Finite Group Databasebeta

← C151×#19591 #50324516

Subgroups — C151×#19591 #50324516

Order 38656.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3247×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic, complemented
3#3226×C151C211yesmaximal, characteristic, complemented
4#2994×C151C211yesmaximal, characteristic, complemented
5#1698×C151C211yesmaximal, characteristic, complemented
6#1697×C151C211yesmaximal, characteristic, complemented
7#1696×C151C211yesmaximal, characteristic, complemented
8#1695×C151C211yesmaximal, characteristic, complemented
9#1678×C151C211yesmaximal, characteristic, complemented
10#1677×C151C211yesmaximal, characteristic, complemented
11#1676×C151C211yesmaximal, characteristic, complemented
12#1675×C151C211yesmaximal, characteristic, complemented
13#1573×C151C211yesmaximal, characteristic, complemented
14#1551×C151C211yesmaximal, characteristic, complemented
15C2×#333×C151C211yesmaximal, characteristic, complemented
16#532×C151C2211yescharacteristic
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#501×C151—21no—
20#500×C151C2211yescharacteristic
21#500×C151C2211yescharacteristic
22#489×C151—21no—
23#486×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#483×C151—21no—
26#480×C151—21no—
27#480×C151—21no—
28#480×C151—21no—
29#478×C151—21no—
30#477×C151C2211yescharacteristic
31#477×C151C2211yescharacteristic
32#477×C151C2211yescharacteristic
33#476×C151C2211yescharacteristic
34#476×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#474×C151—21no—
37#474×C151—21no—
38#466×C151—21no—
39#465×C151—21no—
40#463×C151—21no—
41#460×C151C2211yescharacteristic
42#459×C151C2211yescharacteristic
43#446×C151C2211yescharacteristic
44C8×Q8×C151C2211yescharacteristic
45#436×C151C2211yescharacteristic
46#435×C151—21no—
47C8×D4×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#432×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52#424×C151—21no—
53C2×C4⋊C8×C151C2211yescharacteristic
54C2×C4⋊C8×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#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C22×Q8×C151—21no—
69C2×SD16×C151—21no—
70C2×D8×C151—21no—
71C2×M16×C151—21no—
72C22×C8×C151—21no—
73C22×C8×C151—21no—
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
81#127×C151C2311yescharacteristic
82#126×C151—21no—
83#125×C151D411yescharacteristic
84#124×C151—21no—
85#124×C151D411yescharacteristic
86#123×C151—21no—
87C22⋊Q8×C151D411yescharacteristic
88#121×C151—21no—
89#121×C151—21no—
90#121×C151D411yescharacteristic
91C4×Q8×C151C2311yescharacteristic
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151—21no—
95C4×D4×C151C2311yescharacteristic
96#117×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C42×C151C2311yescharacteristic
100#107×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#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151D411yescharacteristic
115C4⋊C8×C151D411yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
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#102×C151—21no—
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151—21no—
137C22⋊C8×C151D411yescharacteristic
138C22⋊C8×C151D411yescharacteristic
139#97×C151—21no—
140#97×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—82no—
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×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—41no—
156C2×D4×C151C2×D411yescharacteristic
157C22×C4×C151—21no—
158C22×C4×C151—41no—
159C22×C4×C151—41no—
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151#4111yescharacteristic
163SD16×C151—81no—
164D8×C151—81no—
165M16×C151—81no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—81no—
173C2×C8×C151—81no—
174C2×C8×C151—81no—
175C2×C8×C151C2×D411yescharacteristic
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
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—21no—
188C4⋊C4×C151—21no—
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—
199C22⋊C4×C151—41no—
200C42×C151—21no—
201C42×C151C2×D411yescharacteristic
202C42×C151C2×D411yescharacteristic
203C42×C151#4111yescharacteristic
204C42×C151C2411yescharacteristic
205C23×C151—21no—
206C23×C151—41no—
207C23×C151#12111yescharacteristic
208Q8×C151—21no—
209Q8×C151—21no—
210Q8×C151—81no—
211Q8×C151—81no—
212Q8×C151—81no—
213Q8×C151—82no—
214D4×C151—21no—
215D4×C151—21no—
216D4×C151—42no—
217D4×C151—41no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—81no—
222D4×C151—82no—
223C2×C4×C151—22no—
224C2×C4×C151—21no—
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—41no—
232C2×C4×C151—41no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—82no—
237C2×C4×C151—82no—
238C2×C4×C151#12111yescharacteristic
239C2×C4×C151#12111yescharacteristic
240C2×C4×C151#12111yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C8×C151—21no—
245C8×C151—21no—
246C8×C151—21no—
247C8×C151—21no—
248C8×C151—41no—
249C8×C151—41no—
250C8×C151—41no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C22×C151—21no—
255C22×C151—21no—
256C22×C151—41no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151—81no—
262C22×C151#47212yes—
263C22×C151C2×#12111yescharacteristic
264C4×C151—21no—
265C4×C151—21no—
266C4×C151—21no—
267C4×C151—21no—
268C4×C151—41no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—81no—
272C4×C151—81no—
273C4×C151—81no—
274C4×C151#57711yescharacteristic
275C4×C151#57711yescharacteristic
276C4×C151#57811yescharacteristic
277C4×C151#57811yescharacteristic
278C2×C151—22no—
279C2×C151—81no—
280C2×C151—161no—
281C2×C151#304611yescharacteristic
282C2×C151#306311yescharacteristic
283C2×C151C2×#47211yescharacteristic
284#19591C15111yesmaximal, characteristic, direct product factor, Sylow
285C151#1959111yescharacteristic, direct product factor, Sylow
286#3247C2×C15111yescharacteristic
287#3238C2×C15111yescharacteristic, complemented
288#3226C2×C15111yescharacteristic, complemented
289#2994C2×C15111yescharacteristic, complemented
290#1698C2×C15111yescharacteristic, complemented
291#1697C2×C15111yescharacteristic, complemented
292#1696C2×C15111yescharacteristic, complemented
293#1695C2×C15111yescharacteristic, complemented
294#1678C2×C15111yescharacteristic, complemented
295#1677C2×C15111yescharacteristic, complemented
296#1676C2×C15111yescharacteristic, complemented
297#1675C2×C15111yescharacteristic, complemented
298#1573C2×C15111yescharacteristic, complemented
299#1551C2×C15111yescharacteristic, complemented
300C2×#333C2×C15111yescharacteristic, complemented
301#532C22×C15111yescharacteristic
302C2×C4⋊Q8C22×C15111yescharacteristic
303#529C22×C15111yescharacteristic
304#501—21no—
305#500C22×C15111yescharacteristic
306#500C22×C15111yescharacteristic
307#489—21no—
308#486C22×C15111yescharacteristic
309#486C22×C15111yescharacteristic
310#483—21no—
311#480—21no—
312#480—21no—
313#480—21no—
314#478—21no—
315#477C22×C15111yescharacteristic
316#477C22×C15111yescharacteristic
317#477C22×C15111yescharacteristic
318#476C22×C15111yescharacteristic
319#476C22×C15111yescharacteristic
320#476C22×C15111yescharacteristic
321#474—21no—
322#474—21no—
323#466—21no—
324#465—21no—
325#463—21no—
326#460C22×C15111yescharacteristic
327#459C22×C15111yescharacteristic
328#446C22×C15111yescharacteristic
329C8×Q8C22×C15111yescharacteristic
330#436C22×C15111yescharacteristic
331#435—21no—
332C8×D4—21no—
333C8×D4C22×C15111yescharacteristic
334#433—21no—
335#432C22×C15111yescharacteristic
336#431C22×C15111yescharacteristic
337#424—21no—
338C2×C4⋊C8C22×C15111yescharacteristic
339C2×C4⋊C8C22×C15111yescharacteristic
340#335C22×C15111yescharacteristic
341#335C22×C15111yescharacteristic
342#334C22×C15111yescharacteristic
343#334C22×C15111yescharacteristic
344#333C22×C15111yescharacteristic
345#333C22×C15111yescharacteristic
346#333C22×C15111yescharacteristic
347#333C22×C15111yescharacteristic
348#333C22×C15111yescharacteristic
349#333C22×C15111yescharacteristic
350#331C22×C15111yescharacteristic
351#331C22×C15111yescharacteristic
352C2×#41—21no—
353C22×Q8—21no—
354C2×SD16—21no—
355C2×D8—21no—
356C2×M16—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C15111yescharacteristic
364C4⋊Q8C23×C15111yescharacteristic
365C4⋊Q8C23×C15111yescharacteristic
366#127C23×C15111yescharacteristic
367#126—21no—
368#125D4×C15111yescharacteristic
369#124—21no—
370#124D4×C15111yescharacteristic
371#123—21no—
372C22⋊Q8D4×C15111yescharacteristic
373#121—21no—
374#121—21no—
375#121D4×C15111yescharacteristic
376C4×Q8C23×C15111yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C23×C15111yescharacteristic
381#117—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C42C23×C15111yescharacteristic
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8D4×C15111yescharacteristic
400C4⋊C8D4×C15111yescharacteristic
401C4⋊C8C23×C15111yescharacteristic
402C4⋊C8C23×C15111yescharacteristic
403C4⋊C8C23×C15111yescharacteristic
404C4⋊C8C23×C15111yescharacteristic
405C4⋊C8C23×C15111yescharacteristic
406C4⋊C8C23×C15111yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8D4×C15111yescharacteristic
423C22⋊C8D4×C15111yescharacteristic
424#97—21no—
425#97—21no—
426C4×C8—21no—
427C4×C8C23×C15111yescharacteristic
428C4×C8C23×C15111yescharacteristic
429#41—82no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—82no—
435C2×Q8C2×D4×C15111yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4C2×D4×C15111yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4#41×C15111yescharacteristic
448SD16—81no—
449D8—81no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8C2×D4×C15111yescharacteristic
461C2×C8C2×D4×C15111yescharacteristic
462C2×C8C2×D4×C15111yescharacteristic
463C2×C8C2×D4×C15111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C15111yescharacteristic
477C4⋊C4C2×D4×C15111yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42C2×D4×C15111yescharacteristic
487C42C2×D4×C15111yescharacteristic
488C42#41×C15111yescharacteristic
489C42C24×C15111yescharacteristic
490C23—21no—
491C23—41no—
492C23#121×C15111yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8—81no—
497Q8—81no—
498Q8—82no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4#121×C15111yescharacteristic
524C2×C4#121×C15111yescharacteristic
525C2×C4#121×C15111yescharacteristic
526C2×C4C22×D4×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C2×#41×C15111yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22#472×C15112yes—
548C22C2×#121×C15111yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4#577×C15111yescharacteristic
560C4#577×C15111yescharacteristic
561C4#578×C15111yescharacteristic
562C4#578×C15111yescharacteristic
563C2—22no—
564C2—81no—
565C2—161no—
566C2#3046×C15111yescharacteristic
567C2#3063×C15111yescharacteristic
568C2C2×#472×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3247×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
2. #3238×C151C2semidirect
3. #3226×C151C2semidirect
4. #2994×C151C2semidirect
5. #1698×C151C2semidirect
6. #1697×C151C2semidirect
7. #1696×C151C2semidirect
8. #1695×C151C2semidirect
9. #1678×C151C2semidirect
10. #1677×C151C2semidirect
11. #1676×C151C2semidirect
12. #1675×C151C2semidirect
13. #1573×C151C2semidirect
14. #1551×C151C2semidirect
15. C2×#333×C151C2semidirect
284. #19591C151direct (N × H)
285. C151#19591direct (N × H)
287. #3238C2×C151semidirect
288. #3226C2×C151semidirect
289. #2994C2×C151semidirect
290. #1698C2×C151semidirect
291. #1697C2×C151semidirect
292. #1696C2×C151semidirect
293. #1695C2×C151semidirect
294. #1678C2×C151semidirect
295. #1677C2×C151semidirect
296. #1676C2×C151semidirect
297. #1675C2×C151semidirect
298. #1573C2×C151semidirect
299. #1551C2×C151semidirect
300. C2×#333C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3247×C1512
#3238×C1512
#3226×C1512
#2994×C1512
#1698×C1512
#1697×C1512
#1696×C1512
#1695×C1512
#1678×C1512
#1677×C1512
#1676×C1512
#1675×C1512
#1573×C1512
#1551×C1512
C2×#333×C1512
#19591151