Finite Group Databasebeta

← C151×#15102 #50320027

Subgroups — C151×#15102 #50320027

Order 38656.

1182 conjugacy classes of subgroups.

The subgroup lattice has 564 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#1445×C151C212yesmaximal
4#1444×C151C211yesmaximal, characteristic
5#1443×C151C212yesmaximal
6#1442×C151C211yesmaximal, characteristic
7#1441×C151C211yesmaximal, characteristic
8#1441×C151C211yesmaximal, characteristic
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×C151C2212yes—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C42×C151C2211yescharacteristic
18C22×C42×C151C2212yes—
19#387×C151—24no—
20C4×C4⋊C4×C151—24no—
21C2×#95×C151C2212yes—
22C2×#95×C151C2211yescharacteristic
23C2×#95×C151C2211yescharacteristic
24C2×#95×C151C2212yes—
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×C151C2211yescharacteristic
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C23×C4×C151C2312yes—
38C23×C4×C151C2311yescharacteristic
39C23×C4×C151C2311yescharacteristic
40C23×C4×C151C2311yescharacteristic
41C23×C4×C151C2311yescharacteristic
42C23×C4×C151C2311yescharacteristic
43C23×C4×C151C2312yes—
44C23×C4×C151C2312yes—
45C23×C4×C151C2312yes—
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—24no—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—42no—
60C2×C4⋊C4×C151Q814yes—
61C2×C42×C151—22no—
62C2×C42×C151—22no—
63C2×C42×C151—24no—
64C2×C42×C151—42no—
65C2×C42×C151—42no—
66C2×C42×C151D414yes—
67#95×C151—24no—
68#95×C151—22no—
69#95×C151—22no—
70#95×C151—22no—
71#95×C151—22no—
72#95×C151—24no—
73#95×C151—22no—
74#95×C151—24no—
75#95×C151—24no—
76#95×C151—24no—
77#95×C151—24no—
78#95×C151—24no—
79#95×C151—22no—
80#95×C151—42no—
81#95×C151—42no—
82#95×C151—42no—
83C24×C151C2411yescharacteristic
84C22×C4×C151—21no—
85C22×C4×C151—21no—
86C22×C4×C151—22no—
87C22×C4×C151—22no—
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—22no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—22no—
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—22no—
108C22×C4×C151—22no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—21no—
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—22no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—21no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
136C22×C4×C151—22no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×Q812yes—
143C22×C4×C151C2×Q812yes—
144C22×C4×C151C2×Q812yes—
145C22×C4×C151#4114yes—
146C22×C4×C151#4114yes—
147C22×C4×C151#4114yes—
148C22×C4×C151#4112yes—
149C22×C4×C151#4112yes—
150C22×C4×C151#4112yes—
151C4⋊C4×C151—28no—
152C4⋊C4×C151—28no—
153C4⋊C4×C151—28no—
154C4⋊C4×C151—48no—
155C4⋊C4×C151—44no—
156C42×C151—28no—
157C42×C151—48no—
158C23×C151C22×D411yescharacteristic
159C23×C151C22×Q811yescharacteristic
160C23×C151C2×#4111yescharacteristic
161C23×C151C2×#4111yescharacteristic
162C23×C151C2×#4111yescharacteristic
163C23×C151C2×#4112yes—
164C23×C151C2×#4112yes—
165C23×C151C2×#4112yes—
166C23×C151H(5,𝔽2)11yescharacteristic
167C23×C151H(5,𝔽2)11yescharacteristic
168C23×C1512−1+412yes—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—24no—
173C2×C4×C151—24no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—24no—
183C2×C4×C151—24no—
184C2×C4×C151—24no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—22no—
188C2×C4×C151—24no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—24no—
192C2×C4×C151—24no—
193C2×C4×C151—24no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151C22⋊Q814yes—
235C2×C4×C151#12314yes—
236C22×C151C2×C22⋊Q811yescharacteristic
237C22×C151C2×#12311yescharacteristic
238C22×C151#52511yescharacteristic
239C22×C151#52511yescharacteristic
240C22×C151#52912yes—
241C22×C151#52912yes—
242C22×C151#52912yes—
243C22×C151#53211yescharacteristic
244C22×C151#53312yes—
245C22×C151#53511yescharacteristic
246C22×C151#53611yescharacteristic
247C22×C151#53912yes—
248C22×C151#53912yes—
249C22×C151#55112yes—
250C22×C151#55212yes—
251C22×C151#55311yescharacteristic
252C22×C151#55312yes—
253C22×C151#55311yescharacteristic
254C22×C151#55411yescharacteristic
255C22×C151#55411yescharacteristic
256C22×C151#55612yes—
257C22×C151#55612yes—
258C22×C151#55712yes—
259C4×C151—24no—
260C4×C151—24no—
261C4×C151—44no—
262C4×C151—44no—
263C4×C151—44no—
264C4×C151—42no—
265C4×C151—42no—
266C4×C151—42no—
267C4×C151—82no—
268C4×C151—81no—
269C4×C151—81no—
270C2×C151#239611yescharacteristic
271C2×C151#248711yescharacteristic
272C2×C151#249911yescharacteristic
273C2×C151#257312yes—
274C2×C151#258111yescharacteristic
275C2×C151#258512yes—
276C2×C151#258812yes—
277C2×C151#259412yes—
278C2×C151#260311yescharacteristic
279C2×C151#263311yescharacteristic
280C2×C151#285311yescharacteristic
281#15102C15111yesmaximal, characteristic, direct product factor, Sylow
282C151#1510211yescharacteristic, direct product factor, Sylow
283C2×#387C2×C15111yescharacteristic
284C2×C4×C4⋊C4C2×C15111yescharacteristic
285#1445C2×C15112yes—
286#1444C2×C15111yescharacteristic
287#1443C2×C15112yes—
288#1442C2×C15111yescharacteristic
289#1441C2×C15111yescharacteristic
290#1441C2×C15111yescharacteristic
291#1436C2×C15112yes—
292#1436C2×C15112yes—
293#1434C2×C15111yescharacteristic
294C22×C4⋊C4C22×C15111yescharacteristic
295C22×C4⋊C4C22×C15111yescharacteristic
296C22×C4⋊C4C22×C15111yescharacteristic
297C22×C4⋊C4C22×C15112yes—
298C22×C4⋊C4C22×C15111yescharacteristic
299C22×C42C22×C15111yescharacteristic
300C22×C42C22×C15112yes—
301#387—24no—
302C4×C4⋊C4—24no—
303C2×#95C22×C15112yes—
304C2×#95C22×C15111yescharacteristic
305C2×#95C22×C15111yescharacteristic
306C2×#95C22×C15112yes—
307C2×#95C22×C15111yescharacteristic
308C2×#95C22×C15112yes—
309C2×#95C22×C15112yes—
310C2×#95C22×C15112yes—
311C2×#95C22×C15112yes—
312C2×#95C22×C15111yescharacteristic
313C2×#95C22×C15111yescharacteristic
314C2×#95C22×C15112yes—
315C2×#95C22×C15111yescharacteristic
316C2×#95C22×C15112yes—
317C2×#95C22×C15112yes—
318C2×#95C22×C15112yes—
319C23×C4C23×C15111yescharacteristic
320C23×C4C23×C15111yescharacteristic
321C23×C4C23×C15112yes—
322C23×C4C23×C15111yescharacteristic
323C23×C4C23×C15111yescharacteristic
324C23×C4C23×C15112yes—
325C23×C4C23×C15112yes—
326C23×C4C23×C15112yes—
327C23×C4C23×C15111yescharacteristic
328C23×C4C23×C15111yescharacteristic
329C23×C4C23×C15111yescharacteristic
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4Q8×C15114yes—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—42no—
347C2×C42—42no—
348C2×C42D4×C15114yes—
349#95—24no—
350#95—22no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—22no—
357#95—24no—
358#95—22no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—42no—
363#95—42no—
364#95—42no—
365C24C24×C15111yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
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—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4C2×D4×C15112yes—
422C22×C4C2×D4×C15112yes—
423C22×C4C2×D4×C15112yes—
424C22×C4C2×Q8×C15112yes—
425C22×C4C2×Q8×C15112yes—
426C22×C4C2×Q8×C15112yes—
427C22×C4#41×C15114yes—
428C22×C4#41×C15114yes—
429C22×C4#41×C15114yes—
430C22×C4#41×C15112yes—
431C22×C4#41×C15112yes—
432C22×C4#41×C15112yes—
433C4⋊C4—28no—
434C4⋊C4—28no—
435C4⋊C4—28no—
436C4⋊C4—48no—
437C4⋊C4—44no—
438C42—28no—
439C42—48no—
440C23C22×D4×C15111yescharacteristic
441C23C22×Q8×C15111yescharacteristic
442C23C2×#41×C15111yescharacteristic
443C23C2×#41×C15111yescharacteristic
444C23C2×#41×C15111yescharacteristic
445C23C2×#41×C15112yes—
446C23C2×#41×C15112yes—
447C23C2×#41×C15112yes—
448C23H(5,𝔽2)×C15111yescharacteristic
449C23H(5,𝔽2)×C15111yescharacteristic
450C232−1+4×C15112yes—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4C22⋊Q8×C15114yes—
517C2×C4#123×C15114yes—
518C22C2×C22⋊Q8×C15111yescharacteristic
519C22C2×#123×C15111yescharacteristic
520C22#525×C15111yescharacteristic
521C22#525×C15111yescharacteristic
522C22#529×C15112yes—
523C22#529×C15112yes—
524C22#529×C15112yes—
525C22#532×C15111yescharacteristic
526C22#533×C15112yes—
527C22#535×C15111yescharacteristic
528C22#536×C15111yescharacteristic
529C22#539×C15112yes—
530C22#539×C15112yes—
531C22#551×C15112yes—
532C22#552×C15112yes—
533C22#553×C15111yescharacteristic
534C22#553×C15112yes—
535C22#553×C15111yescharacteristic
536C22#554×C15111yescharacteristic
537C22#554×C15111yescharacteristic
538C22#556×C15112yes—
539C22#556×C15112yes—
540C22#557×C15112yes—
541C4—24no—
542C4—24no—
543C4—44no—
544C4—44no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—44no—
549C4—82no—
550C4—81no—
551C4—81no—
552C2#2396×C15111yescharacteristic
553C2#2487×C15111yescharacteristic
554C2#2499×C15111yescharacteristic
555C2#2573×C15112yes—
556C2#2581×C15111yescharacteristic
557C2#2585×C15112yes—
558C2#2588×C15112yes—
559C2#2594×C15112yes—
560C2#2603×C15111yescharacteristic
561C2#2633×C15111yescharacteristic
562C2#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
281. #15102C151direct (N × H)
282. C151#15102direct (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
#1445×C1512
#1444×C1512
#1443×C1512
#1442×C1512
#1441×C1512
#1436×C1512
#1434×C1512
#15102151