Finite Group Databasebeta

← C151×#18938 #50323863

Subgroups — C151×#18938 #50323863

Order 38656.

892 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C151C211yesmaximal, characteristic, complemented
2#3246×C151C211yesmaximal, characteristic, complemented
3#3216×C151C211yesmaximal, characteristic, complemented
4#3207×C151C211yesmaximal, characteristic
5#1645×C151C212yesmaximal, complemented
6#1640×C151C212yesmaximal, complemented
7#1623×C151C212yesmaximal, complemented
8#1620×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1497×C151C211yesmaximal, characteristic, complemented
11#1481×C151C211yesmaximal, characteristic, complemented
12#563×C151—22no—
13#559×C151C2212yes—
14Q82×C151C2212yes—
15#556×C151—21no—
16#556×C151—21no—
17D4×Q8×C151—21no—
18D4×Q8×C151—21no—
19#542×C151—22no—
20#542×C151—22no—
21#536×C151—22no—
22#533×C151C2211yescharacteristic
23#533×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#497×C151—21no—
27#493×C151C2211yescharacteristic
28#492×C151C2211yescharacteristic
29#489×C151—21no—
30#487×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#476×C151—21no—
33#475×C151C2212yes—
34#465×C151—22no—
35#463×C151—22no—
36#462×C151C2212yes—
37#461×C151—21no—
38#460×C151C2212yes—
39#460×C151C2212yes—
40#452×C151—22no—
41#449×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45#333×C151C2212yes—
46#331×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C2×#41×C151D412yes—
53C22×Q8×C151—22no—
54C2×Q16×C151—22no—
55C2×SD16×C151—22no—
56C2×SD16×C151—22no—
57C2×SD16×C151—22no—
58C2×D8×C151—22no—
59C22×C8×C151—21no—
60C4⋊Q8×C151—22no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—24no—
63C4⋊Q8×C151D411yescharacteristic
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151D411yescharacteristic
67C4⋊Q8×C151C2311yescharacteristic
68C4⋊Q8×C151C2311yescharacteristic
69#127×C151C2311yescharacteristic
70#127×C151C2311yescharacteristic
71#126×C151—24no—
72#126×C151—24no—
73#125×C151—21no—
74#125×C151—21no—
75#124×C151—24no—
76#124×C151—21no—
77#124×C151—22no—
78#124×C151—22no—
79#124×C151D412yes—
80#123×C151—24no—
81#123×C151—24no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—24no—
85C22⋊Q8×C151—24no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151D412yes—
89C22⋊Q8×C151D412yes—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151C2312yes—
99C4×Q8×C151C2312yes—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106#117×C151—22no—
107#117×C151—21no—
108#117×C151—21no—
109C2×C42×C151C2311yescharacteristic
110#106×C151—22no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151C2312yes—
114C4⋊C8×C151C2312yes—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123#97×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126#41×C151—82no—
127#41×C151—82no—
128C2×Q8×C151—24no—
129C2×Q8×C151—21no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—84no—
133C2×Q8×C151C2×D412yes—
134C2×Q8×C151C2×D412yes—
135C2×Q8×C151C2×D412yes—
136C2×D4×C151—22no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—41no—
143C2×D4×C151C2×D412yes—
144C22×C4×C151—24no—
145C22×C4×C151—22no—
146C22×C4×C151—41no—
147C22×C4×C151C2×D411yescharacteristic
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150Q16×C151—82no—
151SD16×C151—82no—
152SD16×C151—82no—
153SD16×C151—82no—
154D8×C151—82no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
157C2×C8×C151—22no—
158C2×C8×C151—22no—
159C2×C8×C151—81no—
160C4⋊C4×C151—24no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151C2×D412yes—
177C4⋊C4×C151C2×D412yes—
178C22⋊C4×C151—24no—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—22no—
183C22⋊C4×C151—22no—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—41no—
186C22⋊C4×C151—41no—
187C42×C151—24no—
188C42×C151—22no—
189C42×C151—22no—
190C42×C151C2×D411yescharacteristic
191C42×C151C2×D411yescharacteristic
192C42×C151C2×D411yescharacteristic
193C42×C151C2411yescharacteristic
194C23×C151—22no—
195C23×C151—41no—
196C23×C151#12011yescharacteristic
197Q8×C151—22no—
198Q8×C151—22no—
199Q8×C151—22no—
200Q8×C151—22no—
201Q8×C151—42no—
202Q8×C151—42no—
203Q8×C151—42no—
204Q8×C151—42no—
205Q8×C151—84no—
206D4×C151—42no—
207D4×C151—42no—
208D4×C151—42no—
209D4×C151—41no—
210D4×C151—42no—
211D4×C151—41no—
212D4×C151—41no—
213D4×C151—41no—
214D4×C151—82no—
215D4×C151—82no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—41no—
225C2×C4×C151—44no—
226C2×C4×C151—41no—
227C2×C4×C151—82no—
228C2×C4×C151—84no—
229C2×C4×C151#12011yescharacteristic
230C2×C4×C151#12011yescharacteristic
231C2×C4×C151#12011yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C8×C151—41no—
236C8×C151—41no—
237C8×C151—42no—
238C8×C151—42no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—21no—
242C22×C151—42no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—81no—
246C22×C151—81no—
247C22×C151—81no—
248C22×C151C2×#12011yescharacteristic
249C4×C151—21no—
250C4×C151—21no—
251C4×C151—21no—
252C4×C151—21no—
253C4×C151—42no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—81no—
259C4×C151#57712yes—
260C4×C151#57711yescharacteristic
261C4×C151#57811yescharacteristic
262C2×C151—41no—
263C2×C151—82no—
264C2×C151—161no—
265C2×C151#301011yescharacteristic
266C2×C151#301311yescharacteristic
267C2×C151#301911yescharacteristic
268#18938C15111yesmaximal, characteristic, direct product factor, Sylow
269C151#1893811yescharacteristic, direct product factor, Sylow
270#3550C2×C15111yescharacteristic, complemented
271#3246C2×C15111yescharacteristic, complemented
272#3216C2×C15111yescharacteristic, complemented
273#3207C2×C15111yescharacteristic
274#1645C2×C15112yescomplemented
275#1640C2×C15112yescomplemented
276#1623C2×C15112yescomplemented
277#1620C2×C15112yescomplemented
278#1551C2×C15111yescharacteristic, complemented
279#1497C2×C15111yescharacteristic, complemented
280#1481C2×C15111yescharacteristic, complemented
281#563—22no—
282#559C22×C15112yes—
283Q82C22×C15112yes—
284#556—21no—
285#556—21no—
286D4×Q8—21no—
287D4×Q8—21no—
288#542—22no—
289#542—22no—
290#536—22no—
291#533C22×C15111yescharacteristic
292#533C22×C15111yescharacteristic
293#532C22×C15111yescharacteristic
294#532C22×C15111yescharacteristic
295#497—21no—
296#493C22×C15111yescharacteristic
297#492C22×C15111yescharacteristic
298#489—21no—
299#487C22×C15111yescharacteristic
300#486C22×C15111yescharacteristic
301#476—21no—
302#475C22×C15112yes—
303#465—22no—
304#463—22no—
305#462C22×C15112yes—
306#461—21no—
307#460C22×C15112yes—
308#460C22×C15112yes—
309#452—22no—
310#449—22no—
311#432C22×C15111yescharacteristic
312#431C22×C15111yescharacteristic
313C2×C4⋊C8C22×C15111yescharacteristic
314#333C22×C15112yes—
315#331C22×C15112yes—
316Q8⋊C8C22×C15112yes—
317Q8⋊C8C22×C15112yes—
318Q8⋊C8C22×C15112yes—
319Q8⋊C8C22×C15112yes—
320C2×#41—21no—
321C2×#41D4×C15112yes—
322C22×Q8—22no—
323C2×Q16—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×D8—22no—
328C22×C8—21no—
329C4⋊Q8—24no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8D4×C15111yescharacteristic
333C4⋊Q8D4×C15111yescharacteristic
334C4⋊Q8D4×C15111yescharacteristic
335C4⋊Q8D4×C15111yescharacteristic
336C4⋊Q8C23×C15111yescharacteristic
337C4⋊Q8C23×C15111yescharacteristic
338#127C23×C15111yescharacteristic
339#127C23×C15111yescharacteristic
340#126—24no—
341#126—24no—
342#125—21no—
343#125—21no—
344#124—24no—
345#124—22no—
346#124—22no—
347#124—21no—
348#124D4×C15112yes—
349#123—24no—
350#123—24no—
351C22⋊Q8—22no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8D4×C15112yes—
358C22⋊Q8D4×C15112yes—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C15112yes—
368C4×Q8C23×C15112yes—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375#117—22no—
376#117—21no—
377#117—21no—
378C2×C42C23×C15111yescharacteristic
379#106—22no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8C23×C15112yes—
383C4⋊C8C23×C15112yes—
384#103—22no—
385#103—22no—
386#103—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392#97—21no—
393C4×C8C23×C15111yescharacteristic
394C4×C8C23×C15111yescharacteristic
395#41—82no—
396#41—82no—
397C2×Q8—24no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—84no—
402C2×Q8C2×D4×C15112yes—
403C2×Q8C2×D4×C15112yes—
404C2×Q8C2×D4×C15112yes—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4C2×D4×C15112yes—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—41no—
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C2×D4×C15111yescharacteristic
419Q16—82no—
420SD16—82no—
421SD16—82no—
422SD16—82no—
423D8—82no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—81no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4C2×D4×C15112yes—
446C4⋊C4C2×D4×C15112yes—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C42—24no—
457C42—22no—
458C42—22no—
459C42C2×D4×C15111yescharacteristic
460C42C2×D4×C15111yescharacteristic
461C42C2×D4×C15111yescharacteristic
462C42C24×C15111yescharacteristic
463C23—22no—
464C23—41no—
465C23#120×C15111yescharacteristic
466Q8—22no—
467Q8—22no—
468Q8—22no—
469Q8—22no—
470Q8—42no—
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—84no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—41no—
479D4—41no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—82no—
484D4—82no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—41no—
496C2×C4—82no—
497C2×C4—84no—
498C2×C4#120×C15111yescharacteristic
499C2×C4#120×C15111yescharacteristic
500C2×C4#120×C15111yescharacteristic
501C2×C4C22×D4×C15111yescharacteristic
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C22×D4×C15111yescharacteristic
504C8—41no—
505C8—41no—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C2×#120×C15111yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—81no—
528C4#577×C15112yes—
529C4#577×C15111yescharacteristic
530C4#578×C15111yescharacteristic
531C2—41no—
532C2—82no—
533C2—161no—
534C2#3010×C15111yescharacteristic
535C2#3013×C15111yescharacteristic
536C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3207×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. #3550×C151C2semidirect
2. #3246×C151C2semidirect
3. #3216×C151C2semidirect
5. #1645×C151C2semidirect
6. #1640×C151C2semidirect
7. #1623×C151C2semidirect
8. #1620×C151C2semidirect
9. #1551×C151C2semidirect
10. #1497×C151C2semidirect
11. #1481×C151C2semidirect
268. #18938C151direct (N × H)
269. C151#18938direct (N × H)
270. #3550C2×C151semidirect
271. #3246C2×C151semidirect
272. #3216C2×C151semidirect
274. #1645C2×C151semidirect
275. #1640C2×C151semidirect
276. #1623C2×C151semidirect
277. #1620C2×C151semidirect
278. #1551C2×C151semidirect
279. #1497C2×C151semidirect
280. #1481C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3550×C1512
#3246×C1512
#3216×C1512
#3207×C1512
#1645×C1512
#1640×C1512
#1623×C1512
#1620×C1512
#1551×C1512
#1497×C1512
#1481×C1512
#18938151