Finite Group Databasebeta

← C151×#23480 #50328405

Subgroups — C151×#23480 #50328405

Order 38656.

1902 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4C2×#418×C151C211yesmaximal, characteristic, complemented
5C2×#407×C151C211yesmaximal, characteristic, complemented
6#2280×C151C211yesmaximal, characteristic, complemented
7#2034×C151C214yesmaximal, complemented
8#2033×C151C214yesmaximal, complemented
9#1736×C151C211yesmaximal, characteristic, complemented
10C23×D4×C151—21no—
11C23×D4×C151C2211yescharacteristic
12C24×C4×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C22×M16×C151C2211yescharacteristic
15C2×#121×C151—24no—
16C2×#121×C151—22no—
17C2×#121×C151—24no—
18C2×#121×C151C2214yes—
19C2×#117×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151—21no—
23#428×C151—24no—
24C2×#107×C151C2212yescomplemented
25C2×#106×C151C2212yescomplemented
26#418×C151—24no—
27#418×C151—24no—
28C2×#102×C151C2212yescomplemented
29C2×#102×C151C2214yescomplemented
30C2×#102×C151C2212yescomplemented
31#407×C151—24no—
32C2×C22⋊C8×C151C2214yescomplemented
33#381×C151—21no—
34#380×C151C2212yescomplemented
35#380×C151C2212yescomplemented
36#379×C151—21no—
37C4×C22⋊C4×C151—22no—
38#340×C151C2214yescomplemented
39C25×C151—21no—
40C25×C151D411yescharacteristic
41C22×D4×C151—28no—
42C22×D4×C151—22no—
43C22×D4×C151—21no—
44C22×D4×C151—24no—
45C22×D4×C151—22no—
46C22×D4×C151—22no—
47C22×D4×C151—22no—
48C22×D4×C151—22no—
49C22×D4×C151—48no—
50C22×D4×C151D414yes—
51C22×D4×C151C2312yes—
52C23×C4×C151—22no—
53C23×C4×C151—22no—
54C23×C4×C151—22no—
55C23×C4×C151—22no—
56C23×C4×C151—22no—
57C23×C4×C151—22no—
58C23×C4×C151—21no—
59C23×C4×C151D412yes—
60C23×C4×C151D411yescharacteristic
61C23×C4×C151C2312yes—
62C23×C4×C151C2311yescharacteristic
63C2×M16×C151—22no—
64C2×M16×C151—22no—
65C2×M16×C151—22no—
66C2×M16×C151—22no—
67C2×M16×C151—22no—
68C2×M16×C151D414yescomplemented
69C22×C8×C151C2312yes—
70C22×C8×C151C2312yes—
71#121×C151—216no—
72#121×C151—28no—
73#121×C151—28no—
74#117×C151—22no—
75#117×C151—22no—
76#117×C151—22no—
77#117×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151D414yes—
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C22⋊C4×C151—28no—
86C2×C22⋊C4×C151—24no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—21no—
91C2×C42×C151—21no—
92C2×C42×C151—21no—
93#107×C151—24no—
94#106×C151—24no—
95#102×C151—24no—
96#102×C151—24no—
97#102×C151—28no—
98C22⋊C8×C151—28no—
99#95×C151—22no—
100#95×C151—22no—
101C24×C151—22no—
102C24×C151—24no—
103C24×C151—24no—
104C24×C151—22no—
105C24×C151—22no—
106C24×C151—22no—
107C24×C151—42no—
108C24×C151—44no—
109C24×C151—44no—
110C24×C151—42no—
111C24×C151—42no—
112C24×C151C2×D412yes—
113C24×C151C2×D411yescharacteristic
114C2×D4×C151—216no—
115C2×D4×C151—24no—
116C2×D4×C151—28no—
117C2×D4×C151—28no—
118C2×D4×C151—22no—
119C2×D4×C151—22no—
120C2×D4×C151—22no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—432no—
124C2×D4×C151—48no—
125C2×D4×C151—48no—
126C2×D4×C151—44no—
127C2×D4×C151—42no—
128C2×D4×C151—42no—
129C2×D4×C151—44no—
130C2×D4×C151C2×D414yes—
131C22×C4×C151—22no—
132C22×C4×C151—24no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—24no—
137C22×C4×C151—24no—
138C22×C4×C151—24no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—22no—
148C22×C4×C151—44no—
149C22×C4×C151—44no—
150C22×C4×C151—44no—
151C22×C4×C151—44no—
152C22×C4×C151—44no—
153C22×C4×C151C2×D412yes—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D412yes—
158C22×C4×C151#4112yes—
159C22×C4×C151#4112yes—
160C22×C4×C151#4112yes—
161C22×C4×C151C2411yescharacteristic
162M16×C151—28no—
163M16×C151—44no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151C2×D414yescomplemented
170C4⋊C4×C151—24no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151C2×D414yes—
179C22⋊C4×C151—216no—
180C22⋊C4×C151—44no—
181C22⋊C4×C151—42no—
182C22⋊C4×C151—42no—
183C22⋊C4×C151—44no—
184C42×C151—42no—
185C42×C151—42no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—28no—
189C23×C151—22no—
190C23×C151—22no—
191C23×C151—22no—
192C23×C151—22no—
193C23×C151—22no—
194C23×C151—22no—
195C23×C151—24no—
196C23×C151—48no—
197C23×C151—48no—
198C23×C151—44no—
199C23×C151—48no—
200C23×C151—48no—
201C23×C151—44no—
202C23×C151—42no—
203C23×C151—42no—
204C23×C151—44no—
205C23×C151—44no—
206C23×C151—48no—
207C23×C151—88no—
208C23×C151—88no—
209C23×C151#12012yes—
210C23×C151#12112yes—
211C23×C151#12312yes—
212C23×C151AGL(1,ℤ/8)14yes—
213C23×C151C22×D411yescharacteristic
214D4×C151—24no—
215D4×C151—24no—
216D4×C151—432no—
217D4×C151—42no—
218D4×C151—42no—
219D4×C151—48no—
220C2×C4×C151—22no—
221C2×C4×C151—24no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—48no—
225C2×C4×C151—44no—
226C2×C4×C151—44no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—48no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151#12012yes—
240C2×C4×C151#12114yes—
241C2×C4×C151#12114yes—
242C2×C4×C151#12112yes—
243C2×C4×C151#12314yes—
244C2×C4×C151#12312yes—
245C2×C4×C151#12414yes—
246C2×C4×C151C22×D411yescharacteristic
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151C22×D411yescharacteristic
249C2×C4×C151C2×#4111yescharacteristic
250C2×C4×C151C2×#4111yescharacteristic
251C2×C4×C151C2×#4111yescharacteristic
252C8×C151—24no—
253C8×C151—42no—
254C22×C151—24no—
255C22×C151—22no—
256C22×C151—22no—
257C22×C151—24no—
258C22×C151—24no—
259C22×C151—24no—
260C22×C151—24no—
261C22×C151—416no—
262C22×C151—42no—
263C22×C151—42no—
264C22×C151—42no—
265C22×C151—42no—
266C22×C151—44no—
267C22×C151—44no—
268C22×C151—44no—
269C22×C151—816no—
270C22×C151—84no—
271C22×C151—84no—
272C22×C151#39414yes—
273C22×C151C2×#12011yescharacteristic
274C22×C151C2×#12111yescharacteristic
275C22×C151C2×#12311yescharacteristic
276C22×C151C2×AGL(1,ℤ/8)12yes—
277C22×C151#57512yes—
278C4×C151—42no—
279C4×C151—44no—
280C4×C151—81no—
281C4×C151—81no—
282C4×C151—82no—
283C4×C151#39414yes—
284C4×C151C2×#12111yescharacteristic
285C4×C151C2×#12111yescharacteristic
286C4×C151C2×#12311yescharacteristic
287C4×C151C2×#12411yescharacteristic
288C2×C151—24no—
289C2×C151—44no—
290C2×C151—84no—
291C2×C151C2×#39411yescharacteristic
292C2×C151#300311yescharacteristic
293C2×C151#300511yescharacteristic
294C2×C151#305512yes—
295C2×C151#309412yes—
296#23480C15111yesmaximal, characteristic, direct product factor, Sylow
297C151#2348011yescharacteristic, direct product factor, Sylow
298C22×#121C2×C15111yescharacteristic
299C2×#428C2×C15111yescharacteristic, complemented
300C2×#418C2×C15111yescharacteristic, complemented
301C2×#418C2×C15111yescharacteristic, complemented
302C2×#407C2×C15111yescharacteristic, complemented
303#2280C2×C15111yescharacteristic, complemented
304#2034C2×C15114yescomplemented
305#2033C2×C15114yescomplemented
306#1736C2×C15111yescharacteristic, complemented
307C23×D4—21no—
308C23×D4C22×C15111yescharacteristic
309C24×C4C22×C15111yescharacteristic
310C22×M16C22×C15111yescharacteristic
311C22×M16C22×C15111yescharacteristic
312C2×#121—24no—
313C2×#121—22no—
314C2×#121—24no—
315C2×#121C22×C15114yes—
316C2×#117C22×C15111yescharacteristic
317C2×#117C22×C15111yescharacteristic
318C22×C4⋊C4C22×C15111yescharacteristic
319C22×C22⋊C4—21no—
320#428—24no—
321C2×#107C22×C15112yescomplemented
322C2×#106C22×C15112yescomplemented
323#418—24no—
324#418—24no—
325C2×#102C22×C15112yescomplemented
326C2×#102C22×C15114yescomplemented
327C2×#102C22×C15112yescomplemented
328#407—24no—
329C2×C22⋊C8C22×C15114yescomplemented
330#381—21no—
331#380C22×C15112yescomplemented
332#380C22×C15112yescomplemented
333#379—21no—
334C4×C22⋊C4—22no—
335#340C22×C15114yescomplemented
336C25—21no—
337C25D4×C15111yescharacteristic
338C22×D4—28no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4—22no—
346C22×D4—48no—
347C22×D4D4×C15114yes—
348C22×D4C23×C15112yes—
349C23×C4—21no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4D4×C15111yescharacteristic
357C23×C4D4×C15112yes—
358C23×C4C23×C15112yes—
359C23×C4C23×C15111yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—22no—
365C2×M16D4×C15114yescomplemented
366C22×C8C23×C15112yes—
367C22×C8C23×C15112yes—
368#121—216no—
369#121—28no—
370#121—28no—
371#117—22no—
372#117—22no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4D4×C15114yes—
378C2×C4⋊C4C23×C15112yes—
379C2×C4⋊C4C23×C15111yescharacteristic
380C2×C4⋊C4C23×C15111yescharacteristic
381C2×C4⋊C4C23×C15112yes—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C42—21no—
389C2×C42—21no—
390#107—24no—
391#106—24no—
392#102—24no—
393#102—24no—
394#102—28no—
395C22⋊C8—28no—
396#95—22no—
397#95—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—42no—
405C24—44no—
406C24—44no—
407C24—42no—
408C24—42no—
409C24C2×D4×C15112yes—
410C24C2×D4×C15111yescharacteristic
411C2×D4—216no—
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—432no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4—44no—
427C2×D4C2×D4×C15114yes—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4C2×D4×C15112yes—
451C22×C4C2×D4×C15111yescharacteristic
452C22×C4C2×D4×C15112yes—
453C22×C4C2×D4×C15112yes—
454C22×C4C2×D4×C15112yes—
455C22×C4#41×C15112yes—
456C22×C4#41×C15112yes—
457C22×C4#41×C15112yes—
458C22×C4C24×C15111yescharacteristic
459M16—28no—
460M16—44no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8C2×D4×C15114yescomplemented
467C4⋊C4—24no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4C2×D4×C15114yes—
476C22⋊C4—216no—
477C22⋊C4—44no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—44no—
481C42—42no—
482C42—42no—
483C23—22no—
484C23—22no—
485C23—28no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—48no—
494C23—48no—
495C23—44no—
496C23—48no—
497C23—48no—
498C23—44no—
499C23—48no—
500C23—42no—
501C23—42no—
502C23—44no—
503C23—44no—
504C23—88no—
505C23—88no—
506C23#120×C15112yes—
507C23#121×C15112yes—
508C23#123×C15112yes—
509C23AGL(1,ℤ/8)×C15114yes—
510C23C22×D4×C15111yescharacteristic
511D4—24no—
512D4—24no—
513D4—432no—
514D4—48no—
515D4—42no—
516D4—42no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—48no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4#120×C15112yes—
537C2×C4#121×C15112yes—
538C2×C4#121×C15114yes—
539C2×C4#121×C15114yes—
540C2×C4#123×C15112yes—
541C2×C4#123×C15114yes—
542C2×C4#124×C15114yes—
543C2×C4C22×D4×C15111yescharacteristic
544C2×C4C22×D4×C15111yescharacteristic
545C2×C4C22×D4×C15111yescharacteristic
546C2×C4C2×#41×C15111yescharacteristic
547C2×C4C2×#41×C15111yescharacteristic
548C2×C4C2×#41×C15111yescharacteristic
549C8—24no—
550C8—42no—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—24no—
557C22—24no—
558C22—416no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—816no—
567C22—84no—
568C22—84no—
569C22#394×C15114yes—
570C22C2×#120×C15111yescharacteristic
571C22C2×#121×C15111yescharacteristic
572C22C2×#123×C15111yescharacteristic
573C22C2×AGL(1,ℤ/8)×C15112yes—
574C22#575×C15112yes—
575C4—42no—
576C4—44no—
577C4—81no—
578C4—81no—
579C4—82no—
580C4#394×C15114yes—
581C4C2×#121×C15111yescharacteristic
582C4C2×#121×C15111yescharacteristic
583C4C2×#123×C15111yescharacteristic
584C4C2×#124×C15111yescharacteristic
585C2—24no—
586C2—44no—
587C2—84no—
588C2C2×#394×C15111yescharacteristic
589C2#3003×C15111yescharacteristic
590C2#3005×C15111yescharacteristic
591C2#3055×C15112yes—
592C2#3094×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#121×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C151C2semidirect
3. C2×#418×C151C2semidirect
4. C2×#418×C151C2semidirect
5. C2×#407×C151C2semidirect
6. #2280×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1736×C151C2semidirect
24. C2×#107×C151C22semidirect
25. C2×#106×C151C22semidirect
28. C2×#102×C151C22semidirect
29. C2×#102×C151C22semidirect
30. C2×#102×C151C22semidirect
32. C2×C22⋊C8×C151C22semidirect
34. #380×C151C22semidirect
35. #380×C151C22semidirect
38. #340×C151C22semidirect
68. C2×M16×C151D4semidirect
169. C2×C8×C151C2×D4semidirect
296. #23480C151direct (N × H)
297. C151#23480direct (N × H)
299. C2×#428C2×C151semidirect
300. C2×#418C2×C151semidirect
301. C2×#418C2×C151semidirect
302. C2×#407C2×C151semidirect
303. #2280C2×C151semidirect
304. #2034C2×C151semidirect
305. #2033C2×C151semidirect
306. #1736C2×C151semidirect
321. C2×#107C22×C151semidirect
322. C2×#106C22×C151semidirect
325. C2×#102C22×C151semidirect
326. C2×#102C22×C151semidirect
327. C2×#102C22×C151semidirect
329. C2×C22⋊C8C22×C151semidirect
331. #380C22×C151semidirect
332. #380C22×C151semidirect
335. #340C22×C151semidirect
365. C2×M16D4×C151semidirect
466. C2×C8C2×D4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1512
C2×#428×C1512
C2×#418×C1512
C2×#407×C1512
#2280×C1512
#2034×C1512
#2033×C1512
#1736×C1512
#23480151