Finite Group Databasebeta

← C151×#24180 #50329105

Subgroups — C151×#24180 #50329105

Order 38656.

1146 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic, complemented
3#3036×C151C211yesmaximal, characteristic, complemented
4#2328×C151C211yesmaximal, characteristic, complemented
5#2037×C151C212yesmaximal, complemented
6#2002×C151C212yesmaximal, complemented
7#1995×C151C211yesmaximal, characteristic, complemented
8#1963×C151C211yesmaximal, characteristic, complemented
9#1883×C151C212yesmaximal, complemented
10#1860×C151C212yesmaximal, complemented
11#1800×C151C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C151C2212yes—
13#559×C151—22no—
14#556×C151—21no—
15#555×C151—21no—
16#553×C151—22no—
17#550×C151—21no—
18#547×C151—21no—
19#538×C151—22no—
20#535×C151C2212yes—
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23C2×#127×C151C2211yescharacteristic
24#525×C151—22no—
25#520×C151C2212yes—
26C2×C4×D4×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28#478×C151—22no—
29#476×C151—21no—
30#474×C151—21no—
31#463×C151—22no—
32#461×C151—21no—
33#459×C151—21no—
34#428×C151C2212yes—
35#423×C151C2211yescharacteristic
36#423×C151C2211yescharacteristic
37C2×#104×C151C2212yes—
38C2×#104×C151C2212yes—
39#418×C151C2212yes—
40#417×C151C2212yes—
41C2×#100×C151C2212yes—
42#390×C151C2211yescharacteristic
43#390×C151C2211yescharacteristic
44#386×C151—22no—
45#386×C151—22no—
46#382×C151C2211yescharacteristic
47#376×C151C2211yescharacteristic
48#343×C151C2212yes—
49#339×C151C2212yes—
50#339×C151C2212yes—
51C2×#41×C151—22no—
52C2×#41×C151C2312yes—
53C22×D4×C151—22no—
54C22×D4×C151C2311yescharacteristic
55C22×D4×C151C2311yescharacteristic
56C23×C4×C151—21no—
57C23×C4×C151D412yes—
58AGL(1,ℤ/8)×C151—24no—
59AGL(1,ℤ/8)×C151—42no—
60C2×SD16×C151—22no—
61C2×D8×C151—22no—
62C2×M16×C151C2312yes—
63C2×M16×C151C2312yes—
64C4⋊Q8×C151D411yescharacteristic, complemented
65C4⋊Q8×C151D411yescharacteristic, complemented
66C4⋊Q8×C151D411yescharacteristic, complemented
67#127×C151—22no—
68#127×C151—22no—
69#127×C151—22no—
70#127×C151D411yescharacteristic, complemented
71#126×C151—24no—
72#125×C151D412yescomplemented
73#124×C151—24no—
74#124×C151—22no—
75#124×C151D412yescomplemented
76#123×C151—24no—
77#123×C151—24no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—21no—
81#121×C151—22no—
82#121×C151—24no—
83#121×C151—21no—
84#121×C151—21no—
85#121×C151—22no—
86#121×C151—22no—
87#120×C151—24no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—22no—
91C4×D4×C151—24no—
92C4×D4×C151—22no—
93C4×D4×C151—24no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104#117×C151—22no—
105#117×C151—22no—
106#117×C151C2312yes—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151D412yes—
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117#107×C151—22no—
118#106×C151—22no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151—21no—
123#104×C151—24no—
124#104×C151—42no—
125#103×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#100×C151—42no—
130#95×C151—21no—
131#95×C151—21no—
132#95×C151—22no—
133C24×C151—21no—
134C24×C151C2×D412yes—
135#41×C151—22no—
136#41×C151—22no—
137#41×C151—22no—
138#41×C151—22no—
139#41×C151—84no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151C2×D412yes—
143C2×D4×C151—22no—
144C2×D4×C151—24no—
145C2×D4×C151—24no—
146C2×D4×C151—28no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—82no—
161C2×D4×C151—82no—
162C2×D4×C151C2×D412yes—
163C2×D4×C151#4112yescomplemented
164C22×C4×C151—21no—
165C22×C4×C151—24no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—41no—
172C22×C4×C151—41no—
173C22×C4×C151—82no—
174C22×C4×C151—82no—
175C22×C4×C151C2×D412yes—
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2411yescharacteristic
179SD16×C151—44no—
180D8×C151—44no—
181M16×C151—22no—
182M16×C151—22no—
183M16×C151—22no—
184M16×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C4⋊C4×C151—24no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151C2×D412yes—
199C4⋊C4×C151C2×D412yes—
200C22⋊C4×C151—24no—
201C22⋊C4×C151—24no—
202C22⋊C4×C151—24no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—22no—
208C22⋊C4×C151—41no—
209C22⋊C4×C151—41no—
210C22⋊C4×C151—82no—
211C22⋊C4×C151—82no—
212C42×C151—24no—
213C42×C151—22no—
214C42×C151—21no—
215C42×C151—21no—
216C42×C151—21no—
217C42×C151C2×D411yescharacteristic
218C42×C151C2×D411yescharacteristic
219C42×C151C2×D411yescharacteristic
220C42×C151C2×D411yescharacteristic
221C42×C151#4112yescomplemented
222C23×C151—22no—
223C23×C151—22no—
224C23×C151—22no—
225C23×C151—22no—
226C23×C151—22no—
227C23×C151—42no—
228C23×C151—42no—
229C23×C151—42no—
230C23×C151—42no—
231C23×C151—41no—
232C23×C151—41no—
233C23×C151C22×D411yescharacteristic
234Q8×C151—22no—
235Q8×C151—22no—
236Q8×C151—42no—
237Q8×C151—81no—
238D4×C151—22no—
239D4×C151—22no—
240D4×C151—22no—
241D4×C151—22no—
242D4×C151—42no—
243D4×C151—42no—
244D4×C151—42no—
245D4×C151—41no—
246D4×C151—41no—
247D4×C151—41no—
248D4×C151—41no—
249D4×C151—41no—
250D4×C151—41no—
251D4×C151—81no—
252D4×C151—84no—
253D4×C151—84no—
254D4×C151—88no—
255C2×C4×C151—22no—
256C2×C4×C151—22no—
257C2×C4×C151—22no—
258C2×C4×C151—22no—
259C2×C4×C151—22no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—44no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—42no—
266C2×C4×C151—42no—
267C2×C4×C151—42no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—42no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—82no—
274C2×C4×C151—82no—
275C2×C4×C151—82no—
276C2×C4×C151—84no—
277C2×C4×C151#12011yescharacteristic
278C2×C4×C151#12011yescharacteristic
279C2×C4×C151#12011yescharacteristic
280C2×C4×C151#12011yescharacteristic
281C2×C4×C151C22×D411yescharacteristic
282C2×C4×C151C22×D411yescharacteristic
283C2×C4×C151C2×#4111yescharacteristic
284C2×C4×C151C2×#4111yescharacteristic
285C2×C4×C151H(5,𝔽2)11yescharacteristic
286C2×C4×C1512−1+411yescharacteristic
287C8×C151—42no—
288C8×C151—42no—
289C22×C151—21no—
290C22×C151—21no—
291C22×C151—44no—
292C22×C151—44no—
293C22×C151—42no—
294C22×C151—42no—
295C22×C151—42no—
296C22×C151—42no—
297C22×C151—42no—
298C22×C151—42no—
299C22×C151—42no—
300C22×C151—82no—
301C22×C151—82no—
302C22×C151—81no—
303C22×C151—81no—
304C22×C151C2×#12011yescharacteristic
305C22×C151#52511yescharacteristic
306C22×C151#53711yescharacteristic
307C4×C151—21no—
308C4×C151—21no—
309C4×C151—21no—
310C4×C151—21no—
311C4×C151—42no—
312C4×C151—42no—
313C4×C151—42no—
314C4×C151—42no—
315C4×C151—42no—
316C4×C151—81no—
317C4×C151—81no—
318C4×C151#54611yescharacteristic
319C4×C151#54711yescharacteristic
320C4×C151#54811yescharacteristic
321C4×C151#55011yescharacteristic
322C2×C151—21no—
323C2×C151—21no—
324C2×C151—82no—
325C2×C151—82no—
326C2×C151—82no—
327C2×C151#240711yescharacteristic
328C2×C151#301911yescharacteristic
329C2×C151#302111yescharacteristic
330#24180C15111yesmaximal, characteristic, direct product factor, Sylow
331C151#2418011yescharacteristic, direct product factor, Sylow
332#3506C2×C15111yescharacteristic, complemented
333#3077C2×C15111yescharacteristic, complemented
334#3036C2×C15111yescharacteristic, complemented
335#2328C2×C15111yescharacteristic, complemented
336#2037C2×C15112yescomplemented
337#2002C2×C15112yescomplemented
338#1995C2×C15111yescharacteristic, complemented
339#1963C2×C15111yescharacteristic, complemented
340#1883C2×C15112yescomplemented
341#1860C2×C15112yescomplemented
342#1800C2×C15111yescharacteristic, complemented
343C2×AGL(1,ℤ/8)C22×C15112yes—
344#559—22no—
345#556—21no—
346#555—21no—
347#553—22no—
348#550—21no—
349#547—21no—
350#538—22no—
351#535C22×C15112yes—
352#533C22×C15111yescharacteristic
353#532C22×C15111yescharacteristic
354C2×#127C22×C15111yescharacteristic
355#525—22no—
356#520C22×C15112yes—
357C2×C4×D4C22×C15111yescharacteristic
358C2×C4×D4C22×C15111yescharacteristic
359#478—22no—
360#476—21no—
361#474—21no—
362#463—22no—
363#461—21no—
364#459—21no—
365#428C22×C15112yes—
366#423C22×C15111yescharacteristic
367#423C22×C15111yescharacteristic
368C2×#104C22×C15112yes—
369C2×#104C22×C15112yes—
370#418C22×C15112yes—
371#417C22×C15112yes—
372C2×#100C22×C15112yes—
373#390C22×C15111yescharacteristic
374#390C22×C15111yescharacteristic
375#386—22no—
376#386—22no—
377#382C22×C15111yescharacteristic
378#376C22×C15111yescharacteristic
379#343C22×C15112yes—
380#339C22×C15112yes—
381#339C22×C15112yes—
382C2×#41—22no—
383C2×#41C23×C15112yes—
384C22×D4—22no—
385C22×D4C23×C15111yescharacteristic
386C22×D4C23×C15111yescharacteristic
387C23×C4—21no—
388C23×C4D4×C15112yes—
389AGL(1,ℤ/8)—24no—
390AGL(1,ℤ/8)—42no—
391C2×SD16—22no—
392C2×D8—22no—
393C2×M16C23×C15112yes—
394C2×M16C23×C15112yes—
395C4⋊Q8D4×C15111yescharacteristic, complemented
396C4⋊Q8D4×C15111yescharacteristic, complemented
397C4⋊Q8D4×C15111yescharacteristic, complemented
398#127—22no—
399#127—22no—
400#127—22no—
401#127D4×C15111yescharacteristic, complemented
402#126—24no—
403#125D4×C15112yescomplemented
404#124—24no—
405#124—22no—
406#124D4×C15112yescomplemented
407#123—24no—
408#123—24no—
409C22⋊Q8—22no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412#121—22no—
413#121—24no—
414#121—21no—
415#121—21no—
416#121—22no—
417#121—22no—
418#120—24no—
419C4×Q8—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×D4—24no—
423C4×D4—22no—
424C4×D4—24no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435#117—22no—
436#117—22no—
437#117C23×C15112yes—
438C2×C4⋊C4—22no—
439C2×C4⋊C4C23×C15111yescharacteristic
440C2×C4⋊C4C23×C15111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4D4×C15112yes—
445C2×C42C23×C15111yescharacteristic
446C2×C42C23×C15111yescharacteristic
447C2×C42C23×C15111yescharacteristic
448#107—22no—
449#106—22no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454#104—24no—
455#104—42no—
456#103—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#100—42no—
461#95—21no—
462#95—21no—
463#95—22no—
464C24—21no—
465C24C2×D4×C15112yes—
466#41—22no—
467#41—22no—
468#41—22no—
469#41—22no—
470#41—84no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8C2×D4×C15112yes—
474C2×D4—22no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—28no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—82no—
492C2×D4—82no—
493C2×D4C2×D4×C15112yes—
494C2×D4#41×C15112yescomplemented
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—82no—
505C22×C4—82no—
506C22×C4C2×D4×C15112yes—
507C22×C4C2×D4×C15111yescharacteristic
508C22×C4C2×D4×C15111yescharacteristic
509C22×C4C24×C15111yescharacteristic
510SD16—44no—
511D8—44no—
512M16—22no—
513M16—22no—
514M16—22no—
515M16—22no—
516C2×C8—22no—
517C2×C8—22no—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4C2×D4×C15112yes—
530C4⋊C4C2×D4×C15112yes—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—82no—
542C22⋊C4—82no—
543C42—24no—
544C42—22no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42C2×D4×C15111yescharacteristic
549C42C2×D4×C15111yescharacteristic
550C42C2×D4×C15111yescharacteristic
551C42C2×D4×C15111yescharacteristic
552C42#41×C15112yescomplemented
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—42no—
562C23—41no—
563C23—41no—
564C23C22×D4×C15111yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—42no—
568Q8—81no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—81no—
583D4—88no—
584D4—84no—
585D4—84no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—44no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—84no—
608C2×C4#120×C15111yescharacteristic
609C2×C4#120×C15111yescharacteristic
610C2×C4#120×C15111yescharacteristic
611C2×C4#120×C15111yescharacteristic
612C2×C4C22×D4×C15111yescharacteristic
613C2×C4C22×D4×C15111yescharacteristic
614C2×C4C2×#41×C15111yescharacteristic
615C2×C4C2×#41×C15111yescharacteristic
616C2×C4H(5,𝔽2)×C15111yescharacteristic
617C2×C42−1+4×C15111yescharacteristic
618C8—42no—
619C8—42no—
620C22—21no—
621C22—21no—
622C22—44no—
623C22—44no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—82no—
632C22—82no—
633C22—81no—
634C22—81no—
635C22C2×#120×C15111yescharacteristic
636C22#525×C15111yescharacteristic
637C22#537×C15111yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—21no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4#546×C15111yescharacteristic
650C4#547×C15111yescharacteristic
651C4#548×C15111yescharacteristic
652C4#550×C15111yescharacteristic
653C2—21no—
654C2—21no—
655C2—82no—
656C2—82no—
657C2—82no—
658C2#2407×C15111yescharacteristic
659C2#3019×C15111yescharacteristic
660C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3506×C151C2semidirect
2. #3077×C151C2semidirect
3. #3036×C151C2semidirect
4. #2328×C151C2semidirect
5. #2037×C151C2semidirect
6. #2002×C151C2semidirect
7. #1995×C151C2semidirect
8. #1963×C151C2semidirect
9. #1883×C151C2semidirect
10. #1860×C151C2semidirect
11. #1800×C151C2semidirect
64. C4⋊Q8×C151D4semidirect
65. C4⋊Q8×C151D4semidirect
66. C4⋊Q8×C151D4semidirect
70. #127×C151D4semidirect
72. #125×C151D4semidirect
75. #124×C151D4semidirect
163. C2×D4×C151#41semidirect
221. C42×C151#41semidirect
330. #24180C151direct (N × H)
331. C151#24180direct (N × H)
332. #3506C2×C151semidirect
333. #3077C2×C151semidirect
334. #3036C2×C151semidirect
335. #2328C2×C151semidirect
336. #2037C2×C151semidirect
337. #2002C2×C151semidirect
338. #1995C2×C151semidirect
339. #1963C2×C151semidirect
340. #1883C2×C151semidirect
341. #1860C2×C151semidirect
342. #1800C2×C151semidirect
395. C4⋊Q8D4×C151semidirect
396. C4⋊Q8D4×C151semidirect
397. C4⋊Q8D4×C151semidirect
401. #127D4×C151semidirect
403. #125D4×C151semidirect
406. #124D4×C151semidirect
494. C2×D4#41×C151semidirect
552. C42#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3506×C1512
#3077×C1512
#3036×C1512
#2328×C1512
#2037×C1512
#2002×C1512
#1995×C1512
#1963×C1512
#1883×C1512
#1860×C1512
#1800×C1512
#24180151