Finite Group Databasebeta

← C151×#23977 #50328902

Subgroups — C151×#23977 #50328902

Order 38656.

1286 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C151C211yesmaximal, characteristic
2C2×#448×C151C211yesmaximal, characteristic, complemented
3C2×#419×C151C211yesmaximal, characteristic, complemented
4#2409×C151C211yesmaximal, characteristic, complemented
5#2024×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1895×C151C211yesmaximal, characteristic, complemented
8#1877×C151C212yesmaximal, complemented
9#1873×C151C212yesmaximal, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1825×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C22×M16×C151C2211yescharacteristic
15#555×C151—24no—
16#555×C151—24no—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×#124×C151—21no—
19C2×#124×C151—21no—
20C2×C22⋊Q8×C151C2212yes—
21C2×#121×C151—21no—
22C2×#121×C151C2211yescharacteristic
23C2×#121×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C2×#117×C151—21no—
27C2×#117×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29#448×C151—24no—
30#419×C151—24no—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×#102×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×C151C2312yes—
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151D411yescharacteristic
57C22×D4×C151C2311yescharacteristic
58C23×C4×C151—21no—
59C23×C4×C151—21no—
60C23×C4×C151C2311yescharacteristic
61C23×C4×C151C2311yescharacteristic
62C2×SD16×C151—24no—
63C2×SD16×C151—24no—
64C2×SD16×C151—42no—
65C2×M16×C151—22no—
66C2×M16×C151—42no—
67C22×C8×C151C2312yes—
68C22×C8×C151C2312yes—
69C4⋊Q8×C151—22no—
70C4⋊Q8×C151—22no—
71#124×C151—28no—
72#124×C151—28no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151—42no—
75#121×C151—28no—
76#121×C151—22no—
77#121×C151—22no—
78#121×C151—22no—
79#121×C151D414yes—
80C4×D4×C151—22no—
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C4×D4×C151—22no—
84#117×C151—28no—
85#117×C151—22no—
86#117×C151—22no—
87#117×C151—22no—
88#117×C151D414yes—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151D411yescharacteristic
92C2×C4⋊C4×C151C2312yes—
93C2×C4⋊C4×C151C2311yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C22⋊C4×C151—21no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151D411yescharacteristic
104C2×C22⋊C4×C151D411yescharacteristic
105C2×C42×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108#103×C151—24no—
109#103×C151—24no—
110#103×C151—24no—
111#102×C151—42no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—42no—
114#95×C151—21no—
115#95×C151—22no—
116#95×C151—22no—
117C24×C151—21no—
118C24×C151C2×D411yescharacteristic
119C24×C151C2×D411yescharacteristic
120C2×Q8×C151—24no—
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—44no—
128C2×Q8×C151—48no—
129C2×Q8×C151—44no—
130C2×Q8×C151—42no—
131C2×Q8×C151—82no—
132C2×Q8×C151#4114yes—
133C2×D4×C151—22no—
134C2×D4×C151—24no—
135C2×D4×C151—24no—
136C2×D4×C151—22no—
137C2×D4×C151—21no—
138C2×D4×C151—22no—
139C2×D4×C151—22no—
140C2×D4×C151—41no—
141C2×D4×C151—82no—
142C2×D4×C151—82no—
143C2×D4×C151C2×D412yes—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—24no—
147C22×C4×C151—22no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—44no—
157C22×C4×C151—42no—
158C22×C4×C151—42no—
159C22×C4×C151—42no—
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D412yes—
164C22×C4×C151C2×D412yes—
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2411yescharacteristic
167SD16×C151—48no—
168M16×C151—44no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C2×C8×C151—22no—
174C2×C8×C151—22no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—44no—
183C4⋊C4×C151C2×D412yes—
184C4⋊C4×C151C2×D412yes—
185C4⋊C4×C151C2×D412yes—
186C22⋊C4×C151—24no—
187C22⋊C4×C151—24no—
188C22⋊C4×C151—24no—
189C22⋊C4×C151—24no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—24no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—44no—
194C22⋊C4×C151—42no—
195C42×C151—24no—
196C42×C151—24no—
197C42×C151—21no—
198C42×C151—21no—
199C23×C151—22no—
200C23×C151—21no—
201C23×C151—21no—
202C23×C151—22no—
203C23×C151—22no—
204C23×C151—21no—
205C23×C151—22no—
206C23×C151—21no—
207C23×C151—21no—
208C23×C151—22no—
209C23×C151—42no—
210C23×C151—41no—
211C23×C151—41no—
212C23×C151—42no—
213C23×C151#12012yes—
214C23×C151C22×D411yescharacteristic
215Q8×C151—24no—
216Q8×C151—24no—
217Q8×C151—48no—
218Q8×C151—42no—
219Q8×C151—42no—
220Q8×C151—84no—
221D4×C151—24no—
222D4×C151—44no—
223D4×C151—41no—
224D4×C151—41no—
225D4×C151—84no—
226D4×C151—84no—
227C2×C4×C151—21no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—24no—
233C2×C4×C151—21no—
234C2×C4×C151—22no—
235C2×C4×C151—22no—
236C2×C4×C151—21no—
237C2×C4×C151—22no—
238C2×C4×C151—24no—
239C2×C4×C151—22no—
240C2×C4×C151—22no—
241C2×C4×C151—48no—
242C2×C4×C151—48no—
243C2×C4×C151—42no—
244C2×C4×C151—42no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—42no—
248C2×C4×C151—42no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151#12012yes—
256C2×C4×C151#13712yes—
257C2×C4×C151C22×D411yescharacteristic
258C2×C4×C151C22×D411yescharacteristic
259C2×C4×C151C2×#4112yes—
260C2×C4×C151H(5,𝔽2)12yes—
261C8×C151—42no—
262C8×C151—42no—
263C22×C151—22no—
264C22×C151—22no—
265C22×C151—22no—
266C22×C151—42no—
267C22×C151—42no—
268C22×C151—42no—
269C22×C151—41no—
270C22×C151—42no—
271C22×C151—42no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151—82no—
277C22×C151—82no—
278C22×C151C2×#12011yescharacteristic
279C22×C151#54612yes—
280C22×C151C2×#13711yescharacteristic
281C22×C151#57511yescharacteristic
282C22×C151#57712yes—
283C4×C151—22no—
284C4×C151—22no—
285C4×C151—41no—
286C4×C151—44no—
287C4×C151—42no—
288C4×C151—41no—
289C4×C151—42no—
290C4×C151—42no—
291C4×C151—82no—
292C4×C151#52511yescharacteristic
293C4×C151#53511yescharacteristic
294C4×C151#54612yes—
295C2×C151—42no—
296C2×C151—81no—
297C2×C151—82no—
298C2×C151#240411yescharacteristic
299C2×C151#300711yescharacteristic
300C2×C151#300911yescharacteristic
301C2×C151#332112yes—
302C2×C151#332912yes—
303#23977C15111yesmaximal, characteristic, direct product factor, Sylow
304C151#2397711yescharacteristic, direct product factor, Sylow
305C2×#555C2×C15111yescharacteristic
306C2×#448C2×C15111yescharacteristic, complemented
307C2×#419C2×C15111yescharacteristic, complemented
308#2409C2×C15111yescharacteristic, complemented
309#2024C2×C15112yescomplemented
310#2000C2×C15112yescomplemented
311#1895C2×C15111yescharacteristic, complemented
312#1877C2×C15112yescomplemented
313#1873C2×C15112yescomplemented
314#1870C2×C15111yescharacteristic, complemented
315#1825C2×C15111yescharacteristic, complemented
316C23×Q8C22×C15111yescharacteristic
317C22×SD16C22×C15112yes—
318C22×M16C22×C15111yescharacteristic
319#555—24no—
320#555—24no—
321C2×C4⋊Q8C22×C15111yescharacteristic
322C2×#124—21no—
323C2×#124—21no—
324C2×C22⋊Q8C22×C15112yes—
325C2×#121—21no—
326C2×#121C22×C15111yescharacteristic
327C2×#121C22×C15111yescharacteristic
328C2×C4×D4C22×C15111yescharacteristic
329C2×C4×D4C22×C15111yescharacteristic
330C2×#117—21no—
331C2×#117C22×C15111yescharacteristic
332C2×#117C22×C15111yescharacteristic
333#448—24no—
334#419—24no—
335C2×#103C22×C15112yes—
336C2×#103C22×C15112yes—
337C2×#103C22×C15112yes—
338C2×#102C22×C15112yes—
339C2×C22⋊C8C22×C15111yescharacteristic
340C2×C22⋊C8C22×C15112yes—
341#395—21no—
342#393—21no—
343#391C22×C15112yes—
344#386—21no—
345#385—21no—
346#380C22×C15111yescharacteristic
347#340C22×C15112yes—
348#340C22×C15112yes—
349#340C22×C15112yes—
350#336C22×C15112yes—
351C22×Q8—21no—
352C22×Q8—21no—
353C22×Q8—24no—
354C22×Q8—22no—
355C22×Q8—22no—
356C22×Q8—42no—
357C22×Q8C23×C15112yes—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4D4×C15111yescharacteristic
361C22×D4C23×C15111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C23×C15111yescharacteristic
365C23×C4C23×C15111yescharacteristic
366C2×SD16—24no—
367C2×SD16—24no—
368C2×SD16—42no—
369C2×M16—22no—
370C2×M16—42no—
371C22×C8C23×C15112yes—
372C22×C8C23×C15112yes—
373C4⋊Q8—22no—
374C4⋊Q8—22no—
375#124—28no—
376#124—28no—
377C22⋊Q8—24no—
378C22⋊Q8—42no—
379#121—28no—
380#121—22no—
381#121—22no—
382#121—22no—
383#121D4×C15114yes—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388#117—28no—
389#117—22no—
390#117—22no—
391#117—22no—
392#117D4×C15114yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4D4×C15111yescharacteristic
396C2×C4⋊C4C23×C15112yes—
397C2×C4⋊C4C23×C15111yescharacteristic
398C2×C4⋊C4C23×C15111yescharacteristic
399C2×C4⋊C4C23×C15111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4D4×C15111yescharacteristic
408C2×C22⋊C4D4×C15111yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C15111yescharacteristic
412#103—24no—
413#103—24no—
414#103—24no—
415#102—42no—
416C22⋊C8—22no—
417C22⋊C8—42no—
418#95—21no—
419#95—22no—
420#95—22no—
421C24—21no—
422C24C2×D4×C15111yescharacteristic
423C24C2×D4×C15111yescharacteristic
424C2×Q8—24no—
425C2×Q8—22no—
426C2×Q8—28no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—44no—
432C2×Q8—48no—
433C2×Q8—44no—
434C2×Q8—42no—
435C2×Q8—82no—
436C2×Q8#41×C15114yes—
437C2×D4—22no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—41no—
445C2×D4—82no—
446C2×D4—82no—
447C2×D4C2×D4×C15112yes—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4C2×D4×C15111yescharacteristic
467C22×C4C2×D4×C15112yes—
468C22×C4C2×D4×C15112yes—
469C22×C4C2×D4×C15111yescharacteristic
470C22×C4C24×C15111yescharacteristic
471SD16—48no—
472M16—44no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—44no—
487C4⋊C4C2×D4×C15112yes—
488C4⋊C4C2×D4×C15112yes—
489C4⋊C4C2×D4×C15112yes—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—22no—
495C22⋊C4—24no—
496C22⋊C4—22no—
497C22⋊C4—44no—
498C22⋊C4—42no—
499C42—24no—
500C42—24no—
501C42—21no—
502C42—21no—
503C23—22no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—21no—
508C23—22no—
509C23—22no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—42no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23#120×C15112yes—
518C23C22×D4×C15111yescharacteristic
519Q8—24no—
520Q8—24no—
521Q8—48no—
522Q8—42no—
523Q8—42no—
524Q8—84no—
525D4—24no—
526D4—44no—
527D4—41no—
528D4—41no—
529D4—84no—
530D4—84no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—48no—
546C2×C4—48no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4#120×C15112yes—
560C2×C4#137×C15112yes—
561C2×C4C22×D4×C15111yescharacteristic
562C2×C4C22×D4×C15111yescharacteristic
563C2×C4C2×#41×C15112yes—
564C2×C4H(5,𝔽2)×C15112yes—
565C8—42no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—42no—
571C22—42no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—82no—
581C22—82no—
582C22C2×#120×C15111yescharacteristic
583C22#546×C15112yes—
584C22C2×#137×C15111yescharacteristic
585C22#575×C15111yescharacteristic
586C22#577×C15112yes—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—44no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—42no—
595C4—82no—
596C4#525×C15111yescharacteristic
597C4#535×C15111yescharacteristic
598C4#546×C15112yes—
599C2—42no—
600C2—81no—
601C2—82no—
602C2#2404×C15111yescharacteristic
603C2#3007×C15111yescharacteristic
604C2#3009×C15111yescharacteristic
605C2#3321×C15112yes—
606C2#3329×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×#448×C151C2semidirect
3. C2×#419×C151C2semidirect
4. #2409×C151C2semidirect
5. #2024×C151C2semidirect
6. #2000×C151C2semidirect
7. #1895×C151C2semidirect
8. #1877×C151C2semidirect
9. #1873×C151C2semidirect
10. #1870×C151C2semidirect
11. #1825×C151C2semidirect
303. #23977C151direct (N × H)
304. C151#23977direct (N × H)
306. C2×#448C2×C151semidirect
307. C2×#419C2×C151semidirect
308. #2409C2×C151semidirect
309. #2024C2×C151semidirect
310. #2000C2×C151semidirect
311. #1895C2×C151semidirect
312. #1877C2×C151semidirect
313. #1873C2×C151semidirect
314. #1870C2×C151semidirect
315. #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×#448×C1512
C2×#419×C1512
#2409×C1512
#2024×C1512
#2000×C1512
#1895×C1512
#1877×C1512
#1873×C1512
#1870×C1512
#1825×C1512
#23977151