Finite Group Databasebeta

← C151×#24185 #50329110

Subgroups — C151×#24185 #50329110

Order 38656.

1150 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×#556×C151C211yesmaximal, characteristic, complemented
2C2×#461×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic
4#2538×C151C211yesmaximal, characteristic, complemented
5#2042×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal
7#1984×C151C211yesmaximal, characteristic, complemented
8#1956×C151C211yesmaximal, characteristic, complemented
9#1880×C151C212yesmaximal, complemented
10#1863×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13C22×D8×C151C2211yescharacteristic
14#556×C151—24no—
15#556×C151—24no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#126×C151—22no—
18C2×#124×C151C2212yes—
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151—21no—
21C2×C4×Q8×C151C2212yes—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25C2×#117×C151—21no—
26#461×C151—24no—
27C4×D8×C151—24no—
28C2×#107×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2212yes—
36C2×C4×C8×C151C2211yescharacteristic
37#396×C151—22no—
38#390×C151C2212yes—
39#389×C151C2212yes—
40#384×C151C2211yescharacteristic
41#380×C151—21no—
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151D411yescharacteristic
46C22×Q8×C151C2312yes—
47C22×D4×C151C2311yescharacteristic
48C22×D4×C151C2311yescharacteristic
49C23×C4×C151—21no—
50C23×C4×C151—21no—
51C2×SD16×C151—24no—
52C2×SD16×C151—24no—
53C2×SD16×C151—42no—
54C2×D8×C151—22no—
55C2×D8×C151—22no—
56C2×D8×C151—22no—
57C22×C8×C151C2312yes—
58C22×C8×C151C2311yescharacteristic
59C22×C8×C151C2311yescharacteristic
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151D414yes—
62#126×C151—216no—
63#124×C151—24no—
64#124×C151—24no—
65C22⋊Q8×C151—28no—
66C22⋊Q8×C151—44no—
67C4×Q8×C151—24no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—24no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C4×D4×C151—22no—
74C4×D4×C151D414yes—
75#117×C151—28no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151D411yescharacteristic
83C2×C4⋊C4×C151D412yes—
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151—21no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—22no—
93C2×C42×C151—22no—
94C2×C42×C151C2312yes—
95C2×C42×C151C2311yescharacteristic
96#107×C151—22no—
97C4⋊C8×C151—22no—
98#103×C151—24no—
99#103×C151—24no—
100#103×C151—42no—
101#102×C151—22no—
102#102×C151—22no—
103#102×C151—42no—
104C4×C8×C151—22no—
105#95×C151—22no—
106C24×C151—21no—
107C24×C151—21no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151C2×D414yes—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151C2×D412yes—
128C2×D4×C151#4112yes—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—24no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151—42no—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2411yescharacteristic
144SD16×C151—48no—
145D8×C151—28no—
146C2×C8×C151—21no—
147C2×C8×C151—21no—
148C2×C8×C151—21no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—21no—
153C2×C8×C151—21no—
154C2×C8×C151#4112yes—
155C4⋊C4×C151—28no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—44no—
166C4⋊C4×C151—42no—
167C4⋊C4×C151—81no—
168C4⋊C4×C151C2×D412yes—
169C22⋊C4×C151—28no—
170C22⋊C4×C151—28no—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—44no—
173C22⋊C4×C151—42no—
174C22⋊C4×C151—82no—
175C42×C151—28no—
176C42×C151—22no—
177C42×C151—22no—
178C42×C151C2×D412yes—
179C42×C151C2×D412yes—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151C22×D411yescharacteristic
195Q8×C151—24no—
196Q8×C151—24no—
197Q8×C151—42no—
198Q8×C151—42no—
199Q8×C151—44no—
200D4×C151—22no—
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—22no—
204D4×C151—41no—
205D4×C151—41no—
206D4×C151—41no—
207D4×C151—41no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—22no—
211C2×C4×C151—24no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—48no—
223C2×C4×C151—41no—
224C2×C4×C151—42no—
225C2×C4×C151—41no—
226C2×C4×C151—42no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—84no—
230C2×C4×C151#12012yes—
231C2×C4×C151#12012yes—
232C2×C4×C151#13512yes—
233C2×C4×C151AGL(1,ℤ/8)12yes—
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C22×D411yescharacteristic
236C2×C4×C151C2×#4111yescharacteristic
237C2×C4×C151C2×#4111yescharacteristic
238C2×C4×C151H(5,𝔽2)11yescharacteristic
239C2×C4×C1512−1+411yescharacteristic
240C8×C151—22no—
241C8×C151—41no—
242C8×C151—42no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—81no—
250C22×C151—81no—
251C22×C151—81no—
252C22×C151—81no—
253C22×C151—81no—
254C22×C151—81no—
255C22×C151—81no—
256C22×C151—81no—
257C22×C151C2×#12011yescharacteristic
258C22×C151#54811yescharacteristic
259C22×C151#55011yescharacteristic
260C22×C151C2×#13511yescharacteristic
261C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C151#57711yescharacteristic
263C22×C151#57811yescharacteristic
264C4×C151—22no—
265C4×C151—44no—
266C4×C151—42no—
267C4×C151—42no—
268C4×C151—42no—
269C4×C151—82no—
270C4×C151—81no—
271C4×C151#44914yes—
272C4×C151#52511yescharacteristic
273C4×C151#53711yescharacteristic
274C4×C151#54611yescharacteristic
275C4×C151#54711yescharacteristic
276C2×C151—82no—
277C2×C151—82no—
278C2×C151#240711yescharacteristic
279C2×C151C2×#44911yescharacteristic
280C2×C151#301311yescharacteristic
281C2×C151#336011yescharacteristic
282C2×C151#336711yescharacteristic
283C2×C151#339311yescharacteristic
284C2×C151#339711yescharacteristic
285#24185C15111yesmaximal, characteristic, direct product factor, Sylow
286C151#2418511yescharacteristic, direct product factor, Sylow
287C2×#556C2×C15111yescharacteristic, complemented
288C2×#461C2×C15111yescharacteristic, complemented
289C2×C4×D8C2×C15111yescharacteristic
290#2538C2×C15111yescharacteristic, complemented
291#2042C2×C15112yescomplemented
292#2012C2×C15112yes—
293#1984C2×C15111yescharacteristic, complemented
294#1956C2×C15111yescharacteristic, complemented
295#1880C2×C15112yescomplemented
296#1863C2×C15112yescomplemented
297#1802C2×C15111yescharacteristic, complemented
298C22×SD16C22×C15112yes—
299C22×D8C22×C15111yescharacteristic
300#556—24no—
301#556—24no—
302C2×C4⋊Q8C22×C15111yescharacteristic
303C2×#126—22no—
304C2×#124C22×C15112yes—
305C2×C22⋊Q8—21no—
306C2×C22⋊Q8—21no—
307C2×C4×Q8C22×C15112yes—
308C2×C4×Q8C22×C15111yescharacteristic
309C2×C4×D4C22×C15111yescharacteristic
310C2×C4×D4C22×C15111yescharacteristic
311C2×#117—21no—
312#461—24no—
313C4×D8—24no—
314C2×#107C22×C15111yescharacteristic
315C2×C4⋊C8C22×C15111yescharacteristic
316C2×#103C22×C15112yes—
317C2×#103C22×C15112yes—
318C2×#103C22×C15112yes—
319C2×#102C22×C15111yescharacteristic
320C2×#102C22×C15111yescharacteristic
321C2×#102C22×C15112yes—
322C2×C4×C8C22×C15111yescharacteristic
323#396—22no—
324#390C22×C15112yes—
325#389C22×C15112yes—
326#384C22×C15111yescharacteristic
327#380—21no—
328#340C22×C15112yes—
329#336C22×C15112yes—
330#336C22×C15112yes—
331C22×Q8D4×C15111yescharacteristic
332C22×Q8C23×C15112yes—
333C22×D4C23×C15111yescharacteristic
334C22×D4C23×C15111yescharacteristic
335C23×C4—21no—
336C23×C4—21no—
337C2×SD16—24no—
338C2×SD16—24no—
339C2×SD16—42no—
340C2×D8—22no—
341C2×D8—22no—
342C2×D8—22no—
343C22×C8C23×C15112yes—
344C22×C8C23×C15111yescharacteristic
345C22×C8C23×C15111yescharacteristic
346C4⋊Q8—22no—
347C4⋊Q8D4×C15114yes—
348#126—216no—
349#124—24no—
350#124—24no—
351C22⋊Q8—28no—
352C22⋊Q8—44no—
353C4×Q8—24no—
354C4×Q8—24no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4D4×C15114yes—
361#117—28no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C15111yescharacteristic
369C2×C4⋊C4D4×C15112yes—
370C2×C4⋊C4C23×C15111yescharacteristic
371C2×C4⋊C4C23×C15112yes—
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C22⋊C4—22no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C42—22no—
380C2×C42C23×C15112yes—
381C2×C42C23×C15111yescharacteristic
382#107—22no—
383C4⋊C8—22no—
384#103—24no—
385#103—24no—
386#103—42no—
387#102—22no—
388#102—22no—
389#102—42no—
390C4×C8—22no—
391#95—22no—
392C24—21no—
393C24—21no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8C2×D4×C15114yes—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4C2×D4×C15112yes—
414C2×D4#41×C15112yes—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—24no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4C2×D4×C15112yes—
426C22×C4C2×D4×C15112yes—
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4C2×D4×C15111yescharacteristic
429C22×C4C24×C15111yescharacteristic
430SD16—48no—
431D8—28no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8#41×C15112yes—
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—44no—
452C4⋊C4—42no—
453C4⋊C4—81no—
454C4⋊C4C2×D4×C15112yes—
455C22⋊C4—28no—
456C22⋊C4—28no—
457C22⋊C4—24no—
458C22⋊C4—44no—
459C22⋊C4—42no—
460C22⋊C4—82no—
461C42—28no—
462C42—22no—
463C42—22no—
464C42C2×D4×C15112yes—
465C42C2×D4×C15112yes—
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23C22×D4×C15111yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—44no—
484Q8—42no—
485Q8—42no—
486D4—22no—
487D4—22no—
488D4—22no—
489D4—22no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—41no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—48no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4#120×C15112yes—
517C2×C4#120×C15112yes—
518C2×C4#135×C15112yes—
519C2×C4AGL(1,ℤ/8)×C15112yes—
520C2×C4C22×D4×C15111yescharacteristic
521C2×C4C22×D4×C15111yescharacteristic
522C2×C4C2×#41×C15111yescharacteristic
523C2×C4C2×#41×C15111yescharacteristic
524C2×C4H(5,𝔽2)×C15111yescharacteristic
525C2×C42−1+4×C15111yescharacteristic
526C8—22no—
527C8—41no—
528C8—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C2×#120×C15111yescharacteristic
544C22#548×C15111yescharacteristic
545C22#550×C15111yescharacteristic
546C22C2×#135×C15111yescharacteristic
547C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
548C22#577×C15111yescharacteristic
549C22#578×C15111yescharacteristic
550C4—22no—
551C4—44no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—81no—
557C4#449×C15114yes—
558C4#525×C15111yescharacteristic
559C4#537×C15111yescharacteristic
560C4#546×C15111yescharacteristic
561C4#547×C15111yescharacteristic
562C2—82no—
563C2—82no—
564C2#2407×C15111yescharacteristic
565C2C2×#449×C15111yescharacteristic
566C2#3013×C15111yescharacteristic
567C2#3360×C15111yescharacteristic
568C2#3367×C15111yescharacteristic
569C2#3393×C15111yescharacteristic
570C2#3397×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#556×C151C2semidirect
2. C2×#461×C151C2semidirect
4. #2538×C151C2semidirect
5. #2042×C151C2semidirect
7. #1984×C151C2semidirect
8. #1956×C151C2semidirect
9. #1880×C151C2semidirect
10. #1863×C151C2semidirect
11. #1802×C151C2semidirect
285. #24185C151direct (N × H)
286. C151#24185direct (N × H)
287. C2×#556C2×C151semidirect
288. C2×#461C2×C151semidirect
290. #2538C2×C151semidirect
291. #2042C2×C151semidirect
293. #1984C2×C151semidirect
294. #1956C2×C151semidirect
295. #1880C2×C151semidirect
296. #1863C2×C151semidirect
297. #1802C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#556×C1512
C2×#461×C1512
C2×C4×D8×C1512
#2538×C1512
#2042×C1512
#2012×C1512
#1984×C1512
#1956×C1512
#1880×C1512
#1863×C1512
#1802×C1512
#24185151