Finite Group Databasebeta

← C151×#20944 #50325869

Subgroups — C151×#20944 #50325869

Order 38656.

1702 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic
2#3428×C151C211yesmaximal, characteristic
3C2×#421×C151C211yesmaximal, characteristic
4C2×#419×C151C211yesmaximal, characteristic, complemented
5#2310×C151C211yesmaximal, characteristic, complemented
6#1882×C151C218yesmaximal, complemented
7#1742×C151C211yesmaximal, characteristic, complemented
8#1733×C151C211yesmaximal, characteristic, complemented
9C22×#41×C151C2211yescharacteristic
10C23×Q8×C151C2211yescharacteristic
11C2×#137×C151—24no—
12C2×#137×C151—22no—
13C2×#137×C151C418yescomplemented
14C2×#137×C151C2214yes—
15C22×Q16×C151—21no—
16C22×SD16×C151—21no—
17C22×M16×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19#520×C151—22no—
20#520×C151C2214yes—
21#519×C151—21no—
22#518×C151—21no—
23#518×C151—22no—
24C4×#41×C151—22no—
25C4×#41×C151—22no—
26C2×#117×C151—22no—
27C2×#117×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C2×#117×C151C2211yescharacteristic
30#421×C151—24no—
31C2×#104×C151C2214yes—
32#419×C151—22no—
33#419×C151C2214yescomplemented
34C2×#103×C151—22no—
35#391×C151—22no—
36#391×C151C2214yescomplemented
37#381×C151—22no—
38#343×C151C2214yescomplemented
39#339×C151C2214yescomplemented
40C2×#41×C151—21no—
41C2×#41×C151—21no—
42C2×#41×C151—22no—
43C2×#41×C151—22no—
44C2×#41×C151C2×C414yes—
45C2×#41×C151D414yes—
46C2×#41×C151D412yes—
47C2×#41×C151C2312yes—
48C22×Q8×C151—21no—
49C22×Q8×C151—21no—
50C22×Q8×C151—21no—
51C22×Q8×C151—22no—
52C22×Q8×C151—21no—
53C22×Q8×C151—22no—
54C22×Q8×C151—21no—
55C22×Q8×C151—22no—
56C22×Q8×C151C2×C414yescomplemented
57C22×Q8×C151D411yescharacteristic
58C22×Q8×C151C2312yes—
59C22×D4×C151—21no—
60C22×D4×C151D411yescharacteristic
61C23×C4×C151—21no—
62C23×C4×C151—21no—
63C23×C4×C151C2311yescharacteristic
64#137×C151—216no—
65#137×C151—28no—
66#137×C151C2×C4116yescomplemented
67C2×Q16×C151—28no—
68C2×Q16×C151—24no—
69C2×SD16×C151—28no—
70C2×SD16×C151—24no—
71C2×M16×C151—22no—
72C2×M16×C151—21no—
73C2×M16×C151—21no—
74C2×M16×C151—22no—
75C2×M16×C151—22no—
76C2×M16×C151C2×C414yescomplemented
77C2×M16×C151C2312yes—
78C2×M16×C151C2312yes—
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C4×Q8×C151—24no—
82C4×Q8×C151—24no—
83C4×D4×C151—28no—
84C4×D4×C151—24no—
85C4×D4×C151—24no—
86C4×D4×C151—28no—
87#117×C151—24no—
88#117×C151—24no—
89#117×C151—21no—
90#117×C151—21no—
91#117×C151—21no—
92#117×C151—21no—
93#117×C151—21no—
94#117×C151—21no—
95#117×C151—24no—
96#117×C151—22no—
97#117×C151—22no—
98#117×C151D412yes—
99#117×C151C2312yes—
100C2×C4⋊C4×C151—24no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151D412yes—
103C2×C4⋊C4×C151C2312yes—
104C2×C22⋊C4×C151—24no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151D412yes—
108C2×C42×C151—24no—
109C2×C42×C151—21no—
110C2×C42×C151D412yes—
111C2×C42×C151C2312yes—
112#104×C151—28no—
113#103×C151—28no—
114#95×C151—28no—
115C24×C151—21no—
116C24×C151C2×D411yescharacteristic
117#41×C151—24no—
118#41×C151—24no—
119#41×C151—24no—
120#41×C151—24no—
121#41×C151—24no—
122#41×C151—22no—
123#41×C151—22no—
124#41×C151C22⋊C418yes—
125#41×C151C22×C414yes—
126#41×C151C2×D414yes—
127C2×Q8×C151—24no—
128C2×Q8×C151—21no—
129C2×Q8×C151—22no—
130C2×Q8×C151—22no—
131C2×Q8×C151—24no—
132C2×Q8×C151—24no—
133C2×Q8×C151—24no—
134C2×Q8×C151—24no—
135C2×Q8×C151—22no—
136C2×Q8×C151—22no—
137C2×Q8×C151—22no—
138C2×Q8×C151—22no—
139C2×Q8×C151—41no—
140C2×Q8×C151—41no—
141C2×Q8×C151—42no—
142C2×Q8×C151—42no—
143C2×Q8×C151—42no—
144C2×Q8×C151—42no—
145C2×Q8×C151—42no—
146C2×Q8×C151C22⋊C414yes—
147C2×Q8×C151C22×C414yes—
148C2×Q8×C151C2×D412yes—
149C2×D4×C151—24no—
150C2×D4×C151—22no—
151C2×D4×C151—24no—
152C2×D4×C151—22no—
153C2×D4×C151—21no—
154C2×D4×C151—22no—
155C2×D4×C151C22⋊C414yes—
156C2×D4×C151C2×D412yes—
157C22×C4×C151—21no—
158C22×C4×C151—24no—
159C22×C4×C151—22no—
160C22×C4×C151—24no—
161C22×C4×C151—22no—
162C22×C4×C151—24no—
163C22×C4×C151—22no—
164C22×C4×C151—28no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—41no—
168C22×C4×C151—41no—
169C22×C4×C151—42no—
170C22×C4×C151C22×C412yes—
171C22×C4×C151C2×D414yes—
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D412yes—
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151#4112yes—
179C22×C4×C151#4112yes—
180C22×C4×C151C2411yescharacteristic
181Q16×C151—216no—
182SD16×C151—216no—
183M16×C151—24no—
184M16×C151—22no—
185M16×C151—22no—
186M16×C151—22no—
187M16×C151—42no—
188M16×C151C22×C414yes—
189C2×C8×C151—24no—
190C2×C8×C151—22no—
191C2×C8×C151—22no—
192C2×C8×C151—42no—
193C4⋊C4×C151—28no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—42no—
198C4⋊C4×C151C2×D414yes—
199C22⋊C4×C151—28no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—22no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—42no—
205C42×C151—28no—
206C42×C151—22no—
207C42×C151—22no—
208C42×C151—22no—
209C42×C151—22no—
210C42×C151—22no—
211C42×C151—22no—
212C23×C151—22no—
213C23×C151—24no—
214C23×C151—42no—
215C23×C151—82no—
216C23×C151C4×D412yes—
217C23×C151#12011yescharacteristic
218C23×C151#12011yescharacteristic
219C23×C151#12112yes—
220C23×C151C22×D411yescharacteristic
221Q8×C151—22no—
222Q8×C151—24no—
223Q8×C151—24no—
224Q8×C151—24no—
225Q8×C151—42no—
226Q8×C151—42no—
227Q8×C151—44no—
228Q8×C151—44no—
229Q8×C151C2×C22⋊C414yes—
230D4×C151—24no—
231D4×C151—24no—
232D4×C151—28no—
233D4×C151—22no—
234D4×C151—24no—
235D4×C151C2×C22⋊C414yes—
236C2×C4×C151—22no—
237C2×C4×C151—24no—
238C2×C4×C151—24no—
239C2×C4×C151—24no—
240C2×C4×C151—28no—
241C2×C4×C151—24no—
242C2×C4×C151—24no—
243C2×C4×C151—24no—
244C2×C4×C151—42no—
245C2×C4×C151—42no—
246C2×C4×C151—44no—
247C2×C4×C151—44no—
248C2×C4×C151—44no—
249C2×C4×C151—44no—
250C2×C4×C151—42no—
251C2×C4×C151—82no—
252C2×C4×C151—88no—
253C2×C4×C151C2×C22⋊C412yes—
254C2×C4×C151C2×C22⋊C412yes—
255C2×C4×C151C4×D412yes—
256C2×C4×C151C4×D412yes—
257C2×C4×C151C4×D412yes—
258C2×C4×C151#12011yescharacteristic
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12112yes—
261C2×C4×C151#12112yes—
262C2×C4×C151#12112yes—
263C2×C4×C151#12312yes—
264C2×C4×C151#12312yes—
265C2×C4×C151C23×C411yescharacteristic
266C2×C4×C151C22×D411yescharacteristic
267C2×C4×C151C22×D411yescharacteristic
268C2×C4×C151C22×D411yescharacteristic
269C2×C4×C151C2×#4111yescharacteristic
270C2×C4×C151C2×#4111yescharacteristic
271C8×C151—24no—
272C8×C151—42no—
273C22×C151—22no—
274C22×C151—22no—
275C22×C151—22no—
276C22×C151—24no—
277C22×C151—42no—
278C22×C151—42no—
279C22×C151—44no—
280C22×C151—84no—
281C22×C151#38612yes—
282C22×C151#38612yes—
283C22×C151C2×C4×D411yescharacteristic
284C22×C151C2×#12011yescharacteristic
285C22×C151C2×#12111yescharacteristic
286C4×C151—24no—
287C4×C151—44no—
288C4×C151—44no—
289C4×C151—44no—
290C4×C151—82no—
291C4×C151#38612yes—
292C4×C151#38612yes—
293C4×C151C22×C22⋊C411yescharacteristic
294C4×C151C2×C4×D411yescharacteristic
295C4×C151C2×#12111yescharacteristic
296C4×C151C2×#12311yescharacteristic
297C2×C151—21no—
298C2×C151—22no—
299C2×C151—21no—
300C2×C151—22no—
301C2×C151—44no—
302C2×C151C2×#38611yescharacteristic
303C2×C151#302212yes—
304#20944C15111yesmaximal, characteristic, direct product factor, Sylow
305C151#2094411yescharacteristic, direct product factor, Sylow
306C22×#137C2×C15111yescharacteristic
307#3428C2×C15111yescharacteristic
308C2×#421C2×C15111yescharacteristic
309C2×#419C2×C15111yescharacteristic, complemented
310#2310C2×C15111yescharacteristic, complemented
311#1882C2×C15118yescomplemented
312#1742C2×C15111yescharacteristic, complemented
313#1733C2×C15111yescharacteristic, complemented
314C22×#41C22×C15111yescharacteristic
315C23×Q8C22×C15111yescharacteristic
316C2×#137—24no—
317C2×#137—22no—
318C2×#137C4×C15118yescomplemented
319C2×#137C22×C15114yes—
320C22×Q16—21no—
321C22×SD16—21no—
322C22×M16C22×C15111yescharacteristic
323C22×M16C22×C15111yescharacteristic
324#520—22no—
325#520C22×C15114yes—
326#519—21no—
327#518—21no—
328#518—22no—
329C4×#41—22no—
330C4×#41—22no—
331C2×#117—22no—
332C2×#117C22×C15111yescharacteristic
333C2×#117C22×C15111yescharacteristic
334C2×#117C22×C15111yescharacteristic
335#421—24no—
336C2×#104C22×C15114yes—
337#419—22no—
338#419C22×C15114yescomplemented
339C2×#103—22no—
340#391—22no—
341#391C22×C15114yescomplemented
342#381—22no—
343#343C22×C15114yescomplemented
344#339C22×C15114yescomplemented
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41C2×C4×C15114yes—
350C2×#41D4×C15114yes—
351C2×#41D4×C15112yes—
352C2×#41C23×C15112yes—
353C22×Q8—22no—
354C22×Q8—21no—
355C22×Q8—22no—
356C22×Q8—21no—
357C22×Q8—21no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—21no—
361C22×Q8C2×C4×C15114yescomplemented
362C22×Q8D4×C15111yescharacteristic
363C22×Q8C23×C15112yes—
364C22×D4—21no—
365C22×D4D4×C15111yescharacteristic
366C23×C4—21no—
367C23×C4—21no—
368C23×C4C23×C15111yescharacteristic
369#137—216no—
370#137—28no—
371#137C2×C4×C151116yescomplemented
372C2×Q16—28no—
373C2×Q16—24no—
374C2×SD16—28no—
375C2×SD16—24no—
376C2×M16—22no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—22no—
380C2×M16—22no—
381C2×M16C2×C4×C15114yescomplemented
382C2×M16C23×C15112yes—
383C2×M16C23×C15112yes—
384C22×C8—21no—
385C22×C8—21no—
386C4×Q8—24no—
387C4×Q8—24no—
388C4×D4—28no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—28no—
392#117—24no—
393#117—24no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—24no—
401#117—22no—
402#117—22no—
403#117D4×C15112yes—
404#117C23×C15112yes—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4D4×C15112yes—
408C2×C4⋊C4C23×C15112yes—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4D4×C15112yes—
413C2×C42—24no—
414C2×C42—21no—
415C2×C42D4×C15112yes—
416C2×C42C23×C15112yes—
417#104—28no—
418#103—28no—
419#95—28no—
420C24—21no—
421C24C2×D4×C15111yescharacteristic
422#41—24no—
423#41—24no—
424#41—24no—
425#41—24no—
426#41—24no—
427#41—22no—
428#41—22no—
429#41C22⋊C4×C15118yes—
430#41C22×C4×C15114yes—
431#41C2×D4×C15114yes—
432C2×Q8—24no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—24no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8—24no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—42no—
449C2×Q8—42no—
450C2×Q8—42no—
451C2×Q8C22⋊C4×C15114yes—
452C2×Q8C22×C4×C15114yes—
453C2×Q8C2×D4×C15112yes—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4C22⋊C4×C15114yes—
461C2×D4C2×D4×C15112yes—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—42no—
475C22×C4C22×C4×C15112yes—
476C22×C4C2×D4×C15114yes—
477C22×C4C2×D4×C15111yescharacteristic
478C22×C4C2×D4×C15111yescharacteristic
479C22×C4C2×D4×C15112yes—
480C22×C4C2×D4×C15111yescharacteristic
481C22×C4C2×D4×C15111yescharacteristic
482C22×C4C2×D4×C15111yescharacteristic
483C22×C4#41×C15112yes—
484C22×C4#41×C15112yes—
485C22×C4C24×C15111yescharacteristic
486Q16—216no—
487SD16—216no—
488M16—24no—
489M16—22no—
490M16—22no—
491M16—22no—
492M16—42no—
493M16C22×C4×C15114yes—
494C2×C8—24no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—42no—
498C4⋊C4—28no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—42no—
503C4⋊C4C2×D4×C15114yes—
504C22⋊C4—28no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C42—28no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—22no—
517C23—22no—
518C23—24no—
519C23—42no—
520C23—82no—
521C23C4×D4×C15112yes—
522C23#120×C15111yescharacteristic
523C23#120×C15111yescharacteristic
524C23#121×C15112yes—
525C23C22×D4×C15111yescharacteristic
526Q8—24no—
527Q8—22no—
528Q8—24no—
529Q8—24no—
530Q8—44no—
531Q8—44no—
532Q8—42no—
533Q8—42no—
534Q8C2×C22⋊C4×C15114yes—
535D4—28no—
536D4—24no—
537D4—24no—
538D4—24no—
539D4—22no—
540D4C2×C22⋊C4×C15114yes—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—28no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—82no—
557C2×C4—88no—
558C2×C4C2×C22⋊C4×C15112yes—
559C2×C4C2×C22⋊C4×C15112yes—
560C2×C4C4×D4×C15112yes—
561C2×C4C4×D4×C15112yes—
562C2×C4C4×D4×C15112yes—
563C2×C4#120×C15111yescharacteristic
564C2×C4#120×C15111yescharacteristic
565C2×C4#121×C15112yes—
566C2×C4#121×C15112yes—
567C2×C4#121×C15112yes—
568C2×C4#123×C15112yes—
569C2×C4#123×C15112yes—
570C2×C4C23×C4×C15111yescharacteristic
571C2×C4C22×D4×C15111yescharacteristic
572C2×C4C22×D4×C15111yescharacteristic
573C2×C4C22×D4×C15111yescharacteristic
574C2×C4C2×#41×C15111yescharacteristic
575C2×C4C2×#41×C15111yescharacteristic
576C8—24no—
577C8—42no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—24no—
582C22—42no—
583C22—42no—
584C22—44no—
585C22—84no—
586C22#386×C15112yes—
587C22#386×C15112yes—
588C22C2×C4×D4×C15111yescharacteristic
589C22C2×#120×C15111yescharacteristic
590C22C2×#121×C15111yescharacteristic
591C4—24no—
592C4—44no—
593C4—44no—
594C4—44no—
595C4—82no—
596C4#386×C15112yes—
597C4#386×C15112yes—
598C4C22×C22⋊C4×C15111yescharacteristic
599C4C2×C4×D4×C15111yescharacteristic
600C4C2×#121×C15111yescharacteristic
601C4C2×#123×C15111yescharacteristic
602C2—21no—
603C2—22no—
604C2—22no—
605C2—21no—
606C2—44no—
607C2C2×#386×C15111yescharacteristic
608C2#3022×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#419×C151C2semidirect
5. #2310×C151C2semidirect
6. #1882×C151C2semidirect
7. #1742×C151C2semidirect
8. #1733×C151C2semidirect
13. C2×#137×C151C4semidirect
33. #419×C151C22semidirect
36. #391×C151C22semidirect
38. #343×C151C22semidirect
39. #339×C151C22semidirect
56. C22×Q8×C151C2×C4semidirect
66. #137×C151C2×C4semidirect
76. C2×M16×C151C2×C4semidirect
304. #20944C151direct (N × H)
305. C151#20944direct (N × H)
309. C2×#419C2×C151semidirect
310. #2310C2×C151semidirect
311. #1882C2×C151semidirect
312. #1742C2×C151semidirect
313. #1733C2×C151semidirect
318. C2×#137C4×C151semidirect
338. #419C22×C151semidirect
341. #391C22×C151semidirect
343. #343C22×C151semidirect
344. #339C22×C151semidirect
361. C22×Q8C2×C4×C151semidirect
371. #137C2×C4×C151semidirect
381. C2×M16C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
#3428×C1512
C2×#421×C1512
C2×#419×C1512
#2310×C1512
#1882×C1512
#1742×C1512
#1733×C1512
#20944151