Finite Group Databasebeta

← C151×#18896 #50323821

Subgroups — C151×#18896 #50323821

Order 38656.

978 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C151C211yesmaximal, characteristic, complemented
2#3208×C151C211yesmaximal, characteristic, complemented
3#3205×C151C211yesmaximal, characteristic
4C2×#460×C151C211yesmaximal, characteristic, complemented
5#1626×C151C214yesmaximal, complemented
6#1620×C151C214yesmaximal, complemented
7#1540×C151C211yesmaximal, characteristic, complemented
8#1481×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C22×SD16×C151—21no—
11#559×C151C2212yescomplemented
12#557×C151C2212yescomplemented
13#556×C151—21no—
14#556×C151—22no—
15#554×C151—21no—
16#552×C151—22no—
17#539×C151—22no—
18#536×C151—21no—
19#533×C151C2211yescharacteristic
20#532×C151C2211yescharacteristic
21C2×#127×C151C2211yescharacteristic
22#529×C151—22no—
23#520×C151—21no—
24C2×C4×Q8×C151C2211yescharacteristic
25#493×C151C2212yes—
26#492×C151—21no—
27#486×C151—21no—
28#486×C151C2212yes—
29#460×C151—22no—
30#460×C151C2214yes—
31#460×C151C2214yes—
32#459×C151—22no—
33#450×C151—22no—
34#447×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#102×C151—21no—
39#332×C151C2212yescomplemented
40#331×C151C2212yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42Q8⋊C8×C151C2214yescomplemented
43C2×#41×C151—21no—
44C22×Q8×C151D411yescharacteristic
45C22×D4×C151—21no—
46C22×D4×C151—21no—
47C22×D4×C151—21no—
48C2×SD16×C151—24no—
49C2×SD16×C151—24no—
50C2×SD16×C151—44no—
51C2×D8×C151—24no—
52C22×C8×C151—21no—
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151C2311yescharacteristic
57#127×C151—21no—
58#127×C151—21no—
59#127×C151—21no—
60#127×C151C2312yes—
61#127×C151C2311yescharacteristic
62#126×C151—24no—
63#126×C151—24no—
64#125×C151—22no—
65#125×C151—24no—
66#125×C151—21no—
67#124×C151—21no—
68#124×C151—22no—
69#124×C151—22no—
70#123×C151—24no—
71#123×C151—24no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151D412yes—
77#121×C151—21no—
78#121×C151D412yes—
79C4×Q8×C151—22no—
80C4×Q8×C151—21no—
81C4×Q8×C151—21no—
82C4×Q8×C151—21no—
83C4×Q8×C151—22no—
84C4×Q8×C151D412yes—
85C4×Q8×C151C2312yes—
86C4×Q8×C151C2312yes—
87C4×D4×C151—24no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—21no—
91C4×D4×C151D412yes—
92#117×C151—22no—
93#117×C151—24no—
94#117×C151—21no—
95C2×C4⋊C4×C151—22no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151D411yescharacteristic
98C2×C42×C151—21no—
99C2×C42×C151C2311yescharacteristic
100C4⋊C8×C151—21no—
101C4⋊C8×C151—21no—
102C4⋊C8×C151C2312yes—
103C4⋊C8×C151C2312yes—
104#102×C151—24no—
105#102×C151—24no—
106#102×C151—24no—
107C22⋊C8×C151—21no—
108C22⋊C8×C151—21no—
109C4×C8×C151—21no—
110C4×C8×C151C2312yes—
111C24×C151—41no—
112#41×C151—42no—
113#41×C151—42no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—22no—
118C2×Q8×C151—22no—
119C2×Q8×C151C2×D412yes—
120C2×Q8×C151C2×D412yes—
121C2×D4×C151—22no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—41no—
128C2×D4×C151—41no—
129C2×D4×C151—41no—
130C2×D4×C151—42no—
131C2×D4×C151—42no—
132C2×D4×C151—82no—
133C2×D4×C151—82no—
134C2×D4×C151C2×D412yes—
135C22×C4×C151—21no—
136C22×C4×C151—24no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142SD16×C151—48no—
143SD16×C151—84no—
144D8×C151—84no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—42no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151C2×D412yes—
162C4⋊C4×C151C2×D412yes—
163C4⋊C4×C151C2×D412yes—
164C22⋊C4×C151—24no—
165C22⋊C4×C151—24no—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C42×C151—24no—
171C42×C151—22no—
172C42×C151—22no—
173C42×C151—22no—
174C42×C151C2×D411yescharacteristic
175C42×C151C2×D411yescharacteristic
176C42×C151C2×D411yescharacteristic
177C42×C151C2411yescharacteristic
178C23×C151—22no—
179C23×C151—42no—
180C23×C151—82no—
181C23×C151—82no—
182C23×C151—82no—
183C23×C151#12011yescharacteristic
184Q8×C151—22no—
185Q8×C151—22no—
186Q8×C151—24no—
187Q8×C151—41no—
188Q8×C151—41no—
189Q8×C151—42no—
190Q8×C151—81no—
191D4×C151—42no—
192D4×C151—44no—
193D4×C151—44no—
194D4×C151—41no—
195D4×C151—42no—
196D4×C151—41no—
197D4×C151—42no—
198D4×C151—42no—
199D4×C151—44no—
200D4×C151—82no—
201D4×C151—82no—
202D4×C151—82no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—41no—
210C2×C4×C151—42no—
211C2×C4×C151—44no—
212C2×C4×C151—81no—
213C2×C4×C151—84no—
214C2×C4×C151#12011yescharacteristic
215C2×C4×C151#12011yescharacteristic
216C2×C4×C151#12011yescharacteristic
217C2×C4×C151#13512yes—
218C2×C4×C151AGL(1,ℤ/8)12yes—
219C2×C4×C151C22×D411yescharacteristic
220C2×C4×C151C22×D411yescharacteristic
221C2×C4×C151C22×D411yescharacteristic
222C8×C151—42no—
223C8×C151—42no—
224C8×C151—42no—
225C22×C151—21no—
226C22×C151—21no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—82no—
231C22×C151—82no—
232C22×C151—82no—
233C22×C151—164no—
234C22×C151#44912yes—
235C22×C151C2×#12011yescharacteristic
236C4×C151—21no—
237C4×C151—21no—
238C4×C151—21no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151#44912yes—
245C4×C151C2×#13511yescharacteristic
246C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C151#57712yes—
248C2×C151—22no—
249C2×C151—82no—
250C2×C151—162no—
251C2×C151C2×#44911yescharacteristic
252C2×C151#301011yescharacteristic
253C2×C151#302111yescharacteristic
254#18896C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#1889611yescharacteristic, direct product factor, Sylow
256#3507C2×C15111yescharacteristic, complemented
257#3208C2×C15111yescharacteristic, complemented
258#3205C2×C15111yescharacteristic
259C2×#460C2×C15111yescharacteristic, complemented
260#1626C2×C15114yescomplemented
261#1620C2×C15114yescomplemented
262#1540C2×C15111yescharacteristic, complemented
263#1481C2×C15111yescharacteristic, complemented
264#1479C2×C15111yescharacteristic, complemented
265C22×SD16—21no—
266#559C22×C15112yescomplemented
267#557C22×C15112yescomplemented
268#556—21no—
269#556—22no—
270#554—21no—
271#552—22no—
272#539—22no—
273#536—21no—
274#533C22×C15111yescharacteristic
275#532C22×C15111yescharacteristic
276C2×#127C22×C15111yescharacteristic
277#529—22no—
278#520—21no—
279C2×C4×Q8C22×C15111yescharacteristic
280#493C22×C15112yes—
281#492—21no—
282#486—21no—
283#486C22×C15112yes—
284#460—22no—
285#460C22×C15114yes—
286#460C22×C15114yes—
287#459—22no—
288#450—22no—
289#447—22no—
290#431C22×C15111yescharacteristic
291#431C22×C15111yescharacteristic
292C2×C4⋊C8C22×C15111yescharacteristic
293C2×#102—21no—
294#332C22×C15112yescomplemented
295#331C22×C15112yescomplemented
296Q8⋊C8C22×C15114yescomplemented
297Q8⋊C8C22×C15114yescomplemented
298C2×#41—21no—
299C22×Q8D4×C15111yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C2×SD16—24no—
304C2×SD16—24no—
305C2×SD16—44no—
306C2×D8—24no—
307C22×C8—21no—
308C4⋊Q8—22no—
309C4⋊Q8D4×C15111yescharacteristic
310C4⋊Q8D4×C15111yescharacteristic
311C4⋊Q8C23×C15111yescharacteristic
312#127—21no—
313#127—21no—
314#127—21no—
315#127C23×C15112yes—
316#127C23×C15111yescharacteristic
317#126—24no—
318#126—24no—
319#125—22no—
320#125—24no—
321#125—21no—
322#124—22no—
323#124—22no—
324#124—21no—
325#123—24no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—24no—
330C22⋊Q8—21no—
331C22⋊Q8D4×C15112yes—
332#121—21no—
333#121D4×C15112yes—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8D4×C15112yes—
340C4×Q8C23×C15112yes—
341C4×Q8C23×C15112yes—
342C4×D4—24no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—21no—
346C4×D4D4×C15112yes—
347#117—22no—
348#117—24no—
349#117—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4D4×C15111yescharacteristic
353C2×C42—21no—
354C2×C42C23×C15111yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8C23×C15112yes—
358C4⋊C8C23×C15112yes—
359#102—24no—
360#102—24no—
361#102—24no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C4×C8—21no—
365C4×C8C23×C15112yes—
366C24—41no—
367#41—42no—
368#41—42no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8C2×D4×C15112yes—
375C2×Q8C2×D4×C15112yes—
376C2×D4—22no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—82no—
388C2×D4—82no—
389C2×D4C2×D4×C15112yes—
390C22×C4—21no—
391C22×C4—24no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4C2×D4×C15111yescharacteristic
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×D4×C15111yescharacteristic
397SD16—48no—
398SD16—84no—
399D8—84no—
400C2×C8—22no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—42no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4C2×D4×C15112yes—
417C4⋊C4C2×D4×C15112yes—
418C4⋊C4C2×D4×C15112yes—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—24no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C42—24no—
426C42—22no—
427C42—22no—
428C42—22no—
429C42C2×D4×C15111yescharacteristic
430C42C2×D4×C15111yescharacteristic
431C42C2×D4×C15111yescharacteristic
432C42C24×C15111yescharacteristic
433C23—22no—
434C23—42no—
435C23—82no—
436C23—82no—
437C23—82no—
438C23#120×C15111yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—24no—
442Q8—42no—
443Q8—41no—
444Q8—41no—
445Q8—81no—
446D4—42no—
447D4—44no—
448D4—44no—
449D4—41no—
450D4—42no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—44no—
455D4—82no—
456D4—82no—
457D4—82no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—81no—
468C2×C4—84no—
469C2×C4#120×C15111yescharacteristic
470C2×C4#120×C15111yescharacteristic
471C2×C4#120×C15111yescharacteristic
472C2×C4#135×C15112yes—
473C2×C4AGL(1,ℤ/8)×C15112yes—
474C2×C4C22×D4×C15111yescharacteristic
475C2×C4C22×D4×C15111yescharacteristic
476C2×C4C22×D4×C15111yescharacteristic
477C8—42no—
478C8—42no—
479C8—42no—
480C22—21no—
481C22—21no—
482C22—42no—
483C22—42no—
484C22—42no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—164no—
489C22#449×C15112yes—
490C22C2×#120×C15111yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—42no—
499C4#449×C15112yes—
500C4C2×#135×C15111yescharacteristic
501C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
502C4#577×C15112yes—
503C2—22no—
504C2—82no—
505C2—162no—
506C2C2×#449×C15111yescharacteristic
507C2#3010×C15111yescharacteristic
508C2#3021×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3205×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3507×C151C2semidirect
2. #3208×C151C2semidirect
4. C2×#460×C151C2semidirect
5. #1626×C151C2semidirect
6. #1620×C151C2semidirect
7. #1540×C151C2semidirect
8. #1481×C151C2semidirect
9. #1479×C151C2semidirect
11. #559×C151C22semidirect
12. #557×C151C22semidirect
39. #332×C151C22semidirect
40. #331×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
42. Q8⋊C8×C151C22semidirect
254. #18896C151direct (N × H)
255. C151#18896direct (N × H)
256. #3507C2×C151semidirect
257. #3208C2×C151semidirect
259. C2×#460C2×C151semidirect
260. #1626C2×C151semidirect
261. #1620C2×C151semidirect
262. #1540C2×C151semidirect
263. #1481C2×C151semidirect
264. #1479C2×C151semidirect
266. #559C22×C151semidirect
267. #557C22×C151semidirect
294. #332C22×C151semidirect
295. #331C22×C151semidirect
296. Q8⋊C8C22×C151semidirect
297. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3507×C1512
#3208×C1512
#3205×C1512
C2×#460×C1512
#1626×C1512
#1620×C1512
#1540×C1512
#1481×C1512
#1479×C1512
#18896151