Finite Group Databasebeta

← C151×#23483 #50328408

Subgroups — C151×#23483 #50328408

Order 38656.

1610 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C151C211yesmaximal, characteristic
2C2×#428×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4C22×#102×C151C211yesmaximal, characteristic, complemented
5C2×#408×C151C211yesmaximal, characteristic, complemented
6#2311×C151C211yesmaximal, characteristic, complemented
7#2034×C151C214yesmaximal, complemented
8#2033×C151C214yesmaximal, complemented
9#1735×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11C23×D4×C151C2211yescharacteristic
12C22×M16×C151C2211yescharacteristic
13C23×C8×C151C2211yescharacteristic
14#535×C151—24no—
15#535×C151—24no—
16C2×#127×C151—21no—
17C2×#124×C151—21no—
18C2×#121×C151C2212yes—
19C2×#121×C151C2212yes—
20C2×#120×C151—22no—
21C2×#117×C151C2211yescharacteristic
22C2×#117×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24#428×C151—24no—
25C2×#107×C151C2212yescomplemented
26C2×#106×C151C2212yescomplemented
27#418×C151—24no—
28C2×#102×C151—24no—
29C2×#102×C151C2214yes—
30C2×#102×C151C2214yes—
31#408×C151—24no—
32C2×C22⋊C8×C151C2214yescomplemented
33#391×C151—21no—
34#390×C151—21no—
35#386×C151—22no—
36#380×C151C2214yescomplemented
37#340×C151C2212yescomplemented
38#340×C151C2212yescomplemented
39C25×C151—21no—
40C2×#41×C151—22no—
41C2×#41×C151—22no—
42C2×#41×C151—22no—
43C2×#41×C151—22no—
44C2×#41×C151—22no—
45C2×#41×C151—22no—
46C22×Q8×C151D411yescharacteristic
47C22×D4×C151—21no—
48C22×D4×C151—22no—
49C22×D4×C151—22no—
50C22×D4×C151—22no—
51C22×D4×C151—22no—
52C22×D4×C151—22no—
53C22×D4×C151—22no—
54C22×D4×C151—22no—
55C22×D4×C151D414yes—
56C22×D4×C151D412yes—
57C22×D4×C151D411yescharacteristic
58C22×D4×C151C2312yes—
59C23×C4×C151—21no—
60C23×C4×C151C2312yes—
61C23×C4×C151C2311yescharacteristic
62C2×M16×C151—22no—
63C2×M16×C151—22no—
64C2×M16×C151D414yescomplemented
65C22×C8×C151—22no—
66C22×C8×C151—22no—
67C22×C8×C151—22no—
68C22×C8×C151C2312yes—
69C22×C8×C151C2312yes—
70#127×C151—28no—
71#124×C151—28no—
72#121×C151—24no—
73#121×C151—24no—
74#121×C151—24no—
75#121×C151—24no—
76#120×C151—216no—
77#117×C151—22no—
78#117×C151—22no—
79#117×C151—22no—
80#117×C151D414yes—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2312yes—
86C2×C4⋊C4×C151C2311yescharacteristic
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—24no—
93C2×C42×C151—21no—
94C2×C42×C151—21no—
95#107×C151—24no—
96#106×C151—24no—
97#102×C151—28no—
98#102×C151—28no—
99C22⋊C8×C151—28no—
100#95×C151—24no—
101C24×C151—22no—
102C24×C151—24no—
103C24×C151—42no—
104C24×C151—42no—
105C24×C151—82no—
106C24×C151—82no—
107C24×C151C2×D412yes—
108C24×C151C2×D411yescharacteristic
109#41×C151—44no—
110#41×C151—44no—
111#41×C151—44no—
112#41×C151—44no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×D4×C151—24no—
117C2×D4×C151—24no—
118C2×D4×C151—24no—
119C2×D4×C151—28no—
120C2×D4×C151—28no—
121C2×D4×C151—24no—
122C2×D4×C151—22no—
123C2×D4×C151—28no—
124C2×D4×C151—22no—
125C2×D4×C151—28no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—22no—
131C2×D4×C151—22no—
132C2×D4×C151—44no—
133C2×D4×C151—42no—
134C2×D4×C151—42no—
135C2×D4×C151—44no—
136C2×D4×C151—84no—
137C2×D4×C151—84no—
138C2×D4×C151C2×D414yes—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—22no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—22no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—42no—
150C22×C4×C151—82no—
151C22×C4×C151C2×D412yes—
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D412yes—
154C22×C4×C151C2×D412yes—
155C22×C4×C151C2×D412yes—
156C22×C4×C151#4112yes—
157C22×C4×C151#4112yes—
158C22×C4×C151#4112yes—
159C22×C4×C151C2411yescharacteristic
160M16×C151—28no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—44no—
167C2×C8×C151C2×D414yes—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—22no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—42no—
175C4⋊C4×C151C2×D412yes—
176C4⋊C4×C151C2×D412yes—
177C22⋊C4×C151—28no—
178C22⋊C4×C151—28no—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—42no—
181C22⋊C4×C151—84no—
182C42×C151—24no—
183C42×C151—42no—
184C23×C151—22no—
185C23×C151—22no—
186C23×C151—24no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—24no—
191C23×C151—24no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—44no—
195C23×C151—44no—
196C23×C151—48no—
197C23×C151—84no—
198C23×C151—84no—
199C23×C151—88no—
200C23×C151—88no—
201C23×C151#12012yes—
202C23×C151#12112yes—
203C23×C151#12312yes—
204C23×C151C22×D411yescharacteristic
205Q8×C151—44no—
206D4×C151—24no—
207D4×C151—24no—
208D4×C151—48no—
209D4×C151—42no—
210D4×C151—42no—
211D4×C151—44no—
212D4×C151—48no—
213D4×C151—88no—
214D4×C151—88no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
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—44no—
230C2×C4×C151—42no—
231C2×C4×C151—84no—
232C2×C4×C151#12012yes—
233C2×C4×C151#12114yes—
234C2×C4×C151#12114yes—
235C2×C4×C151#12112yes—
236C2×C4×C151#12314yes—
237C2×C4×C151#12312yes—
238C2×C4×C151#12414yes—
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C2×C4×C151C22×D411yescharacteristic
242C2×C4×C151C2×#4111yescharacteristic
243C2×C4×C151C2×#4111yescharacteristic
244C2×C4×C151C2×#4111yescharacteristic
245C8×C151—24no—
246C8×C151—42no—
247C22×C151—24no—
248C22×C151—22no—
249C22×C151—22no—
250C22×C151—24no—
251C22×C151—44no—
252C22×C151—42no—
253C22×C151—44no—
254C22×C151—42no—
255C22×C151—44no—
256C22×C151—42no—
257C22×C151—44no—
258C22×C151—44no—
259C22×C151—816no—
260C22×C151—84no—
261C22×C151—84no—
262C22×C151#39414yes—
263C22×C151C2×#12011yescharacteristic
264C22×C151C2×#12111yescharacteristic
265C22×C151C2×#12311yescharacteristic
266C22×C151#57612yes—
267C22×C151#57712yes—
268C4×C151—42no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—82no—
272C4×C151—82no—
273C4×C151#39414yes—
274C4×C151C2×#12111yescharacteristic
275C4×C151C2×#12111yescharacteristic
276C4×C151C2×#12311yescharacteristic
277C4×C151C2×#12411yescharacteristic
278C2×C151—24no—
279C2×C151—82no—
280C2×C151—84no—
281C2×C151C2×#39411yescharacteristic
282C2×C151#300811yescharacteristic
283C2×C151#300911yescharacteristic
284C2×C151#306212yes—
285C2×C151#309612yes—
286#23483C15111yesmaximal, characteristic, direct product factor, Sylow
287C151#2348311yescharacteristic, direct product factor, Sylow
288C2×#535C2×C15111yescharacteristic
289C2×#428C2×C15111yescharacteristic, complemented
290C2×#418C2×C15111yescharacteristic, complemented
291C22×#102C2×C15111yescharacteristic, complemented
292C2×#408C2×C15111yescharacteristic, complemented
293#2311C2×C15111yescharacteristic, complemented
294#2034C2×C15114yescomplemented
295#2033C2×C15114yescomplemented
296#1735C2×C15111yescharacteristic, complemented
297C22×#41C22×C15111yescharacteristic
298C23×D4C22×C15111yescharacteristic
299C22×M16C22×C15111yescharacteristic
300C23×C8C22×C15111yescharacteristic
301#535—24no—
302#535—24no—
303C2×#127—21no—
304C2×#124—21no—
305C2×#121C22×C15112yes—
306C2×#121C22×C15112yes—
307C2×#120—22no—
308C2×#117C22×C15111yescharacteristic
309C2×#117C22×C15111yescharacteristic
310C22×C4⋊C4C22×C15111yescharacteristic
311#428—24no—
312C2×#107C22×C15112yescomplemented
313C2×#106C22×C15112yescomplemented
314#418—24no—
315C2×#102—24no—
316C2×#102C22×C15114yes—
317C2×#102C22×C15114yes—
318#408—24no—
319C2×C22⋊C8C22×C15114yescomplemented
320#391—21no—
321#390—21no—
322#386—22no—
323#380C22×C15114yescomplemented
324#340C22×C15112yescomplemented
325#340C22×C15112yescomplemented
326C25—21no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—22no—
333C22×Q8D4×C15111yescharacteristic
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4D4×C15112yes—
343C22×D4D4×C15111yescharacteristic
344C22×D4D4×C15114yes—
345C22×D4C23×C15112yes—
346C23×C4—21no—
347C23×C4C23×C15112yes—
348C23×C4C23×C15111yescharacteristic
349C2×M16—22no—
350C2×M16—22no—
351C2×M16D4×C15114yescomplemented
352C22×C8—22no—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8C23×C15112yes—
356C22×C8C23×C15112yes—
357#127—28no—
358#124—28no—
359#121—24no—
360#121—24no—
361#121—24no—
362#121—24no—
363#120—216no—
364#117—22no—
365#117—22no—
366#117—22no—
367#117D4×C15114yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C15112yes—
372C2×C4⋊C4C23×C15112yes—
373C2×C4⋊C4C23×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—24no—
380C2×C42—21no—
381C2×C42—21no—
382#107—24no—
383#106—24no—
384#102—28no—
385#102—28no—
386C22⋊C8—28no—
387#95—24no—
388C24—22no—
389C24—24no—
390C24—42no—
391C24—42no—
392C24—82no—
393C24—82no—
394C24C2×D4×C15112yes—
395C24C2×D4×C15111yescharacteristic
396#41—44no—
397#41—44no—
398#41—44no—
399#41—44no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—28no—
411C2×D4—22no—
412C2×D4—28no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—44no—
423C2×D4—84no—
424C2×D4—84no—
425C2×D4C2×D4×C15114yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—82no—
438C22×C4C2×D4×C15112yes—
439C22×C4C2×D4×C15111yescharacteristic
440C22×C4C2×D4×C15112yes—
441C22×C4C2×D4×C15112yes—
442C22×C4C2×D4×C15112yes—
443C22×C4#41×C15112yes—
444C22×C4#41×C15112yes—
445C22×C4#41×C15112yes—
446C22×C4C24×C15111yescharacteristic
447M16—28no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—44no—
454C2×C8C2×D4×C15114yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—42no—
462C4⋊C4C2×D4×C15112yes—
463C4⋊C4C2×D4×C15112yes—
464C22⋊C4—28no—
465C22⋊C4—28no—
466C22⋊C4—24no—
467C22⋊C4—42no—
468C22⋊C4—84no—
469C42—24no—
470C42—42no—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—24no—
479C23—48no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23—44no—
484C23—84no—
485C23—84no—
486C23—88no—
487C23—88no—
488C23#120×C15112yes—
489C23#121×C15112yes—
490C23#123×C15112yes—
491C23C22×D4×C15111yescharacteristic
492Q8—44no—
493D4—24no—
494D4—24no—
495D4—48no—
496D4—48no—
497D4—44no—
498D4—42no—
499D4—42no—
500D4—88no—
501D4—88no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—84no—
519C2×C4#120×C15112yes—
520C2×C4#121×C15112yes—
521C2×C4#121×C15114yes—
522C2×C4#121×C15114yes—
523C2×C4#123×C15112yes—
524C2×C4#123×C15114yes—
525C2×C4#124×C15114yes—
526C2×C4C22×D4×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C2×#41×C15111yescharacteristic
530C2×C4C2×#41×C15111yescharacteristic
531C2×C4C2×#41×C15111yescharacteristic
532C8—24no—
533C8—42no—
534C22—22no—
535C22—22no—
536C22—24no—
537C22—24no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—44no—
542C22—42no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—816no—
547C22—84no—
548C22—84no—
549C22#394×C15114yes—
550C22C2×#120×C15111yescharacteristic
551C22C2×#121×C15111yescharacteristic
552C22C2×#123×C15111yescharacteristic
553C22#576×C15112yes—
554C22#577×C15112yes—
555C4—42no—
556C4—42no—
557C4—42no—
558C4—82no—
559C4—82no—
560C4#394×C15114yes—
561C4C2×#121×C15111yescharacteristic
562C4C2×#121×C15111yescharacteristic
563C4C2×#123×C15111yescharacteristic
564C4C2×#124×C15111yescharacteristic
565C2—24no—
566C2—82no—
567C2—84no—
568C2C2×#394×C15111yescharacteristic
569C2#3008×C15111yescharacteristic
570C2#3009×C15111yescharacteristic
571C2#3062×C15112yes—
572C2#3096×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#535×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C151C2semidirect
3. C2×#418×C151C2semidirect
4. C22×#102×C151C2semidirect
5. C2×#408×C151C2semidirect
6. #2311×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1735×C151C2semidirect
25. C2×#107×C151C22semidirect
26. C2×#106×C151C22semidirect
32. C2×C22⋊C8×C151C22semidirect
36. #380×C151C22semidirect
37. #340×C151C22semidirect
38. #340×C151C22semidirect
64. C2×M16×C151D4semidirect
286. #23483C151direct (N × H)
287. C151#23483direct (N × H)
289. C2×#428C2×C151semidirect
290. C2×#418C2×C151semidirect
291. C22×#102C2×C151semidirect
292. C2×#408C2×C151semidirect
293. #2311C2×C151semidirect
294. #2034C2×C151semidirect
295. #2033C2×C151semidirect
296. #1735C2×C151semidirect
312. C2×#107C22×C151semidirect
313. C2×#106C22×C151semidirect
319. C2×C22⋊C8C22×C151semidirect
323. #380C22×C151semidirect
324. #340C22×C151semidirect
325. #340C22×C151semidirect
351. C2×M16D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1512
C2×#428×C1512
C2×#418×C1512
C22×#102×C1512
C2×#408×C1512
#2311×C1512
#2034×C1512
#2033×C1512
#1735×C1512
#23483151