—
319C22×C42C22×C15111yescharacteristic
320#389—28no—
321#389C4×C15118yescomplemented
322#387—28no—
323C2×#95C22×C15112yes—
324C2×#95C22×C15112yes—
325C2×#95C22×C15112yes—
326C2×#95C22×C15112yes—
327C2×#95C22×C15112yes—
328C2×#95C22×C15112yes—
329C2×#95C22×C15112yes—
330C2×#95C22×C15112yes—
331C2×#95C22×C15112yes—
332C2×#95C22×C15112yes—
333C23×C4C23×C15112yes—
334C23×C4C23×C15112yes—
335C23×C4C23×C15112yes—
336C23×C4C23×C15112yes—
337C23×C4C23×C15112yes—
338C23×C4C23×C15111yescharacteristic
339C23×C4C23×C15112yes—
340C23×C4C23×C15111yescharacteristic
341C23×C4C23×C15111yescharacteristic
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4C2×C4×C15118yes—
363C2×C4⋊C4C2×C4×C15114yes—
364C2×C4⋊C4C2×C4×C15114yes—
365C2×C4⋊C4D4×C15114yes—
366C2×C4⋊C4D4×C15114yes—
367C2×C4⋊C4Q8×C15114yes—
368C2×C4⋊C4Q8×C15114yes—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—41no—
372C2×C42—41no—
373C2×C42—42no—
374C2×C42C2×C4×C15114yes—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—42no—
383#95—42no—
384#95C2×C4×C15118yes—
385C24C24×C15111yescharacteristic
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4C22×C4×C15114yes—
435C22×C4C22×C4×C15114yes—
436C22×C4C22×C4×C15112yes—
437C22×C4C22×C4×C15112yes—
438C22×C4C22×C4×C15112yes—
439C22×C4C2×D4×C15114yes—
440C22×C4C2×D4×C15112yes—
441C22×C4C2×D4×C15114yes—
442C22×C4C2×D4×C15112yes—
443C22×C4C2×Q8×C15114yes—
444C22×C4C2×Q8×C15112yes—
445C22×C4C2×Q8×C15114yes—
446C22×C4C2×Q8×C15112yes—
447C22×C4#41×C15112yes—
448C22×C4#41×C15112yes—
449C4⋊C4—216no—
450C4⋊C4—44no—
451C4⋊C4—44no—
452C4⋊C4—44no—
453C4⋊C4—48no—
454C4⋊C4—44no—
455C4⋊C4—44no—
456C4⋊C4—48no—
457C4⋊C4C4⋊C4×C151116yescomplemented
458C42—44no—
459C42—48no—
460C23C23×C4×C15111yescharacteristic
461C23C22×D4×C15111yescharacteristic
462C23C22×D4×C15111yescharacteristic
463C23C22×Q8×C15111yescharacteristic
464C23C22×Q8×C15111yescharacteristic
465C23C2×#41×C15111yescharacteristic
466C23C2×#41×C15111yescharacteristic
467C23H(5,𝔽2)×C15111yescharacteristic
468C23H(5,𝔽2)×C15111yescharacteristic
469C23H(5,𝔽2)×C15111yescharacteristic
470C23H(5,𝔽2)×C15111yescharacteristic
471C232−1+4×C15111yescharacteristic
472C232−1+4×C15111yescharacteristic
473C232−1+4×C15111yescharacteristic
474C232−1+4×C15111yescharacteristic
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4C2×C4⋊C4×C15118yes—
535C2×C4C2×C4⋊C4×C15114yes—
536C2×C4C4×D4×C15114yes—
537C2×C4C4×Q8×C15114yes—
538C22C22×C4⋊C4×C15111yescharacteristic
539C22C2×C4×D4×C15111yescharacteristic
540C22C2×C4×Q8×C15111yescharacteristic
541C22#518×C15111yescharacteristic
542C22#519×C15111yescharacteristic
543C22#520×C15111yescharacteristic
544C22#520×C15111yescharacteristic
545C22#534×C15111yescharacteristic
546C22#537×C15111yescharacteristic
547C22#537×C15111yescharacteristic
548C22#537×C15111yescharacteristic
549C22#538×C15111yescharacteristic
550C22#538×C15111yescharacteristic
551C22#539×C15111yescharacteristic
552C22#539×C15111yescharacteristic
553C22#543×C15111yescharacteristic
554C22#544×C15111yescharacteristic
555C22#544×C15111yescharacteristic
556C22#544×C15111yescharacteristic
557C22D42×C15111yescharacteristic
558C22#547×C15111yescharacteristic
559C22#547×C15111yescharacteristic
560C22D4×Q8×C15111yescharacteristic
561C22D4×Q8×C15111yescharacteristic
562C22D4×Q8×C15111yescharacteristic
563C22#550×C15111yescharacteristic
564C22#554×C15111yescharacteristic
565C22#556×C15111yescharacteristic
566C22#557×C15111yescharacteristic
567C22#557×C15111yescharacteristic
568C22Q82×C15111yescharacteristic
569C22#562×C15111yescharacteristic
570C22#563×C15111yescharacteristic
571C22#563×C15111yescharacteristic
572C22#564×C15111yescharacteristic
573C4—28no—
574C4—24no—
575C4—24no—
576C4—24no—
577C4—44no—
578C4—44no—
579C4—44no—
580C4—82no—
581C4—82no—
582C2#2316×C15111yescharacteristic
583C2#2325×C15111yescharacteristic
584C2#2329×C15111yescharacteristic
585C2D4×C4⋊C4×C15111yescharacteristic
586C2Q8×C4⋊C4×C15111yescharacteristic
587C2#2365×C15111yescharacteristic
588C2#2382×C15111yescharacteristic
589C2#2682×C15111yescharacteristic
590C2#2683×C15111yescharacteristic
591C2#2726×C15111yescharacteristic
592C2#2726×C15111yescharacteristic
593C2#2727×C15111yescharacteristic
594C2#2734×C15111yescharacteristic
595C2#2805×C15111yescharacteristic
596C2#2806×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
22. #389×C151C4semidirect
158. C4⋊C4×C151C4⋊C4semidirect
298. #14441C151direct (N × H)
299. C151#14441direct (N × H)
321. #389C4×C151semidirect
457. C4⋊C4C4⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1512
C2×#387×C1512
#1444×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
#14441151