Finite Group Databasebeta

← C151×#19053 #50323978

Subgroups — C151×#19053 #50323978

Order 38656.

994 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic, complemented
2#3235×C151C211yesmaximal, characteristic, complemented
3#3214×C151C211yesmaximal, characteristic, complemented
4#3150×C151C211yesmaximal, characteristic, complemented
5#1661×C151C214yesmaximal, complemented
6#1656×C151C214yesmaximal, complemented
7#1536×C151C211yesmaximal, characteristic, complemented
8#1531×C151C211yesmaximal, characteristic, complemented
9#1530×C151C211yesmaximal, characteristic, complemented
10C2×#135×C151—22no—
11#562×C151C2214yes—
12#554×C151—21no—
13#554×C151—21no—
14#550×C151—21no—
15#550×C151—21no—
16#547×C151—21no—
17#547×C151—21no—
18#540×C151—22no—
19#537×C151—22no—
20#537×C151—22no—
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#501×C151C2212yes—
26#497×C151—21no—
27#497×C151C2212yes—
28#496×C151—21no—
29#496×C151C2212yes—
30#496×C151C2212yes—
31#490×C151C2212yes—
32#489×C151C2212yes—
33#482×C151—22no—
34#476×C151—21no—
35#474×C151—21no—
36#461×C151—21no—
37#459×C151—21no—
38#449×C151—22no—
39#432×C151C2211yescharacteristic
40#432×C151C2211yescharacteristic
41C2×#97×C151C2211yescharacteristic
42#330×C151C2214yes—
43#329×C151C2214yes—
44#329×C151C2214yes—
45C2×#41×C151—21no—
46C2×#41×C151—22no—
47C2×#41×C151—22no—
48C2×#41×C151D412yes—
49C2×#41×C151D412yes—
50#135×C151—48no—
51C2×Q16×C151—22no—
52C2×SD16×C151—22no—
53C2×SD16×C151—22no—
54C2×SD16×C151—22no—
55C2×D8×C151—22no—
56C2×D8×C151—22no—
57C22×C8×C151—21no—
58C4⋊Q8×C151D411yescharacteristic
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63#127×C151—22no—
64#127×C151D411yescharacteristic
65#127×C151D411yescharacteristic
66#127×C151C2311yescharacteristic
67#125×C151—22no—
68#125×C151C2312yes—
69#124×C151—21no—
70#124×C151C2312yes—
71#124×C151C2312yes—
72#123×C151—24no—
73#123×C151—24no—
74C22⋊Q8×C151—22no—
75C22⋊Q8×C151—22no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—24no—
79C22⋊Q8×C151—24no—
80#121×C151—24no—
81#121×C151—24no—
82#121×C151—22no—
83#121×C151—22no—
84#121×C151—24no—
85#121×C151—24no—
86#121×C151—21no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102#117×C151D412yes—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—22no—
105C2×C42×C151C2311yescharacteristic
106#107×C151—22no—
107#106×C151—22no—
108C4⋊C8×C151—21no—
109C4⋊C8×C151—21no—
110#103×C151—22no—
111#102×C151—22no—
112#102×C151—22no—
113#102×C151—22no—
114C22⋊C8×C151—21no—
115C22⋊C8×C151—21no—
116#97×C151—21no—
117#97×C151C2312yes—
118#97×C151C2312yes—
119#97×C151C2312yes—
120#41×C151—44no—
121#41×C151—44no—
122#41×C151—82no—
123#41×C151—84no—
124#41×C151—84no—
125C2×Q8×C151—21no—
126C2×Q8×C151—21no—
127C2×Q8×C151—21no—
128C2×Q8×C151C2×D412yes—
129C2×Q8×C151C2×D412yes—
130C2×D4×C151—24no—
131C2×D4×C151—24no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—21no—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—41no—
142C2×D4×C151C2×D412yes—
143C2×D4×C151C2×D412yes—
144C22×C4×C151—24no—
145C22×C4×C151—24no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—41no—
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152Q16×C151—44no—
153SD16×C151—44no—
154SD16×C151—44no—
155SD16×C151—82no—
156D8×C151—44no—
157D8×C151—82no—
158C2×C8×C151—24no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151—22no—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—24no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151C2×D412yes—
175C4⋊C4×C151C2×D412yes—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—24no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—22no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—22no—
183C22⋊C4×C151—41no—
184C22⋊C4×C151—41no—
185C42×C151—22no—
186C42×C151C2×D411yescharacteristic
187C42×C151C2×D411yescharacteristic
188C42×C151C2×D411yescharacteristic
189C42×C151C2411yescharacteristic
190C23×C151—22no—
191C23×C151—22no—
192C23×C151—41no—
193C23×C151#12011yescharacteristic
194Q8×C151—42no—
195Q8×C151—42no—
196Q8×C151—42no—
197Q8×C151—42no—
198Q8×C151—42no—
199D4×C151—42no—
200D4×C151—42no—
201D4×C151—42no—
202D4×C151—42no—
203D4×C151—42no—
204D4×C151—42no—
205D4×C151—41no—
206D4×C151—41no—
207D4×C151—42no—
208D4×C151—42no—
209D4×C151—82no—
210D4×C151—82no—
211D4×C151—84no—
212D4×C151—84no—
213D4×C151—82no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—41no—
220C2×C4×C151—41no—
221C2×C4×C151—44no—
222C2×C4×C151—44no—
223C2×C4×C151—41no—
224C2×C4×C151—84no—
225C2×C4×C151—84no—
226C2×C4×C151—82no—
227C2×C4×C151#12011yescharacteristic
228C2×C4×C151#12011yescharacteristic
229C2×C4×C151#12011yescharacteristic
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C22×D411yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C8×C151—24no—
234C8×C151—42no—
235C8×C151—42no—
236C22×C151—21no—
237C22×C151—21no—
238C22×C151—21no—
239C22×C151—42no—
240C22×C151—42no—
241C22×C151—42no—
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—21no—
254C4×C151—42no—
255C4×C151—42no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—81no—
259C4×C151#45312yes—
260C2×C151—41no—
261C2×C151—82no—
262C2×C151—82no—
263C2×C151—161no—
264C2×C151C2×#45311yescharacteristic
265C2×C151#301911yescharacteristic
266C2×C151#302011yescharacteristic
267#19053C15111yesmaximal, characteristic, direct product factor, Sylow
268C151#1905311yescharacteristic, direct product factor, Sylow
269#3548C2×C15111yescharacteristic, complemented
270#3235C2×C15111yescharacteristic, complemented
271#3214C2×C15111yescharacteristic, complemented
272#3150C2×C15111yescharacteristic, complemented
273#1661C2×C15114yescomplemented
274#1656C2×C15114yescomplemented
275#1536C2×C15111yescharacteristic, complemented
276#1531C2×C15111yescharacteristic, complemented
277#1530C2×C15111yescharacteristic, complemented
278C2×#135—22no—
279#562C22×C15114yes—
280#554—21no—
281#554—21no—
282#550—21no—
283#550—21no—
284#547—21no—
285#547—21no—
286#540—22no—
287#537—22no—
288#537—22no—
289#533C22×C15111yescharacteristic
290#532C22×C15111yescharacteristic
291#532C22×C15111yescharacteristic
292#532C22×C15111yescharacteristic
293#501C22×C15112yes—
294#497—21no—
295#497C22×C15112yes—
296#496—21no—
297#496C22×C15112yes—
298#496C22×C15112yes—
299#490C22×C15112yes—
300#489C22×C15112yes—
301#482—22no—
302#476—21no—
303#474—21no—
304#461—21no—
305#459—21no—
306#449—22no—
307#432C22×C15111yescharacteristic
308#432C22×C15111yescharacteristic
309C2×#97C22×C15111yescharacteristic
310#330C22×C15114yes—
311#329C22×C15114yes—
312#329C22×C15114yes—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—21no—
316C2×#41D4×C15112yes—
317C2×#41D4×C15112yes—
318#135—48no—
319C2×Q16—22no—
320C2×SD16—22no—
321C2×SD16—22no—
322C2×SD16—22no—
323C2×D8—22no—
324C2×D8—22no—
325C22×C8—21no—
326C4⋊Q8D4×C15111yescharacteristic
327C4⋊Q8D4×C15111yescharacteristic
328C4⋊Q8D4×C15111yescharacteristic
329C4⋊Q8D4×C15111yescharacteristic
330C4⋊Q8C23×C15111yescharacteristic
331#127—22no—
332#127D4×C15111yescharacteristic
333#127D4×C15111yescharacteristic
334#127C23×C15111yescharacteristic
335#125—22no—
336#125C23×C15112yes—
337#124—21no—
338#124C23×C15112yes—
339#124C23×C15112yes—
340#123—24no—
341#123—24no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—24no—
345C22⋊Q8—24no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348#121—24no—
349#121—24no—
350#121—22no—
351#121—22no—
352#121—24no—
353#121—24no—
354#121—21no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121—21no—
359#121—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370#117D4×C15112yes—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C42C23×C15111yescharacteristic
374#107—22no—
375#106—22no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378#103—22no—
379#102—22no—
380#102—22no—
381#102—22no—
382C22⋊C8—21no—
383C22⋊C8—21no—
384#97—21no—
385#97C23×C15112yes—
386#97C23×C15112yes—
387#97C23×C15112yes—
388#41—44no—
389#41—44no—
390#41—82no—
391#41—84no—
392#41—84no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8C2×D4×C15112yes—
397C2×Q8C2×D4×C15112yes—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—41no—
410C2×D4C2×D4×C15112yes—
411C2×D4C2×D4×C15112yes—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—41no—
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C2×D4×C15111yescharacteristic
419C22×C4C2×D4×C15111yescharacteristic
420Q16—44no—
421SD16—44no—
422SD16—44no—
423SD16—82no—
424D8—44no—
425D8—82no—
426C2×C8—24no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4C2×D4×C15112yes—
443C4⋊C4C2×D4×C15112yes—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C42—22no—
454C42C2×D4×C15111yescharacteristic
455C42C2×D4×C15111yescharacteristic
456C42C2×D4×C15111yescharacteristic
457C42C24×C15111yescharacteristic
458C23—22no—
459C23—22no—
460C23—41no—
461C23#120×C15111yescharacteristic
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466Q8—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—42no—
473D4—41no—
474D4—41no—
475D4—42no—
476D4—42no—
477D4—82no—
478D4—82no—
479D4—84no—
480D4—84no—
481D4—82no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—41no—
492C2×C4—84no—
493C2×C4—84no—
494C2×C4—82no—
495C2×C4#120×C15111yescharacteristic
496C2×C4#120×C15111yescharacteristic
497C2×C4#120×C15111yescharacteristic
498C2×C4C22×D4×C15111yescharacteristic
499C2×C4C22×D4×C15111yescharacteristic
500C2×C4C22×D4×C15111yescharacteristic
501C8—24no—
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22C2×#120×C15111yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—81no—
527C4#453×C15112yes—
528C2—41no—
529C2—82no—
530C2—82no—
531C2—161no—
532C2C2×#453×C15111yescharacteristic
533C2#3019×C15111yescharacteristic
534C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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. #3548×C151C2semidirect
2. #3235×C151C2semidirect
3. #3214×C151C2semidirect
4. #3150×C151C2semidirect
5. #1661×C151C2semidirect
6. #1656×C151C2semidirect
7. #1536×C151C2semidirect
8. #1531×C151C2semidirect
9. #1530×C151C2semidirect
267. #19053C151direct (N × H)
268. C151#19053direct (N × H)
269. #3548C2×C151semidirect
270. #3235C2×C151semidirect
271. #3214C2×C151semidirect
272. #3150C2×C151semidirect
273. #1661C2×C151semidirect
274. #1656C2×C151semidirect
275. #1536C2×C151semidirect
276. #1531C2×C151semidirect
277. #1530C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3235×C1512
#3214×C1512
#3150×C1512
#1661×C1512
#1656×C1512
#1536×C1512
#1531×C1512
#1530×C1512
#19053151