Finite Group Databasebeta

← C151×#19814 #50324739

Subgroups — C151×#19814 #50324739

Order 38656.

590 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3384×C151C211yesmaximal, characteristic
2#3380×C151C211yesmaximal, characteristic
3#3338×C151C211yesmaximal, characteristic, complemented
4#3299×C151C211yesmaximal, characteristic, complemented
5#1723×C151C211yesmaximal, characteristic, complemented
6#1696×C151C211yesmaximal, characteristic, complemented
7#1683×C151C211yesmaximal, characteristic, complemented
8#1675×C151C211yesmaximal, characteristic, complemented
9#1672×C151C211yesmaximal, characteristic, complemented
10#1644×C151C211yesmaximal, characteristic, complemented
11#1637×C151C211yesmaximal, characteristic, complemented
12#1632×C151C211yesmaximal, characteristic, complemented
13#1632×C151C211yesmaximal, characteristic, complemented
14#1584×C151C211yesmaximal, characteristic, complemented
15#1580×C151C211yesmaximal, characteristic
16#554×C151C2211yescharacteristic
17#554×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×C151C2211yescharacteristic
26#487×C151C2211yescharacteristic
27#487×C151C2211yescharacteristic
28#484×C151—21no—
29#484×C151—21no—
30#484×C151—21no—
31#478×C151—21no—
32#478×C151—21no—
33#478×C151—21no—
34#477×C151C2211yescharacteristic
35#477×C151C2211yescharacteristic
36#477×C151C2211yescharacteristic
37#476×C151—21no—
38#476×C151C2211yescharacteristic
39#476×C151C2211yescharacteristic
40#476×C151C2211yescharacteristic
41#474×C151C2211yescharacteristic
42#467×C151—21no—
43#467×C151—21no—
44#462×C151C2211yescharacteristic
45#451×C151—21no—
46#446×C151C2211yescharacteristic
47C8×Q8×C151C2211yescharacteristic
48#442×C151—21no—
49C4×Q16×C151C2211yescharacteristic
50C4×D8×C151—21no—
51C4×D8×C151C2211yescharacteristic
52C8×D4×C151C2211yescharacteristic
53C8×D4×C151C2211yescharacteristic
54C2×#107×C151—21no—
55C2×#103×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C22×Q8×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—41no—
70C2×Q16×C151D411yescharacteristic
71C2×D8×C151D411yescharacteristic
72C22×C8×C151—21no—
73C22×C8×C151—21no—
74C4⋊Q8×C151—21no—
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79#125×C151—21no—
80#125×C151—21no—
81#125×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—41no—
87C22⋊Q8×C151—41no—
88C22⋊Q8×C151—41no—
89C22⋊Q8×C151—41no—
90C4×Q8×C151C2311yescharacteristic
91C4×Q8×C151C2311yescharacteristic
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151C2311yescharacteristic
97C4×D4×C151C2311yescharacteristic
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
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#107×C151—21no—
109#107×C151D411yescharacteristic
110#107×C151D411yescharacteristic
111#106×C151—21no—
112#106×C151—21no—
113#106×C151—21no—
114#106×C151—21no—
115#106×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—41no—
129#103×C151D411yescharacteristic
130#103×C151D411yescharacteristic
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—21no—
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139#97×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×D4×C151C2×D411yescharacteristic
154C2×D4×C151C2×D411yescharacteristic
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—41no—
158C22×C4×C151—41no—
159C22×C4×C151—41no—
160C22×C4×C151—41no—
161Q16×C151—41no—
162Q16×C151—81no—
163Q16×C151—82no—
164D8×C151Q1614yescomplemented
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×C151—81no—
172C2×C8×C151C2×D411yescharacteristic
173C2×C8×C151C2×D411yescharacteristic
174C2×C8×C151C2×D411yescharacteristic
175C2×C8×C151C2×D411yescharacteristic
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×C151C2×D411yescharacteristic
194C4⋊C4×C151C2×D411yescharacteristic
195C4⋊C4×C151C2×D411yescharacteristic
196C4⋊C4×C151C2×D411yescharacteristic
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C22⋊C4×C151—41no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151C2411yescharacteristic
206C23×C151—21no—
207C23×C151—21no—
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—21no—
211Q8×C151—21no—
212Q8×C151—41no—
213Q8×C151—41no—
214Q8×C151—81no—
215Q8×C151—81no—
216Q8×C151—81no—
217Q8×C151—82no—
218D4×C151—21no—
219D4×C151—21no—
220D4×C151C2×Q1612yes—
221D4×C151C2×Q1612yes—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—41no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—82no—
237C2×C4×C151—161no—
238C2×C4×C151—161no—
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—22no—
254C22×C151—41no—
255C22×C151—41no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151D4211yescharacteristic
259C4×C151—21no—
260C4×C151—41no—
261C4×C151—41no—
262C4×C151—41no—
263C4×C151—41no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151—81no—
269C4×C151—81no—
270C4×C151C22×Q1611yescharacteristic
271C4×C151#57511yescharacteristic
272C4×C151#57711yescharacteristic
273C4×C151#57811yescharacteristic
274C2×C151—42no—
275C2×C151—42no—
276C2×C151#326711yescharacteristic
277C2×C151D4×Q1611yescharacteristic
278C2×C151#328811yescharacteristic
279#19814C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#1981411yescharacteristic, direct product factor, Sylow
281#3384C2×C15111yescharacteristic
282#3380C2×C15111yescharacteristic
283#3338C2×C15111yescharacteristic, complemented
284#3299C2×C15111yescharacteristic, complemented
285#1723C2×C15111yescharacteristic, complemented
286#1696C2×C15111yescharacteristic, complemented
287#1683C2×C15111yescharacteristic, complemented
288#1675C2×C15111yescharacteristic, complemented
289#1672C2×C15111yescharacteristic, complemented
290#1644C2×C15111yescharacteristic, complemented
291#1637C2×C15111yescharacteristic, complemented
292#1632C2×C15111yescharacteristic, complemented
293#1632C2×C15111yescharacteristic, complemented
294#1584C2×C15111yescharacteristic, complemented
295#1580C2×C15111yescharacteristic
296#554C22×C15111yescharacteristic
297#554C22×C15111yescharacteristic
298#554C22×C15111yescharacteristic
299D4×Q8C22×C15111yescharacteristic
300#501—21no—
301#500C22×C15111yescharacteristic
302#500C22×C15111yescharacteristic
303#499—21no—
304#498C22×C15111yescharacteristic
305#494C22×C15111yescharacteristic
306#487C22×C15111yescharacteristic
307#487C22×C15111yescharacteristic
308#484—21no—
309#484—21no—
310#484—21no—
311#478—21no—
312#478—21no—
313#478—21no—
314#477C22×C15111yescharacteristic
315#477C22×C15111yescharacteristic
316#477C22×C15111yescharacteristic
317#476—21no—
318#476C22×C15111yescharacteristic
319#476C22×C15111yescharacteristic
320#476C22×C15111yescharacteristic
321#474C22×C15111yescharacteristic
322#467—21no—
323#467—21no—
324#462C22×C15111yescharacteristic
325#451—21no—
326#446C22×C15111yescharacteristic
327C8×Q8C22×C15111yescharacteristic
328#442—21no—
329C4×Q16C22×C15111yescharacteristic
330C4×D8—21no—
331C4×D8C22×C15111yescharacteristic
332C8×D4C22×C15111yescharacteristic
333C8×D4C22×C15111yescharacteristic
334C2×#107—21no—
335C2×#103—21no—
336#335C22×C15111yescharacteristic
337#334C22×C15111yescharacteristic
338#333C22×C15111yescharacteristic
339#333C22×C15111yescharacteristic
340#333C22×C15111yescharacteristic
341#332C22×C15111yescharacteristic
342Q8⋊C8C22×C15111yescharacteristic
343Q8⋊C8C22×C15111yescharacteristic
344D4⋊C8C22×C15111yescharacteristic
345D4⋊C8C22×C15111yescharacteristic
346#322C22×C15111yescharacteristic
347C22×Q8—21no—
348C2×Q16—21no—
349C2×Q16—41no—
350C2×Q16D4×C15111yescharacteristic
351C2×D8D4×C15111yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C15111yescharacteristic
356C4⋊Q8C23×C15111yescharacteristic
357C4⋊Q8C23×C15111yescharacteristic
358C4⋊Q8C23×C15111yescharacteristic
359#125—21no—
360#125—21no—
361#125—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C22⋊Q8—41no—
370C4×Q8C23×C15111yescharacteristic
371C4×Q8C23×C15111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C23×C15111yescharacteristic
377C4×D4C23×C15111yescharacteristic
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107D4×C15111yescharacteristic
390#107D4×C15111yescharacteristic
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C15111yescharacteristic
399C4⋊C8C23×C15111yescharacteristic
400C4⋊C8C23×C15111yescharacteristic
401C4⋊C8C23×C15111yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—41no—
409#103D4×C15111yescharacteristic
410#103D4×C15111yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102D4×C15111yescharacteristic
416#102D4×C15111yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8C23×C15111yescharacteristic
422C4×C8C23×C15111yescharacteristic
423C4×C8C23×C15111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—42no—
430C2×Q8—81no—
431C2×Q8C2×D4×C15111yescharacteristic
432C2×Q8C2×D4×C15111yescharacteristic
433C2×D4C2×D4×C15111yescharacteristic
434C2×D4C2×D4×C15111yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441Q16—41no—
442Q16—81no—
443Q16—82no—
444D8Q16×C15114yescomplemented
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—81no—
452C2×C8C2×D4×C15111yescharacteristic
453C2×C8C2×D4×C15111yescharacteristic
454C2×C8C2×D4×C15111yescharacteristic
455C2×C8C2×D4×C15111yescharacteristic
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—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C15111yescharacteristic
474C4⋊C4C2×D4×C15111yescharacteristic
475C4⋊C4C2×D4×C15111yescharacteristic
476C4⋊C4C2×D4×C15111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42C24×C15111yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496Q8—81no—
497Q8—82no—
498D4—21no—
499D4—21no—
500D4C2×Q16×C15112yes—
501D4C2×Q16×C15112yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—161no—
518C2×C4—161no—
519C2×C4—161no—
520C2×C4C22×D4×C15111yescharacteristic
521C2×C4C22×D4×C15111yescharacteristic
522C2×C4H(5,𝔽2)×C15111yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8C2×Q16×C15112yes—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22D42×C15111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C22×Q16×C15111yescharacteristic
551C4#575×C15111yescharacteristic
552C4#577×C15111yescharacteristic
553C4#578×C15111yescharacteristic
554C2—42no—
555C2—42no—
556C2#3267×C15111yescharacteristic
557C2D4×Q16×C15111yescharacteristic
558C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×D8×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #3338×C151C2semidirect
4. #3299×C151C2semidirect
5. #1723×C151C2semidirect
6. #1696×C151C2semidirect
7. #1683×C151C2semidirect
8. #1675×C151C2semidirect
9. #1672×C151C2semidirect
10. #1644×C151C2semidirect
11. #1637×C151C2semidirect
12. #1632×C151C2semidirect
13. #1632×C151C2semidirect
14. #1584×C151C2semidirect
164. D8×C151Q16semidirect
279. #19814C151direct (N × H)
280. C151#19814direct (N × H)
283. #3338C2×C151semidirect
284. #3299C2×C151semidirect
285. #1723C2×C151semidirect
286. #1696C2×C151semidirect
287. #1683C2×C151semidirect
288. #1675C2×C151semidirect
289. #1672C2×C151semidirect
290. #1644C2×C151semidirect
291. #1637C2×C151semidirect
292. #1632C2×C151semidirect
293. #1632C2×C151semidirect
294. #1584C2×C151semidirect
444. D8Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3384×C1512
#3380×C1512
#3338×C1512
#3299×C1512
#1723×C1512
#1696×C1512
#1683×C1512
#1675×C1512
#1672×C1512
#1644×C1512
#1637×C1512
#1632×C1512
#1584×C1512
#1580×C1512
#19814151