Finite Group Databasebeta

← C151×#23770 #50328695

Subgroups — C151×#23770 #50328695

Order 38656.

750 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2324×C151C211yesmaximal, characteristic
2#2314×C151C211yesmaximal, characteristic, complemented
3#2100×C151C211yesmaximal, characteristic, complemented
4#2093×C151C211yesmaximal, characteristic, complemented
5#2085×C151C211yesmaximal, characteristic, complemented
6#2076×C151C211yesmaximal, characteristic, complemented
7#2075×C151C211yesmaximal, characteristic, complemented
8#2073×C151C211yesmaximal, characteristic, complemented
9#2034×C151C211yesmaximal, characteristic
10#2033×C151C211yesmaximal, characteristic
11#1776×C151C211yesmaximal, characteristic, complemented
12C4×#107×C151C211yesmaximal, characteristic, complemented
13#1762×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic, complemented
16C2×#121×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#117×C151C2211yescharacteristic
19C2×#107×C151C2211yescharacteristic
20C2×#107×C151C2211yescharacteristic
21C2×#107×C151C2211yescharacteristic
22C2×#106×C151C2211yescharacteristic
23C2×#102×C151C2211yescharacteristic
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×C22⋊C8×C151C2211yescharacteristic
29C2×#97×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31#390×C151—21no—
32#390×C151C2211yescharacteristic
33#389×C151C2211yescharacteristic
34#388×C151—21no—
35#388×C151—21no—
36#388×C151—21no—
37#387×C151—21no—
38#387×C151—21no—
39#386×C151—21no—
40#385×C151—21no—
41#384×C151C2211yescharacteristic
42#382×C151C2211yescharacteristic
43#380×C151C2211yescharacteristic
44#380×C151C2211yescharacteristic
45#380×C151C2211yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49#340×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59C22×D4×C151—21no—
60C22×D4×C151C2311yescharacteristic
61C23×C4×C151—21no—
62C23×C4×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67#121×C151—22no—
68#121×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71#117×C151—22no—
72#117×C151—22no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151D411yescharacteristic
77C2×C4⋊C4×C151D411yescharacteristic
78C2×C4⋊C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151C2311yescharacteristic
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151D411yescharacteristic
93C2×C22⋊C4×C151D411yescharacteristic
94C2×C42×C151—21no—
95C2×C42×C151—21no—
96C2×C42×C151—21no—
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99#107×C151—22no—
100#107×C151—22no—
101#107×C151—22no—
102#106×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106#102×C151—22no—
107C22⋊C8×C151—22no—
108C22⋊C8×C151—22no—
109#97×C151—22no—
110C4×C8×C151—22no—
111#95×C151—21no—
112#95×C151—21no—
113#95×C151—21no—
114#95×C151—21no—
115#95×C151—21no—
116#95×C151—21no—
117#95×C151—21no—
118#95×C151—21no—
119#95×C151—21no—
120C24×C151—21no—
121C24×C151C2×D411yescharacteristic
122C2×D4×C151—24no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151—21no—
128C2×D4×C151—81no—
129C2×D4×C151—81no—
130C2×D4×C151#4112yes—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—42no—
145C22×C4×C151—81no—
146C22×C4×C151—81no—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2411yescharacteristic
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151#4112yes—
164C2×C8×C151#4112yes—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—81no—
181C4⋊C4×C151—81no—
182C4⋊C4×C151—81no—
183C4⋊C4×C151#4112yes—
184C22⋊C4×C151—24no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—42no—
188C22⋊C4×C151—81no—
189C22⋊C4×C151—81no—
190C22⋊C4×C151—81no—
191C22⋊C4×C151—81no—
192C22⋊C4×C151—81no—
193C42×C151—21no—
194C42×C151—21no—
195C42×C151—81no—
196C42×C151—81no—
197C42×C151—81no—
198C42×C151#4112yes—
199C42×C151#4112yes—
200C23×C151—21no—
201C23×C151—22no—
202C23×C151—21no—
203C23×C151—21no—
204C23×C151—21no—
205C23×C151—21no—
206C23×C151—21no—
207C23×C151—21no—
208C23×C151—41no—
209C23×C151—41no—
210C23×C151—41no—
211C23×C151—41no—
212C23×C151—41no—
213C23×C151—41no—
214C23×C151C22×D411yescharacteristic
215D4×C151—22no—
216D4×C151—22no—
217D4×C151—41no—
218D4×C151—41no—
219D4×C151—84no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—84no—
259C2×C4×C151#12312yes—
260C2×C4×C151#12312yes—
261C2×C4×C151C2×#4111yescharacteristic
262C2×C4×C151C2×#4111yescharacteristic
263C2×C4×C151C2×#4111yescharacteristic
264C2×C4×C151C2×#4111yescharacteristic
265C2×C4×C151C2×#4111yescharacteristic
266C2×C4×C151C2×#4111yescharacteristic
267C8×C151—22no—
268C8×C151—22no—
269C8×C151—41no—
270C8×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—42no—
275C22×C151—41no—
276C22×C151—42no—
277C22×C151—41no—
278C22×C151—42no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—81no—
282C22×C151—81no—
283C22×C151—81no—
284C22×C151—81no—
285C22×C151C2×#12311yescharacteristic
286C22×C151#52511yescharacteristic
287C22×C151#53211yescharacteristic
288C22×C151#57611yescharacteristic
289C22×C151#57611yescharacteristic
290C22×C151#57711yescharacteristic
291C22×C151#57811yescharacteristic
292C4×C151—22no—
293C4×C151—22no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—42no—
297C4×C151—41no—
298C4×C151—81no—
299C4×C151—81no—
300C4×C151—81no—
301C4×C151—81no—
302C4×C151—81no—
303C4×C151—81no—
304C4×C151#52911yescharacteristic
305C4×C151#52911yescharacteristic
306C4×C151#52911yescharacteristic
307C4×C151#52911yescharacteristic
308C2×C151—81no—
309C2×C151—82no—
310C2×C151#239511yescharacteristic
311C2×C151#309611yescharacteristic
312C2×C151#309811yescharacteristic
313C2×C151#311811yescharacteristic
314C2×C151#312411yescharacteristic
315C2×C151#317611yescharacteristic
316C2×C151#317811yescharacteristic
317#23770C15111yesmaximal, characteristic, direct product factor, Sylow
318C151#2377011yescharacteristic, direct product factor, Sylow
319#2324C2×C15111yescharacteristic
320#2314C2×C15111yescharacteristic, complemented
321#2100C2×C15111yescharacteristic, complemented
322#2093C2×C15111yescharacteristic, complemented
323#2085C2×C15111yescharacteristic, complemented
324#2076C2×C15111yescharacteristic, complemented
325#2075C2×C15111yescharacteristic, complemented
326#2073C2×C15111yescharacteristic, complemented
327#2034C2×C15111yescharacteristic
328#2033C2×C15111yescharacteristic
329#1776C2×C15111yescharacteristic, complemented
330C4×#107C2×C15111yescharacteristic, complemented
331#1762C2×C15111yescharacteristic, complemented
332C4×#102C2×C15111yescharacteristic, complemented
333#1750C2×C15111yescharacteristic, complemented
334C2×#121C22×C15111yescharacteristic
335C2×C4×D4C22×C15111yescharacteristic
336C2×#117C22×C15111yescharacteristic
337C2×#107C22×C15111yescharacteristic
338C2×#107C22×C15111yescharacteristic
339C2×#107C22×C15111yescharacteristic
340C2×#106C22×C15111yescharacteristic
341C2×#102C22×C15111yescharacteristic
342C2×#102C22×C15111yescharacteristic
343C2×#102C22×C15111yescharacteristic
344C2×#102C22×C15111yescharacteristic
345C2×C22⋊C8C22×C15111yescharacteristic
346C2×C22⋊C8C22×C15111yescharacteristic
347C2×#97C22×C15111yescharacteristic
348C2×C4×C8C22×C15111yescharacteristic
349#390—21no—
350#390C22×C15111yescharacteristic
351#389C22×C15111yescharacteristic
352#388—21no—
353#388—21no—
354#388—21no—
355#387—21no—
356#387—21no—
357#386—21no—
358#385—21no—
359#384C22×C15111yescharacteristic
360#382C22×C15111yescharacteristic
361#380C22×C15111yescharacteristic
362#380C22×C15111yescharacteristic
363#380C22×C15111yescharacteristic
364C4×C4⋊C4C22×C15111yescharacteristic
365C4×C4⋊C4C22×C15111yescharacteristic
366C4×C4⋊C4C22×C15111yescharacteristic
367#340C22×C15111yescharacteristic
368#340C22×C15111yescharacteristic
369#340C22×C15111yescharacteristic
370#340C22×C15111yescharacteristic
371#340C22×C15111yescharacteristic
372#340C22×C15111yescharacteristic
373#340C22×C15111yescharacteristic
374#340C22×C15111yescharacteristic
375#336C22×C15111yescharacteristic
376#336C22×C15111yescharacteristic
377C22×D4—21no—
378C22×D4C23×C15111yescharacteristic
379C23×C4—21no—
380C23×C4C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382C22×C8C23×C15111yescharacteristic
383C22×C8C23×C15111yescharacteristic
384C22×C8C23×C15111yescharacteristic
385#121—22no—
386#121—22no—
387C4×D4—22no—
388C4×D4—22no—
389#117—22no—
390#117—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C15111yescharacteristic
395C2×C4⋊C4D4×C15111yescharacteristic
396C2×C4⋊C4C23×C15111yescharacteristic
397C2×C4⋊C4C23×C15111yescharacteristic
398C2×C4⋊C4C23×C15111yescharacteristic
399C2×C4⋊C4C23×C15111yescharacteristic
400C2×C4⋊C4C23×C15111yescharacteristic
401C2×C4⋊C4C23×C15111yescharacteristic
402C2×C4⋊C4C23×C15111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4D4×C15111yescharacteristic
411C2×C22⋊C4D4×C15111yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42C23×C15111yescharacteristic
416C2×C42C23×C15111yescharacteristic
417#107—22no—
418#107—22no—
419#107—22no—
420#106—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424#102—22no—
425C22⋊C8—22no—
426C22⋊C8—22no—
427#97—22no—
428C4×C8—22no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438C24—21no—
439C24C2×D4×C15111yescharacteristic
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4#41×C15112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C24×C15111yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8#41×C15112yes—
482C2×C8#41×C15112yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4#41×C15112yes—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—81no—
514C42—81no—
515C42—81no—
516C42#41×C15112yes—
517C42#41×C15112yes—
518C23—21no—
519C23—22no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×D4×C15111yescharacteristic
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—84no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4#123×C15112yes—
578C2×C4#123×C15112yes—
579C2×C4C2×#41×C15111yescharacteristic
580C2×C4C2×#41×C15111yescharacteristic
581C2×C4C2×#41×C15111yescharacteristic
582C2×C4C2×#41×C15111yescharacteristic
583C2×C4C2×#41×C15111yescharacteristic
584C2×C4C2×#41×C15111yescharacteristic
585C8—22no—
586C8—22no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—42no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C2×#123×C15111yescharacteristic
604C22#525×C15111yescharacteristic
605C22#532×C15111yescharacteristic
606C22#576×C15111yescharacteristic
607C22#576×C15111yescharacteristic
608C22#577×C15111yescharacteristic
609C22#578×C15111yescharacteristic
610C4—22no—
611C4—22no—
612C4—42no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4#529×C15111yescharacteristic
623C4#529×C15111yescharacteristic
624C4#529×C15111yescharacteristic
625C4#529×C15111yescharacteristic
626C2—81no—
627C2—82no—
628C2#2395×C15111yescharacteristic
629C2#3096×C15111yescharacteristic
630C2#3098×C15111yescharacteristic
631C2#3118×C15111yescharacteristic
632C2#3124×C15111yescharacteristic
633C2#3176×C15111yescharacteristic
634C2#3178×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2314×C151C2semidirect
3. #2100×C151C2semidirect
4. #2093×C151C2semidirect
5. #2085×C151C2semidirect
6. #2076×C151C2semidirect
7. #2075×C151C2semidirect
8. #2073×C151C2semidirect
11. #1776×C151C2semidirect
12. C4×#107×C151C2semidirect
13. #1762×C151C2semidirect
14. C4×#102×C151C2semidirect
15. #1750×C151C2semidirect
317. #23770C151direct (N × H)
318. C151#23770direct (N × H)
320. #2314C2×C151semidirect
321. #2100C2×C151semidirect
322. #2093C2×C151semidirect
323. #2085C2×C151semidirect
324. #2076C2×C151semidirect
325. #2075C2×C151semidirect
326. #2073C2×C151semidirect
329. #1776C2×C151semidirect
330. C4×#107C2×C151semidirect
331. #1762C2×C151semidirect
332. C4×#102C2×C151semidirect
333. #1750C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2324×C1512
#2314×C1512
#2100×C1512
#2093×C1512
#2085×C1512
#2076×C1512
#2075×C1512
#2073×C1512
#2034×C1512
#2033×C1512
#1776×C1512
C4×#107×C1512
#1762×C1512
C4×#102×C1512
#1750×C1512
#23770151