Finite Group Databasebeta

← C151×#25010 #50329935

Subgroups — C151×#25010 #50329935

Order 38656.

982 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C151C212yesmaximal, complemented
2#2537×C151C211yesmaximal, characteristic
3D4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
4#2075×C151C212yesmaximal, complemented
5#2033×C151C212yesmaximal, complemented
6#1954×C151C211yesmaximal, characteristic, complemented
7#1947×C151C211yesmaximal, characteristic, complemented
8#1852×C151C212yesmaximal, complemented
9#1845×C151C211yesmaximal, characteristic, complemented
10#1802×C151C211yesmaximal, characteristic, complemented
11C4×#102×C151C211yesmaximal, characteristic, complemented
12C2×#121×C151—21no—
13C2×#121×C151C2212yes—
14C2×C4×D4×C151—21no—
15C2×C4×D4×C151C2211yescharacteristic
16C2×C4×D4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18#480×C151—28no—
19C2×#107×C151C2212yes—
20C2×#107×C151C2212yes—
21C2×#107×C151C2212yes—
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×#102×C151C2211yescharacteristic
24C2×#102×C151C2212yes—
25C2×#102×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2212yes—
27C2×C22⋊C8×C151C2212yes—
28C2×C4×C8×C151C2211yescharacteristic
29#394×C151—22no—
30#389×C151—21no—
31#385×C151—22no—
32#384×C151C2211yescharacteristic
33#384×C151C2211yescharacteristic
34#380×C151—21no—
35#380×C151C2212yes—
36#380×C151C2212yes—
37C4×C4⋊C4×C151C2211yescharacteristic
38#340×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2211yescharacteristic
42C22×D4×C151—22no—
43C22×D4×C151D411yescharacteristic
44C22×D4×C151C2311yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151—22no—
47C23×C4×C151C2312yes—
48C22×C8×C151C2312yes—
49C22×C8×C151C2311yescharacteristic
50C22×C8×C151C2311yescharacteristic
51#121×C151—24no—
52#121×C151—42no—
53#121×C151—44no—
54C4×D4×C151—22no—
55C4×D4×C151—22no—
56C4×D4×C151—22no—
57C4×D4×C151—22no—
58C4×D4×C151—44no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—42no—
66C2×C4⋊C4×C151D411yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C4⋊C4×C151C2312yes—
70C2×C4⋊C4×C151C2312yes—
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151D412yes—
77C2×C42×C151—21no—
78C2×C42×C151C2311yescharacteristic
79#107×C151—24no—
80#107×C151—24no—
81#107×C151—42no—
82C4⋊C8×C151—22no—
83#102×C151—24no—
84#102×C151—22no—
85#102×C151D414yescomplemented
86C22⋊C8×C151—24no—
87C22⋊C8×C151—24no—
88C4×C8×C151—22no—
89#95×C151—21no—
90#95×C151—22no—
91#95×C151—22no—
92C24×C151—21no—
93C24×C151C2×D412yes—
94C2×D4×C151—22no—
95C2×D4×C151—22no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—44no—
102C2×D4×C151—44no—
103C2×D4×C151—82no—
104C2×D4×C151D814yes—
105C2×D4×C151C2×D412yes—
106C22×C4×C151—21no—
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—21no—
114C22×C4×C151—21no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—44no—
118C22×C4×C151—44no—
119C22×C4×C151—42no—
120C22×C4×C151—42no—
121C22×C4×C151—42no—
122C22×C4×C151—82no—
123C22×C4×C151C2×D412yes—
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2411yescharacteristic
127C2×C8×C151—21no—
128C2×C8×C151—21no—
129C2×C8×C151—21no—
130C2×C8×C151—21no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C2×C8×C151C2×D412yes—
135C2×C8×C151#4112yes—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—44no—
147C4⋊C4×C151—42no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151—81no—
150C4⋊C4×C151—81no—
151C4⋊C4×C151C2×D412yes—
152C22⋊C4×C151—24no—
153C22⋊C4×C151—44no—
154C22⋊C4×C151—44no—
155C22⋊C4×C151—44no—
156C22⋊C4×C151—42no—
157C42×C151—42no—
158C42×C151#4112yes—
159C42×C151#4112yes—
160C23×C151—22no—
161C23×C151—22no—
162C23×C151—22no—
163C23×C151—22no—
164C23×C151—22no—
165C23×C151—22no—
166C23×C151—22no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151—41no—
172C23×C151—41no—
173C23×C151C2×D814yes—
174C23×C151C22×D411yescharacteristic
175D4×C151—22no—
176D4×C151—22no—
177D4×C151—28no—
178D4×C151—41no—
179D4×C151—41no—
180D4×C151—88no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—41no—
188C2×C4×C151—41no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—88no—
206C2×C4×C151—84no—
207C2×C4×C151#12312yes—
208C2×C4×C151#12312yes—
209C2×C4×C151C2×D812yes—
210C2×C4×C151#13712yes—
211C2×C4×C151C22×D411yescharacteristic
212C2×C4×C151C2×#4111yescharacteristic
213C2×C4×C151C2×#4111yescharacteristic
214C2×C4×C151C2×#4111yescharacteristic
215C2×C4×C151H(5,𝔽2)11yescharacteristic
216C2×C4×C1512−1+411yescharacteristic
217C8×C151—22no—
218C8×C151—22no—
219C8×C151—42no—
220C22×C151—24no—
221C22×C151—24no—
222C22×C151—24no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—42no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—81no—
231C22×C151—81no—
232C22×C151—81no—
233C22×C151—81no—
234C22×C151C2×#12311yescharacteristic
235C22×C151D4211yescharacteristic
236C22×C151#54711yescharacteristic
237C22×C151C22×D811yescharacteristic
238C22×C151C2×#13711yescharacteristic
239C22×C151#57611yescharacteristic
240C22×C151#57811yescharacteristic
241C4×C151—22no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151—81no—
245C4×C151—81no—
246C4×C151—82no—
247C4×C151—82no—
248C4×C151#48014yescomplemented
249C4×C151#53211yescharacteristic
250C4×C151#54211yescharacteristic
251C4×C151#54711yescharacteristic
252C4×C151#55311yescharacteristic
253C2×C151—44no—
254C2×C151—82no—
255C2×C151#242211yescharacteristic
256C2×C151C2×#48011yescharacteristic
257C2×C151#309811yescharacteristic
258C2×C151#327611yescharacteristic
259C2×C151D4×D811yescharacteristic
260C2×C151#333411yescharacteristic
261C2×C151#335711yescharacteristic
262#25010C15111yesmaximal, characteristic, direct product factor, Sylow
263C151#2501011yescharacteristic, direct product factor, Sylow
264C2×#480C2×C15112yescomplemented
265#2537C2×C15111yescharacteristic
266D4×C4⋊C4C2×C15111yescharacteristic, complemented
267#2075C2×C15112yescomplemented
268#2033C2×C15112yescomplemented
269#1954C2×C15111yescharacteristic, complemented
270#1947C2×C15111yescharacteristic, complemented
271#1852C2×C15112yescomplemented
272#1845C2×C15111yescharacteristic, complemented
273#1802C2×C15111yescharacteristic, complemented
274C4×#102C2×C15111yescharacteristic, complemented
275C2×#121—21no—
276C2×#121C22×C15112yes—
277C2×C4×D4—21no—
278C2×C4×D4C22×C15111yescharacteristic
279C2×C4×D4C22×C15111yescharacteristic
280C22×C4⋊C4C22×C15112yes—
281#480—28no—
282C2×#107C22×C15112yes—
283C2×#107C22×C15112yes—
284C2×#107C22×C15112yes—
285C2×C4⋊C8C22×C15111yescharacteristic
286C2×#102C22×C15112yes—
287C2×#102C22×C15111yescharacteristic
288C2×#102C22×C15111yescharacteristic
289C2×C22⋊C8C22×C15112yes—
290C2×C22⋊C8C22×C15112yes—
291C2×C4×C8C22×C15111yescharacteristic
292#394—22no—
293#389—21no—
294#385—22no—
295#384C22×C15111yescharacteristic
296#384C22×C15111yescharacteristic
297#380—21no—
298#380C22×C15112yes—
299#380C22×C15112yes—
300C4×C4⋊C4C22×C15111yescharacteristic
301#340C22×C15112yes—
302#340C22×C15111yescharacteristic
303#340C22×C15112yes—
304#340C22×C15111yescharacteristic
305C22×D4—22no—
306C22×D4D4×C15111yescharacteristic
307C22×D4C23×C15111yescharacteristic
308C23×C4—22no—
309C23×C4—21no—
310C23×C4C23×C15112yes—
311C22×C8C23×C15112yes—
312C22×C8C23×C15111yescharacteristic
313C22×C8C23×C15111yescharacteristic
314#121—24no—
315#121—42no—
316#121—44no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—44no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4D4×C15111yescharacteristic
330C2×C4⋊C4C23×C15112yes—
331C2×C4⋊C4C23×C15111yescharacteristic
332C2×C4⋊C4C23×C15112yes—
333C2×C4⋊C4C23×C15111yescharacteristic
334C2×C4⋊C4C23×C15111yescharacteristic
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4D4×C15112yes—
340C2×C42—21no—
341C2×C42C23×C15111yescharacteristic
342#107—24no—
343#107—24no—
344#107—42no—
345C4⋊C8—22no—
346#102—24no—
347#102—22no—
348#102D4×C15114yescomplemented
349C22⋊C8—24no—
350C22⋊C8—24no—
351C4×C8—22no—
352#95—21no—
353#95—22no—
354#95—22no—
355C24—21no—
356C24C2×D4×C15112yes—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—44no—
365C2×D4—44no—
366C2×D4—82no—
367C2×D4D8×C15114yes—
368C2×D4C2×D4×C15112yes—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—44no—
381C22×C4—44no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—82no—
386C22×C4C2×D4×C15112yes—
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15111yescharacteristic
389C22×C4C24×C15111yescharacteristic
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8C2×D4×C15112yes—
398C2×C8#41×C15112yes—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—44no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—81no—
413C4⋊C4—81no—
414C4⋊C4C2×D4×C15112yes—
415C22⋊C4—24no—
416C22⋊C4—44no—
417C22⋊C4—44no—
418C22⋊C4—44no—
419C22⋊C4—42no—
420C42—42no—
421C42#41×C15112yes—
422C42#41×C15112yes—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23C2×D8×C15114yes—
437C23C22×D4×C15111yescharacteristic
438D4—28no—
439D4—22no—
440D4—22no—
441D4—41no—
442D4—41no—
443D4—88no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—88no—
469C2×C4—84no—
470C2×C4#123×C15112yes—
471C2×C4#123×C15112yes—
472C2×C4C2×D8×C15112yes—
473C2×C4#137×C15112yes—
474C2×C4C22×D4×C15111yescharacteristic
475C2×C4C2×#41×C15111yescharacteristic
476C2×C4C2×#41×C15111yescharacteristic
477C2×C4C2×#41×C15111yescharacteristic
478C2×C4H(5,𝔽2)×C15111yescharacteristic
479C2×C42−1+4×C15111yescharacteristic
480C8—22no—
481C8—22no—
482C8—42no—
483C22—24no—
484C22—24no—
485C22—24no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22C2×#123×C15111yescharacteristic
498C22D42×C15111yescharacteristic
499C22#547×C15111yescharacteristic
500C22C22×D8×C15111yescharacteristic
501C22C2×#137×C15111yescharacteristic
502C22#576×C15111yescharacteristic
503C22#578×C15111yescharacteristic
504C4—22no—
505C4—42no—
506C4—42no—
507C4—82no—
508C4—82no—
509C4—81no—
510C4—81no—
511C4#480×C15114yescomplemented
512C4#532×C15111yescharacteristic
513C4#542×C15111yescharacteristic
514C4#547×C15111yescharacteristic
515C4#553×C15111yescharacteristic
516C2—44no—
517C2—82no—
518C2#2422×C15111yescharacteristic
519C2C2×#480×C15111yescharacteristic
520C2#3098×C15111yescharacteristic
521C2#3276×C15111yescharacteristic
522C2D4×D8×C15111yescharacteristic
523C2#3334×C15111yescharacteristic
524C2#3357×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2537×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#480×C151C2semidirect
3. D4×C4⋊C4×C151C2semidirect
4. #2075×C151C2semidirect
5. #2033×C151C2semidirect
6. #1954×C151C2semidirect
7. #1947×C151C2semidirect
8. #1852×C151C2semidirect
9. #1845×C151C2semidirect
10. #1802×C151C2semidirect
11. C4×#102×C151C2semidirect
85. #102×C151D4semidirect
248. C4×C151#480semidirect
262. #25010C151direct (N × H)
263. C151#25010direct (N × H)
264. C2×#480C2×C151semidirect
266. D4×C4⋊C4C2×C151semidirect
267. #2075C2×C151semidirect
268. #2033C2×C151semidirect
269. #1954C2×C151semidirect
270. #1947C2×C151semidirect
271. #1852C2×C151semidirect
272. #1845C2×C151semidirect
273. #1802C2×C151semidirect
274. C4×#102C2×C151semidirect
348. #102D4×C151semidirect
511. C4#480×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1512
#2537×C1512
D4×C4⋊C4×C1512
#2075×C1512
#2033×C1512
#1954×C1512
#1947×C1512
#1852×C1512
#1845×C1512
#1802×C1512
C4×#102×C1512
#25010151