Finite Group Databasebeta

← C151×#18679 #50323604

Subgroups — C151×#18679 #50323604

Order 38656.

946 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C151C211yesmaximal, characteristic
2#3249×C151C211yesmaximal, characteristic, complemented
3#3167×C151C211yesmaximal, characteristic, complemented
4#3077×C151C211yesmaximal, characteristic, complemented
5#1652×C151C212yesmaximal, complemented
6#1641×C151C212yesmaximal, complemented
7#1638×C151C212yesmaximal, complemented
8#1631×C151C212yesmaximal, complemented
9#1547×C151C211yesmaximal, characteristic, complemented
10#1493×C151C211yesmaximal, characteristic, complemented
11C2×D4⋊C8×C151C211yesmaximal, characteristic, complemented
12#559×C151—22no—
13#556×C151C2212yes—
14#555×C151—21no—
15#553×C151—22no—
16#550×C151C2212yes—
17#547×C151—21no—
18#538×C151—22no—
19#535×C151—21no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23#525×C151—22no—
24#520×C151—21no—
25C2×C4×D4×C151C2211yescharacteristic
26#498×C151C2211yescharacteristic, complemented
27#492×C151C2211yescharacteristic, complemented
28#487×C151C2211yescharacteristic, complemented
29#486×C151C2211yescharacteristic, complemented
30#478×C151—22no—
31#477×C151—21no—
32#477×C151C2212yescomplemented
33#476×C151C2212yes—
34#474×C151C2212yes—
35#467×C151—22no—
36#465×C151—22no—
37#462×C151—21no—
38#462×C151C2212yescomplemented
39C4×SD16×C151—22no—
40#428×C151—21no—
41#423×C151C2211yescharacteristic
42C2×C4⋊C8×C151C2211yescharacteristic
43#418×C151—21no—
44C2×C4×C8×C151C2211yescharacteristic
45#332×C151C2212yescomplemented
46#331×C151C2212yescomplemented
47Q8⋊C8×C151C2212yescomplemented
48Q8⋊C8×C151C2212yescomplemented
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C2×#41×C151—22no—
53C22×D4×C151D411yescharacteristic
54C23×C4×C151—21no—
55C2×Q16×C151—22no—
56C2×SD16×C151—22no—
57C2×M16×C151—21no—
58C22×C8×C151—21no—
59C22×C8×C151—21no—
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65#127×C151—22no—
66#127×C151C2311yescharacteristic
67#126×C151—24no—
68#125×C151—21no—
69#125×C151—21no—
70#124×C151—24no—
71#124×C151—22no—
72#124×C151—21no—
73#123×C151—24no—
74#123×C151—24no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151D412yes—
80#121×C151—22no—
81#121×C151—22no—
82#121×C151—24no—
83#121×C151—21no—
84#121×C151—22no—
85#121×C151D412yes—
86#120×C151—24no—
87C4×Q8×C151—22no—
88C4×Q8×C151—21no—
89C4×Q8×C151—21no—
90C4×Q8×C151—21no—
91C4×Q8×C151C2312yes—
92C4×D4×C151—24no—
93C4×D4×C151—24no—
94C4×D4×C151—22no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151D412yes—
99C4×D4×C151D412yes—
100C4×D4×C151C2312yes—
101#117×C151—22no—
102#117×C151—21no—
103#117×C151—22no—
104#117×C151—21no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151D411yescharacteristic
107C2×C22⋊C4×C151—21no—
108C2×C42×C151C2311yescharacteristic
109#107×C151—22no—
110#107×C151—22no—
111#106×C151—22no—
112#106×C151—22no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151—21no—
115C4⋊C8×C151C2312yes—
116C4⋊C8×C151C2312yes—
117#103×C151—22no—
118#103×C151—22no—
119#103×C151—22no—
120#102×C151—22no—
121#102×C151—22no—
122#102×C151—22no—
123C4×C8×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126C24×C151—21no—
127#41×C151—42no—
128#41×C151—42no—
129#41×C151—82no—
130#41×C151—82no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151C2×D412yes—
136C2×D4×C151—22no—
137C2×D4×C151—24no—
138C2×D4×C151—24no—
139C2×D4×C151—21no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151C2×D412yes—
145C2×D4×C151C2×D412yes—
146C22×C4×C151—24no—
147C22×C4×C151—21no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—81no—
152C22×C4×C151—81no—
153C22×C4×C151C2×D411yescharacteristic
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156Q16×C151—82no—
157SD16×C151—44no—
158M16×C151—42no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151—42no—
164C2×C8×C151—81no—
165C4⋊C4×C151—24no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—41no—
178C4⋊C4×C151—41no—
179C4⋊C4×C151C2×D412yes—
180C4⋊C4×C151C2×D412yes—
181C4⋊C4×C151C2×D412yes—
182C22⋊C4×C151—24no—
183C22⋊C4×C151—24no—
184C22⋊C4×C151—24no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—41no—
191C42×C151—24no—
192C42×C151—22no—
193C42×C151—41no—
194C42×C151C2×D411yescharacteristic
195C42×C151C2×D411yescharacteristic
196C42×C151C2×D411yescharacteristic
197C42×C151C2411yescharacteristic
198C23×C151—22no—
199C23×C151—22no—
200C23×C151—42no—
201C23×C151—81no—
202C23×C151—81no—
203C23×C151#12011yescharacteristic
204Q8×C151—22no—
205Q8×C151—22no—
206Q8×C151—42no—
207Q8×C151—41no—
208Q8×C151—41no—
209Q8×C151—41no—
210Q8×C151—41no—
211Q8×C151—81no—
212D4×C151—22no—
213D4×C151—22no—
214D4×C151—42no—
215D4×C151—44no—
216D4×C151—41no—
217D4×C151—41no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—42no—
221D4×C151—84no—
222D4×C151—84no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—22no—
229C2×C4×C151—41no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—44no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—82no—
236C2×C4×C151—81no—
237C2×C4×C151—84no—
238C2×C4×C151#12011yescharacteristic
239C2×C4×C151#12011yescharacteristic
240C2×C4×C151#12011yescharacteristic
241C2×C4×C151#13512yes—
242C2×C4×C151#13712yes—
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C8×C151—22no—
247C8×C151—41no—
248C8×C151—42no—
249C8×C151—42no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—84no—
259C22×C151#45212yes—
260C22×C151C2×#12011yescharacteristic
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—42no—
265C4×C151—42no—
266C4×C151—42no—
267C4×C151—42no—
268C4×C151—81no—
269C4×C151—81no—
270C4×C151#45212yes—
271C4×C151C2×#13511yescharacteristic
272C4×C151C2×#13711yescharacteristic
273C4×C151#57611yescharacteristic
274C4×C151#57711yescharacteristic
275C2×C151—22no—
276C2×C151—82no—
277C2×C151—82no—
278C2×C151C2×#45211yescharacteristic
279C2×C151#301211yescharacteristic
280C2×C151#301811yescharacteristic
281#18679C15111yesmaximal, characteristic, direct product factor, Sylow
282C151#1867911yescharacteristic, direct product factor, Sylow
283#3506C2×C15111yescharacteristic
284#3249C2×C15111yescharacteristic, complemented
285#3167C2×C15111yescharacteristic, complemented
286#3077C2×C15111yescharacteristic, complemented
287#1652C2×C15112yescomplemented
288#1641C2×C15112yescomplemented
289#1638C2×C15112yescomplemented
290#1631C2×C15112yescomplemented
291#1547C2×C15111yescharacteristic, complemented
292#1493C2×C15111yescharacteristic, complemented
293C2×D4⋊C8C2×C15111yescharacteristic, complemented
294#559—22no—
295#556C22×C15112yes—
296#555—21no—
297#553—22no—
298#550C22×C15112yes—
299#547—21no—
300#538—22no—
301#535—21no—
302#533C22×C15111yescharacteristic
303#533C22×C15111yescharacteristic
304#532C22×C15111yescharacteristic
305#525—22no—
306#520—21no—
307C2×C4×D4C22×C15111yescharacteristic
308#498C22×C15111yescharacteristic, complemented
309#492C22×C15111yescharacteristic, complemented
310#487C22×C15111yescharacteristic, complemented
311#486C22×C15111yescharacteristic, complemented
312#478—22no—
313#477—21no—
314#477C22×C15112yescomplemented
315#476C22×C15112yes—
316#474C22×C15112yes—
317#467—22no—
318#465—22no—
319#462—21no—
320#462C22×C15112yescomplemented
321C4×SD16—22no—
322#428—21no—
323#423C22×C15111yescharacteristic
324C2×C4⋊C8C22×C15111yescharacteristic
325#418—21no—
326C2×C4×C8C22×C15111yescharacteristic
327#332C22×C15112yescomplemented
328#331C22×C15112yescomplemented
329Q8⋊C8C22×C15112yescomplemented
330Q8⋊C8C22×C15112yescomplemented
331D4⋊C8C22×C15112yes—
332D4⋊C8C22×C15112yes—
333C2×#41—22no—
334C2×#41—21no—
335C22×D4D4×C15111yescharacteristic
336C23×C4—21no—
337C2×Q16—22no—
338C2×SD16—22no—
339C2×M16—21no—
340C22×C8—21no—
341C22×C8—21no—
342C4⋊Q8D4×C15111yescharacteristic
343C4⋊Q8D4×C15111yescharacteristic
344C4⋊Q8C23×C15111yescharacteristic
345C4⋊Q8C23×C15111yescharacteristic
346C4⋊Q8C23×C15111yescharacteristic
347#127—22no—
348#127C23×C15111yescharacteristic
349#126—24no—
350#125—21no—
351#125—21no—
352#124—24no—
353#124—22no—
354#124—21no—
355#123—24no—
356#123—24no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8D4×C15112yes—
362#121—22no—
363#121—22no—
364#121—24no—
365#121—21no—
366#121—22no—
367#121D4×C15112yes—
368#120—24no—
369C4×Q8—22no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C15112yes—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—22no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4D4×C15112yes—
381C4×D4D4×C15112yes—
382C4×D4C23×C15112yes—
383#117—22no—
384#117—21no—
385#117—22no—
386#117—21no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4D4×C15111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C42C23×C15111yescharacteristic
391#107—22no—
392#107—22no—
393#106—22no—
394#106—22no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C15112yes—
398C4⋊C8C23×C15112yes—
399#103—22no—
400#103—22no—
401#103—22no—
402#102—22no—
403#102—22no—
404#102—22no—
405C4×C8—21no—
406C4×C8C23×C15111yescharacteristic
407C4×C8C23×C15111yescharacteristic
408C24—21no—
409#41—42no—
410#41—42no—
411#41—82no—
412#41—82no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8C2×D4×C15112yes—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×D4×C15112yes—
427C2×D4C2×D4×C15112yes—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438Q16—82no—
439SD16—44no—
440M16—42no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—42no—
446C2×C8—81no—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C15112yes—
462C4⋊C4C2×D4×C15112yes—
463C4⋊C4C2×D4×C15112yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C42—24no—
474C42—22no—
475C42—41no—
476C42C2×D4×C15111yescharacteristic
477C42C2×D4×C15111yescharacteristic
478C42C2×D4×C15111yescharacteristic
479C42C24×C15111yescharacteristic
480C23—22no—
481C23—22no—
482C23—42no—
483C23—81no—
484C23—81no—
485C23#120×C15111yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—42no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—81no—
494D4—22no—
495D4—22no—
496D4—42no—
497D4—44no—
498D4—42no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—84no—
504D4—84no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—81no—
519C2×C4—84no—
520C2×C4#120×C15111yescharacteristic
521C2×C4#120×C15111yescharacteristic
522C2×C4#120×C15111yescharacteristic
523C2×C4#135×C15112yes—
524C2×C4#137×C15112yes—
525C2×C4C22×D4×C15111yescharacteristic
526C2×C4C22×D4×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C8—22no—
529C8—41no—
530C8—42no—
531C8—42no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—84no—
541C22#452×C15112yes—
542C22C2×#120×C15111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—81no—
551C4—81no—
552C4#452×C15112yes—
553C4C2×#135×C15111yescharacteristic
554C4C2×#137×C15111yescharacteristic
555C4#576×C15111yescharacteristic
556C4#577×C15111yescharacteristic
557C2—22no—
558C2—82no—
559C2—82no—
560C2C2×#452×C15111yescharacteristic
561C2#3012×C15111yescharacteristic
562C2#3018×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3506×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
2. #3249×C151C2semidirect
3. #3167×C151C2semidirect
4. #3077×C151C2semidirect
5. #1652×C151C2semidirect
6. #1641×C151C2semidirect
7. #1638×C151C2semidirect
8. #1631×C151C2semidirect
9. #1547×C151C2semidirect
10. #1493×C151C2semidirect
11. C2×D4⋊C8×C151C2semidirect
26. #498×C151C22semidirect
27. #492×C151C22semidirect
28. #487×C151C22semidirect
29. #486×C151C22semidirect
32. #477×C151C22semidirect
38. #462×C151C22semidirect
45. #332×C151C22semidirect
46. #331×C151C22semidirect
47. Q8⋊C8×C151C22semidirect
48. Q8⋊C8×C151C22semidirect
281. #18679C151direct (N × H)
282. C151#18679direct (N × H)
284. #3249C2×C151semidirect
285. #3167C2×C151semidirect
286. #3077C2×C151semidirect
287. #1652C2×C151semidirect
288. #1641C2×C151semidirect
289. #1638C2×C151semidirect
290. #1631C2×C151semidirect
291. #1547C2×C151semidirect
292. #1493C2×C151semidirect
293. C2×D4⋊C8C2×C151semidirect
308. #498C22×C151semidirect
309. #492C22×C151semidirect
310. #487C22×C151semidirect
311. #486C22×C151semidirect
314. #477C22×C151semidirect
320. #462C22×C151semidirect
327. #332C22×C151semidirect
328. #331C22×C151semidirect
329. Q8⋊C8C22×C151semidirect
330. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3506×C1512
#3249×C1512
#3167×C1512
#3077×C1512
#1652×C1512
#1641×C1512
#1638×C1512
#1631×C1512
#1547×C1512
#1493×C1512
C2×D4⋊C8×C1512
#18679151