Finite Group Databasebeta

← C151×#19419 #50324344

Subgroups — C151×#19419 #50324344

Order 38656.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3228×C151C211yesmaximal, characteristic, complemented
2#3116×C151C211yesmaximal, characteristic, complemented
3#3106×C151C211yesmaximal, characteristic
4#2988×C151C211yesmaximal, characteristic, complemented
5#1682×C151C211yesmaximal, characteristic, complemented
6#1681×C151C211yesmaximal, characteristic, complemented
7#1678×C151C211yesmaximal, characteristic, complemented
8#1677×C151C211yesmaximal, characteristic, complemented
9#1676×C151C211yesmaximal, characteristic, complemented
10#1675×C151C211yesmaximal, characteristic, complemented
11#1672×C151C211yesmaximal, characteristic, complemented
12#1671×C151C211yesmaximal, characteristic, complemented
13#1572×C151C211yesmaximal, characteristic, complemented
14#1551×C151C211yesmaximal, characteristic, complemented
15#1542×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18C4×#41×C151C2211yescharacteristic
19#500×C151C2211yescharacteristic
20#498×C151C2211yescharacteristic
21#486×C151C2211yescharacteristic
22#486×C151C2211yescharacteristic
23#485×C151—21no—
24#482×C151—21no—
25#482×C151—21no—
26#482×C151—21no—
27#478×C151—21no—
28#478×C151—21no—
29#477×C151C2211yescharacteristic
30#477×C151C2211yescharacteristic
31#476×C151C2211yescharacteristic
32#476×C151C2211yescharacteristic
33#462×C151C2211yescharacteristic
34#461×C151C2211yescharacteristic
35#460×C151C2211yescharacteristic
36#459×C151C2211yescharacteristic
37#452×C151—21no—
38#449×C151—21no—
39C8×Q8×C151C2211yescharacteristic
40C8×Q8×C151C2211yescharacteristic
41#441×C151—21no—
42#440×C151—21no—
43C4×SD16×C151—21no—
44C4×D8×C151—21no—
45C8×D4×C151—21no—
46C8×D4×C151—21no—
47C8×D4×C151C2211yescharacteristic
48C8×D4×C151C2211yescharacteristic
49#432×C151C2211yescharacteristic
50#431×C151—21no—
51#431×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53C2×C4⋊C8×C151—21no—
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#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151D411yescharacteristic
69C2×Q16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×D8×C151—21no—
73C22×C8×C151—21no—
74C22×C8×C151—21no—
75C22×C8×C151—21no—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79#127×C151C2311yescharacteristic
80#125×C151—21no—
81#124×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84#121×C151—21no—
85#121×C151—21no—
86C4×Q8×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151D411yescharacteristic
89C4×Q8×C151C2311yescharacteristic
90C4×D4×C151—21no—
91C4×D4×C151—21no—
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151D411yescharacteristic
95C4×D4×C151C2311yescharacteristic
96#117×C151—21no—
97#117×C151—21no—
98#117×C151D411yescharacteristic
99C2×C42×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—21no—
102#107×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#106×C151—21no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109C4⋊C8×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151D411yescharacteristic
113C4⋊C8×C151D411yescharacteristic
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#102×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—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151D411yescharacteristic
137C22⋊C8×C151D411yescharacteristic
138#97×C151—21no—
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—22no—
145#41×C151—22no—
146#41×C151—82no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
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—21no—
159C22×C4×C151—21no—
160C22×C4×C151—41no—
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151#4111yescharacteristic
164Q16×C151—42no—
165SD16×C151—42no—
166SD16×C151—42no—
167D8×C151—42no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—81no—
175C2×C8×C151—81no—
176C2×C8×C151—81no—
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
180C2×C8×C151C2×D411yescharacteristic
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—41no—
197C22⋊C4×C151—41no—
198C22⋊C4×C151—41no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151—41no—
203C42×C151C2×D411yescharacteristic
204C42×C151C2×D411yescharacteristic
205C42×C151#4111yescharacteristic
206C42×C151C2411yescharacteristic
207C23×C151—21no—
208C23×C151—41no—
209C23×C151#12111yescharacteristic
210Q8×C151—21no—
211Q8×C151—41no—
212Q8×C151—41no—
213Q8×C151—81no—
214Q8×C151—81no—
215Q8×C151#13512yes—
216D4×C151—24no—
217D4×C151—21no—
218D4×C151—41no—
219D4×C151—41no—
220D4×C151—41no—
221D4×C151—41no—
222D4×C151—81no—
223D4×C151—82no—
224D4×C151#13512yes—
225C2×C4×C151—24no—
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—21no—
233C2×C4×C151—41no—
234C2×C4×C151—41no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—81no—
240C2×C4×C151—82no—
241C2×C4×C151#12111yescharacteristic
242C2×C4×C151#12111yescharacteristic
243C2×C4×C151#12111yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C8×C151—21no—
248C8×C151—21no—
249C8×C151—21no—
250C8×C151—21no—
251C8×C151—41no—
252C8×C151—41no—
253C8×C151—41no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—41no—
257C22×C151—21no—
258C22×C151—21no—
259C22×C151—22no—
260C22×C151—21no—
261C22×C151—41no—
262C22×C151—41no—
263C22×C151—81no—
264C22×C151—81no—
265C22×C151—81no—
266C22×C151C2×#12111yescharacteristic
267C4×C151—21no—
268C4×C151—21no—
269C4×C151—22no—
270C4×C151—21no—
271C4×C151—21no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—81no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151C2×#13511yescharacteristic
278C4×C151C2×#13511yescharacteristic
279C4×C151#57711yescharacteristic
280C4×C151#57811yescharacteristic
281C2×C151—41no—
282C2×C151—42no—
283C2×C151—161no—
284C2×C151#304611yescharacteristic
285C2×C151#305011yescharacteristic
286C2×C151#306811yescharacteristic
287#19419C15111yesmaximal, characteristic, direct product factor, Sylow
288C151#1941911yescharacteristic, direct product factor, Sylow
289#3228C2×C15111yescharacteristic, complemented
290#3116C2×C15111yescharacteristic, complemented
291#3106C2×C15111yescharacteristic
292#2988C2×C15111yescharacteristic, complemented
293#1682C2×C15111yescharacteristic, complemented
294#1681C2×C15111yescharacteristic, complemented
295#1678C2×C15111yescharacteristic, complemented
296#1677C2×C15111yescharacteristic, complemented
297#1676C2×C15111yescharacteristic, complemented
298#1675C2×C15111yescharacteristic, complemented
299#1672C2×C15111yescharacteristic, complemented
300#1671C2×C15111yescharacteristic, complemented
301#1572C2×C15111yescharacteristic, complemented
302#1551C2×C15111yescharacteristic, complemented
303#1542C2×C15111yescharacteristic, complemented
304#533C22×C15111yescharacteristic
305#532C22×C15111yescharacteristic
306C4×#41C22×C15111yescharacteristic
307#500C22×C15111yescharacteristic
308#498C22×C15111yescharacteristic
309#486C22×C15111yescharacteristic
310#486C22×C15111yescharacteristic
311#485—21no—
312#482—21no—
313#482—21no—
314#482—21no—
315#478—21no—
316#478—21no—
317#477C22×C15111yescharacteristic
318#477C22×C15111yescharacteristic
319#476C22×C15111yescharacteristic
320#476C22×C15111yescharacteristic
321#462C22×C15111yescharacteristic
322#461C22×C15111yescharacteristic
323#460C22×C15111yescharacteristic
324#459C22×C15111yescharacteristic
325#452—21no—
326#449—21no—
327C8×Q8C22×C15111yescharacteristic
328C8×Q8C22×C15111yescharacteristic
329#441—21no—
330#440—21no—
331C4×SD16—21no—
332C4×D8—21no—
333C8×D4—21no—
334C8×D4—21no—
335C8×D4C22×C15111yescharacteristic
336C8×D4C22×C15111yescharacteristic
337#432C22×C15111yescharacteristic
338#431—21no—
339#431C22×C15111yescharacteristic
340#431C22×C15111yescharacteristic
341C2×C4⋊C8—21no—
342C2×C4⋊C8C22×C15111yescharacteristic
343#335C22×C15111yescharacteristic
344#335C22×C15111yescharacteristic
345#334C22×C15111yescharacteristic
346#334C22×C15111yescharacteristic
347#333C22×C15111yescharacteristic
348#333C22×C15111yescharacteristic
349#333C22×C15111yescharacteristic
350#333C22×C15111yescharacteristic
351#332C22×C15111yescharacteristic
352#332C22×C15111yescharacteristic
353#331C22×C15111yescharacteristic
354#331C22×C15111yescharacteristic
355C2×#41—21no—
356C2×#41D4×C15111yescharacteristic
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×D8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8C23×C15111yescharacteristic
365C4⋊Q8C23×C15111yescharacteristic
366C4⋊Q8C23×C15111yescharacteristic
367#127C23×C15111yescharacteristic
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8D4×C15111yescharacteristic
377C4×Q8C23×C15111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4D4×C15111yescharacteristic
383C4×D4C23×C15111yescharacteristic
384#117—21no—
385#117—21no—
386#117D4×C15111yescharacteristic
387C2×C42—21no—
388C2×C42C23×C15111yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8D4×C15111yescharacteristic
401C4⋊C8D4×C15111yescharacteristic
402C4⋊C8C23×C15111yescharacteristic
403C4⋊C8C23×C15111yescharacteristic
404C4⋊C8C23×C15111yescharacteristic
405C4⋊C8C23×C15111yescharacteristic
406C4⋊C8C23×C15111yescharacteristic
407C4⋊C8C23×C15111yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8D4×C15111yescharacteristic
425C22⋊C8D4×C15111yescharacteristic
426#97—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C23×C15111yescharacteristic
431C4×C8C23×C15111yescharacteristic
432#41—22no—
433#41—22no—
434#41—82no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C15111yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C15111yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4C2×D4×C15111yescharacteristic
450C22×C4C2×D4×C15111yescharacteristic
451C22×C4#41×C15111yescharacteristic
452Q16—42no—
453SD16—42no—
454SD16—42no—
455D8—42no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—81no—
464C2×C8—81no—
465C2×C8C2×D4×C15111yescharacteristic
466C2×C8C2×D4×C15111yescharacteristic
467C2×C8C2×D4×C15111yescharacteristic
468C2×C8C2×D4×C15111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C15111yescharacteristic
480C4⋊C4C2×D4×C15111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42C2×D4×C15111yescharacteristic
492C42C2×D4×C15111yescharacteristic
493C42#41×C15111yescharacteristic
494C42C24×C15111yescharacteristic
495C23—21no—
496C23—41no—
497C23#121×C15111yescharacteristic
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—81no—
503Q8#135×C15112yes—
504D4—24no—
505D4—21no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—81no—
511D4—82no—
512D4#135×C15112yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—81no—
528C2×C4—82no—
529C2×C4#121×C15111yescharacteristic
530C2×C4#121×C15111yescharacteristic
531C2×C4#121×C15111yescharacteristic
532C2×C4C22×D4×C15111yescharacteristic
533C2×C4C22×D4×C15111yescharacteristic
534C2×C4C2×#41×C15111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C22—21no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22C2×#121×C15111yescharacteristic
555C4—21no—
556C4—21no—
557C4—22no—
558C4—21no—
559C4—21no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C2×#135×C15111yescharacteristic
566C4C2×#135×C15111yescharacteristic
567C4#577×C15111yescharacteristic
568C4#578×C15111yescharacteristic
569C2—41no—
570C2—42no—
571C2—161no—
572C2#3046×C15111yescharacteristic
573C2#3050×C15111yescharacteristic
574C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3106×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
1. #3228×C151C2semidirect
2. #3116×C151C2semidirect
4. #2988×C151C2semidirect
5. #1682×C151C2semidirect
6. #1681×C151C2semidirect
7. #1678×C151C2semidirect
8. #1677×C151C2semidirect
9. #1676×C151C2semidirect
10. #1675×C151C2semidirect
11. #1672×C151C2semidirect
12. #1671×C151C2semidirect
13. #1572×C151C2semidirect
14. #1551×C151C2semidirect
15. #1542×C151C2semidirect
287. #19419C151direct (N × H)
288. C151#19419direct (N × H)
289. #3228C2×C151semidirect
290. #3116C2×C151semidirect
292. #2988C2×C151semidirect
293. #1682C2×C151semidirect
294. #1681C2×C151semidirect
295. #1678C2×C151semidirect
296. #1677C2×C151semidirect
297. #1676C2×C151semidirect
298. #1675C2×C151semidirect
299. #1672C2×C151semidirect
300. #1671C2×C151semidirect
301. #1572C2×C151semidirect
302. #1551C2×C151semidirect
303. #1542C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3228×C1512
#3116×C1512
#3106×C1512
#2988×C1512
#1682×C1512
#1681×C1512
#1678×C1512
#1677×C1512
#1676×C1512
#1675×C1512
#1672×C1512
#1671×C1512
#1572×C1512
#1551×C1512
#1542×C1512
#19419151