Finite Group Databasebeta

← C151×#15053 #50319978

Subgroups — C151×#15053 #50319978

Order 38656.

1230 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C151C211yesmaximal, characteristic
2C2×#387×C151C211yesmaximal, characteristic
3#1446×C151C211yesmaximal, characteristic
4#1446×C151C211yesmaximal, characteristic
5#1445×C151C211yesmaximal, characteristic
6#1445×C151C211yesmaximal, characteristic
7#1443×C151C212yesmaximal
8#1442×C151C212yesmaximal
9#1436×C151C212yesmaximal
10#1434×C151C212yesmaximal
11C4×#95×C151C211yesmaximal, characteristic
12C23×Q8×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C42×C151C2212yes—
17C22×C42×C151C2211yescharacteristic
18#391×C151—24no—
19#387×C151—24no—
20C2×#95×C151C2212yes—
21C2×#95×C151C2211yescharacteristic
22C2×#95×C151C2211yescharacteristic
23C2×#95×C151C2211yescharacteristic
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×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2211yescharacteristic
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C22×Q8×C151—22no—
38C22×Q8×C151—24no—
39C22×Q8×C151—22no—
40C22×Q8×C151—22no—
41C22×Q8×C151—42no—
42C23×C4×C151C2311yescharacteristic
43C23×C4×C151C2312yes—
44C23×C4×C151C2311yescharacteristic
45C23×C4×C151C2311yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C23×C4×C151C2312yes—
49C23×C4×C151C2312yes—
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2311yescharacteristic
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—42no—
60C2×C4⋊C4×C151Q814yescomplemented
61C2×C42×C151—24no—
62C2×C42×C151—24no—
63C2×C42×C151—42no—
64C2×C42×C151—42no—
65C2×C42×C151D414yes—
66#95×C151—22no—
67#95×C151—22no—
68#95×C151—22no—
69#95×C151—22no—
70#95×C151—24no—
71#95×C151—24no—
72#95×C151—24no—
73#95×C151—24no—
74#95×C151—22no—
75#95×C151—22no—
76#95×C151—24no—
77#95×C151—24no—
78#95×C151—24no—
79#95×C151—24no—
80#95×C151—24no—
81#95×C151—42no—
82#95×C151—42no—
83C24×C151C2411yescharacteristic
84C2×Q8×C151—28no—
85C2×Q8×C151—48no—
86C2×Q8×C151—48no—
87C2×Q8×C151—44no—
88C2×Q8×C151—44no—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—22no—
95C22×C4×C151—21no—
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—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
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—21no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
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—22no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×Q812yes—
144C22×C4×C151C2×Q812yes—
145C22×C4×C151C2×Q812yes—
146C22×C4×C151#4114yes—
147C22×C4×C151#4114yes—
148C22×C4×C151#4114yes—
149C22×C4×C151#4112yes—
150C22×C4×C151#4112yes—
151C22×C4×C151#4112yes—
152C4⋊C4×C151—28no—
153C4⋊C4×C151—44no—
154C4⋊C4×C151—44no—
155C42×C151—44no—
156C42×C151—48no—
157C23×C151C22×D411yescharacteristic
158C23×C151C22×Q811yescharacteristic
159C23×C151C2×#4111yescharacteristic
160C23×C151C2×#4112yes—
161C23×C151C2×#4111yescharacteristic
162C23×C151C2×#4111yescharacteristic
163C23×C151C2×#4112yes—
164C23×C151C2×#4112yes—
165C23×C151H(5,𝔽2)12yes—
166C23×C1512−1+411yescharacteristic
167C23×C1512−1+411yescharacteristic
168Q8×C151—416no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—24no—
174C2×C4×C151—24no—
175C2×C4×C151—24no—
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—22no—
184C2×C4×C151—24no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—24no—
188C2×C4×C151—24no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—24no—
192C2×C4×C151—24no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—41no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—41no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151C22⋊Q814yes—
231C2×C4×C151#12414yes—
232C22×C151C2×C22⋊Q811yescharacteristic
233C22×C151#52511yescharacteristic
234C22×C151C2×#12411yescharacteristic
235C22×C151#52912yes—
236C22×C151#52912yes—
237C22×C151#52912yes—
238C22×C151#53211yescharacteristic
239C22×C151#53211yescharacteristic
240C22×C151#53312yes—
241C22×C151#53411yescharacteristic
242C22×C151#53611yescharacteristic
243C22×C151#53912yes—
244C22×C151#54212yes—
245C22×C151#55112yes—
246C22×C151#55112yes—
247C22×C151#55112yes—
248C22×C151#55212yes—
249C22×C151#55412yes—
250C22×C151#55611yescharacteristic
251C22×C151#55611yescharacteristic
252C22×C151#55612yes—
253C22×C151#55711yescharacteristic
254C22×C151#55711yescharacteristic
255C4×C151—24no—
256C4×C151—24no—
257C4×C151—44no—
258C4×C151—42no—
259C4×C151—42no—
260C4×C151—42no—
261C4×C151—44no—
262C4×C151—44no—
263C4×C151—81no—
264C4×C151—82no—
265C4×C151—81no—
266C2×C151#239611yescharacteristic
267C2×C151#252012yes—
268C2×C151#252312yes—
269C2×C151#252712yes—
270C2×C151#256111yescharacteristic
271C2×C151#256411yescharacteristic
272C2×C151#256811yescharacteristic
273C2×C151#258812yes—
274C2×C151#260411yescharacteristic
275C2×C151#266311yescharacteristic
276C2×C151#286111yescharacteristic
277#15053C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#1505311yescharacteristic, direct product factor, Sylow
279C2×#391C2×C15111yescharacteristic
280C2×#387C2×C15111yescharacteristic
281#1446C2×C15111yescharacteristic
282#1446C2×C15111yescharacteristic
283#1445C2×C15111yescharacteristic
284#1445C2×C15111yescharacteristic
285#1443C2×C15112yes—
286#1442C2×C15112yes—
287#1436C2×C15112yes—
288#1434C2×C15112yes—
289C4×#95C2×C15111yescharacteristic
290C23×Q8C22×C15111yescharacteristic
291C22×C4⋊C4C22×C15111yescharacteristic
292C22×C4⋊C4C22×C15111yescharacteristic
293C22×C4⋊C4C22×C15111yescharacteristic
294C22×C42C22×C15112yes—
295C22×C42C22×C15111yescharacteristic
296#391—24no—
297#387—24no—
298C2×#95C22×C15112yes—
299C2×#95C22×C15111yescharacteristic
300C2×#95C22×C15111yescharacteristic
301C2×#95C22×C15111yescharacteristic
302C2×#95C22×C15112yes—
303C2×#95C22×C15112yes—
304C2×#95C22×C15112yes—
305C2×#95C22×C15112yes—
306C2×#95C22×C15112yes—
307C2×#95C22×C15112yes—
308C2×#95C22×C15112yes—
309C2×#95C22×C15112yes—
310C2×#95C22×C15111yescharacteristic
311C2×#95C22×C15111yescharacteristic
312C2×#95C22×C15111yescharacteristic
313C2×#95C22×C15112yes—
314C2×#95C22×C15112yes—
315C22×Q8—24no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—42no—
320C23×C4C23×C15112yes—
321C23×C4C23×C15111yescharacteristic
322C23×C4C23×C15111yescharacteristic
323C23×C4C23×C15111yescharacteristic
324C23×C4C23×C15111yescharacteristic
325C23×C4C23×C15112yes—
326C23×C4C23×C15112yes—
327C23×C4C23×C15112yes—
328C23×C4C23×C15111yescharacteristic
329C23×C4C23×C15111yescharacteristic
330C23×C4C23×C15111yescharacteristic
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4Q8×C15114yescomplemented
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42D4×C15114yes—
344#95—24no—
345#95—24no—
346#95—22no—
347#95—22no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—22no—
354#95—22no—
355#95—22no—
356#95—22no—
357#95—24no—
358#95—24no—
359#95—42no—
360#95—42no—
361C24C24×C15111yescharacteristic
362C2×Q8—28no—
363C2×Q8—48no—
364C2×Q8—48no—
365C2×Q8—44no—
366C2×Q8—44no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
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—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4C2×D4×C15112yes—
419C22×C4C2×D4×C15112yes—
420C22×C4C2×D4×C15112yes—
421C22×C4C2×Q8×C15112yes—
422C22×C4C2×Q8×C15112yes—
423C22×C4C2×Q8×C15112yes—
424C22×C4#41×C15114yes—
425C22×C4#41×C15114yes—
426C22×C4#41×C15114yes—
427C22×C4#41×C15112yes—
428C22×C4#41×C15112yes—
429C22×C4#41×C15112yes—
430C4⋊C4—28no—
431C4⋊C4—44no—
432C4⋊C4—44no—
433C42—44no—
434C42—48no—
435C23C22×D4×C15111yescharacteristic
436C23C22×Q8×C15111yescharacteristic
437C23C2×#41×C15111yescharacteristic
438C23C2×#41×C15112yes—
439C23C2×#41×C15111yescharacteristic
440C23C2×#41×C15111yescharacteristic
441C23C2×#41×C15112yes—
442C23C2×#41×C15112yes—
443C23H(5,𝔽2)×C15112yes—
444C232−1+4×C15111yescharacteristic
445C232−1+4×C15111yescharacteristic
446Q8—416no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4C22⋊Q8×C15114yes—
509C2×C4#124×C15114yes—
510C22C2×C22⋊Q8×C15111yescharacteristic
511C22#525×C15111yescharacteristic
512C22C2×#124×C15111yescharacteristic
513C22#529×C15112yes—
514C22#529×C15112yes—
515C22#529×C15112yes—
516C22#532×C15111yescharacteristic
517C22#532×C15111yescharacteristic
518C22#533×C15112yes—
519C22#534×C15111yescharacteristic
520C22#536×C15111yescharacteristic
521C22#539×C15112yes—
522C22#542×C15112yes—
523C22#551×C15112yes—
524C22#551×C15112yes—
525C22#551×C15112yes—
526C22#552×C15112yes—
527C22#554×C15112yes—
528C22#556×C15112yes—
529C22#556×C15111yescharacteristic
530C22#556×C15111yescharacteristic
531C22#557×C15111yescharacteristic
532C22#557×C15111yescharacteristic
533C4—24no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—44no—
538C4—44no—
539C4—44no—
540C4—42no—
541C4—81no—
542C4—82no—
543C4—81no—
544C2#2396×C15111yescharacteristic
545C2#2520×C15112yes—
546C2#2523×C15112yes—
547C2#2527×C15112yes—
548C2#2561×C15111yescharacteristic
549C2#2564×C15111yescharacteristic
550C2#2568×C15111yescharacteristic
551C2#2588×C15112yes—
552C2#2604×C15111yescharacteristic
553C2#2663×C15111yescharacteristic
554C2#2861×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
60. C2×C4⋊C4×C151Q8semidirect
277. #15053C151direct (N × H)
278. C151#15053direct (N × H)
338. C2×C4⋊C4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1512
C2×#387×C1512
#1446×C1512
#1445×C1512
#1443×C1512
#1442×C1512
#1436×C1512
#1434×C1512
C4×#95×C1512
#15053151