Finite Group Databasebeta

← C151×#9946 #50314871

Subgroups — C151×#9946 #50314871

Order 38656.

1060 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3186×C151C211yesmaximal, characteristic, complemented
2C2×#447×C151C211yesmaximal, characteristic, complemented
3#2433×C151C211yesmaximal, characteristic, complemented
4#1964×C151C211yesmaximal, characteristic, complemented
5#1786×C151C211yesmaximal, characteristic, complemented
6#1519×C151C211yesmaximal, characteristic, complemented
7#1282×C151C211yesmaximal, characteristic, complemented
8C23×D4×C151C2211yescharacteristic
9C22×D8×C151—21no—
10C2×#127×C151—21no—
11C2×#121×C151C2211yescharacteristic
12C2×#121×C151C2211yescharacteristic
13C2×#120×C151—22no—
14#480×C151—21no—
15#480×C151—21no—
16#466×C151—22no—
17#447×C151—21no—
18#447×C151—22no—
19#447×C151—21no—
20#447×C151—22no—
21C2×#102×C151—21no—
22C2×#102×C151—22no—
23C2×#99×C151—22no—
24C2×C22⋊C8×C151C2211yescharacteristic
25C2×C22⋊C8×C151C2211yescharacteristic
26#392×C151—22no—
27#390×C151—21no—
28#380×C151C2211yescharacteristic
29C4×C22⋊C4×C151C2211yescharacteristic
30#327×C151—22no—
31C25×C151—21no—
32C22×D4×C151—24no—
33C22×D4×C151—21no—
34C22×D4×C151—21no—
35C22×D4×C151—21no—
36C22×D4×C151—21no—
37C22×D4×C151—21no—
38C22×D4×C151—21no—
39C22×D4×C151—21no—
40C22×D4×C151—44no—
41C22×D4×C151D412yes—
42C22×D4×C151D411yescharacteristic
43C22×D4×C151D411yescharacteristic, complemented
44C23×C4×C151C2311yescharacteristic
45C2×D8×C151—24no—
46C2×D8×C151—22no—
47C2×D8×C151—44no—
48C22×C8×C151—21no—
49C22×C8×C151D412yescomplemented
50#127×C151—44no—
51#121×C151—21no—
52#121×C151—21no—
53#121×C151—21no—
54#121×C151—21no—
55#121×C151—21no—
56#121×C151—21no—
57#121×C151—21no—
58#121×C151—21no—
59#120×C151—44no—
60#120×C151—44no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151D411yescharacteristic, complemented
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—21no—
66C2×C22⋊C4×C151—21no—
67C2×C22⋊C4×C151—21no—
68C2×C22⋊C4×C151D412yes—
69C2×C42×C151—21no—
70#107×C151—22no—
71#102×C151—24no—
72#102×C151—22no—
73#102×C151—22no—
74#102×C151—44no—
75#99×C151—44no—
76C22⋊C8×C151—21no—
77C22⋊C8×C151—21no—
78C22⋊C8×C151—21no—
79C22⋊C8×C151D412yescomplemented
80#95×C151—21no—
81#95×C151—21no—
82C24×C151—22no—
83C24×C151—21no—
84C24×C151—21no—
85C24×C151—44no—
86C24×C151—41no—
87C24×C151—41no—
88C24×C151—42no—
89C24×C151—42no—
90C24×C151—82no—
91C24×C151C2×D411yescharacteristic
92C2×D4×C151—24no—
93C2×D4×C151—24no—
94C2×D4×C151—24no—
95C2×D4×C151—22no—
96C2×D4×C151—21no—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—22no—
100C2×D4×C151—21no—
101C2×D4×C151—42no—
102C2×D4×C151—42no—
103C2×D4×C151—42no—
104C2×D4×C151—42no—
105C2×D4×C151—42no—
106C2×D4×C151—48no—
107C2×D4×C151—44no—
108C2×D4×C151—44no—
109C2×D4×C151—44no—
110C2×D4×C151—48no—
111C2×D4×C151—41no—
112C2×D4×C151—41no—
113C2×D4×C151—41no—
114C2×D4×C151—41no—
115C2×D4×C151—42no—
116C2×D4×C151—42no—
117C2×D4×C151—42no—
118C2×D4×C151—42no—
119C2×D4×C151—41no—
120C2×D4×C151—41no—
121C2×D4×C151—84no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—42no—
126C22×C4×C151—41no—
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151#4111yescharacteristic
133D8×C151—48no—
134D8×C151—82no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—42no—
138C2×C8×C151—42no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—42no—
144C22⋊C4×C151—22no—
145C22⋊C4×C151—48no—
146C22⋊C4×C151—41no—
147C22⋊C4×C151—41no—
148C22⋊C4×C151—41no—
149C22⋊C4×C151—41no—
150C22⋊C4×C151—42no—
151C22⋊C4×C151D814yescomplemented
152C42×C151—42no—
153C23×C151—24no—
154C23×C151—41no—
155C23×C151—41no—
156C23×C151—42no—
157C23×C151—44no—
158C23×C151—44no—
159C23×C151—44no—
160C23×C151—42no—
161C23×C151—42no—
162C23×C151—42no—
163C23×C151—44no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—42no—
167C23×C151—42no—
168C23×C151—82no—
169C23×C151—82no—
170C23×C151—81no—
171C23×C151—81no—
172C23×C151—88no—
173C23×C151—88no—
174C23×C151—82no—
175C23×C151—81no—
176C23×C151—81no—
177C23×C151#12011yescharacteristic
178C23×C151#12111yescharacteristic
179C23×C151#12711yescharacteristic
180C23×C151C2×D812yes—
181C23×C151AGL(1,ℤ/8)12yes—
182D4×C151—24no—
183D4×C151—24no—
184D4×C151—42no—
185D4×C151—42no—
186D4×C151—44no—
187D4×C151—42no—
188D4×C151—44no—
189D4×C151—42no—
190D4×C151—42no—
191D4×C151—81no—
192D4×C151—816no—
193D4×C151—82no—
194D4×C151—82no—
195D4×C151—81no—
196D4×C151—81no—
197D4×C151—81no—
198D4×C151—81no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—24no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—81no—
213C2×C4×C151—81no—
214C2×C4×C151—81no—
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12011yescharacteristic
217C2×C4×C151#12111yescharacteristic
218C2×C4×C151#12111yescharacteristic
219C8×C151—42no—
220C8×C151—42no—
221C22×C151—21no—
222C22×C151—21no—
223C22×C151—21no—
224C22×C151—21no—
225C22×C151—21no—
226C22×C151—21no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—48no—
230C22×C151—44no—
231C22×C151—84no—
232C22×C151—84no—
233C22×C151—88no—
234C22×C151—84no—
235C22×C151—84no—
236C22×C151—82no—
237C22×C151—82no—
238C22×C151—81no—
239C22×C151—81no—
240C22×C151—81no—
241C22×C151—81no—
242C22×C151—81no—
243C22×C151—81no—
244C22×C151—162no—
245C22×C151#39211yescharacteristic
246C22×C151#44712yes—
247C22×C151#45912yes—
248C22×C151#49311yescharacteristic
249C22×C151#49611yescharacteristic
250C4×C151—21no—
251C4×C151—21no—
252C4×C151—21no—
253C4×C151—44no—
254C4×C151—81no—
255C4×C151—81no—
256C4×C151—161no—
257C4×C151B(4,𝔽2)12yes—
258C2×C151—22no—
259C2×C151—21no—
260C2×C151—22no—
261C2×C151—21no—
262C2×C151—84no—
263C2×C151—161no—
264C2×C151—161no—
265C2×C151#200811yescharacteristic
266C2×C151#201111yescharacteristic
267C2×C151#202111yescharacteristic
268#9946C15111yesmaximal, characteristic, direct product factor, Sylow
269C151#994611yescharacteristic, direct product factor, Sylow
270#3186C2×C15111yescharacteristic, complemented
271C2×#447C2×C15111yescharacteristic, complemented
272#2433C2×C15111yescharacteristic, complemented
273#1964C2×C15111yescharacteristic, complemented
274#1786C2×C15111yescharacteristic, complemented
275#1519C2×C15111yescharacteristic, complemented
276#1282C2×C15111yescharacteristic, complemented
277C23×D4C22×C15111yescharacteristic
278C22×D8—21no—
279C2×#127—21no—
280C2×#121C22×C15111yescharacteristic
281C2×#121C22×C15111yescharacteristic
282C2×#120—22no—
283#480—21no—
284#480—21no—
285#466—22no—
286#447—21no—
287#447—22no—
288#447—21no—
289#447—22no—
290C2×#102—21no—
291C2×#102—22no—
292C2×#99—22no—
293C2×C22⋊C8C22×C15111yescharacteristic
294C2×C22⋊C8C22×C15111yescharacteristic
295#392—22no—
296#390—21no—
297#380C22×C15111yescharacteristic
298C4×C22⋊C4C22×C15111yescharacteristic
299#327—22no—
300C25—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—24no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4—44no—
310C22×D4D4×C15111yescharacteristic
311C22×D4D4×C15112yes—
312C22×D4D4×C15111yescharacteristic, complemented
313C23×C4C23×C15111yescharacteristic
314C2×D8—24no—
315C2×D8—22no—
316C2×D8—44no—
317C22×C8—21no—
318C22×C8D4×C15112yescomplemented
319#127—44no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328#120—44no—
329#120—44no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4D4×C15111yescharacteristic
332C2×C4⋊C4D4×C15111yescharacteristic, complemented
333C2×C22⋊C4—24no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4D4×C15112yes—
338C2×C42—21no—
339#107—22no—
340#102—24no—
341#102—22no—
342#102—22no—
343#102—44no—
344#99—44no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8D4×C15112yescomplemented
349#95—21no—
350#95—21no—
351C24—22no—
352C24—21no—
353C24—21no—
354C24—44no—
355C24—41no—
356C24—41no—
357C24—42no—
358C24—42no—
359C24—82no—
360C24C2×D4×C15111yescharacteristic
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—21no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—48no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4—48no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—84no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—41no—
396C22×C4C2×D4×C15111yescharacteristic
397C22×C4C2×D4×C15111yescharacteristic
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15111yescharacteristic
400C22×C4C2×D4×C15111yescharacteristic
401C22×C4#41×C15111yescharacteristic
402D8—48no—
403D8—82no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—42no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—42no—
413C22⋊C4—22no—
414C22⋊C4—48no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—42no—
420C22⋊C4D8×C15114yescomplemented
421C42—42no—
422C23—24no—
423C23—41no—
424C23—41no—
425C23—44no—
426C23—44no—
427C23—42no—
428C23—44no—
429C23—42no—
430C23—42no—
431C23—42no—
432C23—44no—
433C23—41no—
434C23—41no—
435C23—42no—
436C23—42no—
437C23—82no—
438C23—82no—
439C23—81no—
440C23—81no—
441C23—88no—
442C23—88no—
443C23—82no—
444C23—81no—
445C23—81no—
446C23#120×C15111yescharacteristic
447C23#121×C15111yescharacteristic
448C23#127×C15111yescharacteristic
449C23C2×D8×C15112yes—
450C23AGL(1,ℤ/8)×C15112yes—
451D4—24no—
452D4—24no—
453D4—42no—
454D4—42no—
455D4—44no—
456D4—42no—
457D4—44no—
458D4—42no—
459D4—42no—
460D4—81no—
461D4—816no—
462D4—82no—
463D4—82no—
464D4—81no—
465D4—81no—
466D4—81no—
467D4—81no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4#120×C15111yescharacteristic
485C2×C4#120×C15111yescharacteristic
486C2×C4#121×C15111yescharacteristic
487C2×C4#121×C15111yescharacteristic
488C8—42no—
489C8—42no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—42no—
497C22—42no—
498C22—48no—
499C22—44no—
500C22—84no—
501C22—84no—
502C22—88no—
503C22—84no—
504C22—84no—
505C22—82no—
506C22—82no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—162no—
514C22#392×C15111yescharacteristic
515C22#447×C15112yes—
516C22#459×C15112yes—
517C22#493×C15111yescharacteristic
518C22#496×C15111yescharacteristic
519C4—21no—
520C4—21no—
521C4—21no—
522C4—44no—
523C4—81no—
524C4—81no—
525C4—161no—
526C4B(4,𝔽2)×C15112yes—
527C2—22no—
528C2—21no—
529C2—22no—
530C2—21no—
531C2—84no—
532C2—161no—
533C2—161no—
534C2#2008×C15111yescharacteristic
535C2#2011×C15111yescharacteristic
536C2#2021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC23×C4C23×C151
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3186×C151C2semidirect
2. C2×#447×C151C2semidirect
3. #2433×C151C2semidirect
4. #1964×C151C2semidirect
5. #1786×C151C2semidirect
6. #1519×C151C2semidirect
7. #1282×C151C2semidirect
43. C22×D4×C151D4semidirect
49. C22×C8×C151D4semidirect
63. C2×C4⋊C4×C151D4semidirect
79. C22⋊C8×C151D4semidirect
151. C22⋊C4×C151D8semidirect
268. #9946C151direct (N × H)
269. C151#9946direct (N × H)
270. #3186C2×C151semidirect
271. C2×#447C2×C151semidirect
272. #2433C2×C151semidirect
273. #1964C2×C151semidirect
274. #1786C2×C151semidirect
275. #1519C2×C151semidirect
276. #1282C2×C151semidirect
312. C22×D4D4×C151semidirect
318. C22×C8D4×C151semidirect
332. C2×C4⋊C4D4×C151semidirect
348. C22⋊C8D4×C151semidirect
420. C22⋊C4D8×C151semidirect

Maximal subgroups

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

subgroupindex
#3186×C1512
C2×#447×C1512
#2433×C1512
#1964×C1512
#1786×C1512
#1519×C1512
#1282×C1512
#9946151