Finite Group Databasebeta

← C151×#13080 #50318005

Subgroups — C151×#13080 #50318005

Order 38656.

864 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
1C22×#100×C151C211yesmaximal, characteristic
2#2405×C151C211yesmaximal, characteristic
3C2×#352×C151C212yesmaximal, complemented
4#1781×C151C211yesmaximal, characteristic
5#1390×C151C212yesmaximal, complemented
6C23×D4×C151C2211yescharacteristic
7C22×M16×C151—21no—
8C2×#123×C151C411yescharacteristic, complemented
9C2×#123×C151C2211yescharacteristic
10C22×C22⋊C4×C151C411yescharacteristic, complemented
11C2×#100×C151—21no—
12C2×#100×C151—24no—
13C2×#100×C151C2212yes—
14C2×#99×C151—21no—
15C2×#99×C151C2212yes—
16#394×C151—21no—
17#394×C151—21no—
18#386×C151C411yescharacteristic, complemented
19#386×C151C2211yescharacteristic
20#385×C151—21no—
21#379×C151—21no—
22#379×C151—21no—
23#379×C151C411yescharacteristic, complemented
24#352×C151—24no—
25C25×C151C2×C411yescharacteristic
26C25×C151D411yescharacteristic
27C22×D4×C151—22no—
28C22×D4×C151—22no—
29C22×D4×C151—41no—
30C22×D4×C151—41no—
31C22×D4×C151—42no—
32C22×D4×C151C2×C411yescharacteristic
33C22×D4×C151D411yescharacteristic
34C22×D4×C151D411yescharacteristic
35C22×D4×C151C2311yescharacteristic
36C23×C4×C151C2×C411yescharacteristic
37C23×C4×C151C2×C411yescharacteristic
38C23×C4×C151D411yescharacteristic
39C2×M16×C151—24no—
40C2×M16×C151—22no—
41C2×M16×C151—41no—
42C2×M16×C151—42no—
43C22×C8×C151—41no—
44#123×C151—22no—
45#123×C151—22no—
46#123×C151—42no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151—21no—
49C2×C22⋊C4×C151—21no—
50C2×C22⋊C4×C151—21no—
51C2×C22⋊C4×C151—21no—
52C2×C22⋊C4×C151—21no—
53C2×C22⋊C4×C151—21no—
54C2×C22⋊C4×C151—21no—
55C2×C22⋊C4×C151—21no—
56C2×C22⋊C4×C151—22no—
57C2×C22⋊C4×C151—21no—
58C2×C22⋊C4×C151—41no—
59C2×C22⋊C4×C151—41no—
60C2×C22⋊C4×C151—41no—
61C2×C22⋊C4×C151—41no—
62C2×C22⋊C4×C151C2×C411yescharacteristic
63C2×C22⋊C4×C151C2×C411yescharacteristic
64#100×C151—24no—
65#100×C151—22no—
66#100×C151D414yes—
67#99×C151—22no—
68#99×C151—22no—
69#99×C151—42no—
70#95×C151—21no—
71#95×C151—21no—
72C24×C151—21no—
73C24×C151—21no—
74C24×C151—21no—
75C24×C151—21no—
76C24×C151—22no—
77C24×C151—22no—
78C24×C151—41no—
79C24×C151—41no—
80C24×C151—42no—
81C24×C151—42no—
82C24×C151—81no—
83C24×C151—81no—
84C24×C151C22⋊C411yescharacteristic
85C24×C151C22⋊C411yescharacteristic
86C24×C151C22⋊C411yescharacteristic
87C24×C151C22×C411yescharacteristic
88C24×C151C2×D411yescharacteristic
89C2×D4×C151—22no—
90C2×D4×C151—22no—
91C2×D4×C151—22no—
92C2×D4×C151—22no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—41no—
96C2×D4×C151—41no—
97C2×D4×C151—41no—
98C2×D4×C151—41no—
99C2×D4×C151—41no—
100C2×D4×C151—41no—
101C2×D4×C151—44no—
102C2×D4×C151—44no—
103C2×D4×C151—44no—
104C2×D4×C151—44no—
105C2×D4×C151C2×D412yes—
106C2×D4×C151#4112yes—
107C22×C4×C151—21no—
108C22×C4×C151—21no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—41no—
118C22×C4×C151—41no—
119C22×C4×C151—41no—
120C22×C4×C151—42no—
121C22×C4×C151—81no—
122C22×C4×C151C22⋊C411yescharacteristic
123C22×C4×C151C2×D411yescharacteristic
124M16×C151—24no—
125M16×C151—44no—
126M16×C151—42no—
127C2×C8×C151—44no—
128C2×C8×C151—42no—
129C4⋊C4×C151—42no—
130C4⋊C4×C151—41no—
131C4⋊C4×C151—41no—
132C22⋊C4×C151—22no—
133C22⋊C4×C151—42no—
134C22⋊C4×C151—42no—
135C22⋊C4×C151—42no—
136C22⋊C4×C151—41no—
137C22⋊C4×C151—41no—
138C22⋊C4×C151—42no—
139C22⋊C4×C151—41no—
140C22⋊C4×C151—42no—
141C22⋊C4×C151—42no—
142C22⋊C4×C151—81no—
143C22⋊C4×C151—81no—
144C22⋊C4×C151—81no—
145C22⋊C4×C151—82no—
146C22⋊C4×C151—82no—
147C23×C151—22no—
148C23×C151—21no—
149C23×C151—21no—
150C23×C151—21no—
151C23×C151—21no—
152C23×C151—21no—
153C23×C151—21no—
154C23×C151—21no—
155C23×C151—21no—
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160C23×C151—41no—
161C23×C151—42no—
162C23×C151—42no—
163C23×C151—42no—
164C23×C151—42no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151—41no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151—42no—
172C23×C151—42no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—81no—
178C23×C151—81no—
179C23×C151—81no—
180C23×C151—81no—
181C23×C151—84no—
182C23×C151—84no—
183C23×C151—84no—
184C23×C151—84no—
185C23×C151#9911yescharacteristic
186C23×C151#9911yescharacteristic
187C23×C151C2×C22⋊C411yescharacteristic
188C23×C151C4×D412yes—
189C23×C151#12112yes—
190D4×C151—42no—
191D4×C151—42no—
192D4×C151—44no—
193D4×C151—44no—
194D4×C151—42no—
195D4×C151—42no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—21no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—82no—
217C2×C4×C151—82no—
218C2×C4×C151—82no—
219C2×C4×C151—82no—
220C2×C4×C151—82no—
221C2×C4×C151#9912yes—
222C2×C4×C151#12011yescharacteristic
223C2×C4×C151#12311yescharacteristic
224C8×C151—44no—
225C22×C151—21no—
226C22×C151—21no—
227C22×C151—21no—
228C22×C151—21no—
229C22×C151—21no—
230C22×C151—21no—
231C22×C151—21no—
232C22×C151—22no—
233C22×C151—22no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—42no—
240C22×C151—41no—
241C22×C151—41no—
242C22×C151—41no—
243C22×C151—41no—
244C22×C151—41no—
245C22×C151—41no—
246C22×C151—41no—
247C22×C151—41no—
248C22×C151—41no—
249C22×C151—41no—
250C22×C151—81no—
251C22×C151—84no—
252C22×C151—84no—
253C22×C151—81no—
254C22×C151—81no—
255C22×C151—81no—
256C22×C151—84no—
257C22×C151—84no—
258C22×C151#35212yescomplemented
259C22×C151#38611yescharacteristic
260C22×C151C2×#9911yescharacteristic
261C22×C151C2×#9911yescharacteristic
262C4×C151—21no—
263C4×C151—22no—
264C4×C151—21no—
265C4×C151—81no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151—81no—
269C4×C151—162no—
270C2×C151—21no—
271C2×C151—21no—
272C2×C151—22no—
273C2×C151—42no—
274C2×C151—41no—
275C2×C151—42no—
276C2×C151—81no—
277C2×C151—81no—
278C2×C151#189811yescharacteristic
279C2×C151C2×#35211yescharacteristic
280C2×C151#212111yescharacteristic
281#13080C15111yesmaximal, characteristic, direct product factor, Sylow
282C151#1308011yescharacteristic, direct product factor, Sylow
283C22×#100C2×C15111yescharacteristic
284#2405C2×C15111yescharacteristic
285C2×#352C2×C15112yescomplemented
286#1781C2×C15111yescharacteristic
287#1390C2×C15112yescomplemented
288C23×D4C22×C15111yescharacteristic
289C22×M16—21no—
290C2×#123C4×C15111yescharacteristic, complemented
291C2×#123C22×C15111yescharacteristic
292C22×C22⋊C4C4×C15111yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C15112yes—
296C2×#99—21no—
297C2×#99C22×C15112yes—
298#394—21no—
299#394—21no—
300#386C4×C15111yescharacteristic, complemented
301#386C22×C15111yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C15111yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C15111yescharacteristic
308C25D4×C15111yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C15111yescharacteristic
315C22×D4D4×C15111yescharacteristic
316C22×D4D4×C15111yescharacteristic
317C22×D4C23×C15111yescharacteristic
318C23×C4C2×C4×C15111yescharacteristic
319C23×C4C2×C4×C15111yescharacteristic
320C23×C4D4×C15111yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C15111yescharacteristic
345C2×C22⋊C4C2×C4×C15111yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C15114yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C15111yescharacteristic
367C24C22⋊C4×C15111yescharacteristic
368C24C22⋊C4×C15111yescharacteristic
369C24C22×C4×C15111yescharacteristic
370C24C2×D4×C15111yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C15112yes—
388C2×D4#41×C15112yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C15111yescharacteristic
405C22×C4C2×D4×C15111yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C15111yescharacteristic
468C23#99×C15111yescharacteristic
469C23C2×C22⋊C4×C15111yescharacteristic
470C23C4×D4×C15112yes—
471C23#121×C15112yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C15112yes—
504C2×C4#120×C15111yescharacteristic
505C2×C4#123×C15111yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C15112yescomplemented
541C22#386×C15111yescharacteristic
542C22C2×#99×C15111yescharacteristic
543C22C2×#99×C15111yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2#1898×C15111yescharacteristic
561C2C2×#352×C15111yescharacteristic
562C2#2121×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC24C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C23×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#352×C151C2semidirect
5. #1390×C151C2semidirect
8. C2×#123×C151C4semidirect
10. C22×C22⋊C4×C151C4semidirect
18. #386×C151C4semidirect
23. #379×C151C4semidirect
258. C22×C151#352semidirect
281. #13080C151direct (N × H)
282. C151#13080direct (N × H)
285. C2×#352C2×C151semidirect
287. #1390C2×C151semidirect
290. C2×#123C4×C151semidirect
292. C22×C22⋊C4C4×C151semidirect
300. #386C4×C151semidirect
305. #379C4×C151semidirect
540. C22#352×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1512
#2405×C1512
C2×#352×C1512
#1781×C1512
#1390×C1512
#13080151