Finite Group Databasebeta

← C151×#23570 #50328495

Subgroups — C151×#23570 #50328495

Order 38656.

1436 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C212yesmaximal, complemented
3C4×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
4#2058×C151C211yesmaximal, characteristic, complemented
5#2041×C151C211yesmaximal, characteristic, complemented
6#2034×C151C212yesmaximal, complemented
7#2024×C151C211yesmaximal, characteristic, complemented
8#2014×C151C211yesmaximal, characteristic, complemented
9#2000×C151C212yesmaximal, complemented
10C4×#102×C151C212yesmaximal, complemented
11C4×C22⋊C8×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151—21no—
13C22×SD16×C151C2212yes—
14#532×C151—28no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#127×C151C2211yescharacteristic
17C2×#124×C151—21no—
18C2×C22⋊Q8×C151C2211yescharacteristic
19C2×#121×C151—21no—
20C2×#121×C151C2212yes—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151C2212yes—
24C22×C42×C151C2211yescharacteristic
25C4×SD16×C151—28no—
26C2×#106×C151C2212yes—
27C2×#103×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×#102×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×C22⋊C8×C151C2212yes—
32C2×C4×C8×C151C2212yes—
33#391×C151C2211yescharacteristic
34#389×C151C2211yescharacteristic
35#387×C151—21no—
36#385×C151—21no—
37#380×C151C2211yescharacteristic
38C4×C4⋊C4×C151—21no—
39C4×C4⋊C4×C151C2211yescharacteristic
40C4×C22⋊C4×C151—21no—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#336×C151C2211yescharacteristic
44#336×C151C2211yescharacteristic
45C2×#41×C151—28no—
46C2×#41×C151—44no—
47C2×#41×C151—44no—
48C22×Q8×C151—21no—
49C22×Q8×C151C2311yescharacteristic
50C22×D4×C151—21no—
51C22×D4×C151—21no—
52C22×D4×C151—22no—
53C22×D4×C151C2312yes—
54C23×C4×C151—22no—
55C23×C4×C151D411yescharacteristic
56C23×C4×C151D411yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C2×SD16×C151—24no—
59C2×SD16×C151—24no—
60C2×SD16×C151—24no—
61C22×C8×C151C2312yes—
62C22×C8×C151C2312yes—
63C4⋊Q8×C151—24no—
64#127×C151—24no—
65#124×C151—28no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151—22no—
68#121×C151—28no—
69#121×C151—24no—
70#121×C151—24no—
71C4×Q8×C151—24no—
72C4×D4×C151—28no—
73C4×D4×C151—24no—
74C4×D4×C151D418yes—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C42×C151—24no—
88C2×C42×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151D411yescharacteristic
91C2×C42×C151D411yescharacteristic
92C2×C42×C151C2311yescharacteristic
93C2×C42×C151C2311yescharacteristic
94#106×C151—24no—
95#103×C151—24no—
96#102×C151—24no—
97#102×C151—24no—
98#102×C151—24no—
99C22⋊C8×C151—24no—
100C4×C8×C151—24no—
101#95×C151—21no—
102#95×C151—21no—
103#95×C151—21no—
104#95×C151—21no—
105#95×C151—21no—
106C24×C151—22no—
107C24×C151C2×D411yescharacteristic
108#41×C151—432no—
109C2×Q8×C151—24no—
110C2×Q8×C151—21no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—42no—
114C2×Q8×C151—42no—
115C2×Q8×C151#4112yescomplemented
116C2×D4×C151—24no—
117C2×D4×C151—28no—
118C2×D4×C151—24no—
119C2×D4×C151—22no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—42no—
125C2×D4×C151—42no—
126C2×D4×C151—44no—
127C2×D4×C151—44no—
128C2×D4×C151—42no—
129C2×D4×C151—42no—
130C2×D4×C151C2×D414yes—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—28no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—41no—
146C22×C4×C151—44no—
147C22×C4×C151—44no—
148C22×C4×C151SD1614yescomplemented
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2411yescharacteristic
155SD16×C151—216no—
156C2×C8×C151—22no—
157C2×C8×C151—22no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151#4114yescomplemented
162C4⋊C4×C151—24no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—42no—
169C4⋊C4×C151—42no—
170C4⋊C4×C151C2×D414yes—
171C4⋊C4×C151#4112yescomplemented
172C22⋊C4×C151—28no—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—28no—
175C22⋊C4×C151—42no—
176C42×C151—22no—
177C42×C151—22no—
178C42×C151—22no—
179C42×C151—42no—
180C42×C151—42no—
181C42×C151C2×D414yes—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151—21no—
186C23×C151—21no—
187C23×C151—21no—
188C23×C151—24no—
189C23×C151—42no—
190C23×C151—42no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—42no—
195C23×C151C2×SD1612yes—
196C23×C151C22×D411yescharacteristic
197Q8×C151—24no—
198Q8×C151—48no—
199Q8×C151—42no—
200D4×C151—24no—
201D4×C151—24no—
202D4×C151—48no—
203D4×C151—48no—
204D4×C151—416no—
205D4×C151—42no—
206D4×C151—42no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—28no—
214C2×C4×C151—24no—
215C2×C4×C151—21no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—44no—
221C2×C4×C151—41no—
222C2×C4×C151—41no—
223C2×C4×C151—42no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—416no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151#12012yes—
237C2×C4×C151#12012yes—
238C2×C4×C151C2×SD1612yes—
239C2×C4×C151C2×SD1612yes—
240C2×C4×C151#13512yes—
241C2×C4×C151AGL(1,ℤ/8)12yes—
242C2×C4×C151C22×D412yes—
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151C2×#4112yes—
245C2×C4×C151C2×#4111yescharacteristic
246C8×C151—24no—
247C8×C151—42no—
248C22×C151—22no—
249C22×C151—22no—
250C22×C151—22no—
251C22×C151—41no—
252C22×C151—41no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151—44no—
256C22×C151—44no—
257C22×C151—44no—
258C22×C151—82no—
259C22×C151—82no—
260C22×C151—82no—
261C22×C151—82no—
262C22×C151C2×#12011yescharacteristic
263C22×C151#52511yescharacteristic
264C22×C151#53211yescharacteristic
265C22×C151C22×SD1611yescharacteristic
266C22×C151C2×#13511yescharacteristic
267C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
268C22×C151#57511yescharacteristic
269C4×C151—22no—
270C4×C151—22no—
271C4×C151—22no—
272C4×C151—42no—
273C4×C151—41no—
274C4×C151—42no—
275C4×C151—44no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151#45014yes—
279C4×C151#52512yes—
280C4×C151#53212yes—
281C2×C151—42no—
282C2×C151—84no—
283C2×C151#238811yescharacteristic
284C2×C151C2×#45011yescharacteristic
285C2×C151#300211yescharacteristic
286C2×C151#310311yescharacteristic
287C2×C151#310611yescharacteristic
288C2×C151#316711yescharacteristic
289C2×C151#317111yescharacteristic
290#23570C15111yesmaximal, characteristic, direct product factor, Sylow
291C151#2357011yescharacteristic, direct product factor, Sylow
292C2×#532C2×C15111yescharacteristic
293C2×C4×SD16C2×C15112yescomplemented
294C4×C22⋊Q8C2×C15111yescharacteristic, complemented
295#2058C2×C15111yescharacteristic, complemented
296#2041C2×C15111yescharacteristic, complemented
297#2034C2×C15112yescomplemented
298#2024C2×C15111yescharacteristic, complemented
299#2014C2×C15111yescharacteristic, complemented
300#2000C2×C15112yescomplemented
301C4×#102C2×C15112yescomplemented
302C4×C22⋊C8C2×C15111yescharacteristic, complemented
303C22×#41—21no—
304C22×SD16C22×C15112yes—
305#532—28no—
306C2×C4⋊Q8C22×C15111yescharacteristic
307C2×#127C22×C15111yescharacteristic
308C2×#124—21no—
309C2×C22⋊Q8C22×C15111yescharacteristic
310C2×#121—21no—
311C2×#121C22×C15112yes—
312C2×C4×Q8C22×C15111yescharacteristic
313C2×C4×D4—21no—
314C2×C4×D4C22×C15112yes—
315C22×C42C22×C15111yescharacteristic
316C4×SD16—28no—
317C2×#106C22×C15112yes—
318C2×#103C22×C15112yes—
319C2×#102C22×C15112yes—
320C2×#102C22×C15112yes—
321C2×#102C22×C15112yes—
322C2×C22⋊C8C22×C15112yes—
323C2×C4×C8C22×C15112yes—
324#391C22×C15111yescharacteristic
325#389C22×C15111yescharacteristic
326#387—21no—
327#385—21no—
328#380C22×C15111yescharacteristic
329C4×C4⋊C4—21no—
330C4×C4⋊C4C22×C15111yescharacteristic
331C4×C22⋊C4—21no—
332#340C22×C15112yes—
333#340C22×C15112yes—
334#336C22×C15111yescharacteristic
335#336C22×C15111yescharacteristic
336C2×#41—28no—
337C2×#41—44no—
338C2×#41—44no—
339C22×Q8—21no—
340C22×Q8C23×C15111yescharacteristic
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4C23×C15112yes—
345C23×C4—22no—
346C23×C4D4×C15111yescharacteristic
347C23×C4D4×C15111yescharacteristic
348C23×C4C23×C15111yescharacteristic
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16—24no—
352C22×C8C23×C15112yes—
353C22×C8C23×C15112yes—
354C4⋊Q8—24no—
355#127—24no—
356#124—28no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359#121—28no—
360#121—24no—
361#121—24no—
362C4×Q8—24no—
363C4×D4—28no—
364C4×D4—24no—
365C4×D4D4×C15118yes—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C23×C15111yescharacteristic
371C2×C4⋊C4C23×C15111yescharacteristic
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C4⋊C4C23×C15112yes—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C42—24no—
379C2×C42—21no—
380C2×C42—21no—
381C2×C42D4×C15111yescharacteristic
382C2×C42D4×C15111yescharacteristic
383C2×C42C23×C15111yescharacteristic
384C2×C42C23×C15111yescharacteristic
385#106—24no—
386#103—24no—
387#102—24no—
388#102—24no—
389#102—24no—
390C22⋊C8—24no—
391C4×C8—24no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397C24—22no—
398C24C2×D4×C15111yescharacteristic
399#41—432no—
400C2×Q8—24no—
401C2×Q8—21no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8#41×C15112yescomplemented
407C2×D4—24no—
408C2×D4—28no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4C2×D4×C15114yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—44no—
438C22×C4—44no—
439C22×C4SD16×C15114yescomplemented
440C22×C4C2×D4×C15111yescharacteristic
441C22×C4C2×D4×C15111yescharacteristic
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445C22×C4C24×C15111yescharacteristic
446SD16—216no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8#41×C15114yescomplemented
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4C2×D4×C15114yes—
462C4⋊C4#41×C15112yescomplemented
463C22⋊C4—28no—
464C22⋊C4—24no—
465C22⋊C4—28no—
466C22⋊C4—42no—
467C42—22no—
468C42—22no—
469C42—22no—
470C42—42no—
471C42—42no—
472C42C2×D4×C15114yes—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23C2×SD16×C15112yes—
487C23C22×D4×C15111yescharacteristic
488Q8—24no—
489Q8—48no—
490Q8—42no—
491D4—24no—
492D4—24no—
493D4—48no—
494D4—48no—
495D4—416no—
496D4—42no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—28no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—44no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—416no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4#120×C15112yes—
528C2×C4#120×C15112yes—
529C2×C4C2×SD16×C15112yes—
530C2×C4C2×SD16×C15112yes—
531C2×C4#135×C15112yes—
532C2×C4AGL(1,ℤ/8)×C15112yes—
533C2×C4C22×D4×C15112yes—
534C2×C4C2×#41×C15111yescharacteristic
535C2×C4C2×#41×C15112yes—
536C2×C4C2×#41×C15111yescharacteristic
537C8—24no—
538C8—42no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—82no—
550C22—82no—
551C22—82no—
552C22—82no—
553C22C2×#120×C15111yescharacteristic
554C22#525×C15111yescharacteristic
555C22#532×C15111yescharacteristic
556C22C22×SD16×C15111yescharacteristic
557C22C2×#135×C15111yescharacteristic
558C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
559C22#575×C15111yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—42no—
564C4—41no—
565C4—42no—
566C4—44no—
567C4—81no—
568C4—81no—
569C4#450×C15114yes—
570C4#525×C15112yes—
571C4#532×C15112yes—
572C2—42no—
573C2—84no—
574C2#2388×C15111yescharacteristic
575C2C2×#450×C15111yescharacteristic
576C2#3002×C15111yescharacteristic
577C2#3103×C15111yescharacteristic
578C2#3106×C15111yescharacteristic
579C2#3167×C15111yescharacteristic
580C2#3171×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
socleC23×C151C22×D4
prime radicalC2×#532×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C151C2semidirect
3. C4×C22⋊Q8×C151C2semidirect
4. #2058×C151C2semidirect
5. #2041×C151C2semidirect
6. #2034×C151C2semidirect
7. #2024×C151C2semidirect
8. #2014×C151C2semidirect
9. #2000×C151C2semidirect
10. C4×#102×C151C2semidirect
11. C4×C22⋊C8×C151C2semidirect
115. C2×Q8×C151#41semidirect
148. C22×C4×C151SD16semidirect
161. C2×C8×C151#41semidirect
171. C4⋊C4×C151#41semidirect
290. #23570C151direct (N × H)
291. C151#23570direct (N × H)
293. C2×C4×SD16C2×C151semidirect
294. C4×C22⋊Q8C2×C151semidirect
295. #2058C2×C151semidirect
296. #2041C2×C151semidirect
297. #2034C2×C151semidirect
298. #2024C2×C151semidirect
299. #2014C2×C151semidirect
300. #2000C2×C151semidirect
301. C4×#102C2×C151semidirect
302. C4×C22⋊C8C2×C151semidirect
406. C2×Q8#41×C151semidirect
439. C22×C4SD16×C151semidirect
452. C2×C8#41×C151semidirect
462. C4⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1512
C2×C4×SD16×C1512
C4×C22⋊Q8×C1512
#2058×C1512
#2041×C1512
#2034×C1512
#2024×C1512
#2014×C1512
#2000×C1512
C4×#102×C1512
C4×C22⋊C8×C1512
#23570151