Finite Group Databasebeta

← C151×#19379 #50324304

Subgroups — C151×#19379 #50324304

Order 38656.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3252×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic
3#3165×C151C211yesmaximal, characteristic, complemented
4#2969×C151C211yesmaximal, characteristic
5#1696×C151C211yesmaximal, characteristic, complemented
6#1695×C151C211yesmaximal, characteristic, complemented
7#1692×C151C211yesmaximal, characteristic, complemented
8#1691×C151C211yesmaximal, characteristic, complemented
9#1676×C151C211yesmaximal, characteristic, complemented
10#1675×C151C211yesmaximal, characteristic, complemented
11#1672×C151C211yesmaximal, characteristic, complemented
12#1671×C151C211yesmaximal, characteristic, complemented
13#1569×C151C211yesmaximal, characteristic, complemented
14#1554×C151C211yesmaximal, characteristic, complemented
15#1548×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#501×C151—21no—
20#501×C151—21no—
21#501×C151—21no—
22#500×C151C2211yescharacteristic
23#500×C151C2211yescharacteristic
24#498×C151C2211yescharacteristic
25#498×C151C2211yescharacteristic
26#489×C151—21no—
27#483×C151—21no—
28#480×C151—21no—
29#479×C151—21no—
30#477×C151C2211yescharacteristic
31#477×C151C2211yescharacteristic
32#477×C151C2211yescharacteristic
33#476×C151C2211yescharacteristic
34#476×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#470×C151—21no—
37#468×C151—21no—
38#464×C151—21no—
39#462×C151C2211yescharacteristic
40#461×C151C2211yescharacteristic
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43#436×C151—21no—
44#436×C151C2211yescharacteristic
45#435×C151—21no—
46C8×D4×C151C2211yescharacteristic
47#433×C151—21no—
48#432×C151C2211yescharacteristic
49#431×C151C2211yescharacteristic
50#428×C151—21no—
51#428×C151—21no—
52#423×C151C2211yescharacteristic
53#405×C151—21no—
54C4×M16×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#333×C151C2211yescharacteristic
62#333×C151C2211yescharacteristic
63#333×C151C2211yescharacteristic
64#333×C151C2211yescharacteristic
65#332×C151C2211yescharacteristic
66#332×C151C2211yescharacteristic
67C22×Q8×C151—21no—
68C2×Q16×C151—21no—
69C2×SD16×C151—21no—
70C2×M16×C151—21no—
71C2×M16×C151—21no—
72C2×M16×C151D411yescharacteristic
73C2×M16×C151D411yescharacteristic
74C22×C8×C151—21no—
75C4⋊Q8×C151—21no—
76C4⋊Q8×C151—21no—
77C4⋊Q8×C151—21no—
78C4⋊Q8×C151C2311yescharacteristic
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82#126×C151—21no—
83#125×C151—21no—
84#125×C151D411yescharacteristic
85#124×C151D411yescharacteristic
86#123×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151D411yescharacteristic
90#121×C151D411yescharacteristic
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151C2311yescharacteristic
94C4×D4×C151—21no—
95C4×D4×C151C2311yescharacteristic
96#117×C151—21no—
97#117×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—21no—
102#107×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151—21no—
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115C4⋊C8×C151—21no—
116C4⋊C8×C151—21no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136#97×C151—21no—
137#97×C151—21no—
138#97×C151D411yescharacteristic
139#97×C151D411yescharacteristic
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144C2×Q8×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—41no—
149C2×Q8×C151—82no—
150C2×Q8×C151C2×D411yescharacteristic
151C2×D4×C151—21no—
152C2×D4×C151C2×D411yescharacteristic
153C22×C4×C151—21no—
154C22×C4×C151—41no—
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151#4111yescharacteristic
158Q16×C151—81no—
159SD16×C151—81no—
160M16×C151—22no—
161M16×C151—22no—
162M16×C151—42no—
163M16×C151—81no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—42no—
171C2×C8×C151C2×D411yescharacteristic
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—41no—
199C42×C151—21no—
200C42×C151—41no—
201C42×C151C2×D411yescharacteristic
202C42×C151C2×D411yescharacteristic
203C42×C151#4111yescharacteristic
204C42×C151C2411yescharacteristic
205C23×C151—21no—
206C23×C151#12111yescharacteristic
207Q8×C151—21no—
208Q8×C151—21no—
209Q8×C151—41no—
210Q8×C151—41no—
211Q8×C151—81no—
212Q8×C151—81no—
213Q8×C151—81no—
214Q8×C151—82no—
215D4×C151—21no—
216D4×C151—21no—
217D4×C151—81no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—41no—
226C2×C4×C151—41no—
227C2×C4×C151—41no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—82no—
233C2×C4×C151#12111yescharacteristic
234C2×C4×C151#12111yescharacteristic
235C2×C4×C151#12111yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C2×#4111yescharacteristic
239C8×C151—21no—
240C8×C151—21no—
241C8×C151—41no—
242C8×C151—41no—
243C8×C151—41no—
244C8×C151—41no—
245C8×C151—41no—
246C8×C151—41no—
247C8×C151#13712yes—
248C8×C151#13712yes—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—41no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151C2×#12111yescharacteristic
256C4×C151—21no—
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—21no—
260C4×C151—41no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—81no—
264C4×C151—81no—
265C4×C151—81no—
266C4×C151—81no—
267C4×C151C2×#13711yescharacteristic
268C4×C151C2×#13711yescharacteristic
269C4×C151#57711yescharacteristic
270C4×C151#57811yescharacteristic
271C2×C151—41no—
272C2×C151—81no—
273C2×C151#303911yescharacteristic
274C2×C151#306311yescharacteristic
275C2×C151#306811yescharacteristic
276#19379C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#1937911yescharacteristic, direct product factor, Sylow
278#3252C2×C15111yescharacteristic
279#3238C2×C15111yescharacteristic
280#3165C2×C15111yescharacteristic, complemented
281#2969C2×C15111yescharacteristic
282#1696C2×C15111yescharacteristic, complemented
283#1695C2×C15111yescharacteristic, complemented
284#1692C2×C15111yescharacteristic, complemented
285#1691C2×C15111yescharacteristic, complemented
286#1676C2×C15111yescharacteristic, complemented
287#1675C2×C15111yescharacteristic, complemented
288#1672C2×C15111yescharacteristic, complemented
289#1671C2×C15111yescharacteristic, complemented
290#1569C2×C15111yescharacteristic, complemented
291#1554C2×C15111yescharacteristic, complemented
292#1548C2×C15111yescharacteristic, complemented
293#533C22×C15111yescharacteristic
294C2×C4⋊Q8C22×C15111yescharacteristic
295#529C22×C15111yescharacteristic
296#501—21no—
297#501—21no—
298#501—21no—
299#500C22×C15111yescharacteristic
300#500C22×C15111yescharacteristic
301#498C22×C15111yescharacteristic
302#498C22×C15111yescharacteristic
303#489—21no—
304#483—21no—
305#480—21no—
306#479—21no—
307#477C22×C15111yescharacteristic
308#477C22×C15111yescharacteristic
309#477C22×C15111yescharacteristic
310#476C22×C15111yescharacteristic
311#476C22×C15111yescharacteristic
312#476C22×C15111yescharacteristic
313#470—21no—
314#468—21no—
315#464—21no—
316#462C22×C15111yescharacteristic
317#461C22×C15111yescharacteristic
318#446C22×C15111yescharacteristic
319C8×Q8C22×C15111yescharacteristic
320#436—21no—
321#436C22×C15111yescharacteristic
322#435—21no—
323C8×D4C22×C15111yescharacteristic
324#433—21no—
325#432C22×C15111yescharacteristic
326#431C22×C15111yescharacteristic
327#428—21no—
328#428—21no—
329#423C22×C15111yescharacteristic
330#405—21no—
331C4×M16C22×C15111yescharacteristic
332#335C22×C15111yescharacteristic
333#335C22×C15111yescharacteristic
334#334C22×C15111yescharacteristic
335#334C22×C15111yescharacteristic
336#333C22×C15111yescharacteristic
337#333C22×C15111yescharacteristic
338#333C22×C15111yescharacteristic
339#333C22×C15111yescharacteristic
340#333C22×C15111yescharacteristic
341#333C22×C15111yescharacteristic
342#332C22×C15111yescharacteristic
343#332C22×C15111yescharacteristic
344C22×Q8—21no—
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16D4×C15111yescharacteristic
350C2×M16D4×C15111yescharacteristic
351C22×C8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C15111yescharacteristic
356C4⋊Q8C23×C15111yescharacteristic
357C4⋊Q8C23×C15111yescharacteristic
358C4⋊Q8C23×C15111yescharacteristic
359#126—21no—
360#125—21no—
361#125D4×C15111yescharacteristic
362#124D4×C15111yescharacteristic
363#123—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8D4×C15111yescharacteristic
367#121D4×C15111yescharacteristic
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C23×C15111yescharacteristic
371C4×D4—21no—
372C4×D4C23×C15111yescharacteristic
373#117—21no—
374#117—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C42C23×C15111yescharacteristic
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398C4⋊C8C23×C15111yescharacteristic
399C4⋊C8C23×C15111yescharacteristic
400C4⋊C8C23×C15111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#102—21no—
407#102—21no—
408#102—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97—21no—
415#97D4×C15111yescharacteristic
416#97D4×C15111yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8C23×C15111yescharacteristic
420C4×C8C23×C15111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×D4×C15111yescharacteristic
428C2×D4—21no—
429C2×D4C2×D4×C15111yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434C22×C4#41×C15111yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—22no—
439M16—42no—
440M16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8C2×D4×C15111yescharacteristic
449C2×C8C2×D4×C15111yescharacteristic
450C2×C8C2×D4×C15111yescharacteristic
451C2×C8C2×D4×C15111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C15111yescharacteristic
469C4⋊C4C2×D4×C15111yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C42—21no—
477C42—41no—
478C42C2×D4×C15111yescharacteristic
479C42C2×D4×C15111yescharacteristic
480C42#41×C15111yescharacteristic
481C42C24×C15111yescharacteristic
482C23—21no—
483C23#121×C15111yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491Q8—82no—
492D4—21no—
493D4—21no—
494D4—81no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4#121×C15111yescharacteristic
511C2×C4#121×C15111yescharacteristic
512C2×C4#121×C15111yescharacteristic
513C2×C4C22×D4×C15111yescharacteristic
514C2×C4C22×D4×C15111yescharacteristic
515C2×C4C2×#41×C15111yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8#137×C15112yes—
525C8#137×C15112yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22C2×#121×C15111yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4C2×#137×C15111yescharacteristic
545C4C2×#137×C15111yescharacteristic
546C4#577×C15111yescharacteristic
547C4#578×C15111yescharacteristic
548C2—41no—
549C2—81no—
550C2#3039×C15111yescharacteristic
551C2#3063×C15111yescharacteristic
552C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#121×C151D4
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
3. #3165×C151C2semidirect
5. #1696×C151C2semidirect
6. #1695×C151C2semidirect
7. #1692×C151C2semidirect
8. #1691×C151C2semidirect
9. #1676×C151C2semidirect
10. #1675×C151C2semidirect
11. #1672×C151C2semidirect
12. #1671×C151C2semidirect
13. #1569×C151C2semidirect
14. #1554×C151C2semidirect
15. #1548×C151C2semidirect
276. #19379C151direct (N × H)
277. C151#19379direct (N × H)
280. #3165C2×C151semidirect
282. #1696C2×C151semidirect
283. #1695C2×C151semidirect
284. #1692C2×C151semidirect
285. #1691C2×C151semidirect
286. #1676C2×C151semidirect
287. #1675C2×C151semidirect
288. #1672C2×C151semidirect
289. #1671C2×C151semidirect
290. #1569C2×C151semidirect
291. #1554C2×C151semidirect
292. #1548C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3252×C1512
#3238×C1512
#3165×C1512
#2969×C1512
#1696×C1512
#1695×C1512
#1692×C1512
#1691×C1512
#1676×C1512
#1675×C1512
#1672×C1512
#1671×C1512
#1569×C1512
#1554×C1512
#1548×C1512
#19379151