Finite Group Databasebeta

← C151×#9229 #50314154

Subgroups — C151×#9229 #50314154

Order 38656.

646 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C151C211yesmaximal, characteristic
2C2×#436×C151C211yesmaximal, characteristic, complemented
3#1957×C151C211yesmaximal, characteristic, complemented
4#1802×C151C211yesmaximal, characteristic, complemented
5C2×#331×C151C211yesmaximal, characteristic, complemented
6#1296×C151C211yesmaximal, characteristic, complemented
7#1277×C151C211yesmaximal, characteristic, complemented
8C22×D8×C151—21no—
9C22×M16×C151—21no—
10C2×#127×C151C2211yescharacteristic
11C2×C4×D4×C151C2211yescharacteristic
12#459×C151—22no—
13#459×C151C414yescomplemented
14#436×C151—22no—
15#436×C151—22no—
16C2×C4⋊C8×C151C2211yescharacteristic
17C2×C4⋊C8×C151C2211yescharacteristic
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×#102×C151—21no—
20C2×#102×C151—21no—
21C2×#102×C151—21no—
22C2×#102×C151—21no—
23C2×C22⋊C8×C151—21no—
24C2×C4×C8×C151C2211yescharacteristic
25#384×C151C2211yescharacteristic
26#340×C151—21no—
27#331×C151—22no—
28C22×D4×C151—21no—
29C22×D4×C151—21no—
30C22×D4×C151—21no—
31C22×D4×C151D411yescharacteristic
32C23×C4×C151—21no—
33C2×D8×C151—24no—
34C2×D8×C151—42no—
35C2×D8×C151—42no—
36C2×M16×C151—24no—
37C2×M16×C151—42no—
38C2×M16×C151—42no—
39C22×C8×C151—21no—
40C22×C8×C151—21no—
41C22×C8×C151—21no—
42C22×C8×C151D411yescharacteristic
43C22×C8×C151D411yescharacteristic
44#127×C151—21no—
45#127×C151—21no—
46#127×C151—21no—
47#127×C151C2×C412yes—
48C4×D4×C151—21no—
49C4×D4×C151—21no—
50C4×D4×C151C2×C412yes—
51C4×D4×C151D412yes—
52C2×C4⋊C4×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151D411yescharacteristic
56C2×C22⋊C4×C151—21no—
57C2×C42×C151C2311yescharacteristic
58C4⋊C8×C151—21no—
59C4⋊C8×C151—21no—
60C4⋊C8×C151—21no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151C2×C412yes—
63C4⋊C8×C151D412yes—
64#102×C151—24no—
65#102×C151—42no—
66#102×C151—42no—
67#102×C151—42no—
68C22⋊C8×C151—24no—
69C4×C8×C151—21no—
70C4×C8×C151—21no—
71C24×C151—21no—
72C24×C151—41no—
73C2×D4×C151—22no—
74C2×D4×C151—22no—
75C2×D4×C151—22no—
76C2×D4×C151—21no—
77C2×D4×C151—21no—
78C2×D4×C151—21no—
79C2×D4×C151—21no—
80C2×D4×C151—21no—
81C2×D4×C151—41no—
82C2×D4×C151—41no—
83C2×D4×C151—41no—
84C2×D4×C151—41no—
85C2×D4×C151—41no—
86C2×D4×C151—41no—
87C2×D4×C151—41no—
88C2×D4×C151—41no—
89C2×D4×C151—41no—
90C2×D4×C151—41no—
91C2×D4×C151—41no—
92C2×D4×C151—81no—
93C2×D4×C151—81no—
94C2×D4×C151C22⋊C412yes—
95C22×C4×C151—21no—
96C22×C4×C151—22no—
97C22×C4×C151—22no—
98C22×C4×C151—41no—
99C22×C4×C151—41no—
100C22×C4×C151—41no—
101C22×C4×C151—41no—
102C22×C4×C151—41no—
103C22×C4×C151C2×D411yescharacteristic
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151#4111yescharacteristic
106D8×C151—48no—
107M16×C151—48no—
108C2×C8×C151—21no—
109C2×C8×C151—21no—
110C2×C8×C151—22no—
111C2×C8×C151—21no—
112C2×C8×C151—22no—
113C2×C8×C151—21no—
114C2×C8×C151—21no—
115C2×C8×C151—41no—
116C2×C8×C151—41no—
117C2×C8×C151—41no—
118C2×C8×C151—41no—
119C2×C8×C151—41no—
120C2×C8×C151—41no—
121C2×C8×C151—41no—
122C2×C8×C151D812yescomplemented
123C4⋊C4×C151—21no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151—41no—
126C4⋊C4×C151—41no—
127C4⋊C4×C151—41no—
128C4⋊C4×C151—81no—
129C4⋊C4×C151C22⋊C412yes—
130C22⋊C4×C151—22no—
131C22⋊C4×C151—22no—
132C42×C151C22×C411yescharacteristic
133C42×C151C2×D411yescharacteristic
134C42×C151C2×D411yescharacteristic
135C42×C151#4111yescharacteristic
136C23×C151—22no—
137C23×C151—41no—
138C23×C151—41no—
139C23×C151—41no—
140C23×C151—41no—
141C23×C151—41no—
142C23×C151—41no—
143C23×C151—42no—
144C23×C151—81no—
145C23×C151—81no—
146C23×C151—81no—
147C23×C151—81no—
148C23×C151—81no—
149C23×C151—81no—
150C23×C151#12111yescharacteristic
151D4×C151—22no—
152D4×C151—22no—
153D4×C151—42no—
154D4×C151—42no—
155D4×C151—42no—
156D4×C151—42no—
157D4×C151—41no—
158D4×C151—41no—
159D4×C151—82no—
160D4×C151—82no—
161D4×C151—81no—
162D4×C151—81no—
163D4×C151—81no—
164D4×C151—81no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—22no—
168C2×C4×C151—41no—
169C2×C4×C151—41no—
170C2×C4×C151—42no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151—42no—
174C2×C4×C151—81no—
175C2×C4×C151—81no—
176C2×C4×C151—81no—
177C2×C4×C151C2×C22⋊C411yescharacteristic
178C2×C4×C151C4×D411yescharacteristic
179C2×C4×C151C4×D411yescharacteristic
180C2×C4×C151#12011yescharacteristic
181C2×C4×C151#12111yescharacteristic
182C2×C4×C151#12311yescharacteristic
183C2×C4×C151C2×D811yescharacteristic
184C2×C4×C151#13511yescharacteristic
185C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C151#13711yescharacteristic
191C8×C151—22no—
192C8×C151—42no—
193C8×C151—42no—
194C8×C151—41no—
195C8×C151—81no—
196C22×C151—42no—
197C22×C151—42no—
198C22×C151—42no—
199C22×C151—81no—
200C22×C151—81no—
201C22×C151—81no—
202C22×C151—81no—
203C22×C151—82no—
204C22×C151—82no—
205C22×C151—82no—
206C22×C151—161no—
207C22×C151—161no—
208C22×C151—161no—
209C22×C151—161no—
210C22×C151#38611yescharacteristic
211C22×C151#45911yescharacteristic
212C22×C151#46311yescharacteristic
213C22×C151#46811yescharacteristic
214C22×C151#46911yescharacteristic
215C22×C151#47111yescharacteristic
216C22×C151#47211yescharacteristic
217C4×C151—21no—
218C4×C151—21no—
219C4×C151—42no—
220C4×C151—161no—
221C4×C151#41711yescharacteristic
222C4×C151#41811yescharacteristic
223C4×C151C4×D811yescharacteristic
224C4×C151#44211yescharacteristic
225C4×C151#44711yescharacteristic
226C4×C151#44911yescharacteristic
227C4×C151#46811yescharacteristic
228C4×C151#46911yescharacteristic
229C2×C151—82no—
230C2×C151—162no—
231C2×C151#168511yescharacteristic
232C2×C151#168711yescharacteristic
233C2×C151#169711yescharacteristic
234C2×C151#170111yescharacteristic
235C2×C151#187911yescharacteristic
236C2×C151#189511yescharacteristic
237C2×C151#190711yescharacteristic
238#9229C15111yesmaximal, characteristic, direct product factor, Sylow
239C151#922911yescharacteristic, direct product factor, Sylow
240C2×#459C2×C15111yescharacteristic
241C2×#436C2×C15111yescharacteristic, complemented
242#1957C2×C15111yescharacteristic, complemented
243#1802C2×C15111yescharacteristic, complemented
244C2×#331C2×C15111yescharacteristic, complemented
245#1296C2×C15111yescharacteristic, complemented
246#1277C2×C15111yescharacteristic, complemented
247C22×D8—21no—
248C22×M16—21no—
249C2×#127C22×C15111yescharacteristic
250C2×C4×D4C22×C15111yescharacteristic
251#459—22no—
252#459C4×C15114yescomplemented
253#436—22no—
254#436—22no—
255C2×C4⋊C8C22×C15111yescharacteristic
256C2×C4⋊C8C22×C15111yescharacteristic
257C2×C4⋊C8C22×C15111yescharacteristic
258C2×#102—21no—
259C2×#102—21no—
260C2×#102—21no—
261C2×#102—21no—
262C2×C22⋊C8—21no—
263C2×C4×C8C22×C15111yescharacteristic
264#384C22×C15111yescharacteristic
265#340—21no—
266#331—22no—
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4D4×C15111yescharacteristic
271C23×C4—21no—
272C2×D8—24no—
273C2×D8—42no—
274C2×D8—42no—
275C2×M16—24no—
276C2×M16—42no—
277C2×M16—42no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8D4×C15111yescharacteristic
282C22×C8D4×C15111yescharacteristic
283#127—21no—
284#127—21no—
285#127—21no—
286#127C2×C4×C15112yes—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4C2×C4×C15112yes—
290C4×D4D4×C15112yes—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4D4×C15111yescharacteristic
295C2×C22⋊C4—21no—
296C2×C42C23×C15111yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300C4⋊C8—21no—
301C4⋊C8C2×C4×C15112yes—
302C4⋊C8D4×C15112yes—
303#102—24no—
304#102—42no—
305#102—42no—
306#102—42no—
307C22⋊C8—24no—
308C4×C8—21no—
309C4×C8—21no—
310C24—21no—
311C24—41no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—81no—
332C2×D4—81no—
333C2×D4C22⋊C4×C15112yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4C2×D4×C15111yescharacteristic
343C22×C4C2×D4×C15111yescharacteristic
344C22×C4#41×C15111yescharacteristic
345D8—48no—
346M16—48no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8D8×C15112yescomplemented
362C4⋊C4—21no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—81no—
368C4⋊C4C22⋊C4×C15112yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42C22×C4×C15111yescharacteristic
372C42C2×D4×C15111yescharacteristic
373C42C2×D4×C15111yescharacteristic
374C42#41×C15111yescharacteristic
375C23—22no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—42no—
383C23—81no—
384C23—81no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—81no—
389C23#121×C15111yescharacteristic
390D4—22no—
391D4—22no—
392D4—42no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—41no—
397D4—41no—
398D4—82no—
399D4—82no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—81no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4C2×C22⋊C4×C15111yescharacteristic
417C2×C4C4×D4×C15111yescharacteristic
418C2×C4C4×D4×C15111yescharacteristic
419C2×C4#120×C15111yescharacteristic
420C2×C4#121×C15111yescharacteristic
421C2×C4#123×C15111yescharacteristic
422C2×C4C2×D8×C15111yescharacteristic
423C2×C4#135×C15111yescharacteristic
424C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
425C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
426C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
427C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
428C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
429C2×C4#137×C15111yescharacteristic
430C8—22no—
431C8—42no—
432C8—42no—
433C8—41no—
434C8—81no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—82no—
443C22—82no—
444C22—82no—
445C22—161no—
446C22—161no—
447C22—161no—
448C22—161no—
449C22#386×C15111yescharacteristic
450C22#459×C15111yescharacteristic
451C22#463×C15111yescharacteristic
452C22#468×C15111yescharacteristic
453C22#469×C15111yescharacteristic
454C22#471×C15111yescharacteristic
455C22#472×C15111yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—161no—
460C4#417×C15111yescharacteristic
461C4#418×C15111yescharacteristic
462C4C4×D8×C15111yescharacteristic
463C4#442×C15111yescharacteristic
464C4#447×C15111yescharacteristic
465C4#449×C15111yescharacteristic
466C4#468×C15111yescharacteristic
467C4#469×C15111yescharacteristic
468C2—82no—
469C2—162no—
470C2#1685×C15111yescharacteristic
471C2#1687×C15111yescharacteristic
472C2#1697×C15111yescharacteristic
473C2#1701×C15111yescharacteristic
474C2#1879×C15111yescharacteristic
475C2#1895×C15111yescharacteristic
476C2#1907×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC2×#459×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#436×C151C2semidirect
3. #1957×C151C2semidirect
4. #1802×C151C2semidirect
5. C2×#331×C151C2semidirect
6. #1296×C151C2semidirect
7. #1277×C151C2semidirect
13. #459×C151C4semidirect
122. C2×C8×C151D8semidirect
238. #9229C151direct (N × H)
239. C151#9229direct (N × H)
241. C2×#436C2×C151semidirect
242. #1957C2×C151semidirect
243. #1802C2×C151semidirect
244. C2×#331C2×C151semidirect
245. #1296C2×C151semidirect
246. #1277C2×C151semidirect
252. #459C4×C151semidirect
361. C2×C8D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1512
C2×#436×C1512
#1957×C1512
#1802×C1512
C2×#331×C1512
#1296×C1512
#1277×C1512
#9229151