Finite Group Databasebeta

← C151×#11115 #50316040

Subgroups — C151×#11115 #50316040

Order 38656.

864 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2911×C151C211yesmaximal, characteristic, complemented
2C2×#421×C151C211yesmaximal, characteristic
3C2×#421×C151C211yesmaximal, characteristic
4C2×#410×C151C211yesmaximal, characteristic
5#1742×C151C211yesmaximal, characteristic, complemented
6#1740×C151C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
8C22×#41×C151C2211yescharacteristic
9C22×M16×C151C2211yescharacteristic
10C22×M16×C151C2211yescharacteristic
11C2×#117×C151C2211yescharacteristic
12C2×#117×C151C2211yescharacteristic
13C2×#117×C151C2211yescharacteristic
14C2×#117×C151C2211yescharacteristic
15#428×C151—22no—
16#428×C151—22no—
17#427×C151—22no—
18#421×C151—22no—
19#421×C151—22no—
20#421×C151—22no—
21#421×C151—22no—
22C2×#104×C151—22no—
23C2×#104×C151C414yescomplemented
24#410×C151—22no—
25#410×C151—22no—
26C2×#99×C151—22no—
27#343×C151—22no—
28#342×C151—22no—
29H(3,ℤ/4)×C151—22no—
30C2×#41×C151—21no—
31C2×#41×C151—21no—
32C2×#41×C151—21no—
33C2×#41×C151—21no—
34C2×#41×C151—21no—
35C2×#41×C151—21no—
36C2×#41×C151—21no—
37C2×#41×C151—21no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151C2×C412yes—
41C2×#41×C151D412yes—
42C22×Q8×C151Q811yescharacteristic
43C22×D4×C151—21no—
44C22×D4×C151Q811yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151C2311yescharacteristic
47C2×M16×C151—21no—
48C2×M16×C151—21no—
49C2×M16×C151—21no—
50C2×M16×C151—21no—
51C2×M16×C151—21no—
52C2×M16×C151—21no—
53C2×M16×C151—21no—
54C2×M16×C151—21no—
55C2×M16×C151C2×C412yes—
56C2×M16×C151D412yes—
57C2×M16×C151D412yes—
58C2×M16×C151D412yes—
59C22×C8×C151—21no—
60C22×C8×C151—21no—
61#117×C151—21no—
62#117×C151—21no—
63#117×C151—21no—
64#117×C151—21no—
65#117×C151—21no—
66#117×C151—21no—
67#117×C151—21no—
68#117×C151—21no—
69#117×C151—21no—
70#117×C151—21no—
71#117×C151—21no—
72#117×C151—21no—
73#117×C151—21no—
74#117×C151—21no—
75#117×C151D412yes—
76#117×C151D412yes—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—21no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151D412yes—
85C2×C42×C151—21no—
86C2×C42×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151C2×C412yes—
89#107×C151—24no—
90#106×C151—24no—
91#104×C151—28no—
92#104×C151—28no—
93#99×C151—28no—
94C24×C151—21no—
95C24×C151C2×D411yescharacteristic
96#41×C151—22no—
97#41×C151—22no—
98#41×C151—22no—
99#41×C151—22no—
100#41×C151—22no—
101#41×C151—22no—
102#41×C151—22no—
103#41×C151—22no—
104#41×C151—41no—
105#41×C151—41no—
106#41×C151—41no—
107#41×C151—41no—
108#41×C151—41no—
109#41×C151—41no—
110#41×C151—41no—
111#41×C151—41no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151C4⋊C412yes—
118C2×D4×C151—22no—
119C2×D4×C151—22no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—41no—
126C2×D4×C151—41no—
127C2×D4×C151—41no—
128C2×D4×C151—41no—
129C2×D4×C151C4⋊C412yes—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—41no—
136C22×C4×C151—41no—
137C22×C4×C151—41no—
138C22×C4×C151—41no—
139C22×C4×C151—41no—
140C22×C4×C151—41no—
141C22×C4×C151C22×C411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×Q811yescharacteristic
149C22×C4×C151#4111yescharacteristic
150C22×C4×C151#4111yescharacteristic
151C22×C4×C151#4111yescharacteristic
152C22×C4×C151#4111yescharacteristic
153C22×C4×C151#4111yescharacteristic
154C22×C4×C151#4111yescharacteristic
155M16×C151—22no—
156M16×C151—22no—
157M16×C151—22no—
158M16×C151—22no—
159M16×C151—22no—
160M16×C151—41no—
161M16×C151—41no—
162M16×C151C22⋊C414yes—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—41no—
168C2×C8×C151—41no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—41no—
172C4⋊C4×C151—41no—
173C4⋊C4×C151—41no—
174C4⋊C4×C151—41no—
175C4⋊C4×C151—41no—
176C4⋊C4×C151—41no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—22no—
181C22⋊C4×C151—41no—
182C22⋊C4×C151—41no—
183C22⋊C4×C151—41no—
184C22⋊C4×C151—41no—
185C42×C151—22no—
186C42×C151—22no—
187C42×C151—22no—
188C42×C151—22no—
189C42×C151—41no—
190C42×C151—41no—
191C42×C151—41no—
192C42×C151—41no—
193C23×C151—22no—
194C23×C151—41no—
195C23×C151—41no—
196C23×C151—81no—
197C23×C151—82no—
198C23×C151C4×D411yescharacteristic
199C23×C151#12011yescharacteristic
200C23×C151#12111yescharacteristic
201C23×C151#12111yescharacteristic
202C23×C151C22⋊Q811yescharacteristic
203C23×C151#12311yescharacteristic
204C23×C151#12711yescharacteristic
205Q8×C151—22no—
206Q8×C151—22no—
207Q8×C151—41no—
208Q8×C151—41no—
209D4×C151—22no—
210D4×C151—22no—
211D4×C151—42no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—41no—
216D4×C151—41no—
217C2×C4×C151—22no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—82no—
229C2×C4×C151—82no—
230C2×C4×C151—82no—
231C2×C4×C151—82no—
232C2×C4×C151C2×C22⋊C411yescharacteristic
233C2×C4×C151C2×C4⋊C411yescharacteristic
234C2×C4×C151#11711yescharacteristic
235C2×C4×C151C4×D411yescharacteristic
236C2×C4×C151C4×D411yescharacteristic
237C2×C4×C151C4×D411yescharacteristic
238C2×C4×C151#12011yescharacteristic
239C2×C4×C151#12011yescharacteristic
240C2×C4×C151#12111yescharacteristic
241C2×C4×C151#12111yescharacteristic
242C2×C4×C151#12111yescharacteristic
243C2×C4×C151#12111yescharacteristic
244C2×C4×C151#12111yescharacteristic
245C2×C4×C151#12111yescharacteristic
246C2×C4×C151C22⋊Q811yescharacteristic
247C2×C4×C151C22⋊Q811yescharacteristic
248C2×C4×C151C22⋊Q811yescharacteristic
249C2×C4×C151C22⋊Q811yescharacteristic
250C2×C4×C151C22⋊Q811yescharacteristic
251C2×C4×C151#12311yescharacteristic
252C2×C4×C151#12311yescharacteristic
253C2×C4×C151#12311yescharacteristic
254C2×C4×C151#12311yescharacteristic
255C2×C4×C151#12411yescharacteristic
256C2×C4×C151#12411yescharacteristic
257C2×C4×C151#12411yescharacteristic
258C2×C4×C151#12611yescharacteristic
259C2×C4×C151#12611yescharacteristic
260C8×C151—24no—
261C8×C151—42no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—41no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—41no—
269C22×C151—42no—
270C22×C151—82no—
271C22×C151—82no—
272C22×C151—82no—
273C22×C151#38511yescharacteristic
274C22×C151#38811yescharacteristic
275C22×C151#39011yescharacteristic
276C22×C151#39211yescharacteristic
277C22×C151#39411yescharacteristic
278C22×C151#39611yescharacteristic
279C22×C151#39911yescharacteristic
280C4×C151—42no—
281C4×C151—82no—
282C4×C151—82no—
283C4×C151—82no—
284C4×C151—82no—
285C4×C151#38011yescharacteristic
286C4×C151#38511yescharacteristic
287C4×C151#38611yescharacteristic
288C4×C151#38811yescharacteristic
289C4×C151#39311yescharacteristic
290C4×C151#39411yescharacteristic
291C4×C151#39611yescharacteristic
292C4×C151#39711yescharacteristic
293C2×C151—21no—
294C2×C151—21no—
295C2×C151—21no—
296C2×C151—21no—
297C2×C151—21no—
298C2×C151—21no—
299C2×C151—21no—
300C2×C151—82no—
301C2×C151#143911yescharacteristic
302#11115C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#1111511yescharacteristic, direct product factor, Sylow
304#2911C2×C15111yescharacteristic, complemented
305C2×#421C2×C15111yescharacteristic
306C2×#421C2×C15111yescharacteristic
307C2×#410C2×C15111yescharacteristic
308#1742C2×C15111yescharacteristic, complemented
309#1740C2×C15111yescharacteristic, complemented
310C2×H(3,ℤ/4)C2×C15111yescharacteristic, complemented
311C22×#41C22×C15111yescharacteristic
312C22×M16C22×C15111yescharacteristic
313C22×M16C22×C15111yescharacteristic
314C2×#117C22×C15111yescharacteristic
315C2×#117C22×C15111yescharacteristic
316C2×#117C22×C15111yescharacteristic
317C2×#117C22×C15111yescharacteristic
318#428—22no—
319#428—22no—
320#427—22no—
321#421—22no—
322#421—22no—
323#421—22no—
324#421—22no—
325C2×#104—22no—
326C2×#104C4×C15114yescomplemented
327#410—22no—
328#410—22no—
329C2×#99—22no—
330#343—22no—
331#342—22no—
332H(3,ℤ/4)—22no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41C2×C4×C15112yes—
344C2×#41D4×C15112yes—
345C22×Q8Q8×C15111yescharacteristic
346C22×D4—21no—
347C22×D4Q8×C15111yescharacteristic
348C23×C4—21no—
349C23×C4C23×C15111yescharacteristic
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16C2×C4×C15112yes—
359C2×M16D4×C15112yes—
360C2×M16D4×C15112yes—
361C2×M16D4×C15112yes—
362C22×C8—21no—
363C22×C8—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117D4×C15112yes—
379#117D4×C15112yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4D4×C15112yes—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42C2×C4×C15112yes—
392#107—24no—
393#106—24no—
394#104—28no—
395#104—28no—
396#99—28no—
397C24—21no—
398C24C2×D4×C15111yescharacteristic
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C4⋊C4×C15112yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4C4⋊C4×C15112yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4C22×C4×C15111yescharacteristic
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×Q8×C15111yescharacteristic
452C22×C4#41×C15111yescharacteristic
453C22×C4#41×C15111yescharacteristic
454C22×C4#41×C15111yescharacteristic
455C22×C4#41×C15111yescharacteristic
456C22×C4#41×C15111yescharacteristic
457C22×C4#41×C15111yescharacteristic
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—41no—
464M16—41no—
465M16C22⋊C4×C15114yes—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—41no—
493C42—41no—
494C42—41no—
495C42—41no—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—81no—
500C23—82no—
501C23C4×D4×C15111yescharacteristic
502C23#120×C15111yescharacteristic
503C23#121×C15111yescharacteristic
504C23#121×C15111yescharacteristic
505C23C22⋊Q8×C15111yescharacteristic
506C23#123×C15111yescharacteristic
507C23#127×C15111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—41no—
519D4—41no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4C2×C22⋊C4×C15111yescharacteristic
536C2×C4C2×C4⋊C4×C15111yescharacteristic
537C2×C4#117×C15111yescharacteristic
538C2×C4C4×D4×C15111yescharacteristic
539C2×C4C4×D4×C15111yescharacteristic
540C2×C4C4×D4×C15111yescharacteristic
541C2×C4#120×C15111yescharacteristic
542C2×C4#120×C15111yescharacteristic
543C2×C4#121×C15111yescharacteristic
544C2×C4#121×C15111yescharacteristic
545C2×C4#121×C15111yescharacteristic
546C2×C4#121×C15111yescharacteristic
547C2×C4#121×C15111yescharacteristic
548C2×C4#121×C15111yescharacteristic
549C2×C4C22⋊Q8×C15111yescharacteristic
550C2×C4C22⋊Q8×C15111yescharacteristic
551C2×C4C22⋊Q8×C15111yescharacteristic
552C2×C4C22⋊Q8×C15111yescharacteristic
553C2×C4C22⋊Q8×C15111yescharacteristic
554C2×C4#123×C15111yescharacteristic
555C2×C4#123×C15111yescharacteristic
556C2×C4#123×C15111yescharacteristic
557C2×C4#123×C15111yescharacteristic
558C2×C4#124×C15111yescharacteristic
559C2×C4#124×C15111yescharacteristic
560C2×C4#124×C15111yescharacteristic
561C2×C4#126×C15111yescharacteristic
562C2×C4#126×C15111yescharacteristic
563C8—24no—
564C8—42no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—82no—
574C22—82no—
575C22—82no—
576C22#385×C15111yescharacteristic
577C22#388×C15111yescharacteristic
578C22#390×C15111yescharacteristic
579C22#392×C15111yescharacteristic
580C22#394×C15111yescharacteristic
581C22#396×C15111yescharacteristic
582C22#399×C15111yescharacteristic
583C4—42no—
584C4—82no—
585C4—82no—
586C4—82no—
587C4—82no—
588C4#380×C15111yescharacteristic
589C4#385×C15111yescharacteristic
590C4#386×C15111yescharacteristic
591C4#388×C15111yescharacteristic
592C4#393×C15111yescharacteristic
593C4#394×C15111yescharacteristic
594C4#396×C15111yescharacteristic
595C4#397×C15111yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—82no—
604C2#1439×C15111yescharacteristic
subgroupG/H
centerC4×C151#388
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
socleC2×C151#1439
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2911×C151C2semidirect
5. #1742×C151C2semidirect
6. #1740×C151C2semidirect
7. C2×H(3,ℤ/4)×C151C2semidirect
23. C2×#104×C151C4semidirect
302. #11115C151direct (N × H)
303. C151#11115direct (N × H)
304. #2911C2×C151semidirect
308. #1742C2×C151semidirect
309. #1740C2×C151semidirect
310. C2×H(3,ℤ/4)C2×C151semidirect
326. C2×#104C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2911×C1512
C2×#421×C1512
C2×#410×C1512
#1742×C1512
#1740×C1512
C2×H(3,ℤ/4)×C1512
#11115151