Finite Group Databasebeta

← C151×#18538 #50323463

Subgroups — C151×#18538 #50323463

Order 38656.

922 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3482×C151C211yesmaximal, characteristic
2#3139×C151C211yesmaximal, characteristic, complemented
3#3079×C151C211yesmaximal, characteristic, complemented
4#3079×C151C211yesmaximal, characteristic, complemented
5#1638×C151C212yesmaximal, complemented
6#1637×C151C212yesmaximal, complemented
7#1636×C151C212yesmaximal, complemented
8#1635×C151C212yesmaximal, complemented
9#1561×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1489×C151C211yesmaximal, characteristic, complemented
12#557×C151C2211yescharacteristic
13#556×C151—21no—
14#556×C151C2211yescharacteristic
15#552×C151—22no—
16#552×C151—21no—
17D4×Q8×C151C2211yescharacteristic
18#548×C151—21no—
19#547×C151—21no—
20#547×C151C2211yescharacteristic
21#533×C151—21no—
22#533×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#529×C151—21no—
25#529×C151—22no—
26C4×#41×C151—21no—
27C4×#41×C151C2211yescharacteristic
28C4×#41×C151C2211yescharacteristic
29C2×C4×Q8×C151—21no—
30#491×C151—22no—
31#487×C151C2212yes—
32#487×C151C2212yes—
33#477×C151C2212yes—
34#477×C151C2212yes—
35#476×C151C2212yes—
36#476×C151C2212yes—
37#475×C151—21no—
38#475×C151—21no—
39#474×C151—21no—
40#474×C151—21no—
41#428×C151—21no—
42#428×C151—21no—
43#423×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#419×C151—22no—
46#417×C151—21no—
47#417×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#332×C151C2212yes—
50#332×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53D4⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—21no—
56C2×#41×C151D411yescharacteristic
57C2×#41×C151D411yescharacteristic
58C22×Q8×C151—21no—
59C22×Q8×C151—21no—
60C2×M16×C151—21no—
61C2×M16×C151—21no—
62C2×M16×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151C2312yes—
69C4⋊Q8×C151C2311yescharacteristic
70C4⋊Q8×C151C2311yescharacteristic
71#126×C151—22no—
72#126×C151—22no—
73#126×C151—22no—
74#125×C151—22no—
75#125×C151—22no—
76#125×C151—21no—
77#125×C151D412yes—
78#124×C151—22no—
79#124×C151—21no—
80#123×C151—22no—
81#123×C151—22no—
82#123×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—21no—
90#121×C151—22no—
91#121×C151—21no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×Q8×C151D411yescharacteristic
100C4×Q8×C151D411yescharacteristic
101C4×Q8×C151C2311yescharacteristic
102C4×Q8×C151C2311yescharacteristic
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—21no—
106C4×D4×C151—21no—
107C4×D4×C151—21no—
108C4×D4×C151—21no—
109C4×D4×C151—21no—
110C4×D4×C151D411yescharacteristic
111C4×D4×C151D411yescharacteristic
112C4×D4×C151C2311yescharacteristic
113C4×D4×C151C2311yescharacteristic
114#117×C151—22no—
115#117×C151—22no—
116#117×C151—21no—
117#117×C151—21no—
118#117×C151—21no—
119#117×C151D412yes—
120#117×C151D411yescharacteristic
121#117×C151D411yescharacteristic
122C2×C4⋊C4×C151—22no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C42×C151—22no—
127C2×C42×C151—21no—
128C2×C42×C151—21no—
129C2×C42×C151C2311yescharacteristic
130#107×C151—22no—
131#107×C151—22no—
132#106×C151—22no—
133#106×C151—22no—
134C4⋊C8×C151—21no—
135C4⋊C8×C151—21no—
136C4⋊C8×C151C2312yes—
137C4⋊C8×C151C2312yes—
138#103×C151—24no—
139#103×C151—24no—
140#103×C151—22no—
141#103×C151—22no—
142#102×C151—22no—
143#102×C151—22no—
144#97×C151—21no—
145C4×C8×C151C2312yes—
146#41×C151—22no—
147#41×C151—22no—
148#41×C151—41no—
149#41×C151—41no—
150#41×C151—42no—
151#41×C151—42no—
152C2×Q8×C151—22no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—22no—
156C2×Q8×C151—44no—
157C2×Q8×C151—42no—
158C2×Q8×C151—42no—
159C2×Q8×C151—41no—
160C2×Q8×C151C2×D411yescharacteristic
161C2×Q8×C151C2×D411yescharacteristic
162C2×D4×C151—22no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—41no—
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179M16×C151—42no—
180M16×C151—42no—
181M16×C151—42no—
182C2×C8×C151—22no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151C2×D412yes—
204C4⋊C4×C151C2×D412yes—
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D411yescharacteristic
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C22⋊C4×C151—22no—
210C22⋊C4×C151—22no—
211C22⋊C4×C151—22no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—21no—
219C22⋊C4×C151—21no—
220C42×C151—22no—
221C42×C151—22no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—22no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151C2×D411yescharacteristic
230C42×C151C2×D411yescharacteristic
231C42×C151C2×D411yescharacteristic
232C42×C151C2411yescharacteristic
233C23×C151—21no—
234C23×C151—21no—
235C23×C151#12011yescharacteristic
236Q8×C151—21no—
237Q8×C151—21no—
238Q8×C151—21no—
239Q8×C151—44no—
240Q8×C151—44no—
241Q8×C151—41no—
242Q8×C151—41no—
243Q8×C151—41no—
244Q8×C151—41no—
245Q8×C151—82no—
246Q8×C151#13712yes—
247D4×C151—21no—
248D4×C151—21no—
249D4×C151—21no—
250D4×C151—42no—
251D4×C151—42no—
252D4×C151—44no—
253D4×C151#13712yes—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—22no—
260C2×C4×C151—21no—
261C2×C4×C151—22no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—42no—
268C2×C4×C151—42no—
269C2×C4×C151—44no—
270C2×C4×C151—44no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—42no—
276C2×C4×C151—42no—
277C2×C4×C151—42no—
278C2×C4×C151—82no—
279C2×C4×C151#12011yescharacteristic
280C2×C4×C151#12011yescharacteristic
281C2×C4×C151#12011yescharacteristic
282C2×C4×C151C22×D411yescharacteristic
283C2×C4×C151C22×D411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C8×C151—42no—
286C8×C151—42no—
287C8×C151—42no—
288C22×C151—21no—
289C22×C151—21no—
290C22×C151—22no—
291C22×C151—21no—
292C22×C151—41no—
293C22×C151—41no—
294C22×C151—41no—
295C22×C151—41no—
296C22×C151—41no—
297C22×C151C2×#12011yescharacteristic
298C4×C151—21no—
299C4×C151—21no—
300C4×C151—22no—
301C4×C151—21no—
302C4×C151—41no—
303C4×C151—41no—
304C4×C151—42no—
305C4×C151—42no—
306C4×C151—41no—
307C4×C151—41no—
308C4×C151—41no—
309C4×C151—82no—
310C4×C151#45412yes—
311C4×C151C2×#13711yescharacteristic
312C4×C151C2×#13711yescharacteristic
313C4×C151#57511yescharacteristic
314C4×C151#57511yescharacteristic
315C2×C151—41no—
316C2×C151—42no—
317C2×C151—81no—
318C2×C151#300711yescharacteristic
319C2×C151#300711yescharacteristic
320C2×C151C2×#45411yescharacteristic
321#18538C15111yesmaximal, characteristic, direct product factor, Sylow
322C151#1853811yescharacteristic, direct product factor, Sylow
323#3482C2×C15111yescharacteristic
324#3139C2×C15111yescharacteristic, complemented
325#3079C2×C15111yescharacteristic, complemented
326#3079C2×C15111yescharacteristic, complemented
327#1638C2×C15112yescomplemented
328#1637C2×C15112yescomplemented
329#1636C2×C15112yescomplemented
330#1635C2×C15112yescomplemented
331#1561C2×C15111yescharacteristic, complemented
332#1489C2×C15111yescharacteristic, complemented
333#1489C2×C15111yescharacteristic, complemented
334#557C22×C15111yescharacteristic
335#556—21no—
336#556C22×C15111yescharacteristic
337#552—22no—
338#552—21no—
339D4×Q8C22×C15111yescharacteristic
340#548—21no—
341#547—21no—
342#547C22×C15111yescharacteristic
343#533—21no—
344#533C22×C15111yescharacteristic
345C2×C4⋊Q8C22×C15111yescharacteristic
346#529—21no—
347#529—22no—
348C4×#41—21no—
349C4×#41C22×C15111yescharacteristic
350C4×#41C22×C15111yescharacteristic
351C2×C4×Q8—21no—
352#491—22no—
353#487C22×C15112yes—
354#487C22×C15112yes—
355#477C22×C15112yes—
356#477C22×C15112yes—
357#476C22×C15112yes—
358#476C22×C15112yes—
359#475—21no—
360#475—21no—
361#474—21no—
362#474—21no—
363#428—21no—
364#428—21no—
365#423C22×C15111yescharacteristic
366#423C22×C15111yescharacteristic
367#419—22no—
368#417—21no—
369#417—21no—
370C4×M16C22×C15111yescharacteristic
371#332C22×C15112yes—
372#332C22×C15112yes—
373Q8⋊C8C22×C15112yes—
374Q8⋊C8C22×C15112yes—
375D4⋊C8C22×C15112yes—
376D4⋊C8C22×C15112yes—
377C2×#41—21no—
378C2×#41D4×C15111yescharacteristic
379C2×#41D4×C15111yescharacteristic
380C22×Q8—21no—
381C22×Q8—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C23×C15112yes—
391C4⋊Q8C23×C15111yescharacteristic
392C4⋊Q8C23×C15111yescharacteristic
393#126—22no—
394#126—22no—
395#126—22no—
396#125—22no—
397#125—22no—
398#125—21no—
399#125D4×C15112yes—
400#124—22no—
401#124—21no—
402#123—22no—
403#123—22no—
404#123—22no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—22no—
411C22⋊Q8—21no—
412#121—22no—
413#121—21no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8D4×C15111yescharacteristic
422C4×Q8D4×C15111yescharacteristic
423C4×Q8C23×C15111yescharacteristic
424C4×Q8C23×C15111yescharacteristic
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4D4×C15111yescharacteristic
433C4×D4D4×C15111yescharacteristic
434C4×D4C23×C15111yescharacteristic
435C4×D4C23×C15111yescharacteristic
436#117—22no—
437#117—22no—
438#117—21no—
439#117—21no—
440#117—21no—
441#117D4×C15111yescharacteristic
442#117D4×C15111yescharacteristic
443#117D4×C15112yes—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C42—22no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C15111yescharacteristic
452#107—22no—
453#107—22no—
454#106—22no—
455#106—22no—
456C4⋊C8—21no—
457C4⋊C8—21no—
458C4⋊C8C23×C15112yes—
459C4⋊C8C23×C15112yes—
460#103—22no—
461#103—22no—
462#103—24no—
463#103—24no—
464#102—22no—
465#102—22no—
466#97—21no—
467C4×C8C23×C15112yes—
468#41—22no—
469#41—22no—
470#41—41no—
471#41—41no—
472#41—42no—
473#41—42no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—44no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—41no—
482C2×Q8C2×D4×C15111yescharacteristic
483C2×Q8C2×D4×C15111yescharacteristic
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×D4×C15111yescharacteristic
488C2×D4C2×D4×C15111yescharacteristic
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—41no—
498C22×C4C2×D4×C15111yescharacteristic
499C22×C4C2×D4×C15111yescharacteristic
500C22×C4C2×D4×C15111yescharacteristic
501M16—42no—
502M16—42no—
503M16—42no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4C2×D4×C15112yes—
526C4⋊C4C2×D4×C15112yes—
527C4⋊C4C2×D4×C15111yescharacteristic
528C4⋊C4C2×D4×C15111yescharacteristic
529C4⋊C4C2×D4×C15111yescharacteristic
530C4⋊C4C2×D4×C15111yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C42—22no—
543C42—22no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—22no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42C2×D4×C15111yescharacteristic
552C42C2×D4×C15111yescharacteristic
553C42C2×D4×C15111yescharacteristic
554C42C24×C15111yescharacteristic
555C23—21no—
556C23—21no—
557C23#120×C15111yescharacteristic
558Q8—21no—
559Q8—21no—
560Q8—21no—
561Q8—44no—
562Q8—44no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—82no—
568Q8#137×C15112yes—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—42no—
573D4—42no—
574D4—44no—
575D4#137×C15112yes—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—82no—
601C2×C4#120×C15111yescharacteristic
602C2×C4#120×C15111yescharacteristic
603C2×C4#120×C15111yescharacteristic
604C2×C4C22×D4×C15111yescharacteristic
605C2×C4C22×D4×C15111yescharacteristic
606C2×C4C22×D4×C15111yescharacteristic
607C8—42no—
608C8—42no—
609C8—42no—
610C22—21no—
611C22—21no—
612C22—22no—
613C22—21no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22C2×#120×C15111yescharacteristic
620C4—21no—
621C4—21no—
622C4—22no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—82no—
632C4#454×C15112yes—
633C4C2×#137×C15111yescharacteristic
634C4C2×#137×C15111yescharacteristic
635C4#575×C15111yescharacteristic
636C4#575×C15111yescharacteristic
637C2—41no—
638C2—42no—
639C2—81no—
640C2#3007×C15111yescharacteristic
641C2#3007×C15111yescharacteristic
642C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3482×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
2. #3139×C151C2semidirect
3. #3079×C151C2semidirect
4. #3079×C151C2semidirect
5. #1638×C151C2semidirect
6. #1637×C151C2semidirect
7. #1636×C151C2semidirect
8. #1635×C151C2semidirect
9. #1561×C151C2semidirect
10. #1489×C151C2semidirect
11. #1489×C151C2semidirect
321. #18538C151direct (N × H)
322. C151#18538direct (N × H)
324. #3139C2×C151semidirect
325. #3079C2×C151semidirect
326. #3079C2×C151semidirect
327. #1638C2×C151semidirect
328. #1637C2×C151semidirect
329. #1636C2×C151semidirect
330. #1635C2×C151semidirect
331. #1561C2×C151semidirect
332. #1489C2×C151semidirect
333. #1489C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3482×C1512
#3139×C1512
#3079×C1512
#1638×C1512
#1637×C1512
#1636×C1512
#1635×C1512
#1561×C1512
#1489×C1512
#18538151