Finite Group Databasebeta

← C151×#23970 #50328895

Subgroups — C151×#23970 #50328895

Order 38656.

1278 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#451×C151C211yesmaximal, characteristic, complemented
3C22×#103×C151C211yesmaximal, characteristic, complemented
4#2409×C151C211yesmaximal, characteristic
5#2024×C151C212yesmaximal, complemented
6#2001×C151C212yesmaximal, complemented
7#1892×C151C211yesmaximal, characteristic, complemented
8#1878×C151C212yesmaximal, complemented
9#1872×C151C212yesmaximal, complemented
10#1869×C151C211yesmaximal, characteristic
11#1824×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×Q16×C151C2212yes—
14C23×C8×C151C2211yescharacteristic
15#554×C151—24no—
16#554×C151—24no—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×#125×C151—21no—
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151—21no—
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×C22⋊Q8×C151C2212yes—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151—21no—
26C2×C4×D4×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C4⋊C4×C151C2211yescharacteristic
29#451×C151—24no—
30C2×#103×C151—24no—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×#103×C151C2212yes—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2212yes—
37#395×C151—21no—
38#393×C151—21no—
39#391×C151C2212yes—
40#386×C151—21no—
41#385×C151—21no—
42#380×C151C2211yescharacteristic
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—22no—
48C22×Q8×C151—24no—
49C22×Q8×C151—21no—
50C22×Q8×C151—22no—
51C22×Q8×C151—21no—
52C22×Q8×C151—42no—
53C22×Q8×C151C2311yescharacteristic
54C22×Q8×C151C2312yes—
55C22×D4×C151D411yescharacteristic
56C23×C4×C151—21no—
57C23×C4×C151—21no—
58C23×C4×C151—21no—
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C2×Q16×C151—24no—
62C2×Q16×C151—24no—
63C2×Q16×C151—42no—
64C22×C8×C151—22no—
65C22×C8×C151—42no—
66C22×C8×C151C2312yes—
67C22×C8×C151C2312yes—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—22no—
70#125×C151—28no—
71C22⋊Q8×C151—28no—
72C22⋊Q8×C151—28no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—22no—
75C22⋊Q8×C151—22no—
76C22⋊Q8×C151—24no—
77C22⋊Q8×C151—42no—
78C22⋊Q8×C151D414yes—
79C4×Q8×C151—22no—
80C4×Q8×C151—22no—
81C4×D4×C151—28no—
82C4×D4×C151—22no—
83C4×D4×C151—22no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—22no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C4⋊C4×C151D414yes—
96C2×C4⋊C4×C151C2312yes—
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—22no—
104C2×C22⋊C4×C151D411yescharacteristic
105C2×C22⋊C4×C151D411yescharacteristic
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108#103×C151—24no—
109#103×C151—24no—
110#103×C151—24no—
111#103×C151—42no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—42no—
114#95×C151—21no—
115#95×C151—22no—
116#95×C151—22no—
117C24×C151C2×D411yescharacteristic
118C24×C151C2×D411yescharacteristic
119C2×Q8×C151—24no—
120C2×Q8×C151—21no—
121C2×Q8×C151—22no—
122C2×Q8×C151—28no—
123C2×Q8×C151—22no—
124C2×Q8×C151—22no—
125C2×Q8×C151—22no—
126C2×Q8×C151—22no—
127C2×Q8×C151—22no—
128C2×Q8×C151—22no—
129C2×Q8×C151—44no—
130C2×Q8×C151—48no—
131C2×Q8×C151—44no—
132C2×Q8×C151—42no—
133C2×Q8×C151—82no—
134C2×Q8×C151C2×D412yes—
135C2×Q8×C151#4114yes—
136C2×D4×C151—22no—
137C2×D4×C151—22no—
138C2×D4×C151Q1614yescomplemented
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—24no—
147C22×C4×C151—24no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—44no—
154C22×C4×C151—42no—
155C22×C4×C151—82no—
156C22×C4×C151—82no—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D412yes—
161C22×C4×C151C2×D412yes—
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2411yescharacteristic
164Q16×C151—48no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—44no—
172C4⋊C4×C151—24no—
173C4⋊C4×C151—24no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—24no—
177C4⋊C4×C151—24no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—44no—
185C4⋊C4×C151C2×D412yes—
186C4⋊C4×C151C2×D412yes—
187C4⋊C4×C151C2×D412yes—
188C22⋊C4×C151—24no—
189C22⋊C4×C151—24no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—44no—
193C22⋊C4×C151—42no—
194C42×C151—24no—
195C42×C151—21no—
196C42×C151—21no—
197C23×C151—22no—
198C23×C151—22no—
199C23×C151—21no—
200C23×C151—22no—
201C23×C151—21no—
202C23×C151—22no—
203C23×C151#12012yes—
204C23×C151C2×Q1612yes—
205C23×C151C2×Q1612yes—
206C23×C151#13712yes—
207C23×C151C22×D411yescharacteristic
208Q8×C151—24no—
209Q8×C151—24no—
210Q8×C151—24no—
211Q8×C151—48no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—42no—
215Q8×C151—42no—
216Q8×C151—84no—
217D4×C151—28no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—21no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—24no—
224C2×C4×C151—21no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—24no—
231C2×C4×C151—22no—
232C2×C4×C151—22no—
233C2×C4×C151—48no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—42no—
245C2×C4×C151—42no—
246C2×C4×C151—84no—
247C2×C4×C151—84no—
248C2×C4×C151#12012yes—
249C2×C4×C151C2×Q1612yes—
250C2×C4×C151C22×D411yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C2×#4112yes—
253C2×C4×C151H(5,𝔽2)12yes—
254C8×C151—42no—
255C8×C151—42no—
256C22×C151—22no—
257C22×C151—22no—
258C22×C151—24no—
259C22×C151—24no—
260C22×C151—22no—
261C22×C151—24no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—42no—
265C22×C151#45114yes—
266C22×C151C2×#12011yescharacteristic
267C22×C151#54612yes—
268C22×C151C22×Q1611yescharacteristic
269C22×C151C2×#13711yescharacteristic
270C22×C151#57712yes—
271C4×C151—22no—
272C4×C151—22no—
273C4×C151—41no—
274C4×C151—44no—
275C4×C151—42no—
276C4×C151—41no—
277C4×C151—42no—
278C4×C151—42no—
279C4×C151—42no—
280C4×C151—82no—
281C4×C151#52511yescharacteristic
282C4×C151#53511yescharacteristic
283C4×C151#54612yes—
284C2×C151—24no—
285C2×C151—42no—
286C2×C151#240411yescharacteristic
287C2×C151C2×#45111yescharacteristic
288C2×C151#300911yescharacteristic
289C2×C151#329912yes—
290C2×C151#331612yes—
291#23970C15111yesmaximal, characteristic, direct product factor, Sylow
292C151#2397011yescharacteristic, direct product factor, Sylow
293C2×#554C2×C15111yescharacteristic
294C2×#451C2×C15111yescharacteristic, complemented
295C22×#103C2×C15111yescharacteristic, complemented
296#2409C2×C15111yescharacteristic
297#2024C2×C15112yescomplemented
298#2001C2×C15112yescomplemented
299#1892C2×C15111yescharacteristic, complemented
300#1878C2×C15112yescomplemented
301#1872C2×C15112yescomplemented
302#1869C2×C15111yescharacteristic
303#1824C2×C15111yescharacteristic, complemented
304C23×Q8C22×C15111yescharacteristic
305C22×Q16C22×C15112yes—
306C23×C8C22×C15111yescharacteristic
307#554—24no—
308#554—24no—
309C2×C4⋊Q8C22×C15111yescharacteristic
310C2×#125—21no—
311C2×C22⋊Q8—21no—
312C2×C22⋊Q8—21no—
313C2×C22⋊Q8C22×C15111yescharacteristic
314C2×C22⋊Q8C22×C15112yes—
315C2×C22⋊Q8C22×C15111yescharacteristic
316C2×C4×Q8C22×C15111yescharacteristic
317C2×C4×D4—21no—
318C2×C4×D4C22×C15111yescharacteristic
319C22×C4⋊C4C22×C15111yescharacteristic
320C22×C4⋊C4C22×C15111yescharacteristic
321#451—24no—
322C2×#103—24no—
323C2×#103C22×C15112yes—
324C2×#103C22×C15112yes—
325C2×#103C22×C15112yes—
326C2×#103C22×C15112yes—
327C2×C22⋊C8C22×C15111yescharacteristic
328C2×C22⋊C8C22×C15112yes—
329#395—21no—
330#393—21no—
331#391C22×C15112yes—
332#386—21no—
333#385—21no—
334#380C22×C15111yescharacteristic
335#340C22×C15112yes—
336#340C22×C15112yes—
337#340C22×C15112yes—
338#336C22×C15112yes—
339C22×Q8—21no—
340C22×Q8—21no—
341C22×Q8—24no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—42no—
345C22×Q8C23×C15112yes—
346C22×Q8C23×C15111yescharacteristic
347C22×D4D4×C15111yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4C23×C15111yescharacteristic
352C23×C4C23×C15111yescharacteristic
353C2×Q16—24no—
354C2×Q16—24no—
355C2×Q16—42no—
356C22×C8—22no—
357C22×C8—42no—
358C22×C8C23×C15112yes—
359C22×C8C23×C15112yes—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362#125—28no—
363C22⋊Q8—28no—
364C22⋊Q8—28no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—24no—
369C22⋊Q8—42no—
370C22⋊Q8D4×C15114yes—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×D4—28no—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4D4×C15111yescharacteristic
387C2×C4⋊C4D4×C15114yes—
388C2×C4⋊C4C23×C15112yes—
389C2×C4⋊C4C23×C15111yescharacteristic
390C2×C4⋊C4C23×C15111yescharacteristic
391C2×C4⋊C4C23×C15111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D4×C15111yescharacteristic
397C2×C22⋊C4D4×C15111yescharacteristic
398C2×C42—21no—
399C2×C42C23×C15111yescharacteristic
400#103—24no—
401#103—24no—
402#103—24no—
403#103—42no—
404C22⋊C8—22no—
405C22⋊C8—42no—
406#95—21no—
407#95—22no—
408#95—22no—
409C24C2×D4×C15111yescharacteristic
410C24C2×D4×C15111yescharacteristic
411C2×Q8—24no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—28no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—44no—
422C2×Q8—48no—
423C2×Q8—44no—
424C2×Q8—42no—
425C2×Q8—82no—
426C2×Q8C2×D4×C15112yes—
427C2×Q8#41×C15114yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4Q16×C15114yescomplemented
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—44no—
446C22×C4—42no—
447C22×C4—82no—
448C22×C4—82no—
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4C2×D4×C15111yescharacteristic
452C22×C4C2×D4×C15112yes—
453C22×C4C2×D4×C15112yes—
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C24×C15111yescharacteristic
456Q16—48no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—44no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—44no—
477C4⋊C4C2×D4×C15112yes—
478C4⋊C4C2×D4×C15112yes—
479C4⋊C4C2×D4×C15112yes—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—44no—
485C22⋊C4—42no—
486C42—24no—
487C42—21no—
488C42—21no—
489C23—22no—
490C23—22no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—22no—
495C23#120×C15112yes—
496C23C2×Q16×C15112yes—
497C23C2×Q16×C15112yes—
498C23#137×C15112yes—
499C23C22×D4×C15111yescharacteristic
500Q8—24no—
501Q8—24no—
502Q8—24no—
503Q8—48no—
504Q8—41no—
505Q8—42no—
506Q8—41no—
507Q8—42no—
508Q8—84no—
509D4—28no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—48no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—84no—
539C2×C4—84no—
540C2×C4#120×C15112yes—
541C2×C4C2×Q16×C15112yes—
542C2×C4C22×D4×C15111yescharacteristic
543C2×C4C22×D4×C15111yescharacteristic
544C2×C4C2×#41×C15112yes—
545C2×C4H(5,𝔽2)×C15112yes—
546C8—42no—
547C8—42no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—24no—
552C22—22no—
553C22—24no—
554C22—41no—
555C22—41no—
556C22—42no—
557C22#451×C15114yes—
558C22C2×#120×C15111yescharacteristic
559C22#546×C15112yes—
560C22C22×Q16×C15111yescharacteristic
561C22C2×#137×C15111yescharacteristic
562C22#577×C15112yes—
563C4—22no—
564C4—22no—
565C4—41no—
566C4—44no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—42no—
571C4—42no—
572C4—82no—
573C4#525×C15111yescharacteristic
574C4#535×C15111yescharacteristic
575C4#546×C15112yes—
576C2—24no—
577C2—42no—
578C2#2404×C15111yescharacteristic
579C2C2×#451×C15111yescharacteristic
580C2#3009×C15111yescharacteristic
581C2#3299×C15112yes—
582C2#3316×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
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×#451×C151C2semidirect
3. C22×#103×C151C2semidirect
5. #2024×C151C2semidirect
6. #2001×C151C2semidirect
7. #1892×C151C2semidirect
8. #1878×C151C2semidirect
9. #1872×C151C2semidirect
11. #1824×C151C2semidirect
138. C2×D4×C151Q16semidirect
291. #23970C151direct (N × H)
292. C151#23970direct (N × H)
294. C2×#451C2×C151semidirect
295. C22×#103C2×C151semidirect
297. #2024C2×C151semidirect
298. #2001C2×C151semidirect
299. #1892C2×C151semidirect
300. #1878C2×C151semidirect
301. #1872C2×C151semidirect
303. #1824C2×C151semidirect
430. C2×D4Q16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#451×C1512
C22×#103×C1512
#2409×C1512
#2024×C1512
#2001×C1512
#1892×C1512
#1878×C1512
#1872×C1512
#1869×C1512
#1824×C1512
#23970151