Finite Group Databasebeta

← C151×#14878 #50319803

Subgroups — C151×#14878 #50319803

Order 38656.

1634 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C151C211yesmaximal, characteristic
2C2×#398×C151C212yesmaximal
3C2×#387×C151C211yesmaximal, characteristic
4#1446×C151C211yesmaximal, characteristic
5#1446×C151C211yesmaximal, characteristic
6#1444×C151C211yesmaximal, characteristic
7#1442×C151C211yesmaximal, characteristic
8#1441×C151C212yesmaximal
9#1436×C151C212yesmaximal
10#1436×C151C212yesmaximal
11C4⋊#95×C151C211yesmaximal, characteristic
12C23×Q8×C151C2211yescharacteristic
13C2×C4×Q8×C151—28no—
14C2×C4×Q8×C151—24no—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18C22×C4⋊C4×C151C2212yes—
19C22×C4⋊C4×C151C2212yes—
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C42×C151C2212yes—
22C22×C42×C151C2211yescharacteristic
23#398×C151—28no—
24#387×C151—24no—
25C2×#95×C151C2212yes—
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2211yescharacteristic
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2211yescharacteristic
36C2×#95×C151C2211yescharacteristic
37C2×#95×C151C2211yescharacteristic
38C2×#95×C151C2212yes—
39C22×Q8×C151—24no—
40C22×Q8×C151—22no—
41C22×Q8×C151—24no—
42C22×Q8×C151—22no—
43C22×Q8×C151Q814yes—
44C23×C4×C151C2311yescharacteristic
45C23×C4×C151C2312yes—
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2312yes—
48C23×C4×C151C2311yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2312yes—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C4×Q8×C151—232no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—24no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—24no—
64C2×C4⋊C4×C151—24no—
65C2×C4⋊C4×C151—24no—
66C2×C4⋊C4×C151—24no—
67C2×C4⋊C4×C151—24no—
68C2×C4⋊C4×C151—42no—
69C2×C4⋊C4×C151—42no—
70C2×C4⋊C4×C151D418yes—
71C2×C4⋊C4×C151Q814yescomplemented
72C2×C42×C151—24no—
73C2×C42×C151—24no—
74C2×C42×C151—24no—
75C2×C42×C151—24no—
76C2×C42×C151D414yes—
77#95×C151—22no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—22no—
81#95×C151—24no—
82#95×C151—24no—
83#95×C151—24no—
84#95×C151—24no—
85#95×C151—22no—
86#95×C151—24no—
87#95×C151—24no—
88#95×C151—24no—
89#95×C151—22no—
90#95×C151—42no—
91C24×C151C2411yescharacteristic
92C2×Q8×C151—28no—
93C2×Q8×C151—28no—
94C2×Q8×C151—216no—
95C2×Q8×C151—28no—
96C2×Q8×C151—216no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—22no—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—21no—
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—22no—
145C22×C4×C151C2×D414yes—
146C22×C4×C151C2×D412yes—
147C22×C4×C151C2×D414yes—
148C22×C4×C151C2×D414yes—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×D412yes—
151C22×C4×C151C2×Q812yes—
152C22×C4×C151C2×Q812yes—
153C22×C4×C151C2×Q812yes—
154C22×C4×C151C2×Q814yes—
155C22×C4×C151C2×Q812yes—
156C22×C4×C151#4114yes—
157C22×C4×C151#4112yes—
158C22×C4×C151#4114yes—
159C22×C4×C151#4112yes—
160C4⋊C4×C151—28no—
161C4⋊C4×C151—216no—
162C4⋊C4×C151—28no—
163C4⋊C4×C151—48no—
164C4⋊C4×C151—48no—
165C4⋊C4×C151—44no—
166C42×C151—216no—
167C42×C151—28no—
168C23×C151C22×D411yescharacteristic
169C23×C151C22×D412yes—
170C23×C151C22×Q811yescharacteristic
171C23×C151C22×Q811yescharacteristic
172C23×C151C2×#4112yes—
173C23×C151C2×#4111yescharacteristic
174C23×C151C2×#4111yescharacteristic
175C23×C151C2×#4112yes—
176C23×C151H(5,𝔽2)11yescharacteristic
177C23×C1512−1+412yes—
178C23×C1512−1+411yescharacteristic
179Q8×C151—232no—
180C2×C4×C151—24no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—24no—
184C2×C4×C151—24no—
185C2×C4×C151—24no—
186C2×C4×C151—22no—
187C2×C4×C151—24no—
188C2×C4×C151—24no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—24no—
195C2×C4×C151—24no—
196C2×C4×C151—24no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—41no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—41no—
223C2×C4×C151—41no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151#12014yes—
240C2×C4×C151C22⋊Q814yes—
241C2×C4×C151C22⋊Q818yes—
242C2×C4×C151C22⋊Q814yes—
243C22×C151C2×#12011yescharacteristic
244C22×C151C2×C22⋊Q811yescharacteristic
245C22×C151C2×C22⋊Q811yescharacteristic
246C22×C151C2×C22⋊Q812yes—
247C22×C151#52511yescharacteristic
248C22×C151#52512yes—
249C22×C151#52912yes—
250C22×C151#53211yescharacteristic
251C22×C151#53312yes—
252C22×C151#53611yescharacteristic
253C22×C151#53711yescharacteristic
254C22×C151#54112yes—
255C22×C151#54212yes—
256C22×C151#54612yes—
257C22×C151#54712yes—
258C22×C151#54812yes—
259C22×C151D4×Q812yes—
260C22×C151#55212yes—
261C22×C151#55712yes—
262C22×C151#55711yescharacteristic
263C22×C151#55711yescharacteristic
264C22×C151Q8211yescharacteristic
265C22×C151#55911yescharacteristic
266C4×C151—28no—
267C4×C151—24no—
268C4×C151—24no—
269C4×C151—24no—
270C4×C151—42no—
271C4×C151—42no—
272C4×C151—44no—
273C4×C151—44no—
274C4×C151—81no—
275C4×C151—81no—
276C4×C151—82no—
277C2×C151#239611yescharacteristic
278C2×C151#240911yescharacteristic
279C2×C151#243011yescharacteristic
280C2×C151#245112yes—
281C2×C151#245312yes—
282C2×C151#245812yes—
283C2×C151#246212yes—
284C2×C151#256511yescharacteristic
285C2×C151#258211yescharacteristic
286C2×C151#263711yescharacteristic
287C2×C151#284811yescharacteristic
288#14878C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#1487811yescharacteristic, direct product factor, Sylow
290C22×C4×Q8C2×C15111yescharacteristic
291C2×#398C2×C15112yes—
292C2×#387C2×C15111yescharacteristic
293#1446C2×C15111yescharacteristic
294#1446C2×C15111yescharacteristic
295#1444C2×C15111yescharacteristic
296#1442C2×C15111yescharacteristic
297#1441C2×C15112yes—
298#1436C2×C15112yes—
299#1436C2×C15112yes—
300C4⋊#95C2×C15111yescharacteristic
301C23×Q8C22×C15111yescharacteristic
302C2×C4×Q8—28no—
303C2×C4×Q8—24no—
304C22×C4⋊C4C22×C15111yescharacteristic
305C22×C4⋊C4C22×C15111yescharacteristic
306C22×C4⋊C4C22×C15112yes—
307C22×C4⋊C4C22×C15112yes—
308C22×C4⋊C4C22×C15112yes—
309C22×C4⋊C4C22×C15111yescharacteristic
310C22×C42C22×C15112yes—
311C22×C42C22×C15111yescharacteristic
312#398—28no—
313#387—24no—
314C2×#95C22×C15112yes—
315C2×#95C22×C15112yes—
316C2×#95C22×C15112yes—
317C2×#95C22×C15112yes—
318C2×#95C22×C15111yescharacteristic
319C2×#95C22×C15111yescharacteristic
320C2×#95C22×C15111yescharacteristic
321C2×#95C22×C15112yes—
322C2×#95C22×C15112yes—
323C2×#95C22×C15112yes—
324C2×#95C22×C15111yescharacteristic
325C2×#95C22×C15111yescharacteristic
326C2×#95C22×C15111yescharacteristic
327C2×#95C22×C15112yes—
328C22×Q8—24no—
329C22×Q8—22no—
330C22×Q8—24no—
331C22×Q8—22no—
332C22×Q8Q8×C15114yes—
333C23×C4C23×C15111yescharacteristic
334C23×C4C23×C15112yes—
335C23×C4C23×C15111yescharacteristic
336C23×C4C23×C15111yescharacteristic
337C23×C4C23×C15111yescharacteristic
338C23×C4C23×C15112yes—
339C23×C4C23×C15112yes—
340C23×C4C23×C15112yes—
341C23×C4C23×C15111yescharacteristic
342C23×C4C23×C15111yescharacteristic
343C23×C4C23×C15111yescharacteristic
344C4×Q8—232no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4D4×C15118yes—
360C2×C4⋊C4Q8×C15114yescomplemented
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42D4×C15114yes—
366#95—24no—
367#95—22no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—42no—
380C24C24×C15111yescharacteristic
381C2×Q8—28no—
382C2×Q8—28no—
383C2×Q8—216no—
384C2×Q8—216no—
385C2×Q8—28no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4C2×D4×C15114yes—
435C22×C4C2×D4×C15112yes—
436C22×C4C2×D4×C15114yes—
437C22×C4C2×D4×C15114yes—
438C22×C4C2×D4×C15112yes—
439C22×C4C2×D4×C15112yes—
440C22×C4C2×Q8×C15112yes—
441C22×C4C2×Q8×C15112yes—
442C22×C4C2×Q8×C15112yes—
443C22×C4C2×Q8×C15112yes—
444C22×C4C2×Q8×C15114yes—
445C22×C4#41×C15114yes—
446C22×C4#41×C15112yes—
447C22×C4#41×C15114yes—
448C22×C4#41×C15112yes—
449C4⋊C4—28no—
450C4⋊C4—216no—
451C4⋊C4—28no—
452C4⋊C4—48no—
453C4⋊C4—48no—
454C4⋊C4—44no—
455C42—216no—
456C42—28no—
457C23C22×D4×C15111yescharacteristic
458C23C22×D4×C15112yes—
459C23C22×Q8×C15111yescharacteristic
460C23C22×Q8×C15111yescharacteristic
461C23C2×#41×C15112yes—
462C23C2×#41×C15111yescharacteristic
463C23C2×#41×C15111yescharacteristic
464C23C2×#41×C15112yes—
465C23H(5,𝔽2)×C15111yescharacteristic
466C232−1+4×C15112yes—
467C232−1+4×C15111yescharacteristic
468Q8—232no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4#120×C15114yes—
529C2×C4C22⋊Q8×C15114yes—
530C2×C4C22⋊Q8×C15118yes—
531C2×C4C22⋊Q8×C15114yes—
532C22C2×#120×C15111yescharacteristic
533C22C2×C22⋊Q8×C15112yes—
534C22C2×C22⋊Q8×C15111yescharacteristic
535C22C2×C22⋊Q8×C15111yescharacteristic
536C22#525×C15111yescharacteristic
537C22#525×C15112yes—
538C22#529×C15112yes—
539C22#532×C15111yescharacteristic
540C22#533×C15112yes—
541C22#536×C15111yescharacteristic
542C22#537×C15111yescharacteristic
543C22#541×C15112yes—
544C22#542×C15112yes—
545C22#546×C15112yes—
546C22#547×C15112yes—
547C22#548×C15112yes—
548C22D4×Q8×C15112yes—
549C22#552×C15112yes—
550C22#557×C15112yes—
551C22#557×C15111yescharacteristic
552C22#557×C15111yescharacteristic
553C22Q82×C15111yescharacteristic
554C22#559×C15111yescharacteristic
555C4—28no—
556C4—24no—
557C4—24no—
558C4—24no—
559C4—42no—
560C4—42no—
561C4—44no—
562C4—44no—
563C4—81no—
564C4—81no—
565C4—82no—
566C2#2396×C15111yescharacteristic
567C2#2409×C15111yescharacteristic
568C2#2430×C15111yescharacteristic
569C2#2451×C15112yes—
570C2#2453×C15112yes—
571C2#2458×C15112yes—
572C2#2462×C15112yes—
573C2#2565×C15111yescharacteristic
574C2#2582×C15111yescharacteristic
575C2#2637×C15111yescharacteristic
576C2#2848×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
71. C2×C4⋊C4×C151Q8semidirect
288. #14878C151direct (N × H)
289. C151#14878direct (N × H)
360. C2×C4⋊C4Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1512
C2×#398×C1512
C2×#387×C1512
#1446×C1512
#1444×C1512
#1442×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
#14878151