Finite Group Databasebeta

← C151×#18912 #50323837

Subgroups — C151×#18912 #50323837

Order 38656.

1218 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic, complemented
2#3205×C151C211yesmaximal, characteristic, complemented
3#3205×C151C211yesmaximal, characteristic, complemented
4C2×#460×C151C211yesmaximal, characteristic, complemented
5#1627×C151C214yesmaximal, complemented
6#1621×C151C214yesmaximal, complemented
7#1540×C151C211yesmaximal, characteristic, complemented
8#1480×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C2×2−1+4×C151—21no—
11C22×SD16×C151—21no—
12#550×C151—21no—
13#550×C151C2212yescomplemented
14D4×Q8×C151—21no—
15D4×Q8×C151C2212yescomplemented
16#548×C151—22no—
17#548×C151—22no—
18#537×C151—22no—
19#537×C151—21no—
20#532×C151—22no—
21#532×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×#127×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25#493×C151—21no—
26#493×C151C2212yes—
27#486×C151—21no—
28#486×C151C2212yes—
29#460×C151—22no—
30#460×C151C2214yes—
31#459×C151—22no—
32#459×C151C2214yes—
33#447×C151—22no—
34#447×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#102×C151—21no—
39#332×C151C2212yescomplemented
40#331×C151C2212yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
432−1+4×C151—44no—
442−1+4×C151—44no—
45C2×#41×C151—24no—
46C2×#41×C151—22no—
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C2×#41×C151—22no—
50C22×Q8×C151—22no—
51C22×Q8×C151—22no—
52C22×Q8×C151D411yescharacteristic
53C22×D4×C151—21no—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C2×SD16×C151—24no—
57C2×SD16×C151—44no—
58C2×D8×C151—24no—
59C2×D8×C151—24no—
60C22×C8×C151—21no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151D411yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64#127×C151—22no—
65#127×C151—21no—
66#127×C151—21no—
67#127×C151—21no—
68#127×C151D411yescharacteristic
69#127×C151C2312yes—
70#127×C151C2311yescharacteristic
71#124×C151—24no—
72#124×C151—21no—
73#124×C151—21no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—22no—
76C22⋊Q8×C151—24no—
77C22⋊Q8×C151—22no—
78#121×C151—24no—
79#121×C151—22no—
80#121×C151—24no—
81#121×C151—24no—
82#121×C151—21no—
83#121×C151—21no—
84#121×C151—22no—
85#121×C151D412yes—
86#121×C151D412yes—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151D412yes—
90C4×Q8×C151C2312yes—
91C4×D4×C151—24no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151D412yes—
97C4×D4×C151C2312yes—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151D411yescharacteristic
100C2×C42×C151—21no—
101C2×C42×C151C2311yescharacteristic
102C4⋊C8×C151—21no—
103C4⋊C8×C151—21no—
104C4⋊C8×C151C2312yes—
105C4⋊C8×C151C2312yes—
106#102×C151—24no—
107#102×C151—24no—
108#102×C151—24no—
109C22⋊C8×C151—21no—
110C22⋊C8×C151—21no—
111C4×C8×C151—21no—
112C4×C8×C151C2312yes—
113C24×C151—41no—
114#41×C151—416no—
115#41×C151—44no—
116#41×C151—48no—
117#41×C151—44no—
118#41×C151—42no—
119#41×C151—42no—
120#41×C151—42no—
121#41×C151—42no—
122C2×Q8×C151—24no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—22no—
126C2×Q8×C151—21no—
127C2×Q8×C151—44no—
128C2×Q8×C151—48no—
129C2×Q8×C151—44no—
130C2×Q8×C151D814yescomplemented
131C2×Q8×C151C2×D412yes—
132C2×D4×C151—24no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—24no—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—22no—
143C2×D4×C151—41no—
144C2×D4×C151—41no—
145C2×D4×C151—41no—
146C2×D4×C151—42no—
147C2×D4×C151—42no—
148C2×D4×C151—82no—
149C2×D4×C151—82no—
150C2×D4×C151C2×D412yes—
151C2×D4×C151C2×D412yes—
152C22×C4×C151—21no—
153C22×C4×C151—24no—
154C22×C4×C151—24no—
155C22×C4×C151—21no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D411yescharacteristic
161SD16×C151—48no—
162D8×C151—84no—
163D8×C151—84no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—42no—
168C4⋊C4×C151—24no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151C2×D412yes—
175C4⋊C4×C151C2×D412yes—
176C4⋊C4×C151C2×D412yes—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—24no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—22no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—22no—
183C42×C151—22no—
184C42×C151—22no—
185C42×C151C2×D411yescharacteristic
186C42×C151C2×D411yescharacteristic
187C42×C151C2×D411yescharacteristic
188C42×C151C2411yescharacteristic
189C23×C151—22no—
190C23×C151—22no—
191C23×C151—42no—
192C23×C151—82no—
193C23×C151—82no—
194C23×C151—82no—
195C23×C151#12011yescharacteristic
196Q8×C151—22no—
197Q8×C151—24no—
198Q8×C151—48no—
199Q8×C151—41no—
200Q8×C151—41no—
201Q8×C151—42no—
202Q8×C151C2×D814yes—
203D4×C151—24no—
204D4×C151—42no—
205D4×C151—48no—
206D4×C151—44no—
207D4×C151—44no—
208D4×C151—44no—
209D4×C151—41no—
210D4×C151—42no—
211D4×C151—41no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—44no—
215D4×C151—42no—
216D4×C151—81no—
217D4×C151—82no—
218D4×C151—82no—
219D4×C151—84no—
220D4×C151—82no—
221C2×C4×C151—22no—
222C2×C4×C151—24no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—41no—
228C2×C4×C151—48no—
229C2×C4×C151—48no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—44no—
233C2×C4×C151—81no—
234C2×C4×C151#12011yescharacteristic
235C2×C4×C151#12011yescharacteristic
236C2×C4×C151#12011yescharacteristic
237C2×C4×C151C2×D812yes—
238C2×C4×C151AGL(1,ℤ/8)12yes—
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C8×C151—42no—
243C8×C151—42no—
244C8×C151—42no—
245C22×C151—21no—
246C22×C151—21no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—82no—
254C22×C151—82no—
255C22×C151—82no—
256C22×C151—164no—
257C22×C151#44712yes—
258C22×C151C2×#12011yescharacteristic
259C4×C151—24no—
260C4×C151—21no—
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—42no—
264C4×C151—42no—
265C4×C151—42no—
266C4×C151#44712yes—
267C4×C151C22×D811yescharacteristic
268C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C151#57712yes—
270C2×C151—22no—
271C2×C151—82no—
272C2×C151—82no—
273C2×C151—162no—
274C2×C151C2×#44711yescharacteristic
275C2×C151#301011yescharacteristic
276C2×C151#302111yescharacteristic
277#18912C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#1891211yescharacteristic, direct product factor, Sylow
279#3497C2×C15111yescharacteristic, complemented
280#3205C2×C15111yescharacteristic, complemented
281#3205C2×C15111yescharacteristic, complemented
282C2×#460C2×C15111yescharacteristic, complemented
283#1627C2×C15114yescomplemented
284#1621C2×C15114yescomplemented
285#1540C2×C15111yescharacteristic, complemented
286#1480C2×C15111yescharacteristic, complemented
287#1479C2×C15111yescharacteristic, complemented
288C2×2−1+4—21no—
289C22×SD16—21no—
290#550—21no—
291#550C22×C15112yescomplemented
292D4×Q8—21no—
293D4×Q8C22×C15112yescomplemented
294#548—22no—
295#548—22no—
296#537—22no—
297#537—21no—
298#532—22no—
299#532C22×C15111yescharacteristic
300#532C22×C15111yescharacteristic
301C2×#127C22×C15111yescharacteristic
302C2×C4×Q8C22×C15111yescharacteristic
303#493—21no—
304#493C22×C15112yes—
305#486—21no—
306#486C22×C15112yes—
307#460—22no—
308#460C22×C15114yes—
309#459—22no—
310#459C22×C15114yes—
311#447—22no—
312#447—22no—
313#431C22×C15111yescharacteristic
314#431C22×C15111yescharacteristic
315C2×C4⋊C8C22×C15111yescharacteristic
316C2×#102—21no—
317#332C22×C15112yescomplemented
318#331C22×C15112yescomplemented
319Q8⋊C8C22×C15114yescomplemented
320D4⋊C8C22×C15114yescomplemented
3212−1+4—44no—
3222−1+4—44no—
323C2×#41—24no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41—21no—
327C2×#41—21no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8D4×C15111yescharacteristic
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C2×SD16—24no—
335C2×SD16—44no—
336C2×D8—24no—
337C2×D8—24no—
338C22×C8—21no—
339C4⋊Q8—22no—
340C4⋊Q8D4×C15111yescharacteristic
341C4⋊Q8C23×C15111yescharacteristic
342#127—22no—
343#127—21no—
344#127—21no—
345#127—21no—
346#127D4×C15111yescharacteristic
347#127C23×C15112yes—
348#127C23×C15111yescharacteristic
349#124—24no—
350#124—21no—
351#124—21no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—22no—
355C22⋊Q8—24no—
356#121—24no—
357#121—22no—
358#121—24no—
359#121—24no—
360#121—21no—
361#121—21no—
362#121—22no—
363#121D4×C15112yes—
364#121D4×C15112yes—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8D4×C15112yes—
368C4×Q8C23×C15112yes—
369C4×D4—24no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4D4×C15112yes—
375C4×D4C23×C15112yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C15111yescharacteristic
378C2×C42—21no—
379C2×C42C23×C15111yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8C23×C15112yes—
383C4⋊C8C23×C15112yes—
384#102—24no—
385#102—24no—
386#102—24no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C4×C8—21no—
390C4×C8C23×C15112yes—
391C24—41no—
392#41—416no—
393#41—48no—
394#41—44no—
395#41—44no—
396#41—42no—
397#41—42no—
398#41—42no—
399#41—42no—
400C2×Q8—24no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—21no—
405C2×Q8—48no—
406C2×Q8—44no—
407C2×Q8—44no—
408C2×Q8D8×C15114yescomplemented
409C2×Q8C2×D4×C15112yes—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—82no—
427C2×D4—82no—
428C2×D4C2×D4×C15112yes—
429C2×D4C2×D4×C15112yes—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439SD16—48no—
440D8—84no—
441D8—84no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—42no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4C2×D4×C15112yes—
453C4⋊C4C2×D4×C15112yes—
454C4⋊C4C2×D4×C15112yes—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C42—22no—
462C42—22no—
463C42C2×D4×C15111yescharacteristic
464C42C2×D4×C15111yescharacteristic
465C42C2×D4×C15111yescharacteristic
466C42C24×C15111yescharacteristic
467C23—22no—
468C23—22no—
469C23—42no—
470C23—82no—
471C23—82no—
472C23—82no—
473C23#120×C15111yescharacteristic
474Q8—24no—
475Q8—22no—
476Q8—48no—
477Q8—42no—
478Q8—41no—
479Q8—41no—
480Q8C2×D8×C15114yes—
481D4—24no—
482D4—42no—
483D4—48no—
484D4—44no—
485D4—44no—
486D4—44no—
487D4—42no—
488D4—41no—
489D4—42no—
490D4—41no—
491D4—42no—
492D4—42no—
493D4—44no—
494D4—81no—
495D4—82no—
496D4—82no—
497D4—84no—
498D4—82no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—48no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—81no—
512C2×C4#120×C15111yescharacteristic
513C2×C4#120×C15111yescharacteristic
514C2×C4#120×C15111yescharacteristic
515C2×C4C2×D8×C15112yes—
516C2×C4AGL(1,ℤ/8)×C15112yes—
517C2×C4C22×D4×C15111yescharacteristic
518C2×C4C22×D4×C15111yescharacteristic
519C2×C4C22×D4×C15111yescharacteristic
520C8—42no—
521C8—42no—
522C8—42no—
523C22—21no—
524C22—21no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—164no—
535C22#447×C15112yes—
536C22C2×#120×C15111yescharacteristic
537C4—24no—
538C4—21no—
539C4—21no—
540C4—21no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4#447×C15112yes—
545C4C22×D8×C15111yescharacteristic
546C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
547C4#577×C15112yes—
548C2—22no—
549C2—82no—
550C2—82no—
551C2—162no—
552C2C2×#447×C15111yescharacteristic
553C2#3010×C15111yescharacteristic
554C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3497×C151C2semidirect
2. #3205×C151C2semidirect
3. #3205×C151C2semidirect
4. C2×#460×C151C2semidirect
5. #1627×C151C2semidirect
6. #1621×C151C2semidirect
7. #1540×C151C2semidirect
8. #1480×C151C2semidirect
9. #1479×C151C2semidirect
13. #550×C151C22semidirect
15. D4×Q8×C151C22semidirect
39. #332×C151C22semidirect
40. #331×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
130. C2×Q8×C151D8semidirect
277. #18912C151direct (N × H)
278. C151#18912direct (N × H)
279. #3497C2×C151semidirect
280. #3205C2×C151semidirect
281. #3205C2×C151semidirect
282. C2×#460C2×C151semidirect
283. #1627C2×C151semidirect
284. #1621C2×C151semidirect
285. #1540C2×C151semidirect
286. #1480C2×C151semidirect
287. #1479C2×C151semidirect
291. #550C22×C151semidirect
293. D4×Q8C22×C151semidirect
317. #332C22×C151semidirect
318. #331C22×C151semidirect
319. Q8⋊C8C22×C151semidirect
320. D4⋊C8C22×C151semidirect
408. C2×Q8D8×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3205×C1512
C2×#460×C1512
#1627×C1512
#1621×C1512
#1540×C1512
#1480×C1512
#1479×C1512
#18912151