Finite Group Databasebeta

← C151×#19815 #50324740

Subgroups — C151×#19815 #50324740

Order 38656.

580 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#3395×C151C211yesmaximal, characteristic, complemented
2#3386×C151C211yesmaximal, characteristic
3#3381×C151C211yesmaximal, characteristic
4#3299×C151C211yesmaximal, characteristic
5#1723×C151C211yesmaximal, characteristic, complemented
6#1692×C151C211yesmaximal, characteristic, complemented
7#1684×C151C211yesmaximal, characteristic, complemented
8#1674×C151C211yesmaximal, characteristic, complemented
9#1669×C151C211yesmaximal, characteristic
10#1649×C151C211yesmaximal, characteristic
11#1648×C151C211yesmaximal, characteristic, complemented
12#1644×C151C211yesmaximal, characteristic
13#1636×C151C211yesmaximal, characteristic, complemented
14#1584×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic
16#557×C151C2211yescharacteristic
17#557×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19D4×Q8×C151C2211yescharacteristic
20#501×C151—21no—
21#500×C151C2211yescharacteristic
22#500×C151C2211yescharacteristic
23#499×C151—21no—
24#498×C151C2211yescharacteristic
25#494×C151—21no—
26#494×C151C2211yescharacteristic
27#487×C151C2211yescharacteristic
28#487×C151C2211yescharacteristic
29#484×C151—21no—
30#479×C151—21no—
31#478×C151—21no—
32#478×C151—21no—
33#477×C151—21no—
34#477×C151C2211yescharacteristic
35#477×C151C2211yescharacteristic
36#475×C151C2211yescharacteristic
37#474×C151C2211yescharacteristic
38#474×C151C2211yescharacteristic
39#467×C151—21no—
40#462×C151—21no—
41#462×C151—21no—
42#462×C151C2211yescharacteristic
43#462×C151C2211yescharacteristic
44#462×C151C2211yescharacteristic
45#451×C151—21no—
46#446×C151C2211yescharacteristic
47C8×Q8×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#440×C151—21no—
50C4×Q16×C151—21no—
51C4×Q16×C151C2211yescharacteristic
52C4×SD16×C151—21no—
53C4×SD16×C151C2211yescharacteristic
54C8×D4×C151C2211yescharacteristic
55C2×#103×C151—21no—
56#335×C151C2211yescharacteristic
57#335×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64Q8⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C22×Q8×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—21no—
70C2×Q16×C151—21no—
71C2×Q16×C151—21no—
72C2×Q16×C151—21no—
73C2×Q16×C151D411yescharacteristic
74C2×SD16×C151D411yescharacteristic
75C22×C8×C151—21no—
76C4⋊Q8×C151—21no—
77C4⋊Q8×C151—21no—
78C4⋊Q8×C151—21no—
79C4⋊Q8×C151C2311yescharacteristic
80C4⋊Q8×C151C2311yescharacteristic
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83#125×C151—21no—
84#125×C151—21no—
85#125×C151—21no—
86#125×C151—41no—
87#125×C151—41no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151—41no—
91C22⋊Q8×C151—41no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151C2311yescharacteristic
97C4×Q8×C151C2311yescharacteristic
98C4×Q8×C151C2311yescharacteristic
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151C2311yescharacteristic
102C2×C4⋊C4×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#107×C151—21no—
106#107×C151—21no—
107#107×C151—21no—
108#107×C151—21no—
109#107×C151—41no—
110#107×C151D411yescharacteristic
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151D411yescharacteristic
115C4⋊C8×C151—21no—
116C4⋊C8×C151—21no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121C4⋊C8×C151C2311yescharacteristic
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—21no—
128#103×C151—21no—
129#103×C151—21no—
130#103×C151—41no—
131#103×C151D411yescharacteristic
132#103×C151D411yescharacteristic
133#103×C151D411yescharacteristic
134#102×C151—21no—
135#102×C151—21no—
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138#97×C151—21no—
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151C2311yescharacteristic
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—42no—
150C2×Q8×C151—81no—
151C2×Q8×C151C2×D411yescharacteristic
152C2×Q8×C151C2×D411yescharacteristic
153C2×Q8×C151C2×D411yescharacteristic
154C2×D4×C151C2×D411yescharacteristic
155C22×C4×C151—21no—
156C22×C4×C151—41no—
157C22×C4×C151—41no—
158Q16×C151—41no—
159Q16×C151—42no—
160Q16×C151—81no—
161Q16×C151—81no—
162Q16×C151—81no—
163Q16×C151—81no—
164SD16×C151Q1614yescomplemented
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—81no—
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—41no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151—41no—
194C4⋊C4×C151—41no—
195C4⋊C4×C151C2×D411yescharacteristic
196C4⋊C4×C151C2×D411yescharacteristic
197C4⋊C4×C151C2×D411yescharacteristic
198C4⋊C4×C151C2×D411yescharacteristic
199C22⋊C4×C151—21no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—41no—
206C42×C151—41no—
207C42×C151C2411yescharacteristic
208C23×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—41no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—81no—
221Q8×C151—82no—
222Q8×C151C2×Q1612yes—
223D4×C151—21no—
224D4×C151C2×Q1612yes—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—82no—
239C2×C4×C151—161no—
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151H(5,𝔽2)11yescharacteristic
243C8×C151—21no—
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—41no—
247C8×C151—41no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151C2×Q1612yes—
252C22×C151—22no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151D4211yescharacteristic
256C4×C151—22no—
257C4×C151—21no—
258C4×C151—41no—
259C4×C151—41no—
260C4×C151—41no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—41no—
264C4×C151—81no—
265C4×C151—81no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151C22×Q1611yescharacteristic
269C4×C151#57511yescharacteristic
270C4×C151#57611yescharacteristic
271C4×C151#57811yescharacteristic
272C2×C151—42no—
273C2×C151#326811yescharacteristic
274C2×C151D4×Q1611yescharacteristic
275C2×C151#328911yescharacteristic
276#19815C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#1981511yescharacteristic, direct product factor, Sylow
278#3395C2×C15111yescharacteristic, complemented
279#3386C2×C15111yescharacteristic
280#3381C2×C15111yescharacteristic
281#3299C2×C15111yescharacteristic
282#1723C2×C15111yescharacteristic, complemented
283#1692C2×C15111yescharacteristic, complemented
284#1684C2×C15111yescharacteristic, complemented
285#1674C2×C15111yescharacteristic, complemented
286#1669C2×C15111yescharacteristic
287#1649C2×C15111yescharacteristic
288#1648C2×C15111yescharacteristic, complemented
289#1644C2×C15111yescharacteristic
290#1636C2×C15111yescharacteristic, complemented
291#1584C2×C15111yescharacteristic, complemented
292SD16⋊C8C2×C15111yescharacteristic
293#557C22×C15111yescharacteristic
294#557C22×C15111yescharacteristic
295#554C22×C15111yescharacteristic
296D4×Q8C22×C15111yescharacteristic
297#501—21no—
298#500C22×C15111yescharacteristic
299#500C22×C15111yescharacteristic
300#499—21no—
301#498C22×C15111yescharacteristic
302#494—21no—
303#494C22×C15111yescharacteristic
304#487C22×C15111yescharacteristic
305#487C22×C15111yescharacteristic
306#484—21no—
307#479—21no—
308#478—21no—
309#478—21no—
310#477—21no—
311#477C22×C15111yescharacteristic
312#477C22×C15111yescharacteristic
313#475C22×C15111yescharacteristic
314#474C22×C15111yescharacteristic
315#474C22×C15111yescharacteristic
316#467—21no—
317#462—21no—
318#462—21no—
319#462C22×C15111yescharacteristic
320#462C22×C15111yescharacteristic
321#462C22×C15111yescharacteristic
322#451—21no—
323#446C22×C15111yescharacteristic
324C8×Q8C22×C15111yescharacteristic
325C8×Q8C22×C15111yescharacteristic
326#440—21no—
327C4×Q16—21no—
328C4×Q16C22×C15111yescharacteristic
329C4×SD16—21no—
330C4×SD16C22×C15111yescharacteristic
331C8×D4C22×C15111yescharacteristic
332C2×#103—21no—
333#335C22×C15111yescharacteristic
334#335C22×C15111yescharacteristic
335#333C22×C15111yescharacteristic
336#332C22×C15111yescharacteristic
337#332C22×C15111yescharacteristic
338#332C22×C15111yescharacteristic
339Q8⋊C8C22×C15111yescharacteristic
340Q8⋊C8C22×C15111yescharacteristic
341Q8⋊C8C22×C15111yescharacteristic
342D4⋊C8C22×C15111yescharacteristic
343#322C22×C15111yescharacteristic
344C22×Q8—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—21no—
350C2×Q16D4×C15111yescharacteristic
351C2×SD16D4×C15111yescharacteristic
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8C23×C15111yescharacteristic
357C4⋊Q8C23×C15111yescharacteristic
358C4⋊Q8C23×C15111yescharacteristic
359C4⋊Q8C23×C15111yescharacteristic
360#125—21no—
361#125—21no—
362#125—21no—
363#125—41no—
364#125—41no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C15111yescharacteristic
374C4×Q8C23×C15111yescharacteristic
375C4×Q8C23×C15111yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C23×C15111yescharacteristic
379C2×C4⋊C4—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—41no—
387#107D4×C15111yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C15111yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C15111yescharacteristic
396C4⋊C8C23×C15111yescharacteristic
397C4⋊C8C23×C15111yescharacteristic
398C4⋊C8C23×C15111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C15111yescharacteristic
409#103D4×C15111yescharacteristic
410#103D4×C15111yescharacteristic
411#102—21no—
412#102—21no—
413#102D4×C15111yescharacteristic
414C22⋊C8—21no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C15111yescharacteristic
419C4×C8C23×C15111yescharacteristic
420C4×C8C23×C15111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—42no—
427C2×Q8—81no—
428C2×Q8C2×D4×C15111yescharacteristic
429C2×Q8C2×D4×C15111yescharacteristic
430C2×Q8C2×D4×C15111yescharacteristic
431C2×D4C2×D4×C15111yescharacteristic
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435Q16—41no—
436Q16—42no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440Q16—81no—
441SD16Q16×C15114yescomplemented
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
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—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C15111yescharacteristic
473C4⋊C4C2×D4×C15111yescharacteristic
474C4⋊C4C2×D4×C15111yescharacteristic
475C4⋊C4C2×D4×C15111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42C24×C15111yescharacteristic
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—81no—
498Q8—82no—
499Q8C2×Q16×C15112yes—
500D4—21no—
501D4C2×Q16×C15112yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—161no—
517C2×C4C22×D4×C15111yescharacteristic
518C2×C4C22×D4×C15111yescharacteristic
519C2×C4H(5,𝔽2)×C15111yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8C2×Q16×C15112yes—
529C22—22no—
530C22—41no—
531C22—41no—
532C22D42×C15111yescharacteristic
533C4—22no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4C22×Q16×C15111yescharacteristic
546C4#575×C15111yescharacteristic
547C4#576×C15111yescharacteristic
548C4#578×C15111yescharacteristic
549C2—42no—
550C2#3268×C15111yescharacteristic
551C2D4×Q16×C15111yescharacteristic
552C2#3289×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×D4×C151C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3395×C151C2semidirect
5. #1723×C151C2semidirect
6. #1692×C151C2semidirect
7. #1684×C151C2semidirect
8. #1674×C151C2semidirect
11. #1648×C151C2semidirect
13. #1636×C151C2semidirect
14. #1584×C151C2semidirect
164. SD16×C151Q16semidirect
276. #19815C151direct (N × H)
277. C151#19815direct (N × H)
278. #3395C2×C151semidirect
282. #1723C2×C151semidirect
283. #1692C2×C151semidirect
284. #1684C2×C151semidirect
285. #1674C2×C151semidirect
288. #1648C2×C151semidirect
290. #1636C2×C151semidirect
291. #1584C2×C151semidirect
441. SD16Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3395×C1512
#3386×C1512
#3381×C1512
#3299×C1512
#1723×C1512
#1692×C1512
#1684×C1512
#1674×C1512
#1669×C1512
#1649×C1512
#1648×C1512
#1644×C1512
#1636×C1512
#1584×C1512
SD16⋊C8×C1512
#19815151