Finite Group Databasebeta

← C151×#15363 #50320288

Subgroups — C151×#15363 #50320288

Order 38656.

1406 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C151C212yesmaximal
2C2×#389×C151C212yesmaximal
3C2×#389×C151C212yesmaximal
4#1444×C151C212yesmaximal
5#1444×C151C211yesmaximal, characteristic
6#1444×C151C211yesmaximal, characteristic
7#1444×C151C211yesmaximal, characteristic
8#1441×C151C212yesmaximal
9#1436×C151C212yesmaximal
10C22×C4⋊C4×C151C2212yes—
11C22×C4⋊C4×C151C2211yescharacteristic
12C22×C4⋊C4×C151C2212yes—
13C22×C4⋊C4×C151C2212yes—
14C22×C4⋊C4×C151C2212yes—
15C22×C4⋊C4×C151C2212yes—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C42×C151C2212yes—
20#398×C151—28no—
21#389×C151—28no—
22#389×C151—28no—
23C2×#95×C151C2212yes—
24C2×#95×C151C2212yes—
25C2×#95×C151C2212yes—
26C2×#95×C151C2211yescharacteristic
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2212yes—
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C23×C4×C151C2312yes—
35C23×C4×C151C2312yes—
36C23×C4×C151C2312yes—
37C23×C4×C151C2311yescharacteristic
38C23×C4×C151C2311yescharacteristic
39C23×C4×C151C2312yes—
40C23×C4×C151C2311yescharacteristic
41C23×C4×C151C2312yes—
42C23×C4×C151C2312yes—
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—24no—
49C2×C4⋊C4×C151—24no—
50C2×C4⋊C4×C151—24no—
51C2×C4⋊C4×C151—24no—
52C2×C4⋊C4×C151—24no—
53C2×C4⋊C4×C151—24no—
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×C151—42no—
60C2×C4⋊C4×C151—41no—
61C2×C4⋊C4×C151—42no—
62C2×C4⋊C4×C151—41no—
63C2×C4⋊C4×C151—42no—
64C2×C4⋊C4×C151—41no—
65C2×C4⋊C4×C151—42no—
66C2×C4⋊C4×C151Q818yes—
67C2×C42×C151—24no—
68C2×C42×C151—24no—
69C2×C42×C151—42no—
70#95×C151—24no—
71#95×C151—24no—
72#95×C151—24no—
73#95×C151—24no—
74#95×C151—22no—
75#95×C151—24no—
76#95×C151—42no—
77#95×C151—41no—
78#95×C151D414yes—
79#95×C151D418yes—
80#95×C151Q814yes—
81C24×C151C2411yescharacteristic
82C22×C4×C151—22no—
83C22×C4×C151—22no—
84C22×C4×C151—22no—
85C22×C4×C151—22no—
86C22×C4×C151—22no—
87C22×C4×C151—22no—
88C22×C4×C151—22no—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—22no—
94C22×C4×C151—22no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—21no—
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—21no—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
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×C151C2×D414yes—
128C22×C4×C151C2×D412yes—
129C22×C4×C151C2×D414yes—
130C22×C4×C151C2×D414yes—
131C22×C4×C151C2×D414yes—
132C22×C4×C151C2×Q812yes—
133C22×C4×C151C2×Q814yes—
134C22×C4×C151C2×Q814yes—
135C22×C4×C151C2×Q814yes—
136C22×C4×C151C2×Q814yes—
137C22×C4×C151#4112yes—
138C22×C4×C151#4114yes—
139C4⋊C4×C151—216no—
140C4⋊C4×C151—216no—
141C4⋊C4×C151—48no—
142C4⋊C4×C151—48no—
143C4⋊C4×C151—44no—
144C4⋊C4×C151—48no—
145C4⋊C4×C151—44no—
146C4⋊C4×C151—48no—
147C4⋊C4×C151—44no—
148C42×C151—48no—
149C23×C151C22×D411yescharacteristic
150C23×C151C22×D412yes—
151C23×C151C22×Q812yes—
152C23×C151C22×Q811yescharacteristic
153C23×C151C2×#4112yes—
154C23×C151C2×#4111yescharacteristic
155C23×C151H(5,𝔽2)12yes—
156C23×C151H(5,𝔽2)11yescharacteristic
157C23×C1512−1+411yescharacteristic
158C23×C1512−1+411yescharacteristic
159C23×C1512−1+411yescharacteristic
160C2×C4×C151—24no—
161C2×C4×C151—24no—
162C2×C4×C151—24no—
163C2×C4×C151—24no—
164C2×C4×C151—24no—
165C2×C4×C151—24no—
166C2×C4×C151—24no—
167C2×C4×C151—24no—
168C2×C4×C151—24no—
169C2×C4×C151—24no—
170C2×C4×C151—24no—
171C2×C4×C151—24no—
172C2×C4×C151—24no—
173C2×C4×C151—24no—
174C2×C4×C151—24no—
175C2×C4×C151—22no—
176C2×C4×C151—24no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—24no—
180C2×C4×C151—24no—
181C2×C4×C151—24no—
182C2×C4×C151—24no—
183C2×C4×C151—24no—
184C2×C4×C151—24no—
185C2×C4×C151—24no—
186C2×C4×C151—24no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—42no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—42no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
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×C151C22⋊Q818yes—
216C2×C4×C151C4⋊Q818yes—
217C22×C151C2×C22⋊Q812yes—
218C22×C151#52512yes—
219C22×C151C2×C4⋊Q812yes—
220C22×C151#53711yescharacteristic
221C22×C151#53712yes—
222C22×C151#53912yes—
223C22×C151#53911yescharacteristic
224C22×C151#54412yes—
225C22×C151#54411yescharacteristic
226C22×C151D4212yes—
227C22×C151D4211yescharacteristic
228C22×C151#54712yes—
229C22×C151#54711yescharacteristic
230C22×C151D4×Q811yescharacteristic
231C22×C151D4×Q812yes—
232C22×C151#55412yes—
233C22×C151#55412yes—
234C22×C151#55712yes—
235C22×C151#55711yescharacteristic
236C22×C151Q8211yescharacteristic
237C22×C151#55911yescharacteristic
238C22×C151#56011yescharacteristic
239C22×C151#56411yescharacteristic
240C4×C151—28no—
241C4×C151—28no—
242C4×C151—44no—
243C4×C151—42no—
244C4×C151—44no—
245C4×C151—44no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—82no—
249C2×C151#244012yes—
250C2×C151#244912yes—
251C2×C151#245511yescharacteristic
252C2×C151#255111yescharacteristic
253C2×C151#258211yescharacteristic
254C2×C151#258412yes—
255C2×C151#267511yescharacteristic
256C2×C151#272611yescharacteristic
257C2×C151#272612yes—
258C2×C151#279211yescharacteristic
259C2×C151#280711yescharacteristic
260#15363C15111yesmaximal, characteristic, direct product factor, Sylow
261C151#1536311yescharacteristic, direct product factor, Sylow
262C2×#398C2×C15112yes—
263C2×#389C2×C15112yes—
264C2×#389C2×C15112yes—
265#1444C2×C15111yescharacteristic
266#1444C2×C15111yescharacteristic
267#1444C2×C15111yescharacteristic
268#1444C2×C15112yes—
269#1441C2×C15112yes—
270#1436C2×C15112yes—
271C22×C4⋊C4C22×C15112yes—
272C22×C4⋊C4C22×C15111yescharacteristic
273C22×C4⋊C4C22×C15112yes—
274C22×C4⋊C4C22×C15112yes—
275C22×C4⋊C4C22×C15112yes—
276C22×C4⋊C4C22×C15112yes—
277C22×C4⋊C4C22×C15111yescharacteristic
278C22×C4⋊C4C22×C15112yes—
279C22×C4⋊C4C22×C15111yescharacteristic
280C22×C42C22×C15112yes—
281#398—28no—
282#389—28no—
283#389—28no—
284C2×#95C22×C15112yes—
285C2×#95C22×C15112yes—
286C2×#95C22×C15112yes—
287C2×#95C22×C15111yescharacteristic
288C2×#95C22×C15112yes—
289C2×#95C22×C15112yes—
290C2×#95C22×C15112yes—
291C2×#95C22×C15111yescharacteristic
292C2×#95C22×C15112yes—
293C2×#95C22×C15111yescharacteristic
294C2×#95C22×C15111yescharacteristic
295C23×C4C23×C15112yes—
296C23×C4C23×C15112yes—
297C23×C4C23×C15111yescharacteristic
298C23×C4C23×C15111yescharacteristic
299C23×C4C23×C15111yescharacteristic
300C23×C4C23×C15112yes—
301C23×C4C23×C15112yes—
302C23×C4C23×C15112yes—
303C23×C4C23×C15112yes—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4Q8×C15118yes—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—42no—
331#95—22no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—42no—
338#95—41no—
339#95D4×C15114yes—
340#95D4×C15118yes—
341#95Q8×C15114yes—
342C24C24×C15111yescharacteristic
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4C2×D4×C15114yes—
389C22×C4C2×D4×C15112yes—
390C22×C4C2×D4×C15114yes—
391C22×C4C2×D4×C15114yes—
392C22×C4C2×D4×C15114yes—
393C22×C4C2×Q8×C15112yes—
394C22×C4C2×Q8×C15114yes—
395C22×C4C2×Q8×C15114yes—
396C22×C4C2×Q8×C15114yes—
397C22×C4C2×Q8×C15114yes—
398C22×C4#41×C15112yes—
399C22×C4#41×C15114yes—
400C4⋊C4—216no—
401C4⋊C4—216no—
402C4⋊C4—48no—
403C4⋊C4—48no—
404C4⋊C4—44no—
405C4⋊C4—48no—
406C4⋊C4—44no—
407C4⋊C4—48no—
408C4⋊C4—44no—
409C42—48no—
410C23C22×D4×C15111yescharacteristic
411C23C22×D4×C15112yes—
412C23C22×Q8×C15112yes—
413C23C22×Q8×C15111yescharacteristic
414C23C2×#41×C15112yes—
415C23C2×#41×C15111yescharacteristic
416C23H(5,𝔽2)×C15112yes—
417C23H(5,𝔽2)×C15111yescharacteristic
418C232−1+4×C15111yescharacteristic
419C232−1+4×C15111yescharacteristic
420C232−1+4×C15111yescharacteristic
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4C22⋊Q8×C15118yes—
477C2×C4C4⋊Q8×C15118yes—
478C22C2×C22⋊Q8×C15112yes—
479C22#525×C15112yes—
480C22C2×C4⋊Q8×C15112yes—
481C22#537×C15111yescharacteristic
482C22#537×C15112yes—
483C22#539×C15112yes—
484C22#539×C15111yescharacteristic
485C22#544×C15112yes—
486C22#544×C15111yescharacteristic
487C22D42×C15112yes—
488C22D42×C15111yescharacteristic
489C22#547×C15112yes—
490C22#547×C15111yescharacteristic
491C22D4×Q8×C15111yescharacteristic
492C22D4×Q8×C15112yes—
493C22#554×C15112yes—
494C22#554×C15112yes—
495C22#557×C15112yes—
496C22#557×C15111yescharacteristic
497C22Q82×C15111yescharacteristic
498C22#559×C15111yescharacteristic
499C22#560×C15111yescharacteristic
500C22#564×C15111yescharacteristic
501C4—28no—
502C4—28no—
503C4—44no—
504C4—42no—
505C4—44no—
506C4—42no—
507C4—44no—
508C4—42no—
509C4—82no—
510C2#2440×C15112yes—
511C2#2449×C15112yes—
512C2#2455×C15111yescharacteristic
513C2#2551×C15111yescharacteristic
514C2#2582×C15111yescharacteristic
515C2#2584×C15112yes—
516C2#2675×C15111yescharacteristic
517C2#2726×C15111yescharacteristic
518C2#2726×C15112yes—
519C2#2792×C15111yescharacteristic
520C2#2807×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
260. #15363C151direct (N × H)
261. C151#15363direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#398×C1512
C2×#389×C1512
#1444×C1512
#1441×C1512
#1436×C1512
#15363151