Finite Group Databasebeta

← C151×#24133 #50329058

Subgroups — C151×#24133 #50329058

Order 38656.

1140 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C151C211yesmaximal, characteristic
2C2×#475×C151C211yesmaximal, characteristic, complemented
3C2×#440×C151C211yesmaximal, characteristic, complemented
4#2536×C151C211yesmaximal, characteristic, complemented
5#2034×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1955×C151C211yesmaximal, characteristic, complemented
9#1873×C151C212yesmaximal, complemented
10#1854×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13#555×C151—24no—
14#555×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#124×C151—22no—
17C2×C22⋊Q8×C151C2212yes—
18C2×#121×C151—21no—
19C2×#121×C151C2212yes—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151—21no—
24C2×#117×C151C2212yes—
25#475×C151—24no—
26#440×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×#106×C151C2212yes—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2212yes—
34C2×C22⋊C8×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36C2×#97×C151C2211yescharacteristic
37#398×C151—21no—
38#394×C151—21no—
39#388×C151—22no—
40#382×C151C2211yescharacteristic
41#380×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151C2311yescharacteristic
47C22×D4×C151—22no—
48C22×D4×C151D411yescharacteristic
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151C2312yes—
52C2×SD16×C151—22no—
53C2×SD16×C151—22no—
54C2×SD16×C151—22no—
55C22×C8×C151C2311yescharacteristic
56C22×C8×C151C2312yes—
57C22×C8×C151C2311yescharacteristic
58C4⋊Q8×C151—22no—
59C4⋊Q8×C151D414yes—
60#124×C151—216no—
61C22⋊Q8×C151—24no—
62C22⋊Q8×C151—42no—
63#121×C151—28no—
64#121×C151—24no—
65#121×C151—24no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×D4×C151—22no—
69C4×D4×C151—22no—
70C4×D4×C151—22no—
71C4×D4×C151D414yes—
72#117×C151—28no—
73#117×C151—24no—
74#117×C151—24no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151D411yescharacteristic
79C2×C4⋊C4×C151C2312yes—
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—21no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—22no—
87C2×C22⋊C4×C151—22no—
88C2×C22⋊C4×C151D412yes—
89C2×C42×C151—22no—
90C2×C42×C151—21no—
91C2×C42×C151C2311yescharacteristic
92#107×C151—22no—
93#106×C151—24no—
94C4⋊C8×C151—22no—
95#103×C151—22no—
96#103×C151—24no—
97#102×C151—22no—
98#102×C151—42no—
99C22⋊C8×C151—24no—
100C22⋊C8×C151—42no—
101#97×C151—22no—
102#95×C151—22no—
103#95×C151—21no—
104#95×C151—21no—
105C24×C151—21no—
106C24×C151C2×D412yes—
107C2×Q8×C151—24no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—82no—
114C2×Q8×C151#4112yes—
115C2×D4×C151—28no—
116C2×D4×C151—22no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—42no—
123C2×D4×C151—82no—
124C2×D4×C151—82no—
125C2×D4×C151C2×D412yes—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—22no—
129C22×C4×C151—24no—
130C22×C4×C151—22no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—22no—
137C22×C4×C151—21no—
138C22×C4×C151—44no—
139C22×C4×C151C2×D412yes—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2411yescharacteristic
143SD16×C151—28no—
144C2×C8×C151—21no—
145C2×C8×C151—21no—
146C2×C8×C151—21no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C2×C8×C151—21no—
150C2×C8×C151—22no—
151C2×C8×C151—21no—
152C2×C8×C151#4112yes—
153C4⋊C4×C151—24no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—44no—
162C4⋊C4×C151—42no—
163C4⋊C4×C151C2×D414yes—
164C4⋊C4×C151C2×D412yes—
165C22⋊C4×C151—28no—
166C22⋊C4×C151—28no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—44no—
170C22⋊C4×C151—44no—
171C42×C151—28no—
172C42×C151—42no—
173C42×C151C2×D412yes—
174C42×C151C2×D412yes—
175C23×C151—22no—
176C23×C151—22no—
177C23×C151—22no—
178C23×C151—22no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—22no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151C22×D411yescharacteristic
188Q8×C151—22no—
189Q8×C151—22no—
190Q8×C151—41no—
191Q8×C151—41no—
192Q8×C151—84no—
193D4×C151—22no—
194D4×C151—22no—
195D4×C151—44no—
196D4×C151—41no—
197D4×C151—41no—
198D4×C151—88no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—24no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—48no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—41no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151#12012yes—
223C2×C4×C151#12012yes—
224C2×C4×C151C22×D411yescharacteristic
225C2×C4×C151C22×D411yescharacteristic
226C2×C4×C151C2×#4111yescharacteristic
227C2×C4×C151C2×#4111yescharacteristic
228C2×C4×C151H(5,𝔽2)11yescharacteristic
229C2×C4×C1512−1+411yescharacteristic
230C8×C151—22no—
231C8×C151—41no—
232C8×C151—42no—
233C22×C151—42no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—42no—
240C22×C151—42no—
241C22×C151—42no—
242C22×C151—42no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151C2×#12011yescharacteristic
246C22×C151#54611yescharacteristic
247C22×C151#54711yescharacteristic
248C22×C151#57512yes—
249C22×C151#57712yes—
250C4×C151—22no—
251C4×C151—22no—
252C4×C151—42no—
253C4×C151—42no—
254C4×C151—42no—
255C4×C151—44no—
256C4×C151—81no—
257C4×C151—82no—
258C4×C151#52511yescharacteristic
259C4×C151#53711yescharacteristic
260C4×C151#54811yescharacteristic
261C4×C151#55011yescharacteristic
262C2×C151—82no—
263C2×C151—82no—
264C2×C151#240711yescharacteristic
265C2×C151#300511yescharacteristic
266C2×C151#300911yescharacteristic
267C2×C151#332112yes—
268C2×C151#334812yes—
269#24133C15111yesmaximal, characteristic, direct product factor, Sylow
270C151#2413311yescharacteristic, direct product factor, Sylow
271C2×#555C2×C15111yescharacteristic
272C2×#475C2×C15111yescharacteristic, complemented
273C2×#440C2×C15111yescharacteristic, complemented
274#2536C2×C15111yescharacteristic, complemented
275#2034C2×C15112yescomplemented
276#2000C2×C15112yescomplemented
277#1993C2×C15111yescharacteristic, complemented
278#1955C2×C15111yescharacteristic, complemented
279#1873C2×C15112yescomplemented
280#1854C2×C15112yescomplemented
281#1804C2×C15111yescharacteristic, complemented
282C22×SD16C22×C15111yescharacteristic
283#555—24no—
284#555—24no—
285C2×C4⋊Q8C22×C15111yescharacteristic
286C2×#124—22no—
287C2×C22⋊Q8C22×C15112yes—
288C2×#121—21no—
289C2×#121C22×C15112yes—
290C2×C4×Q8C22×C15111yescharacteristic
291C2×C4×D4C22×C15111yescharacteristic
292C2×C4×D4C22×C15111yescharacteristic
293C2×#117—21no—
294C2×#117C22×C15112yes—
295#475—24no—
296#440—24no—
297C2×#107C22×C15111yescharacteristic
298C2×#106C22×C15112yes—
299C2×C4⋊C8C22×C15111yescharacteristic
300C2×#103C22×C15112yes—
301C2×#103C22×C15111yescharacteristic
302C2×#102C22×C15111yescharacteristic
303C2×#102C22×C15112yes—
304C2×C22⋊C8C22×C15112yes—
305C2×C22⋊C8C22×C15112yes—
306C2×#97C22×C15111yescharacteristic
307#398—21no—
308#394—21no—
309#388—22no—
310#382C22×C15111yescharacteristic
311#380C22×C15112yes—
312#340C22×C15112yes—
313#340C22×C15112yes—
314#340C22×C15112yes—
315C22×Q8—21no—
316C22×Q8C23×C15111yescharacteristic
317C22×D4—22no—
318C22×D4D4×C15111yescharacteristic
319C22×D4C23×C15111yescharacteristic
320C23×C4—21no—
321C23×C4C23×C15112yes—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—22no—
325C22×C8C23×C15111yescharacteristic
326C22×C8C23×C15112yes—
327C22×C8C23×C15111yescharacteristic
328C4⋊Q8—22no—
329C4⋊Q8D4×C15114yes—
330#124—216no—
331C22⋊Q8—24no—
332C22⋊Q8—42no—
333#121—28no—
334#121—24no—
335#121—24no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4D4×C15114yes—
342#117—28no—
343#117—24no—
344#117—24no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4D4×C15111yescharacteristic
349C2×C4⋊C4C23×C15111yescharacteristic
350C2×C4⋊C4C23×C15112yes—
351C2×C4⋊C4C23×C15111yescharacteristic
352C2×C4⋊C4C23×C15112yes—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4D4×C15112yes—
359C2×C42—22no—
360C2×C42—21no—
361C2×C42C23×C15111yescharacteristic
362#107—22no—
363#106—24no—
364C4⋊C8—22no—
365#103—22no—
366#103—24no—
367#102—22no—
368#102—42no—
369C22⋊C8—24no—
370C22⋊C8—42no—
371#97—22no—
372#95—22no—
373#95—21no—
374#95—21no—
375C24—21no—
376C24C2×D4×C15112yes—
377C2×Q8—24no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—82no—
384C2×Q8#41×C15112yes—
385C2×D4—28no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—82no—
394C2×D4—82no—
395C2×D4C2×D4×C15112yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—44no—
409C22×C4C2×D4×C15112yes—
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C24×C15111yescharacteristic
413SD16—28no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8—21no—
422C2×C8#41×C15112yes—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—44no—
432C4⋊C4—42no—
433C4⋊C4C2×D4×C15114yes—
434C4⋊C4C2×D4×C15112yes—
435C22⋊C4—28no—
436C22⋊C4—28no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—44no—
440C22⋊C4—44no—
441C42—28no—
442C42—42no—
443C42C2×D4×C15112yes—
444C42C2×D4×C15112yes—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—22no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23C22×D4×C15111yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—41no—
461Q8—41no—
462Q8—84no—
463D4—22no—
464D4—22no—
465D4—44no—
466D4—41no—
467D4—41no—
468D4—88no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—48no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4#120×C15112yes—
493C2×C4#120×C15112yes—
494C2×C4C22×D4×C15111yescharacteristic
495C2×C4C22×D4×C15111yescharacteristic
496C2×C4C2×#41×C15111yescharacteristic
497C2×C4C2×#41×C15111yescharacteristic
498C2×C4H(5,𝔽2)×C15111yescharacteristic
499C2×C42−1+4×C15111yescharacteristic
500C8—22no—
501C8—41no—
502C8—42no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—82no—
514C22—82no—
515C22C2×#120×C15111yescharacteristic
516C22#546×C15111yescharacteristic
517C22#547×C15111yescharacteristic
518C22#575×C15112yes—
519C22#577×C15112yes—
520C4—22no—
521C4—22no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—44no—
526C4—81no—
527C4—82no—
528C4#525×C15111yescharacteristic
529C4#537×C15111yescharacteristic
530C4#548×C15111yescharacteristic
531C4#550×C15111yescharacteristic
532C2—82no—
533C2—82no—
534C2#2407×C15111yescharacteristic
535C2#3005×C15111yescharacteristic
536C2#3009×C15111yescharacteristic
537C2#3321×C15112yes—
538C2#3348×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#555×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#475×C151C2semidirect
3. C2×#440×C151C2semidirect
4. #2536×C151C2semidirect
5. #2034×C151C2semidirect
6. #2000×C151C2semidirect
7. #1993×C151C2semidirect
8. #1955×C151C2semidirect
9. #1873×C151C2semidirect
10. #1854×C151C2semidirect
11. #1804×C151C2semidirect
269. #24133C151direct (N × H)
270. C151#24133direct (N × H)
272. C2×#475C2×C151semidirect
273. C2×#440C2×C151semidirect
274. #2536C2×C151semidirect
275. #2034C2×C151semidirect
276. #2000C2×C151semidirect
277. #1993C2×C151semidirect
278. #1955C2×C151semidirect
279. #1873C2×C151semidirect
280. #1854C2×C151semidirect
281. #1804C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1512
C2×#475×C1512
C2×#440×C1512
#2536×C1512
#2034×C1512
#2000×C1512
#1993×C1512
#1955×C1512
#1873×C1512
#1854×C1512
#1804×C1512
#24133151