Finite Group Databasebeta

← C151×#24837 #50329762

Subgroups — C151×#24837 #50329762

Order 38656.

904 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#477×C151C211yesmaximal, characteristic, complemented
2C22×C4⋊C8×C151C211yesmaximal, characteristic
3#2857×C151C211yesmaximal, characteristic
4C4×C22⋊Q8×C151C211yesmaximal, characteristic
5#2087×C151C212yesmaximal, complemented
6#2068×C151C212yesmaximal, complemented
7#1987×C151C211yesmaximal, characteristic, complemented
8#1947×C151C211yesmaximal, characteristic, complemented
9#1892×C151C212yesmaximal
10#1808×C151C212yesmaximal
11#1803×C151C211yesmaximal, characteristic, complemented
12C23×C8×C151C2212yes—
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C22⋊Q8×C151—21no—
15C2×C22⋊Q8×C151C2211yescharacteristic
16C2×C4×Q8×C151C2211yescharacteristic
17C22×C42×C151C2211yescharacteristic
18#477×C151—24no—
19C2×#107×C151C2212yes—
20C2×#107×C151C2212yes—
21C2×C4⋊C8×C151—24no—
22C2×C4⋊C8×C151C2212yes—
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27#391×C151—21no—
28#391×C151C2211yescharacteristic
29#389×C151—21no—
30#389×C151C2211yescharacteristic
31#389×C151C2212yes—
32#387×C151—21no—
33#385×C151—21no—
34#384×C151C2211yescharacteristic
35#380×C151—21no—
36#380×C151C2212yes—
37#380×C151C2211yescharacteristic
38C4×C4⋊C4×C151—21no—
39C4×C4⋊C4×C151C2211yescharacteristic
40C4×C22⋊C4×C151—21no—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151C2311yescharacteristic
47C23×C4×C151D411yescharacteristic
48C23×C4×C151D411yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C22×C8×C151—24no—
51C22×C8×C151—24no—
52C22×C8×C151—42no—
53C22×C8×C151C2312yes—
54C22×C8×C151C2312yes—
55C4⋊Q8×C151—22no—
56C4⋊Q8×C151—22no—
57C22⋊Q8×C151—22no—
58C22⋊Q8×C151—44no—
59C22⋊Q8×C151Q814yescomplemented
60C4×Q8×C151—22no—
61C4×Q8×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2312yes—
71C2×C4⋊C4×C151C2312yes—
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—22no—
77C2×C42×C151—22no—
78C2×C42×C151—22no—
79C2×C42×C151—21no—
80C2×C42×C151—21no—
81C2×C42×C151D411yescharacteristic
82C2×C42×C151D411yescharacteristic
83C2×C42×C151C2311yescharacteristic
84C2×C42×C151C2311yescharacteristic
85#107×C151—24no—
86#107×C151—42no—
87C4⋊C8×C151—24no—
88C4⋊C8×C151—22no—
89C4⋊C8×C151D414yes—
90#103×C151—24no—
91#103×C151—42no—
92#95×C151—21no—
93#95×C151—21no—
94#95×C151—21no—
95#95×C151—21no—
96#95×C151—21no—
97#95×C151—22no—
98#95×C151—22no—
99C24×C151C2×D411yescharacteristic
100C2×Q8×C151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—42no—
106C2×Q8×C151—42no—
107C2×Q8×C151—42no—
108C2×Q8×C151C2×Q812yes—
109C22×C4×C151—22no—
110C22×C4×C151—22no—
111C22×C4×C151—21no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—21no—
115C22×C4×C151—22no—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—22no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—41no—
124C22×C4×C151Q1614yes—
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×Q812yes—
131C22×C4×C151#4112yes—
132C22×C4×C151C2411yescharacteristic
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—48no—
139C2×C8×C151C2×D414yes—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—42no—
152C4⋊C4×C151—44no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151—42no—
155C4⋊C4×C151—42no—
156C4⋊C4×C151C2×Q812yes—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—42no—
159C22⋊C4×C151—44no—
160C42×C151—22no—
161C42×C151—22no—
162C42×C151—21no—
163C42×C151—21no—
164C42×C151—42no—
165C42×C151—42no—
166C42×C151C2×D412yes—
167C42×C151#4112yes—
168C23×C151—21no—
169C23×C151—21no—
170C23×C151—21no—
171C23×C151—21no—
172C23×C151C22⋊Q812yes—
173C23×C151C2×Q1612yes—
174C23×C151AGL(1,ℤ/8)12yes—
175C23×C151C22×D411yescharacteristic
176Q8×C151—22no—
177Q8×C151—22no—
178Q8×C151—41no—
179Q8×C151—41no—
180Q8×C151—84no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—28no—
192C2×C4×C151—21no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—44no—
198C2×C4×C151—41no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—42no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151—42no—
213C2×C4×C151—41no—
214C2×C4×C151#12112yes—
215C2×C4×C151#12112yes—
216C2×C4×C151C22⋊Q812yes—
217C2×C4×C151C2×Q1612yes—
218C2×C4×C151C2×Q1612yes—
219C2×C4×C151#13512yes—
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×Q811yescharacteristic
222C2×C4×C151C2×#4111yescharacteristic
223C2×C4×C151C2×#4111yescharacteristic
224C2×C4×C151H(5,𝔽2)11yescharacteristic
225C2×C4×C1512−1+411yescharacteristic
226C8×C151—24no—
227C8×C151—42no—
228C22×C151—22no—
229C22×C151—22no—
230C22×C151—22no—
231C22×C151—22no—
232C22×C151—22no—
233C22×C151—22no—
234C22×C151#47714yescomplemented
235C22×C151C2×#12111yescharacteristic
236C22×C151C2×C22⋊Q811yescharacteristic
237C22×C151#53711yescharacteristic
238C22×C151C22×Q1611yescharacteristic
239C22×C151C2×#13511yescharacteristic
240C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
241C22×C151#57511yescharacteristic
242C4×C151—22no—
243C4×C151—22no—
244C4×C151—22no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—41no—
248C4×C151—81no—
249C4×C151—82no—
250C4×C151—81no—
251C4×C151—82no—
252C4×C151#46714yes—
253C4×C151#54611yescharacteristic
254C4×C151D4×Q811yescharacteristic
255C4×C151#55211yescharacteristic
256C4×C151#55411yescharacteristic
257C2×C151—24no—
258C2×C151#241711yescharacteristic
259C2×C151C2×#46711yescharacteristic
260C2×C151#305511yescharacteristic
261C2×C151C2×#47711yescharacteristic
262C2×C151#307611yescharacteristic
263C2×C151#324711yescharacteristic
264C2×C151#324911yescharacteristic
265#24837C15111yesmaximal, characteristic, direct product factor, Sylow
266C151#2483711yescharacteristic, direct product factor, Sylow
267C2×#477C2×C15111yescharacteristic, complemented
268C22×C4⋊C8C2×C15111yescharacteristic
269#2857C2×C15111yescharacteristic
270C4×C22⋊Q8C2×C15111yescharacteristic
271#2087C2×C15112yescomplemented
272#2068C2×C15112yescomplemented
273#1987C2×C15111yescharacteristic, complemented
274#1947C2×C15111yescharacteristic, complemented
275#1892C2×C15112yes—
276#1808C2×C15112yes—
277#1803C2×C15111yescharacteristic, complemented
278C23×C8C22×C15112yes—
279C2×C4⋊Q8C22×C15111yescharacteristic
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8C22×C15111yescharacteristic
282C2×C4×Q8C22×C15111yescharacteristic
283C22×C42C22×C15111yescharacteristic
284#477—24no—
285C2×#107C22×C15112yes—
286C2×#107C22×C15112yes—
287C2×C4⋊C8—24no—
288C2×C4⋊C8C22×C15111yescharacteristic
289C2×C4⋊C8C22×C15112yes—
290C2×C4⋊C8C22×C15111yescharacteristic
291C2×#103C22×C15112yes—
292C2×#103C22×C15112yes—
293#391—21no—
294#391C22×C15111yescharacteristic
295#389—21no—
296#389C22×C15112yes—
297#389C22×C15111yescharacteristic
298#387—21no—
299#385—21no—
300#384C22×C15111yescharacteristic
301#380—21no—
302#380C22×C15111yescharacteristic
303#380C22×C15112yes—
304C4×C4⋊C4—21no—
305C4×C4⋊C4C22×C15111yescharacteristic
306C4×C22⋊C4—21no—
307#340C22×C15112yes—
308#340C22×C15112yes—
309#340C22×C15112yes—
310#340C22×C15112yes—
311C22×Q8—21no—
312C22×Q8C23×C15111yescharacteristic
313C23×C4D4×C15111yescharacteristic
314C23×C4D4×C15111yescharacteristic
315C23×C4C23×C15111yescharacteristic
316C22×C8—24no—
317C22×C8—24no—
318C22×C8—42no—
319C22×C8C23×C15112yes—
320C22×C8C23×C15112yes—
321C4⋊Q8—22no—
322C4⋊Q8—22no—
323C22⋊Q8—22no—
324C22⋊Q8—44no—
325C22⋊Q8Q8×C15114yescomplemented
326C4×Q8—22no—
327C4×Q8—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4C23×C15111yescharacteristic
336C2×C4⋊C4C23×C15112yes—
337C2×C4⋊C4C23×C15111yescharacteristic
338C2×C4⋊C4C23×C15112yes—
339C2×C4⋊C4C23×C15111yescharacteristic
340C2×C22⋊C4—21no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—21no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42D4×C15111yescharacteristic
348C2×C42D4×C15111yescharacteristic
349C2×C42C23×C15111yescharacteristic
350C2×C42C23×C15111yescharacteristic
351#107—24no—
352#107—42no—
353C4⋊C8—24no—
354C4⋊C8—22no—
355C4⋊C8D4×C15114yes—
356#103—24no—
357#103—42no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—22no—
364#95—22no—
365C24C2×D4×C15111yescharacteristic
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—42no—
372C2×Q8—42no—
373C2×Q8—42no—
374C2×Q8C2×Q8×C15112yes—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—41no—
390C22×C4Q16×C15114yes—
391C22×C4C2×D4×C15111yescharacteristic
392C22×C4C2×D4×C15111yescharacteristic
393C22×C4C2×D4×C15111yescharacteristic
394C22×C4C2×D4×C15111yescharacteristic
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×Q8×C15112yes—
397C22×C4#41×C15112yes—
398C22×C4C24×C15111yescharacteristic
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—48no—
405C2×C8C2×D4×C15114yes—
406C4⋊C4—24no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—42no—
417C4⋊C4—44no—
418C4⋊C4—42no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—42no—
422C4⋊C4C2×Q8×C15112yes—
423C22⋊C4—24no—
424C22⋊C4—44no—
425C22⋊C4—42no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—42no—
431C42—42no—
432C42C2×D4×C15112yes—
433C42#41×C15112yes—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23C22⋊Q8×C15112yes—
439C23C2×Q16×C15112yes—
440C23AGL(1,ℤ/8)×C15112yes—
441C23C22×D4×C15111yescharacteristic
442Q8—22no—
443Q8—22no—
444Q8—41no—
445Q8—41no—
446Q8—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—28no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—44no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4#121×C15112yes—
481C2×C4#121×C15112yes—
482C2×C4C22⋊Q8×C15112yes—
483C2×C4C2×Q16×C15112yes—
484C2×C4C2×Q16×C15112yes—
485C2×C4#135×C15112yes—
486C2×C4C22×D4×C15111yescharacteristic
487C2×C4C22×Q8×C15111yescharacteristic
488C2×C4C2×#41×C15111yescharacteristic
489C2×C4C2×#41×C15111yescharacteristic
490C2×C4H(5,𝔽2)×C15111yescharacteristic
491C2×C42−1+4×C15111yescharacteristic
492C8—24no—
493C8—42no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22#477×C15114yescomplemented
501C22C2×#121×C15111yescharacteristic
502C22C2×C22⋊Q8×C15111yescharacteristic
503C22#537×C15111yescharacteristic
504C22C22×Q16×C15111yescharacteristic
505C22C2×#135×C15111yescharacteristic
506C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
507C22#575×C15111yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—41no—
513C4—42no—
514C4—81no—
515C4—82no—
516C4—82no—
517C4—81no—
518C4#467×C15114yes—
519C4#546×C15111yescharacteristic
520C4D4×Q8×C15111yescharacteristic
521C4#552×C15111yescharacteristic
522C4#554×C15111yescharacteristic
523C2—24no—
524C2#2417×C15111yescharacteristic
525C2C2×#467×C15111yescharacteristic
526C2#3055×C15111yescharacteristic
527C2C2×#477×C15111yescharacteristic
528C2#3076×C15111yescharacteristic
529C2#3247×C15111yescharacteristic
530C2#3249×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#477×C151C2semidirect
5. #2087×C151C2semidirect
6. #2068×C151C2semidirect
7. #1987×C151C2semidirect
8. #1947×C151C2semidirect
11. #1803×C151C2semidirect
59. C22⋊Q8×C151Q8semidirect
234. C22×C151#477semidirect
265. #24837C151direct (N × H)
266. C151#24837direct (N × H)
267. C2×#477C2×C151semidirect
271. #2087C2×C151semidirect
272. #2068C2×C151semidirect
273. #1987C2×C151semidirect
274. #1947C2×C151semidirect
277. #1803C2×C151semidirect
325. C22⋊Q8Q8×C151semidirect
500. C22#477×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#477×C1512
C22×C4⋊C8×C1512
#2857×C1512
C4×C22⋊Q8×C1512
#2087×C1512
#2068×C1512
#1987×C1512
#1947×C1512
#1892×C1512
#1808×C1512
#1803×C1512
#24837151