Finite Group Databasebeta

← C151×#24098 #50329023

Subgroups — C151×#24098 #50329023

Order 38656.

1118 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic
2C2×#484×C151C211yesmaximal, characteristic, complemented
3C22×#107×C151C211yesmaximal, characteristic, complemented
4#2487×C151C211yesmaximal, characteristic
5#2057×C151C212yesmaximal, complemented
6#2036×C151C212yesmaximal, complemented
7#1892×C151C211yesmaximal, characteristic, complemented
8#1869×C151C211yesmaximal, characteristic
9#1863×C151C212yesmaximal, complemented
10#1852×C151C212yesmaximal, complemented
11#1824×C151C211yesmaximal, characteristic, complemented
12C23×C8×C151C2211yescharacteristic
13#554×C151—24no—
14#554×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151—21no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151—21no—
23C2×C4×D4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27#484×C151—24no—
28C2×#107×C151—24no—
29C2×#107×C151C2212yes—
30C2×#107×C151C2212yes—
31C2×#107×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2212yes—
36#400×C151—21no—
37#399×C151—21no—
38#389×C151C2212yes—
39#386×C151—21no—
40#385×C151—21no—
41#380×C151C2211yescharacteristic
42#380×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—21no—
48C22×Q8×C151C2311yescharacteristic
49C22×D4×C151D411yescharacteristic
50C23×C4×C151—21no—
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C22×C8×C151—22no—
56C22×C8×C151—24no—
57C22×C8×C151C2312yes—
58C22×C8×C151C2312yes—
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151—22no—
61#125×C151—28no—
62C22⋊Q8×C151—28no—
63C22⋊Q8×C151—28no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—22no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151D414yes—
68C4×Q8×C151—22no—
69C4×Q8×C151—22no—
70C4×D4×C151—28no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151D414yes—
88C2×C4⋊C4×C151C2312yes—
89C2×C4⋊C4×C151C2312yes—
90C2×C4⋊C4×C151C2311yescharacteristic
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151—21no—
95C2×C22⋊C4×C151—21no—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151D411yescharacteristic
98C2×C22⋊C4×C151D411yescharacteristic
99C2×C42×C151—21no—
100C2×C42×C151C2311yescharacteristic
101#107×C151—24no—
102#107×C151—24no—
103#107×C151—24no—
104#103×C151—24no—
105#103×C151—24no—
106C22⋊C8×C151—22no—
107C22⋊C8×C151—24no—
108#95×C151—22no—
109#95×C151—21no—
110#95×C151—22no—
111C24×C151C2×D411yescharacteristic
112C24×C151C2×D411yescharacteristic
113C2×Q8×C151—24no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—82no—
118C2×Q8×C151C2×D412yes—
119C2×D4×C151—22no—
120C2×D4×C151—22no—
121C2×D4×C151Q1614yes—
122C22×C4×C151—22no—
123C22×C4×C151—22no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—24no—
129C22×C4×C151—24no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—42no—
137C22×C4×C151—82no—
138C22×C4×C151—82no—
139C22×C4×C151—82no—
140C22×C4×C151C2×D411yescharacteristic
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×D411yescharacteristic
146C22×C4×C151C2411yescharacteristic
147C2×C8×C151—28no—
148C2×C8×C151—22no—
149C2×C8×C151—22no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151#4114yes—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—42no—
169C4⋊C4×C151—82no—
170C4⋊C4×C151C2×D412yes—
171C4⋊C4×C151C2×D412yes—
172C4⋊C4×C151C2×D412yes—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—24no—
175C22⋊C4×C151—22no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—82no—
179C42×C151—24no—
180C42×C151—21no—
181C42×C151—21no—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—21no—
185C23×C151—22no—
186C23×C151—21no—
187C23×C151—22no—
188C23×C151#12012yes—
189C23×C151C2×Q1612yes—
190C23×C151C2×Q1612yes—
191C23×C151#13712yes—
192C23×C151C22×D411yescharacteristic
193Q8×C151—24no—
194Q8×C151—41no—
195Q8×C151—41no—
196Q8×C151—84no—
197D4×C151—28no—
198C2×C4×C151—21no—
199C2×C4×C151—22no—
200C2×C4×C151—21no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—24no—
204C2×C4×C151—21no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—21no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—84no—
226C2×C4×C151—84no—
227C2×C4×C151—84no—
228C2×C4×C151#12012yes—
229C2×C4×C151C2×Q1612yes—
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C22×D411yescharacteristic
232C2×C4×C151C2×#4112yes—
233C2×C4×C1512−1+412yes—
234C8×C151—24no—
235C8×C151—42no—
236C22×C151—24no—
237C22×C151—24no—
238C22×C151—22no—
239C22×C151—22no—
240C22×C151—24no—
241C22×C151—22no—
242C22×C151—42no—
243C22×C151—41no—
244C22×C151—41no—
245C22×C151#45114yes—
246C22×C151C2×#12011yescharacteristic
247C22×C151#54712yes—
248C22×C151C22×Q1611yescharacteristic
249C22×C151C2×#13711yescharacteristic
250C22×C151#57612yes—
251C4×C151—22no—
252C4×C151—22no—
253C4×C151—41no—
254C4×C151—42no—
255C4×C151—41no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—42no—
259C4×C151—82no—
260C4×C151—82no—
261C4×C151#52511yescharacteristic
262C4×C151#53611yescharacteristic
263C4×C151#54712yes—
264C2×C151—24no—
265C2×C151—42no—
266C2×C151#240611yescharacteristic
267C2×C151C2×#45111yescharacteristic
268C2×C151#300811yescharacteristic
269C2×C151#333812yes—
270C2×C151#334612yes—
271#24098C15111yesmaximal, characteristic, direct product factor, Sylow
272C151#2409811yescharacteristic, direct product factor, Sylow
273C2×#554C2×C15111yescharacteristic
274C2×#484C2×C15111yescharacteristic, complemented
275C22×#107C2×C15111yescharacteristic, complemented
276#2487C2×C15111yescharacteristic
277#2057C2×C15112yescomplemented
278#2036C2×C15112yescomplemented
279#1892C2×C15111yescharacteristic, complemented
280#1869C2×C15111yescharacteristic
281#1863C2×C15112yescomplemented
282#1852C2×C15112yescomplemented
283#1824C2×C15111yescharacteristic, complemented
284C23×C8C22×C15111yescharacteristic
285#554—24no—
286#554—24no—
287C2×C4⋊Q8C22×C15111yescharacteristic
288C2×#125—21no—
289C2×C22⋊Q8—21no—
290C2×C22⋊Q8—21no—
291C2×C22⋊Q8C22×C15111yescharacteristic
292C2×C22⋊Q8C22×C15111yescharacteristic
293C2×C4×Q8C22×C15111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C22×C15111yescharacteristic
296C22×C4⋊C4C22×C15111yescharacteristic
297C22×C4⋊C4C22×C15111yescharacteristic
298C22×C4⋊C4C22×C15111yescharacteristic
299#484—24no—
300C2×#107—24no—
301C2×#107C22×C15112yes—
302C2×#107C22×C15112yes—
303C2×#107C22×C15112yes—
304C2×#103C22×C15112yes—
305C2×#103C22×C15112yes—
306C2×C22⋊C8C22×C15111yescharacteristic
307C2×C22⋊C8C22×C15112yes—
308#400—21no—
309#399—21no—
310#389C22×C15112yes—
311#386—21no—
312#385—21no—
313#380C22×C15111yescharacteristic
314#380C22×C15112yes—
315#340C22×C15112yes—
316#340C22×C15112yes—
317#340C22×C15112yes—
318#336C22×C15112yes—
319C22×Q8—21no—
320C22×Q8C23×C15111yescharacteristic
321C22×D4D4×C15111yescharacteristic
322C23×C4—21no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4C23×C15111yescharacteristic
326C23×C4C23×C15111yescharacteristic
327C22×C8—22no—
328C22×C8—24no—
329C22×C8C23×C15112yes—
330C22×C8C23×C15112yes—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333#125—28no—
334C22⋊Q8—28no—
335C22⋊Q8—28no—
336C22⋊Q8—22no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8D4×C15114yes—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×D4—28no—
343C4×D4—22no—
344C4×D4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4D4×C15111yescharacteristic
359C2×C4⋊C4D4×C15114yes—
360C2×C4⋊C4C23×C15112yes—
361C2×C4⋊C4C23×C15112yes—
362C2×C4⋊C4C23×C15111yescharacteristic
363C2×C4⋊C4C23×C15111yescharacteristic
364C2×C4⋊C4C23×C15111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4D4×C15111yescharacteristic
370C2×C22⋊C4D4×C15111yescharacteristic
371C2×C42—21no—
372C2×C42C23×C15111yescharacteristic
373#107—24no—
374#107—24no—
375#107—24no—
376#103—24no—
377#103—24no—
378C22⋊C8—22no—
379C22⋊C8—24no—
380#95—22no—
381#95—21no—
382#95—22no—
383C24C2×D4×C15111yescharacteristic
384C24C2×D4×C15111yescharacteristic
385C2×Q8—24no—
386C2×Q8—21no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—82no—
390C2×Q8C2×D4×C15112yes—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4Q16×C15114yes—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—42no—
409C22×C4—82no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4C2×D4×C15111yescharacteristic
413C22×C4C2×D4×C15111yescharacteristic
414C22×C4C2×D4×C15111yescharacteristic
415C22×C4C2×D4×C15112yes—
416C22×C4C2×D4×C15112yes—
417C22×C4C2×D4×C15111yescharacteristic
418C22×C4C24×C15111yescharacteristic
419C2×C8—28no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8#41×C15114yes—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—42no—
441C4⋊C4—82no—
442C4⋊C4C2×D4×C15112yes—
443C4⋊C4C2×D4×C15112yes—
444C4⋊C4C2×D4×C15112yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—42no—
450C22⋊C4—82no—
451C42—24no—
452C42—21no—
453C42—21no—
454C23—22no—
455C23—22no—
456C23—21no—
457C23—22no—
458C23—21no—
459C23—22no—
460C23#120×C15112yes—
461C23C2×Q16×C15112yes—
462C23C2×Q16×C15112yes—
463C23#137×C15112yes—
464C23C22×D4×C15111yescharacteristic
465Q8—24no—
466Q8—41no—
467Q8—41no—
468Q8—84no—
469D4—28no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—84no—
498C2×C4—84no—
499C2×C4—84no—
500C2×C4#120×C15112yes—
501C2×C4C2×Q16×C15112yes—
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C22×D4×C15111yescharacteristic
504C2×C4C2×#41×C15112yes—
505C2×C42−1+4×C15112yes—
506C8—24no—
507C8—42no—
508C22—22no—
509C22—22no—
510C22—24no—
511C22—24no—
512C22—22no—
513C22—24no—
514C22—41no—
515C22—41no—
516C22—42no—
517C22#451×C15114yes—
518C22C2×#120×C15111yescharacteristic
519C22#547×C15112yes—
520C22C22×Q16×C15111yescharacteristic
521C22C2×#137×C15111yescharacteristic
522C22#576×C15112yes—
523C4—22no—
524C4—22no—
525C4—41no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—82no—
532C4—82no—
533C4#525×C15111yescharacteristic
534C4#536×C15111yescharacteristic
535C4#547×C15112yes—
536C2—24no—
537C2—42no—
538C2#2406×C15111yescharacteristic
539C2C2×#451×C15111yescharacteristic
540C2#3008×C15111yescharacteristic
541C2#3338×C15112yes—
542C2#3346×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#484×C151C2semidirect
3. C22×#107×C151C2semidirect
5. #2057×C151C2semidirect
6. #2036×C151C2semidirect
7. #1892×C151C2semidirect
9. #1863×C151C2semidirect
10. #1852×C151C2semidirect
11. #1824×C151C2semidirect
271. #24098C151direct (N × H)
272. C151#24098direct (N × H)
274. C2×#484C2×C151semidirect
275. C22×#107C2×C151semidirect
277. #2057C2×C151semidirect
278. #2036C2×C151semidirect
279. #1892C2×C151semidirect
281. #1863C2×C151semidirect
282. #1852C2×C151semidirect
283. #1824C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#484×C1512
C22×#107×C1512
#2487×C1512
#2057×C1512
#2036×C1512
#1892×C1512
#1869×C1512
#1863×C1512
#1852×C1512
#1824×C1512
#24098151