Finite Group Databasebeta

← C151×#21014 #50325939

Subgroups — C151×#21014 #50325939

Order 38656.

1748 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3449×C151C211yesmaximal, characteristic
2#3428×C151C211yesmaximal, characteristic, complemented
3C2×#410×C151C211yesmaximal, characteristic, complemented
4C2×#410×C151C212yesmaximal, complemented
5#1913×C151C218yesmaximal, complemented
6#1740×C151C212yesmaximal, complemented
7C22×#41×C151C2211yescharacteristic
8C22×#41×C151C2211yescharacteristic
9#537×C151—22no—
10#536×C151—21no—
11#536×C151C412yescomplemented
12#535×C151—21no—
13#535×C151C412yescomplemented
14#534×C151C2214yes—
15#532×C151—22no—
16#525×C151—22no—
17#525×C151C414yescomplemented
18#520×C151—24no—
19#519×C151—21no—
20#518×C151—21no—
21#518×C151C2214yes—
22C4×#41×C151—24no—
23C2×#117×C151—22no—
24C2×#117×C151C2212yes—
25C2×#117×C151C2211yescharacteristic
26C2×#117×C151C2212yes—
27#410×C151—22no—
28#410×C151—22no—
29#410×C151—24no—
30#410×C151—24no—
31C2×#99×C151C2214yes—
32C2×#99×C151C2218yes—
33#342×C151C2218yes—
34C2×#41×C151—22no—
35C2×#41×C151—22no—
36C2×#41×C151—22no—
37C2×#41×C151—22no—
38C2×#41×C151—22no—
39C2×#41×C151—22no—
40C2×#41×C151—21no—
41C2×#41×C151—21no—
42C2×#41×C151—21no—
43C2×#41×C151—21no—
44C2×#41×C151—22no—
45C2×#41×C151—22no—
46C2×#41×C151C2×C412yes—
47C2×#41×C151C2×C412yes—
48C2×#41×C151D412yes—
49C2×#41×C151D412yes—
50C22×Q8×C151C2×C411yescharacteristic, complemented
51C22×Q8×C151D411yescharacteristic
52C22×D4×C151C2×C411yescharacteristic, complemented
53C22×D4×C151D411yescharacteristic
54C22×D4×C151C2312yes—
55C22×D4×C151C2312yes—
56C23×C4×C151C2×C412yescomplemented
57C23×C4×C151D412yes—
58C23×C4×C151C2311yescharacteristic
59C4⋊Q8×C151—22no—
60#127×C151—22no—
61#124×C151—22no—
62#124×C151—22no—
63#123×C151—24no—
64#123×C151C2×C418yescomplemented
65C22⋊Q8×C151—24no—
66C22⋊Q8×C151—24no—
67#121×C151—24no—
68#121×C151—28no—
69#121×C151—24no—
70#120×C151—24no—
71#120×C151C2×C418yescomplemented
72C4×Q8×C151—28no—
73C4×D4×C151—28no—
74C4×D4×C151—28no—
75C4×D4×C151—216no—
76#117×C151—24no—
77#117×C151—24no—
78#117×C151—22no—
79#117×C151—24no—
80#117×C151—22no—
81#117×C151—21no—
82#117×C151—21no—
83#117×C151—22no—
84#117×C151—22no—
85#117×C151—22no—
86#117×C151—22no—
87#117×C151C2×C412yescomplemented
88#117×C151C2×C412yescomplemented
89#117×C151D414yescomplemented
90#117×C151D414yescomplemented
91C2×C4⋊C4×C151—24no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—22no—
95C2×C22⋊C4×C151—24no—
96C2×C22⋊C4×C151C2314yes—
97C2×C22⋊C4×C151C2312yes—
98C2×C22⋊C4×C151C2314yes—
99C2×C42×C151—24no—
100C2×C42×C151—22no—
101C2×C42×C151—21no—
102C2×C42×C151—22no—
103#99×C151—28no—
104#99×C151—216no—
105C24×C151C22×C412yes—
106C24×C151C2×D412yes—
107C24×C151C2411yescharacteristic
108#41×C151—24no—
109#41×C151—24no—
110#41×C151—24no—
111#41×C151—24no—
112#41×C151—24no—
113#41×C151—24no—
114#41×C151—24no—
115#41×C151—24no—
116#41×C151—42no—
117#41×C151—41no—
118#41×C151—41no—
119#41×C151—42no—
120#41×C151—42no—
121#41×C151—42no—
122#41×C151—42no—
123#41×C151—42no—
124#41×C151—41no—
125#41×C151—41no—
126C2×Q8×C151—21no—
127C2×Q8×C151—21no—
128C2×Q8×C151—22no—
129C2×Q8×C151—22no—
130C2×Q8×C151—22no—
131C2×Q8×C151—22no—
132C2×Q8×C151C22⋊C412yes—
133C2×Q8×C151C22⋊C412yes—
134C2×D4×C151—24no—
135C2×D4×C151—24no—
136C2×D4×C151—24no—
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—24no—
140C2×D4×C151—28no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—22no—
147C2×D4×C151C22⋊C412yes—
148C2×D4×C151C22⋊C412yes—
149C2×D4×C151C22×C414yes—
150C2×D4×C151C2×D414yes—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—28no—
156C22×C4×C151—24no—
157C22×C4×C151—22no—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—24no—
161C22×C4×C151—24no—
162C22×C4×C151—24no—
163C22×C4×C151C22⋊C414yes—
164C22×C4×C151C22⋊C414yes—
165C22×C4×C151C22×C412yes—
166C22×C4×C151C22×C411yescharacteristic
167C22×C4×C151C22×C411yescharacteristic
168C22×C4×C151C2×D412yes—
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D412yes—
174C22×C4×C151C2×D412yes—
175C22×C4×C151#4112yes—
176C22×C4×C151#4112yes—
177C4⋊C4×C151—28no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—28no—
181C4⋊C4×C151—24no—
182C4⋊C4×C151—24no—
183C4⋊C4×C151—42no—
184C4⋊C4×C151—42no—
185C22⋊C4×C151—28no—
186C22⋊C4×C151—28no—
187C22⋊C4×C151—24no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—28no—
190C22⋊C4×C151—24no—
191C22⋊C4×C151—24no—
192C22⋊C4×C151C22×C414yes—
193C22⋊C4×C151C2×D418yes—
194C42×C151—28no—
195C42×C151—22no—
196C42×C151—22no—
197C42×C151—24no—
198C42×C151—24no—
199C42×C151—42no—
200C42×C151—42no—
201C23×C151—22no—
202C23×C151—22no—
203C23×C151—22no—
204C23×C151—24no—
205C23×C151—81no—
206C23×C151—82no—
207C23×C151—82no—
208C23×C151C2×C22⋊C414yes—
209C23×C151C23×C411yescharacteristic
210C23×C151C22×D411yescharacteristic
211C23×C151C22×D411yescharacteristic
212C23×C151C22×D412yes—
213C23×C151C2×#4112yes—
214Q8×C151—24no—
215Q8×C151—24no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—42no—
219D4×C151—28no—
220D4×C151—28no—
221D4×C151—24no—
222D4×C151—24no—
223D4×C151—42no—
224D4×C151—44no—
225D4×C151—42no—
226D4×C151—41no—
227D4×C151—41no—
228D4×C151—42no—
229D4×C151—88no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—24no—
233C2×C4×C151—24no—
234C2×C4×C151—24no—
235C2×C4×C151—24no—
236C2×C4×C151—22no—
237C2×C4×C151—24no—
238C2×C4×C151—24no—
239C2×C4×C151—28no—
240C2×C4×C151—42no—
241C2×C4×C151—44no—
242C2×C4×C151—42no—
243C2×C4×C151—44no—
244C2×C4×C151—84no—
245C2×C4×C151—88no—
246C2×C4×C151—82no—
247C2×C4×C151—84no—
248C2×C4×C151C2×C22⋊C414yes—
249C2×C4×C151C2×C22⋊C411yescharacteristic
250C2×C4×C151C2×C22⋊C411yescharacteristic
251C2×C4×C151C2×C22⋊C411yescharacteristic
252C2×C4×C151C2×C22⋊C411yescharacteristic
253C2×C4×C151C4×D412yes—
254C2×C4×C151C4×D412yes—
255C2×C4×C151C4×D412yes—
256C2×C4×C151C4×D412yes—
257C2×C4×C151#12012yes—
258C2×C4×C151#12011yescharacteristic
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12112yes—
261C2×C4×C151#12112yes—
262C2×C4×C151#12112yes—
263C2×C4×C151#12112yes—
264C2×C4×C151#12312yes—
265C2×C4×C151#12311yescharacteristic
266C2×C4×C151#12311yescharacteristic
267C22×C151—24no—
268C22×C151—42no—
269C22×C151—41no—
270C22×C151—42no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—44no—
274C22×C151—44no—
275C22×C151—44no—
276C22×C151—42no—
277C22×C151—82no—
278C22×C151—84no—
279C22×C151C22×C22⋊C411yescharacteristic
280C22×C151C2×C4×D412yes—
281C22×C151C2×#12011yescharacteristic
282C22×C151C2×#12112yes—
283C22×C151C2×#12311yescharacteristic
284C4×C151—24no—
285C4×C151—48no—
286C4×C151—44no—
287C4×C151—42no—
288C4×C151—84no—
289C4×C151#38611yescharacteristic
290C4×C151#38611yescharacteristic
291C4×C151#38611yescharacteristic
292C4×C151#38612yes—
293C4×C151#38612yes—
294C4×C151#38611yescharacteristic
295C2×C151—21no—
296C2×C151—21no—
297C2×C151—22no—
298C2×C151—22no—
299C2×C151—21no—
300C2×C151—44no—
301C2×C151—82no—
302C2×C151C2×#38611yescharacteristic
303#21014C15111yesmaximal, characteristic, direct product factor, Sylow
304C151#2101411yescharacteristic, direct product factor, Sylow
305#3449C2×C15111yescharacteristic
306#3428C2×C15111yescharacteristic, complemented
307C2×#410C2×C15111yescharacteristic, complemented
308C2×#410C2×C15112yescomplemented
309#1913C2×C15118yescomplemented
310#1740C2×C15112yescomplemented
311C22×#41C22×C15111yescharacteristic
312C22×#41C22×C15111yescharacteristic
313#537—22no—
314#536—21no—
315#536C4×C15112yescomplemented
316#535—21no—
317#535C4×C15112yescomplemented
318#534C22×C15114yes—
319#532—22no—
320#525—22no—
321#525C4×C15114yescomplemented
322#520—24no—
323#519—21no—
324#518—21no—
325#518C22×C15114yes—
326C4×#41—24no—
327C2×#117—22no—
328C2×#117C22×C15112yes—
329C2×#117C22×C15111yescharacteristic
330C2×#117C22×C15112yes—
331#410—22no—
332#410—22no—
333#410—24no—
334#410—24no—
335C2×#99C22×C15114yes—
336C2×#99C22×C15118yes—
337#342C22×C15118yes—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41C2×C4×C15112yes—
351C2×#41C2×C4×C15112yes—
352C2×#41D4×C15112yes—
353C2×#41D4×C15112yes—
354C22×Q8C2×C4×C15111yescharacteristic, complemented
355C22×Q8D4×C15111yescharacteristic
356C22×D4C2×C4×C15111yescharacteristic, complemented
357C22×D4D4×C15111yescharacteristic
358C22×D4C23×C15112yes—
359C22×D4C23×C15112yes—
360C23×C4C2×C4×C15112yescomplemented
361C23×C4D4×C15112yes—
362C23×C4C23×C15111yescharacteristic
363C4⋊Q8—22no—
364#127—22no—
365#124—22no—
366#124—22no—
367#123—24no—
368#123C2×C4×C15118yescomplemented
369C22⋊Q8—24no—
370C22⋊Q8—24no—
371#121—24no—
372#121—28no—
373#121—24no—
374#120—24no—
375#120C2×C4×C15118yescomplemented
376C4×Q8—28no—
377C4×D4—28no—
378C4×D4—28no—
379C4×D4—216no—
380#117—24no—
381#117—24no—
382#117—22no—
383#117—24no—
384#117—22no—
385#117—21no—
386#117—21no—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—22no—
391#117C2×C4×C15112yescomplemented
392#117C2×C4×C15112yescomplemented
393#117D4×C15114yescomplemented
394#117D4×C15114yescomplemented
395C2×C4⋊C4—24no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4C23×C15114yes—
401C2×C22⋊C4C23×C15112yes—
402C2×C22⋊C4C23×C15114yes—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—21no—
406C2×C42—22no—
407#99—28no—
408#99—216no—
409C24C22×C4×C15112yes—
410C24C2×D4×C15112yes—
411C24C24×C15111yescharacteristic
412#41—24no—
413#41—24no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—24no—
418#41—24no—
419#41—24no—
420#41—41no—
421#41—42no—
422#41—41no—
423#41—42no—
424#41—42no—
425#41—42no—
426#41—42no—
427#41—41no—
428#41—41no—
429#41—42no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8C22⋊C4×C15112yes—
437C2×Q8C22⋊C4×C15112yes—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—24no—
444C2×D4—28no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4C22⋊C4×C15112yes—
452C2×D4C22⋊C4×C15112yes—
453C2×D4C22×C4×C15114yes—
454C2×D4C2×D4×C15114yes—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—28no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4C22⋊C4×C15114yes—
468C22×C4C22⋊C4×C15114yes—
469C22×C4C22×C4×C15112yes—
470C22×C4C22×C4×C15111yescharacteristic
471C22×C4C22×C4×C15111yescharacteristic
472C22×C4C2×D4×C15112yes—
473C22×C4C2×D4×C15111yescharacteristic
474C22×C4C2×D4×C15111yescharacteristic
475C22×C4C2×D4×C15111yescharacteristic
476C22×C4C2×D4×C15111yescharacteristic
477C22×C4C2×D4×C15112yes—
478C22×C4C2×D4×C15112yes—
479C22×C4#41×C15112yes—
480C22×C4#41×C15112yes—
481C4⋊C4—28no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—28no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C22⋊C4—28no—
490C22⋊C4—28no—
491C22⋊C4—24no—
492C22⋊C4—22no—
493C22⋊C4—28no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4C22×C4×C15114yes—
497C22⋊C4C2×D4×C15118yes—
498C42—28no—
499C42—22no—
500C42—22no—
501C42—24no—
502C42—24no—
503C42—42no—
504C42—42no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—81no—
510C23—82no—
511C23—82no—
512C23C2×C22⋊C4×C15114yes—
513C23C23×C4×C15111yescharacteristic
514C23C22×D4×C15111yescharacteristic
515C23C22×D4×C15111yescharacteristic
516C23C22×D4×C15112yes—
517C23C2×#41×C15112yes—
518Q8—24no—
519Q8—24no—
520Q8—41no—
521Q8—41no—
522Q8—42no—
523D4—28no—
524D4—28no—
525D4—24no—
526D4—24no—
527D4—42no—
528D4—44no—
529D4—42no—
530D4—41no—
531D4—41no—
532D4—42no—
533D4—88no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—28no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—44no—
547C2×C4—44no—
548C2×C4—84no—
549C2×C4—88no—
550C2×C4—82no—
551C2×C4—84no—
552C2×C4C2×C22⋊C4×C15114yes—
553C2×C4C2×C22⋊C4×C15111yescharacteristic
554C2×C4C2×C22⋊C4×C15111yescharacteristic
555C2×C4C2×C22⋊C4×C15111yescharacteristic
556C2×C4C2×C22⋊C4×C15111yescharacteristic
557C2×C4C4×D4×C15112yes—
558C2×C4C4×D4×C15112yes—
559C2×C4C4×D4×C15112yes—
560C2×C4C4×D4×C15112yes—
561C2×C4#120×C15111yescharacteristic
562C2×C4#120×C15112yes—
563C2×C4#120×C15111yescharacteristic
564C2×C4#121×C15112yes—
565C2×C4#121×C15112yes—
566C2×C4#121×C15112yes—
567C2×C4#121×C15112yes—
568C2×C4#123×C15111yescharacteristic
569C2×C4#123×C15111yescharacteristic
570C2×C4#123×C15112yes—
571C22—24no—
572C22—42no—
573C22—41no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—44no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—82no—
582C22—84no—
583C22C22×C22⋊C4×C15111yescharacteristic
584C22C2×C4×D4×C15112yes—
585C22C2×#120×C15111yescharacteristic
586C22C2×#121×C15112yes—
587C22C2×#123×C15111yescharacteristic
588C4—24no—
589C4—48no—
590C4—44no—
591C4—42no—
592C4—84no—
593C4#386×C15111yescharacteristic
594C4#386×C15111yescharacteristic
595C4#386×C15111yescharacteristic
596C4#386×C15111yescharacteristic
597C4#386×C15112yes—
598C4#386×C15112yes—
599C2—21no—
600C2—21no—
601C2—22no—
602C2—22no—
603C2—21no—
604C2—44no—
605C2—82no—
606C2C2×#386×C15111yescharacteristic
subgroupG/H
centerC4×C151#386
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
socleC2×C151C2×#386
prime radical#3449×C151C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3428×C151C2semidirect
3. C2×#410×C151C2semidirect
4. C2×#410×C151C2semidirect
5. #1913×C151C2semidirect
6. #1740×C151C2semidirect
11. #536×C151C4semidirect
13. #535×C151C4semidirect
17. #525×C151C4semidirect
50. C22×Q8×C151C2×C4semidirect
52. C22×D4×C151C2×C4semidirect
56. C23×C4×C151C2×C4semidirect
64. #123×C151C2×C4semidirect
71. #120×C151C2×C4semidirect
87. #117×C151C2×C4semidirect
88. #117×C151C2×C4semidirect
89. #117×C151D4semidirect
90. #117×C151D4semidirect
303. #21014C151direct (N × H)
304. C151#21014direct (N × H)
306. #3428C2×C151semidirect
307. C2×#410C2×C151semidirect
308. C2×#410C2×C151semidirect
309. #1913C2×C151semidirect
310. #1740C2×C151semidirect
315. #536C4×C151semidirect
317. #535C4×C151semidirect
321. #525C4×C151semidirect
354. C22×Q8C2×C4×C151semidirect
356. C22×D4C2×C4×C151semidirect
360. C23×C4C2×C4×C151semidirect
368. #123C2×C4×C151semidirect
375. #120C2×C4×C151semidirect
391. #117C2×C4×C151semidirect
392. #117C2×C4×C151semidirect
393. #117D4×C151semidirect
394. #117D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3449×C1512
#3428×C1512
C2×#410×C1512
#1913×C1512
#1740×C1512
#21014151