Finite Group Databasebeta

← C151×#17683 #50322608

Subgroups — C151×#17683 #50322608

Order 38656.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3518×C151C211yesmaximal, characteristic
2#2970×C151C211yesmaximal, characteristic, complemented
3#2923×C151C211yesmaximal, characteristic, complemented
4#1537×C151C212yesmaximal, complemented
5#1535×C151C212yesmaximal, complemented
6#1532×C151C212yesmaximal, complemented
7#1531×C151C211yesmaximal, characteristic, complemented
8#1531×C151C212yesmaximal, complemented
9#1529×C151C211yesmaximal, characteristic, complemented
10#1526×C151C211yesmaximal, characteristic, complemented
11#1524×C151C211yesmaximal, characteristic, complemented
12Q82×C151C411yescharacteristic
13#556×C151—21no—
14#556×C151—22no—
15#556×C151C412yes—
16#556×C151C411yescharacteristic
17#555×C151C412yes—
18#555×C151C411yescharacteristic
19D4×Q8×C151C411yescharacteristic
20#548×C151—21no—
21#542×C151—21no—
22#542×C151—22no—
23#533×C151C2211yescharacteristic
24#533×C151C2212yes—
25#529×C151C2211yescharacteristic
26#529×C151C2212yes—
27#519×C151—21no—
28C4×#41×C151C2211yescharacteristic
29#446×C151—21no—
30#435×C151—22no—
31C8×D4×C151—21no—
32#433×C151—22no—
33#432×C151C2212yes—
34#432×C151C2212yes—
35#432×C151C2211yescharacteristic
36#432×C151C2212yes—
37#424×C151—21no—
38#408×C151—21no—
39C4×M16×C151C2211yescharacteristic
40C4×M16×C151C2211yescharacteristic
41C2×#97×C151C2211yescharacteristic
42C2×#97×C151C2212yes—
43#330×C151C2211yescharacteristic
44#330×C151C2211yescharacteristic
45#330×C151C2212yes—
46#330×C151C2212yes—
47#330×C151C2212yes—
48#330×C151C2212yes—
49#330×C151C2212yes—
50#329×C151C2211yescharacteristic
51#329×C151C2211yescharacteristic
52#329×C151C2212yes—
53C2×#41×C151D411yescharacteristic
54C22×Q8×C151—21no—
55C2×M16×C151—21no—
56C2×M16×C151—21no—
57C22×C8×C151—21no—
58C22×C8×C151—22no—
59C4⋊Q8×C151—22no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151C2×C411yescharacteristic
62C4⋊Q8×C151C2×C412yes—
63C4⋊Q8×C151C2×C411yescharacteristic
64C4⋊Q8×C151C2×C412yes—
65#126×C151—22no—
66#126×C151—22no—
67#126×C151—22no—
68#126×C151—21no—
69#126×C151—22no—
70#125×C151C2311yescharacteristic
71#125×C151C2312yes—
72#124×C151—21no—
73#124×C151—22no—
74#124×C151—22no—
75#124×C151—22no—
76#124×C151—22no—
77#124×C151C2311yescharacteristic
78#123×C151—22no—
79#123×C151—21no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151C2×C411yescharacteristic
87C22⋊Q8×C151C2×C412yes—
88#121×C151—21no—
89#121×C151—22no—
90#121×C151C2×C411yescharacteristic
91#121×C151C2×C412yes—
92C4×Q8×C151—22no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—22no—
96C4×Q8×C151—21no—
97C4×Q8×C151—22no—
98C4×Q8×C151—21no—
99C4×Q8×C151C2×C411yescharacteristic
100C4×Q8×C151C2×C411yescharacteristic
101C4×Q8×C151C2×C412yes—
102C4×Q8×C151D411yescharacteristic
103C4×D4×C151—21no—
104C4×D4×C151—22no—
105C4×D4×C151C2×C411yescharacteristic
106C4×D4×C151C2×C412yes—
107C4×D4×C151C2×C411yescharacteristic
108C4×D4×C151C2×C412yes—
109C4×D4×C151D411yescharacteristic
110C4×D4×C151D412yes—
111#117×C151—22no—
112#117×C151—21no—
113#117×C151—21no—
114#117×C151—22no—
115#117×C151C2×C412yes—
116#117×C151C2×C412yes—
117#117×C151C2×C412yes—
118#117×C151D411yescharacteristic
119#117×C151D412yes—
120C2×C42×C151C2311yescharacteristic
121C2×C42×C151C2312yes—
122C4⋊C8×C151—22no—
123C4⋊C8×C151—22no—
124C4⋊C8×C151—21no—
125C4⋊C8×C151—22no—
126C22⋊C8×C151—22no—
127C22⋊C8×C151—22no—
128C22⋊C8×C151—22no—
129C22⋊C8×C151—21no—
130#97×C151—21no—
131#97×C151—22no—
132#97×C151C2311yescharacteristic
133#97×C151C2311yescharacteristic
134#97×C151C2311yescharacteristic
135#97×C151C2312yes—
136#97×C151C2312yes—
137#97×C151C2311yescharacteristic
138C4×C8×C151—21no—
139C4×C8×C151—21no—
140#41×C151—42no—
141C2×Q8×C151—22no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—22no—
145C2×Q8×C151—44no—
146C2×Q8×C151C22⋊C411yescharacteristic
147C2×Q8×C151C22×C411yescharacteristic
148C2×D4×C151—21no—
149C2×D4×C151—22no—
150C2×D4×C151C22⋊C411yescharacteristic
151C2×D4×C151C22⋊C412yes—
152C2×D4×C151C22×C411yescharacteristic
153C22×C4×C151—22no—
154C22×C4×C151—21no—
155C22×C4×C151C22×C411yescharacteristic
156C22×C4×C151C22×C412yes—
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2×D411yescharacteristic
161M16×C151—42no—
162M16×C151—42no—
163C2×C8×C151—21no—
164C2×C8×C151—22no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—22no—
169C2×C8×C151—44no—
170C2×C8×C151—42no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151C22⋊C412yes—
184C4⋊C4×C151C22⋊C411yescharacteristic
185C4⋊C4×C151C22⋊C412yes—
186C4⋊C4×C151C22⋊C411yescharacteristic
187C4⋊C4×C151C22×C412yes—
188C4⋊C4×C151C22×C411yescharacteristic
189C4⋊C4×C151C22×C412yes—
190C4⋊C4×C151C22×C411yescharacteristic
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—22no—
194C22⋊C4×C151—21no—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151C22⋊C412yes—
203C22⋊C4×C151C22⋊C412yes—
204C22⋊C4×C151C22⋊C412yes—
205C42×C151—22no—
206C42×C151—22no—
207C42×C151—22no—
208C42×C151—22no—
209C42×C151—21no—
210C42×C151C22×C412yes—
211C42×C151C22×C411yescharacteristic
212C42×C151C2×D411yescharacteristic
213C42×C151C2×D411yescharacteristic
214C42×C151C2×D412yes—
215C42×C151C2×D412yes—
216C42×C151C2411yescharacteristic
217C23×C151—21no—
218C23×C151C2×C22⋊C411yescharacteristic
219C23×C151C2×C22⋊C412yes—
220Q8×C151—22no—
221Q8×C151—41no—
222Q8×C151—44no—
223Q8×C151—42no—
224Q8×C151—82no—
225Q8×C151—81no—
226D4×C151—22no—
227D4×C151—42no—
228D4×C151—41no—
229D4×C151—82no—
230D4×C151—81no—
231C2×C4×C151—22no—
232C2×C4×C151—22no—
233C2×C4×C151—21no—
234C2×C4×C151—22no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—42no—
242C2×C4×C151—44no—
243C2×C4×C151—42no—
244C2×C4×C151C2×C22⋊C412yes—
245C2×C4×C151C2×C22⋊C411yescharacteristic
246C2×C4×C151C2×C22⋊C412yes—
247C2×C4×C151C2×C22⋊C411yescharacteristic
248C2×C4×C151C2×C22⋊C412yes—
249C2×C4×C151C2×C22⋊C411yescharacteristic
250C2×C4×C151C23×C411yescharacteristic
251C2×C4×C151C22×D411yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C8×C151—22no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—42no—
257C8×C151—42no—
258C8×C151—41no—
259C22×C151—21no—
260C22×C151—22no—
261C22×C151—21no—
262C22×C151—22no—
263C22×C151—22no—
264C22×C151—21no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151C22×C22⋊C411yescharacteristic
269C4×C151—21no—
270C4×C151—21no—
271C4×C151—22no—
272C4×C151—21no—
273C4×C151—22no—
274C4×C151—21no—
275C4×C151—22no—
276C4×C151—21no—
277C4×C151—41no—
278C4×C151—42no—
279C4×C151—41no—
280C4×C151—42no—
281C4×C151—41no—
282C4×C151#42112yes—
283C2×C151—41no—
284C2×C151—42no—
285C2×C151—81no—
286C2×C151#288911yescharacteristic
287C2×C151C2×#42111yescharacteristic
288C2×C151#290111yescharacteristic
289#17683C15111yesmaximal, characteristic, direct product factor, Sylow
290C151#1768311yescharacteristic, direct product factor, Sylow
291#3518C2×C15111yescharacteristic
292#2970C2×C15111yescharacteristic, complemented
293#2923C2×C15111yescharacteristic, complemented
294#1537C2×C15112yescomplemented
295#1535C2×C15112yescomplemented
296#1532C2×C15112yescomplemented
297#1531C2×C15112yescomplemented
298#1531C2×C15111yescharacteristic, complemented
299#1529C2×C15111yescharacteristic, complemented
300#1526C2×C15111yescharacteristic, complemented
301#1524C2×C15111yescharacteristic, complemented
302Q82C4×C15111yescharacteristic
303#556—21no—
304#556—22no—
305#556C4×C15111yescharacteristic
306#556C4×C15112yes—
307#555C4×C15111yescharacteristic
308#555C4×C15112yes—
309D4×Q8C4×C15111yescharacteristic
310#548—21no—
311#542—21no—
312#542—22no—
313#533C22×C15112yes—
314#533C22×C15111yescharacteristic
315#529C22×C15111yescharacteristic
316#529C22×C15112yes—
317#519—21no—
318C4×#41C22×C15111yescharacteristic
319#446—21no—
320#435—22no—
321C8×D4—21no—
322#433—22no—
323#432C22×C15112yes—
324#432C22×C15112yes—
325#432C22×C15112yes—
326#432C22×C15111yescharacteristic
327#424—21no—
328#408—21no—
329C4×M16C22×C15111yescharacteristic
330C4×M16C22×C15111yescharacteristic
331C2×#97C22×C15111yescharacteristic
332C2×#97C22×C15112yes—
333#330C22×C15111yescharacteristic
334#330C22×C15112yes—
335#330C22×C15112yes—
336#330C22×C15112yes—
337#330C22×C15111yescharacteristic
338#330C22×C15112yes—
339#330C22×C15112yes—
340#329C22×C15111yescharacteristic
341#329C22×C15111yescharacteristic
342#329C22×C15112yes—
343C2×#41D4×C15111yescharacteristic
344C22×Q8—21no—
345C2×M16—21no—
346C2×M16—21no—
347C22×C8—21no—
348C22×C8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—21no—
351C4⋊Q8C2×C4×C15112yes—
352C4⋊Q8C2×C4×C15111yescharacteristic
353C4⋊Q8C2×C4×C15112yes—
354C4⋊Q8C2×C4×C15111yescharacteristic
355#126—22no—
356#126—22no—
357#126—22no—
358#126—21no—
359#126—22no—
360#125C23×C15111yescharacteristic
361#125C23×C15112yes—
362#124—21no—
363#124—22no—
364#124—22no—
365#124—22no—
366#124—22no—
367#124C23×C15111yescharacteristic
368#123—22no—
369#123—21no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—21no—
376C22⋊Q8C2×C4×C15111yescharacteristic
377C22⋊Q8C2×C4×C15112yes—
378#121—21no—
379#121—22no—
380#121C2×C4×C15111yescharacteristic
381#121C2×C4×C15112yes—
382C4×Q8—21no—
383C4×Q8—22no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—22no—
387C4×Q8—21no—
388C4×Q8—22no—
389C4×Q8C2×C4×C15111yescharacteristic
390C4×Q8C2×C4×C15112yes—
391C4×Q8C2×C4×C15111yescharacteristic
392C4×Q8D4×C15111yescharacteristic
393C4×D4—21no—
394C4×D4—22no—
395C4×D4C2×C4×C15111yescharacteristic
396C4×D4C2×C4×C15112yes—
397C4×D4C2×C4×C15111yescharacteristic
398C4×D4C2×C4×C15112yes—
399C4×D4D4×C15111yescharacteristic
400C4×D4D4×C15112yes—
401#117—22no—
402#117—21no—
403#117—21no—
404#117—22no—
405#117C2×C4×C15112yes—
406#117C2×C4×C15112yes—
407#117C2×C4×C15112yes—
408#117D4×C15111yescharacteristic
409#117D4×C15112yes—
410C2×C42C23×C15111yescharacteristic
411C2×C42C23×C15112yes—
412C4⋊C8—22no—
413C4⋊C8—22no—
414C4⋊C8—21no—
415C4⋊C8—22no—
416C22⋊C8—22no—
417C22⋊C8—22no—
418C22⋊C8—22no—
419C22⋊C8—21no—
420#97—21no—
421#97—22no—
422#97C23×C15111yescharacteristic
423#97C23×C15111yescharacteristic
424#97C23×C15111yescharacteristic
425#97C23×C15112yes—
426#97C23×C15111yescharacteristic
427#97C23×C15112yes—
428C4×C8—21no—
429C4×C8—21no—
430#41—42no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—44no—
436C2×Q8C22⋊C4×C15111yescharacteristic
437C2×Q8C22×C4×C15111yescharacteristic
438C2×D4—21no—
439C2×D4—22no—
440C2×D4C22⋊C4×C15111yescharacteristic
441C2×D4C22⋊C4×C15112yes—
442C2×D4C22×C4×C15111yescharacteristic
443C22×C4—22no—
444C22×C4—21no—
445C22×C4C22×C4×C15111yescharacteristic
446C22×C4C22×C4×C15112yes—
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15112yes—
449C22×C4C2×D4×C15112yes—
450C22×C4C2×D4×C15111yescharacteristic
451M16—42no—
452M16—42no—
453C2×C8—21no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—22no—
459C2×C8—44no—
460C2×C8—42no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4C22⋊C4×C15112yes—
474C4⋊C4C22⋊C4×C15111yescharacteristic
475C4⋊C4C22⋊C4×C15112yes—
476C4⋊C4C22⋊C4×C15111yescharacteristic
477C4⋊C4C22×C4×C15111yescharacteristic
478C4⋊C4C22×C4×C15112yes—
479C4⋊C4C22×C4×C15111yescharacteristic
480C4⋊C4C22×C4×C15112yes—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—22no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4C22⋊C4×C15112yes—
493C22⋊C4C22⋊C4×C15112yes—
494C22⋊C4C22⋊C4×C15112yes—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—22no—
499C42—21no—
500C42C22×C4×C15112yes—
501C42C22×C4×C15111yescharacteristic
502C42C2×D4×C15111yescharacteristic
503C42C2×D4×C15111yescharacteristic
504C42C2×D4×C15112yes—
505C42C2×D4×C15112yes—
506C42C24×C15111yescharacteristic
507C23—21no—
508C23C2×C22⋊C4×C15111yescharacteristic
509C23C2×C22⋊C4×C15112yes—
510Q8—22no—
511Q8—41no—
512Q8—44no—
513Q8—42no—
514Q8—82no—
515Q8—81no—
516D4—22no—
517D4—42no—
518D4—41no—
519D4—82no—
520D4—81no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4C2×C22⋊C4×C15111yescharacteristic
535C2×C4C2×C22⋊C4×C15112yes—
536C2×C4C2×C22⋊C4×C15112yes—
537C2×C4C2×C22⋊C4×C15111yescharacteristic
538C2×C4C2×C22⋊C4×C15112yes—
539C2×C4C2×C22⋊C4×C15111yescharacteristic
540C2×C4C23×C4×C15111yescharacteristic
541C2×C4C22×D4×C15111yescharacteristic
542C2×C4C22×D4×C15111yescharacteristic
543C8—22no—
544C8—41no—
545C8—41no—
546C8—42no—
547C8—42no—
548C8—41no—
549C22—21no—
550C22—22no—
551C22—21no—
552C22—22no—
553C22—22no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22C22×C22⋊C4×C15111yescharacteristic
559C4—21no—
560C4—21no—
561C4—22no—
562C4—21no—
563C4—22no—
564C4—21no—
565C4—22no—
566C4—21no—
567C4—41no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4#421×C15112yes—
573C2—41no—
574C2—42no—
575C2—81no—
576C2#2889×C15111yescharacteristic
577C2C2×#421×C15111yescharacteristic
578C2#2901×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC42C24×C151
prime radical#3518×C151C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C4×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2970×C151C2semidirect
3. #2923×C151C2semidirect
4. #1537×C151C2semidirect
5. #1535×C151C2semidirect
6. #1532×C151C2semidirect
7. #1531×C151C2semidirect
8. #1531×C151C2semidirect
9. #1529×C151C2semidirect
10. #1526×C151C2semidirect
11. #1524×C151C2semidirect
289. #17683C151direct (N × H)
290. C151#17683direct (N × H)
292. #2970C2×C151semidirect
293. #2923C2×C151semidirect
294. #1537C2×C151semidirect
295. #1535C2×C151semidirect
296. #1532C2×C151semidirect
297. #1531C2×C151semidirect
298. #1531C2×C151semidirect
299. #1529C2×C151semidirect
300. #1526C2×C151semidirect
301. #1524C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3518×C1512
#2970×C1512
#2923×C1512
#1537×C1512
#1535×C1512
#1532×C1512
#1531×C1512
#1529×C1512
#1526×C1512
#1524×C1512
#17683151