Finite Group Databasebeta

← C151×#9079 #50314004

Subgroups — C151×#9079 #50314004

Order 38656.

1136 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C8×C151C211yesmaximal, characteristic, complemented
2C2×#386×C151C211yesmaximal, characteristic
3#1779×C151C211yesmaximal, characteristic, complemented
4C2×#323×C151C212yesmaximal, complemented
5#1280×C151C212yesmaximal, complemented
6C23×D4×C151C411yescharacteristic
7C24×C4×C151C2211yescharacteristic
8C23×C8×C151—21no—
9C22×C22⋊C4×C151C411yescharacteristic
10C22×C22⋊C4×C151C411yescharacteristic
11C22×C22⋊C4×C151C2211yescharacteristic
12C2×C22⋊C8×C151—21no—
13C2×C22⋊C8×C151—24no—
14C2×C22⋊C8×C151—21no—
15C2×C22⋊C8×C151—21no—
16C2×C22⋊C8×C151C2212yes—
17C2×C22⋊C8×C151C2212yes—
18#386×C151—21no—
19#386×C151—21no—
20#386×C151—21no—
21#386×C151—21no—
22C2×#95×C151C411yescharacteristic
23C2×#95×C151C2211yescharacteristic
24#323×C151—24no—
25C25×C151C2×C411yescharacteristic
26C25×C151C2×C411yescharacteristic
27C22×D4×C151—21no—
28C22×D4×C151—21no—
29C22×D4×C151—22no—
30C22×D4×C151—42no—
31C22×D4×C151—42no—
32C22×D4×C151C814yescomplemented
33C23×C4×C151—22no—
34C23×C4×C151—22no—
35C23×C4×C151—42no—
36C23×C4×C151—42no—
37C23×C4×C151C2×C411yescharacteristic
38C23×C4×C151C2×C411yescharacteristic
39C23×C4×C151C2×C411yescharacteristic
40C23×C4×C151C2×C411yescharacteristic
41C23×C4×C151D411yescharacteristic
42C23×C4×C151D411yescharacteristic
43C23×C4×C151D411yescharacteristic
44C23×C4×C151D411yescharacteristic
45C23×C4×C151C2311yescharacteristic
46C22×C8×C151—24no—
47C22×C8×C151—22no—
48C22×C8×C151—22no—
49C22×C8×C151—42no—
50C22×C8×C151—42no—
51C2×C22⋊C4×C151—21no—
52C2×C22⋊C4×C151—21no—
53C2×C22⋊C4×C151—21no—
54C2×C22⋊C4×C151—21no—
55C2×C22⋊C4×C151—22no—
56C2×C22⋊C4×C151—22no—
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—21no—
59C2×C22⋊C4×C151—42no—
60C2×C22⋊C4×C151—42no—
61C22⋊C8×C151—24no—
62C22⋊C8×C151—22no—
63C22⋊C8×C151—22no—
64C22⋊C8×C151—22no—
65C22⋊C8×C151—42no—
66C22⋊C8×C151—42no—
67C22⋊C8×C151D414yescomplemented
68#95×C151—21no—
69#95×C151—21no—
70#95×C151—21no—
71#95×C151—21no—
72C24×C151—22no—
73C24×C151—22no—
74C24×C151—22no—
75C24×C151—22no—
76C24×C151—21no—
77C24×C151—21no—
78C24×C151—22no—
79C24×C151—22no—
80C24×C151—41no—
81C24×C151—41no—
82C24×C151—41no—
83C24×C151—41no—
84C24×C151—41no—
85C24×C151—41no—
86C24×C151C22⋊C411yescharacteristic
87C24×C151C22⋊C411yescharacteristic
88C24×C151C2×C812yes—
89C24×C151C2×C812yescomplemented
90C24×C151M1612yes—
91C24×C151C22×C411yescharacteristic
92C2×D4×C151—24no—
93C2×D4×C151—24no—
94C2×D4×C151—48no—
95C2×D4×C151—42no—
96C2×D4×C151—42no—
97C2×D4×C151—42no—
98C2×D4×C151—42no—
99C2×D4×C151—48no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151—22no—
105C22×C4×C151—21no—
106C22×C4×C151—22no—
107C22×C4×C151—21no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—41no—
119C22×C4×C151—41no—
120C22×C4×C151—41no—
121C22×C4×C151—41no—
122C22×C4×C151—41no—
123C22×C4×C151—41no—
124C22×C4×C151—41no—
125C22×C4×C151—48no—
126C22×C4×C151—48no—
127C22×C4×C151—41no—
128C22×C4×C151—41no—
129C22×C4×C151—41no—
130C22×C4×C151—41no—
131C22×C4×C151—41no—
132C22×C4×C151—41no—
133C22×C4×C151C22⋊C411yescharacteristic
134C22×C4×C151C22⋊C411yescharacteristic
135C22×C4×C151C2×C812yescomplemented
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D412yes—
139C22×C4×C151#4112yes—
140C2×C8×C151—24no—
141C2×C8×C151—48no—
142C2×C8×C151—42no—
143C2×C8×C151—42no—
144C2×C8×C151—42no—
145C2×C8×C151—42no—
146C2×C8×C151—42no—
147C22⋊C4×C151—42no—
148C22⋊C4×C151—42no—
149C22⋊C4×C151—42no—
150C22⋊C4×C151—42no—
151C22⋊C4×C151—41no—
152C22⋊C4×C151—42no—
153C22⋊C4×C151—41no—
154C23×C151—21no—
155C23×C151—21no—
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151—21no—
162C23×C151—24no—
163C23×C151—24no—
164C23×C151—21no—
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—21no—
170C23×C151—24no—
171C23×C151—24no—
172C23×C151—22no—
173C23×C151—24no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—44no—
177C23×C151—44no—
178C23×C151—44no—
179C23×C151—44no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—42no—
191C23×C151—82no—
192C23×C151—82no—
193C23×C151—82no—
194C23×C151—82no—
195C23×C151C22⋊C812yes—
196C23×C151C22⋊C812yes—
197C23×C151#9912yes—
198C23×C151#10012yes—
199C23×C151C2×C22⋊C411yescharacteristic
200C23×C151C4×D412yes—
201C23×C151C22×C811yescharacteristic
202C23×C151C2×M1611yescharacteristic
203C23×C151#13112yes—
204D4×C151—48no—
205D4×C151—48no—
206C2×C4×C151—24no—
207C2×C4×C151—24no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—22no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—44no—
221C2×C4×C151—44no—
222C2×C4×C151—44no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—82no—
236C2×C4×C151—82no—
237C2×C4×C151#9912yes—
238C2×C4×C151#12011yescharacteristic
239C2×C4×C151#12112yes—
240C2×C4×C151#12311yescharacteristic
241C8×C151—44no—
242C8×C151—82no—
243C22×C151—22no—
244C22×C151—22no—
245C22×C151—22no—
246C22×C151—22no—
247C22×C151—22no—
248C22×C151—21no—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—22no—
253C22×C151—22no—
254C22×C151—22no—
255C22×C151—22no—
256C22×C151—22no—
257C22×C151—22no—
258C22×C151—22no—
259C22×C151—22no—
260C22×C151—48no—
261C22×C151—48no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—41no—
265C22×C151—41no—
266C22×C151—42no—
267C22×C151—42no—
268C22×C151—42no—
269C22×C151—84no—
270C22×C151—84no—
271C22×C151—81no—
272C22×C151—81no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151#32314yescomplemented
276C22×C151#38611yescharacteristic
277C22×C151C2×C22⋊C811yescharacteristic
278C22×C151#40811yescharacteristic
279C22×C151C2×#9911yescharacteristic
280C22×C151C2×#9911yescharacteristic
281C22×C151C2×#10011yescharacteristic
282C22×C151#41311yescharacteristic
283C22×C151C8×D412yes—
284C22×C151#43512yes—
285C4×C151—21no—
286C4×C151—22no—
287C4×C151—22no—
288C4×C151—21no—
289C4×C151—41no—
290C4×C151—42no—
291C4×C151—81no—
292C4×C151—81no—
293C2×C151—22no—
294C2×C151—22no—
295C2×C151—24no—
296C2×C151—42no—
297C2×C151—82no—
298C2×C151C2×#32311yescharacteristic
299C2×C151#145911yescharacteristic
300C2×C151#146811yescharacteristic
301C2×C151#147111yescharacteristic
302C2×C151#186911yescharacteristic
303C2×C151#189811yescharacteristic
304C2×C151#190011yescharacteristic
305#9079C15111yesmaximal, characteristic, direct product factor, Sylow
306C151#907911yescharacteristic, direct product factor, Sylow
307C22×C22⋊C8C2×C15111yescharacteristic, complemented
308C2×#386C2×C15111yescharacteristic
309#1779C2×C15111yescharacteristic, complemented
310C2×#323C2×C15112yescomplemented
311#1280C2×C15112yescomplemented
312C23×D4C4×C15111yescharacteristic
313C24×C4C22×C15111yescharacteristic
314C23×C8—21no—
315C22×C22⋊C4C4×C15111yescharacteristic
316C22×C22⋊C4C4×C15111yescharacteristic
317C22×C22⋊C4C22×C15111yescharacteristic
318C2×C22⋊C8—21no—
319C2×C22⋊C8—24no—
320C2×C22⋊C8—21no—
321C2×C22⋊C8—21no—
322C2×C22⋊C8C22×C15112yes—
323C2×C22⋊C8C22×C15112yes—
324#386—21no—
325#386—21no—
326#386—21no—
327#386—21no—
328C2×#95C4×C15111yescharacteristic
329C2×#95C22×C15111yescharacteristic
330#323—24no—
331C25C2×C4×C15111yescharacteristic
332C25C2×C4×C15111yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4C8×C15114yescomplemented
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×C4×C15111yescharacteristic
344C23×C4C2×C4×C15111yescharacteristic
345C23×C4C2×C4×C15111yescharacteristic
346C23×C4C2×C4×C15111yescharacteristic
347C23×C4D4×C15111yescharacteristic
348C23×C4D4×C15111yescharacteristic
349C23×C4D4×C15111yescharacteristic
350C23×C4D4×C15111yescharacteristic
351C23×C4C23×C15111yescharacteristic
352C22×C8—24no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—42no—
356C22×C8—42no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—24no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8D4×C15114yescomplemented
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—41no—
387C24—41no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24C22⋊C4×C15111yescharacteristic
393C24C22⋊C4×C15111yescharacteristic
394C24C2×C8×C15112yes—
395C24C2×C8×C15112yescomplemented
396C24M16×C15112yes—
397C24C22×C4×C15111yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—48no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C15111yescharacteristic
440C22×C4C22⋊C4×C15111yescharacteristic
441C22×C4C2×C8×C15112yescomplemented
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15112yes—
445C22×C4#41×C15112yes—
446C2×C8—24no—
447C2×C8—48no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—24no—
475C23—24no—
476C23—24no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—42no—
497C23—82no—
498C23—82no—
499C23—82no—
500C23—82no—
501C23C22⋊C8×C15112yes—
502C23C22⋊C8×C15112yes—
503C23#99×C15112yes—
504C23#100×C15112yes—
505C23C2×C22⋊C4×C15111yescharacteristic
506C23C4×D4×C15112yes—
507C23C22×C8×C15111yescharacteristic
508C23C2×M16×C15111yescharacteristic
509C23#131×C15112yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#99×C15112yes—
544C2×C4#120×C15111yescharacteristic
545C2×C4#121×C15112yes—
546C2×C4#123×C15111yescharacteristic
547C8—44no—
548C8—82no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—48no—
567C22—48no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—84no—
576C22—84no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22#323×C15114yescomplemented
582C22#386×C15111yescharacteristic
583C22C2×C22⋊C8×C15111yescharacteristic
584C22#408×C15111yescharacteristic
585C22C2×#99×C15111yescharacteristic
586C22C2×#99×C15111yescharacteristic
587C22C2×#100×C15111yescharacteristic
588C22#413×C15111yescharacteristic
589C22C8×D4×C15112yes—
590C22#435×C15112yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—24no—
602C2—42no—
603C2—82no—
604C2C2×#323×C15111yescharacteristic
605C2#1459×C15111yescharacteristic
606C2#1468×C15111yescharacteristic
607C2#1471×C15111yescharacteristic
608C2#1869×C15111yescharacteristic
609C2#1898×C15111yescharacteristic
610C2#1900×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC23C22×C8×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC23×D4×C151C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊C8×C151C2semidirect
3. #1779×C151C2semidirect
4. C2×#323×C151C2semidirect
5. #1280×C151C2semidirect
32. C22×D4×C151C8semidirect
67. C22⋊C8×C151D4semidirect
89. C24×C151C2×C8semidirect
135. C22×C4×C151C2×C8semidirect
275. C22×C151#323semidirect
305. #9079C151direct (N × H)
306. C151#9079direct (N × H)
307. C22×C22⋊C8C2×C151semidirect
309. #1779C2×C151semidirect
310. C2×#323C2×C151semidirect
311. #1280C2×C151semidirect
338. C22×D4C8×C151semidirect
373. C22⋊C8D4×C151semidirect
395. C24C2×C8×C151semidirect
441. C22×C4C2×C8×C151semidirect
581. C22#323×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C8×C1512
C2×#386×C1512
#1779×C1512
C2×#323×C1512
#1280×C1512
#9079151