Finite Group Databasebeta

← C151×#20931 #50325856

Subgroups — C151×#20931 #50325856

Order 38656.

1766 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic
2C2×#520×C151C211yesmaximal, characteristic
3C2×#416×C151C211yesmaximal, characteristic
4C22×#103×C151C211yesmaximal, characteristic, complemented
5#2310×C151C211yesmaximal, characteristic, complemented
6#1878×C151C214yesmaximal, complemented
7#1877×C151C214yesmaximal, complemented
8#1736×C151C211yesmaximal, characteristic, complemented
9#1729×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11C23×Q8×C151C2211yescharacteristic
12C2×#137×C151—24no—
13C2×#137×C151—24no—
14C2×#137×C151C418yescomplemented
15C22×Q16×C151C2212yes—
16C22×SD16×C151C2212yes—
17C22×M16×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19#520×C151—24no—
20#520×C151—24no—
21C2×C4×Q8×C151C2212yes—
22C2×C4×D4×C151—22no—
23C2×C4×D4×C151C2212yes—
24C2×#117×C151—21no—
25C2×#117×C151C2211yescharacteristic
26C2×#117×C151C2211yescharacteristic
27C22×C4⋊C4×C151—21no—
28C22×C4⋊C4×C151C2211yescharacteristic
29#416×C151—24no—
30C2×#103×C151—24no—
31C2×#103×C151C2214yes—
32C2×#103×C151C2212yes—
33C2×#102×C151C2212yes—
34#391×C151—21no—
35#391×C151—21no—
36#391×C151C2214yes—
37#381×C151—22no—
38#340×C151C2214yes—
39#336×C151C2214yes—
40C2×#41×C151—22no—
41C2×#41×C151—22no—
42C2×#41×C151—22no—
43C2×#41×C151C2×C414yes—
44C2×#41×C151D414yes—
45C2×#41×C151D414yes—
46C22×Q8×C151—22no—
47C22×Q8×C151—22no—
48C22×Q8×C151—22no—
49C22×Q8×C151—22no—
50C22×Q8×C151—21no—
51C22×Q8×C151—22no—
52C22×Q8×C151C2×C414yescomplemented
53C22×Q8×C151C2312yes—
54C22×Q8×C151C2311yescharacteristic
55C22×D4×C151—21no—
56C22×D4×C151C2311yescharacteristic
57C23×C4×C151—21no—
58C23×C4×C151—22no—
59C23×C4×C151—21no—
60C23×C4×C151—21no—
61C23×C4×C151C2311yescharacteristic
62#137×C151—232no—
63C2×Q16×C151—24no—
64C2×Q16×C151—24no—
65C2×Q16×C151C2×C418yescomplemented
66C2×SD16×C151—24no—
67C2×SD16×C151—24no—
68C2×SD16×C151C2×C418yescomplemented
69C2×M16×C151—22no—
70C2×M16×C151—22no—
71C2×M16×C151C2×C414yescomplemented
72C22×C8×C151—22no—
73C22×C8×C151—22no—
74C22×C8×C151—22no—
75C22×C8×C151C2312yes—
76C22×C8×C151C2312yes—
77C4×Q8×C151—24no—
78C4×Q8×C151—24no—
79C4×D4×C151—216no—
80C4×D4×C151—24no—
81C4×D4×C151—24no—
82#117×C151—28no—
83#117×C151—22no—
84#117×C151—22no—
85#117×C151—22no—
86#117×C151—22no—
87C2×C4⋊C4×C151—28no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151D411yescharacteristic
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D414yes—
94C2×C4⋊C4×C151C2312yes—
95C2×C4⋊C4×C151C2312yes—
96C2×C22⋊C4×C151—22no—
97C2×C22⋊C4×C151—21no—
98C2×C22⋊C4×C151D412yes—
99C2×C42×C151—22no—
100C2×C42×C151—21no—
101C2×C42×C151C2312yes—
102#103×C151—28no—
103#103×C151—24no—
104#102×C151—24no—
105#95×C151—24no—
106#95×C151—24no—
107C24×C151—21no—
108C24×C151C2×D411yescharacteristic
109#41×C151—28no—
110#41×C151—28no—
111#41×C151—28no—
112#41×C151C22⋊C4116yes—
113C2×Q8×C151—24no—
114C2×Q8×C151—21no—
115C2×Q8×C151—21no—
116C2×Q8×C151—21no—
117C2×Q8×C151—22no—
118C2×Q8×C151—28no—
119C2×Q8×C151—28no—
120C2×Q8×C151—22no—
121C2×Q8×C151—22no—
122C2×Q8×C151—22no—
123C2×Q8×C151—22no—
124C2×Q8×C151—42no—
125C2×Q8×C151—42no—
126C2×Q8×C151—44no—
127C2×Q8×C151—44no—
128C2×Q8×C151C22×C414yes—
129C2×Q8×C151C22×C412yes—
130C2×Q8×C151C2×D412yes—
131C2×Q8×C151C2×D412yes—
132C2×D4×C151—24no—
133C2×D4×C151—24no—
134C2×D4×C151—24no—
135C2×D4×C151—21no—
136C2×D4×C151—21no—
137C2×D4×C151—21no—
138C2×D4×C151C22×C412yes—
139C2×D4×C151C2×D412yes—
140C2×D4×C151C2×D412yes—
141C22×C4×C151—21no—
142C22×C4×C151—24no—
143C22×C4×C151—24no—
144C22×C4×C151—24no—
145C22×C4×C151—24no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—28no—
149C22×C4×C151—24no—
150C22×C4×C151—22no—
151C22×C4×C151—42no—
152C22×C4×C151—42no—
153C22×C4×C151—84no—
154C22×C4×C151—82no—
155C22×C4×C151C22×C412yes—
156C22×C4×C151C2×D412yes—
157C22×C4×C151C2×D412yes—
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D412yes—
162C22×C4×C151#4112yes—
163C22×C4×C151#4112yes—
164C22×C4×C151C2411yescharacteristic
165Q16×C151—216no—
166SD16×C151—216no—
167M16×C151—28no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C2×C8×C151—44no—
174C2×C8×C151C22×C414yes—
175C4⋊C4×C151—28no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—24no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151C2×D414yes—
183C22⋊C4×C151—28no—
184C22⋊C4×C151—24no—
185C22⋊C4×C151—42no—
186C42×C151—28no—
187C42×C151—22no—
188C42×C151—22no—
189C42×C151—42no—
190C23×C151—22no—
191C23×C151—22no—
192C23×C151—22no—
193C23×C151—22no—
194C23×C151—22no—
195C23×C151—42no—
196C23×C151—42no—
197C23×C151C4×D412yes—
198C23×C151#12012yes—
199C23×C151#12112yes—
200C23×C151C22×D411yescharacteristic
201Q8×C151—22no—
202Q8×C151—22no—
203Q8×C151—22no—
204Q8×C151—24no—
205Q8×C151—24no—
206Q8×C151—42no—
207Q8×C151—42no—
208Q8×C151—48no—
209Q8×C151C2×C22⋊C414yes—
210D4×C151—216no—
211D4×C151—22no—
212D4×C151—22no—
213D4×C151—22no—
214D4×C151C2×C22⋊C414yes—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—216no—
219C2×C4×C151—24no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—24no—
223C2×C4×C151—24no—
224C2×C4×C151—24no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—44no—
228C2×C4×C151—48no—
229C2×C4×C151—42no—
230C2×C4×C151—42no—
231C2×C4×C151—42no—
232C2×C4×C151—84no—
233C2×C4×C151—88no—
234C2×C4×C151C2×C22⋊C414yes—
235C2×C4×C151C4×D414yes—
236C2×C4×C151C4×D412yes—
237C2×C4×C151#12012yes—
238C2×C4×C151#12114yes—
239C2×C4×C151#12112yes—
240C2×C4×C151#12314yes—
241C2×C4×C151C23×C411yescharacteristic
242C2×C4×C151C22×D411yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C2×#4111yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C8×C151—24no—
248C8×C151—42no—
249C22×C151—24no—
250C22×C151—22no—
251C22×C151—22no—
252C22×C151—24no—
253C22×C151—24no—
254C22×C151—44no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—44no—
258C22×C151#38614yes—
259C22×C151C2×C4×D411yescharacteristic
260C22×C151C2×#12011yescharacteristic
261C22×C151C2×#12111yescharacteristic
262C22×C151#57712yes—
263C22×C151#57812yes—
264C4×C151—24no—
265C4×C151—42no—
266C4×C151—44no—
267C4×C151—42no—
268C4×C151—44no—
269C4×C151—82no—
270C4×C151#38614yes—
271C4×C151C22×C22⋊C411yescharacteristic
272C4×C151C2×C4×D411yescharacteristic
273C4×C151C2×#12111yescharacteristic
274C4×C151C2×#12311yescharacteristic
275C2×C151—24no—
276C2×C151—44no—
277C2×C151C2×#38611yescharacteristic
278C2×C151#294712yes—
279C2×C151#300911yescharacteristic
280C2×C151#301111yescharacteristic
281C2×C151#304612yes—
282#20931C15111yesmaximal, characteristic, direct product factor, Sylow
283C151#2093111yescharacteristic, direct product factor, Sylow
284C22×#137C2×C15111yescharacteristic
285C2×#520C2×C15111yescharacteristic
286C2×#416C2×C15111yescharacteristic
287C22×#103C2×C15111yescharacteristic, complemented
288#2310C2×C15111yescharacteristic, complemented
289#1878C2×C15114yescomplemented
290#1877C2×C15114yescomplemented
291#1736C2×C15111yescharacteristic, complemented
292#1729C2×C15111yescharacteristic, complemented
293C22×#41C22×C15111yescharacteristic
294C23×Q8C22×C15111yescharacteristic
295C2×#137—24no—
296C2×#137—24no—
297C2×#137C4×C15118yescomplemented
298C22×Q16C22×C15112yes—
299C22×SD16C22×C15112yes—
300C22×M16C22×C15111yescharacteristic
301C23×C8C22×C15111yescharacteristic
302#520—24no—
303#520—24no—
304C2×C4×Q8C22×C15112yes—
305C2×C4×D4—22no—
306C2×C4×D4C22×C15112yes—
307C2×#117—21no—
308C2×#117C22×C15111yescharacteristic
309C2×#117C22×C15111yescharacteristic
310C22×C4⋊C4—21no—
311C22×C4⋊C4C22×C15111yescharacteristic
312#416—24no—
313C2×#103—24no—
314C2×#103C22×C15114yes—
315C2×#103C22×C15112yes—
316C2×#102C22×C15112yes—
317#391—21no—
318#391—21no—
319#391C22×C15114yes—
320#381—22no—
321#340C22×C15114yes—
322#336C22×C15114yes—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41C2×C4×C15114yes—
327C2×#41D4×C15114yes—
328C2×#41D4×C15114yes—
329C22×Q8—22no—
330C22×Q8—21no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8C2×C4×C15114yescomplemented
336C22×Q8C23×C15112yes—
337C22×Q8C23×C15111yescharacteristic
338C22×D4—21no—
339C22×D4C23×C15111yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—21no—
343C23×C4—22no—
344C23×C4C23×C15111yescharacteristic
345#137—232no—
346C2×Q16—24no—
347C2×Q16—24no—
348C2×Q16C2×C4×C15118yescomplemented
349C2×SD16—24no—
350C2×SD16—24no—
351C2×SD16C2×C4×C15118yescomplemented
352C2×M16—22no—
353C2×M16—22no—
354C2×M16C2×C4×C15114yescomplemented
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8C23×C15112yes—
359C22×C8C23×C15112yes—
360C4×Q8—24no—
361C4×Q8—24no—
362C4×D4—216no—
363C4×D4—24no—
364C4×D4—24no—
365#117—28no—
366#117—22no—
367#117—22no—
368#117—22no—
369#117—22no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4D4×C15111yescharacteristic
375C2×C4⋊C4D4×C15111yescharacteristic
376C2×C4⋊C4D4×C15114yes—
377C2×C4⋊C4C23×C15112yes—
378C2×C4⋊C4C23×C15112yes—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4D4×C15112yes—
382C2×C42—22no—
383C2×C42—21no—
384C2×C42C23×C15112yes—
385#103—24no—
386#103—28no—
387#102—24no—
388#95—24no—
389#95—24no—
390C24—21no—
391C24C2×D4×C15111yescharacteristic
392#41—28no—
393#41—28no—
394#41—28no—
395#41C22⋊C4×C151116yes—
396C2×Q8—24no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—28no—
402C2×Q8—28no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—42no—
408C2×Q8—44no—
409C2×Q8—42no—
410C2×Q8—44no—
411C2×Q8C22×C4×C15114yes—
412C2×Q8C22×C4×C15112yes—
413C2×Q8C2×D4×C15112yes—
414C2×Q8C2×D4×C15112yes—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4C22×C4×C15112yes—
422C2×D4C2×D4×C15112yes—
423C2×D4C2×D4×C15112yes—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—28no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—84no—
437C22×C4—82no—
438C22×C4C22×C4×C15112yes—
439C22×C4C2×D4×C15112yes—
440C22×C4C2×D4×C15112yes—
441C22×C4C2×D4×C15112yes—
442C22×C4C2×D4×C15112yes—
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15112yes—
445C22×C4#41×C15112yes—
446C22×C4#41×C15112yes—
447C22×C4C24×C15111yescharacteristic
448Q16—216no—
449SD16—216no—
450M16—28no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—44no—
457C2×C8C22×C4×C15114yes—
458C4⋊C4—28no—
459C4⋊C4—22no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4C2×D4×C15114yes—
466C22⋊C4—28no—
467C22⋊C4—24no—
468C22⋊C4—42no—
469C42—28no—
470C42—22no—
471C42—22no—
472C42—42no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—42no—
479C23—42no—
480C23C4×D4×C15112yes—
481C23#120×C15112yes—
482C23#121×C15112yes—
483C23C22×D4×C15111yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—22no—
487Q8—24no—
488Q8—24no—
489Q8—48no—
490Q8—42no—
491Q8—42no—
492Q8C2×C22⋊C4×C15114yes—
493D4—216no—
494D4—22no—
495D4—22no—
496D4—22no—
497D4C2×C22⋊C4×C15114yes—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—216no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—48no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—44no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—84no—
516C2×C4—88no—
517C2×C4C2×C22⋊C4×C15114yes—
518C2×C4C4×D4×C15112yes—
519C2×C4C4×D4×C15114yes—
520C2×C4#120×C15112yes—
521C2×C4#121×C15112yes—
522C2×C4#121×C15114yes—
523C2×C4#123×C15114yes—
524C2×C4C23×C4×C15111yescharacteristic
525C2×C4C22×D4×C15111yescharacteristic
526C2×C4C22×D4×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C2×#41×C15111yescharacteristic
529C2×C4C2×#41×C15111yescharacteristic
530C8—24no—
531C8—42no—
532C22—24no—
533C22—22no—
534C22—22no—
535C22—24no—
536C22—24no—
537C22—44no—
538C22—42no—
539C22—42no—
540C22—44no—
541C22#386×C15114yes—
542C22C2×C4×D4×C15111yescharacteristic
543C22C2×#120×C15111yescharacteristic
544C22C2×#121×C15111yescharacteristic
545C22#577×C15112yes—
546C22#578×C15112yes—
547C4—24no—
548C4—42no—
549C4—44no—
550C4—42no—
551C4—44no—
552C4—82no—
553C4#386×C15114yes—
554C4C22×C22⋊C4×C15111yescharacteristic
555C4C2×C4×D4×C15111yescharacteristic
556C4C2×#121×C15111yescharacteristic
557C4C2×#123×C15111yescharacteristic
558C2—24no—
559C2—44no—
560C2C2×#386×C15111yescharacteristic
561C2#2947×C15112yes—
562C2#3009×C15111yescharacteristic
563C2#3011×C15111yescharacteristic
564C2#3046×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×#103×C151C2semidirect
5. #2310×C151C2semidirect
6. #1878×C151C2semidirect
7. #1877×C151C2semidirect
8. #1736×C151C2semidirect
9. #1729×C151C2semidirect
14. C2×#137×C151C4semidirect
52. C22×Q8×C151C2×C4semidirect
65. C2×Q16×C151C2×C4semidirect
68. C2×SD16×C151C2×C4semidirect
71. C2×M16×C151C2×C4semidirect
282. #20931C151direct (N × H)
283. C151#20931direct (N × H)
287. C22×#103C2×C151semidirect
288. #2310C2×C151semidirect
289. #1878C2×C151semidirect
290. #1877C2×C151semidirect
291. #1736C2×C151semidirect
292. #1729C2×C151semidirect
297. C2×#137C4×C151semidirect
335. C22×Q8C2×C4×C151semidirect
348. C2×Q16C2×C4×C151semidirect
351. C2×SD16C2×C4×C151semidirect
354. C2×M16C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#520×C1512
C2×#416×C1512
C22×#103×C1512
#2310×C1512
#1878×C1512
#1877×C1512
#1736×C1512
#1729×C1512
#20931151