Finite Group Databasebeta

← C151×#22439 #50327364

Subgroups — C151×#22439 #50327364

Order 38656.

1466 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C151C211yesmaximal, characteristic
2C2×#440×C151C212yesmaximal, complemented
3#2341×C151C211yesmaximal, characteristic, complemented
4#2339×C151C211yesmaximal, characteristic, complemented
5#1973×C151C212yesmaximal, complemented
6#1879×C151C212yesmaximal, complemented
7#1878×C151C212yesmaximal, complemented
8#1808×C151C211yesmaximal, characteristic, complemented
9#1788×C151C211yesmaximal, characteristic, complemented
10#1788×C151C211yesmaximal, characteristic, complemented
11#1752×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151C2211yescharacteristic
13C22×#41×C151C2211yescharacteristic
14C2×#135×C151—28no—
15C2×#135×C151C418yescomplemented
16C22×Q16×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C23×C8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2212yes—
22C2×C4×D4×C151C2212yes—
23#440×C151—28no—
24C2×#107×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2211yescharacteristic
30C2×#97×C151C2212yes—
31#391×C151C2212yes—
32#390×C151—22no—
33#390×C151C2212yes—
34#386×C151—22no—
35#381×C151—21no—
36#380×C151—21no—
37#380×C151C2211yescharacteristic
38#380×C151C2211yescharacteristic
39C4×C22⋊C4×C151—21no—
40C4×C22⋊C4×C151C2211yescharacteristic
41C2×#95×C151—21no—
42#340×C151C2212yes—
43#336×C151C2212yes—
44C2×#41×C151—24no—
45C2×#41×C151—22no—
46C2×#41×C151—22no—
47C2×#41×C151—24no—
48C2×#41×C151—42no—
49C2×#41×C151—42no—
50C2×#41×C151C2×C414yes—
51C2×#41×C151C2×C414yescomplemented
52C22×Q8×C151C2311yescharacteristic
53C22×Q8×C151C2311yescharacteristic
54C22×D4×C151—21no—
55C22×D4×C151—21no—
56C22×D4×C151C2311yescharacteristic
57C22×D4×C151C2311yescharacteristic
58C23×C4×C151—21no—
59C23×C4×C151—21no—
60C23×C4×C151—22no—
61C23×C4×C151C2311yescharacteristic
62#135×C151—232no—
63C2×Q16×C151—24no—
64C2×Q16×C151C2×C414yescomplemented
65C2×SD16×C151—24no—
66C2×SD16×C151C2×C414yes—
67C2×SD16×C151C2×C414yescomplemented
68C2×SD16×C151D418yes—
69C2×D8×C151—24no—
70C2×D8×C151C2×C414yes—
71C22×C8×C151—24no—
72C22×C8×C151C2×C414yescomplemented
73C22×C8×C151C2312yes—
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C4×Q8×C151—24no—
77C4×Q8×C151—42no—
78C4×D4×C151—24no—
79C4×D4×C151—42no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2312yes—
83C2×C22⋊C4×C151—22no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—21no—
87C2×C22⋊C4×C151—21no—
88C2×C22⋊C4×C151D412yes—
89C2×C42×C151—22no—
90C2×C42×C151C2312yes—
91#107×C151—24no—
92#103×C151—24no—
93#103×C151—42no—
94#102×C151—24no—
95#102×C151—42no—
96C22⋊C8×C151—22no—
97#97×C151—24no—
98#95×C151—21no—
99#95×C151—22no—
100#95×C151—21no—
101#95×C151—22no—
102#95×C151D411yescharacteristic
103#95×C151D411yescharacteristic
104C24×C151—21no—
105C24×C151—21no—
106C24×C151C2×D411yescharacteristic
107#41×C151—28no—
108#41×C151—28no—
109#41×C151—44no—
110#41×C151—44no—
111#41×C151—48no—
112#41×C151—48no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151C22×C412yes—
119C2×Q8×C151C22×C412yes—
120C2×Q8×C151C2×D414yes—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—22no—
124C2×D4×C151—21no—
125C2×D4×C151—21no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—44no—
129C2×D4×C151—44no—
130C2×D4×C151C22×C412yes—
131C2×D4×C151C22×C412yes—
132C2×D4×C151C2×D414yes—
133C22×C4×C151—21no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—21no—
137C22×C4×C151—24no—
138C22×C4×C151—24no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—44no—
142C22×C4×C151—44no—
143C22×C4×C151—44no—
144C22×C4×C151—44no—
145C22×C4×C151—82no—
146C22×C4×C151C22×C412yes—
147C22×C4×C151C2×D412yes—
148C22×C4×C151C2×D412yes—
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151#4112yes—
151C22×C4×C151C2411yescharacteristic
152Q16×C151—28no—
153SD16×C151—28no—
154SD16×C151C22⋊C4116yescomplemented
155D8×C151—28no—
156C2×C8×C151—22no—
157C2×C8×C151—28no—
158C2×C8×C151—22no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151C22×C412yes—
162C2×C8×C151C22×C412yes—
163C2×C8×C151C2×D414yes—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—44no—
169C22⋊C4×C151—42no—
170C22⋊C4×C151—44no—
171C22⋊C4×C151—44no—
172C22⋊C4×C151—82no—
173C22⋊C4×C151—81no—
174C22⋊C4×C151—81no—
175C42×C151—22no—
176C42×C151—22no—
177C42×C151—44no—
178C23×C151—22no—
179C23×C151—24no—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—22no—
185C23×C151—42no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151—42no—
189C23×C151—42no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151C4×D412yes—
193C23×C151C22×D411yescharacteristic
194Q8×C151—22no—
195Q8×C151—24no—
196Q8×C151—22no—
197Q8×C151—22no—
198Q8×C151—42no—
199Q8×C151C2×C22⋊C414yes—
200D4×C151—22no—
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—24no—
204D4×C151—48no—
205D4×C151—48no—
206D4×C151—42no—
207D4×C151C2×C22⋊C414yes—
208C2×C4×C151—22no—
209C2×C4×C151—24no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—24no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—48no—
222C2×C4×C151—48no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—88no—
231C2×C4×C151C4×D412yes—
232C2×C4×C151C23×C411yescharacteristic
233C2×C4×C151C22×D412yes—
234C2×C4×C151C2×#4111yescharacteristic
235C2×C4×C151H(5,𝔽2)12yes—
236C8×C151—22no—
237C8×C151—42no—
238C8×C151C2×C22⋊C414yes—
239C22×C151—22no—
240C22×C151—24no—
241C22×C151—22no—
242C22×C151—22no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—44no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—44no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—82no—
253C22×C151—82no—
254C22×C151C2×C4×D411yescharacteristic
255C22×C151D4212yes—
256C22×C151#57512yes—
257C22×C151#57611yescharacteristic
258C22×C151#57811yescharacteristic
259C4×C151—22no—
260C4×C151—24no—
261C4×C151—42no—
262C4×C151—42no—
263C4×C151—42no—
264C4×C151—82no—
265C4×C151—82no—
266C4×C151C22×C22⋊C411yescharacteristic
267C4×C151#51811yescharacteristic
268C4×C151#54612yes—
269C2×C151—42no—
270C2×C151—44no—
271C2×C151—82no—
272C2×C151D4×C22⋊C411yescharacteristic
273C2×C151#294311yescharacteristic
274C2×C151#295111yescharacteristic
275C2×C151#326812yes—
276C2×C151#326912yes—
277#22439C15111yesmaximal, characteristic, direct product factor, Sylow
278C151#2243911yescharacteristic, direct product factor, Sylow
279C22×#135C2×C15111yescharacteristic
280C2×#440C2×C15112yescomplemented
281#2341C2×C15111yescharacteristic, complemented
282#2339C2×C15111yescharacteristic, complemented
283#1973C2×C15112yescomplemented
284#1879C2×C15112yescomplemented
285#1878C2×C15112yescomplemented
286#1808C2×C15111yescharacteristic, complemented
287#1788C2×C15111yescharacteristic, complemented
288#1788C2×C15111yescharacteristic, complemented
289#1752C2×C15111yescharacteristic, complemented
290C22×#41C22×C15111yescharacteristic
291C22×#41C22×C15111yescharacteristic
292C2×#135—28no—
293C2×#135C4×C15118yescomplemented
294C22×Q16C22×C15111yescharacteristic
295C22×SD16C22×C15111yescharacteristic
296C22×SD16C22×C15111yescharacteristic
297C22×D8C22×C15111yescharacteristic
298C23×C8C22×C15111yescharacteristic
299C2×C4×Q8C22×C15112yes—
300C2×C4×D4C22×C15112yes—
301#440—28no—
302C2×#107C22×C15112yes—
303C2×#103C22×C15112yes—
304C2×#103C22×C15112yes—
305C2×#102C22×C15112yes—
306C2×#102C22×C15112yes—
307C2×C22⋊C8C22×C15111yescharacteristic
308C2×#97C22×C15112yes—
309#391C22×C15112yes—
310#390—22no—
311#390C22×C15112yes—
312#386—22no—
313#381—21no—
314#380—21no—
315#380C22×C15111yescharacteristic
316#380C22×C15111yescharacteristic
317C4×C22⋊C4—21no—
318C4×C22⋊C4C22×C15111yescharacteristic
319C2×#95—21no—
320#340C22×C15112yes—
321#336C22×C15112yes—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—42no—
327C2×#41—42no—
328C2×#41C2×C4×C15114yes—
329C2×#41C2×C4×C15114yescomplemented
330C22×Q8C23×C15111yescharacteristic
331C22×Q8C23×C15111yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4C23×C15111yescharacteristic
335C22×D4C23×C15111yescharacteristic
336C23×C4—21no—
337C23×C4—21no—
338C23×C4—22no—
339C23×C4C23×C15111yescharacteristic
340#135—232no—
341C2×Q16—24no—
342C2×Q16C2×C4×C15114yescomplemented
343C2×SD16—24no—
344C2×SD16C2×C4×C15114yes—
345C2×SD16C2×C4×C15114yescomplemented
346C2×SD16D4×C15118yes—
347C2×D8—24no—
348C2×D8C2×C4×C15114yes—
349C22×C8—24no—
350C22×C8C2×C4×C15114yescomplemented
351C22×C8C23×C15112yes—
352C22×C8C23×C15111yescharacteristic
353C22×C8C23×C15111yescharacteristic
354C4×Q8—24no—
355C4×Q8—42no—
356C4×D4—24no—
357C4×D4—42no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4C23×C15112yes—
360C2×C4⋊C4C23×C15112yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4D4×C15112yes—
367C2×C42—22no—
368C2×C42C23×C15112yes—
369#107—24no—
370#103—24no—
371#103—42no—
372#102—24no—
373#102—42no—
374C22⋊C8—22no—
375#97—24no—
376#95—21no—
377#95—22no—
378#95—21no—
379#95—22no—
380#95D4×C15111yescharacteristic
381#95D4×C15111yescharacteristic
382C24—21no—
383C24—21no—
384C24C2×D4×C15111yescharacteristic
385#41—28no—
386#41—28no—
387#41—44no—
388#41—44no—
389#41—48no—
390#41—48no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8C22×C4×C15112yes—
397C2×Q8C22×C4×C15112yes—
398C2×Q8C2×D4×C15114yes—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4C22×C4×C15112yes—
409C2×D4C22×C4×C15112yes—
410C2×D4C2×D4×C15114yes—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—44no—
422C22×C4—44no—
423C22×C4—82no—
424C22×C4C22×C4×C15112yes—
425C22×C4C2×D4×C15112yes—
426C22×C4C2×D4×C15112yes—
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4#41×C15112yes—
429C22×C4C24×C15111yescharacteristic
430Q16—28no—
431SD16—28no—
432SD16C22⋊C4×C151116yescomplemented
433D8—28no—
434C2×C8—22no—
435C2×C8—28no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8C22×C4×C15112yes—
440C2×C8C22×C4×C15112yes—
441C2×C8C2×D4×C15114yes—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—44no—
447C22⋊C4—42no—
448C22⋊C4—44no—
449C22⋊C4—44no—
450C22⋊C4—82no—
451C22⋊C4—81no—
452C22⋊C4—81no—
453C42—22no—
454C42—22no—
455C42—44no—
456C23—22no—
457C23—24no—
458C23—22no—
459C23—22no—
460C23—21no—
461C23—21no—
462C23—22no—
463C23—42no—
464C23—41no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23C4×D4×C15112yes—
471C23C22×D4×C15111yescharacteristic
472Q8—22no—
473Q8—24no—
474Q8—22no—
475Q8—22no—
476Q8—42no—
477Q8C2×C22⋊C4×C15114yes—
478D4—22no—
479D4—22no—
480D4—22no—
481D4—24no—
482D4—48no—
483D4—48no—
484D4—42no—
485D4C2×C22⋊C4×C15114yes—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—48no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—88no—
509C2×C4C4×D4×C15112yes—
510C2×C4C23×C4×C15111yescharacteristic
511C2×C4C22×D4×C15112yes—
512C2×C4C2×#41×C15111yescharacteristic
513C2×C4H(5,𝔽2)×C15112yes—
514C8—22no—
515C8—42no—
516C8C2×C22⋊C4×C15114yes—
517C22—22no—
518C22—24no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—44no—
524C22—42no—
525C22—42no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—82no—
531C22—82no—
532C22C2×C4×D4×C15111yescharacteristic
533C22D42×C15112yes—
534C22#575×C15112yes—
535C22#576×C15111yescharacteristic
536C22#578×C15111yescharacteristic
537C4—22no—
538C4—24no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—82no—
543C4—82no—
544C4C22×C22⋊C4×C15111yescharacteristic
545C4#518×C15111yescharacteristic
546C4#546×C15112yes—
547C2—42no—
548C2—44no—
549C2—82no—
550C2D4×C22⋊C4×C15111yescharacteristic
551C2#2943×C15111yescharacteristic
552C2#2951×C15111yescharacteristic
553C2#3268×C15112yes—
554C2#3269×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×#135×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C151C2semidirect
3. #2341×C151C2semidirect
4. #2339×C151C2semidirect
5. #1973×C151C2semidirect
6. #1879×C151C2semidirect
7. #1878×C151C2semidirect
8. #1808×C151C2semidirect
9. #1788×C151C2semidirect
10. #1788×C151C2semidirect
11. #1752×C151C2semidirect
15. C2×#135×C151C4semidirect
51. C2×#41×C151C2×C4semidirect
64. C2×Q16×C151C2×C4semidirect
67. C2×SD16×C151C2×C4semidirect
72. C22×C8×C151C2×C4semidirect
154. SD16×C151C22⋊C4semidirect
277. #22439C151direct (N × H)
278. C151#22439direct (N × H)
280. C2×#440C2×C151semidirect
281. #2341C2×C151semidirect
282. #2339C2×C151semidirect
283. #1973C2×C151semidirect
284. #1879C2×C151semidirect
285. #1878C2×C151semidirect
286. #1808C2×C151semidirect
287. #1788C2×C151semidirect
288. #1788C2×C151semidirect
289. #1752C2×C151semidirect
293. C2×#135C4×C151semidirect
329. C2×#41C2×C4×C151semidirect
342. C2×Q16C2×C4×C151semidirect
345. C2×SD16C2×C4×C151semidirect
350. C22×C8C2×C4×C151semidirect
432. SD16C22⋊C4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1512
C2×#440×C1512
#2341×C1512
#2339×C1512
#1973×C1512
#1879×C1512
#1878×C1512
#1808×C1512
#1788×C1512
#1752×C1512
#22439151