Finite Group Databasebeta

← C151×#24330 #50329255

Subgroups — C151×#24330 #50329255

Order 38656.

1262 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic
2C2×#475×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic
4#2582×C151C211yesmaximal, characteristic, complemented
5#2058×C151C212yesmaximal, complemented
6#2024×C151C212yesmaximal, complemented
7#1990×C151C211yesmaximal, characteristic, complemented
8#1984×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal
10#1864×C151C212yesmaximal
11#1802×C151C211yesmaximal, characteristic
12C23×Q8×C151—21no—
13C22×SD16×C151C2211yescharacteristic
14D4×Q8×C151—24no—
15D4×Q8×C151—24no—
16C2×C4⋊Q8×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151—22no—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151C2212yes—
23C2×C4×D4×C151C2211yescharacteristic
24#475×C151—24no—
25C4×SD16×C151—24no—
26C2×#106×C151C2212yes—
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2212yes—
30C2×#103×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2212yes—
33C2×C4×C8×C151C2211yescharacteristic
34#398×C151—22no—
35#391×C151—21no—
36#391×C151C2212yes—
37#389×C151—21no—
38#389×C151C2212yes—
39#384×C151C2211yescharacteristic
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151—28no—
46C22×Q8×C151—22no—
47C22×Q8×C151—21no—
48C22×Q8×C151—44no—
49C22×Q8×C151—44no—
50C22×Q8×C151D411yescharacteristic
51C22×Q8×C151C2311yescharacteristic
52C22×D4×C151C2311yescharacteristic
53C23×C4×C151—22no—
54C23×C4×C151—21no—
55C2×SD16×C151—22no—
56C2×SD16×C151—22no—
57C2×SD16×C151Q814yescomplemented
58C22×C8×C151C2311yescharacteristic
59C22×C8×C151C2312yes—
60C22×C8×C151C2311yescharacteristic
61C4⋊Q8×C151—24no—
62C4⋊Q8×C151—24no—
63C4⋊Q8×C151—22no—
64C4⋊Q8×C151D414yes—
65C22⋊Q8×C151—216no—
66C22⋊Q8×C151—28no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×D4×C151—24no—
72C4×D4×C151—24no—
73C4×D4×C151—22no—
74C4×D4×C151D414yes—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151D411yescharacteristic
82C2×C4⋊C4×C151D412yes—
83C2×C4⋊C4×C151C2312yes—
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2312yes—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—21no—
89C2×C42×C151—21no—
90C2×C42×C151C2312yes—
91C2×C42×C151C2311yescharacteristic
92#106×C151—22no—
93#106×C151—24no—
94C4⋊C8×C151—22no—
95#103×C151—22no—
96#103×C151—24no—
97#102×C151—22no—
98#102×C151—24no—
99C4×C8×C151—22no—
100#95×C151—22no—
101#95×C151—22no—
102#95×C151—22no—
103C24×C151—21no—
104C2×Q8×C151—28no—
105C2×Q8×C151—22no—
106C2×Q8×C151—24no—
107C2×Q8×C151—22no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—44no—
114C2×Q8×C151—432no—
115C2×Q8×C151—44no—
116C2×Q8×C151—42no—
117C2×Q8×C151—42no—
118C2×Q8×C151SD1614yescomplemented
119C2×Q8×C151C2×Q812yescomplemented
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151C2×D412yes—
124C2×D4×C151C2×Q812yes—
125C2×D4×C151#4112yes—
126C22×C4×C151—28no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—24no—
131C22×C4×C151—22no—
132C22×C4×C151—21no—
133C22×C4×C151—44no—
134C22×C4×C151—44no—
135C22×C4×C151—42no—
136C22×C4×C151—42no—
137C22×C4×C151C2×D412yes—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2411yescharacteristic
142SD16×C151—28no—
143C2×C8×C151—21no—
144C2×C8×C151—21no—
145C2×C8×C151—21no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151—22no—
151C2×C8×C151C2×Q812yescomplemented
152C4⋊C4×C151—28no—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151—42no—
164C4⋊C4×C151—81no—
165C4⋊C4×C151—82no—
166C4⋊C4×C151C2×D414yes—
167C4⋊C4×C151C2×D412yes—
168C22⋊C4×C151—28no—
169C22⋊C4×C151—24no—
170C42×C151—22no—
171C42×C151—22no—
172C42×C151—42no—
173C42×C151C2×D412yes—
174C42×C151C2×D412yes—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151—41no—
181C23×C151—41no—
182C23×C151C22×D411yescharacteristic
183Q8×C151—28no—
184Q8×C151—22no—
185Q8×C151—22no—
186Q8×C151—416no—
187Q8×C151—41no—
188Q8×C151—41no—
189Q8×C151—48no—
190D4×C151—22no—
191D4×C151—22no—
192D4×C151—22no—
193D4×C151C22⋊Q814yes—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—21no—
197C2×C4×C151—21no—
198C2×C4×C151—22no—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—416no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—42no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—48no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151#12012yes—
219C2×C4×C151#12012yes—
220C2×C4×C151C2×SD1614yes—
221C2×C4×C151C2×SD1612yes—
222C2×C4×C151AGL(1,ℤ/8)12yes—
223C2×C4×C151C22×D411yescharacteristic
224C2×C4×C151C22×D411yescharacteristic
225C2×C4×C151C22×Q811yescharacteristic
226C2×C4×C151C2×#4111yescharacteristic
227C2×C4×C1512−1+411yescharacteristic
228C2×C4×C1512−1+411yescharacteristic
229C8×C151—22no—
230C8×C151—41no—
231C8×C151—42no—
232C22×C151—24no—
233C22×C151—42no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151C2×#12011yescharacteristic
240C22×C151#54811yescharacteristic
241C22×C151D4×Q811yescharacteristic
242C22×C151C22×SD1611yescharacteristic
243C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C151#57711yescharacteristic
245C22×C151#57811yescharacteristic
246C4×C151—24no—
247C4×C151—22no—
248C4×C151—42no—
249C4×C151—44no—
250C4×C151—42no—
251C4×C151—42no—
252C4×C151—82no—
253C4×C151—81no—
254C4×C151#45014yes—
255C4×C151C2×C22⋊Q811yescharacteristic
256C4×C151#53611yescharacteristic
257C4×C151#54811yescharacteristic
258C4×C151D4×Q811yescharacteristic
259C2×C151—44no—
260C2×C151#240911yescharacteristic
261C2×C151C2×#45011yescharacteristic
262C2×C151#301311yescharacteristic
263C2×C151#335911yescharacteristic
264C2×C151#337311yescharacteristic
265C2×C151Q8×SD1611yescharacteristic
266C2×C151#338611yescharacteristic
267#24330C15111yesmaximal, characteristic, direct product factor, Sylow
268C151#2433011yescharacteristic, direct product factor, Sylow
269C2×D4×Q8C2×C15111yescharacteristic
270C2×#475C2×C15111yescharacteristic, complemented
271C2×C4×SD16C2×C15111yescharacteristic
272#2582C2×C15111yescharacteristic, complemented
273#2058C2×C15112yescomplemented
274#2024C2×C15112yescomplemented
275#1990C2×C15111yescharacteristic, complemented
276#1984C2×C15111yescharacteristic, complemented
277#1877C2×C15112yes—
278#1864C2×C15112yes—
279#1802C2×C15111yescharacteristic
280C23×Q8—21no—
281C22×SD16C22×C15111yescharacteristic
282D4×Q8—24no—
283D4×Q8—24no—
284C2×C4⋊Q8C22×C15112yes—
285C2×C4⋊Q8C22×C15111yescharacteristic
286C2×C22⋊Q8—21no—
287C2×C22⋊Q8—22no—
288C2×C4×Q8C22×C15111yescharacteristic
289C2×C4×Q8C22×C15111yescharacteristic
290C2×C4×D4C22×C15112yes—
291C2×C4×D4C22×C15111yescharacteristic
292#475—24no—
293C4×SD16—24no—
294C2×#106C22×C15112yes—
295C2×#106C22×C15111yescharacteristic
296C2×C4⋊C8C22×C15111yescharacteristic
297C2×#103C22×C15112yes—
298C2×#103C22×C15111yescharacteristic
299C2×#102C22×C15112yes—
300C2×#102C22×C15111yescharacteristic
301C2×C4×C8C22×C15111yescharacteristic
302#398—22no—
303#391—21no—
304#391C22×C15112yes—
305#389—21no—
306#389C22×C15112yes—
307#384C22×C15111yescharacteristic
308#340C22×C15112yes—
309#340C22×C15112yes—
310#340C22×C15112yes—
311#336C22×C15112yes—
312#336C22×C15112yes—
313C22×Q8—28no—
314C22×Q8—22no—
315C22×Q8—21no—
316C22×Q8—44no—
317C22×Q8—44no—
318C22×Q8D4×C15111yescharacteristic
319C22×Q8C23×C15111yescharacteristic
320C22×D4C23×C15111yescharacteristic
321C23×C4—22no—
322C23×C4—21no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×SD16Q8×C15114yescomplemented
326C22×C8C23×C15111yescharacteristic
327C22×C8C23×C15112yes—
328C22×C8C23×C15111yescharacteristic
329C4⋊Q8—24no—
330C4⋊Q8—24no—
331C4⋊Q8—22no—
332C4⋊Q8D4×C15114yes—
333C22⋊Q8—28no—
334C22⋊Q8—216no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4D4×C15114yes—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4D4×C15111yescharacteristic
350C2×C4⋊C4D4×C15112yes—
351C2×C4⋊C4C23×C15111yescharacteristic
352C2×C4⋊C4C23×C15112yes—
353C2×C4⋊C4C23×C15112yes—
354C2×C4⋊C4C23×C15111yescharacteristic
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C42—21no—
358C2×C42C23×C15112yes—
359C2×C42C23×C15111yescharacteristic
360#106—22no—
361#106—24no—
362C4⋊C8—22no—
363#103—22no—
364#103—24no—
365#102—24no—
366#102—22no—
367C4×C8—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371C24—21no—
372C2×Q8—28no—
373C2×Q8—22no—
374C2×Q8—24no—
375C2×Q8—22no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—44no—
382C2×Q8—432no—
383C2×Q8—44no—
384C2×Q8—42no—
385C2×Q8—42no—
386C2×Q8SD16×C15114yescomplemented
387C2×Q8C2×Q8×C15112yescomplemented
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4C2×D4×C15112yes—
392C2×D4C2×Q8×C15112yes—
393C2×D4#41×C15112yes—
394C22×C4—28no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4C2×D4×C15112yes—
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15112yes—
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C24×C15111yescharacteristic
410SD16—28no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8C2×Q8×C15112yescomplemented
420C4⋊C4—28no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—42no—
431C4⋊C4—42no—
432C4⋊C4—81no—
433C4⋊C4—82no—
434C4⋊C4C2×D4×C15114yes—
435C4⋊C4C2×D4×C15112yes—
436C22⋊C4—28no—
437C22⋊C4—24no—
438C42—22no—
439C42—22no—
440C42—42no—
441C42C2×D4×C15112yes—
442C42C2×D4×C15112yes—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23C22×D4×C15111yescharacteristic
451Q8—28no—
452Q8—22no—
453Q8—22no—
454Q8—416no—
455Q8—48no—
456Q8—41no—
457Q8—41no—
458D4—22no—
459D4—22no—
460D4—22no—
461D4C22⋊Q8×C15114yes—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—416no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—48no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4#120×C15112yes—
487C2×C4#120×C15112yes—
488C2×C4C2×SD16×C15114yes—
489C2×C4C2×SD16×C15112yes—
490C2×C4AGL(1,ℤ/8)×C15112yes—
491C2×C4C22×D4×C15111yescharacteristic
492C2×C4C22×D4×C15111yescharacteristic
493C2×C4C22×Q8×C15111yescharacteristic
494C2×C4C2×#41×C15111yescharacteristic
495C2×C42−1+4×C15111yescharacteristic
496C2×C42−1+4×C15111yescharacteristic
497C8—22no—
498C8—41no—
499C8—42no—
500C22—24no—
501C22—42no—
502C22—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22C2×#120×C15111yescharacteristic
508C22#548×C15111yescharacteristic
509C22D4×Q8×C15111yescharacteristic
510C22C22×SD16×C15111yescharacteristic
511C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
512C22#577×C15111yescharacteristic
513C22#578×C15111yescharacteristic
514C4—24no—
515C4—22no—
516C4—42no—
517C4—44no—
518C4—42no—
519C4—42no—
520C4—82no—
521C4—81no—
522C4#450×C15114yes—
523C4C2×C22⋊Q8×C15111yescharacteristic
524C4#536×C15111yescharacteristic
525C4#548×C15111yescharacteristic
526C4D4×Q8×C15111yescharacteristic
527C2—44no—
528C2#2409×C15111yescharacteristic
529C2C2×#450×C15111yescharacteristic
530C2#3013×C15111yescharacteristic
531C2#3359×C15111yescharacteristic
532C2#3373×C15111yescharacteristic
533C2Q8×SD16×C15111yescharacteristic
534C2#3386×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#475×C151C2semidirect
4. #2582×C151C2semidirect
5. #2058×C151C2semidirect
6. #2024×C151C2semidirect
7. #1990×C151C2semidirect
8. #1984×C151C2semidirect
57. C2×SD16×C151Q8semidirect
118. C2×Q8×C151SD16semidirect
119. C2×Q8×C151C2×Q8semidirect
151. C2×C8×C151C2×Q8semidirect
267. #24330C151direct (N × H)
268. C151#24330direct (N × H)
270. C2×#475C2×C151semidirect
272. #2582C2×C151semidirect
273. #2058C2×C151semidirect
274. #2024C2×C151semidirect
275. #1990C2×C151semidirect
276. #1984C2×C151semidirect
325. C2×SD16Q8×C151semidirect
386. C2×Q8SD16×C151semidirect
387. C2×Q8C2×Q8×C151semidirect
419. C2×C8C2×Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1512
C2×#475×C1512
C2×C4×SD16×C1512
#2582×C1512
#2058×C1512
#2024×C1512
#1990×C1512
#1984×C1512
#1877×C1512
#1864×C1512
#1802×C1512
#24330151