Finite Group Databasebeta

← C151×#23929 #50328854

Subgroups — C151×#23929 #50328854

Order 38656.

1824 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C151C212yesmaximal, complemented
2C2×#452×C151C212yesmaximal, complemented
3C2×#449×C151C212yesmaximal, complemented
4#2001×C151C211yesmaximal, characteristic, complemented
5#2000×C151C212yesmaximal, complemented
6#1999×C151C211yesmaximal, characteristic, complemented
7#1874×C151C212yesmaximal, complemented
8#1872×C151C212yesmaximal, complemented
9#1780×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2212yes—
11C22×#41×C151C2211yescharacteristic
12C22×Q16×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C22×D8×C151C2211yescharacteristic
15#537×C151—28no—
16#537×C151—28no—
17C2×C22⋊Q8×C151—22no—
18C2×C22⋊Q8×C151C2212yes—
19C2×C22⋊Q8×C151C2212yes—
20C2×#121×C151—22no—
21C2×#121×C151—22no—
22C2×#121×C151—22no—
23C2×#121×C151C2212yes—
24C2×#121×C151C2212yes—
25C22×C4⋊C4×C151C2212yes—
26#452×C151—28no—
27#449×C151—28no—
28C2×#103×C151C2212yes—
29C2×#103×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×#102×C151C2212yes—
32C2×C22⋊C8×C151C2212yes—
33C2×C22⋊C8×C151C2212yes—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36#340×C151C2211yescharacteristic
37#340×C151C2212yes—
38#340×C151C2211yescharacteristic
39C2×#41×C151—24no—
40C2×#41×C151—24no—
41C2×#41×C151—24no—
42C2×#41×C151—24no—
43C2×#41×C151—24no—
44C2×#41×C151—24no—
45C2×#41×C151—42no—
46C2×#41×C151—42no—
47C2×#41×C151—41no—
48C2×#41×C151—41no—
49C22×Q8×C151D411yescharacteristic
50C22×Q8×C151C2312yes—
51C22×D4×C151—22no—
52C22×D4×C151—22no—
53C22×D4×C151—22no—
54C22×D4×C151D412yes—
55C22×D4×C151D411yescharacteristic
56C22×D4×C151C2312yes—
57C23×C4×C151—22no—
58C23×C4×C151—22no—
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2312yes—
61C2×Q16×C151—24no—
62C2×Q16×C151—41no—
63C2×SD16×C151—24no—
64C2×SD16×C151—24no—
65C2×SD16×C151—42no—
66C2×D8×C151—24no—
67C2×D8×C151—41no—
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2312yes—
70C22×C8×C151C2311yescharacteristic
71C22⋊Q8×C151—216no—
72C22⋊Q8×C151—24no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151D418yescomplemented
76#121×C151—216no—
77#121×C151—216no—
78#121×C151—216no—
79#121×C151—24no—
80#121×C151—24no—
81#121×C151—24no—
82#121×C151D418yescomplemented
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—24no—
87C2×C4⋊C4×C151—24no—
88C2×C4⋊C4×C151C2312yes—
89C2×C4⋊C4×C151C2312yes—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—22no—
93C2×C22⋊C4×C151—22no—
94#103×C151—24no—
95#103×C151—24no—
96#102×C151—24no—
97#102×C151—24no—
98C22⋊C8×C151—24no—
99C22⋊C8×C151—24no—
100C22⋊C8×C151—41no—
101C22⋊C8×C151—41no—
102C24×C151—22no—
103C24×C151C2×D411yescharacteristic
104C24×C151C2×D412yes—
105#41×C151—44no—
106#41×C151—48no—
107#41×C151—44no—
108#41×C151—48no—
109#41×C151—48no—
110#41×C151—48no—
111#41×C151—48no—
112C2×Q8×C151—24no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—41no—
119C2×Q8×C151C2×D414yes—
120C2×D4×C151—28no—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—28no—
124C2×D4×C151—28no—
125C2×D4×C151—24no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—22no—
131C2×D4×C151—42no—
132C2×D4×C151—41no—
133C2×D4×C151—44no—
134C2×D4×C151—44no—
135C2×D4×C151—82no—
136C2×D4×C151—82no—
137C2×D4×C151—82no—
138C2×D4×C151—82no—
139C2×D4×C151C2×D414yes—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—28no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—28no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—44no—
154C22×C4×C151—44no—
155C22×C4×C151—82no—
156C22×C4×C151—82no—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D414yes—
160C22×C4×C151C2×D414yes—
161C22×C4×C151C2411yescharacteristic
162Q16×C151—44no—
163SD16×C151—48no—
164D8×C151—44no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—21no—
170C2×C8×C151—22no—
171C2×C8×C151—21no—
172C4⋊C4×C151—28no—
173C4⋊C4×C151—28no—
174C4⋊C4×C151—28no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151C2×D414yes—
178C4⋊C4×C151C2×D414yes—
179C22⋊C4×C151—28no—
180C22⋊C4×C151—28no—
181C22⋊C4×C151—28no—
182C22⋊C4×C151—28no—
183C23×C151—22no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—24no—
190C23×C151—22no—
191C23×C151—21no—
192C23×C151—21no—
193C23×C151—22no—
194C23×C151—21no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151#12014yes—
202C23×C151C22×D411yescharacteristic
203Q8×C151—24no—
204Q8×C151—24no—
205Q8×C151—44no—
206Q8×C151—42no—
207Q8×C151—42no—
208D4×C151—24no—
209D4×C151—24no—
210D4×C151—48no—
211D4×C151—44no—
212D4×C151—416no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—88no—
216D4×C151—88no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—24no—
220C2×C4×C151—24no—
221C2×C4×C151—24no—
222C2×C4×C151—24no—
223C2×C4×C151—22no—
224C2×C4×C151—24no—
225C2×C4×C151—24no—
226C2×C4×C151—24no—
227C2×C4×C151—21no—
228C2×C4×C151—416no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
236C2×C4×C151—42no—
237C2×C4×C151—41no—
238C2×C4×C151—88no—
239C2×C4×C151#12014yes—
240C2×C4×C151C22×D412yes—
241C2×C4×C151C22×D412yes—
242C2×C4×C151H(5,𝔽2)11yescharacteristic
243C2×C4×C151H(5,𝔽2)11yescharacteristic
244C8×C151—41no—
245C8×C151—42no—
246C8×C151—41no—
247C22×C151—24no—
248C22×C151—24no—
249C22×C151—24no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—44no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151—42no—
259C22×C151—44no—
260C22×C151—42no—
261C22×C151—44no—
262C22×C151—82no—
263C22×C151—82no—
264C22×C151—82no—
265C22×C151—82no—
266C22×C151C2×#12012yes—
267C22×C151#53411yescharacteristic
268C22×C151#57611yescharacteristic
269C22×C151#57712yes—
270C22×C151#57811yescharacteristic
271C4×C151—24no—
272C4×C151—41no—
273C4×C151—44no—
274C4×C151—44no—
275C4×C151—44no—
276C4×C151D4211yescharacteristic
277C4×C151D4212yes—
278C4×C151D4211yescharacteristic
279C2×C151—44no—
280C2×C151—81no—
281C2×C151—84no—
282C2×C151#240311yescharacteristic
283C2×C151#301212yes—
284C2×C151#301312yes—
285C2×C151#320311yescharacteristic
286C2×C151#320411yescharacteristic
287#23929C15111yesmaximal, characteristic, direct product factor, Sylow
288C151#2392911yescharacteristic, direct product factor, Sylow
289C2×#537C2×C15112yescomplemented
290C2×#452C2×C15112yescomplemented
291C2×#449C2×C15112yescomplemented
292#2001C2×C15111yescharacteristic, complemented
293#2000C2×C15112yescomplemented
294#1999C2×C15111yescharacteristic, complemented
295#1874C2×C15112yescomplemented
296#1872C2×C15112yescomplemented
297#1780C2×C15111yescharacteristic, complemented
298C22×#41C22×C15112yes—
299C22×#41C22×C15111yescharacteristic
300C22×Q16C22×C15111yescharacteristic
301C22×SD16C22×C15112yes—
302C22×D8C22×C15111yescharacteristic
303#537—28no—
304#537—28no—
305C2×C22⋊Q8—22no—
306C2×C22⋊Q8C22×C15112yes—
307C2×C22⋊Q8C22×C15112yes—
308C2×#121—22no—
309C2×#121—22no—
310C2×#121—22no—
311C2×#121C22×C15112yes—
312C2×#121C22×C15112yes—
313C22×C4⋊C4C22×C15112yes—
314#452—28no—
315#449—28no—
316C2×#103C22×C15112yes—
317C2×#103C22×C15112yes—
318C2×#102C22×C15112yes—
319C2×#102C22×C15112yes—
320C2×C22⋊C8C22×C15112yes—
321C2×C22⋊C8C22×C15112yes—
322C2×C22⋊C8C22×C15111yescharacteristic
323C2×C22⋊C8C22×C15111yescharacteristic
324#340C22×C15111yescharacteristic
325#340C22×C15112yes—
326#340C22×C15111yescharacteristic
327C2×#41—24no—
328C2×#41—24no—
329C2×#41—24no—
330C2×#41—24no—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—41no—
334C2×#41—41no—
335C2×#41—42no—
336C2×#41—42no—
337C22×Q8D4×C15111yescharacteristic
338C22×Q8C23×C15112yes—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4D4×C15111yescharacteristic
343C22×D4D4×C15112yes—
344C22×D4C23×C15112yes—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4C23×C15111yescharacteristic
348C23×C4C23×C15112yes—
349C2×Q16—24no—
350C2×Q16—41no—
351C2×SD16—24no—
352C2×SD16—24no—
353C2×SD16—42no—
354C2×D8—24no—
355C2×D8—41no—
356C22×C8C23×C15111yescharacteristic
357C22×C8C23×C15112yes—
358C22×C8C23×C15111yescharacteristic
359C22⋊Q8—216no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—24no—
363C22⋊Q8D4×C15118yescomplemented
364#121—216no—
365#121—216no—
366#121—216no—
367#121—24no—
368#121—24no—
369#121—24no—
370#121D4×C15118yescomplemented
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4C23×C15112yes—
377C2×C4⋊C4C23×C15112yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382#103—24no—
383#103—24no—
384#102—24no—
385#102—24no—
386C22⋊C8—24no—
387C22⋊C8—24no—
388C22⋊C8—41no—
389C22⋊C8—41no—
390C24—22no—
391C24C2×D4×C15111yescharacteristic
392C24C2×D4×C15112yes—
393#41—44no—
394#41—48no—
395#41—44no—
396#41—48no—
397#41—48no—
398#41—48no—
399#41—48no—
400C2×Q8—24no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—41no—
407C2×Q8C2×D4×C15114yes—
408C2×D4—28no—
409C2×D4—24no—
410C2×D4—24no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—24no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—82no—
424C2×D4—82no—
425C2×D4—82no—
426C2×D4—82no—
427C2×D4C2×D4×C15114yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—28no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—82no—
444C22×C4—82no—
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15112yes—
447C22×C4C2×D4×C15114yes—
448C22×C4C2×D4×C15114yes—
449C22×C4C24×C15111yescharacteristic
450Q16—44no—
451SD16—48no—
452D8—44no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—21no—
458C2×C8—22no—
459C2×C8—21no—
460C4⋊C4—28no—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4C2×D4×C15114yes—
466C4⋊C4C2×D4×C15114yes—
467C22⋊C4—28no—
468C22⋊C4—28no—
469C22⋊C4—28no—
470C22⋊C4—28no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—24no—
479C23—21no—
480C23—21no—
481C23—22no—
482C23—21no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23#120×C15114yes—
490C23C22×D4×C15111yescharacteristic
491Q8—24no—
492Q8—24no—
493Q8—44no—
494Q8—42no—
495Q8—42no—
496D4—24no—
497D4—24no—
498D4—48no—
499D4—44no—
500D4—416no—
501D4—42no—
502D4—42no—
503D4—88no—
504D4—88no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—416no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—88no—
527C2×C4#120×C15114yes—
528C2×C4C22×D4×C15112yes—
529C2×C4C22×D4×C15112yes—
530C2×C4H(5,𝔽2)×C15111yescharacteristic
531C2×C4H(5,𝔽2)×C15111yescharacteristic
532C8—41no—
533C8—42no—
534C8—41no—
535C22—24no—
536C22—24no—
537C22—24no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—42no—
547C22—44no—
548C22—42no—
549C22—44no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22—82no—
554C22C2×#120×C15112yes—
555C22#534×C15111yescharacteristic
556C22#576×C15111yescharacteristic
557C22#577×C15112yes—
558C22#578×C15111yescharacteristic
559C4—24no—
560C4—41no—
561C4—44no—
562C4—44no—
563C4—44no—
564C4D42×C15111yescharacteristic
565C4D42×C15112yes—
566C4D42×C15111yescharacteristic
567C2—44no—
568C2—81no—
569C2—84no—
570C2#2403×C15111yescharacteristic
571C2#3012×C15112yes—
572C2#3013×C15112yes—
573C2#3203×C15111yescharacteristic
574C2#3204×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#537×C151C2semidirect
2. C2×#452×C151C2semidirect
3. C2×#449×C151C2semidirect
4. #2001×C151C2semidirect
5. #2000×C151C2semidirect
6. #1999×C151C2semidirect
7. #1874×C151C2semidirect
8. #1872×C151C2semidirect
9. #1780×C151C2semidirect
75. C22⋊Q8×C151D4semidirect
82. #121×C151D4semidirect
287. #23929C151direct (N × H)
288. C151#23929direct (N × H)
289. C2×#537C2×C151semidirect
290. C2×#452C2×C151semidirect
291. C2×#449C2×C151semidirect
292. #2001C2×C151semidirect
293. #2000C2×C151semidirect
294. #1999C2×C151semidirect
295. #1874C2×C151semidirect
296. #1872C2×C151semidirect
297. #1780C2×C151semidirect
363. C22⋊Q8D4×C151semidirect
370. #121D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1512
C2×#452×C1512
C2×#449×C1512
#2001×C1512
#2000×C1512
#1999×C1512
#1874×C1512
#1872×C1512
#1780×C1512
#23929151