Finite Group Databasebeta

← C151×#18936 #50323861

Subgroups — C151×#18936 #50323861

Order 38656.

948 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3548×C151C211yesmaximal, characteristic, complemented
2#3245×C151C211yesmaximal, characteristic, complemented
3#3216×C151C211yesmaximal, characteristic, complemented
4#3207×C151C211yesmaximal, characteristic, complemented
5#1644×C151C212yesmaximal, complemented
6#1641×C151C212yesmaximal, complemented
7#1622×C151C212yesmaximal, complemented
8#1621×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1481×C151C211yesmaximal, characteristic, complemented
12#562×C151—22no—
13#554×C151—21no—
14#554×C151C2212yes—
15#550×C151—21no—
16#550×C151C2212yes—
17#547×C151—21no—
18#547×C151—21no—
19#540×C151—22no—
20#537×C151—22no—
21#537×C151—22no—
22#533×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#497×C151—21no—
27#493×C151C2211yescharacteristic
28#492×C151C2211yescharacteristic
29#489×C151—21no—
30#487×C151C2211yescharacteristic
31#486×C151C2211yescharacteristic
32#474×C151—21no—
33#474×C151C2212yes—
34#466×C151—22no—
35#463×C151—22no—
36#462×C151C2212yes—
37#460×C151C2212yes—
38#459×C151—21no—
39#459×C151C2212yes—
40#452×C151—22no—
41#449×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45#333×C151C2212yes—
46#331×C151C2212yes—
47Q8⋊C8×C151C2212yes—
48Q8⋊C8×C151C2212yes—
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—22no—
52C2×#41×C151—21no—
53C2×#41×C151—21no—
54C2×#41×C151—22no—
55C2×#41×C151D412yes—
56C2×Q16×C151—22no—
57C2×SD16×C151—22no—
58C2×SD16×C151—22no—
59C2×D8×C151—22no—
60C2×D8×C151—22no—
61C22×C8×C151—21no—
62C4⋊Q8×C151D411yescharacteristic
63C4⋊Q8×C151D411yescharacteristic
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151C2311yescharacteristic
66C4⋊Q8×C151C2311yescharacteristic
67#127×C151—22no—
68#127×C151D411yescharacteristic
69#127×C151C2311yescharacteristic
70#127×C151C2311yescharacteristic
71#125×C151—22no—
72#125×C151—21no—
73#124×C151—21no—
74#124×C151—21no—
75#124×C151D412yes—
76#123×C151—24no—
77#123×C151—24no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151D412yes—
84#121×C151—24no—
85#121×C151—24no—
86#121×C151—22no—
87#121×C151—24no—
88#121×C151—24no—
89#121×C151—21no—
90#121×C151—21no—
91#121×C151—21no—
92#121×C151—22no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151D412yes—
96C4×Q8×C151—21no—
97C4×Q8×C151C2312yes—
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×C151C2312yes—
106#117×C151—21no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—22no—
109C2×C42×C151C2311yescharacteristic
110#107×C151—22no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151C2312yes—
114C4⋊C8×C151C2312yes—
115#103×C151—22no—
116#103×C151—22no—
117#102×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123#97×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126#41×C151—82no—
127#41×C151—82no—
128#41×C151—82no—
129#41×C151—82no—
130#41×C151—82no—
131#41×C151—84no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151C2×D412yes—
136C2×Q8×C151C2×D412yes—
137C2×D4×C151—24no—
138C2×D4×C151—24no—
139C2×D4×C151—22no—
140C2×D4×C151—22no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—41no—
149C2×D4×C151C2×D412yes—
150C2×D4×C151C2×D412yes—
151C22×C4×C151—24no—
152C22×C4×C151—24no—
153C22×C4×C151—22no—
154C22×C4×C151—22no—
155C22×C4×C151—41no—
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159Q16×C151—82no—
160SD16×C151—82no—
161SD16×C151—82no—
162D8×C151—82no—
163D8×C151—82no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—81no—
169C4⋊C4×C151—24no—
170C4⋊C4×C151—24no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151C2×D412yes—
182C4⋊C4×C151C2×D412yes—
183C22⋊C4×C151—24no—
184C22⋊C4×C151—24no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—41no—
191C22⋊C4×C151—41no—
192C42×C151—22no—
193C42×C151C2×D411yescharacteristic
194C42×C151C2×D411yescharacteristic
195C42×C151C2×D411yescharacteristic
196C42×C151C2411yescharacteristic
197C23×C151—22no—
198C23×C151—22no—
199C23×C151—41no—
200C23×C151#12011yescharacteristic
201Q8×C151—22no—
202Q8×C151—22no—
203Q8×C151—42no—
204Q8×C151—42no—
205Q8×C151—42no—
206Q8×C151—81no—
207D4×C151—22no—
208D4×C151—22no—
209D4×C151—42no—
210D4×C151—42no—
211D4×C151—42no—
212D4×C151—42no—
213D4×C151—42no—
214D4×C151—41no—
215D4×C151—41no—
216D4×C151—41no—
217D4×C151—41no—
218D4×C151—81no—
219D4×C151—82no—
220D4×C151—82no—
221D4×C151—84no—
222D4×C151—84no—
223D4×C151—82no—
224C2×C4×C151—22no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—22no—
228C2×C4×C151—22no—
229C2×C4×C151—22no—
230C2×C4×C151—22no—
231C2×C4×C151—41no—
232C2×C4×C151—44no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—41no—
236C2×C4×C151—82no—
237C2×C4×C151—84no—
238C2×C4×C151—84no—
239C2×C4×C151#12011yescharacteristic
240C2×C4×C151#12011yescharacteristic
241C2×C4×C151#12011yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C8×C151—41no—
246C8×C151—41no—
247C8×C151—42no—
248C8×C151—42no—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—81no—
259C22×C151—81no—
260C22×C151—81no—
261C22×C151C2×#12011yescharacteristic
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—21no—
265C4×C151—21no—
266C4×C151—42no—
267C4×C151—42no—
268C4×C151—42no—
269C4×C151—42no—
270C4×C151—81no—
271C4×C151#57612yes—
272C4×C151#57711yescharacteristic
273C4×C151#57811yescharacteristic
274C2×C151—41no—
275C2×C151—82no—
276C2×C151—82no—
277C2×C151—161no—
278C2×C151#300811yescharacteristic
279C2×C151#301311yescharacteristic
280C2×C151#301911yescharacteristic
281#18936C15111yesmaximal, characteristic, direct product factor, Sylow
282C151#1893611yescharacteristic, direct product factor, Sylow
283#3548C2×C15111yescharacteristic, complemented
284#3245C2×C15111yescharacteristic, complemented
285#3216C2×C15111yescharacteristic, complemented
286#3207C2×C15111yescharacteristic, complemented
287#1644C2×C15112yescomplemented
288#1641C2×C15112yescomplemented
289#1622C2×C15112yescomplemented
290#1621C2×C15112yescomplemented
291#1551C2×C15111yescharacteristic, complemented
292#1496C2×C15111yescharacteristic, complemented
293#1481C2×C15111yescharacteristic, complemented
294#562—22no—
295#554—21no—
296#554C22×C15112yes—
297#550—21no—
298#550C22×C15112yes—
299#547—21no—
300#547—21no—
301#540—22no—
302#537—22no—
303#537—22no—
304#533C22×C15111yescharacteristic
305#532C22×C15111yescharacteristic
306#532C22×C15111yescharacteristic
307#532C22×C15111yescharacteristic
308#497—21no—
309#493C22×C15111yescharacteristic
310#492C22×C15111yescharacteristic
311#489—21no—
312#487C22×C15111yescharacteristic
313#486C22×C15111yescharacteristic
314#474—21no—
315#474C22×C15112yes—
316#466—22no—
317#463—22no—
318#462C22×C15112yes—
319#460C22×C15112yes—
320#459—21no—
321#459C22×C15112yes—
322#452—22no—
323#449—22no—
324#432C22×C15111yescharacteristic
325#431C22×C15111yescharacteristic
326C2×C4⋊C8C22×C15111yescharacteristic
327#333C22×C15112yes—
328#331C22×C15112yes—
329Q8⋊C8C22×C15112yes—
330Q8⋊C8C22×C15112yes—
331D4⋊C8C22×C15112yes—
332D4⋊C8C22×C15112yes—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41D4×C15112yes—
338C2×Q16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×D8—22no—
342C2×D8—22no—
343C22×C8—21no—
344C4⋊Q8D4×C15111yescharacteristic
345C4⋊Q8D4×C15111yescharacteristic
346C4⋊Q8D4×C15111yescharacteristic
347C4⋊Q8C23×C15111yescharacteristic
348C4⋊Q8C23×C15111yescharacteristic
349#127—22no—
350#127D4×C15111yescharacteristic
351#127C23×C15111yescharacteristic
352#127C23×C15111yescharacteristic
353#125—22no—
354#125—21no—
355#124—21no—
356#124—21no—
357#124D4×C15112yes—
358#123—24no—
359#123—24no—
360C22⋊Q8—22no—
361C22⋊Q8—24no—
362C22⋊Q8—22no—
363C22⋊Q8—24no—
364C22⋊Q8—21no—
365C22⋊Q8D4×C15112yes—
366#121—24no—
367#121—24no—
368#121—22no—
369#121—24no—
370#121—24no—
371#121—21no—
372#121—21no—
373#121—21no—
374#121—22no—
375#121—21no—
376#121—21no—
377#121D4×C15112yes—
378C4×Q8—21no—
379C4×Q8C23×C15112yes—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C15112yes—
388#117—21no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C42C23×C15111yescharacteristic
392#107—22no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8C23×C15112yes—
396C4⋊C8C23×C15112yes—
397#103—22no—
398#103—22no—
399#102—22no—
400#102—22no—
401#102—22no—
402#102—22no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405#97—21no—
406C4×C8C23×C15111yescharacteristic
407C4×C8C23×C15111yescharacteristic
408#41—82no—
409#41—82no—
410#41—82no—
411#41—82no—
412#41—82no—
413#41—84no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8C2×D4×C15112yes—
418C2×Q8C2×D4×C15112yes—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—41no—
431C2×D4C2×D4×C15112yes—
432C2×D4C2×D4×C15112yes—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4C2×D4×C15111yescharacteristic
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C2×D4×C15111yescharacteristic
441Q16—82no—
442SD16—82no—
443SD16—82no—
444D8—82no—
445D8—82no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—81no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4C2×D4×C15112yes—
464C4⋊C4C2×D4×C15112yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—22no—
475C42C2×D4×C15111yescharacteristic
476C42C2×D4×C15111yescharacteristic
477C42C2×D4×C15111yescharacteristic
478C42C24×C15111yescharacteristic
479C23—22no—
480C23—22no—
481C23—41no—
482C23#120×C15111yescharacteristic
483Q8—22no—
484Q8—22no—
485Q8—42no—
486Q8—42no—
487Q8—42no—
488Q8—81no—
489D4—22no—
490D4—22no—
491D4—42no—
492D4—42no—
493D4—42no—
494D4—42no—
495D4—42no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501D4—82no—
502D4—82no—
503D4—84no—
504D4—84no—
505D4—82no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4—84no—
520C2×C4—84no—
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—41no—
528C8—41no—
529C8—42no—
530C8—42no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22C2×#120×C15111yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—81no—
553C4#576×C15112yes—
554C4#577×C15111yescharacteristic
555C4#578×C15111yescharacteristic
556C2—41no—
557C2—82no—
558C2—82no—
559C2—161no—
560C2#3008×C15111yescharacteristic
561C2#3013×C15111yescharacteristic
562C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
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. #3548×C151C2semidirect
2. #3245×C151C2semidirect
3. #3216×C151C2semidirect
4. #3207×C151C2semidirect
5. #1644×C151C2semidirect
6. #1641×C151C2semidirect
7. #1622×C151C2semidirect
8. #1621×C151C2semidirect
9. #1551×C151C2semidirect
10. #1496×C151C2semidirect
11. #1481×C151C2semidirect
281. #18936C151direct (N × H)
282. C151#18936direct (N × H)
283. #3548C2×C151semidirect
284. #3245C2×C151semidirect
285. #3216C2×C151semidirect
286. #3207C2×C151semidirect
287. #1644C2×C151semidirect
288. #1641C2×C151semidirect
289. #1622C2×C151semidirect
290. #1621C2×C151semidirect
291. #1551C2×C151semidirect
292. #1496C2×C151semidirect
293. #1481C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3548×C1512
#3245×C1512
#3216×C1512
#3207×C1512
#1644×C1512
#1641×C1512
#1622×C1512
#1621×C1512
#1551×C1512
#1496×C1512
#1481×C1512
#18936151