Finite Group Databasebeta

← C151×#18884 #50323809

Subgroups — C151×#18884 #50323809

Order 38656.

942 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3503×C151C211yesmaximal, characteristic, complemented
2#3246×C151C211yesmaximal, characteristic, complemented
3#3227×C151C211yesmaximal, characteristic, complemented
4#3035×C151C211yesmaximal, characteristic
5#1653×C151C212yesmaximal, complemented
6#1651×C151C212yesmaximal, complemented
7#1627×C151C212yesmaximal, complemented
8#1626×C151C212yesmaximal, complemented
9C2×#332×C151C211yesmaximal, characteristic, complemented
10#1481×C151C211yesmaximal, characteristic, complemented
11#1477×C151C211yesmaximal, characteristic, complemented
12C2×#135×C151—21no—
13Q82×C151—21no—
14#557×C151C2212yes—
15#554×C151—21no—
16#554×C151—22no—
17D4×Q8×C151—22no—
18D4×Q8×C151C2212yes—
19#544×C151—22no—
20#544×C151—21no—
21#533×C151—21no—
22#533×C151C2211yescharacteristic
23#532×C151C2211yescharacteristic
24C2×C4⋊Q8×C151—21no—
25C2×C4⋊Q8×C151C2211yescharacteristic
26#520×C151—21no—
27C4×#41×C151C2211yescharacteristic
28#498×C151C2212yes—
29#486×C151C2212yes—
30#481×C151—22no—
31#476×C151—22no—
32#476×C151—21no—
33#475×C151C2212yes—
34#465×C151—22no—
35#464×C151—21no—
36#463×C151—21no—
37#462×C151C2211yescharacteristic
38#461×C151—21no—
39#461×C151C2211yescharacteristic
40#460×C151C2211yescharacteristic
41#460×C151C2212yes—
42#459×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44C2×C4⋊C8×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#416×C151—21no—
47#332×C151C2212yes—
48#332×C151C2212yes—
49Q8⋊C8×C151C2212yes—
50Q8⋊C8×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52D4⋊C8×C151C2212yes—
53C2×#41×C151—21no—
54C2×#41×C151D411yescharacteristic
55C22×Q8×C151—21no—
56C22×Q8×C151—22no—
57#135×C151—44no—
58C2×Q16×C151—21no—
59C2×SD16×C151—21no—
60C2×SD16×C151—21no—
61C2×SD16×C151—22no—
62C2×D8×C151—21no—
63C22×C8×C151—21no—
64C22×C8×C151—21no—
65C4⋊Q8×C151—22no—
66C4⋊Q8×C151—22no—
67C4⋊Q8×C151—24no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151—22no—
72C4⋊Q8×C151D412yes—
73C4⋊Q8×C151D411yescharacteristic
74C4⋊Q8×C151D411yescharacteristic
75C4⋊Q8×C151C2311yescharacteristic
76C4⋊Q8×C151C2312yes—
77#127×C151C2311yescharacteristic
78#125×C151—22no—
79#125×C151—24no—
80#125×C151—22no—
81#125×C151—21no—
82#124×C151—21no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—24no—
85C22⋊Q8×C151—24no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—22no—
88C22⋊Q8×C151—24no—
89C22⋊Q8×C151D412yes—
90#121×C151—21no—
91#121×C151—21no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—21no—
95C4×Q8×C151—22no—
96C4×Q8×C151D411yescharacteristic
97C4×Q8×C151C2311yescharacteristic
98C4×Q8×C151C2312yes—
99C4×D4×C151—24no—
100C4×D4×C151—22no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151—21no—
105C4×D4×C151D411yescharacteristic
106C4×D4×C151C2311yescharacteristic
107#117×C151—22no—
108#117×C151—21no—
109#117×C151—21no—
110#117×C151D411yescharacteristic
111C2×C4⋊C4×C151—22no—
112C2×C4⋊C4×C151—22no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151D412yes—
115C2×C42×C151—21no—
116C2×C42×C151C2311yescharacteristic
117#106×C151—22no—
118#106×C151—24no—
119C4⋊C8×C151—21no—
120C4⋊C8×C151—21no—
121C4⋊C8×C151—21no—
122C4⋊C8×C151C2311yescharacteristic
123C4⋊C8×C151C2311yescharacteristic
124C4⋊C8×C151C2312yes—
125#103×C151—21no—
126#103×C151—21no—
127#103×C151—22no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—22no—
131#102×C151—24no—
132C22⋊C8×C151—21no—
133C4×C8×C151C2312yes—
134#41×C151—22no—
135#41×C151—42no—
136#41×C151—42no—
137#41×C151SD1614yescomplemented
138C2×Q8×C151—24no—
139C2×Q8×C151—21no—
140C2×Q8×C151—22no—
141C2×Q8×C151—22no—
142C2×Q8×C151—21no—
143C2×Q8×C151—81no—
144C2×Q8×C151—81no—
145C2×Q8×C151—82no—
146C2×Q8×C151—82no—
147C2×Q8×C151C2×D412yes—
148C2×Q8×C151C2×D411yescharacteristic
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—41no—
154C2×D4×C151C2×D411yescharacteristic
155C22×C4×C151—21no—
156C22×C4×C151—24no—
157C22×C4×C151—22no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—41no—
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D411yescharacteristic
164Q16×C151—42no—
165SD16×C151—42no—
166SD16×C151—42no—
167SD16×C151—82no—
168D8×C151—42no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—42no—
174C2×C8×C151—81no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—24no—
177C4⋊C4×C151—24no—
178C4⋊C4×C151—24no—
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×C151—21no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151C2×D411yescharacteristic
192C4⋊C4×C151C2×D411yescharacteristic
193C4⋊C4×C151C2×D414yes—
194C4⋊C4×C151C2×D412yes—
195C22⋊C4×C151—24no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C42×C151—24no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—21no—
206C42×C151—22no—
207C42×C151C2×D411yescharacteristic
208C42×C151C2×D411yescharacteristic
209C42×C151C2×D411yescharacteristic
210C42×C151C2411yescharacteristic
211C23×C151—21no—
212C23×C151—41no—
213C23×C151#12011yescharacteristic
214Q8×C151—21no—
215Q8×C151—22no—
216Q8×C151—22no—
217Q8×C151—42no—
218Q8×C151—42no—
219Q8×C151—42no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—82no—
223Q8×C151—84no—
224Q8×C151C2×SD1612yes—
225D4×C151—24no—
226D4×C151—21no—
227D4×C151—42no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—82no—
233D4×C151C2×SD1612yes—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—24no—
238C2×C4×C151—21no—
239C2×C4×C151—24no—
240C2×C4×C151—22no—
241C2×C4×C151—22no—
242C2×C4×C151—21no—
243C2×C4×C151—41no—
244C2×C4×C151—42no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—82no—
249C2×C4×C151—84no—
250C2×C4×C151—82no—
251C2×C4×C151#12011yescharacteristic
252C2×C4×C151#12011yescharacteristic
253C2×C4×C151#12011yescharacteristic
254C2×C4×C151C2×SD1612yes—
255C2×C4×C151#13712yes—
256C2×C4×C151C22×D411yescharacteristic
257C2×C4×C151C22×D411yescharacteristic
258C2×C4×C151C22×D411yescharacteristic
259C8×C151—42no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—42no—
263C22×C151—21no—
264C22×C151—21no—
265C22×C151—22no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—81no—
269C22×C151—81no—
270C22×C151—81no—
271C22×C151#44812yes—
272C22×C151C2×#12011yescharacteristic
273C4×C151—22no—
274C4×C151—21no—
275C4×C151—21no—
276C4×C151—21no—
277C4×C151—41no—
278C4×C151—42no—
279C4×C151—44no—
280C4×C151—41no—
281C4×C151—42no—
282C4×C151—81no—
283C4×C151#44812yes—
284C4×C151C22×SD1611yescharacteristic
285C4×C151C2×#13711yescharacteristic
286C4×C151#57611yescharacteristic
287C4×C151#57711yescharacteristic
288C2×C151—22no—
289C2×C151—42no—
290C2×C151—161no—
291C2×C151C2×#44811yescharacteristic
292C2×C151#301211yescharacteristic
293C2×C151#302011yescharacteristic
294#18884C15111yesmaximal, characteristic, direct product factor, Sylow
295C151#1888411yescharacteristic, direct product factor, Sylow
296#3503C2×C15111yescharacteristic, complemented
297#3246C2×C15111yescharacteristic, complemented
298#3227C2×C15111yescharacteristic, complemented
299#3035C2×C15111yescharacteristic
300#1653C2×C15112yescomplemented
301#1651C2×C15112yescomplemented
302#1627C2×C15112yescomplemented
303#1626C2×C15112yescomplemented
304C2×#332C2×C15111yescharacteristic, complemented
305#1481C2×C15111yescharacteristic, complemented
306#1477C2×C15111yescharacteristic, complemented
307C2×#135—21no—
308Q82—21no—
309#557C22×C15112yes—
310#554—21no—
311#554—22no—
312D4×Q8—22no—
313D4×Q8C22×C15112yes—
314#544—22no—
315#544—21no—
316#533—21no—
317#533C22×C15111yescharacteristic
318#532C22×C15111yescharacteristic
319C2×C4⋊Q8—21no—
320C2×C4⋊Q8C22×C15111yescharacteristic
321#520—21no—
322C4×#41C22×C15111yescharacteristic
323#498C22×C15112yes—
324#486C22×C15112yes—
325#481—22no—
326#476—22no—
327#476—21no—
328#475C22×C15112yes—
329#465—22no—
330#464—21no—
331#463—21no—
332#462C22×C15111yescharacteristic
333#461—21no—
334#461C22×C15111yescharacteristic
335#460C22×C15111yescharacteristic
336#460C22×C15112yes—
337#459C22×C15111yescharacteristic
338#431C22×C15111yescharacteristic
339C2×C4⋊C8C22×C15111yescharacteristic
340C2×C4⋊C8C22×C15111yescharacteristic
341#416—21no—
342#332C22×C15112yes—
343#332C22×C15112yes—
344Q8⋊C8C22×C15112yes—
345Q8⋊C8C22×C15112yes—
346Q8⋊C8C22×C15112yes—
347D4⋊C8C22×C15112yes—
348C2×#41—21no—
349C2×#41D4×C15111yescharacteristic
350C22×Q8—22no—
351C22×Q8—21no—
352#135—44no—
353C2×Q16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—22no—
357C2×D8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8—24no—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—21no—
366C4⋊Q8—21no—
367C4⋊Q8D4×C15111yescharacteristic
368C4⋊Q8D4×C15112yes—
369C4⋊Q8D4×C15111yescharacteristic
370C4⋊Q8C23×C15111yescharacteristic
371C4⋊Q8C23×C15112yes—
372#127C23×C15111yescharacteristic
373#125—22no—
374#125—24no—
375#125—22no—
376#125—21no—
377#124—21no—
378C22⋊Q8—22no—
379C22⋊Q8—24no—
380C22⋊Q8—24no—
381C22⋊Q8—21no—
382C22⋊Q8—22no—
383C22⋊Q8—24no—
384C22⋊Q8D4×C15112yes—
385#121—21no—
386#121—21no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—21no—
391C4×Q8D4×C15111yescharacteristic
392C4×Q8C23×C15111yescharacteristic
393C4×Q8C23×C15112yes—
394C4×D4—24no—
395C4×D4—22no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4D4×C15111yescharacteristic
401C4×D4C23×C15111yescharacteristic
402#117—22no—
403#117—21no—
404#117—21no—
405#117D4×C15111yescharacteristic
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4D4×C15112yes—
410C2×C42—21no—
411C2×C42C23×C15111yescharacteristic
412#106—22no—
413#106—24no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8C23×C15112yes—
418C4⋊C8C23×C15111yescharacteristic
419C4⋊C8C23×C15111yescharacteristic
420#103—22no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—22no—
426#102—24no—
427C22⋊C8—21no—
428C4×C8C23×C15112yes—
429#41—22no—
430#41—42no—
431#41—42no—
432#41SD16×C15114yescomplemented
433C2×Q8—24no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—81no—
439C2×Q8—81no—
440C2×Q8—82no—
441C2×Q8—82no—
442C2×Q8C2×D4×C15112yes—
443C2×Q8C2×D4×C15111yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C2×D4×C15111yescharacteristic
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4C2×D4×C15111yescharacteristic
457C22×C4C2×D4×C15111yescharacteristic
458C22×C4C2×D4×C15111yescharacteristic
459Q16—42no—
460SD16—42no—
461SD16—42no—
462SD16—82no—
463D8—42no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—42no—
469C2×C8—81no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4C2×D4×C15111yescharacteristic
487C4⋊C4C2×D4×C15111yescharacteristic
488C4⋊C4C2×D4×C15114yes—
489C4⋊C4C2×D4×C15112yes—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—24no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—22no—
502C42C2×D4×C15111yescharacteristic
503C42C2×D4×C15111yescharacteristic
504C42C2×D4×C15111yescharacteristic
505C42C24×C15111yescharacteristic
506C23—21no—
507C23—41no—
508C23#120×C15111yescharacteristic
509Q8—21no—
510Q8—22no—
511Q8—22no—
512Q8—42no—
513Q8—42no—
514Q8—42no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—84no—
519Q8C2×SD16×C15112yes—
520D4—24no—
521D4—21no—
522D4—42no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—82no—
528D4C2×SD16×C15112yes—
529C2×C4—21no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—84no—
545C2×C4—82no—
546C2×C4#120×C15111yescharacteristic
547C2×C4#120×C15111yescharacteristic
548C2×C4#120×C15111yescharacteristic
549C2×C4C2×SD16×C15112yes—
550C2×C4#137×C15112yes—
551C2×C4C22×D4×C15111yescharacteristic
552C2×C4C22×D4×C15111yescharacteristic
553C2×C4C22×D4×C15111yescharacteristic
554C8—42no—
555C8—41no—
556C8—41no—
557C8—42no—
558C22—21no—
559C22—21no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22#448×C15112yes—
567C22C2×#120×C15111yescharacteristic
568C4—22no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—42no—
574C4—44no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4#448×C15112yes—
579C4C22×SD16×C15111yescharacteristic
580C4C2×#137×C15111yescharacteristic
581C4#576×C15111yescharacteristic
582C4#577×C15111yescharacteristic
583C2—22no—
584C2—42no—
585C2—161no—
586C2C2×#448×C15111yescharacteristic
587C2#3012×C15111yescharacteristic
588C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3035×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3503×C151C2semidirect
2. #3246×C151C2semidirect
3. #3227×C151C2semidirect
5. #1653×C151C2semidirect
6. #1651×C151C2semidirect
7. #1627×C151C2semidirect
8. #1626×C151C2semidirect
9. C2×#332×C151C2semidirect
10. #1481×C151C2semidirect
11. #1477×C151C2semidirect
137. #41×C151SD16semidirect
294. #18884C151direct (N × H)
295. C151#18884direct (N × H)
296. #3503C2×C151semidirect
297. #3246C2×C151semidirect
298. #3227C2×C151semidirect
300. #1653C2×C151semidirect
301. #1651C2×C151semidirect
302. #1627C2×C151semidirect
303. #1626C2×C151semidirect
304. C2×#332C2×C151semidirect
305. #1481C2×C151semidirect
306. #1477C2×C151semidirect
432. #41SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3503×C1512
#3246×C1512
#3227×C1512
#3035×C1512
#1653×C1512
#1651×C1512
#1627×C1512
#1626×C1512
C2×#332×C1512
#1481×C1512
#1477×C1512
#18884151