Finite Group Databasebeta

← C151×#22226 #50327151

Subgroups — C151×#22226 #50327151

Order 38656.

926 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#490×C151C211yesmaximal, characteristic
2C4×#127×C151C211yesmaximal, characteristic
3C4×#125×C151C211yesmaximal, characteristic, complemented
4#1992×C151C211yesmaximal, characteristic, complemented
5#1961×C151C211yesmaximal, characteristic
6#1926×C151C212yesmaximal, complemented
7#1925×C151C212yesmaximal, complemented
8#1864×C151C212yesmaximal, complemented
9#1862×C151C212yesmaximal, complemented
10#1847×C151C211yesmaximal, characteristic, complemented
11#1745×C151C211yesmaximal, characteristic, complemented
12C2×#127×C151C2211yescharacteristic
13C2×#125×C151C2211yescharacteristic
14C2×C4×D4×C151—21no—
15C2×C4×D4×C151—21no—
16C2×C4×D4×C151C2212yes—
17#490×C151C418yescomplemented
18C2×#107×C151C2212yes—
19C2×#106×C151C2212yes—
20C2×#102×C151C2212yes—
21C2×#102×C151C2212yes—
22C2×#102×C151C2212yes—
23C2×#102×C151C2212yes—
24C2×#97×C151C2211yescharacteristic
25C2×#97×C151C2211yescharacteristic
26#390×C151—21no—
27#390×C151—21no—
28#390×C151C2212yes—
29#389×C151C2211yescharacteristic
30#389×C151C2211yescharacteristic
31#387×C151—21no—
32#387×C151—21no—
33#384×C151C2211yescharacteristic
34#382×C151C2211yescharacteristic
35C4×C4⋊C4×C151—21no—
36C4×C4⋊C4×C151—21no—
37C4×C4⋊C4×C151C2211yescharacteristic
38C4×C4⋊C4×C151C2211yescharacteristic
39C43×C151C2211yescharacteristic
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43#336×C151C2212yes—
44C22×D4×C151—21no—
45C22×D4×C151—21no—
46C22×D4×C151C2312yes—
47C23×C4×C151—22no—
48C22×C8×C151C2312yes—
49C22×C8×C151C2312yes—
50#127×C151—22no—
51#127×C151C2×C414yes—
52#125×C151—22no—
53#125×C151C2×C414yescomplemented
54C4×D4×C151—42no—
55C4×D4×C151—42no—
56C4×D4×C151—44no—
57C4×D4×C151—44no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151C2312yes—
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C42×C151—21no—
73C2×C42×C151—21no—
74C2×C42×C151D411yescharacteristic
75C2×C42×C151D411yescharacteristic
76C2×C42×C151D411yescharacteristic
77C2×C42×C151D411yescharacteristic
78C2×C42×C151C2311yescharacteristic
79C2×C42×C151C2311yescharacteristic
80C2×C42×C151C2311yescharacteristic
81#107×C151—42no—
82#106×C151—42no—
83#102×C151—42no—
84#102×C151—42no—
85#102×C151C2×C418yescomplemented
86#102×C151C2×C418yescomplemented
87#97×C151—22no—
88#97×C151C2×C414yescomplemented
89#95×C151—21no—
90#95×C151—21no—
91#95×C151—21no—
92#95×C151—21no—
93#95×C151—21no—
94#95×C151—21no—
95C24×C151—22no—
96C2×D4×C151—24no—
97C2×D4×C151—24no—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151—22no—
101C2×D4×C151—22no—
102C2×D4×C151—22no—
103C2×D4×C151—42no—
104C2×D4×C151—42no—
105C2×D4×C151—42no—
106C2×D4×C151—42no—
107C2×D4×C151C22×C414yes—
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—22no—
113C22×C4×C151—44no—
114C22×C4×C151—44no—
115C22×C4×C151—44no—
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151C2×D411yescharacteristic
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2411yescharacteristic
123C2×C8×C151—22no—
124C2×C8×C151—22no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C2×C8×C151C22×C414yes—
129C4⋊C4×C151—24no—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—42no—
138C4⋊C4×C151—42no—
139C4⋊C4×C151—42no—
140C4⋊C4×C151—42no—
141C4⋊C4×C151C22×C412yes—
142C4⋊C4×C151C22×C412yes—
143C22⋊C4×C151—44no—
144C22⋊C4×C151—44no—
145C22⋊C4×C151—44no—
146C42×C151—22no—
147C42×C151—22no—
148C42×C151—22no—
149C42×C151—22no—
150C42×C151—41no—
151C42×C151—41no—
152C42×C151—42no—
153C42×C151—42no—
154C42×C151C22×C412yes—
155C42×C151#4112yes—
156C23×C151—24no—
157C23×C151—42no—
158C23×C151—42no—
159C23×C151—42no—
160C23×C151—42no—
161C23×C151—42no—
162C23×C151—42no—
163C23×C151C22×D411yescharacteristic
164D4×C151—24no—
165D4×C151—24no—
166D4×C151—48no—
167D4×C151—48no—
168D4×C151—42no—
169D4×C151—42no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—21no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—41no—
187C2×C4×C151—41no—
188C2×C4×C151—41no—
189C2×C4×C151—41no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—88no—
200C2×C4×C151C4×D412yes—
201C2×C4×C151C4×D412yes—
202C2×C4×C151AGL(1,ℤ/8)12yes—
203C2×C4×C151AGL(1,ℤ/8)12yes—
204C2×C4×C151C23×C411yescharacteristic
205C2×C4×C151C2×#4111yescharacteristic
206C2×C4×C151H(5,𝔽2)12yes—
207C2×C4×C1512−1+412yes—
208C8×C151—24no—
209C8×C151—42no—
210C22×C151—44no—
211C22×C151—44no—
212C22×C151—44no—
213C22×C151—82no—
214C22×C151—82no—
215C22×C151—82no—
216C22×C151—82no—
217C22×C151C2×C4×D411yescharacteristic
218C22×C151#53511yescharacteristic
219C22×C151#53611yescharacteristic
220C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
221C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
222C22×C151#57511yescharacteristic
223C22×C151#57511yescharacteristic
224C4×C151—22no—
225C4×C151—22no—
226C4×C151—22no—
227C4×C151—22no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—41no—
231C4×C151—41no—
232C4×C151—81no—
233C4×C151—82no—
234C4×C151—81no—
235C4×C151#52012yes—
236C4×C151#54212yes—
237C2×C151—84no—
238C2×C151#232611yescharacteristic
239C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
240C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
241C2×C151#321711yescharacteristic
242C2×C151#321911yescharacteristic
243C2×C151#323411yescharacteristic
244C2×C151#323511yescharacteristic
245#22226C15111yesmaximal, characteristic, direct product factor, Sylow
246C151#2222611yescharacteristic, direct product factor, Sylow
247C2×#490C2×C15111yescharacteristic
248C4×#127C2×C15111yescharacteristic
249C4×#125C2×C15111yescharacteristic, complemented
250#1992C2×C15111yescharacteristic, complemented
251#1961C2×C15111yescharacteristic
252#1926C2×C15112yescomplemented
253#1925C2×C15112yescomplemented
254#1864C2×C15112yescomplemented
255#1862C2×C15112yescomplemented
256#1847C2×C15111yescharacteristic, complemented
257#1745C2×C15111yescharacteristic, complemented
258C2×#127C22×C15111yescharacteristic
259C2×#125C22×C15111yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4—21no—
262C2×C4×D4C22×C15112yes—
263#490C4×C15118yescomplemented
264C2×#107C22×C15112yes—
265C2×#106C22×C15112yes—
266C2×#102C22×C15112yes—
267C2×#102C22×C15112yes—
268C2×#102C22×C15112yes—
269C2×#102C22×C15112yes—
270C2×#97C22×C15111yescharacteristic
271C2×#97C22×C15111yescharacteristic
272#390—21no—
273#390—21no—
274#390C22×C15112yes—
275#389C22×C15111yescharacteristic
276#389C22×C15111yescharacteristic
277#387—21no—
278#387—21no—
279#384C22×C15111yescharacteristic
280#382C22×C15111yescharacteristic
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4C22×C15111yescharacteristic
284C4×C4⋊C4C22×C15111yescharacteristic
285C43C22×C15111yescharacteristic
286#340C22×C15112yes—
287#340C22×C15112yes—
288#336C22×C15112yes—
289#336C22×C15112yes—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4C23×C15112yes—
293C23×C4—22no—
294C22×C8C23×C15112yes—
295C22×C8C23×C15112yes—
296#127—22no—
297#127C2×C4×C15114yes—
298#125—22no—
299#125C2×C4×C15114yescomplemented
300C4×D4—42no—
301C4×D4—42no—
302C4×D4—44no—
303C4×D4—44no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4C23×C15112yes—
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C4⋊C4C23×C15111yescharacteristic
313C2×C4⋊C4C23×C15111yescharacteristic
314C2×C4⋊C4C23×C15111yescharacteristic
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42D4×C15111yescharacteristic
321C2×C42D4×C15111yescharacteristic
322C2×C42D4×C15111yescharacteristic
323C2×C42D4×C15111yescharacteristic
324C2×C42C23×C15111yescharacteristic
325C2×C42C23×C15111yescharacteristic
326C2×C42C23×C15111yescharacteristic
327#107—42no—
328#106—42no—
329#102—42no—
330#102—42no—
331#102C2×C4×C15118yescomplemented
332#102C2×C4×C15118yescomplemented
333#97—22no—
334#97C2×C4×C15114yescomplemented
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341C24—22no—
342C2×D4—24no—
343C2×D4—24no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—42no—
350C2×D4—42no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4C22×C4×C15114yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—44no—
360C22×C4—44no—
361C22×C4—44no—
362C22×C4C2×D4×C15111yescharacteristic
363C22×C4C2×D4×C15111yescharacteristic
364C22×C4C2×D4×C15111yescharacteristic
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C2×D4×C15111yescharacteristic
367C22×C4C2×D4×C15111yescharacteristic
368C22×C4C24×C15111yescharacteristic
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8C22×C4×C15114yes—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4C22×C4×C15112yes—
388C4⋊C4C22×C4×C15112yes—
389C22⋊C4—44no—
390C22⋊C4—44no—
391C22⋊C4—44no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—22no—
396C42—41no—
397C42—41no—
398C42—42no—
399C42—42no—
400C42C22×C4×C15112yes—
401C42#41×C15112yes—
402C23—24no—
403C23—42no—
404C23—42no—
405C23—42no—
406C23—42no—
407C23—42no—
408C23—42no—
409C23C22×D4×C15111yescharacteristic
410D4—24no—
411D4—24no—
412D4—48no—
413D4—48no—
414D4—42no—
415D4—42no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—88no—
446C2×C4C4×D4×C15112yes—
447C2×C4C4×D4×C15112yes—
448C2×C4AGL(1,ℤ/8)×C15112yes—
449C2×C4AGL(1,ℤ/8)×C15112yes—
450C2×C4C23×C4×C15111yescharacteristic
451C2×C4C2×#41×C15111yescharacteristic
452C2×C4H(5,𝔽2)×C15112yes—
453C2×C42−1+4×C15112yes—
454C8—24no—
455C8—42no—
456C22—44no—
457C22—44no—
458C22—44no—
459C22—82no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22C2×C4×D4×C15111yescharacteristic
464C22#535×C15111yescharacteristic
465C22#536×C15111yescharacteristic
466C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
467C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
468C22#575×C15111yescharacteristic
469C22#575×C15111yescharacteristic
470C4—22no—
471C4—22no—
472C4—22no—
473C4—22no—
474C4—42no—
475C4—42no—
476C4—41no—
477C4—41no—
478C4—82no—
479C4—81no—
480C4—81no—
481C4#520×C15112yes—
482C4#542×C15112yes—
483C2—84no—
484C2#2326×C15111yescharacteristic
485C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
486C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
487C2#3217×C15111yescharacteristic
488C2#3219×C15111yescharacteristic
489C2#3234×C15111yescharacteristic
490C2#3235×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C43×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×#125×C151C2semidirect
4. #1992×C151C2semidirect
6. #1926×C151C2semidirect
7. #1925×C151C2semidirect
8. #1864×C151C2semidirect
9. #1862×C151C2semidirect
10. #1847×C151C2semidirect
11. #1745×C151C2semidirect
17. #490×C151C4semidirect
53. #125×C151C2×C4semidirect
85. #102×C151C2×C4semidirect
86. #102×C151C2×C4semidirect
88. #97×C151C2×C4semidirect
245. #22226C151direct (N × H)
246. C151#22226direct (N × H)
249. C4×#125C2×C151semidirect
250. #1992C2×C151semidirect
252. #1926C2×C151semidirect
253. #1925C2×C151semidirect
254. #1864C2×C151semidirect
255. #1862C2×C151semidirect
256. #1847C2×C151semidirect
257. #1745C2×C151semidirect
263. #490C4×C151semidirect
299. #125C2×C4×C151semidirect
331. #102C2×C4×C151semidirect
332. #102C2×C4×C151semidirect
334. #97C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#490×C1512
C4×#127×C1512
C4×#125×C1512
#1992×C1512
#1961×C1512
#1926×C1512
#1925×C1512
#1864×C1512
#1862×C1512
#1847×C1512
#1745×C1512
#22226151