Finite Group Databasebeta

← C151×#24338 #50329263

Subgroups — C151×#24338 #50329263

Order 38656.

1296 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic, complemented
3C2×#442×C151C211yesmaximal, characteristic
4#2580×C151C211yesmaximal, characteristic, complemented
5#2058×C151C212yesmaximal, complemented
6#2023×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1985×C151C211yesmaximal, characteristic, complemented
9#1879×C151C212yesmaximal
10#1864×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151—21no—
13C22×D8×C151C2211yescharacteristic
14D4×Q8×C151—24no—
15D4×Q8×C151—24no—
16C2×C4⋊Q8×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×C22⋊Q8×C151—22no—
19C2×C22⋊Q8×C151—21no—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2212yes—
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24#476×C151—24no—
25#442×C151—24no—
26C2×#106×C151C2212yes—
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#102×C151C2211yescharacteristic
30C2×#102×C151C2212yes—
31C2×#102×C151C2212yes—
32C2×#102×C151C2211yescharacteristic
33C2×#97×C151C2211yescharacteristic
34#399×C151—21no—
35#393×C151—21no—
36#390×C151C2212yes—
37#389×C151C2212yes—
38#385×C151—22no—
39#382×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—48no—
49C22×Q8×C151D411yescharacteristic
50C22×D4×C151C2311yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C23×C4×C151—22no—
53C23×C4×C151—21no—
54C23×C4×C151—21no—
55C2×D8×C151—22no—
56C2×D8×C151—22no—
57C2×D8×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×D4×C151—24no—
70C4×D4×C151—24no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151D414yes—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151D412yes—
79C2×C4⋊C4×C151D411yescharacteristic
80C2×C4⋊C4×C151C2312yes—
81C2×C4⋊C4×C151C2311yescharacteristic
82C2×C4⋊C4×C151C2312yes—
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—21no—
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151—22no—
89C2×C42×C151C2312yes—
90C2×C42×C151C2311yescharacteristic
91#106×C151—22no—
92#106×C151—24no—
93C4⋊C8×C151—22no—
94#102×C151—22no—
95#102×C151—24no—
96#102×C151—22no—
97#102×C151—24no—
98#97×C151—22no—
99#95×C151—21no—
100#95×C151—21no—
101#95×C151—22no—
102C24×C151—21no—
103C24×C151—21no—
104C2×Q8×C151—28no—
105C2×Q8×C151—22no—
106C2×Q8×C151—24no—
107C2×Q8×C151—24no—
108C2×Q8×C151—44no—
109C2×Q8×C151—44no—
110C2×Q8×C151—432no—
111C2×Q8×C151—44no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151C2×D412yes—
121C2×D4×C151C2×Q812yes—
122C2×D4×C151C2×Q812yescomplemented
123C2×D4×C151#4112yes—
124C22×C4×C151—28no—
125C22×C4×C151—21no—
126C22×C4×C151—22no—
127C22×C4×C151—24no—
128C22×C4×C151—22no—
129C22×C4×C151—21no—
130C22×C4×C151—44no—
131C22×C4×C151—44no—
132C22×C4×C151—44no—
133C22×C4×C151—42no—
134C22×C4×C151—82no—
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2×D411yescharacteristic
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D412yes—
139C22×C4×C151C2411yescharacteristic
140D8×C151—28no—
141C2×C8×C151—21no—
142C2×C8×C151—21no—
143C2×C8×C151—21no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—21no—
147C2×C8×C151—21no—
148C2×C8×C151—22no—
149C2×C8×C151C2×Q812yescomplemented
150C4⋊C4×C151—28no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—82no—
161C4⋊C4×C151C2×D414yes—
162C4⋊C4×C151C2×D412yes—
163C22⋊C4×C151—28no—
164C22⋊C4×C151—24no—
165C22⋊C4×C151—42no—
166C22⋊C4×C151—44no—
167C22⋊C4×C151—82no—
168C42×C151—22no—
169C42×C151—22no—
170C42×C151C2×D412yes—
171C42×C151C2×D412yes—
172C23×C151—22no—
173C23×C151—22no—
174C23×C151—22no—
175C23×C151—22no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151C22×D411yescharacteristic
183Q8×C151—28no—
184Q8×C151—48no—
185Q8×C151—416no—
186D4×C151—22no—
187D4×C151—22no—
188D4×C151—22no—
189D4×C151—22no—
190D4×C151—22no—
191D4×C151—41no—
192D4×C151—41no—
193D4×C151C22⋊Q814yes—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—48no—
204C2×C4×C151—416no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—84no—
214C2×C4×C151#12012yes—
215C2×C4×C151#12012yes—
216C2×C4×C151AGL(1,ℤ/8)14yes—
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C22×D411yescharacteristic
219C2×C4×C151C22×Q811yescharacteristic
220C2×C4×C151C2×#4111yescharacteristic
221C2×C4×C1512−1+411yescharacteristic
222C2×C4×C1512−1+411yescharacteristic
223C8×C151—22no—
224C8×C151—41no—
225C8×C151—42no—
226C22×C151—24no—
227C22×C151—44no—
228C22×C151—44no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—44no—
232C22×C151—42no—
233C22×C151—82no—
234C22×C151—81no—
235C22×C151—81no—
236C22×C151C2×#12011yescharacteristic
237C22×C151#54811yescharacteristic
238C22×C151D4×Q811yescharacteristic
239C22×C151C2×AGL(1,ℤ/8)12yes—
240C22×C151#57712yes—
241C4×C151—22no—
242C4×C151—24no—
243C4×C151—22no—
244C4×C151—42no—
245C4×C151—44no—
246C4×C151—42no—
247C4×C151—82no—
248C4×C151—81no—
249C4×C151C2×C22⋊Q811yescharacteristic
250C4×C151#53611yescharacteristic
251C4×C151#54811yescharacteristic
252C4×C151D4×Q811yescharacteristic
253C2×C151—44no—
254C2×C151—82no—
255C2×C151#240911yescharacteristic
256C2×C151#300311yescharacteristic
257C2×C151#301011yescharacteristic
258C2×C151#337312yes—
259C2×C151#338412yes—
260#24338C15111yesmaximal, characteristic, direct product factor, Sylow
261C151#2433811yescharacteristic, direct product factor, Sylow
262C2×D4×Q8C2×C15111yescharacteristic, complemented
263C2×#476C2×C15111yescharacteristic, complemented
264C2×#442C2×C15111yescharacteristic
265#2580C2×C15111yescharacteristic, complemented
266#2058C2×C15112yescomplemented
267#2023C2×C15112yescomplemented
268#1993C2×C15111yescharacteristic, complemented
269#1985C2×C15111yescharacteristic, complemented
270#1879C2×C15112yes—
271#1864C2×C15112yescomplemented
272#1804C2×C15111yescharacteristic, complemented
273C23×Q8—21no—
274C22×D8C22×C15111yescharacteristic
275D4×Q8—24no—
276D4×Q8—24no—
277C2×C4⋊Q8C22×C15112yes—
278C2×C4⋊Q8C22×C15111yescharacteristic
279C2×C22⋊Q8—22no—
280C2×C22⋊Q8—21no—
281C2×C4×Q8C22×C15111yescharacteristic
282C2×C4×D4C22×C15111yescharacteristic
283C2×C4×D4C22×C15112yes—
284C2×C4×D4C22×C15111yescharacteristic
285#476—24no—
286#442—24no—
287C2×#106C22×C15111yescharacteristic
288C2×#106C22×C15112yes—
289C2×C4⋊C8C22×C15111yescharacteristic
290C2×#102C22×C15112yes—
291C2×#102C22×C15111yescharacteristic
292C2×#102C22×C15112yes—
293C2×#102C22×C15111yescharacteristic
294C2×#97C22×C15111yescharacteristic
295#399—21no—
296#393—21no—
297#390C22×C15112yes—
298#389C22×C15112yes—
299#385—22no—
300#382C22×C15111yescharacteristic
301#340C22×C15112yes—
302#340C22×C15112yes—
303#340C22×C15112yes—
304#336C22×C15112yes—
305#336C22×C15112yes—
306C22×Q8—28no—
307C22×Q8—21no—
308C22×Q8—22no—
309C22×Q8—48no—
310C22×Q8D4×C15111yescharacteristic
311C22×D4C23×C15111yescharacteristic
312C22×D4C23×C15111yescharacteristic
313C23×C4—22no—
314C23×C4—21no—
315C23×C4—21no—
316C2×D8—22no—
317C2×D8—22no—
318C2×D8Q8×C15114yescomplemented
319C22×C8C23×C15111yescharacteristic
320C22×C8C23×C15112yes—
321C22×C8C23×C15111yescharacteristic
322C4⋊Q8—24no—
323C4⋊Q8—24no—
324C4⋊Q8—22no—
325C4⋊Q8D4×C15114yes—
326C22⋊Q8—28no—
327C22⋊Q8—216no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4D4×C15114yes—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4D4×C15112yes—
340C2×C4⋊C4D4×C15111yescharacteristic
341C2×C4⋊C4C23×C15111yescharacteristic
342C2×C4⋊C4C23×C15112yes—
343C2×C4⋊C4C23×C15112yes—
344C2×C4⋊C4C23×C15111yescharacteristic
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C42C23×C15112yes—
351C2×C42C23×C15111yescharacteristic
352#106—22no—
353#106—24no—
354C4⋊C8—22no—
355#102—24no—
356#102—22no—
357#102—22no—
358#102—24no—
359#97—22no—
360#95—21no—
361#95—21no—
362#95—22no—
363C24—21no—
364C24—21no—
365C2×Q8—28no—
366C2×Q8—22no—
367C2×Q8—24no—
368C2×Q8—24no—
369C2×Q8—44no—
370C2×Q8—44no—
371C2×Q8—432no—
372C2×Q8—44no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4C2×D4×C15112yes—
382C2×D4C2×Q8×C15112yes—
383C2×D4C2×Q8×C15112yescomplemented
384C2×D4#41×C15112yes—
385C22×C4—28no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—24no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—44no—
394C22×C4—42no—
395C22×C4—82no—
396C22×C4C2×D4×C15112yes—
397C22×C4C2×D4×C15111yescharacteristic
398C22×C4C2×D4×C15111yescharacteristic
399C22×C4C2×D4×C15112yes—
400C22×C4C24×C15111yescharacteristic
401D8—28no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—22no—
410C2×C8C2×Q8×C15112yescomplemented
411C4⋊C4—28no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—82no—
422C4⋊C4C2×D4×C15114yes—
423C4⋊C4C2×D4×C15112yes—
424C22⋊C4—28no—
425C22⋊C4—24no—
426C22⋊C4—42no—
427C22⋊C4—44no—
428C22⋊C4—82no—
429C42—22no—
430C42—22no—
431C42C2×D4×C15112yes—
432C42C2×D4×C15112yes—
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—42no—
438C23—42no—
439C23—41no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23C22×D4×C15111yescharacteristic
444Q8—28no—
445Q8—48no—
446Q8—416no—
447D4—22no—
448D4—22no—
449D4—22no—
450D4—22no—
451D4—22no—
452D4—41no—
453D4—41no—
454D4C22⋊Q8×C15114yes—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
465C2×C4—416no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4#120×C15112yes—
476C2×C4#120×C15112yes—
477C2×C4AGL(1,ℤ/8)×C15114yes—
478C2×C4C22×D4×C15111yescharacteristic
479C2×C4C22×D4×C15111yescharacteristic
480C2×C4C22×Q8×C15111yescharacteristic
481C2×C4C2×#41×C15111yescharacteristic
482C2×C42−1+4×C15111yescharacteristic
483C2×C42−1+4×C15111yescharacteristic
484C8—22no—
485C8—41no—
486C8—42no—
487C22—24no—
488C22—44no—
489C22—44no—
490C22—42no—
491C22—42no—
492C22—44no—
493C22—42no—
494C22—82no—
495C22—81no—
496C22—81no—
497C22C2×#120×C15111yescharacteristic
498C22#548×C15111yescharacteristic
499C22D4×Q8×C15111yescharacteristic
500C22C2×AGL(1,ℤ/8)×C15112yes—
501C22#577×C15112yes—
502C4—22no—
503C4—24no—
504C4—22no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—82no—
509C4—81no—
510C4C2×C22⋊Q8×C15111yescharacteristic
511C4#536×C15111yescharacteristic
512C4#548×C15111yescharacteristic
513C4D4×Q8×C15111yescharacteristic
514C2—44no—
515C2—82no—
516C2#2409×C15111yescharacteristic
517C2#3003×C15111yescharacteristic
518C2#3010×C15111yescharacteristic
519C2#3373×C15112yes—
520C2#3384×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
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
1. C2×D4×Q8×C151C2semidirect
2. C2×#476×C151C2semidirect
4. #2580×C151C2semidirect
5. #2058×C151C2semidirect
6. #2023×C151C2semidirect
7. #1993×C151C2semidirect
8. #1985×C151C2semidirect
10. #1864×C151C2semidirect
11. #1804×C151C2semidirect
57. C2×D8×C151Q8semidirect
122. C2×D4×C151C2×Q8semidirect
149. C2×C8×C151C2×Q8semidirect
260. #24338C151direct (N × H)
261. C151#24338direct (N × H)
262. C2×D4×Q8C2×C151semidirect
263. C2×#476C2×C151semidirect
265. #2580C2×C151semidirect
266. #2058C2×C151semidirect
267. #2023C2×C151semidirect
268. #1993C2×C151semidirect
269. #1985C2×C151semidirect
271. #1864C2×C151semidirect
272. #1804C2×C151semidirect
318. C2×D8Q8×C151semidirect
383. C2×D4C2×Q8×C151semidirect
410. 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×#476×C1512
C2×#442×C1512
#2580×C1512
#2058×C1512
#2023×C1512
#1993×C1512
#1985×C1512
#1879×C1512
#1864×C1512
#1804×C1512
#24338151