Finite Group Databasebeta

← C151×#24830 #50329755

Subgroups — C151×#24830 #50329755

Order 38656.

900 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C151C211yesmaximal, characteristic, complemented
2C2×#442×C151C211yesmaximal, characteristic
3#2563×C151C211yesmaximal, characteristic, complemented
4#2349×C151C211yesmaximal, characteristic, complemented
5#2085×C151C212yesmaximal, complemented
6#2067×C151C212yesmaximal, complemented
7#1993×C151C211yesmaximal, characteristic, complemented
8#1940×C151C211yesmaximal, characteristic, complemented
9#1879×C151C212yesmaximal
10#1804×C151C211yesmaximal, characteristic, complemented
11#1804×C151C212yesmaximal, complemented
12C22×D8×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C4×D4×C151C2211yescharacteristic
15C2×C4×D4×C151C2212yes—
16C2×C4×D4×C151C2211yescharacteristic
17#474×C151—24no—
18#442×C151—24no—
19C2×#107×C151C2212yes—
20C2×#106×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#102×C151C2211yescharacteristic
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2212yes—
27C2×#97×C151C2211yescharacteristic
28#393×C151—21no—
29#393×C151—21no—
30#390×C151C2212yes—
31#389×C151C2212yes—
32#385×C151—22no—
33#382×C151C2212yes—
34#382×C151C2211yescharacteristic
35#380×C151—22no—
36#380×C151—21no—
37C4×C4⋊C4×C151C2211yescharacteristic
38C2×#95×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×D4×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C23×C4×C151—22no—
49C2×D8×C151—22no—
50C2×D8×C151—22no—
51C2×D8×C151Q814yescomplemented
52C22×C8×C151C2312yes—
53C22×C8×C151C2311yescharacteristic
54C22×C8×C151C2311yescharacteristic
55C4⋊Q8×C151—22no—
56C4⋊Q8×C151—22no—
57C4×D4×C151—24no—
58C4×D4×C151—22no—
59C4×D4×C151—22no—
60C4×D4×C151—22no—
61C4×D4×C151—42no—
62C4×D4×C151D414yes—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151D412yes—
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C22⋊C4×C151—21no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C42×C151C2312yes—
76C2×C42×C151C2311yescharacteristic
77#107×C151—24no—
78#106×C151—22no—
79C4⋊C8×C151—22no—
80C4⋊C8×C151—42no—
81#102×C151—22no—
82#102×C151—24no—
83#102×C151—22no—
84#102×C151—42no—
85#97×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151—21no—
91#95×C151D411yescharacteristic
92#95×C151D411yescharacteristic
93C24×C151—21no—
94C24×C151—21no—
95C2×Q8×C151—42no—
96C2×Q8×C151—82no—
97C2×D4×C151—21no—
98C2×D4×C151—21no—
99C2×D4×C151—21no—
100C2×D4×C151—21no—
101C2×D4×C151—21no—
102C2×D4×C151—21no—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151C2×D412yes—
106C2×D4×C151C2×Q812yes—
107C2×D4×C151C2×Q812yes—
108C2×D4×C151#4112yes—
109C22×C4×C151—21no—
110C22×C4×C151—24no—
111C22×C4×C151—21no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—44no—
115C22×C4×C151—44no—
116C22×C4×C151—44no—
117C22×C4×C151—42no—
118C22×C4×C151—82no—
119C22×C4×C151—82no—
120C22×C4×C151C2×D412yes—
121C22×C4×C151C2×D412yes—
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151C2×D411yescharacteristic
124C22×C4×C151C2411yescharacteristic
125D8×C151—28no—
126C2×C8×C151—21no—
127C2×C8×C151—21no—
128C2×C8×C151—21no—
129C2×C8×C151—22no—
130C2×C8×C151—22no—
131C2×C8×C151—21no—
132C2×C8×C151—22no—
133C2×C8×C151—21no—
134C2×C8×C151C2×Q812yes—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—21no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—42no—
143C4⋊C4×C151—42no—
144C4⋊C4×C151—82no—
145C4⋊C4×C151C2×D412yes—
146C22⋊C4×C151—24no—
147C22⋊C4×C151—44no—
148C22⋊C4×C151—42no—
149C22⋊C4×C151—82no—
150C22⋊C4×C151—82no—
151C42×C151—22no—
152C42×C151—22no—
153C42×C151C2×D412yes—
154C42×C151#4112yes—
155C23×C151—22no—
156C23×C151—22no—
157C23×C151—22no—
158C23×C151—22no—
159C23×C151—42no—
160C23×C151—42no—
161C23×C151—41no—
162C23×C151—41no—
163C23×C151—42no—
164C23×C151—42no—
165C23×C151C22×D411yescharacteristic
166Q8×C151—84no—
167D4×C151—22no—
168D4×C151—22no—
169D4×C151—22no—
170D4×C151—22no—
171D4×C151—22no—
172D4×C151—41no—
173D4×C151—41no—
174D4×C151C22⋊Q814yes—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—42no—
185C2×C4×C151—42no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—84no—
194C2×C4×C151—84no—
195C2×C4×C151—88no—
196C2×C4×C151#12112yes—
197C2×C4×C151#12112yes—
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C22×Q811yescharacteristic
200C2×C4×C151C2×#4111yescharacteristic
201C2×C4×C151C2×#4111yescharacteristic
202C2×C4×C151H(5,𝔽2)11yescharacteristic
203C2×C4×C1512−1+411yescharacteristic
204C8×C151—22no—
205C8×C151—41no—
206C8×C151—42no—
207C22×C151—24no—
208C22×C151—44no—
209C22×C151—42no—
210C22×C151—42no—
211C22×C151—44no—
212C22×C151—44no—
213C22×C151—42no—
214C22×C151—81no—
215C22×C151—81no—
216C22×C151—82no—
217C22×C151C2×#12111yescharacteristic
218C22×C151#54611yescharacteristic
219C22×C151D4×Q811yescharacteristic
220C22×C151#57512yes—
221C22×C151#57612yes—
222C4×C151—22no—
223C4×C151—22no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—42no—
227C4×C151—81no—
228C4×C151—82no—
229C4×C151—82no—
230C4×C151C2×C22⋊Q811yescharacteristic
231C4×C151#53711yescharacteristic
232C4×C151#55211yescharacteristic
233C4×C151#55411yescharacteristic
234C2×C151—44no—
235C2×C151—82no—
236C2×C151#241711yescharacteristic
237C2×C151#304011yescharacteristic
238C2×C151#304111yescharacteristic
239C2×C151#331912yes—
240C2×C151#338912yes—
241#24830C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#2483011yescharacteristic, direct product factor, Sylow
243C2×#474C2×C15111yescharacteristic, complemented
244C2×#442C2×C15111yescharacteristic
245#2563C2×C15111yescharacteristic, complemented
246#2349C2×C15111yescharacteristic, complemented
247#2085C2×C15112yescomplemented
248#2067C2×C15112yescomplemented
249#1993C2×C15111yescharacteristic, complemented
250#1940C2×C15111yescharacteristic, complemented
251#1879C2×C15112yes—
252#1804C2×C15111yescharacteristic, complemented
253#1804C2×C15112yescomplemented
254C22×D8C22×C15111yescharacteristic
255C2×C4⋊Q8C22×C15111yescharacteristic
256C2×C4×D4C22×C15111yescharacteristic
257C2×C4×D4C22×C15112yes—
258C2×C4×D4C22×C15111yescharacteristic
259#474—24no—
260#442—24no—
261C2×#107C22×C15112yes—
262C2×#106C22×C15111yescharacteristic
263C2×C4⋊C8C22×C15111yescharacteristic
264C2×C4⋊C8C22×C15112yes—
265C2×#102C22×C15111yescharacteristic
266C2×#102C22×C15112yes—
267C2×#102C22×C15111yescharacteristic
268C2×#102C22×C15112yes—
269C2×#97C22×C15111yescharacteristic
270#393—21no—
271#393—21no—
272#390C22×C15112yes—
273#389C22×C15112yes—
274#385—22no—
275#382C22×C15112yes—
276#382C22×C15111yescharacteristic
277#380—22no—
278#380—21no—
279C4×C4⋊C4C22×C15111yescharacteristic
280C2×#95—21no—
281#340C22×C15112yes—
282#340C22×C15112yes—
283#340C22×C15112yes—
284#336C22×C15112yes—
285C22×Q8—21no—
286C22×D4C23×C15111yescharacteristic
287C22×D4C23×C15111yescharacteristic
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—22no—
291C2×D8—22no—
292C2×D8—22no—
293C2×D8Q8×C15114yescomplemented
294C22×C8C23×C15112yes—
295C22×C8C23×C15111yescharacteristic
296C22×C8C23×C15111yescharacteristic
297C4⋊Q8—22no—
298C4⋊Q8—22no—
299C4×D4—24no—
300C4×D4—22no—
301C4×D4—22no—
302C4×D4—22no—
303C4×D4—42no—
304C4×D4D4×C15114yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4D4×C15112yes—
308C2×C4⋊C4C23×C15112yes—
309C2×C4⋊C4C23×C15111yescharacteristic
310C2×C4⋊C4C23×C15112yes—
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C42C23×C15112yes—
318C2×C42C23×C15111yescharacteristic
319#107—24no—
320#106—22no—
321C4⋊C8—22no—
322C4⋊C8—42no—
323#102—22no—
324#102—24no—
325#102—22no—
326#102—42no—
327#97—22no—
328#95—21no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—21no—
333#95D4×C15111yescharacteristic
334#95D4×C15111yescharacteristic
335C24—21no—
336C24—21no—
337C2×Q8—42no—
338C2×Q8—82no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4C2×D4×C15112yes—
348C2×D4C2×Q8×C15112yes—
349C2×D4C2×Q8×C15112yes—
350C2×D4#41×C15112yes—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—44no—
357C22×C4—44no—
358C22×C4—44no—
359C22×C4—42no—
360C22×C4—82no—
361C22×C4—82no—
362C22×C4C2×D4×C15112yes—
363C22×C4C2×D4×C15112yes—
364C22×C4C2×D4×C15111yescharacteristic
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C24×C15111yescharacteristic
367D8—28no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8C2×Q8×C15112yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—82no—
387C4⋊C4C2×D4×C15112yes—
388C22⋊C4—24no—
389C22⋊C4—44no—
390C22⋊C4—42no—
391C22⋊C4—82no—
392C22⋊C4—82no—
393C42—22no—
394C42—22no—
395C42C2×D4×C15112yes—
396C42#41×C15112yes—
397C23—22no—
398C23—22no—
399C23—22no—
400C23—22no—
401C23—42no—
402C23—42no—
403C23—41no—
404C23—41no—
405C23—42no—
406C23—42no—
407C23C22×D4×C15111yescharacteristic
408Q8—84no—
409D4—22no—
410D4—22no—
411D4—22no—
412D4—22no—
413D4—22no—
414D4—41no—
415D4—41no—
416D4C22⋊Q8×C15114yes—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—84no—
436C2×C4—84no—
437C2×C4—88no—
438C2×C4#121×C15112yes—
439C2×C4#121×C15112yes—
440C2×C4C22×D4×C15111yescharacteristic
441C2×C4C22×Q8×C15111yescharacteristic
442C2×C4C2×#41×C15111yescharacteristic
443C2×C4C2×#41×C15111yescharacteristic
444C2×C4H(5,𝔽2)×C15111yescharacteristic
445C2×C42−1+4×C15111yescharacteristic
446C8—22no—
447C8—41no—
448C8—42no—
449C22—24no—
450C22—44no—
451C22—42no—
452C22—42no—
453C22—44no—
454C22—44no—
455C22—42no—
456C22—81no—
457C22—81no—
458C22—82no—
459C22C2×#121×C15111yescharacteristic
460C22#546×C15111yescharacteristic
461C22D4×Q8×C15111yescharacteristic
462C22#575×C15112yes—
463C22#576×C15112yes—
464C4—22no—
465C4—22no—
466C4—42no—
467C4—42no—
468C4—42no—
469C4—81no—
470C4—82no—
471C4—82no—
472C4C2×C22⋊Q8×C15111yescharacteristic
473C4#537×C15111yescharacteristic
474C4#552×C15111yescharacteristic
475C4#554×C15111yescharacteristic
476C2—44no—
477C2—82no—
478C2#2417×C15111yescharacteristic
479C2#3040×C15111yescharacteristic
480C2#3041×C15111yescharacteristic
481C2#3319×C15112yes—
482C2#3389×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#474×C151C2semidirect
3. #2563×C151C2semidirect
4. #2349×C151C2semidirect
5. #2085×C151C2semidirect
6. #2067×C151C2semidirect
7. #1993×C151C2semidirect
8. #1940×C151C2semidirect
10. #1804×C151C2semidirect
11. #1804×C151C2semidirect
51. C2×D8×C151Q8semidirect
241. #24830C151direct (N × H)
242. C151#24830direct (N × H)
243. C2×#474C2×C151semidirect
245. #2563C2×C151semidirect
246. #2349C2×C151semidirect
247. #2085C2×C151semidirect
248. #2067C2×C151semidirect
249. #1993C2×C151semidirect
250. #1940C2×C151semidirect
252. #1804C2×C151semidirect
253. #1804C2×C151semidirect
293. C2×D8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1512
C2×#442×C1512
#2563×C1512
#2349×C1512
#2085×C1512
#2067×C1512
#1993×C1512
#1940×C1512
#1879×C1512
#1804×C1512
#24830151