Finite Group Databasebeta

← C151×#24187 #50329112

Subgroups — C151×#24187 #50329112

Order 38656.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C151C211yesmaximal, characteristic, complemented
2C2×#461×C151C211yesmaximal, characteristic
3C2×C4×SD16×C151C211yesmaximal, characteristic
4#2538×C151C211yesmaximal, characteristic
5#2043×C151C212yesmaximal, complemented
6#2013×C151C212yesmaximal
7#1984×C151C211yesmaximal, characteristic, complemented
8#1956×C151C211yesmaximal, characteristic, complemented
9#1880×C151C212yesmaximal
10#1865×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14#557×C151—24no—
15#557×C151—24no—
16C2×C4⋊Q8×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×#125×C151—21no—
19C2×#125×C151—22no—
20C2×C22⋊Q8×C151—21no—
21C2×C4×Q8×C151—21no—
22C2×C4×Q8×C151C2212yes—
23C2×C4×Q8×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26#461×C151—24no—
27C4×SD16×C151—24no—
28C2×#106×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2212yes—
34C2×#103×C151C2212yes—
35C2×#102×C151C2211yescharacteristic
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×Q8×C151C2311yescharacteristic
48C22×D4×C151C2311yescharacteristic
49C23×C4×C151—21no—
50C2×SD16×C151—22no—
51C2×SD16×C151—24no—
52C2×SD16×C151—22no—
53C2×SD16×C151—22no—
54C2×SD16×C151—24no—
55C2×SD16×C151—42no—
56C22×C8×C151C2312yes—
57C22×C8×C151C2311yescharacteristic
58C22×C8×C151C2311yescharacteristic
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151—24no—
61C4⋊Q8×C151—24no—
62C4⋊Q8×C151D414yes—
63#125×C151—216no—
64#125×C151—28no—
65C22⋊Q8×C151—44no—
66C4×Q8×C151—28no—
67C4×Q8×C151—24no—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×Q8×C151—24no—
72C4×Q8×C151D414yes—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151D411yescharacteristic
85C2×C4⋊C4×C151D412yes—
86C2×C4⋊C4×C151C2312yes—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—22no—
92C2×C42×C151—22no—
93C2×C42×C151—21no—
94C2×C42×C151C2312yes—
95C2×C42×C151C2311yescharacteristic
96#106×C151—22no—
97C4⋊C8×C151—22no—
98#103×C151—24no—
99#103×C151—22no—
100#103×C151—24no—
101#103×C151—42no—
102#103×C151—42no—
103#102×C151—22no—
104C4×C8×C151—22no—
105#95×C151—22no—
106C24×C151—21no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151—22no—
110C2×Q8×C151—21no—
111C2×Q8×C151—22no—
112C2×Q8×C151—21no—
113C2×Q8×C151—22no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—22no—
117C2×Q8×C151—21no—
118C2×Q8×C151—22no—
119C2×Q8×C151SD1614yescomplemented
120C2×Q8×C151C2×D414yes—
121C2×Q8×C151C2×D412yes—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—21no—
127C2×D4×C151#4112yes—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—22no—
133C22×C4×C151—42no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151C2×D412yes—
137C22×C4×C151C2×D411yescharacteristic
138C22×C4×C151C2×D412yes—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2411yescharacteristic
141SD16×C151—28no—
142SD16×C151—48no—
143C2×C8×C151—21no—
144C2×C8×C151—21no—
145C2×C8×C151—21no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—21no—
149C2×C8×C151—22no—
150C2×C8×C151—21no—
151C2×C8×C151#4112yes—
152C4⋊C4×C151—28no—
153C4⋊C4×C151—28no—
154C4⋊C4×C151—28no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—42no—
166C4⋊C4×C151—44no—
167C4⋊C4×C151—81no—
168C4⋊C4×C151C2×D412yes—
169C22⋊C4×C151—42no—
170C22⋊C4×C151—44no—
171C22⋊C4×C151—82no—
172C42×C151—28no—
173C42×C151—24no—
174C42×C151—22no—
175C42×C151—22no—
176C42×C151C2×D412yes—
177C42×C151C2×D412yes—
178C23×C151—22no—
179C23×C151—41no—
180C23×C151—41no—
181C23×C151—41no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151C22×D411yescharacteristic
186Q8×C151—28no—
187Q8×C151—22no—
188Q8×C151—22no—
189Q8×C151—24no—
190Q8×C151—24no—
191Q8×C151—42no—
192Q8×C151—42no—
193Q8×C151—41no—
194Q8×C151—41no—
195D4×C151—22no—
196D4×C151—22no—
197D4×C151—41no—
198D4×C151—41no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—21no—
202C2×C4×C151—21no—
203C2×C4×C151—24no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—41no—
220C2×C4×C151—42no—
221C2×C4×C151—84no—
222C2×C4×C151#12012yes—
223C2×C4×C151#12012yes—
224C2×C4×C151C2×SD1614yes—
225C2×C4×C151C2×SD1612yes—
226C2×C4×C151#13712yes—
227C2×C4×C151C22×D411yescharacteristic
228C2×C4×C151C22×D411yescharacteristic
229C2×C4×C151C2×#4111yescharacteristic
230C2×C4×C151C2×#4111yescharacteristic
231C2×C4×C151H(5,𝔽2)11yescharacteristic
232C2×C4×C1512−1+411yescharacteristic
233C8×C151—22no—
234C8×C151—41no—
235C8×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—81no—
240C22×C151—81no—
241C22×C151—81no—
242C22×C151—81no—
243C22×C151C2×#12011yescharacteristic
244C22×C151#54811yescharacteristic
245C22×C151#55011yescharacteristic
246C22×C151C22×SD1611yescharacteristic
247C22×C151C2×#13711yescharacteristic
248C22×C151#57711yescharacteristic
249C22×C151#57811yescharacteristic
250C4×C151—24no—
251C4×C151—22no—
252C4×C151—42no—
253C4×C151—44no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—82no—
257C4×C151—81no—
258C4×C151#44814yes—
259C4×C151#52511yescharacteristic
260C4×C151#53711yescharacteristic
261C4×C151#54611yescharacteristic
262C4×C151#54711yescharacteristic
263C2×C151—82no—
264C2×C151#240711yescharacteristic
265C2×C151C2×#44811yescharacteristic
266C2×C151#301311yescharacteristic
267C2×C151#335911yescharacteristic
268C2×C151#337211yescharacteristic
269C2×C151#339211yescharacteristic
270C2×C151#339811yescharacteristic
271#24187C15111yesmaximal, characteristic, direct product factor, Sylow
272C151#2418711yescharacteristic, direct product factor, Sylow
273C2×#557C2×C15111yescharacteristic, complemented
274C2×#461C2×C15111yescharacteristic
275C2×C4×SD16C2×C15111yescharacteristic
276#2538C2×C15111yescharacteristic
277#2043C2×C15112yescomplemented
278#2013C2×C15112yes—
279#1984C2×C15111yescharacteristic, complemented
280#1956C2×C15111yescharacteristic, complemented
281#1880C2×C15112yes—
282#1865C2×C15112yescomplemented
283#1803C2×C15111yescharacteristic, complemented
284C22×SD16C22×C15111yescharacteristic
285C22×SD16C22×C15112yes—
286#557—24no—
287#557—24no—
288C2×C4⋊Q8C22×C15112yes—
289C2×C4⋊Q8C22×C15111yescharacteristic
290C2×#125—21no—
291C2×#125—22no—
292C2×C22⋊Q8—21no—
293C2×C4×Q8—21no—
294C2×C4×Q8C22×C15112yes—
295C2×C4×Q8C22×C15111yescharacteristic
296C2×C4×Q8C22×C15111yescharacteristic
297C2×C4×D4C22×C15111yescharacteristic
298#461—24no—
299C4×SD16—24no—
300C2×#106C22×C15111yescharacteristic
301C2×C4⋊C8C22×C15111yescharacteristic
302C2×#103C22×C15112yes—
303C2×#103C22×C15112yes—
304C2×#103C22×C15111yescharacteristic
305C2×#103C22×C15112yes—
306C2×#103C22×C15112yes—
307C2×#102C22×C15111yescharacteristic
308C2×C4×C8C22×C15111yescharacteristic
309#396—22no—
310#390C22×C15112yes—
311#389C22×C15112yes—
312#384C22×C15111yescharacteristic
313#380—21no—
314#340C22×C15112yes—
315#336C22×C15112yes—
316#336C22×C15112yes—
317C22×Q8D4×C15111yescharacteristic
318C22×Q8C23×C15112yes—
319C22×Q8C23×C15111yescharacteristic
320C22×D4C23×C15111yescharacteristic
321C23×C4—21no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—24no—
325C2×SD16—24no—
326C2×SD16—22no—
327C2×SD16—42no—
328C22×C8C23×C15112yes—
329C22×C8C23×C15111yescharacteristic
330C22×C8C23×C15111yescharacteristic
331C4⋊Q8—24no—
332C4⋊Q8—24no—
333C4⋊Q8—22no—
334C4⋊Q8D4×C15114yes—
335#125—216no—
336#125—28no—
337C22⋊Q8—44no—
338C4×Q8—28no—
339C4×Q8—24no—
340C4×Q8—24no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8D4×C15114yes—
345C4×D4—22no—
346C4×D4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C15111yescharacteristic
357C2×C4⋊C4D4×C15112yes—
358C2×C4⋊C4C23×C15111yescharacteristic
359C2×C4⋊C4C23×C15112yes—
360C2×C4⋊C4C23×C15111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C42—22no—
365C2×C42—21no—
366C2×C42C23×C15112yes—
367C2×C42C23×C15111yescharacteristic
368#106—22no—
369C4⋊C8—22no—
370#103—22no—
371#103—24no—
372#103—24no—
373#103—42no—
374#103—42no—
375#102—22no—
376C4×C8—22no—
377#95—22no—
378C24—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—21no—
383C2×Q8—22no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8SD16×C15114yescomplemented
392C2×Q8C2×D4×C15114yes—
393C2×Q8C2×D4×C15112yes—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—21no—
399C2×D4#41×C15112yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—42no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4C2×D4×C15112yes—
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15112yes—
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C24×C15111yescharacteristic
413SD16—28no—
414SD16—48no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—21no—
423C2×C8#41×C15112yes—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—28no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—42no—
438C4⋊C4—44no—
439C4⋊C4—81no—
440C4⋊C4C2×D4×C15112yes—
441C22⋊C4—42no—
442C22⋊C4—44no—
443C22⋊C4—82no—
444C42—28no—
445C42—24no—
446C42—22no—
447C42—22no—
448C42C2×D4×C15112yes—
449C42C2×D4×C15112yes—
450C23—22no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23C22×D4×C15111yescharacteristic
458Q8—28no—
459Q8—22no—
460Q8—22no—
461Q8—24no—
462Q8—24no—
463Q8—42no—
464Q8—42no—
465Q8—41no—
466Q8—41no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4#120×C15112yes—
495C2×C4#120×C15112yes—
496C2×C4C2×SD16×C15114yes—
497C2×C4C2×SD16×C15112yes—
498C2×C4#137×C15112yes—
499C2×C4C22×D4×C15111yescharacteristic
500C2×C4C22×D4×C15111yescharacteristic
501C2×C4C2×#41×C15111yescharacteristic
502C2×C4C2×#41×C15111yescharacteristic
503C2×C4H(5,𝔽2)×C15111yescharacteristic
504C2×C42−1+4×C15111yescharacteristic
505C8—22no—
506C8—41no—
507C8—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22C2×#120×C15111yescharacteristic
516C22#548×C15111yescharacteristic
517C22#550×C15111yescharacteristic
518C22C22×SD16×C15111yescharacteristic
519C22C2×#137×C15111yescharacteristic
520C22#577×C15111yescharacteristic
521C22#578×C15111yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—44no—
526C4—42no—
527C4—42no—
528C4—82no—
529C4—81no—
530C4#448×C15114yes—
531C4#525×C15111yescharacteristic
532C4#537×C15111yescharacteristic
533C4#546×C15111yescharacteristic
534C4#547×C15111yescharacteristic
535C2—82no—
536C2#2407×C15111yescharacteristic
537C2C2×#448×C15111yescharacteristic
538C2#3013×C15111yescharacteristic
539C2#3359×C15111yescharacteristic
540C2#3372×C15111yescharacteristic
541C2#3392×C15111yescharacteristic
542C2#3398×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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×#557×C151C2semidirect
5. #2043×C151C2semidirect
7. #1984×C151C2semidirect
8. #1956×C151C2semidirect
10. #1865×C151C2semidirect
11. #1803×C151C2semidirect
119. C2×Q8×C151SD16semidirect
271. #24187C151direct (N × H)
272. C151#24187direct (N × H)
273. C2×#557C2×C151semidirect
277. #2043C2×C151semidirect
279. #1984C2×C151semidirect
280. #1956C2×C151semidirect
282. #1865C2×C151semidirect
283. #1803C2×C151semidirect
391. C2×Q8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1512
C2×#461×C1512
C2×C4×SD16×C1512
#2538×C1512
#2043×C1512
#2013×C1512
#1984×C1512
#1956×C1512
#1880×C1512
#1865×C1512
#1803×C1512
#24187151