Finite Group Databasebeta

← C151×#19023 #50323948

Subgroups — C151×#19023 #50323948

Order 38656.

880 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#3559×C151C211yesmaximal, characteristic
2#3239×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4C2×#491×C151C211yesmaximal, characteristic, complemented
5#1664×C151C214yesmaximal, complemented
6#1662×C151C214yesmaximal, complemented
7#1530×C151C211yesmaximal, characteristic, complemented
8#1528×C151C211yesmaximal, characteristic, complemented
9#1524×C151C211yesmaximal, characteristic, complemented
10#563×C151C2212yes—
11#562×C151C2212yes—
12#554×C151—21no—
13#553×C151—21no—
14#553×C151—21no—
15#547×C151—22no—
16#547×C151—21no—
17#544×C151—21no—
18#540×C151—21no—
19#539×C151—22no—
20#539×C151—21no—
21#537×C151—21no—
22#532×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#529×C151C2211yescharacteristic
25C2×#125×C151C2211yescharacteristic
26#501×C151C2212yes—
27#491×C151—22no—
28#491×C151C2214yes—
29#489×C151C2214yes—
30#489×C151C2212yes—
31#487×C151—21no—
32#486×C151—21no—
33#484×C151—21no—
34#481×C151—21no—
35#475×C151—21no—
36#474×C151—21no—
37#432×C151C2211yescharacteristic
38#417×C151—22no—
39C2×#103×C151—21no—
40C2×#103×C151—21no—
41C4×M16×C151C2211yescharacteristic
42C2×#97×C151C2211yescharacteristic
43#330×C151C2214yes—
44#330×C151C2212yes—
45#329×C151C2212yes—
46#329×C151C2214yes—
47C2×#41×C151—22no—
48C2×#41×C151D412yes—
49C22×Q8×C151—21no—
50C2×M16×C151—21no—
51C22×C8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151—22no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151D411yescharacteristic
58C4⋊Q8×C151C2312yes—
59#127×C151D411yescharacteristic
60#126×C151—22no—
61#126×C151—22no—
62#126×C151—21no—
63#125×C151—22no—
64#125×C151—21no—
65#125×C151—21no—
66#125×C151—21no—
67#125×C151D412yes—
68#125×C151C2312yes—
69#125×C151C2311yescharacteristic
70#124×C151C2311yescharacteristic
71#124×C151C2312yes—
72#123×C151—22no—
73#123×C151—22no—
74#123×C151—22no—
75#123×C151—22no—
76#123×C151—21no—
77#123×C151—22no—
78#123×C151—22no—
79C22⋊Q8×C151—22no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151D411yescharacteristic
86#121×C151—22no—
87#121×C151—22no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—22no—
91#121×C151—22no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151D411yescharacteristic
95C4×Q8×C151D411yescharacteristic
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151D411yescharacteristic
104#117×C151—21no—
105#117×C151—21no—
106C2×C4⋊C4×C151—22no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151D411yescharacteristic
114C2×C42×C151C2311yescharacteristic
115#107×C151—22no—
116#106×C151—22no—
117C4⋊C8×C151—21no—
118#103×C151—24no—
119#103×C151—24no—
120#103×C151—24no—
121#103×C151—22no—
122#102×C151—24no—
123#102×C151—22no—
124C22⋊C8×C151—21no—
125#97×C151—21no—
126#97×C151C2312yes—
127#97×C151C2312yes—
128#97×C151C2312yes—
129C4×C8×C151—21no—
130#41×C151—44no—
131#41×C151—84no—
132C2×Q8×C151—22no—
133C2×Q8×C151—22no—
134C2×Q8×C151—44no—
135C2×Q8×C151—41no—
136C2×Q8×C151C2×D411yescharacteristic
137C2×Q8×C151C2×D412yes—
138C2×D4×C151—22no—
139C2×D4×C151—21no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151C2×D411yescharacteristic
145C2×D4×C151C2×D412yes—
146C22×C4×C151—21no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—22no—
153C22×C4×C151—41no—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157M16×C151—42no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151—42no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—41no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151C2×D412yes—
183C4⋊C4×C151C2×D412yes—
184C4⋊C4×C151C2×D411yescharacteristic
185C4⋊C4×C151C2×D411yescharacteristic
186C22⋊C4×C151—22no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—21no—
192C22⋊C4×C151—21no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—21no—
198C42×C151—22no—
199C42×C151—21no—
200C42×C151C2×D411yescharacteristic
201C42×C151C2×D411yescharacteristic
202C42×C151C2×D411yescharacteristic
203C42×C151C2411yescharacteristic
204C23×C151—22no—
205C23×C151—21no—
206C23×C151#12011yescharacteristic
207Q8×C151—41no—
208Q8×C151—42no—
209Q8×C151—44no—
210Q8×C151—82no—
211Q8×C151—82no—
212D4×C151—42no—
213D4×C151—41no—
214D4×C151—44no—
215D4×C151—42no—
216D4×C151—42no—
217D4×C151—81no—
218D4×C151—82no—
219D4×C151—82no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—21no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—22no—
228C2×C4×C151—41no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—82no—
233C2×C4×C151—81no—
234C2×C4×C151—82no—
235C2×C4×C151—82no—
236C2×C4×C151—82no—
237C2×C4×C151—82no—
238C2×C4×C151#12011yescharacteristic
239C2×C4×C151#12011yescharacteristic
240C2×C4×C151#12011yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C8×C151—42no—
245C8×C151—42no—
246C8×C151—42no—
247C22×C151—21no—
248C22×C151—21no—
249C22×C151—42no—
250C22×C151—41no—
251C22×C151—41no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—41no—
255C22×C151#45512yes—
256C22×C151C2×#12011yescharacteristic
257C4×C151—21no—
258C4×C151—21no—
259C4×C151—21no—
260C4×C151—21no—
261C4×C151—21no—
262C4×C151—42no—
263C4×C151—42no—
264C4×C151—41no—
265C4×C151—41no—
266C4×C151—42no—
267C4×C151—41no—
268C4×C151—82no—
269C4×C151#45412yes—
270C2×C151—22no—
271C2×C151—82no—
272C2×C151—81no—
273C2×C151C2×#45511yescharacteristic
274C2×C151C2×#45411yescharacteristic
275C2×C151#302211yescharacteristic
276#19023C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#1902311yescharacteristic, direct product factor, Sylow
278#3559C2×C15111yescharacteristic
279#3239C2×C15111yescharacteristic, complemented
280#3141C2×C15111yescharacteristic, complemented
281C2×#491C2×C15111yescharacteristic, complemented
282#1664C2×C15114yescomplemented
283#1662C2×C15114yescomplemented
284#1530C2×C15111yescharacteristic, complemented
285#1528C2×C15111yescharacteristic, complemented
286#1524C2×C15111yescharacteristic, complemented
287#563C22×C15112yes—
288#562C22×C15112yes—
289#554—21no—
290#553—21no—
291#553—21no—
292#547—22no—
293#547—21no—
294#544—21no—
295#540—21no—
296#539—22no—
297#539—21no—
298#537—21no—
299#532C22×C15111yescharacteristic
300C2×C4⋊Q8C22×C15111yescharacteristic
301#529C22×C15111yescharacteristic
302C2×#125C22×C15111yescharacteristic
303#501C22×C15112yes—
304#491—22no—
305#491C22×C15114yes—
306#489C22×C15114yes—
307#489C22×C15112yes—
308#487—21no—
309#486—21no—
310#484—21no—
311#481—21no—
312#475—21no—
313#474—21no—
314#432C22×C15111yescharacteristic
315#417—22no—
316C2×#103—21no—
317C2×#103—21no—
318C4×M16C22×C15111yescharacteristic
319C2×#97C22×C15111yescharacteristic
320#330C22×C15114yes—
321#330C22×C15112yes—
322#329C22×C15112yes—
323#329C22×C15114yes—
324C2×#41—22no—
325C2×#41D4×C15112yes—
326C22×Q8—21no—
327C2×M16—21no—
328C22×C8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—22no—
331C4⋊Q8—21no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8D4×C15111yescharacteristic
335C4⋊Q8C23×C15112yes—
336#127D4×C15111yescharacteristic
337#126—22no—
338#126—22no—
339#126—21no—
340#125—22no—
341#125—21no—
342#125—21no—
343#125—21no—
344#125D4×C15112yes—
345#125C23×C15112yes—
346#125C23×C15111yescharacteristic
347#124C23×C15111yescharacteristic
348#124C23×C15112yes—
349#123—22no—
350#123—22no—
351#123—22no—
352#123—22no—
353#123—21no—
354#123—22no—
355#123—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8D4×C15111yescharacteristic
363#121—22no—
364#121—22no—
365#121—21no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121—21no—
371#121D4×C15111yescharacteristic
372C4×Q8D4×C15111yescharacteristic
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4D4×C15111yescharacteristic
381#117—21no—
382#117—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4D4×C15111yescharacteristic
390C2×C4⋊C4D4×C15111yescharacteristic
391C2×C42C23×C15111yescharacteristic
392#107—22no—
393#106—22no—
394C4⋊C8—21no—
395#103—24no—
396#103—22no—
397#103—24no—
398#103—24no—
399#102—24no—
400#102—22no—
401C22⋊C8—21no—
402#97—21no—
403#97C23×C15112yes—
404#97C23×C15112yes—
405#97C23×C15112yes—
406C4×C8—21no—
407#41—44no—
408#41—84no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—44no—
412C2×Q8—41no—
413C2×Q8C2×D4×C15111yescharacteristic
414C2×Q8C2×D4×C15112yes—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C2×D4×C15111yescharacteristic
422C2×D4C2×D4×C15112yes—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—41no—
431C22×C4C2×D4×C15111yescharacteristic
432C22×C4C2×D4×C15111yescharacteristic
433C22×C4C2×D4×C15111yescharacteristic
434M16—42no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—42no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4C2×D4×C15112yes—
460C4⋊C4C2×D4×C15112yes—
461C4⋊C4C2×D4×C15111yescharacteristic
462C4⋊C4C2×D4×C15111yescharacteristic
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—21no—
475C42—22no—
476C42—21no—
477C42C2×D4×C15111yescharacteristic
478C42C2×D4×C15111yescharacteristic
479C42C2×D4×C15111yescharacteristic
480C42C24×C15111yescharacteristic
481C23—22no—
482C23—21no—
483C23#120×C15111yescharacteristic
484Q8—42no—
485Q8—41no—
486Q8—44no—
487Q8—82no—
488Q8—82no—
489D4—42no—
490D4—41no—
491D4—44no—
492D4—42no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—82no—
510C2×C4—81no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4#120×C15111yescharacteristic
516C2×C4#120×C15111yescharacteristic
517C2×C4#120×C15111yescharacteristic
518C2×C4C22×D4×C15111yescharacteristic
519C2×C4C22×D4×C15111yescharacteristic
520C2×C4C22×D4×C15111yescharacteristic
521C8—42no—
522C8—42no—
523C8—42no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—41no—
528C22—41no—
529C22—42no—
530C22—42no—
531C22—41no—
532C22#455×C15112yes—
533C22C2×#120×C15111yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—42no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—41no—
545C4—82no—
546C4#454×C15112yes—
547C2—22no—
548C2—82no—
549C2—81no—
550C2C2×#455×C15111yescharacteristic
551C2C2×#454×C15111yescharacteristic
552C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3559×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. #3239×C151C2semidirect
3. #3141×C151C2semidirect
4. C2×#491×C151C2semidirect
5. #1664×C151C2semidirect
6. #1662×C151C2semidirect
7. #1530×C151C2semidirect
8. #1528×C151C2semidirect
9. #1524×C151C2semidirect
276. #19023C151direct (N × H)
277. C151#19023direct (N × H)
279. #3239C2×C151semidirect
280. #3141C2×C151semidirect
281. C2×#491C2×C151semidirect
282. #1664C2×C151semidirect
283. #1662C2×C151semidirect
284. #1530C2×C151semidirect
285. #1528C2×C151semidirect
286. #1524C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3559×C1512
#3239×C1512
#3141×C1512
C2×#491×C1512
#1664×C1512
#1662×C1512
#1530×C1512
#1528×C1512
#1524×C1512
#19023151