Finite Group Databasebeta

← C151×#24502 #50329427

Subgroups — C151×#24502 #50329427

Order 38656.

992 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×#451×C151C211yesmaximal, characteristic
2C2×#431×C151C211yesmaximal, characteristic
3#2855×C151C211yesmaximal, characteristic
4C2×#391×C151C211yesmaximal, characteristic
5#2068×C151C212yesmaximal, complemented
6#2056×C151C212yesmaximal, complemented
7#1969×C151C212yesmaximal, complemented
8#1933×C151C212yesmaximal, complemented
9#1872×C151C211yesmaximal, characteristic
10#1852×C151C211yesmaximal, characteristic
11#1787×C151C211yesmaximal, characteristic
12C23×Q8×C151C2211yescharacteristic
13C22×Q16×C151C2212yes—
14C2×C22⋊Q8×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C42×C151C2211yescharacteristic
17#451×C151—24no—
18#431×C151—24no—
19C2×#107×C151C2212yes—
20C2×C4⋊C8×C151C2212yes—
21C2×#103×C151C2212yes—
22C2×#103×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×C22⋊C8×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27C2×C4×C8×C151C2212yes—
28#391×C151—21no—
29#391×C151—21no—
30#391×C151C2211yescharacteristic
31#391×C151C2211yescharacteristic
32#391×C151C2212yes—
33#391×C151C2212yes—
34#389×C151C2211yescharacteristic
35#389×C151C2211yescharacteristic
36#387×C151—21no—
37#387×C151—21no—
38#385×C151—21no—
39#381×C151—21no—
40#380×C151C2211yescharacteristic
41C2×#95×C151—21no—
42C2×#95×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151—24no—
47C22×Q8×C151—22no—
48C22×Q8×C151—22no—
49C22×Q8×C151—42no—
50C22×Q8×C151C2311yescharacteristic
51C22×Q8×C151C2312yes—
52C23×C4×C151—21no—
53C23×C4×C151—21no—
54C23×C4×C151D411yescharacteristic
55C23×C4×C151D411yescharacteristic
56C23×C4×C151C2311yescharacteristic
57C2×Q16×C151—24no—
58C2×Q16×C151—24no—
59C2×Q16×C151—42no—
60C22×C8×C151C2312yes—
61C22×C8×C151C2312yes—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151—22no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—42no—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2312yes—
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—21no—
75C2×C42×C151—22no—
76C2×C42×C151—22no—
77C2×C42×C151D411yescharacteristic
78C2×C42×C151D411yescharacteristic
79C2×C42×C151C2311yescharacteristic
80C2×C42×C151C2311yescharacteristic
81#107×C151—42no—
82C4⋊C8×C151—24no—
83#103×C151—24no—
84#103×C151—24no—
85#103×C151—42no—
86#103×C151—42no—
87C22⋊C8×C151—22no—
88C22⋊C8×C151D414yes—
89C4×C8×C151—24no—
90#95×C151—22no—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—21no—
95#95×C151—21no—
96#95×C151—21no—
97#95×C151—21no—
98#95×C151—21no—
99#95×C151—21no—
100#95×C151—21no—
101C24×C151C2×D411yescharacteristic
102C2×Q8×C151—24no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—21no—
106C2×Q8×C151—22no—
107C2×Q8×C151—21no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—22no—
111C2×Q8×C151—22no—
112C2×Q8×C151—48no—
113C2×Q8×C151—48no—
114C2×Q8×C151—42no—
115C2×Q8×C151—42no—
116C2×Q8×C151#4114yes—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—24no—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—21no—
130C22×C4×C151—41no—
131C22×C4×C151—42no—
132C22×C4×C151—42no—
133C22×C4×C151—42no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151Q1614yescomplemented
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151#4112yes—
144C22×C4×C151C2411yescharacteristic
145Q16×C151—48no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151C2×D414yes—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—42no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151—42no—
161C4⋊C4×C151—42no—
162C22⋊C4×C151—42no—
163C22⋊C4×C151—42no—
164C42×C151—22no—
165C42×C151—22no—
166C42×C151—21no—
167C42×C151—21no—
168C42×C151—21no—
169C42×C151—21no—
170C23×C151—21no—
171C23×C151—21no—
172C23×C151—21no—
173C23×C151—21no—
174C23×C151#12112yes—
175C23×C151C2×Q1612yes—
176C23×C151#13512yes—
177C23×C151C22×D411yescharacteristic
178Q8×C151—24no—
179Q8×C151—24no—
180Q8×C151—48no—
181Q8×C151—42no—
182Q8×C151—42no—
183Q8×C151—42no—
184Q8×C151—42no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—21no—
193C2×C4×C151—28no—
194C2×C4×C151—24no—
195C2×C4×C151—24no—
196C2×C4×C151—21no—
197C2×C4×C151—24no—
198C2×C4×C151—21no—
199C2×C4×C151—21no—
200C2×C4×C151—44no—
201C2×C4×C151—48no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—41no—
209C2×C4×C151—42no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—42no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—42no—
219C2×C4×C151—84no—
220C2×C4×C151#12112yes—
221C2×C4×C151C2×Q1612yes—
222C2×C4×C151C2×Q1612yes—
223C2×C4×C151#13712yes—
224C2×C4×C151C22×D411yescharacteristic
225C2×C4×C151C2×#4112yes—
226C2×C4×C151C2×#4111yescharacteristic
227C2×C4×C151H(5,𝔽2)12yes—
228C8×C151—24no—
229C8×C151—42no—
230C22×C151—22no—
231C22×C151—22no—
232C22×C151—22no—
233C22×C151—22no—
234C22×C151—22no—
235C22×C151—22no—
236C22×C151#46714yes—
237C22×C151C2×#12111yescharacteristic
238C22×C151#52511yescharacteristic
239C22×C151#53511yescharacteristic
240C22×C151C22×Q1611yescharacteristic
241C22×C151C2×#13511yescharacteristic
242C22×C151C2×#13711yescharacteristic
243C22×C151#57511yescharacteristic
244C4×C151—22no—
245C4×C151—22no—
246C4×C151—22no—
247C4×C151—22no—
248C4×C151—44no—
249C4×C151—41no—
250C4×C151—81no—
251C4×C151—81no—
252C4×C151—81no—
253C4×C151—82no—
254C4×C151—81no—
255C4×C151#54612yes—
256C4×C151#55112yes—
257C2×C151—24no—
258C2×C151#241111yescharacteristic
259C2×C151C2×#46711yescharacteristic
260C2×C151#305611yescharacteristic
261C2×C151#310411yescharacteristic
262C2×C151#310811yescharacteristic
263C2×C151#320911yescharacteristic
264C2×C151#321111yescharacteristic
265#24502C15111yesmaximal, characteristic, direct product factor, Sylow
266C151#2450211yescharacteristic, direct product factor, Sylow
267C2×#451C2×C15111yescharacteristic
268C2×#431C2×C15111yescharacteristic
269#2855C2×C15111yescharacteristic
270C2×#391C2×C15111yescharacteristic
271#2068C2×C15112yescomplemented
272#2056C2×C15112yescomplemented
273#1969C2×C15112yescomplemented
274#1933C2×C15112yescomplemented
275#1872C2×C15111yescharacteristic
276#1852C2×C15111yescharacteristic
277#1787C2×C15111yescharacteristic
278C23×Q8C22×C15111yescharacteristic
279C22×Q16C22×C15112yes—
280C2×C22⋊Q8C22×C15111yescharacteristic
281C22×C4⋊C4C22×C15111yescharacteristic
282C22×C42C22×C15111yescharacteristic
283#451—24no—
284#431—24no—
285C2×#107C22×C15112yes—
286C2×C4⋊C8C22×C15112yes—
287C2×#103C22×C15112yes—
288C2×#103C22×C15112yes—
289C2×#103C22×C15112yes—
290C2×#103C22×C15112yes—
291C2×C22⋊C8C22×C15111yescharacteristic
292C2×C22⋊C8C22×C15111yescharacteristic
293C2×C4×C8C22×C15112yes—
294#391—21no—
295#391—21no—
296#391C22×C15111yescharacteristic
297#391C22×C15112yes—
298#391C22×C15111yescharacteristic
299#391C22×C15112yes—
300#389C22×C15111yescharacteristic
301#389C22×C15111yescharacteristic
302#387—21no—
303#387—21no—
304#385—21no—
305#381—21no—
306#380C22×C15111yescharacteristic
307C2×#95—21no—
308C2×#95—21no—
309#340C22×C15112yes—
310#340C22×C15112yes—
311C22×Q8—24no—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—42no—
316C22×Q8C23×C15111yescharacteristic
317C22×Q8C23×C15112yes—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4D4×C15111yescharacteristic
321C23×C4D4×C15111yescharacteristic
322C23×C4C23×C15111yescharacteristic
323C2×Q16—24no—
324C2×Q16—24no—
325C2×Q16—42no—
326C22×C8C23×C15112yes—
327C22×C8C23×C15112yes—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4C23×C15112yes—
336C2×C4⋊C4C23×C15111yescharacteristic
337C2×C4⋊C4C23×C15111yescharacteristic
338C2×C4⋊C4C23×C15111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42D4×C15111yescharacteristic
344C2×C42D4×C15111yescharacteristic
345C2×C42C23×C15111yescharacteristic
346C2×C42C23×C15111yescharacteristic
347#107—42no—
348C4⋊C8—24no—
349#103—24no—
350#103—24no—
351#103—42no—
352#103—42no—
353C22⋊C8—22no—
354C22⋊C8D4×C15114yes—
355C4×C8—24no—
356#95—22no—
357#95—22no—
358#95—22no—
359#95—22no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367C24C2×D4×C15111yescharacteristic
368C2×Q8—24no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—48no—
379C2×Q8—48no—
380C2×Q8—42no—
381C2×Q8—42no—
382C2×Q8#41×C15114yes—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4Q16×C15114yescomplemented
403C22×C4C2×D4×C15111yescharacteristic
404C22×C4C2×D4×C15111yescharacteristic
405C22×C4C2×D4×C15112yes—
406C22×C4C2×D4×C15111yescharacteristic
407C22×C4C2×D4×C15111yescharacteristic
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4#41×C15112yes—
410C22×C4C24×C15111yescharacteristic
411Q16—48no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8C2×D4×C15114yes—
418C4⋊C4—21no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—42no—
425C4⋊C4—42no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C22⋊C4—42no—
429C22⋊C4—42no—
430C42—22no—
431C42—22no—
432C42—21no—
433C42—21no—
434C42—21no—
435C42—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23#121×C15112yes—
441C23C2×Q16×C15112yes—
442C23#135×C15112yes—
443C23C22×D4×C15111yescharacteristic
444Q8—24no—
445Q8—24no—
446Q8—48no—
447Q8—42no—
448Q8—42no—
449Q8—42no—
450Q8—42no—
451C2×C4—28no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—44no—
467C2×C4—48no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—84no—
486C2×C4#121×C15112yes—
487C2×C4C2×Q16×C15112yes—
488C2×C4C2×Q16×C15112yes—
489C2×C4#137×C15112yes—
490C2×C4C22×D4×C15111yescharacteristic
491C2×C4C2×#41×C15112yes—
492C2×C4C2×#41×C15111yescharacteristic
493C2×C4H(5,𝔽2)×C15112yes—
494C8—24no—
495C8—42no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22#467×C15114yes—
503C22C2×#121×C15111yescharacteristic
504C22#525×C15111yescharacteristic
505C22#535×C15111yescharacteristic
506C22C22×Q16×C15111yescharacteristic
507C22C2×#135×C15111yescharacteristic
508C22C2×#137×C15111yescharacteristic
509C22#575×C15111yescharacteristic
510C4—22no—
511C4—22no—
512C4—22no—
513C4—22no—
514C4—44no—
515C4—41no—
516C4—81no—
517C4—81no—
518C4—82no—
519C4—81no—
520C4—81no—
521C4#546×C15112yes—
522C4#551×C15112yes—
523C2—24no—
524C2#2411×C15111yescharacteristic
525C2C2×#467×C15111yescharacteristic
526C2#3056×C15111yescharacteristic
527C2#3104×C15111yescharacteristic
528C2#3108×C15111yescharacteristic
529C2#3209×C15111yescharacteristic
530C2#3211×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
5. #2068×C151C2semidirect
6. #2056×C151C2semidirect
7. #1969×C151C2semidirect
8. #1933×C151C2semidirect
136. C22×C4×C151Q16semidirect
265. #24502C151direct (N × H)
266. C151#24502direct (N × H)
271. #2068C2×C151semidirect
272. #2056C2×C151semidirect
273. #1969C2×C151semidirect
274. #1933C2×C151semidirect
402. C22×C4Q16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#451×C1512
C2×#431×C1512
#2855×C1512
C2×#391×C1512
#2068×C1512
#2056×C1512
#1969×C1512
#1933×C1512
#1872×C1512
#1852×C1512
#1787×C1512
#24502151