Finite Group Databasebeta

← C151×#17682 #50322607

Subgroups — C151×#17682 #50322607

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#3515×C151C211yesmaximal, characteristic
2#2971×C151C211yesmaximal, characteristic, complemented
3#2923×C151C211yesmaximal, characteristic, complemented
4#1535×C151C212yesmaximal, complemented
5#1534×C151C212yesmaximal, complemented
6#1531×C151C211yesmaximal, characteristic, complemented
7#1529×C151C211yesmaximal, characteristic, complemented
8#1529×C151C212yesmaximal, complemented
9#1528×C151C212yesmaximal, complemented
10#1526×C151C211yesmaximal, characteristic, complemented
11#1524×C151C211yesmaximal, characteristic, complemented
12#557×C151C411yescharacteristic
13#554×C151C411yescharacteristic
14#554×C151C411yescharacteristic
15#553×C151C412yes—
16#552×C151—22no—
17#552×C151—21no—
18#552×C151C412yes—
19#547×C151—21no—
20#547×C151C411yescharacteristic
21#541×C151—21no—
22#539×C151—22no—
23#533×C151C2211yescharacteristic
24#529×C151C2211yescharacteristic
25#529×C151C2212yes—
26C2×#125×C151C2212yes—
27#520×C151—21no—
28C4×#41×C151C2211yescharacteristic
29C8×Q8×C151—21no—
30#436×C151—21no—
31#436×C151—22no—
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
41C4×M16×C151C2212yes—
42C2×#97×C151C2211yescharacteristic
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×C151—21no—
54C2×#41×C151D411yescharacteristic
55C2×M16×C151—21no—
56C2×M16×C151—22no—
57C2×M16×C151—21no—
58C22×C8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151C2×C411yescharacteristic
61C4⋊Q8×C151C2×C411yescharacteristic
62#126×C151—22no—
63#126×C151—22no—
64#126×C151—22no—
65#126×C151—21no—
66#125×C151—22no—
67#125×C151—22no—
68#125×C151—21no—
69#125×C151—22no—
70#125×C151—22no—
71#125×C151C2×C412yes—
72#125×C151C2×C412yes—
73#125×C151C2311yescharacteristic
74#125×C151C2312yes—
75#124×C151C2311yescharacteristic
76#123×C151—22no—
77#123×C151—21no—
78#123×C151—22no—
79#123×C151—22no—
80#123×C151—22no—
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—22no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151C2×C411yescharacteristic
88C22⋊Q8×C151C2×C412yes—
89#121×C151—22no—
90#121×C151C2×C412yes—
91#121×C151C2×C411yescharacteristic
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151C2×C411yescharacteristic
96C4×Q8×C151C2×C412yes—
97C4×Q8×C151C2×C411yescharacteristic
98C4×Q8×C151D411yescharacteristic
99C4×D4×C151—21no—
100C4×D4×C151—22no—
101C4×D4×C151—21no—
102C4×D4×C151—22no—
103C4×D4×C151C2×C411yescharacteristic
104C4×D4×C151C2×C412yes—
105C4×D4×C151C2×C411yescharacteristic
106C4×D4×C151C2×C412yes—
107C4×D4×C151D411yescharacteristic
108C4×D4×C151D412yes—
109#117×C151—22no—
110#117×C151—21no—
111#117×C151—22no—
112#117×C151C2×C412yes—
113#117×C151D411yescharacteristic
114#117×C151D412yes—
115C2×C4⋊C4×C151—22no—
116C2×C4⋊C4×C151—22no—
117C2×C4⋊C4×C151—21no—
118C2×C4⋊C4×C151C2×C412yes—
119C2×C4⋊C4×C151C2×C412yes—
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×C151C2311yescharacteristic
132#97×C151C2311yescharacteristic
133#97×C151C2311yescharacteristic
134#97×C151C2312yes—
135#97×C151C2311yescharacteristic
136#97×C151C2312yes—
137C4×C8×C151—21no—
138C4×C8×C151—21no—
139C4×C8×C151—22no—
140#41×C151—42no—
141#41×C151—44no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151C22⋊C411yescharacteristic
145C2×Q8×C151C22×C411yescharacteristic
146C2×D4×C151—22no—
147C2×D4×C151—21no—
148C2×D4×C151C22⋊C411yescharacteristic
149C2×D4×C151C22⋊C412yes—
150C2×D4×C151C22×C411yescharacteristic
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151C22×C412yes—
156C22×C4×C151C22×C411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D412yes—
159C22×C4×C151C2×D412yes—
160C22×C4×C151C2×D411yescharacteristic
161M16×C151—44no—
162M16×C151—42no—
163M16×C151—42no—
164C2×C8×C151—21no—
165C2×C8×C151—22no—
166C2×C8×C151—21no—
167C2×C8×C151—22no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—42no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151C22⋊C411yescharacteristic
188C4⋊C4×C151C22⋊C411yescharacteristic
189C4⋊C4×C151C22⋊C412yes—
190C4⋊C4×C151C22⋊C412yes—
191C4⋊C4×C151C22×C411yescharacteristic
192C4⋊C4×C151C22×C411yescharacteristic
193C4⋊C4×C151C22×C412yes—
194C4⋊C4×C151C22×C412yes—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151C22⋊C412yes—
205C22⋊C4×C151C22⋊C412yes—
206C22⋊C4×C151C22⋊C412yes—
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—42no—
223Q8×C151—81no—
224D4×C151—22no—
225D4×C151—42no—
226D4×C151—41no—
227D4×C151—44no—
228D4×C151—81no—
229C2×C4×C151—22no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—41no—
238C2×C4×C151—42no—
239C2×C4×C151—41no—
240C2×C4×C151—44no—
241C2×C4×C151—42no—
242C2×C4×C151—82no—
243C2×C4×C151—82no—
244C2×C4×C151C2×C22⋊C411yescharacteristic
245C2×C4×C151C2×C22⋊C412yes—
246C2×C4×C151C2×C22⋊C411yescharacteristic
247C2×C4×C151C2×C22⋊C412yes—
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—41no—
258C8×C151—42no—
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—41no—
279C4×C151—42no—
280C4×C151—41no—
281C4×C151—42no—
282C4×C151#42112yes—
283C2×C151—41no—
284C2×C151—42no—
285C2×C151—81no—
286C2×C151#288911yescharacteristic
287C2×C151C2×#42111yescharacteristic
288C2×C151#290111yescharacteristic
289#17682C15111yesmaximal, characteristic, direct product factor, Sylow
290C151#1768211yescharacteristic, direct product factor, Sylow
291#3515C2×C15111yescharacteristic
292#2971C2×C15111yescharacteristic, complemented
293#2923C2×C15111yescharacteristic, complemented
294#1535C2×C15112yescomplemented
295#1534C2×C15112yescomplemented
296#1531C2×C15111yescharacteristic, complemented
297#1529C2×C15111yescharacteristic, complemented
298#1529C2×C15112yescomplemented
299#1528C2×C15112yescomplemented
300#1526C2×C15111yescharacteristic, complemented
301#1524C2×C15111yescharacteristic, complemented
302#557C4×C15111yescharacteristic
303#554C4×C15111yescharacteristic
304#554C4×C15111yescharacteristic
305#553C4×C15112yes—
306#552—22no—
307#552—21no—
308#552C4×C15112yes—
309#547—21no—
310#547C4×C15111yescharacteristic
311#541—21no—
312#539—22no—
313#533C22×C15111yescharacteristic
314#529C22×C15111yescharacteristic
315#529C22×C15112yes—
316C2×#125C22×C15112yes—
317#520—21no—
318C4×#41C22×C15111yescharacteristic
319C8×Q8—21no—
320#436—21no—
321#436—22no—
322#433—22no—
323#432C22×C15112yes—
324#432C22×C15112yes—
325#432C22×C15111yescharacteristic
326#432C22×C15112yes—
327#424—21no—
328#408—21no—
329C4×M16C22×C15111yescharacteristic
330C4×M16C22×C15111yescharacteristic
331C4×M16C22×C15112yes—
332C2×#97C22×C15111yescharacteristic
333#330C22×C15111yescharacteristic
334#330C22×C15111yescharacteristic
335#330C22×C15112yes—
336#330C22×C15112yes—
337#330C22×C15112yes—
338#330C22×C15112yes—
339#330C22×C15112yes—
340#329C22×C15111yescharacteristic
341#329C22×C15111yescharacteristic
342#329C22×C15112yes—
343C2×#41—21no—
344C2×#41D4×C15111yescharacteristic
345C2×M16—21no—
346C2×M16—22no—
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C2×C4×C15111yescharacteristic
351C4⋊Q8C2×C4×C15111yescharacteristic
352#126—22no—
353#126—22no—
354#126—22no—
355#126—21no—
356#125—22no—
357#125—22no—
358#125—21no—
359#125—22no—
360#125—22no—
361#125C2×C4×C15112yes—
362#125C2×C4×C15112yes—
363#125C23×C15111yescharacteristic
364#125C23×C15112yes—
365#124C23×C15111yescharacteristic
366#123—22no—
367#123—21no—
368#123—22no—
369#123—22no—
370#123—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—22no—
375C22⋊Q8—21no—
376C22⋊Q8—22no—
377C22⋊Q8C2×C4×C15111yescharacteristic
378C22⋊Q8C2×C4×C15112yes—
379#121—22no—
380#121C2×C4×C15112yes—
381#121C2×C4×C15111yescharacteristic
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C2×C4×C15112yes—
386C4×Q8C2×C4×C15111yescharacteristic
387C4×Q8C2×C4×C15111yescharacteristic
388C4×Q8D4×C15111yescharacteristic
389C4×D4—21no—
390C4×D4—22no—
391C4×D4—21no—
392C4×D4—22no—
393C4×D4C2×C4×C15111yescharacteristic
394C4×D4C2×C4×C15112yes—
395C4×D4C2×C4×C15111yescharacteristic
396C4×D4C2×C4×C15112yes—
397C4×D4D4×C15111yescharacteristic
398C4×D4D4×C15112yes—
399#117—22no—
400#117—21no—
401#117—22no—
402#117C2×C4×C15112yes—
403#117D4×C15111yescharacteristic
404#117D4×C15112yes—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4C2×C4×C15112yes—
409C2×C4⋊C4C2×C4×C15112yes—
410C2×C42C23×C15112yes—
411C2×C42C23×C15111yescharacteristic
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#97C23×C15111yescharacteristic
422#97C23×C15111yescharacteristic
423#97C23×C15111yescharacteristic
424#97C23×C15111yescharacteristic
425#97C23×C15112yes—
426#97C23×C15112yes—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—22no—
430#41—42no—
431#41—44no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C22⋊C4×C15111yescharacteristic
435C2×Q8C22×C4×C15111yescharacteristic
436C2×D4—22no—
437C2×D4—21no—
438C2×D4C22⋊C4×C15111yescharacteristic
439C2×D4C22⋊C4×C15112yes—
440C2×D4C22×C4×C15111yescharacteristic
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4C22×C4×C15112yes—
446C22×C4C22×C4×C15111yescharacteristic
447C22×C4C2×D4×C15111yescharacteristic
448C22×C4C2×D4×C15112yes—
449C22×C4C2×D4×C15112yes—
450C22×C4C2×D4×C15111yescharacteristic
451M16—44no—
452M16—42no—
453M16—42no—
454C2×C8—21no—
455C2×C8—22no—
456C2×C8—21no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4C22⋊C4×C15111yescharacteristic
478C4⋊C4C22⋊C4×C15111yescharacteristic
479C4⋊C4C22⋊C4×C15112yes—
480C4⋊C4C22⋊C4×C15112yes—
481C4⋊C4C22×C4×C15111yescharacteristic
482C4⋊C4C22×C4×C15111yescharacteristic
483C4⋊C4C22×C4×C15112yes—
484C4⋊C4C22×C4×C15112yes—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4C22⋊C4×C15112yes—
495C22⋊C4C22⋊C4×C15112yes—
496C22⋊C4C22⋊C4×C15112yes—
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—42no—
513Q8—81no—
514D4—22no—
515D4—42no—
516D4—41no—
517D4—44no—
518D4—81no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4C2×C22⋊C4×C15111yescharacteristic
535C2×C4C2×C22⋊C4×C15112yes—
536C2×C4C2×C22⋊C4×C15111yescharacteristic
537C2×C4C2×C22⋊C4×C15112yes—
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—41no—
548C8—42no—
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—41no—
569C4—42no—
570C4—41no—
571C4—42no—
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#3515×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. #2971×C151C2semidirect
3. #2923×C151C2semidirect
4. #1535×C151C2semidirect
5. #1534×C151C2semidirect
6. #1531×C151C2semidirect
7. #1529×C151C2semidirect
8. #1529×C151C2semidirect
9. #1528×C151C2semidirect
10. #1526×C151C2semidirect
11. #1524×C151C2semidirect
289. #17682C151direct (N × H)
290. C151#17682direct (N × H)
292. #2971C2×C151semidirect
293. #2923C2×C151semidirect
294. #1535C2×C151semidirect
295. #1534C2×C151semidirect
296. #1531C2×C151semidirect
297. #1529C2×C151semidirect
298. #1529C2×C151semidirect
299. #1528C2×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
#3515×C1512
#2971×C1512
#2923×C1512
#1535×C1512
#1534×C1512
#1531×C1512
#1529×C1512
#1528×C1512
#1526×C1512
#1524×C1512
#17682151