Finite Group Databasebeta

← C151×#17416 #50322341

Subgroups — C151×#17416 #50322341

Order 38656.

1290 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic
2#2880×C151C212yesmaximal, complemented
3#1472×C151C212yesmaximal, complemented
4#1468×C151C214yesmaximal, complemented
5#1465×C151C211yesmaximal, characteristic, complemented
6#1463×C151C212yesmaximal, complemented
7#1459×C151C211yesmaximal, characteristic, complemented
8C2×#324×C151C212yesmaximal, complemented
9C22×#41×C151C411yescharacteristic
10C22×#41×C151C2211yescharacteristic
11C2×#131×C151—22no—
12#547×C151—22no—
13#547×C151—24no—
14#547×C151—22no—
15C2×C4⋊Q8×C151C411yescharacteristic
16C2×#123×C151C412yes—
17C2×#123×C151C2212yes—
18C2×C22⋊Q8×C151C411yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×#121×C151C412yes—
21C2×C4×D4×C151C411yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2212yes—
24#408×C151—22no—
25#408×C151—24no—
26#407×C151C2214yes—
27#407×C151C2212yes—
28C2×C22⋊C8×C151C2214yes—
29C2×C22⋊C8×C151C2212yes—
30#324×C151C2211yescharacteristic
31#324×C151C2212yes—
32#324×C151C2214yes—
33#324×C151C2211yescharacteristic
34#324×C151C2214yes—
35#323×C151C2212yes—
36#323×C151C2212yes—
37C2×#41×C151—22no—
38C2×#41×C151—21no—
39C2×#41×C151—21no—
40C2×#41×C151—44no—
41C2×#41×C151—44no—
42C2×#41×C151D412yes—
43C2×#41×C151D412yes—
44C2×#41×C151D414yes—
45C22×Q8×C151C2×C411yescharacteristic
46C22×Q8×C151C2×C411yescharacteristic
47C22×D4×C151C2×C411yescharacteristic
48C22×D4×C151C2×C411yescharacteristic
49C22×D4×C151C2×C412yes—
50C22×D4×C151C2×C412yes—
51C23×C4×C151C2×C412yes—
52C23×C4×C151C2×C412yes—
53C23×C4×C151C2×C411yescharacteristic
54C23×C4×C151C2312yes—
55C23×C4×C151C2311yescharacteristic
56#131×C151—48no—
57C2×M16×C151—24no—
58C2×M16×C151—22no—
59C22×C8×C151—24no—
60C22×C8×C151—22no—
61C4⋊Q8×C151—22no—
62C4⋊Q8×C151—22no—
63#123×C151—24no—
64#123×C151—24no—
65#123×C151—24no—
66#123×C151—24no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—22no—
70C22⋊Q8×C151—22no—
71#121×C151—24no—
72#121×C151—24no—
73C4×D4×C151—22no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151—22no—
77C4×D4×C151—22no—
78C2×C4⋊C4×C151—24no—
79C2×C4⋊C4×C151—24no—
80C2×C4⋊C4×C151C2×C412yes—
81C2×C4⋊C4×C151C2×C412yes—
82C2×C4⋊C4×C151C2×C411yescharacteristic
83C2×C4⋊C4×C151C2×C412yes—
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2312yes—
86C2×C22⋊C4×C151C2×C412yes—
87C2×C22⋊C4×C151C2×C411yescharacteristic
88C2×C22⋊C4×C151C2×C412yes—
89C2×C22⋊C4×C151C2×C412yes—
90C2×C22⋊C4×C151C2311yescharacteristic
91C2×C42×C151C2×C411yescharacteristic
92C22⋊C8×C151—24no—
93C22⋊C8×C151—22no—
94C22⋊C8×C151—24no—
95C22⋊C8×C151—22no—
96C22⋊C8×C151C2312yes—
97C22⋊C8×C151C2314yes—
98C22⋊C8×C151C2312yes—
99C24×C151C22×C412yes—
100C24×C151C22×C411yescharacteristic
101C24×C151C22×C411yescharacteristic
102#41×C151—28no—
103#41×C151—48no—
104#41×C151—44no—
105#41×C151—48no—
106#41×C151—44no—
107#41×C151—44no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—42no—
111C2×Q8×C151—42no—
112C2×Q8×C151C22⋊C412yes—
113C2×Q8×C151C22⋊C412yes—
114C2×D4×C151—24no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—41no—
120C2×D4×C151—44no—
121C2×D4×C151—44no—
122C2×D4×C151C22⋊C412yes—
123C2×D4×C151C22⋊C411yescharacteristic
124C2×D4×C151C22⋊C414yes—
125C2×D4×C151C22⋊C414yes—
126C2×D4×C151C22⋊C411yescharacteristic
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—22no—
130C22×C4×C151—22no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—24no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—44no—
137C22×C4×C151—42no—
138C22×C4×C151—44no—
139C22×C4×C151C22×C412yes—
140C22×C4×C151C22×C411yescharacteristic
141C22×C4×C151C22×C411yescharacteristic
142C22×C4×C151C22×C411yescharacteristic
143C22×C4×C151C22×C411yescharacteristic
144C22×C4×C151C22×C412yes—
145C22×C4×C151C22×C412yes—
146C22×C4×C151C2×D414yes—
147C22×C4×C151C2×D412yes—
148C22×C4×C151C2×D414yes—
149C22×C4×C151C2×D412yes—
150C22×C4×C151C2411yescharacteristic
151M16×C151—48no—
152M16×C151—44no—
153C2×C8×C151—22no—
154C2×C8×C151—24no—
155C2×C8×C151—22no—
156C2×C8×C151—48no—
157C2×C8×C151—44no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—24no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—24no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—24no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—22no—
167C22⋊C4×C151—22no—
168C22⋊C4×C151—24no—
169C22⋊C4×C151—24no—
170C22⋊C4×C151—22no—
171C42×C151—21no—
172C42×C151—21no—
173C23×C151—22no—
174C23×C151—22no—
175C23×C151—24no—
176C23×C151—21no—
177C23×C151—21no—
178C23×C151—21no—
179C23×C151—21no—
180C23×C151—21no—
181C23×C151—42no—
182C23×C151—41no—
183C23×C151—41no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151C2×C22⋊C412yes—
187C23×C151C2×C22⋊C412yes—
188C23×C151C2×C22⋊C412yes—
189C23×C151C23×C411yescharacteristic
190Q8×C151—24no—
191Q8×C151—42no—
192Q8×C151—42no—
193Q8×C151—42no—
194D4×C151—28no—
195D4×C151—24no—
196D4×C151—22no—
197D4×C151—44no—
198D4×C151—44no—
199D4×C151—44no—
200D4×C151—44no—
201D4×C151#9914yes—
202C2×C4×C151—21no—
203C2×C4×C151—21no—
204C2×C4×C151—28no—
205C2×C4×C151—22no—
206C2×C4×C151—24no—
207C2×C4×C151—22no—
208C2×C4×C151—21no—
209C2×C4×C151—22no—
210C2×C4×C151—21no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—44no—
216C2×C4×C151—41no—
217C2×C4×C151—44no—
218C2×C4×C151—44no—
219C2×C4×C151—42no—
220C2×C4×C151—44no—
221C2×C4×C151—44no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151C2×C22⋊C411yescharacteristic
227C2×C4×C151C2×C22⋊C414yes—
228C2×C4×C151C2×C22⋊C411yescharacteristic
229C2×C4×C151#13112yescomplemented
230C2×C4×C151C22×D412yes—
231C8×C151—42no—
232C8×C151—44no—
233C8×C151—42no—
234C22×C151—22no—
235C22×C151—21no—
236C22×C151—21no—
237C22×C151—22no—
238C22×C151—22no—
239C22×C151—22no—
240C22×C151—22no—
241C22×C151—22no—
242C22×C151—22no—
243C22×C151—22no—
244C22×C151—44no—
245C22×C151—44no—
246C22×C151—41no—
247C22×C151—41no—
248C22×C151—41no—
249C22×C151—81no—
250C22×C151—81no—
251C22×C151—81no—
252C22×C151—81no—
253C22×C151C2×#9914yes—
254C22×C151C22×C22⋊C411yescharacteristic
255C22×C151C2×#13111yescharacteristic
256C22×C151#56811yescharacteristic
257C4×C151—22no—
258C4×C151—22no—
259C4×C151—21no—
260C4×C151—24no—
261C4×C151—42no—
262C4×C151—41no—
263C4×C151—42no—
264C4×C151—41no—
265C4×C151C2×#9912yes—
266C2×C151—21no—
267C2×C151—21no—
268C2×C151—24no—
269C2×C151—42no—
270C2×C151—42no—
271C2×C151—81no—
272C2×C151#288011yescharacteristic
273C2×C151C22×#9911yescharacteristic
274C2×C151#288911yescharacteristic
275#17416C15111yesmaximal, characteristic, direct product factor, Sylow
276C151#1741611yescharacteristic, direct product factor, Sylow
277C2×#547C2×C15111yescharacteristic
278#2880C2×C15112yescomplemented
279#1472C2×C15112yescomplemented
280#1468C2×C15114yescomplemented
281#1465C2×C15111yescharacteristic, complemented
282#1463C2×C15112yescomplemented
283#1459C2×C15111yescharacteristic, complemented
284C2×#324C2×C15112yescomplemented
285C22×#41C4×C15111yescharacteristic
286C22×#41C22×C15111yescharacteristic
287C2×#131—22no—
288#547—22no—
289#547—24no—
290#547—22no—
291C2×C4⋊Q8C4×C15111yescharacteristic
292C2×#123C4×C15112yes—
293C2×#123C22×C15112yes—
294C2×C22⋊Q8C4×C15111yescharacteristic
295C2×C22⋊Q8C22×C15111yescharacteristic
296C2×#121C4×C15112yes—
297C2×C4×D4C4×C15111yescharacteristic
298C2×C4×D4C22×C15111yescharacteristic
299C22×C4⋊C4C22×C15112yes—
300#408—22no—
301#408—24no—
302#407C22×C15114yes—
303#407C22×C15112yes—
304C2×C22⋊C8C22×C15114yes—
305C2×C22⋊C8C22×C15112yes—
306#324C22×C15111yescharacteristic
307#324C22×C15112yes—
308#324C22×C15114yes—
309#324C22×C15111yescharacteristic
310#324C22×C15114yes—
311#323C22×C15112yes—
312#323C22×C15112yes—
313C2×#41—21no—
314C2×#41—22no—
315C2×#41—21no—
316C2×#41—44no—
317C2×#41—44no—
318C2×#41D4×C15112yes—
319C2×#41D4×C15114yes—
320C2×#41D4×C15112yes—
321C22×Q8C2×C4×C15111yescharacteristic
322C22×Q8C2×C4×C15111yescharacteristic
323C22×D4C2×C4×C15111yescharacteristic
324C22×D4C2×C4×C15111yescharacteristic
325C22×D4C2×C4×C15112yes—
326C22×D4C2×C4×C15112yes—
327C23×C4C2×C4×C15112yes—
328C23×C4C2×C4×C15112yes—
329C23×C4C2×C4×C15111yescharacteristic
330C23×C4C23×C15112yes—
331C23×C4C23×C15111yescharacteristic
332#131—48no—
333C2×M16—24no—
334C2×M16—22no—
335C22×C8—24no—
336C22×C8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339#123—24no—
340#123—24no—
341#123—24no—
342#123—24no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347#121—24no—
348#121—24no—
349C4×D4—22no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—22no—
353C4×D4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4C2×C4×C15112yes—
357C2×C4⋊C4C2×C4×C15112yes—
358C2×C4⋊C4C2×C4×C15111yescharacteristic
359C2×C4⋊C4C2×C4×C15112yes—
360C2×C4⋊C4C23×C15111yescharacteristic
361C2×C4⋊C4C23×C15112yes—
362C2×C22⋊C4C2×C4×C15112yes—
363C2×C22⋊C4C2×C4×C15111yescharacteristic
364C2×C22⋊C4C2×C4×C15112yes—
365C2×C22⋊C4C2×C4×C15112yes—
366C2×C22⋊C4C23×C15111yescharacteristic
367C2×C42C2×C4×C15111yescharacteristic
368C22⋊C8—24no—
369C22⋊C8—22no—
370C22⋊C8—24no—
371C22⋊C8—22no—
372C22⋊C8C23×C15112yes—
373C22⋊C8C23×C15112yes—
374C22⋊C8C23×C15114yes—
375C24C22×C4×C15112yes—
376C24C22×C4×C15111yescharacteristic
377C24C22×C4×C15111yescharacteristic
378#41—28no—
379#41—48no—
380#41—44no—
381#41—48no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8—42no—
388C2×Q8C22⋊C4×C15112yes—
389C2×Q8C22⋊C4×C15112yes—
390C2×D4—24no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—41no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4C22⋊C4×C15112yes—
399C2×D4C22⋊C4×C15111yescharacteristic
400C2×D4C22⋊C4×C15114yes—
401C2×D4C22⋊C4×C15114yes—
402C2×D4C22⋊C4×C15111yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—24no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—44no—
413C22×C4—42no—
414C22×C4—44no—
415C22×C4C22×C4×C15112yes—
416C22×C4C22×C4×C15111yescharacteristic
417C22×C4C22×C4×C15111yescharacteristic
418C22×C4C22×C4×C15111yescharacteristic
419C22×C4C22×C4×C15111yescharacteristic
420C22×C4C22×C4×C15112yes—
421C22×C4C22×C4×C15112yes—
422C22×C4C2×D4×C15114yes—
423C22×C4C2×D4×C15112yes—
424C22×C4C2×D4×C15114yes—
425C22×C4C2×D4×C15112yes—
426C22×C4C24×C15111yescharacteristic
427M16—48no—
428M16—44no—
429C2×C8—22no—
430C2×C8—24no—
431C2×C8—22no—
432C2×C8—48no—
433C2×C8—44no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—24no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—22no—
447C42—21no—
448C42—21no—
449C23—24no—
450C23—22no—
451C23—22no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—42no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23C2×C22⋊C4×C15112yes—
463C23C2×C22⋊C4×C15112yes—
464C23C2×C22⋊C4×C15112yes—
465C23C23×C4×C15111yescharacteristic
466Q8—24no—
467Q8—42no—
468Q8—42no—
469Q8—42no—
470D4—24no—
471D4—28no—
472D4—22no—
473D4—44no—
474D4—44no—
475D4—44no—
476D4—44no—
477D4#99×C15114yes—
478C2×C4—28no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4C2×C22⋊C4×C15111yescharacteristic
503C2×C4C2×C22⋊C4×C15114yes—
504C2×C4C2×C22⋊C4×C15111yescharacteristic
505C2×C4#131×C15112yescomplemented
506C2×C4C22×D4×C15112yes—
507C8—42no—
508C8—44no—
509C8—42no—
510C22—22no—
511C22—21no—
512C22—21no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—22no—
518C22—22no—
519C22—22no—
520C22—44no—
521C22—44no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22C2×#99×C15114yes—
530C22C22×C22⋊C4×C15111yescharacteristic
531C22C2×#131×C15111yescharacteristic
532C22#568×C15111yescharacteristic
533C4—22no—
534C4—22no—
535C4—21no—
536C4—24no—
537C4—42no—
538C4—41no—
539C4—42no—
540C4—41no—
541C4C2×#99×C15112yes—
542C2—21no—
543C2—21no—
544C2—24no—
545C2—42no—
546C2—42no—
547C2—81no—
548C2#2880×C15111yescharacteristic
549C2C22×#99×C15111yescharacteristic
550C2#2889×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#547×C151C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2880×C151C2semidirect
3. #1472×C151C2semidirect
4. #1468×C151C2semidirect
5. #1465×C151C2semidirect
6. #1463×C151C2semidirect
7. #1459×C151C2semidirect
8. C2×#324×C151C2semidirect
229. C2×C4×C151#131semidirect
275. #17416C151direct (N × H)
276. C151#17416direct (N × H)
278. #2880C2×C151semidirect
279. #1472C2×C151semidirect
280. #1468C2×C151semidirect
281. #1465C2×C151semidirect
282. #1463C2×C151semidirect
283. #1459C2×C151semidirect
284. C2×#324C2×C151semidirect
505. C2×C4#131×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
#2880×C1512
#1472×C1512
#1468×C1512
#1465×C1512
#1463×C1512
#1459×C1512
C2×#324×C1512
#17416151