Finite Group Databasebeta

← C151×#24678 #50329603

Subgroups — C151×#24678 #50329603

Order 38656.

850 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#475×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic
3#2542×C151C211yesmaximal, characteristic
4#2355×C151C211yesmaximal, characteristic, complemented
5#2072×C151C212yesmaximal, complemented
6#2055×C151C212yesmaximal
7#1990×C151C211yesmaximal, characteristic, complemented
8#1948×C151C212yesmaximal, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1926×C151C212yesmaximal
11#1802×C151C211yesmaximal, characteristic
12C22×SD16×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C2×C22⋊Q8×C151—21no—
15C2×C22⋊Q8×C151—21no—
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#475×C151—24no—
19C4×SD16×C151—24no—
20C2×#106×C151C2211yescharacteristic
21C2×#106×C151C2212yes—
22C2×C4⋊C8×C151C2212yes—
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2212yes—
28C2×C4×C8×C151C2211yescharacteristic
29#399×C151—22no—
30#391×C151C2212yes—
31#390×C151C2212yes—
32#387×C151—22no—
33#384×C151C2211yescharacteristic
34#384×C151C2212yes—
35#382×C151—21no—
36C4×C4⋊C4×C151—21no—
37C4×C4⋊C4×C151C2212yes—
38C4×C4⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2311yescharacteristic
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55C22⋊Q8×C151—44no—
56C22⋊Q8×C151—44no—
57C4×Q8×C151—22no—
58C4×Q8×C151D414yes—
59C4×D4×C151—22no—
60C4×D4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151D411yescharacteristic
68C2×C4⋊C4×C151D411yescharacteristic
69C2×C4⋊C4×C151C2312yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2312yes—
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—21no—
76C2×C42×C151—21no—
77C2×C42×C151—22no—
78C2×C42×C151C2312yes—
79C2×C42×C151C2311yescharacteristic
80#106×C151—22no—
81#106×C151—24no—
82C4⋊C8×C151—24no—
83C4⋊C8×C151—22no—
84#103×C151—22no—
85#103×C151—24no—
86#102×C151—24no—
87#102×C151—22no—
88C4×C8×C151—22no—
89#95×C151—22no—
90#95×C151—22no—
91#95×C151—22no—
92#95×C151D412yes—
93C24×C151—21no—
94C2×Q8×C151—21no—
95C2×Q8×C151—21no—
96C2×Q8×C151—21no—
97C2×Q8×C151—21no—
98C2×Q8×C151—21no—
99C2×Q8×C151—42no—
100C2×Q8×C151—42no—
101C2×Q8×C151—42no—
102C2×Q8×C151C2×D412yes—
103C2×D4×C151—21no—
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151#4112yes—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—22no—
113C22×C4×C151—21no—
114C22×C4×C151—42no—
115C22×C4×C151—42no—
116C22×C4×C151—42no—
117C22×C4×C151C2×D412yes—
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D412yes—
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2411yescharacteristic
122SD16×C151—28no—
123C2×C8×C151—21no—
124C2×C8×C151—21no—
125C2×C8×C151—21no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C2×C8×C151—22no—
129C2×C8×C151—21no—
130C2×C8×C151—21no—
131C2×C8×C151#4112yes—
132C4⋊C4×C151—24no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—44no—
142C4⋊C4×C151—42no—
143C4⋊C4×C151—44no—
144C4⋊C4×C151—42no—
145C4⋊C4×C151—81no—
146C4⋊C4×C151SD1614yescomplemented
147C4⋊C4×C151C2×D412yes—
148C22⋊C4×C151—44no—
149C22⋊C4×C151—42no—
150C22⋊C4×C151—44no—
151C42×C151—24no—
152C42×C151—22no—
153C42×C151—22no—
154C42×C151—82no—
155C42×C151C2×D412yes—
156C42×C151#4112yes—
157C23×C151—22no—
158C23×C151—41no—
159C23×C151—41no—
160C23×C151—41no—
161C23×C151—41no—
162C23×C151—41no—
163C23×C151—41no—
164C23×C151C22×D411yescharacteristic
165Q8×C151—22no—
166Q8×C151—22no—
167Q8×C151—41no—
168Q8×C151—41no—
169Q8×C151—84no—
170D4×C151—22no—
171D4×C151—22no—
172D4×C151—41no—
173D4×C151—41no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—41no—
184C2×C4×C151—41no—
185C2×C4×C151—41no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—41no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—84no—
197C2×C4×C151#12112yes—
198C2×C4×C151#12112yes—
199C2×C4×C151C2×SD1614yes—
200C2×C4×C151C2×SD1612yes—
201C2×C4×C151AGL(1,ℤ/8)12yes—
202C2×C4×C151C22×D411yescharacteristic
203C2×C4×C151C2×#4111yescharacteristic
204C2×C4×C151C2×#4111yescharacteristic
205C2×C4×C151C2×#4111yescharacteristic
206C2×C4×C1512−1+411yescharacteristic
207C2×C4×C1512−1+411yescharacteristic
208C8×C151—22no—
209C8×C151—42no—
210C8×C151—41no—
211C22×C151—42no—
212C22×C151—42no—
213C22×C151—42no—
214C22×C151—81no—
215C22×C151—81no—
216C22×C151—81no—
217C22×C151—81no—
218C22×C151C2×#12111yescharacteristic
219C22×C151#54711yescharacteristic
220C22×C151#54811yescharacteristic
221C22×C151C22×SD1611yescharacteristic
222C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
223C22×C151#57711yescharacteristic
224C22×C151#57811yescharacteristic
225C4×C151—24no—
226C4×C151—22no—
227C4×C151—42no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—82no—
231C4×C151—81no—
232C4×C151—82no—
233C4×C151#46014yes—
234C4×C151#52511yescharacteristic
235C4×C151#53611yescharacteristic
236C4×C151#55211yescharacteristic
237C4×C151#55611yescharacteristic
238C2×C151—82no—
239C2×C151#241511yescharacteristic
240C2×C151C2×#46011yescharacteristic
241C2×C151#304611yescharacteristic
242C2×C151#333511yescharacteristic
243C2×C151#335311yescharacteristic
244C2×C151#335911yescharacteristic
245C2×C151#337311yescharacteristic
246#24678C15111yesmaximal, characteristic, direct product factor, Sylow
247C151#2467811yescharacteristic, direct product factor, Sylow
248C2×#475C2×C15111yescharacteristic, complemented
249C2×C4×SD16C2×C15111yescharacteristic
250#2542C2×C15111yescharacteristic
251#2355C2×C15111yescharacteristic, complemented
252#2072C2×C15112yescomplemented
253#2055C2×C15112yes—
254#1990C2×C15111yescharacteristic, complemented
255#1948C2×C15112yescomplemented
256#1939C2×C15111yescharacteristic, complemented
257#1926C2×C15112yes—
258#1802C2×C15111yescharacteristic
259C22×SD16C22×C15111yescharacteristic
260C2×C4⋊Q8C22×C15111yescharacteristic
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8—21no—
263C2×C4×Q8C22×C15111yescharacteristic
264C2×C4×D4C22×C15111yescharacteristic
265#475—24no—
266C4×SD16—24no—
267C2×#106C22×C15112yes—
268C2×#106C22×C15111yescharacteristic
269C2×C4⋊C8C22×C15111yescharacteristic
270C2×C4⋊C8C22×C15112yes—
271C2×#103C22×C15112yes—
272C2×#103C22×C15111yescharacteristic
273C2×#102C22×C15112yes—
274C2×#102C22×C15111yescharacteristic
275C2×C4×C8C22×C15111yescharacteristic
276#399—22no—
277#391C22×C15112yes—
278#390C22×C15112yes—
279#387—22no—
280#384C22×C15111yescharacteristic
281#384C22×C15112yes—
282#382—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4C22×C15112yes—
285C4×C4⋊C4C22×C15111yescharacteristic
286#340C22×C15112yes—
287#340C22×C15112yes—
288#340C22×C15112yes—
289#336C22×C15112yes—
290C22×Q8—21no—
291C22×Q8C23×C15111yescharacteristic
292C22×D4C23×C15111yescharacteristic
293C23×C4—21no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—22no—
297C22×C8C23×C15111yescharacteristic
298C22×C8C23×C15112yes—
299C22×C8C23×C15111yescharacteristic
300C4⋊Q8—22no—
301C4⋊Q8—22no—
302C22⋊Q8—44no—
303C22⋊Q8—44no—
304C4×Q8—22no—
305C4×Q8D4×C15114yes—
306C4×D4—22no—
307C4×D4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C15111yescharacteristic
315C2×C4⋊C4D4×C15111yescharacteristic
316C2×C4⋊C4C23×C15111yescharacteristic
317C2×C4⋊C4C23×C15112yes—
318C2×C4⋊C4C23×C15112yes—
319C2×C4⋊C4C23×C15111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C42—21no—
324C2×C42—22no—
325C2×C42C23×C15112yes—
326C2×C42C23×C15111yescharacteristic
327#106—22no—
328#106—24no—
329C4⋊C8—24no—
330C4⋊C8—22no—
331#103—22no—
332#103—24no—
333#102—24no—
334#102—22no—
335C4×C8—22no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95D4×C15112yes—
340C24—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—42no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8C2×D4×C15112yes—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4#41×C15112yes—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4C2×D4×C15112yes—
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C2×D4×C15112yes—
367C22×C4C2×D4×C15111yescharacteristic
368C22×C4C24×C15111yescharacteristic
369SD16—28no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8#41×C15112yes—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—44no—
389C4⋊C4—42no—
390C4⋊C4—44no—
391C4⋊C4—42no—
392C4⋊C4—81no—
393C4⋊C4SD16×C15114yescomplemented
394C4⋊C4C2×D4×C15112yes—
395C22⋊C4—44no—
396C22⋊C4—42no—
397C22⋊C4—44no—
398C42—24no—
399C42—22no—
400C42—22no—
401C42—82no—
402C42C2×D4×C15112yes—
403C42#41×C15112yes—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23C22×D4×C15111yescharacteristic
412Q8—22no—
413Q8—22no—
414Q8—41no—
415Q8—41no—
416Q8—84no—
417D4—22no—
418D4—22no—
419D4—41no—
420D4—41no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—84no—
444C2×C4#121×C15112yes—
445C2×C4#121×C15112yes—
446C2×C4C2×SD16×C15114yes—
447C2×C4C2×SD16×C15112yes—
448C2×C4AGL(1,ℤ/8)×C15112yes—
449C2×C4C22×D4×C15111yescharacteristic
450C2×C4C2×#41×C15111yescharacteristic
451C2×C4C2×#41×C15111yescharacteristic
452C2×C4C2×#41×C15111yescharacteristic
453C2×C42−1+4×C15111yescharacteristic
454C2×C42−1+4×C15111yescharacteristic
455C8—22no—
456C8—42no—
457C8—41no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×#121×C15111yescharacteristic
466C22#547×C15111yescharacteristic
467C22#548×C15111yescharacteristic
468C22C22×SD16×C15111yescharacteristic
469C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
470C22#577×C15111yescharacteristic
471C22#578×C15111yescharacteristic
472C4—22no—
473C4—24no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—82no—
478C4—81no—
479C4—82no—
480C4#460×C15114yes—
481C4#525×C15111yescharacteristic
482C4#536×C15111yescharacteristic
483C4#552×C15111yescharacteristic
484C4#556×C15111yescharacteristic
485C2—82no—
486C2#2415×C15111yescharacteristic
487C2C2×#460×C15111yescharacteristic
488C2#3046×C15111yescharacteristic
489C2#3335×C15111yescharacteristic
490C2#3353×C15111yescharacteristic
491C2#3359×C15111yescharacteristic
492C2#3373×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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×#475×C151C2semidirect
4. #2355×C151C2semidirect
5. #2072×C151C2semidirect
7. #1990×C151C2semidirect
8. #1948×C151C2semidirect
9. #1939×C151C2semidirect
146. C4⋊C4×C151SD16semidirect
246. #24678C151direct (N × H)
247. C151#24678direct (N × H)
248. C2×#475C2×C151semidirect
251. #2355C2×C151semidirect
252. #2072C2×C151semidirect
254. #1990C2×C151semidirect
255. #1948C2×C151semidirect
256. #1939C2×C151semidirect
393. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#475×C1512
C2×C4×SD16×C1512
#2542×C1512
#2355×C1512
#2072×C1512
#2055×C1512
#1990×C1512
#1948×C1512
#1939×C1512
#1926×C1512
#1802×C1512
#24678151