Finite Group Databasebeta

← C151×#19022 #50323947

Subgroups — C151×#19022 #50323947

Order 38656.

892 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#3559×C151C211yesmaximal, characteristic
2#3218×C151C211yesmaximal, characteristic, complemented
3C2×#501×C151C211yesmaximal, characteristic, complemented
4#3141×C151C211yesmaximal, characteristic, complemented
5#1664×C151C214yesmaximal, complemented
6#1661×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×C151—22no—
27#501×C151C2214yes—
28#497×C151C2212yes—
29#491×C151C2212yes—
30#489×C151C2214yes—
31#487×C151—21no—
32#486×C151—21no—
33#462×C151—21no—
34#461×C151—21no—
35#451×C151—21no—
36#448×C151—21no—
37#432×C151C2211yescharacteristic
38C2×#107×C151—21no—
39C2×#106×C151—21no—
40#417×C151—22no—
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×Q16×C151—22no—
51C2×SD16×C151—22no—
52C2×M16×C151—21no—
53C22×C8×C151—21no—
54C4⋊Q8×C151—21no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151C2312yes—
61#127×C151D411yescharacteristic
62#126×C151—22no—
63#126×C151—22no—
64#126×C151—21no—
65#125×C151—22no—
66#125×C151—21no—
67#125×C151—21no—
68#125×C151—21no—
69#125×C151D412yes—
70#125×C151C2311yescharacteristic
71#125×C151C2312yes—
72#124×C151C2312yes—
73#124×C151C2311yescharacteristic
74#123×C151—22no—
75#123×C151—22no—
76#123×C151—22no—
77#123×C151—22no—
78#123×C151—21no—
79#123×C151—22no—
80#123×C151—22no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151D411yescharacteristic
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—22no—
93#121×C151—22no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151D411yescharacteristic
97C4×Q8×C151D411yescharacteristic
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151D411yescharacteristic
106#117×C151—21no—
107#117×C151—21no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151D411yescharacteristic
115C2×C4⋊C4×C151D411yescharacteristic
116C2×C42×C151C2311yescharacteristic
117#107×C151—24no—
118#106×C151—24no—
119C4⋊C8×C151—21no—
120#103×C151—22no—
121#103×C151—22no—
122#103×C151—24no—
123#102×C151—24no—
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—41no—
135C2×Q8×C151—82no—
136C2×Q8×C151C2×D412yes—
137C2×Q8×C151C2×D411yescharacteristic
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×D412yes—
145C2×D4×C151C2×D411yescharacteristic
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
157Q16×C151—82no—
158SD16×C151—82no—
159M16×C151—42no—
160C2×C8×C151—24no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—41no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151C2×D411yescharacteristic
185C4⋊C4×C151C2×D411yescharacteristic
186C4⋊C4×C151C2×D412yes—
187C4⋊C4×C151C2×D412yes—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—21no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—21no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—21no—
200C42×C151—22no—
201C42×C151—21no—
202C42×C151C2×D411yescharacteristic
203C42×C151C2×D411yescharacteristic
204C42×C151C2×D411yescharacteristic
205C42×C151C2411yescharacteristic
206C23×C151—22no—
207C23×C151—21no—
208C23×C151#12011yescharacteristic
209Q8×C151—42no—
210Q8×C151—41no—
211Q8×C151—42no—
212Q8×C151—42no—
213Q8×C151—82no—
214Q8×C151—82no—
215D4×C151—42no—
216D4×C151—41no—
217D4×C151—44no—
218D4×C151—42no—
219D4×C151—42no—
220D4×C151—81no—
221D4×C151—82no—
222D4×C151—82no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—21no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—22no—
231C2×C4×C151—41no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—82no—
236C2×C4×C151—81no—
237C2×C4×C151—82no—
238C2×C4×C151—82no—
239C2×C4×C151—82no—
240C2×C4×C151—82no—
241C2×C4×C151#12011yescharacteristic
242C2×C4×C151#12011yescharacteristic
243C2×C4×C151#12011yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C22×D411yescharacteristic
247C8×C151—24no—
248C8×C151—42no—
249C8×C151—42no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—42no—
253C22×C151—41no—
254C22×C151—41no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—41no—
258C22×C151#45512yes—
259C22×C151C2×#12011yescharacteristic
260C4×C151—21no—
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—21no—
265C4×C151—42no—
266C4×C151—42no—
267C4×C151—41no—
268C4×C151—41no—
269C4×C151—42no—
270C4×C151—41no—
271C4×C151—82no—
272C4×C151#45612yes—
273C2×C151—22no—
274C2×C151—82no—
275C2×C151—81no—
276C2×C151C2×#45511yescharacteristic
277C2×C151C2×#45611yescharacteristic
278C2×C151#302111yescharacteristic
279#19022C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#1902211yescharacteristic, direct product factor, Sylow
281#3559C2×C15111yescharacteristic
282#3218C2×C15111yescharacteristic, complemented
283C2×#501C2×C15111yescharacteristic, complemented
284#3141C2×C15111yescharacteristic, complemented
285#1664C2×C15114yescomplemented
286#1661C2×C15114yescomplemented
287#1530C2×C15111yescharacteristic, complemented
288#1528C2×C15111yescharacteristic, complemented
289#1524C2×C15111yescharacteristic, complemented
290#563C22×C15112yes—
291#562C22×C15112yes—
292#554—21no—
293#553—21no—
294#553—21no—
295#547—22no—
296#547—21no—
297#544—21no—
298#540—21no—
299#539—22no—
300#539—21no—
301#537—21no—
302#532C22×C15111yescharacteristic
303C2×C4⋊Q8C22×C15111yescharacteristic
304#529C22×C15111yescharacteristic
305C2×#125C22×C15111yescharacteristic
306#501—22no—
307#501C22×C15114yes—
308#497C22×C15112yes—
309#491C22×C15112yes—
310#489C22×C15114yes—
311#487—21no—
312#486—21no—
313#462—21no—
314#461—21no—
315#451—21no—
316#448—21no—
317#432C22×C15111yescharacteristic
318C2×#107—21no—
319C2×#106—21no—
320#417—22no—
321C4×M16C22×C15111yescharacteristic
322C2×#97C22×C15111yescharacteristic
323#330C22×C15114yes—
324#330C22×C15112yes—
325#329C22×C15112yes—
326#329C22×C15114yes—
327C2×#41—22no—
328C2×#41D4×C15112yes—
329C22×Q8—21no—
330C2×Q16—22no—
331C2×SD16—22no—
332C2×M16—21no—
333C22×C8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—22no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8D4×C15111yescharacteristic
340C4⋊Q8C23×C15112yes—
341#127D4×C15111yescharacteristic
342#126—22no—
343#126—22no—
344#126—21no—
345#125—22no—
346#125—21no—
347#125—21no—
348#125—21no—
349#125D4×C15112yes—
350#125C23×C15112yes—
351#125C23×C15111yescharacteristic
352#124C23×C15111yescharacteristic
353#124C23×C15112yes—
354#123—22no—
355#123—22no—
356#123—22no—
357#123—22no—
358#123—21no—
359#123—22no—
360#123—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8D4×C15111yescharacteristic
368#121—22no—
369#121—22no—
370#121—21no—
371#121—21no—
372#121—22no—
373#121—22no—
374#121—21no—
375#121—21no—
376#121D4×C15111yescharacteristic
377C4×Q8D4×C15111yescharacteristic
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4D4×C15111yescharacteristic
386#117—21no—
387#117—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4D4×C15111yescharacteristic
395C2×C4⋊C4D4×C15111yescharacteristic
396C2×C42C23×C15111yescharacteristic
397#107—24no—
398#106—24no—
399C4⋊C8—21no—
400#103—24no—
401#103—22no—
402#103—22no—
403#102—24no—
404C22⋊C8—21no—
405#97—21no—
406#97C23×C15112yes—
407#97C23×C15112yes—
408#97C23×C15112yes—
409C4×C8—21no—
410#41—44no—
411#41—84no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—41no—
415C2×Q8—82no—
416C2×Q8C2×D4×C15112yes—
417C2×Q8C2×D4×C15111yescharacteristic
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×D4×C15112yes—
425C2×D4C2×D4×C15111yescharacteristic
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4C2×D4×C15111yescharacteristic
435C22×C4C2×D4×C15111yescharacteristic
436C22×C4C2×D4×C15111yescharacteristic
437Q16—82no—
438SD16—82no—
439M16—42no—
440C2×C8—24no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C15111yescharacteristic
465C4⋊C4C2×D4×C15111yescharacteristic
466C4⋊C4C2×D4×C15112yes—
467C4⋊C4C2×D4×C15112yes—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C42—22no—
481C42—21no—
482C42C2×D4×C15111yescharacteristic
483C42C2×D4×C15111yescharacteristic
484C42C2×D4×C15111yescharacteristic
485C42C24×C15111yescharacteristic
486C23—22no—
487C23—21no—
488C23#120×C15111yescharacteristic
489Q8—41no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493Q8—82no—
494Q8—82no—
495D4—41no—
496D4—42no—
497D4—44no—
498D4—42no—
499D4—42no—
500D4—81no—
501D4—82no—
502D4—82no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4#120×C15111yescharacteristic
522C2×C4#120×C15111yescharacteristic
523C2×C4#120×C15111yescharacteristic
524C2×C4C22×D4×C15111yescharacteristic
525C2×C4C22×D4×C15111yescharacteristic
526C2×C4C22×D4×C15111yescharacteristic
527C8—24no—
528C8—42no—
529C8—42no—
530C22—21no—
531C22—21no—
532C22—42no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22#455×C15112yes—
539C22C2×#120×C15111yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—42no—
546C4—42no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—82no—
552C4#456×C15112yes—
553C2—22no—
554C2—82no—
555C2—81no—
556C2C2×#455×C15111yescharacteristic
557C2C2×#456×C15111yescharacteristic
558C2#3021×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. #3218×C151C2semidirect
3. C2×#501×C151C2semidirect
4. #3141×C151C2semidirect
5. #1664×C151C2semidirect
6. #1661×C151C2semidirect
7. #1530×C151C2semidirect
8. #1528×C151C2semidirect
9. #1524×C151C2semidirect
279. #19022C151direct (N × H)
280. C151#19022direct (N × H)
282. #3218C2×C151semidirect
283. C2×#501C2×C151semidirect
284. #3141C2×C151semidirect
285. #1664C2×C151semidirect
286. #1661C2×C151semidirect
287. #1530C2×C151semidirect
288. #1528C2×C151semidirect
289. #1524C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3559×C1512
#3218×C1512
C2×#501×C1512
#3141×C1512
#1664×C1512
#1661×C1512
#1530×C1512
#1528×C1512
#1524×C1512
#19022151