Finite Group Databasebeta

← C151×#24608 #50329533

Subgroups — C151×#24608 #50329533

Order 38656.

922 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C151C211yesmaximal, characteristic
2C2×#432×C151C211yesmaximal, characteristic, complemented
3#2854×C151C211yesmaximal, characteristic
4C2×#389×C151C211yesmaximal, characteristic, complemented
5#2087×C151C212yesmaximal, complemented
6#2065×C151C212yesmaximal, complemented
7#1944×C151C212yesmaximal, complemented
8#1936×C151C212yesmaximal, complemented
9#1874×C151C211yesmaximal, characteristic
10#1853×C151C211yesmaximal, characteristic, complemented
11#1823×C151C211yesmaximal, characteristic, complemented
12C2×#123×C151—21no—
13C2×#121×C151C2211yescharacteristic
14C22×C4⋊C4×C151—21no—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C42×C151C2211yescharacteristic
18#480×C151—24no—
19#432×C151—24no—
20C2×#107×C151C2212yes—
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#102×C151C2212yes—
25C2×C22⋊C8×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27C2×#97×C151C2212yes—
28#390×C151C2211yescharacteristic
29#390×C151C2211yescharacteristic
30#389×C151—21no—
31#389×C151—21no—
32#389×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#389×C151C2212yes—
35#389×C151C2212yes—
36#388×C151—21no—
37#388×C151—21no—
38#386×C151—21no—
39#380×C151C2211yescharacteristic
40C2×#95×C151—21no—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×D4×C151—21no—
46C22×D4×C151C2311yescharacteristic
47C23×C4×C151—21no—
48C23×C4×C151—21no—
49C23×C4×C151D411yescharacteristic
50C23×C4×C151D411yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C22×C8×C151C2312yes—
53C22×C8×C151C2312yes—
54#123×C151—44no—
55#121×C151—22no—
56#121×C151—22no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—24no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—44no—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C4⋊C4×C151C2312yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2312yes—
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151—21no—
78C2×C42×C151—22no—
79C2×C42×C151—22no—
80C2×C42×C151D411yescharacteristic
81C2×C42×C151D411yescharacteristic
82C2×C42×C151C2311yescharacteristic
83C2×C42×C151C2311yescharacteristic
84#107×C151—24no—
85#106×C151—24no—
86C4⋊C8×C151—24no—
87#102×C151—24no—
88#102×C151—24no—
89C22⋊C8×C151—22no—
90C22⋊C8×C151D414yes—
91#97×C151—24no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—21no—
95#95×C151—21no—
96#95×C151—21no—
97C24×C151—21no—
98C24×C151C2×D411yescharacteristic
99C2×D4×C151—21no—
100C2×D4×C151—22no—
101C2×D4×C151—21no—
102C2×D4×C151—22no—
103C2×D4×C151—42no—
104C2×D4×C151—42no—
105C2×D4×C151—42no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—24no—
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—41no—
120C22×C4×C151—42no—
121C22×C4×C151—42no—
122C22×C4×C151—42no—
123C22×C4×C151—42no—
124C22×C4×C151—42no—
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D412yes—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151#4112yes—
132C22×C4×C151C2411yescharacteristic
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151C2×D414yes—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—44no—
148C4⋊C4×C151—44no—
149C4⋊C4×C151—42no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—42no—
152C4⋊C4×C151#4114yes—
153C22⋊C4×C151—42no—
154C22⋊C4×C151—42no—
155C22⋊C4×C151—42no—
156C22⋊C4×C151—42no—
157C22⋊C4×C151—42no—
158C22⋊C4×C151—42no—
159C42×C151—22no—
160C42×C151—22no—
161C42×C151—21no—
162C42×C151—21no—
163C42×C151—21no—
164C42×C151—21no—
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151#12112yes—
177C23×C151AGL(1,ℤ/8)12yes—
178C23×C151AGL(1,ℤ/8)12yes—
179C23×C151C22×D411yescharacteristic
180D4×C151—42no—
181D4×C151—42no—
182D4×C151—84no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—24no—
188C2×C4×C151—24no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—24no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—21no—
199C2×C4×C151—44no—
200C2×C4×C151—48no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—44no—
204C2×C4×C151—41no—
205C2×C4×C151—42no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—41no—
212C2×C4×C151—42no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—84no—
217C2×C4×C151#12112yes—
218C2×C4×C151#13712yes—
219C2×C4×C151C22×D411yescharacteristic
220C2×C4×C151C2×#4112yes—
221C2×C4×C151C2×#4111yescharacteristic
222C2×C4×C1512−1+412yes—
223C8×C151—24no—
224C8×C151—42no—
225C22×C151—22no—
226C22×C151—22no—
227C22×C151—22no—
228C22×C151—22no—
229C22×C151—22no—
230C22×C151—22no—
231C22×C151—81no—
232C22×C151—81no—
233C22×C151—81no—
234C22×C151—81no—
235C22×C151—81no—
236C22×C151—81no—
237C22×C151—81no—
238C22×C151#46914yes—
239C22×C151C2×#12111yescharacteristic
240C22×C151#52511yescharacteristic
241C22×C151#53611yescharacteristic
242C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C151C2×#13711yescharacteristic
245C22×C151#57511yescharacteristic
246C4×C151—22no—
247C4×C151—22no—
248C4×C151—44no—
249C4×C151—41no—
250C4×C151—41no—
251C4×C151—41no—
252C4×C151—81no—
253C4×C151—81no—
254C4×C151—82no—
255C4×C151—81no—
256C4×C151#54712yes—
257C4×C151#55212yes—
258C2×C151—24no—
259C2×C151—161no—
260C2×C151#241311yescharacteristic
261C2×C151C2×#46911yescharacteristic
262C2×C151#305611yescharacteristic
263C2×C151#311211yescharacteristic
264C2×C151#311411yescharacteristic
265C2×C151#323411yescharacteristic
266C2×C151#323811yescharacteristic
267#24608C15111yesmaximal, characteristic, direct product factor, Sylow
268C151#2460811yescharacteristic, direct product factor, Sylow
269C2×#480C2×C15111yescharacteristic
270C2×#432C2×C15111yescharacteristic, complemented
271#2854C2×C15111yescharacteristic
272C2×#389C2×C15111yescharacteristic, complemented
273#2087C2×C15112yescomplemented
274#2065C2×C15112yescomplemented
275#1944C2×C15112yescomplemented
276#1936C2×C15112yescomplemented
277#1874C2×C15111yescharacteristic
278#1853C2×C15111yescharacteristic, complemented
279#1823C2×C15111yescharacteristic, complemented
280C2×#123—21no—
281C2×#121C22×C15111yescharacteristic
282C22×C4⋊C4—21no—
283C22×C4⋊C4C22×C15111yescharacteristic
284C22×C4⋊C4C22×C15111yescharacteristic
285C22×C42C22×C15111yescharacteristic
286#480—24no—
287#432—24no—
288C2×#107C22×C15112yes—
289C2×#106C22×C15112yes—
290C2×C4⋊C8C22×C15112yes—
291C2×#102C22×C15112yes—
292C2×#102C22×C15112yes—
293C2×C22⋊C8C22×C15111yescharacteristic
294C2×C22⋊C8C22×C15111yescharacteristic
295C2×#97C22×C15112yes—
296#390C22×C15111yescharacteristic
297#390C22×C15111yescharacteristic
298#389—21no—
299#389—21no—
300#389C22×C15112yes—
301#389C22×C15111yescharacteristic
302#389C22×C15111yescharacteristic
303#389C22×C15112yes—
304#388—21no—
305#388—21no—
306#386—21no—
307#380C22×C15111yescharacteristic
308C2×#95—21no—
309#340C22×C15112yes—
310#340C22×C15112yes—
311#340C22×C15112yes—
312#340C22×C15112yes—
313C22×D4—21no—
314C22×D4C23×C15111yescharacteristic
315C23×C4—21no—
316C23×C4—21no—
317C23×C4D4×C15111yescharacteristic
318C23×C4D4×C15111yescharacteristic
319C23×C4C23×C15111yescharacteristic
320C22×C8C23×C15112yes—
321C22×C8C23×C15112yes—
322#123—44no—
323#121—22no—
324#121—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C23×C15112yes—
336C2×C4⋊C4C23×C15111yescharacteristic
337C2×C4⋊C4C23×C15111yescharacteristic
338C2×C4⋊C4C23×C15111yescharacteristic
339C2×C4⋊C4C23×C15112yes—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42D4×C15111yescharacteristic
349C2×C42D4×C15111yescharacteristic
350C2×C42C23×C15111yescharacteristic
351C2×C42C23×C15111yescharacteristic
352#107—24no—
353#106—24no—
354C4⋊C8—24no—
355#102—24no—
356#102—24no—
357C22⋊C8—22no—
358C22⋊C8D4×C15114yes—
359#97—24no—
360#95—22no—
361#95—22no—
362#95—21no—
363#95—21no—
364#95—21no—
365C24—21no—
366C24C2×D4×C15111yescharacteristic
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—42no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—42no—
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C2×D4×C15111yescharacteristic
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×D4×C15111yescharacteristic
397C22×C4C2×D4×C15112yes—
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4#41×C15112yes—
400C22×C4C24×C15111yescharacteristic
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8C2×D4×C15114yes—
407C4⋊C4—24no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—44no—
416C4⋊C4—44no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C4⋊C4#41×C15114yes—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—42no—
426C22⋊C4—42no—
427C42—22no—
428C42—22no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23#121×C15112yes—
445C23AGL(1,ℤ/8)×C15112yes—
446C23AGL(1,ℤ/8)×C15112yes—
447C23C22×D4×C15111yescharacteristic
448D4—42no—
449D4—42no—
450D4—84no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—44no—
468C2×C4—48no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—84no—
485C2×C4#121×C15112yes—
486C2×C4#137×C15112yes—
487C2×C4C22×D4×C15111yescharacteristic
488C2×C4C2×#41×C15112yes—
489C2×C4C2×#41×C15111yescharacteristic
490C2×C42−1+4×C15112yes—
491C8—24no—
492C8—42no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22#469×C15114yes—
507C22C2×#121×C15111yescharacteristic
508C22#525×C15111yescharacteristic
509C22#536×C15111yescharacteristic
510C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
511C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
512C22C2×#137×C15111yescharacteristic
513C22#575×C15111yescharacteristic
514C4—22no—
515C4—22no—
516C4—44no—
517C4—41no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—82no—
523C4—81no—
524C4#547×C15112yes—
525C4#552×C15112yes—
526C2—24no—
527C2—161no—
528C2#2413×C15111yescharacteristic
529C2C2×#469×C15111yescharacteristic
530C2#3056×C15111yescharacteristic
531C2#3112×C15111yescharacteristic
532C2#3114×C15111yescharacteristic
533C2#3234×C15111yescharacteristic
534C2#3238×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#432×C151C2semidirect
4. C2×#389×C151C2semidirect
5. #2087×C151C2semidirect
6. #2065×C151C2semidirect
7. #1944×C151C2semidirect
8. #1936×C151C2semidirect
10. #1853×C151C2semidirect
11. #1823×C151C2semidirect
267. #24608C151direct (N × H)
268. C151#24608direct (N × H)
270. C2×#432C2×C151semidirect
272. C2×#389C2×C151semidirect
273. #2087C2×C151semidirect
274. #2065C2×C151semidirect
275. #1944C2×C151semidirect
276. #1936C2×C151semidirect
278. #1853C2×C151semidirect
279. #1823C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1512
C2×#432×C1512
#2854×C1512
C2×#389×C1512
#2087×C1512
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#1936×C1512
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#1823×C1512
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