Finite Group Databasebeta

← C151×#24523 #50329448

Subgroups — C151×#24523 #50329448

Order 38656.

874 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3094×C151C211yesmaximal, characteristic
2C2×#448×C151C211yesmaximal, characteristic
3#2924×C151C211yesmaximal, characteristic, complemented
4C2×#419×C151C211yesmaximal, characteristic, complemented
5#2064×C151C212yesmaximal, complemented
6#2046×C151C212yesmaximal, complemented
7#1977×C151C212yesmaximal, complemented
8#1930×C151C212yesmaximal, complemented
9#1900×C151C211yesmaximal, characteristic
10#1855×C151C211yesmaximal, characteristic, complemented
11#1784×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C22×M16×C151C2211yescharacteristic
15C2×#121×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17#482×C151—21no—
18#482×C151—21no—
19#481×C151—21no—
20#480×C151—21no—
21#448×C151—21no—
22#448×C151—21no—
23#448×C151—22no—
24#433×C151—22no—
25#432×C151—21no—
26#431×C151—21no—
27C2×#108×C151C2212yes—
28#428×C151C2211yescharacteristic
29#428×C151C2211yescharacteristic
30#424×C151C2212yes—
31#419×C151—21no—
32#419×C151—21no—
33#419×C151C2212yes—
34#419×C151C2212yes—
35#418×C151C2211yescharacteristic
36#418×C151C2211yescharacteristic
37C2×#103×C151—21no—
38C2×#103×C151—21no—
39C2×#103×C151C2212yes—
40C2×#101×C151C2212yes—
41C2×#101×C151C2212yes—
42C2×#100×C151C2212yes—
43#407×C151C2211yescharacteristic
44#407×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#405×C151C2212yes—
47#343×C151C2212yes—
48#341×C151C2212yes—
49C22×Q8×C151—21no—
50C22×Q8×C151—21no—
51C22×Q8×C151—24no—
52C22×Q8×C151—21no—
53C22×Q8×C151—21no—
54C22×Q8×C151—21no—
55C22×Q8×C151—42no—
56C22×Q8×C151C2312yes—
57C22×D4×C151—21no—
58C22×D4×C151C2311yescharacteristic
59C23×C4×C151—21no—
60C23×C4×C151C2311yescharacteristic
61C2×SD16×C151—22no—
62C2×SD16×C151—22no—
63C2×SD16×C151—24no—
64C2×SD16×C151—42no—
65C2×M16×C151—21no—
66C2×M16×C151—42no—
67C2×M16×C151C2311yescharacteristic
68C2×M16×C151C2312yes—
69C2×M16×C151C2312yes—
70C2×M16×C151C2311yescharacteristic
71C22×C8×C151—21no—
72C22×C8×C151C2312yes—
73#121×C151—21no—
74#121×C151—21no—
75#121×C151—21no—
76#121×C151—21no—
77#117×C151—21no—
78#117×C151—21no—
79#117×C151D411yescharacteristic
80#117×C151D411yescharacteristic
81#117×C151C2311yescharacteristic
82#117×C151C2311yescharacteristic
83C2×C4⋊C4×C151D411yescharacteristic
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C42×C151—21no—
89#108×C151—42no—
90#107×C151—21no—
91#107×C151—21no—
92#106×C151—21no—
93#106×C151—21no—
94C4⋊C8×C151—22no—
95C4⋊C8×C151—22no—
96#103×C151—22no—
97#103×C151—22no—
98#103×C151—22no—
99#103×C151—22no—
100#103×C151—22no—
101#103×C151—22no—
102#102×C151—21no—
103#102×C151—21no—
104#102×C151—21no—
105#102×C151—21no—
106#101×C151—24no—
107#101×C151—42no—
108#100×C151—42no—
109C22⋊C8×C151—21no—
110C22⋊C8×C151—21no—
111C22⋊C8×C151—21no—
112C22⋊C8×C151—21no—
113C22⋊C8×C151D411yescharacteristic
114C22⋊C8×C151D411yescharacteristic
115C22⋊C8×C151D412yes—
116#97×C151—22no—
117C4×C8×C151—22no—
118C24×C151—21no—
119C24×C151#4111yescharacteristic
120C2×Q8×C151—22no—
121C2×Q8×C151—24no—
122C2×Q8×C151—24no—
123C2×Q8×C151—22no—
124C2×Q8×C151—22no—
125C2×Q8×C151—22no—
126C2×Q8×C151—22no—
127C2×Q8×C151—44no—
128C2×Q8×C151—44no—
129C2×Q8×C151—44no—
130C2×Q8×C151—42no—
131C2×Q8×C151—42no—
132C2×Q8×C151—41no—
133C2×Q8×C151—41no—
134C2×Q8×C151#4114yes—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—41no—
140C2×D4×C151—41no—
141C2×D4×C151—82no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—44no—
149C22×C4×C151—41no—
150C22×C4×C151—41no—
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151#4111yescharacteristic
156C22×C4×C151C2411yescharacteristic
157SD16×C151—44no—
158SD16×C151—44no—
159M16×C151—22no—
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—22no—
163M16×C151—22no—
164M16×C151—22no—
165M16×C151—42no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—22no—
172C2×C8×C151—42no—
173C2×C8×C151C2×D412yes—
174C2×C8×C151C2×D412yes—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151C2×D411yescharacteristic
180C4⋊C4×C151C2×D411yescharacteristic
181C4⋊C4×C151C2×D411yescharacteristic
182C4⋊C4×C151C2×D411yescharacteristic
183C22⋊C4×C151—21no—
184C22⋊C4×C151—21no—
185C22⋊C4×C151—21no—
186C22⋊C4×C151—21no—
187C22⋊C4×C151—41no—
188C22⋊C4×C151—41no—
189C42×C151—21no—
190C42×C151—21no—
191C42×C151—21no—
192C42×C151—21no—
193C23×C151—22no—
194C23×C151—22no—
195C23×C151—41no—
196C23×C151—41no—
197C23×C151—42no—
198C23×C151—81no—
199C23×C151—81no—
200C23×C151#12111yescharacteristic
201C23×C151#12111yescharacteristic
202C23×C151C2×#4111yescharacteristic
203Q8×C151—24no—
204Q8×C151—24no—
205Q8×C151—44no—
206Q8×C151—44no—
207Q8×C151—42no—
208Q8×C151—42no—
209D4×C151—41no—
210D4×C151—41no—
211D4×C151—42no—
212D4×C151—82no—
213D4×C151—82no—
214C2×C4×C151—22no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—24no—
226C2×C4×C151—44no—
227C2×C4×C151—44no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—41no—
232C2×C4×C151—81no—
233C2×C4×C151—81no—
234C2×C4×C151#12111yescharacteristic
235C2×C4×C151#12111yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C2×#4112yes—
239C2×C4×C151H(5,𝔽2)12yes—
240C8×C151—22no—
241C8×C151—22no—
242C8×C151—41no—
243C8×C151—42no—
244C8×C151—41no—
245C8×C151—42no—
246C22×C151—21no—
247C22×C151—21no—
248C22×C151—21no—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—21no—
253C22×C151—44no—
254C22×C151—81no—
255C22×C151—81no—
256C22×C151—81no—
257C22×C151—162no—
258C22×C151#47112yes—
259C22×C151C2×#12111yescharacteristic
260C22×C151#55112yes—
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—44no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—41no—
267C4×C151—41no—
268C4×C151—81no—
269C4×C151#52511yescharacteristic
270C4×C151#53511yescharacteristic
271C4×C151#54612yes—
272C2×C151—22no—
273C2×C151—22no—
274C2×C151—41no—
275C2×C151—161no—
276C2×C151#241111yescharacteristic
277C2×C151C2×#47111yescharacteristic
278C2×C151#306911yescharacteristic
279#24523C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#2452311yescharacteristic, direct product factor, Sylow
281#3094C2×C15111yescharacteristic
282C2×#448C2×C15111yescharacteristic
283#2924C2×C15111yescharacteristic, complemented
284C2×#419C2×C15111yescharacteristic, complemented
285#2064C2×C15112yescomplemented
286#2046C2×C15112yescomplemented
287#1977C2×C15112yescomplemented
288#1930C2×C15112yescomplemented
289#1900C2×C15111yescharacteristic
290#1855C2×C15111yescharacteristic, complemented
291#1784C2×C15111yescharacteristic, complemented
292C23×Q8C22×C15111yescharacteristic
293C22×SD16C22×C15112yes—
294C22×M16C22×C15111yescharacteristic
295C2×#121C22×C15111yescharacteristic
296C2×#117C22×C15111yescharacteristic
297#482—21no—
298#482—21no—
299#481—21no—
300#480—21no—
301#448—21no—
302#448—21no—
303#448—22no—
304#433—22no—
305#432—21no—
306#431—21no—
307C2×#108C22×C15112yes—
308#428C22×C15111yescharacteristic
309#428C22×C15111yescharacteristic
310#424C22×C15112yes—
311#419—21no—
312#419—21no—
313#419C22×C15112yes—
314#419C22×C15112yes—
315#418C22×C15111yescharacteristic
316#418C22×C15111yescharacteristic
317C2×#103—21no—
318C2×#103—21no—
319C2×#103C22×C15112yes—
320C2×#101C22×C15112yes—
321C2×#101C22×C15112yes—
322C2×#100C22×C15112yes—
323#407C22×C15111yescharacteristic
324#407C22×C15111yescharacteristic
325C2×C22⋊C8C22×C15111yescharacteristic
326#405C22×C15112yes—
327#343C22×C15112yes—
328#341C22×C15112yes—
329C22×Q8—21no—
330C22×Q8—24no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—21no—
335C22×Q8—42no—
336C22×Q8C23×C15112yes—
337C22×D4—21no—
338C22×D4C23×C15111yescharacteristic
339C23×C4—21no—
340C23×C4C23×C15111yescharacteristic
341C2×SD16—24no—
342C2×SD16—22no—
343C2×SD16—22no—
344C2×SD16—42no—
345C2×M16—21no—
346C2×M16—42no—
347C2×M16C23×C15112yes—
348C2×M16C23×C15111yescharacteristic
349C2×M16C23×C15112yes—
350C2×M16C23×C15111yescharacteristic
351C22×C8—21no—
352C22×C8C23×C15112yes—
353#121—21no—
354#121—21no—
355#121—21no—
356#121—21no—
357#117—21no—
358#117—21no—
359#117D4×C15111yescharacteristic
360#117D4×C15111yescharacteristic
361#117C23×C15111yescharacteristic
362#117C23×C15111yescharacteristic
363C2×C4⋊C4D4×C15111yescharacteristic
364C2×C4⋊C4D4×C15111yescharacteristic
365C2×C4⋊C4C23×C15111yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C42—21no—
369#108—42no—
370#107—21no—
371#107—21no—
372#106—21no—
373#106—21no—
374C4⋊C8—22no—
375C4⋊C8—22no—
376#103—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#103—22no—
381#103—22no—
382#102—21no—
383#102—21no—
384#102—21no—
385#102—21no—
386#101—24no—
387#101—42no—
388#100—42no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C15111yescharacteristic
394C22⋊C8D4×C15111yescharacteristic
395C22⋊C8D4×C15112yes—
396#97—22no—
397C4×C8—22no—
398C24—21no—
399C24#41×C15111yescharacteristic
400C2×Q8—22no—
401C2×Q8—24no—
402C2×Q8—24no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×Q8—44no—
409C2×Q8—44no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8#41×C15114yes—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—82no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—44no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4#41×C15111yescharacteristic
436C22×C4C24×C15111yescharacteristic
437SD16—44no—
438SD16—44no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—22no—
445M16—42no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—22no—
452C2×C8—42no—
453C2×C8C2×D4×C15112yes—
454C2×C8C2×D4×C15112yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4C2×D4×C15111yescharacteristic
460C4⋊C4C2×D4×C15111yescharacteristic
461C4⋊C4C2×D4×C15111yescharacteristic
462C4⋊C4C2×D4×C15111yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C23—22no—
474C23—22no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—81no—
479C23—81no—
480C23#121×C15111yescharacteristic
481C23#121×C15111yescharacteristic
482C23C2×#41×C15111yescharacteristic
483Q8—24no—
484Q8—24no—
485Q8—44no—
486Q8—44no—
487Q8—42no—
488Q8—42no—
489D4—41no—
490D4—41no—
491D4—42no—
492D4—82no—
493D4—82no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—24no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4#121×C15111yescharacteristic
515C2×C4#121×C15111yescharacteristic
516C2×C4C22×D4×C15111yescharacteristic
517C2×C4C22×D4×C15111yescharacteristic
518C2×C4C2×#41×C15112yes—
519C2×C4H(5,𝔽2)×C15112yes—
520C8—22no—
521C8—22no—
522C8—41no—
523C8—42no—
524C8—41no—
525C8—42no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—44no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—162no—
538C22#471×C15112yes—
539C22C2×#121×C15111yescharacteristic
540C22#551×C15112yes—
541C4—21no—
542C4—21no—
543C4—44no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4#525×C15111yescharacteristic
550C4#535×C15111yescharacteristic
551C4#546×C15112yes—
552C2—22no—
553C2—22no—
554C2—41no—
555C2—161no—
556C2#2411×C15111yescharacteristic
557C2C2×#471×C15111yescharacteristic
558C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2924×C151C2semidirect
4. C2×#419×C151C2semidirect
5. #2064×C151C2semidirect
6. #2046×C151C2semidirect
7. #1977×C151C2semidirect
8. #1930×C151C2semidirect
10. #1855×C151C2semidirect
11. #1784×C151C2semidirect
279. #24523C151direct (N × H)
280. C151#24523direct (N × H)
283. #2924C2×C151semidirect
284. C2×#419C2×C151semidirect
285. #2064C2×C151semidirect
286. #2046C2×C151semidirect
287. #1977C2×C151semidirect
288. #1930C2×C151semidirect
290. #1855C2×C151semidirect
291. #1784C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3094×C1512
C2×#448×C1512
#2924×C1512
C2×#419×C1512
#2064×C1512
#2046×C1512
#1977×C1512
#1930×C1512
#1900×C1512
#1855×C1512
#1784×C1512
#24523151