Finite Group Databasebeta

← C151×#15098 #50320023

Subgroups — C151×#15098 #50320023

Order 38656.

1270 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×#389×C151C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
3#1444×C151C211yesmaximal, characteristic
4#1444×C151C211yesmaximal, characteristic
5#1444×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×C151C2212yes—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2212yes—
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2212yes—
19C22×C42×C151C2211yescharacteristic
20C22×C42×C151C2211yescharacteristic
21C22×C42×C151C2211yescharacteristic
22#389×C151—24no—
23C4×C4⋊C4×C151—24no—
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×C151C2312yes—
38C23×C4×C151C2311yescharacteristic
39C23×C4×C151C2312yes—
40C23×C4×C151C2312yes—
41C23×C4×C151C2311yescharacteristic
42C23×C4×C151C2311yescharacteristic
43C23×C4×C151C2312yes—
44C23×C4×C151C2311yescharacteristic
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—22no—
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—24no—
56C2×C4⋊C4×C151—22no—
57C2×C4⋊C4×C151—24no—
58C2×C4⋊C4×C151—24no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—42no—
61C2×C4⋊C4×C151—42no—
62C2×C4⋊C4×C151—42no—
63C2×C4⋊C4×C151—42no—
64C2×C4⋊C4×C151—42no—
65C2×C4⋊C4×C151—42no—
66C2×C4⋊C4×C151Q814yes—
67C2×C42×C151—22no—
68C2×C42×C151—22no—
69C2×C42×C151—22no—
70C2×C42×C151—22no—
71C2×C42×C151—42no—
72C2×C42×C151—42no—
73C2×C42×C151D414yes—
74#95×C151—22no—
75#95×C151—22no—
76#95×C151—24no—
77#95×C151—24no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151—24no—
81#95×C151—24no—
82#95×C151—42no—
83#95×C151—42no—
84#95×C151—42no—
85#95×C151—42no—
86#95×C151Q818yes—
87C24×C151C2411yescharacteristic
88C22×C4×C151—21no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151—21no—
93C22×C4×C151—22no—
94C22×C4×C151—21no—
95C22×C4×C151—22no—
96C22×C4×C151—22no—
97C22×C4×C151—21no—
98C22×C4×C151—21no—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—21no—
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—22no—
123C22×C4×C151—22no—
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—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×C151C2×D412yes—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×Q814yes—
142C22×C4×C151C2×Q814yes—
143C22×C4×C151C2×Q812yes—
144C22×C4×C151C2×Q812yes—
145C22×C4×C151C2×Q812yes—
146C22×C4×C151C2×Q814yes—
147C22×C4×C151#4114yes—
148C22×C4×C151#4112yes—
149C22×C4×C151#4112yes—
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—44no—
158C4⋊C4×C151—48no—
159C4⋊C4×C151—48no—
160C42×C151—28no—
161C42×C151—44no—
162C42×C151—44no—
163C23×C151C22×D411yescharacteristic
164C23×C151C22×Q811yescharacteristic
165C23×C151C22×Q812yes—
166C23×C151C2×#4111yescharacteristic
167C23×C151C2×#4111yescharacteristic
168C23×C151C2×#4111yescharacteristic
169C23×C151C2×#4111yescharacteristic
170C23×C151C2×#4111yescharacteristic
171C23×C151C2×#4112yes—
172C23×C151H(5,𝔽2)12yes—
173C23×C151H(5,𝔽2)12yes—
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—22no—
183C2×C4×C151—22no—
184C2×C4×C151—24no—
185C2×C4×C151—24no—
186C2×C4×C151—24no—
187C2×C4×C151—24no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—22no—
193C2×C4×C151—24no—
194C2×C4×C151—24no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—24no—
199C2×C4×C151—24no—
200C2×C4×C151—24no—
201C2×C4×C151—24no—
202C2×C4×C151—24no—
203C2×C4×C151—24no—
204C2×C4×C151—24no—
205C2×C4×C151—24no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
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—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
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×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151C22⋊Q814yes—
237C2×C4×C151#12514yes—
238C2×C4×C151C4⋊Q814yes—
239C22×C151C2×C22⋊Q811yescharacteristic
240C22×C151#52511yescharacteristic
241C22×C151#52511yescharacteristic
242C22×C151#52511yescharacteristic
243C22×C151C2×#12511yescharacteristic
244C22×C151#52911yescharacteristic
245C22×C151#52911yescharacteristic
246C22×C151C2×C4⋊Q811yescharacteristic
247C22×C151#53311yescharacteristic
248C22×C151#53312yes—
249C22×C151#53312yes—
250C22×C151#53411yescharacteristic
251C22×C151#53511yescharacteristic
252C22×C151#53812yes—
253C22×C151#54012yes—
254C22×C151#55112yes—
255C22×C151#55312yes—
256C22×C151#55312yes—
257C22×C151#55412yes—
258C22×C151#55412yes—
259C22×C151#55412yes—
260C22×C151#55412yes—
261C22×C151Q8212yes—
262C4×C151—24no—
263C4×C151—24no—
264C4×C151—24no—
265C4×C151—42no—
266C4×C151—44no—
267C4×C151—42no—
268C4×C151—44no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—44no—
272C4×C151—82no—
273C2×C151#239911yescharacteristic
274C2×C151#250712yes—
275C2×C151#252212yes—
276C2×C151#256711yescharacteristic
277C2×C151#257911yescharacteristic
278C2×C151#258311yescharacteristic
279C2×C151#258612yes—
280C2×C151#258712yes—
281C2×C151#259811yescharacteristic
282C2×C151#263511yescharacteristic
283C2×C151#285111yescharacteristic
284#15098C15111yesmaximal, characteristic, direct product factor, Sylow
285C151#1509811yescharacteristic, direct product factor, Sylow
286C2×#389C2×C15111yescharacteristic
287C2×C4×C4⋊C4C2×C15111yescharacteristic
288#1444C2×C15111yescharacteristic
289#1444C2×C15112yes—
290#1444C2×C15111yescharacteristic
291#1441C2×C15111yescharacteristic
292#1441C2×C15112yes—
293#1441C2×C15111yescharacteristic
294#1436C2×C15112yes—
295#1436C2×C15112yes—
296#1434C2×C15111yescharacteristic
297C22×C4⋊C4C22×C15111yescharacteristic
298C22×C4⋊C4C22×C15111yescharacteristic
299C22×C4⋊C4C22×C15112yes—
300C22×C4⋊C4C22×C15111yescharacteristic
301C22×C4⋊C4C22×C15112yes—
302C22×C4⋊C4C22×C15111yescharacteristic
303C22×C4⋊C4C22×C15112yes—
304C22×C42C22×C15111yescharacteristic
305C22×C42C22×C15111yescharacteristic
306C22×C42C22×C15111yescharacteristic
307#389—24no—
308C4×C4⋊C4—24no—
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×C15112yes—
323C23×C4C23×C15112yes—
324C23×C4C23×C15112yes—
325C23×C4C23×C15111yescharacteristic
326C23×C4C23×C15112yes—
327C23×C4C23×C15111yescharacteristic
328C23×C4C23×C15111yescharacteristic
329C23×C4C23×C15111yescharacteristic
330C23×C4C23×C15111yescharacteristic
331C23×C4C23×C15111yescharacteristic
332C23×C4C23×C15111yescharacteristic
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
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—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4Q8×C15114yes—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42D4×C15114yes—
359#95—24no—
360#95—22no—
361#95—22no—
362#95—24no—
363#95—24no—
364#95—22no—
365#95—22no—
366#95—24no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95Q8×C15118yes—
372C24C24×C15111yescharacteristic
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
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—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4C2×D4×C15112yes—
424C22×C4C2×D4×C15112yes—
425C22×C4C2×D4×C15112yes—
426C22×C4C2×Q8×C15114yes—
427C22×C4C2×Q8×C15114yes—
428C22×C4C2×Q8×C15112yes—
429C22×C4C2×Q8×C15112yes—
430C22×C4C2×Q8×C15112yes—
431C22×C4C2×Q8×C15114yes—
432C22×C4#41×C15114yes—
433C22×C4#41×C15112yes—
434C22×C4#41×C15112yes—
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—44no—
443C4⋊C4—48no—
444C4⋊C4—48no—
445C42—28no—
446C42—44no—
447C42—44no—
448C23C22×D4×C15111yescharacteristic
449C23C22×Q8×C15111yescharacteristic
450C23C22×Q8×C15112yes—
451C23C2×#41×C15111yescharacteristic
452C23C2×#41×C15111yescharacteristic
453C23C2×#41×C15111yescharacteristic
454C23C2×#41×C15111yescharacteristic
455C23C2×#41×C15111yescharacteristic
456C23C2×#41×C15112yes—
457C23H(5,𝔽2)×C15112yes—
458C23H(5,𝔽2)×C15112yes—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4C22⋊Q8×C15114yes—
522C2×C4#125×C15114yes—
523C2×C4C4⋊Q8×C15114yes—
524C22C2×C22⋊Q8×C15111yescharacteristic
525C22#525×C15111yescharacteristic
526C22#525×C15111yescharacteristic
527C22#525×C15111yescharacteristic
528C22C2×#125×C15111yescharacteristic
529C22#529×C15111yescharacteristic
530C22#529×C15111yescharacteristic
531C22C2×C4⋊Q8×C15111yescharacteristic
532C22#533×C15111yescharacteristic
533C22#533×C15112yes—
534C22#533×C15112yes—
535C22#534×C15111yescharacteristic
536C22#535×C15111yescharacteristic
537C22#538×C15112yes—
538C22#540×C15112yes—
539C22#551×C15112yes—
540C22#553×C15112yes—
541C22#553×C15112yes—
542C22#554×C15112yes—
543C22#554×C15112yes—
544C22#554×C15112yes—
545C22#554×C15112yes—
546C22Q82×C15112yes—
547C4—24no—
548C4—24no—
549C4—24no—
550C4—42no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—44no—
555C4—42no—
556C4—44no—
557C4—82no—
558C2#2399×C15111yescharacteristic
559C2#2507×C15112yes—
560C2#2522×C15112yes—
561C2#2567×C15111yescharacteristic
562C2#2579×C15111yescharacteristic
563C2#2583×C15111yescharacteristic
564C2#2586×C15112yes—
565C2#2587×C15112yes—
566C2#2598×C15111yescharacteristic
567C2#2635×C15111yescharacteristic
568C2#2851×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. #15098C151direct (N × H)
285. C151#15098direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C1512
C2×C4×C4⋊C4×C1512
#1444×C1512
#1441×C1512
#1436×C1512
#1434×C1512
#15098151