Finite Group Databasebeta

← C151×#23983 #50328908

Subgroups — C151×#23983 #50328908

Order 38656.

1228 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C151C211yesmaximal, characteristic
2C2×#451×C151C211yesmaximal, characteristic, complemented
3C2×#419×C151C211yesmaximal, characteristic, complemented
4#2409×C151C211yesmaximal, characteristic
5#2026×C151C212yesmaximal, complemented
6#2001×C151C212yesmaximal, complemented
7#1894×C151C211yesmaximal, characteristic, complemented
8#1878×C151C212yesmaximal, complemented
9#1872×C151C212yesmaximal, complemented
10#1870×C151C211yesmaximal, characteristic
11#1825×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×Q16×C151C2212yes—
14C22×M16×C151C2211yescharacteristic
15#552×C151—24no—
16#552×C151—24no—
17C2×#126×C151—21no—
18C2×#125×C151—21no—
19C2×#125×C151C2211yescharacteristic
20C2×#123×C151—21no—
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×C22⋊Q8×C151C2212yes—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C2×#117×C151—21no—
27C2×#117×C151C2211yescharacteristic
28C22×C4⋊C4×C151C2211yescharacteristic
29#451×C151—24no—
30#419×C151—24no—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×#103×C151C2212yes—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2212yes—
37#395×C151—21no—
38#393×C151—21no—
39#391×C151C2212yes—
40#386×C151—21no—
41#385×C151—21no—
42#380×C151C2211yescharacteristic
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151—22no—
48C22×Q8×C151—24no—
49C22×Q8×C151—22no—
50C22×Q8×C151—21no—
51C22×Q8×C151—42no—
52C22×Q8×C151C2311yescharacteristic
53C22×Q8×C151C2312yes—
54C22×D4×C151D411yescharacteristic
55C23×C4×C151—21no—
56C23×C4×C151—21no—
57C23×C4×C151C2311yescharacteristic
58C23×C4×C151C2311yescharacteristic
59C2×Q16×C151—24no—
60C2×Q16×C151—24no—
61C2×Q16×C151—42no—
62C2×M16×C151—22no—
63C2×M16×C151—42no—
64C22×C8×C151C2312yes—
65C22×C8×C151C2312yes—
66#126×C151—28no—
67#125×C151—28no—
68#125×C151—22no—
69#125×C151—22no—
70#123×C151—28no—
71C22⋊Q8×C151—22no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—42no—
76C22⋊Q8×C151D414yes—
77C4×Q8×C151—22no—
78C4×Q8×C151—22no—
79C4×D4×C151—22no—
80C4×D4×C151—22no—
81#117×C151—28no—
82#117×C151—22no—
83#117×C151D414yes—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C4⋊C4×C151C2312yes—
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C22⋊C4×C151—21no—
99C2×C22⋊C4×C151—21no—
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—22no—
103C2×C22⋊C4×C151D411yescharacteristic
104C2×C22⋊C4×C151D411yescharacteristic
105C2×C42×C151—21no—
106C2×C42×C151—21no—
107C2×C42×C151C2311yescharacteristic
108#103×C151—24no—
109#103×C151—24no—
110#103×C151—24no—
111#103×C151—42no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—42no—
114#95×C151—21no—
115#95×C151—22no—
116#95×C151—22no—
117C24×C151C2×D411yescharacteristic
118C24×C151C2×D411yescharacteristic
119C2×Q8×C151—21no—
120C2×Q8×C151—22no—
121C2×Q8×C151—28no—
122C2×Q8×C151—22no—
123C2×Q8×C151—22no—
124C2×Q8×C151—22no—
125C2×Q8×C151—22no—
126C2×Q8×C151—22no—
127C2×Q8×C151—22no—
128C2×Q8×C151—44no—
129C2×Q8×C151—48no—
130C2×Q8×C151—44no—
131C2×Q8×C151—42no—
132C2×Q8×C151C2×D412yes—
133C2×Q8×C151#4114yes—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—41no—
137C22×C4×C151—22no—
138C22×C4×C151—22no—
139C22×C4×C151—24no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—44no—
151C22×C4×C151—42no—
152C22×C4×C151—42no—
153C22×C4×C151—42no—
154C22×C4×C151C2×D411yescharacteristic
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2411yescharacteristic
161Q16×C151—48no—
162M16×C151—44no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C4⋊C4×C151—24no—
170C4⋊C4×C151—24no—
171C4⋊C4×C151—24no—
172C4⋊C4×C151—24no—
173C4⋊C4×C151—24no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—44no—
182C4⋊C4×C151C2×D412yes—
183C4⋊C4×C151C2×D412yes—
184C4⋊C4×C151C2×D412yes—
185C22⋊C4×C151—24no—
186C22⋊C4×C151—24no—
187C22⋊C4×C151—24no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—44no—
191C22⋊C4×C151—42no—
192C42×C151—24no—
193C42×C151—24no—
194C42×C151—21no—
195C42×C151—21no—
196C23×C151—21no—
197C23×C151—22no—
198C23×C151—22no—
199C23×C151—21no—
200C23×C151—21no—
201C23×C151—21no—
202C23×C151—22no—
203C23×C151—22no—
204C23×C151#12012yes—
205C23×C151#13712yes—
206C23×C151C22×D411yescharacteristic
207Q8×C151—24no—
208Q8×C151—24no—
209Q8×C151—24no—
210Q8×C151—48no—
211Q8×C151—41no—
212Q8×C151—41no—
213Q8×C151—42no—
214Q8×C151—42no—
215D4×C151—44no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—24no—
220C2×C4×C151—22no—
221C2×C4×C151—21no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—22no—
227C2×C4×C151—24no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—22no—
232C2×C4×C151—48no—
233C2×C4×C151—48no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—42no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—42no—
245C2×C4×C151—42no—
246C2×C4×C151—42no—
247C2×C4×C151—42no—
248C2×C4×C151#12012yes—
249C2×C4×C151C22×D411yescharacteristic
250C2×C4×C151C22×D411yescharacteristic
251C2×C4×C151C2×#4112yes—
252C2×C4×C151H(5,𝔽2)12yes—
253C8×C151—42no—
254C8×C151—42no—
255C22×C151—22no—
256C22×C151—22no—
257C22×C151—22no—
258C22×C151—22no—
259C22×C151—24no—
260C22×C151—41no—
261C22×C151—41no—
262C22×C151—42no—
263C22×C151—42no—
264C22×C151—42no—
265C22×C151C2×#12011yescharacteristic
266C22×C151#54612yes—
267C22×C151C2×#13711yescharacteristic
268C22×C151#57511yescharacteristic
269C22×C151#57812yes—
270C4×C151—22no—
271C4×C151—41no—
272C4×C151—44no—
273C4×C151—42no—
274C4×C151—41no—
275C4×C151—42no—
276C4×C151—42no—
277C4×C151—41no—
278C4×C151—42no—
279C4×C151—82no—
280C4×C151#52511yescharacteristic
281C4×C151#53511yescharacteristic
282C4×C151#54612yes—
283C2×C151—42no—
284C2×C151—42no—
285C2×C151#240411yescharacteristic
286C2×C151#300711yescharacteristic
287C2×C151#301111yescharacteristic
288C2×C151#331212yes—
289C2×C151#332712yes—
290#23983C15111yesmaximal, characteristic, direct product factor, Sylow
291C151#2398311yescharacteristic, direct product factor, Sylow
292C2×#552C2×C15111yescharacteristic
293C2×#451C2×C15111yescharacteristic, complemented
294C2×#419C2×C15111yescharacteristic, complemented
295#2409C2×C15111yescharacteristic
296#2026C2×C15112yescomplemented
297#2001C2×C15112yescomplemented
298#1894C2×C15111yescharacteristic, complemented
299#1878C2×C15112yescomplemented
300#1872C2×C15112yescomplemented
301#1870C2×C15111yescharacteristic
302#1825C2×C15111yescharacteristic, complemented
303C23×Q8C22×C15111yescharacteristic
304C22×Q16C22×C15112yes—
305C22×M16C22×C15111yescharacteristic
306#552—24no—
307#552—24no—
308C2×#126—21no—
309C2×#125—21no—
310C2×#125C22×C15111yescharacteristic
311C2×#123—21no—
312C2×C22⋊Q8C22×C15111yescharacteristic
313C2×C22⋊Q8C22×C15112yes—
314C2×C22⋊Q8C22×C15111yescharacteristic
315C2×C4×Q8C22×C15111yescharacteristic
316C2×C4×D4C22×C15111yescharacteristic
317C2×#117—21no—
318C2×#117C22×C15111yescharacteristic
319C22×C4⋊C4C22×C15111yescharacteristic
320#451—24no—
321#419—24no—
322C2×#103C22×C15112yes—
323C2×#103C22×C15112yes—
324C2×#103C22×C15112yes—
325C2×#103C22×C15112yes—
326C2×C22⋊C8C22×C15111yescharacteristic
327C2×C22⋊C8C22×C15112yes—
328#395—21no—
329#393—21no—
330#391C22×C15112yes—
331#386—21no—
332#385—21no—
333#380C22×C15111yescharacteristic
334#340C22×C15112yes—
335#340C22×C15112yes—
336#340C22×C15112yes—
337#336C22×C15112yes—
338C22×Q8—21no—
339C22×Q8—24no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—42no—
343C22×Q8C23×C15112yes—
344C22×Q8C23×C15111yescharacteristic
345C22×D4D4×C15111yescharacteristic
346C23×C4—21no—
347C23×C4—21no—
348C23×C4C23×C15111yescharacteristic
349C23×C4C23×C15111yescharacteristic
350C2×Q16—24no—
351C2×Q16—24no—
352C2×Q16—42no—
353C2×M16—22no—
354C2×M16—42no—
355C22×C8C23×C15112yes—
356C22×C8C23×C15112yes—
357#126—28no—
358#125—28no—
359#125—22no—
360#125—22no—
361#123—28no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—24no—
366C22⋊Q8—42no—
367C22⋊Q8D4×C15114yes—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×D4—22no—
371C4×D4—22no—
372#117—28no—
373#117—22no—
374#117D4×C15114yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4D4×C15111yescharacteristic
385C2×C4⋊C4C23×C15112yes—
386C2×C4⋊C4C23×C15111yescharacteristic
387C2×C4⋊C4C23×C15111yescharacteristic
388C2×C4⋊C4C23×C15111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4D4×C15111yescharacteristic
395C2×C22⋊C4D4×C15111yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C15111yescharacteristic
399#103—24no—
400#103—24no—
401#103—24no—
402#103—42no—
403C22⋊C8—22no—
404C22⋊C8—42no—
405#95—21no—
406#95—22no—
407#95—22no—
408C24C2×D4×C15111yescharacteristic
409C24C2×D4×C15111yescharacteristic
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—28no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—44no—
420C2×Q8—48no—
421C2×Q8—44no—
422C2×Q8—42no—
423C2×Q8C2×D4×C15112yes—
424C2×Q8#41×C15114yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—41no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C2×D4×C15111yescharacteristic
446C22×C4C2×D4×C15111yescharacteristic
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15111yescharacteristic
449C22×C4C2×D4×C15112yes—
450C22×C4C2×D4×C15112yes—
451C22×C4C24×C15111yescharacteristic
452Q16—48no—
453M16—44no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—22no—
459C2×C8—22no—
460C4⋊C4—24no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—44no—
473C4⋊C4C2×D4×C15112yes—
474C4⋊C4C2×D4×C15112yes—
475C4⋊C4C2×D4×C15112yes—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—44no—
482C22⋊C4—42no—
483C42—24no—
484C42—24no—
485C42—21no—
486C42—21no—
487C23—21no—
488C23—22no—
489C23—22no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—22no—
494C23—22no—
495C23#120×C15112yes—
496C23#137×C15112yes—
497C23C22×D4×C15111yescharacteristic
498Q8—24no—
499Q8—24no—
500Q8—24no—
501Q8—48no—
502Q8—41no—
503Q8—42no—
504Q8—41no—
505Q8—42no—
506D4—44no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—48no—
524C2×C4—48no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4#120×C15112yes—
540C2×C4C22×D4×C15111yescharacteristic
541C2×C4C22×D4×C15111yescharacteristic
542C2×C4C2×#41×C15112yes—
543C2×C4H(5,𝔽2)×C15112yes—
544C8—42no—
545C8—42no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—41no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22C2×#120×C15111yescharacteristic
557C22#546×C15112yes—
558C22C2×#137×C15111yescharacteristic
559C22#575×C15111yescharacteristic
560C22#578×C15112yes—
561C4—22no—
562C4—41no—
563C4—44no—
564C4—42no—
565C4—41no—
566C4—42no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—82no—
571C4#525×C15111yescharacteristic
572C4#535×C15111yescharacteristic
573C4#546×C15112yes—
574C2—42no—
575C2—42no—
576C2#2404×C15111yescharacteristic
577C2#3007×C15111yescharacteristic
578C2#3011×C15111yescharacteristic
579C2#3312×C15112yes—
580C2#3327×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×#451×C151C2semidirect
3. C2×#419×C151C2semidirect
5. #2026×C151C2semidirect
6. #2001×C151C2semidirect
7. #1894×C151C2semidirect
8. #1878×C151C2semidirect
9. #1872×C151C2semidirect
11. #1825×C151C2semidirect
290. #23983C151direct (N × H)
291. C151#23983direct (N × H)
293. C2×#451C2×C151semidirect
294. C2×#419C2×C151semidirect
296. #2026C2×C151semidirect
297. #2001C2×C151semidirect
298. #1894C2×C151semidirect
299. #1878C2×C151semidirect
300. #1872C2×C151semidirect
302. #1825C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C1512
C2×#451×C1512
C2×#419×C1512
#2409×C1512
#2026×C1512
#2001×C1512
#1894×C1512
#1878×C1512
#1872×C1512
#1870×C1512
#1825×C1512
#23983151