Finite Group Databasebeta

← C151×#24104 #50329029

Subgroups — C151×#24104 #50329029

Order 38656.

1146 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C151C211yesmaximal, characteristic
2C2×#481×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2486×C151C211yesmaximal, characteristic, complemented
5#2058×C151C212yesmaximal, complemented
6#2034×C151C212yesmaximal, complemented
7#1895×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1862×C151C212yesmaximal, complemented
10#1854×C151C212yesmaximal, complemented
11#1825×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151C2211yescharacteristic
13#555×C151—24no—
14#555×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#124×C151—21no—
17C2×#124×C151—21no—
18C2×#123×C151—21no—
19C2×#121×C151—21no—
20C2×#121×C151C2211yescharacteristic
21C2×#121×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151—21no—
25C2×#117×C151C2211yescharacteristic
26C2×#117×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28#481×C151—24no—
29#428×C151—24no—
30C2×#107×C151C2212yes—
31C2×#106×C151C2212yes—
32C2×#106×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2212yes—
37#398×C151—21no—
38#397×C151—21no—
39#389×C151C2212yes—
40#381×C151—21no—
41#380×C151C2211yescharacteristic
42#380×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—21no—
48C22×D4×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151D411yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C23×C4×C151—21no—
53C23×C4×C151—21no—
54C23×C4×C151C2311yescharacteristic
55C23×C4×C151C2311yescharacteristic
56C2×M16×C151—22no—
57C2×M16×C151—24no—
58C22×C8×C151C2312yes—
59C22×C8×C151C2312yes—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—22no—
62#124×C151—28no—
63#124×C151—28no—
64#123×C151—44no—
65#121×C151—28no—
66#121×C151—22no—
67#121×C151—22no—
68#121×C151—22no—
69#121×C151D414yes—
70C4×D4×C151—22no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74#117×C151—28no—
75#117×C151—22no—
76#117×C151—22no—
77#117×C151—22no—
78#117×C151D414yes—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151C2312yes—
86C2×C4⋊C4×C151C2312yes—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151D411yescharacteristic
98C2×C22⋊C4×C151D411yescharacteristic
99C2×C42×C151—21no—
100C2×C42×C151—21no—
101C2×C42×C151C2311yescharacteristic
102#107×C151—24no—
103#106×C151—24no—
104#106×C151—24no—
105#102×C151—24no—
106#102×C151—24no—
107C22⋊C8×C151—22no—
108C22⋊C8×C151—24no—
109#95×C151—22no—
110#95×C151—21no—
111#95×C151—22no—
112C24×C151—21no—
113C24×C151C2×D411yescharacteristic
114C24×C151C2×D411yescharacteristic
115C2×Q8×C151—24no—
116C2×Q8×C151—82no—
117C2×D4×C151—22no—
118C2×D4×C151—24no—
119C2×D4×C151—24no—
120C2×D4×C151—22no—
121C2×D4×C151—21no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—41no—
125C2×D4×C151—82no—
126C2×D4×C151—82no—
127C2×D4×C151C2×D412yes—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—24no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—22no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—42no—
141C22×C4×C151—42no—
142C22×C4×C151—42no—
143C22×C4×C151—42no—
144C22×C4×C151—42no—
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2×D411yescharacteristic
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D412yes—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2411yescharacteristic
152M16×C151—28no—
153C2×C8×C151—22no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C2×C8×C151—22no—
158C2×C8×C151#4114yes—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—42no—
169C4⋊C4×C151—44no—
170C4⋊C4×C151C2×D412yes—
171C4⋊C4×C151C2×D412yes—
172C4⋊C4×C151C2×D412yes—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—24no—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—24no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—42no—
181C22⋊C4×C151—44no—
182C42×C151—24no—
183C42×C151—24no—
184C42×C151—21no—
185C42×C151—21no—
186C23×C151—22no—
187C23×C151—21no—
188C23×C151—21no—
189C23×C151—22no—
190C23×C151—22no—
191C23×C151—21no—
192C23×C151—22no—
193C23×C151—21no—
194C23×C151—21no—
195C23×C151—22no—
196C23×C151—42no—
197C23×C151—41no—
198C23×C151—41no—
199C23×C151—42no—
200C23×C151#12012yes—
201C23×C151C22×D411yescharacteristic
202Q8×C151—84no—
203D4×C151—24no—
204D4×C151—44no—
205D4×C151—41no—
206D4×C151—41no—
207D4×C151—84no—
208D4×C151—84no—
209C2×C4×C151—21no—
210C2×C4×C151—22no—
211C2×C4×C151—21no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—24no—
215C2×C4×C151—21no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—48no—
223C2×C4×C151—41no—
224C2×C4×C151—41no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—84no—
237C2×C4×C151#12012yes—
238C2×C4×C151AGL(1,ℤ/8)12yes—
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C2×#4112yes—
242C2×C4×C1512−1+412yes—
243C8×C151—24no—
244C8×C151—42no—
245C22×C151—22no—
246C22×C151—22no—
247C22×C151—22no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—41no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—42no—
258C22×C151—82no—
259C22×C151—82no—
260C22×C151C2×#12011yescharacteristic
261C22×C151#54712yes—
262C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C151#57511yescharacteristic
264C22×C151#57712yes—
265C4×C151—22no—
266C4×C151—22no—
267C4×C151—41no—
268C4×C151—42no—
269C4×C151—41no—
270C4×C151—42no—
271C4×C151—42no—
272C4×C151—82no—
273C4×C151—82no—
274C4×C151#52511yescharacteristic
275C4×C151#53611yescharacteristic
276C4×C151#54712yes—
277C2×C151—42no—
278C2×C151—81no—
279C2×C151—82no—
280C2×C151#240611yescharacteristic
281C2×C151#300611yescharacteristic
282C2×C151#300911yescharacteristic
283C2×C151#334812yes—
284C2×C151#335412yes—
285#24104C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#2410411yescharacteristic, direct product factor, Sylow
287C2×#555C2×C15111yescharacteristic
288C2×#481C2×C15111yescharacteristic, complemented
289C2×#428C2×C15111yescharacteristic, complemented
290#2486C2×C15111yescharacteristic, complemented
291#2058C2×C15112yescomplemented
292#2034C2×C15112yescomplemented
293#1895C2×C15111yescharacteristic, complemented
294#1870C2×C15111yescharacteristic, complemented
295#1862C2×C15112yescomplemented
296#1854C2×C15112yescomplemented
297#1825C2×C15111yescharacteristic, complemented
298C22×M16C22×C15111yescharacteristic
299#555—24no—
300#555—24no—
301C2×C4⋊Q8C22×C15111yescharacteristic
302C2×#124—21no—
303C2×#124—21no—
304C2×#123—21no—
305C2×#121—21no—
306C2×#121C22×C15111yescharacteristic
307C2×#121C22×C15111yescharacteristic
308C2×C4×D4C22×C15111yescharacteristic
309C2×C4×D4C22×C15111yescharacteristic
310C2×#117—21no—
311C2×#117C22×C15111yescharacteristic
312C2×#117C22×C15111yescharacteristic
313C22×C4⋊C4C22×C15111yescharacteristic
314#481—24no—
315#428—24no—
316C2×#107C22×C15112yes—
317C2×#106C22×C15112yes—
318C2×#106C22×C15112yes—
319C2×#102C22×C15112yes—
320C2×#102C22×C15112yes—
321C2×C22⋊C8C22×C15111yescharacteristic
322C2×C22⋊C8C22×C15112yes—
323#398—21no—
324#397—21no—
325#389C22×C15112yes—
326#381—21no—
327#380C22×C15111yescharacteristic
328#380C22×C15112yes—
329#340C22×C15112yes—
330#340C22×C15112yes—
331#340C22×C15112yes—
332#336C22×C15112yes—
333C22×Q8—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4D4×C15111yescharacteristic
337C22×D4C23×C15111yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4C23×C15111yescharacteristic
341C23×C4C23×C15111yescharacteristic
342C2×M16—22no—
343C2×M16—24no—
344C22×C8C23×C15112yes—
345C22×C8C23×C15112yes—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348#124—28no—
349#124—28no—
350#123—44no—
351#121—28no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121D4×C15114yes—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360#117—28no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117D4×C15114yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4D4×C15111yescharacteristic
371C2×C4⋊C4C23×C15112yes—
372C2×C4⋊C4C23×C15112yes—
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4D4×C15111yescharacteristic
384C2×C22⋊C4D4×C15111yescharacteristic
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C23×C15111yescharacteristic
388#107—24no—
389#106—24no—
390#106—24no—
391#102—24no—
392#102—24no—
393C22⋊C8—22no—
394C22⋊C8—24no—
395#95—22no—
396#95—21no—
397#95—22no—
398C24—21no—
399C24C2×D4×C15111yescharacteristic
400C24C2×D4×C15111yescharacteristic
401C2×Q8—24no—
402C2×Q8—82no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—41no—
411C2×D4—82no—
412C2×D4—82no—
413C2×D4C2×D4×C15112yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434C22×C4C2×D4×C15112yes—
435C22×C4C2×D4×C15112yes—
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C24×C15111yescharacteristic
438M16—28no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8#41×C15114yes—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—44no—
456C4⋊C4C2×D4×C15112yes—
457C4⋊C4C2×D4×C15112yes—
458C4⋊C4C2×D4×C15112yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—22no—
464C22⋊C4—24no—
465C22⋊C4—22no—
466C22⋊C4—42no—
467C22⋊C4—44no—
468C42—24no—
469C42—24no—
470C42—21no—
471C42—21no—
472C23—22no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—21no—
477C23—22no—
478C23—22no—
479C23—21no—
480C23—21no—
481C23—22no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23#120×C15112yes—
487C23C22×D4×C15111yescharacteristic
488Q8—84no—
489D4—24no—
490D4—44no—
491D4—41no—
492D4—41no—
493D4—84no—
494D4—84no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—48no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—84no—
523C2×C4#120×C15112yes—
524C2×C4AGL(1,ℤ/8)×C15112yes—
525C2×C4C22×D4×C15111yescharacteristic
526C2×C4C22×D4×C15111yescharacteristic
527C2×C4C2×#41×C15112yes—
528C2×C42−1+4×C15112yes—
529C8—24no—
530C8—42no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—42no—
539C22—41no—
540C22—41no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22C2×#120×C15111yescharacteristic
547C22#547×C15112yes—
548C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
549C22#575×C15111yescharacteristic
550C22#577×C15112yes—
551C4—22no—
552C4—22no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—82no—
560C4#525×C15111yescharacteristic
561C4#536×C15111yescharacteristic
562C4#547×C15112yes—
563C2—42no—
564C2—81no—
565C2—82no—
566C2#2406×C15111yescharacteristic
567C2#3006×C15111yescharacteristic
568C2#3009×C15111yescharacteristic
569C2#3348×C15112yes—
570C2#3354×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#555×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#481×C151C2semidirect
3. C2×#428×C151C2semidirect
4. #2486×C151C2semidirect
5. #2058×C151C2semidirect
6. #2034×C151C2semidirect
7. #1895×C151C2semidirect
8. #1870×C151C2semidirect
9. #1862×C151C2semidirect
10. #1854×C151C2semidirect
11. #1825×C151C2semidirect
285. #24104C151direct (N × H)
286. C151#24104direct (N × H)
288. C2×#481C2×C151semidirect
289. C2×#428C2×C151semidirect
290. #2486C2×C151semidirect
291. #2058C2×C151semidirect
292. #2034C2×C151semidirect
293. #1895C2×C151semidirect
294. #1870C2×C151semidirect
295. #1862C2×C151semidirect
296. #1854C2×C151semidirect
297. #1825C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1512
C2×#481×C1512
C2×#428×C1512
#2486×C1512
#2058×C1512
#2034×C1512
#1895×C1512
#1870×C1512
#1862×C1512
#1854×C1512
#1825×C1512
#24104151