Finite Group Databasebeta

← C151×#18427 #50323352

Subgroups — C151×#18427 #50323352

Order 38656.

996 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3558×C151C211yesmaximal, characteristic
2#3218×C151C211yesmaximal, characteristic, complemented
3#3206×C151C211yesmaximal, characteristic, complemented
4#2640×C151C211yesmaximal, characteristic, complemented
5#1606×C151C214yesmaximal, complemented
6#1601×C151C214yesmaximal, complemented
7#1505×C151C211yesmaximal, characteristic, complemented
8#1500×C151C211yesmaximal, characteristic, complemented
9#1469×C151C211yesmaximal, characteristic, complemented
10#562×C151—21no—
11H(3,𝔽4)×C151—21no—
12#559×C151—21no—
13#548×C151—21no—
14#546×C151—21no—
15#546×C151—22no—
16D42×C151—21no—
17#542×C151—21no—
18#538×C151—22no—
19#538×C151C2212yes—
20#535×C151—21no—
21#534×C151C2212yes—
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic, complemented
24#529×C151C2211yescharacteristic
25C2×#124×C151C2211yescharacteristic
26#497×C151—21no—
27#492×C151—21no—
28#491×C151—21no—
29#487×C151—21no—
30#462×C151—21no—
31#461×C151—22no—
32#461×C151—21no—
33#451×C151C2212yescomplemented
34#448×C151C2212yes—
35#448×C151C2214yescomplemented
36#432×C151C2211yescharacteristic, complemented
37#431×C151C2211yescharacteristic, complemented
38#397×C151—22no—
39#393×C151C2214yescomplemented
40#391×C151—21no—
41#390×C151—21no—
42#376×C151C2211yescharacteristic, complemented
43#328×C151C2212yescomplemented
44#327×C151C2212yes—
45#327×C151C2214yescomplemented
46#323×C151C2214yescomplemented
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C22×Q8×C151D411yescharacteristic
50C22×Q8×C151C2312yes—
51C22×D4×C151—21no—
52C22×D4×C151—22no—
53C22×D4×C151D411yescharacteristic
54C2×Q16×C151—22no—
55C2×SD16×C151—22no—
56C2×SD16×C151—24no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151D411yescharacteristic
62#127×C151—21no—
63#127×C151D411yescharacteristic
64#126×C151—22no—
65#126×C151—21no—
66#125×C151D411yescharacteristic
67#124×C151—21no—
68#124×C151—22no—
69#124×C151—22no—
70#124×C151—21no—
71#124×C151—21no—
72#124×C151—21no—
73#124×C151—21no—
74#124×C151—21no—
75#124×C151—22no—
76#124×C151D411yescharacteristic
77#123×C151—22no—
78#123×C151—21no—
79#123×C151—22no—
80#123×C151—22no—
81#123×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—21no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151C2311yescharacteristic
86#121×C151—22no—
87#121×C151—22no—
88#121×C151—22no—
89#121×C151—21no—
90#121×C151—22no—
91#121×C151—21no—
92#121×C151—22no—
93#121×C151C2311yescharacteristic
94#121×C151C2312yes—
95#120×C151—22no—
96#120×C151—22no—
97#120×C151—22no—
98#120×C151—22no—
99#120×C151—22no—
100C4×Q8×C151—21no—
101C4×Q8×C151D411yescharacteristic
102C4×D4×C151—22no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151—22no—
106C4×D4×C151—21no—
107C4×D4×C151D411yescharacteristic
108C4×D4×C151D412yes—
109#117×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C22⋊C4×C151—22no—
113C2×C22⋊C4×C151—24no—
114C2×C22⋊C4×C151D412yes—
115C2×C22⋊C4×C151C2312yes—
116C2×C42×C151—21no—
117C2×C42×C151C2311yescharacteristic
118C4⋊C8×C151—21no—
119C4⋊C8×C151—21no—
120#103×C151—22no—
121#103×C151—24no—
122#103×C151—22no—
123C22⋊C8×C151C2312yes—
124C22⋊C8×C151C2312yes—
125#97×C151—21no—
126C4×C8×C151—21no—
127#95×C151—21no—
128#95×C151—24no—
129#95×C151C2312yes—
130C24×C151—22no—
131C24×C151C2×D412yes—
132#41×C151—82no—
133#41×C151—82no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—22no—
138C2×Q8×C151—22no—
139C2×Q8×C151—42no—
140C2×Q8×C151—82no—
141C2×Q8×C151C2×D411yescharacteristic
142C2×D4×C151—22no—
143C2×D4×C151—21no—
144C2×D4×C151—22no—
145C2×D4×C151—22no—
146C2×D4×C151—22no—
147C2×D4×C151—22no—
148C2×D4×C151—22no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—42no—
154C2×D4×C151—82no—
155C2×D4×C151—84no—
156C2×D4×C151C2×D411yescharacteristic
157C2×D4×C151C2×D412yes—
158C22×C4×C151—22no—
159C22×C4×C151—22no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D412yes—
167C22×C4×C151C2411yescharacteristic
168Q16×C151—82no—
169SD16×C151—84no—
170SD16×C151—82no—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—41no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151—41no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151C2×D412yes—
185C4⋊C4×C151C2×D411yescharacteristic
186C4⋊C4×C151C2×D411yescharacteristic
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—21no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—22no—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—84no—
204C42×C151—22no—
205C42×C151—21no—
206C42×C151—42no—
207C42×C151C2×D411yescharacteristic
208C42×C151C2×D411yescharacteristic
209C42×C151C2×D411yescharacteristic
210C42×C151C2×D411yescharacteristic
211C23×C151—21no—
212C23×C151—22no—
213C23×C151—22no—
214C23×C151—24no—
215C23×C151—42no—
216C23×C151—42no—
217C23×C151—82no—
218C23×C151—82no—
219C23×C151—82no—
220C23×C151C22×D411yescharacteristic
221Q8×C151—41no—
222Q8×C151—44no—
223Q8×C151—42no—
224Q8×C151—42no—
225Q8×C151—42no—
226Q8×C151—81no—
227Q8×C151—81no—
228D4×C151—42no—
229D4×C151—41no—
230D4×C151—44no—
231D4×C151—42no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—81no—
235D4×C151—81no—
236D4×C151—82no—
237D4×C151—82no—
238D4×C151—82no—
239D4×C151—82no—
240D4×C151—82no—
241C2×C4×C151—22no—
242C2×C4×C151—22no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—41no—
249C2×C4×C151—42no—
250C2×C4×C151—42no—
251C2×C4×C151—44no—
252C2×C4×C151—42no—
253C2×C4×C151—42no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—82no—
257C2×C4×C151—82no—
258C2×C4×C151—82no—
259C2×C4×C151#12011yescharacteristic
260C2×C4×C151#12011yescharacteristic
261C2×C4×C151#12011yescharacteristic
262C2×C4×C151#12011yescharacteristic
263C2×C4×C151C22×D411yescharacteristic
264C2×C4×C151C22×D411yescharacteristic
265C8×C151—42no—
266C8×C151—42no—
267C22×C151—21no—
268C22×C151—21no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—42no—
274C22×C151—42no—
275C22×C151—42no—
276C22×C151—41no—
277C22×C151—42no—
278C22×C151—84no—
279C22×C151—164no—
280C22×C151C2×#12011yescharacteristic
281C22×C151#57712yes—
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—21no—
285C4×C151—21no—
286C4×C151—21no—
287C4×C151—41no—
288C4×C151—42no—
289C4×C151—41no—
290C4×C151—42no—
291C4×C151—41no—
292C4×C151—82no—
293C4×C151—82no—
294C4×C151#45512yes—
295C2×C151—22no—
296C2×C151—82no—
297C2×C151—82no—
298C2×C151—81no—
299C2×C151#300911yescharacteristic
300C2×C151C2×#45511yescharacteristic
301C2×C151#302711yescharacteristic
302#18427C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#1842711yescharacteristic, direct product factor, Sylow
304#3558C2×C15111yescharacteristic
305#3218C2×C15111yescharacteristic, complemented
306#3206C2×C15111yescharacteristic, complemented
307#2640C2×C15111yescharacteristic, complemented
308#1606C2×C15114yescomplemented
309#1601C2×C15114yescomplemented
310#1505C2×C15111yescharacteristic, complemented
311#1500C2×C15111yescharacteristic, complemented
312#1469C2×C15111yescharacteristic, complemented
313#562—21no—
314H(3,𝔽4)—21no—
315#559—21no—
316#548—21no—
317#546—21no—
318#546—22no—
319D42—21no—
320#542—21no—
321#538—22no—
322#538C22×C15112yes—
323#535—21no—
324#534C22×C15112yes—
325#532C22×C15111yescharacteristic
326C2×C4⋊Q8C22×C15111yescharacteristic, complemented
327#529C22×C15111yescharacteristic
328C2×#124C22×C15111yescharacteristic
329#497—21no—
330#492—21no—
331#491—21no—
332#487—21no—
333#462—21no—
334#461—22no—
335#461—21no—
336#451C22×C15112yescomplemented
337#448C22×C15112yes—
338#448C22×C15114yescomplemented
339#432C22×C15111yescharacteristic, complemented
340#431C22×C15111yescharacteristic, complemented
341#397—22no—
342#393C22×C15114yescomplemented
343#391—21no—
344#390—21no—
345#376C22×C15111yescharacteristic, complemented
346#328C22×C15112yescomplemented
347#327C22×C15112yes—
348#327C22×C15114yescomplemented
349#323C22×C15114yescomplemented
350C2×#41—21no—
351C2×#41—21no—
352C22×Q8D4×C15111yescharacteristic
353C22×Q8C23×C15112yes—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4D4×C15111yescharacteristic
357C2×Q16—22no—
358C2×SD16—22no—
359C2×SD16—24no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8D4×C15111yescharacteristic
365#127—21no—
366#127D4×C15111yescharacteristic
367#126—22no—
368#126—21no—
369#125D4×C15111yescharacteristic
370#124—21no—
371#124—22no—
372#124—22no—
373#124—22no—
374#124—21no—
375#124—21no—
376#124—21no—
377#124—21no—
378#124—21no—
379#124D4×C15111yescharacteristic
380#123—22no—
381#123—21no—
382#123—22no—
383#123—22no—
384#123—22no—
385C22⋊Q8—22no—
386C22⋊Q8—21no—
387C22⋊Q8—22no—
388C22⋊Q8C23×C15111yescharacteristic
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—22no—
394#121—21no—
395#121—22no—
396#121C23×C15111yescharacteristic
397#121C23×C15112yes—
398#120—22no—
399#120—22no—
400#120—22no—
401#120—22no—
402#120—22no—
403C4×Q8—21no—
404C4×Q8D4×C15111yescharacteristic
405C4×D4—22no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4D4×C15111yescharacteristic
411C4×D4D4×C15112yes—
412#117—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4D4×C15112yes—
418C2×C22⋊C4C23×C15112yes—
419C2×C42—21no—
420C2×C42C23×C15111yescharacteristic
421C4⋊C8—21no—
422C4⋊C8—21no—
423#103—22no—
424#103—24no—
425#103—22no—
426C22⋊C8C23×C15112yes—
427C22⋊C8C23×C15112yes—
428#97—21no—
429C4×C8—21no—
430#95—21no—
431#95—24no—
432#95C23×C15112yes—
433C24—22no—
434C24C2×D4×C15112yes—
435#41—82no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—42no—
443C2×Q8—82no—
444C2×Q8C2×D4×C15111yescharacteristic
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—42no—
457C2×D4—82no—
458C2×D4—84no—
459C2×D4C2×D4×C15111yescharacteristic
460C2×D4C2×D4×C15112yes—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4C2×D4×C15111yescharacteristic
468C22×C4C2×D4×C15111yescharacteristic
469C22×C4C2×D4×C15112yes—
470C22×C4C24×C15111yescharacteristic
471Q16—82no—
472SD16—84no—
473SD16—82no—
474C2×C8—22no—
475C2×C8—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4C2×D4×C15112yes—
488C4⋊C4C2×D4×C15111yescharacteristic
489C4⋊C4C2×D4×C15111yescharacteristic
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—84no—
507C42—22no—
508C42—21no—
509C42—42no—
510C42C2×D4×C15111yescharacteristic
511C42C2×D4×C15111yescharacteristic
512C42C2×D4×C15111yescharacteristic
513C42C2×D4×C15111yescharacteristic
514C23—22no—
515C23—21no—
516C23—22no—
517C23—24no—
518C23—42no—
519C23—42no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23C22×D4×C15111yescharacteristic
524Q8—41no—
525Q8—44no—
526Q8—42no—
527Q8—42no—
528Q8—42no—
529Q8—81no—
530Q8—81no—
531D4—42no—
532D4—41no—
533D4—42no—
534D4—44no—
535D4—42no—
536D4—42no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—82no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—44no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4#120×C15111yescharacteristic
563C2×C4#120×C15111yescharacteristic
564C2×C4#120×C15111yescharacteristic
565C2×C4#120×C15111yescharacteristic
566C2×C4C22×D4×C15111yescharacteristic
567C2×C4C22×D4×C15111yescharacteristic
568C8—42no—
569C8—42no—
570C22—21no—
571C22—21no—
572C22—42no—
573C22—42no—
574C22—41no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—41no—
580C22—42no—
581C22—84no—
582C22—164no—
583C22C2×#120×C15111yescharacteristic
584C22#577×C15112yes—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—82no—
596C4—82no—
597C4#455×C15112yes—
598C2—22no—
599C2—82no—
600C2—81no—
601C2—82no—
602C2#3009×C15111yescharacteristic
603C2C2×#455×C15111yescharacteristic
604C2#3027×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3558×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3218×C151C2semidirect
3. #3206×C151C2semidirect
4. #2640×C151C2semidirect
5. #1606×C151C2semidirect
6. #1601×C151C2semidirect
7. #1505×C151C2semidirect
8. #1500×C151C2semidirect
9. #1469×C151C2semidirect
23. C2×C4⋊Q8×C151C22semidirect
33. #451×C151C22semidirect
35. #448×C151C22semidirect
36. #432×C151C22semidirect
37. #431×C151C22semidirect
39. #393×C151C22semidirect
42. #376×C151C22semidirect
43. #328×C151C22semidirect
45. #327×C151C22semidirect
46. #323×C151C22semidirect
302. #18427C151direct (N × H)
303. C151#18427direct (N × H)
305. #3218C2×C151semidirect
306. #3206C2×C151semidirect
307. #2640C2×C151semidirect
308. #1606C2×C151semidirect
309. #1601C2×C151semidirect
310. #1505C2×C151semidirect
311. #1500C2×C151semidirect
312. #1469C2×C151semidirect
326. C2×C4⋊Q8C22×C151semidirect
336. #451C22×C151semidirect
338. #448C22×C151semidirect
339. #432C22×C151semidirect
340. #431C22×C151semidirect
342. #393C22×C151semidirect
345. #376C22×C151semidirect
346. #328C22×C151semidirect
348. #327C22×C151semidirect
349. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3558×C1512
#3218×C1512
#3206×C1512
#2640×C1512
#1606×C1512
#1601×C1512
#1505×C1512
#1500×C1512
#1469×C1512
#18427151