Finite Group Databasebeta

← C151×#15101 #50320026

Subgroups — C151×#15101 #50320026

Order 38656.

1226 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387×C151C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
3#1444×C151C211yesmaximal, characteristic
4#1444×C151C211yesmaximal, characteristic
5#1442×C151C212yesmaximal
6#1441×C151C211yesmaximal, characteristic
7#1441×C151C211yesmaximal, characteristic
8#1441×C151C212yesmaximal
9#1436×C151C212yesmaximal
10#1436×C151C212yesmaximal
11#1434×C151C211yesmaximal, characteristic
12C22×C4⋊C4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17C22×C4⋊C4×C151C2212yes—
18C22×C42×C151C2211yescharacteristic
19C22×C42×C151C2212yes—
20#387×C151—24no—
21C4×C4⋊C4×C151—24no—
22C2×#95×C151C2211yescharacteristic
23C2×#95×C151C2211yescharacteristic
24C2×#95×C151C2211yescharacteristic
25C2×#95×C151C2211yescharacteristic
26C2×#95×C151C2212yes—
27C2×#95×C151C2212yes—
28C2×#95×C151C2212yes—
29C2×#95×C151C2212yes—
30C2×#95×C151C2211yescharacteristic
31C2×#95×C151C2211yescharacteristic
32C2×#95×C151C2212yes—
33C2×#95×C151C2212yes—
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C23×C4×C151C2311yescharacteristic
38C23×C4×C151C2311yescharacteristic
39C23×C4×C151C2311yescharacteristic
40C23×C4×C151C2312yes—
41C23×C4×C151C2312yes—
42C23×C4×C151C2311yescharacteristic
43C23×C4×C151C2312yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2311yescharacteristic
46C23×C4×C151C2311yescharacteristic
47C23×C4×C151C2311yescharacteristic
48C2×C4⋊C4×C151—22no—
49C2×C4⋊C4×C151—22no—
50C2×C4⋊C4×C151—22no—
51C2×C4⋊C4×C151—24no—
52C2×C4⋊C4×C151—24no—
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—24no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—42no—
62C2×C4⋊C4×C151—42no—
63C2×C4⋊C4×C151—42no—
64C2×C42×C151—22no—
65C2×C42×C151—22no—
66C2×C42×C151—24no—
67C2×C42×C151—42no—
68C2×C42×C151—42no—
69C2×C42×C151D414yes—
70#95×C151—24no—
71#95×C151—22no—
72#95×C151—22no—
73#95×C151—22no—
74#95×C151—22no—
75#95×C151—24no—
76#95×C151—22no—
77#95×C151—22no—
78#95×C151—24no—
79#95×C151—24no—
80#95×C151—42no—
81#95×C151—42no—
82#95×C151—42no—
83#95×C151—42no—
84#95×C151Q818yes—
85C24×C151C2411yescharacteristic
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—22no—
89C22×C4×C151—22no—
90C22×C4×C151—22no—
91C22×C4×C151—21no—
92C22×C4×C151—22no—
93C22×C4×C151—22no—
94C22×C4×C151—21no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—22no—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151—22no—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
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—22no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D412yes—
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×Q814yes—
145C22×C4×C151C2×Q814yes—
146C22×C4×C151C2×Q814yes—
147C22×C4×C151#4112yes—
148C22×C4×C151#4114yes—
149C22×C4×C151#4114yes—
150C22×C4×C151#4112yes—
151C22×C4×C151#4112yes—
152C22×C4×C151#4112yes—
153C4⋊C4×C151—28no—
154C4⋊C4×C151—28no—
155C4⋊C4×C151—28no—
156C4⋊C4×C151—48no—
157C4⋊C4×C151—48no—
158C4⋊C4×C151—44no—
159C42×C151—28no—
160C42×C151—48no—
161C23×C151C22×D411yescharacteristic
162C23×C151C22×Q812yes—
163C23×C151C2×#4111yescharacteristic
164C23×C151C2×#4111yescharacteristic
165C23×C151C2×#4112yes—
166C23×C151C2×#4112yes—
167C23×C151C2×#4111yescharacteristic
168C23×C151C2×#4111yescharacteristic
169C23×C151H(5,𝔽2)12yes—
170C23×C151H(5,𝔽2)11yescharacteristic
171C23×C1512−1+411yescharacteristic
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—24no—
176C2×C4×C151—24no—
177C2×C4×C151—22no—
178C2×C4×C151—24no—
179C2×C4×C151—24no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—24no—
183C2×C4×C151—22no—
184C2×C4×C151—24no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—24no—
188C2×C4×C151—22no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—24no—
192C2×C4×C151—24no—
193C2×C4×C151—22no—
194C2×C4×C151—24no—
195C2×C4×C151—22no—
196C2×C4×C151—24no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—41no—
217C2×C4×C151—42no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151#12314yes—
238C2×C4×C151C4⋊Q814yes—
239C22×C151C2×#12311yescharacteristic
240C22×C151#52511yescharacteristic
241C22×C151#52511yescharacteristic
242C22×C151#52511yescharacteristic
243C22×C151#52912yes—
244C22×C151#52912yes—
245C22×C151C2×C4⋊Q811yescharacteristic
246C22×C151#53312yes—
247C22×C151#53312yes—
248C22×C151#53511yescharacteristic
249C22×C151#53711yescharacteristic
250C22×C151#53812yes—
251C22×C151#53912yes—
252C22×C151#55112yes—
253C22×C151#55211yescharacteristic
254C22×C151#55312yes—
255C22×C151#55311yescharacteristic
256C22×C151#55412yes—
257C22×C151#55412yes—
258C22×C151#55412yes—
259C22×C151#55511yescharacteristic
260C22×C151#55611yescharacteristic
261C22×C151#55712yes—
262C4×C151—24no—
263C4×C151—24no—
264C4×C151—44no—
265C4×C151—44no—
266C4×C151—42no—
267C4×C151—44no—
268C4×C151—44no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—81no—
272C4×C151—81no—
273C2×C151#239911yescharacteristic
274C2×C151#248511yescharacteristic
275C2×C151#250211yescharacteristic
276C2×C151#257412yes—
277C2×C151#258411yescharacteristic
278C2×C151#258512yes—
279C2×C151#258712yes—
280C2×C151#258812yes—
281C2×C151#259811yescharacteristic
282C2×C151#263611yescharacteristic
283C2×C151#285311yescharacteristic
284#15101C15111yesmaximal, characteristic, direct product factor, Sylow
285C151#1510111yescharacteristic, direct product factor, Sylow
286C2×#387C2×C15111yescharacteristic
287C2×C4×C4⋊C4C2×C15111yescharacteristic
288#1444C2×C15111yescharacteristic
289#1444C2×C15111yescharacteristic
290#1442C2×C15112yes—
291#1441C2×C15111yescharacteristic
292#1441C2×C15111yescharacteristic
293#1441C2×C15112yes—
294#1436C2×C15112yes—
295#1436C2×C15112yes—
296#1434C2×C15111yescharacteristic
297C22×C4⋊C4C22×C15111yescharacteristic
298C22×C4⋊C4C22×C15111yescharacteristic
299C22×C4⋊C4C22×C15111yescharacteristic
300C22×C4⋊C4C22×C15111yescharacteristic
301C22×C4⋊C4C22×C15112yes—
302C22×C4⋊C4C22×C15112yes—
303C22×C42C22×C15111yescharacteristic
304C22×C42C22×C15112yes—
305#387—24no—
306C4×C4⋊C4—24no—
307C2×#95C22×C15111yescharacteristic
308C2×#95C22×C15111yescharacteristic
309C2×#95C22×C15111yescharacteristic
310C2×#95C22×C15111yescharacteristic
311C2×#95C22×C15112yes—
312C2×#95C22×C15112yes—
313C2×#95C22×C15112yes—
314C2×#95C22×C15112yes—
315C2×#95C22×C15111yescharacteristic
316C2×#95C22×C15111yescharacteristic
317C2×#95C22×C15112yes—
318C2×#95C22×C15112yes—
319C2×#95C22×C15112yes—
320C2×#95C22×C15112yes—
321C2×#95C22×C15112yes—
322C23×C4C23×C15111yescharacteristic
323C23×C4C23×C15111yescharacteristic
324C23×C4C23×C15112yes—
325C23×C4C23×C15112yes—
326C23×C4C23×C15111yescharacteristic
327C23×C4C23×C15111yescharacteristic
328C23×C4C23×C15112yes—
329C23×C4C23×C15112yes—
330C23×C4C23×C15111yescharacteristic
331C23×C4C23×C15111yescharacteristic
332C23×C4C23×C15111yescharacteristic
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—42no—
353C2×C42—42no—
354C2×C42D4×C15114yes—
355#95—24no—
356#95—22no—
357#95—22no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—22no—
362#95—22no—
363#95—22no—
364#95—22no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95Q8×C15118yes—
370C24C24×C15111yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4C2×D4×C15112yes—
427C22×C4C2×D4×C15112yes—
428C22×C4C2×D4×C15112yes—
429C22×C4C2×Q8×C15114yes—
430C22×C4C2×Q8×C15114yes—
431C22×C4C2×Q8×C15114yes—
432C22×C4#41×C15112yes—
433C22×C4#41×C15114yes—
434C22×C4#41×C15114yes—
435C22×C4#41×C15112yes—
436C22×C4#41×C15112yes—
437C22×C4#41×C15112yes—
438C4⋊C4—28no—
439C4⋊C4—28no—
440C4⋊C4—28no—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C4⋊C4—44no—
444C42—28no—
445C42—48no—
446C23C22×D4×C15111yescharacteristic
447C23C22×Q8×C15112yes—
448C23C2×#41×C15111yescharacteristic
449C23C2×#41×C15111yescharacteristic
450C23C2×#41×C15112yes—
451C23C2×#41×C15112yes—
452C23C2×#41×C15111yescharacteristic
453C23C2×#41×C15111yescharacteristic
454C23H(5,𝔽2)×C15112yes—
455C23H(5,𝔽2)×C15111yescharacteristic
456C232−1+4×C15111yescharacteristic
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4#123×C15114yes—
523C2×C4C4⋊Q8×C15114yes—
524C22C2×#123×C15111yescharacteristic
525C22#525×C15111yescharacteristic
526C22#525×C15111yescharacteristic
527C22#525×C15111yescharacteristic
528C22#529×C15112yes—
529C22#529×C15112yes—
530C22C2×C4⋊Q8×C15111yescharacteristic
531C22#533×C15112yes—
532C22#533×C15112yes—
533C22#535×C15111yescharacteristic
534C22#537×C15111yescharacteristic
535C22#538×C15112yes—
536C22#539×C15112yes—
537C22#551×C15112yes—
538C22#552×C15111yescharacteristic
539C22#553×C15112yes—
540C22#553×C15111yescharacteristic
541C22#554×C15112yes—
542C22#554×C15112yes—
543C22#554×C15112yes—
544C22#555×C15111yescharacteristic
545C22#556×C15111yescharacteristic
546C22#557×C15112yes—
547C4—24no—
548C4—24no—
549C4—42no—
550C4—44no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—44no—
555C4—44no—
556C4—81no—
557C4—81no—
558C2#2399×C15111yescharacteristic
559C2#2485×C15111yescharacteristic
560C2#2502×C15111yescharacteristic
561C2#2574×C15112yes—
562C2#2584×C15111yescharacteristic
563C2#2585×C15112yes—
564C2#2587×C15112yes—
565C2#2588×C15112yes—
566C2#2598×C15111yescharacteristic
567C2#2636×C15111yescharacteristic
568C2#2853×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
284. #15101C151direct (N × H)
285. C151#15101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#387×C1512
C2×C4×C4⋊C4×C1512
#1444×C1512
#1442×C1512
#1441×C1512
#1436×C1512
#1434×C1512
#15101151