Finite Group Databasebeta

← C151×#9520 #50314445

Subgroups — C151×#9520 #50314445

Order 38656.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3003×C151C211yesmaximal, characteristic
2#2976×C151C211yesmaximal, characteristic, complemented
3#1786×C151C211yesmaximal, characteristic, complemented
4#1783×C151C211yesmaximal, characteristic, complemented
5#1513×C151C211yesmaximal, characteristic, complemented
6#1305×C151C211yesmaximal, characteristic, complemented
7#1293×C151C211yesmaximal, characteristic, complemented
8C23×D4×C151C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C151—21no—
10#525×C151C2211yescharacteristic
11#450×C151—21no—
12#450×C151C412yescomplemented
13#447×C151—21no—
14#447×C151C412yescomplemented
15#436×C151—21no—
16#435×C151—21no—
17#435×C151—21no—
18C8×D4×C151—21no—
19#433×C151—21no—
20#418×C151—21no—
21C2×#102×C151—21no—
22C2×#102×C151—21no—
23C2×#100×C151—21no—
24C2×#100×C151—21no—
25#408×C151—21no—
26#407×C151C2211yescharacteristic
27#407×C151C2211yescharacteristic
28#407×C151C2211yescharacteristic
29C2×C22⋊C8×C151C2211yescharacteristic
30#380×C151C2211yescharacteristic
31#328×C151—21no—
32#327×C151—21no—
33C25×C151—21no—
34C2×#41×C151D411yescharacteristic
35C22×D4×C151—21no—
36C22×D4×C151—21no—
37C22×D4×C151—21no—
38C22×D4×C151—21no—
39C22×D4×C151—21no—
40C22×D4×C151—42no—
41C22×D4×C151—42no—
42C22×D4×C151C2×C412yes—
43C23×C4×C151C2311yescharacteristic
44AGL(1,ℤ/8)×C151—42no—
45AGL(1,ℤ/8)×C151—42no—
46C2×SD16×C151—22no—
47C2×D8×C151—22no—
48C2×M16×C151—21no—
49C2×M16×C151—21no—
50C2×M16×C151—21no—
51C2×M16×C151D411yescharacteristic
52C2×M16×C151D411yescharacteristic
53C22×C8×C151—21no—
54C22×C8×C151D411yescharacteristic
55C22×C8×C151D411yescharacteristic
56#123×C151—21no—
57C22⋊Q8×C151C2×C411yescharacteristic
58C22⋊Q8×C151D411yescharacteristic
59#121×C151C2×C411yescharacteristic
60#121×C151D411yescharacteristic
61#120×C151—21no—
62C4×D4×C151—21no—
63C4×D4×C151—21no—
64#117×C151D411yescharacteristic
65C2×C4⋊C4×C151—21no—
66C2×C22⋊C4×C151—21no—
67C4⋊C8×C151—21no—
68C4⋊C8×C151—21no—
69#102×C151—22no—
70#102×C151—22no—
71#102×C151—42no—
72#102×C151—42no—
73#100×C151—42no—
74#100×C151—42no—
75C22⋊C8×C151—21no—
76C22⋊C8×C151—21no—
77C22⋊C8×C151—21no—
78C22⋊C8×C151—21no—
79C22⋊C8×C151—21no—
80C22⋊C8×C151—21no—
81C22⋊C8×C151—21no—
82C22⋊C8×C151—21no—
83C22⋊C8×C151—21no—
84C22⋊C8×C151C2×C412yes—
85#97×C151—21no—
86C4×C8×C151—21no—
87#95×C151—21no—
88C24×C151—22no—
89C24×C151—44no—
90C24×C151—41no—
91C24×C151—41no—
92C24×C151—81no—
93C24×C151—81no—
94C24×C151—82no—
95C24×C151#4111yescharacteristic
96#41×C151—41no—
97#41×C151—41no—
98C2×Q8×C151C22⋊C411yescharacteristic
99C2×D4×C151—22no—
100C2×D4×C151—22no—
101C2×D4×C151—22no—
102C2×D4×C151—22no—
103C2×D4×C151—22no—
104C2×D4×C151—22no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—22no—
109C2×D4×C151—22no—
110C2×D4×C151—41no—
111C2×D4×C151—41no—
112C2×D4×C151—41no—
113C2×D4×C151—41no—
114C2×D4×C151—41no—
115C2×D4×C151—41no—
116C2×D4×C151—44no—
117C2×D4×C151—44no—
118C2×D4×C151—44no—
119C2×D4×C151—41no—
120C2×D4×C151—41no—
121C2×D4×C151C22⋊C411yescharacteristic
122C22×C4×C151—21no—
123C22×C4×C151—41no—
124C22×C4×C151—41no—
125C22×C4×C151—41no—
126C22×C4×C151C22×C411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151#4111yescharacteristic
132SD16×C151—44no—
133D8×C151—44no—
134M16×C151—41no—
135M16×C151—41no—
136M16×C151—41no—
137M16×C151—41no—
138M16×C151—41no—
139M16×C151—41no—
140M16×C151—81no—
141C2×C8×C151—22no—
142C2×C8×C151—21no—
143C2×C8×C151—21no—
144C2×C8×C151—21no—
145C2×C8×C151—21no—
146C2×C8×C151—41no—
147C2×C8×C151—41no—
148C2×C8×C151—41no—
149C2×C8×C151—81no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151C22⋊C411yescharacteristic
155C4⋊C4×C151C22⋊C411yescharacteristic
156C22⋊C4×C151—21no—
157C22⋊C4×C151—21no—
158C22⋊C4×C151—21no—
159C22⋊C4×C151—21no—
160C22⋊C4×C151—21no—
161C22⋊C4×C151—81no—
162C42×C151—21no—
163C23×C151—21no—
164C23×C151—21no—
165C23×C151—24no—
166C23×C151—21no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151—42no—
170C23×C151—42no—
171C23×C151—42no—
172C23×C151—42no—
173C23×C151—42no—
174C23×C151—42no—
175C23×C151—82no—
176C23×C151—82no—
177C23×C151—82no—
178C23×C151—81no—
179C23×C151—81no—
180C23×C151—82no—
181C23×C151—88no—
182C23×C151—88no—
183C23×C151—81no—
184C23×C151—81no—
185C23×C151C4×D411yescharacteristic
186C23×C151#12111yescharacteristic
187C23×C151#12311yescharacteristic
188Q8×C151—41no—
189D4×C151—24no—
190D4×C151—24no—
191D4×C151—41no—
192D4×C151—42no—
193D4×C151—42no—
194D4×C151—42no—
195D4×C151—42no—
196D4×C151—41no—
197D4×C151—41no—
198D4×C151—42no—
199D4×C151—42no—
200D4×C151—81no—
201D4×C151—81no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—81no—
217C2×C4×C151—81no—
218C2×C4×C151—81no—
219C2×C4×C151C2×C22⋊C411yescharacteristic
220C2×C4×C151C4×D411yescharacteristic
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151#12111yescharacteristic
223C8×C151—42no—
224C8×C151—41no—
225C8×C151—41no—
226C8×C151—41no—
227C8×C151—41no—
228C8×C151—81no—
229C22×C151—21no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—21no—
235C22×C151—21no—
236C22×C151—21no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—41no—
240C22×C151—44no—
241C22×C151—41no—
242C22×C151—41no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151—82no—
246C22×C151—82no—
247C22×C151—84no—
248C22×C151—84no—
249C22×C151—84no—
250C22×C151—84no—
251C22×C151—82no—
252C22×C151—82no—
253C22×C151#38611yescharacteristic
254C22×C151#47111yescharacteristic
255C22×C151#47211yescharacteristic
256C4×C151—21no—
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—41no—
260C4×C151—41no—
261C4×C151—41no—
262C4×C151—161no—
263C4×C151B(4,𝔽2)11yescharacteristic
264C4×C151B(4,𝔽2)11yescharacteristic
265C2×C151—21no—
266C2×C151—21no—
267C2×C151—41no—
268C2×C151—41no—
269C2×C151—81no—
270C2×C151—84no—
271C2×C151#188911yescharacteristic
272C2×C151#190311yescharacteristic
273C2×C151#190711yescharacteristic
274#9520C15111yesmaximal, characteristic, direct product factor, Sylow
275C151#952011yescharacteristic, direct product factor, Sylow
276#3003C2×C15111yescharacteristic
277#2976C2×C15111yescharacteristic, complemented
278#1786C2×C15111yescharacteristic, complemented
279#1783C2×C15111yescharacteristic, complemented
280#1513C2×C15111yescharacteristic, complemented
281#1305C2×C15111yescharacteristic, complemented
282#1293C2×C15111yescharacteristic, complemented
283C23×D4C22×C15111yescharacteristic
284C2×AGL(1,ℤ/8)—21no—
285#525C22×C15111yescharacteristic
286#450—21no—
287#450C4×C15112yescomplemented
288#447—21no—
289#447C4×C15112yescomplemented
290#436—21no—
291#435—21no—
292#435—21no—
293C8×D4—21no—
294#433—21no—
295#418—21no—
296C2×#102—21no—
297C2×#102—21no—
298C2×#100—21no—
299C2×#100—21no—
300#408—21no—
301#407C22×C15111yescharacteristic
302#407C22×C15111yescharacteristic
303#407C22×C15111yescharacteristic
304C2×C22⋊C8C22×C15111yescharacteristic
305#380C22×C15111yescharacteristic
306#328—21no—
307#327—21no—
308C25—21no—
309C2×#41D4×C15111yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4C2×C4×C15112yes—
318C23×C4C23×C15111yescharacteristic
319AGL(1,ℤ/8)—42no—
320AGL(1,ℤ/8)—42no—
321C2×SD16—22no—
322C2×D8—22no—
323C2×M16—21no—
324C2×M16—21no—
325C2×M16—21no—
326C2×M16D4×C15111yescharacteristic
327C2×M16D4×C15111yescharacteristic
328C22×C8—21no—
329C22×C8D4×C15111yescharacteristic
330C22×C8D4×C15111yescharacteristic
331#123—21no—
332C22⋊Q8C2×C4×C15111yescharacteristic
333C22⋊Q8D4×C15111yescharacteristic
334#121C2×C4×C15111yescharacteristic
335#121D4×C15111yescharacteristic
336#120—21no—
337C4×D4—21no—
338C4×D4—21no—
339#117D4×C15111yescharacteristic
340C2×C4⋊C4—21no—
341C2×C22⋊C4—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344#102—22no—
345#102—22no—
346#102—42no—
347#102—42no—
348#100—42no—
349#100—42no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8—21no—
353C22⋊C8—21no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8C2×C4×C15112yes—
360#97—21no—
361C4×C8—21no—
362#95—21no—
363C24—22no—
364C24—44no—
365C24—41no—
366C24—41no—
367C24—81no—
368C24—81no—
369C24—82no—
370C24#41×C15111yescharacteristic
371#41—41no—
372#41—41no—
373C2×Q8C22⋊C4×C15111yescharacteristic
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4C22⋊C4×C15111yescharacteristic
397C22×C4—21no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C22×C4×C15111yescharacteristic
402C22×C4C2×D4×C15111yescharacteristic
403C22×C4C2×D4×C15111yescharacteristic
404C22×C4C2×D4×C15111yescharacteristic
405C22×C4C2×D4×C15111yescharacteristic
406C22×C4#41×C15111yescharacteristic
407SD16—44no—
408D8—44no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—41no—
415M16—81no—
416C2×C8—22no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—41no—
424C2×C8—81no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C22⋊C4×C15111yescharacteristic
430C4⋊C4C22⋊C4×C15111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—81no—
437C42—21no—
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C15111yescharacteristic
461C23#121×C15111yescharacteristic
462C23#123×C15111yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C22⋊C4×C15111yescharacteristic
495C2×C4C4×D4×C15111yescharacteristic
496C2×C4#120×C15111yescharacteristic
497C2×C4#121×C15111yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22#386×C15111yescharacteristic
529C22#471×C15111yescharacteristic
530C22#472×C15111yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4B(4,𝔽2)×C15111yescharacteristic
539C4B(4,𝔽2)×C15111yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2#1889×C15111yescharacteristic
547C2#1903×C15111yescharacteristic
548C2#1907×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radical#3003×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2976×C151C2semidirect
3. #1786×C151C2semidirect
4. #1783×C151C2semidirect
5. #1513×C151C2semidirect
6. #1305×C151C2semidirect
7. #1293×C151C2semidirect
12. #450×C151C4semidirect
14. #447×C151C4semidirect
274. #9520C151direct (N × H)
275. C151#9520direct (N × H)
277. #2976C2×C151semidirect
278. #1786C2×C151semidirect
279. #1783C2×C151semidirect
280. #1513C2×C151semidirect
281. #1305C2×C151semidirect
282. #1293C2×C151semidirect
287. #450C4×C151semidirect
289. #447C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3003×C1512
#2976×C1512
#1786×C1512
#1783×C1512
#1513×C1512
#1305×C1512
#1293×C1512
#9520151