Finite Group Databasebeta

← C151×#23930 #50328855

Subgroups — C151×#23930 #50328855

Order 38656.

1768 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C151C211yesmaximal, characteristic, complemented
2C2×#447×C151C212yesmaximal, complemented
3C2×#390×C151C211yesmaximal, characteristic, complemented
4#2023×C151C212yesmaximal, complemented
5#2011×C151C212yesmaximal, complemented
6#1879×C151C214yesmaximal, complemented
7#1874×C151C212yesmaximal, complemented
8#1817×C151C211yesmaximal, characteristic, complemented
9C22×#41×C151—21no—
10C23×D4×C151C2211yescharacteristic
11C22×D8×C151C2214yes—
12#532×C151—28no—
13C2×C4⋊Q8×C151C2211yescharacteristic, complemented
14C2×#127×C151C2211yescharacteristic, complemented
15C2×#124×C151—21no—
16C2×#121×C151—21no—
17C2×#121×C151C2212yes—
18C2×C4×D4×C151—21no—
19C2×C4×D4×C151C2212yescomplemented
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C22⋊C4×C151—21no—
22C22×C22⋊C4×C151—21no—
23C22×C42×C151C2211yescharacteristic
24#447×C151—28no—
25C2×#102×C151C2214yes—
26C2×#102×C151C2214yescomplemented
27C2×C22⋊C8×C151C2212yes—
28#390×C151—21no—
29#390×C151—21no—
30#390×C151C2212yes—
31#390×C151C2212yes—
32#340×C151C2214yescomplemented
33#336×C151C2212yescomplemented
34#336×C151C2212yescomplemented
35C25×C151—21no—
36C2×#41×C151—28no—
37C2×#41×C151—44no—
38C2×#41×C151—44no—
39C22×Q8×C151—21no—
40C22×D4×C151—24no—
41C22×D4×C151—21no—
42C22×D4×C151—21no—
43C22×D4×C151—21no—
44C22×D4×C151—22no—
45C22×D4×C151—24no—
46C22×D4×C151—42no—
47C22×D4×C151C2312yes—
48C22×D4×C151C2312yes—
49C23×C4×C151—22no—
50C23×C4×C151—21no—
51C23×C4×C151D411yescharacteristic
52C23×C4×C151D411yescharacteristic
53C23×C4×C151C2311yescharacteristic
54C2×D8×C151—28no—
55C2×D8×C151—28no—
56C2×D8×C151—44no—
57C22×C8×C151C2314yes—
58C4⋊Q8×C151—24no—
59#127×C151—24no—
60#124×C151—28no—
61#121×C151—28no—
62#121×C151—24no—
63#121×C151D418yes—
64C4×D4×C151—28no—
65C4×D4×C151—24no—
66C4×D4×C151—24no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—42no—
70C2×C4⋊C4×C151C2312yes—
71C2×C4⋊C4×C151C2312yes—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—44no—
79C2×C22⋊C4×C151—44no—
80C2×C42×C151—24no—
81C2×C42×C151D411yescharacteristic
82C2×C42×C151D411yescharacteristic
83C2×C42×C151C2311yescharacteristic
84C2×C42×C151C2311yescharacteristic
85#102×C151—28no—
86#102×C151—44no—
87C22⋊C8×C151—24no—
88C24×C151—24no—
89C24×C151—22no—
90C24×C151—22no—
91C24×C151—42no—
92C24×C151—42no—
93C24×C151—42no—
94C24×C151—42no—
95C24×C151—42no—
96C24×C151—42no—
97C24×C151C2×D411yescharacteristic
98#41×C151—432no—
99C2×Q8×C151—24no—
100C2×Q8×C151—42no—
101C2×Q8×C151—42no—
102C2×D4×C151—24no—
103C2×D4×C151—24no—
104C2×D4×C151—24no—
105C2×D4×C151—28no—
106C2×D4×C151—24no—
107C2×D4×C151—22no—
108C2×D4×C151—24no—
109C2×D4×C151—22no—
110C2×D4×C151—24no—
111C2×D4×C151—24no—
112C2×D4×C151—416no—
113C2×D4×C151—42no—
114C2×D4×C151—42no—
115C2×D4×C151—42no—
116C2×D4×C151—44no—
117C2×D4×C151—44no—
118C2×D4×C151—42no—
119C2×D4×C151—42no—
120C2×D4×C151—42no—
121C2×D4×C151C2×D414yes—
122C2×D4×C151#4114yescomplemented
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—22no—
126C22×C4×C151—22no—
127C22×C4×C151—28no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—41no—
133C22×C4×C151—44no—
134C22×C4×C151—44no—
135C22×C4×C151—42no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151D814yescomplemented
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D414yes—
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146D8×C151—416no—
147C2×C8×C151—24no—
148C2×C8×C151—24no—
149C2×C8×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—24no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151C2×D414yes—
155C22⋊C4×C151—28no—
156C22⋊C4×C151—28no—
157C22⋊C4×C151—44no—
158C22⋊C4×C151—44no—
159C22⋊C4×C151—44no—
160C22⋊C4×C151—44no—
161C42×C151—22no—
162C42×C151—22no—
163C42×C151—22no—
164C42×C151—22no—
165C23×C151—21no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—21no—
169C23×C151—24no—
170C23×C151—24no—
171C23×C151—48no—
172C23×C151—48no—
173C23×C151—48no—
174C23×C151—42no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—84no—
187C23×C151—84no—
188C23×C151—84no—
189C23×C151—84no—
190C23×C151#12012yes—
191C23×C151C2×D812yes—
192C23×C151AGL(1,ℤ/8)12yes—
193C23×C151C22×D411yescharacteristic
194Q8×C151—48no—
195D4×C151—28no—
196D4×C151—28no—
197D4×C151—48no—
198D4×C151—48no—
199D4×C151—48no—
200D4×C151—416no—
201D4×C151—44no—
202D4×C151—44no—
203C2×C4×C151—21no—
204C2×C4×C151—21no—
205C2×C4×C151—21no—
206C2×C4×C151—21no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—21no—
211C2×C4×C151—28no—
212C2×C4×C151—28no—
213C2×C4×C151—24no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—44no—
218C2×C4×C151—416no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—84no—
225C2×C4×C151#12012yes—
226C2×C4×C151C2×D812yes—
227C2×C4×C151C2×D812yes—
228C2×C4×C151AGL(1,ℤ/8)12yes—
229C2×C4×C151C22×D412yes—
230C2×C4×C151C2×#4112yes—
231C2×C4×C151H(5,𝔽2)12yes—
232C8×C151—44no—
233C22×C151—22no—
234C22×C151—22no—
235C22×C151—22no—
236C22×C151—22no—
237C22×C151—22no—
238C22×C151—22no—
239C22×C151—44no—
240C22×C151—44no—
241C22×C151—44no—
242C22×C151—44no—
243C22×C151—44no—
244C22×C151—44no—
245C22×C151—816no—
246C22×C151—82no—
247C22×C151—82no—
248C22×C151—82no—
249C22×C151—82no—
250C22×C151—82no—
251C22×C151—82no—
252C22×C151—82no—
253C22×C151—82no—
254C22×C151#44714yes—
255C22×C151C2×#12011yescharacteristic
256C22×C151#52511yescharacteristic
257C22×C151#53511yescharacteristic
258C22×C151C22×D811yescharacteristic
259C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C151#57511yescharacteristic
262C4×C151—22no—
263C4×C151—22no—
264C4×C151—22no—
265C4×C151—22no—
266C4×C151—44no—
267C4×C151—41no—
268C4×C151—82no—
269C4×C151#54614yes—
270C2×C151—24no—
271C2×C151—84no—
272C2×C151—84no—
273C2×C151#240411yescharacteristic
274C2×C151C2×#44711yescharacteristic
275C2×C151#300611yescharacteristic
276C2×C151#310011yescharacteristic
277C2×C151#310911yescharacteristic
278C2×C151#320511yescharacteristic
279C2×C151#321311yescharacteristic
280#23930C15111yesmaximal, characteristic, direct product factor, Sylow
281C151#2393011yescharacteristic, direct product factor, Sylow
282C2×#532C2×C15111yescharacteristic, complemented
283C2×#447C2×C15112yescomplemented
284C2×#390C2×C15111yescharacteristic, complemented
285#2023C2×C15112yescomplemented
286#2011C2×C15112yescomplemented
287#1879C2×C15114yescomplemented
288#1874C2×C15112yescomplemented
289#1817C2×C15111yescharacteristic, complemented
290C22×#41—21no—
291C23×D4C22×C15111yescharacteristic
292C22×D8C22×C15114yes—
293#532—28no—
294C2×C4⋊Q8C22×C15111yescharacteristic, complemented
295C2×#127C22×C15111yescharacteristic, complemented
296C2×#124—21no—
297C2×#121—21no—
298C2×#121C22×C15112yes—
299C2×C4×D4—21no—
300C2×C4×D4C22×C15112yescomplemented
301C22×C4⋊C4C22×C15111yescharacteristic
302C22×C22⋊C4—21no—
303C22×C22⋊C4—21no—
304C22×C42C22×C15111yescharacteristic
305#447—28no—
306C2×#102C22×C15114yes—
307C2×#102C22×C15114yescomplemented
308C2×C22⋊C8C22×C15112yes—
309#390—21no—
310#390—21no—
311#390C22×C15112yes—
312#390C22×C15112yes—
313#340C22×C15114yescomplemented
314#336C22×C15112yescomplemented
315#336C22×C15112yescomplemented
316C25—21no—
317C2×#41—28no—
318C2×#41—44no—
319C2×#41—44no—
320C22×Q8—21no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—24no—
327C22×D4—42no—
328C22×D4C23×C15112yes—
329C22×D4C23×C15112yes—
330C23×C4—22no—
331C23×C4—21no—
332C23×C4D4×C15111yescharacteristic
333C23×C4D4×C15111yescharacteristic
334C23×C4C23×C15111yescharacteristic
335C2×D8—28no—
336C2×D8—28no—
337C2×D8—44no—
338C22×C8C23×C15114yes—
339C4⋊Q8—24no—
340#127—24no—
341#124—28no—
342#121—28no—
343#121—24no—
344#121D4×C15118yes—
345C4×D4—28no—
346C4×D4—24no—
347C4×D4—24no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C23×C15112yes—
352C2×C4⋊C4C23×C15112yes—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C42—24no—
362C2×C42D4×C15111yescharacteristic
363C2×C42D4×C15111yescharacteristic
364C2×C42C23×C15111yescharacteristic
365C2×C42C23×C15111yescharacteristic
366#102—28no—
367#102—44no—
368C22⋊C8—24no—
369C24—24no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24—42no—
377C24—42no—
378C24C2×D4×C15111yescharacteristic
379#41—432no—
380C2×Q8—24no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—28no—
387C2×D4—24no—
388C2×D4—22no—
389C2×D4—24no—
390C2×D4—22no—
391C2×D4—24no—
392C2×D4—24no—
393C2×D4—416no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—42no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4C2×D4×C15114yes—
403C2×D4#41×C15114yescomplemented
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—28no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—44no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4D8×C15114yescomplemented
420C22×C4C2×D4×C15111yescharacteristic
421C22×C4C2×D4×C15111yescharacteristic
422C22×C4C2×D4×C15114yes—
423C22×C4C2×D4×C15111yescharacteristic
424C22×C4C2×D4×C15111yescharacteristic
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C24×C15111yescharacteristic
427D8—416no—
428C2×C8—24no—
429C2×C8—24no—
430C2×C8—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—24no—
434C4⋊C4—42no—
435C4⋊C4C2×D4×C15114yes—
436C22⋊C4—28no—
437C22⋊C4—28no—
438C22⋊C4—44no—
439C22⋊C4—44no—
440C22⋊C4—44no—
441C22⋊C4—44no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—22no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—24no—
451C23—24no—
452C23—48no—
453C23—48no—
454C23—48no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—84no—
468C23—84no—
469C23—84no—
470C23—84no—
471C23#120×C15112yes—
472C23C2×D8×C15112yes—
473C23AGL(1,ℤ/8)×C15112yes—
474C23C22×D4×C15111yescharacteristic
475Q8—48no—
476D4—28no—
477D4—28no—
478D4—48no—
479D4—48no—
480D4—48no—
481D4—416no—
482D4—44no—
483D4—44no—
484C2×C4—28no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—28no—
494C2×C4—21no—
495C2×C4—24no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—44no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—84no—
506C2×C4#120×C15112yes—
507C2×C4C2×D8×C15112yes—
508C2×C4C2×D8×C15112yes—
509C2×C4AGL(1,ℤ/8)×C15112yes—
510C2×C4C22×D4×C15112yes—
511C2×C4C2×#41×C15112yes—
512C2×C4H(5,𝔽2)×C15112yes—
513C8—44no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—44no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—44no—
526C22—816no—
527C22—82no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22#447×C15114yes—
536C22C2×#120×C15111yescharacteristic
537C22#525×C15111yescharacteristic
538C22#535×C15111yescharacteristic
539C22C22×D8×C15111yescharacteristic
540C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
541C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
542C22#575×C15111yescharacteristic
543C4—22no—
544C4—22no—
545C4—22no—
546C4—22no—
547C4—44no—
548C4—41no—
549C4—82no—
550C4#546×C15114yes—
551C2—24no—
552C2—84no—
553C2—84no—
554C2#2404×C15111yescharacteristic
555C2C2×#447×C15111yescharacteristic
556C2#3006×C15111yescharacteristic
557C2#3100×C15111yescharacteristic
558C2#3109×C15111yescharacteristic
559C2#3205×C15111yescharacteristic
560C2#3213×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#532×C151C2semidirect
2. C2×#447×C151C2semidirect
3. C2×#390×C151C2semidirect
4. #2023×C151C2semidirect
5. #2011×C151C2semidirect
6. #1879×C151C2semidirect
7. #1874×C151C2semidirect
8. #1817×C151C2semidirect
13. C2×C4⋊Q8×C151C22semidirect
14. C2×#127×C151C22semidirect
19. C2×C4×D4×C151C22semidirect
26. C2×#102×C151C22semidirect
32. #340×C151C22semidirect
33. #336×C151C22semidirect
34. #336×C151C22semidirect
122. C2×D4×C151#41semidirect
138. C22×C4×C151D8semidirect
280. #23930C151direct (N × H)
281. C151#23930direct (N × H)
282. C2×#532C2×C151semidirect
283. C2×#447C2×C151semidirect
284. C2×#390C2×C151semidirect
285. #2023C2×C151semidirect
286. #2011C2×C151semidirect
287. #1879C2×C151semidirect
288. #1874C2×C151semidirect
289. #1817C2×C151semidirect
294. C2×C4⋊Q8C22×C151semidirect
295. C2×#127C22×C151semidirect
300. C2×C4×D4C22×C151semidirect
307. C2×#102C22×C151semidirect
313. #340C22×C151semidirect
314. #336C22×C151semidirect
315. #336C22×C151semidirect
403. C2×D4#41×C151semidirect
419. C22×C4D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1512
C2×#447×C1512
C2×#390×C1512
#2023×C1512
#2011×C1512
#1879×C1512
#1874×C1512
#1817×C1512
#23930151