Finite Group Databasebeta

← C151×#18207 #50323132

Subgroups — C151×#18207 #50323132

Order 38656.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C151C211yesmaximal, characteristic
2C2×#484×C151C211yesmaximal, characteristic, complemented
3C2×#481×C151C211yesmaximal, characteristic, complemented
4#2487×C151C211yesmaximal, characteristic, complemented
5#1618×C151C214yesmaximal, complemented
6#1615×C151C214yesmaximal, complemented
7#1520×C151C211yesmaximal, characteristic, complemented
8#1519×C151C211yesmaximal, characteristic, complemented
9#1459×C151C211yesmaximal, characteristic, complemented
10#553×C151—22no—
11#553×C151—21no—
12#552×C151—21no—
13#551×C151—22no—
14#548×C151—21no—
15#546×C151—21no—
16#539×C151C2212yes—
17#538×C151C2212yes—
18#534×C151—21no—
19#529×C151—21no—
20#525×C151—21no—
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×#121×C151C2211yescharacteristic
23#518×C151—21no—
24C2×C4×D4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2211yescharacteristic
26#484×C151—22no—
27#484×C151C2214yescomplemented
28#481×C151—22no—
29#481×C151C2214yes—
30C2×#107×C151—21no—
31C2×#106×C151—21no—
32C2×#103×C151—21no—
33C2×#102×C151—21no—
34C2×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36#400×C151C2212yescomplemented
37#399×C151C2212yescomplemented
38#389×C151—21no—
39#386×C151—21no—
40#385×C151—21no—
41#380×C151—21no—
42#380×C151C2211yescharacteristic
43#328×C151C2214yescomplemented
44#327×C151C2214yes—
45#324×C151C2212yescomplemented
46#323×C151C2212yescomplemented
47C2×#41×C151—21no—
48C22×Q8×C151D411yescharacteristic
49C22×D4×C151—21no—
50C22×D4×C151D411yescharacteristic
51C22×D4×C151D411yescharacteristic
52C23×C4×C151—21no—
53C23×C4×C151D411yescharacteristic
54C23×C4×C151C2311yescharacteristic
55C22×C8×C151—21no—
56C22×C8×C151—21no—
57#126×C151—22no—
58#126×C151—22no—
59#126×C151—22no—
60#125×C151—21no—
61#125×C151—22no—
62#124×C151—21no—
63#124×C151—22no—
64#123×C151—22no—
65#123×C151—22no—
66#123×C151—22no—
67#123×C151—22no—
68#123×C151—22no—
69C22⋊Q8×C151—21no—
70C22⋊Q8×C151—21no—
71C22⋊Q8×C151—21no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151D412yes—
74C22⋊Q8×C151C2312yes—
75#121×C151—21no—
76#121×C151—22no—
77#121×C151—22no—
78#121×C151—22no—
79#121×C151—21no—
80#121×C151—21no—
81#121×C151D412yes—
82#121×C151C2312yes—
83#120×C151—22no—
84#120×C151—22no—
85C4×Q8×C151—21no—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151—21no—
90C4×D4×C151—21no—
91C4×D4×C151—21no—
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96#117×C151—22no—
97#117×C151—21no—
98#117×C151—22no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151—21no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—22no—
107C2×C4⋊C4×C151D411yescharacteristic
108C2×C4⋊C4×C151D411yescharacteristic
109C2×C4⋊C4×C151C2312yes—
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C22⋊C4×C151—22no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151D411yescharacteristic
117C2×C22⋊C4×C151C2311yescharacteristic
118C2×C42×C151D411yescharacteristic
119#107×C151—24no—
120#106×C151—24no—
121#103×C151—24no—
122#102×C151—24no—
123C22⋊C8×C151—21no—
124C22⋊C8×C151—21no—
125C22⋊C8×C151C2312yes—
126C22⋊C8×C151C2312yes—
127#95×C151—22no—
128#95×C151—22no—
129#95×C151C2312yes—
130C24×C151—21no—
131C24×C151C2×D411yescharacteristic
132C24×C151C2×D411yescharacteristic
133#41×C151—82no—
134C2×Q8×C151—21no—
135C2×Q8×C151—42no—
136C2×Q8×C151C2×D412yes—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—22no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—21no—
146C2×D4×C151—42no—
147C2×D4×C151—42no—
148C2×D4×C151—42no—
149C2×D4×C151C2×D412yes—
150C22×C4×C151—21no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—22no—
158C22×C4×C151—22no—
159C22×C4×C151—42no—
160C22×C4×C151—42no—
161C22×C4×C151—41no—
162C22×C4×C151—41no—
163C22×C4×C151—82no—
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151C2×D411yescharacteristic
170C22×C4×C151C2×D411yescharacteristic
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2411yescharacteristic
173C2×C8×C151—22no—
174C2×C8×C151—22no—
175C2×C8×C151—42no—
176C2×C8×C151—42no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—42no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151—82no—
193C4⋊C4×C151C2×D412yes—
194C4⋊C4×C151C2×D412yes—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—22no—
206C22⋊C4×C151—22no—
207C22⋊C4×C151—21no—
208C22⋊C4×C151—21no—
209C22⋊C4×C151—42no—
210C22⋊C4×C151—82no—
211C42×C151—22no—
212C42×C151—22no—
213C42×C151—21no—
214C42×C151—21no—
215C23×C151—22no—
216C23×C151—21no—
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—41no—
220C23×C151—41no—
221C23×C151—41no—
222C23×C151—41no—
223C23×C151—42no—
224C23×C151—81no—
225C23×C151—81no—
226C23×C151#12011yescharacteristic
227C23×C151#12011yescharacteristic
228C23×C151#13512yes—
229C23×C151#13712yes—
230C23×C151C22×D411yescharacteristic
231Q8×C151—42no—
232Q8×C151—42no—
233D4×C151—42no—
234D4×C151—42no—
235D4×C151—42no—
236D4×C151—42no—
237D4×C151—42no—
238D4×C151—44no—
239D4×C151—42no—
240D4×C151—82no—
241D4×C151—82no—
242C2×C4×C151—22no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—22no—
249C2×C4×C151—21no—
250C2×C4×C151—22no—
251C2×C4×C151—21no—
252C2×C4×C151—21no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151—42no—
257C2×C4×C151—42no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—42no—
261C2×C4×C151—42no—
262C2×C4×C151—42no—
263C2×C4×C151—42no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151—81no—
267C2×C4×C151—81no—
268C2×C4×C151—81no—
269C2×C4×C151—82no—
270C2×C4×C151—82no—
271C2×C4×C151—82no—
272C2×C4×C151—82no—
273C2×C4×C151#12011yescharacteristic
274C2×C4×C151#12011yescharacteristic
275C2×C4×C151C22×D411yescharacteristic
276C2×C4×C151C22×D411yescharacteristic
277C8×C151—42no—
278C8×C151—42no—
279C22×C151—21no—
280C22×C151—21no—
281C22×C151—21no—
282C22×C151—21no—
283C22×C151—21no—
284C22×C151—21no—
285C22×C151—42no—
286C22×C151—42no—
287C22×C151—42no—
288C22×C151—41no—
289C22×C151—42no—
290C22×C151—42no—
291C22×C151—41no—
292C22×C151—41no—
293C22×C151—42no—
294C22×C151—81no—
295C22×C151—162no—
296C22×C151#45212yes—
297C22×C151#45212yes—
298C22×C151C2×#12011yescharacteristic
299C22×C151C2×#13511yescharacteristic
300C22×C151C2×#13711yescharacteristic
301C4×C151—21no—
302C4×C151—21no—
303C4×C151—21no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—41no—
307C4×C151—42no—
308C4×C151—41no—
309C4×C151—42no—
310C4×C151—82no—
311C4×C151—82no—
312C4×C151#45812yes—
313C2×C151—21no—
314C2×C151—21no—
315C2×C151—22no—
316C2×C151—22no—
317C2×C151—81no—
318C2×C151—82no—
319C2×C151C2×#45211yescharacteristic
320C2×C151#302111yescharacteristic
321C2×C151C2×#45811yescharacteristic
322#18207C15111yesmaximal, characteristic, direct product factor, Sylow
323C151#1820711yescharacteristic, direct product factor, Sylow
324#3505C2×C15111yescharacteristic
325C2×#484C2×C15111yescharacteristic, complemented
326C2×#481C2×C15111yescharacteristic, complemented
327#2487C2×C15111yescharacteristic, complemented
328#1618C2×C15114yescomplemented
329#1615C2×C15114yescomplemented
330#1520C2×C15111yescharacteristic, complemented
331#1519C2×C15111yescharacteristic, complemented
332#1459C2×C15111yescharacteristic, complemented
333#553—22no—
334#553—21no—
335#552—21no—
336#551—22no—
337#548—21no—
338#546—21no—
339#539C22×C15112yes—
340#538C22×C15112yes—
341#534—21no—
342#529—21no—
343#525—21no—
344C2×C22⋊Q8C22×C15111yescharacteristic
345C2×#121C22×C15111yescharacteristic
346#518—21no—
347C2×C4×D4C22×C15111yescharacteristic
348C22×C4⋊C4C22×C15111yescharacteristic
349#484—22no—
350#484C22×C15114yescomplemented
351#481—22no—
352#481C22×C15114yes—
353C2×#107—21no—
354C2×#106—21no—
355C2×#103—21no—
356C2×#102—21no—
357C2×C22⋊C8C22×C15111yescharacteristic
358C2×C22⋊C8C22×C15111yescharacteristic
359#400C22×C15112yescomplemented
360#399C22×C15112yescomplemented
361#389—21no—
362#386—21no—
363#385—21no—
364#380—21no—
365#380C22×C15111yescharacteristic
366#328C22×C15114yescomplemented
367#327C22×C15114yes—
368#324C22×C15112yescomplemented
369#323C22×C15112yescomplemented
370C2×#41—21no—
371C22×Q8D4×C15111yescharacteristic
372C22×D4—21no—
373C22×D4D4×C15111yescharacteristic
374C22×D4D4×C15111yescharacteristic
375C23×C4—21no—
376C23×C4D4×C15111yescharacteristic
377C23×C4C23×C15111yescharacteristic
378C22×C8—21no—
379C22×C8—21no—
380#126—22no—
381#126—22no—
382#126—22no—
383#125—21no—
384#125—22no—
385#124—21no—
386#124—22no—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392C22⋊Q8—21no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8D4×C15112yes—
397C22⋊Q8C23×C15112yes—
398#121—21no—
399#121—22no—
400#121—22no—
401#121—22no—
402#121—21no—
403#121—21no—
404#121D4×C15112yes—
405#121C23×C15112yes—
406#120—22no—
407#120—22no—
408C4×Q8—21no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—22no—
418C4×D4—22no—
419#117—22no—
420#117—21no—
421#117—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4D4×C15111yescharacteristic
431C2×C4⋊C4D4×C15111yescharacteristic
432C2×C4⋊C4C23×C15112yes—
433C2×C4⋊C4C23×C15111yescharacteristic
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4D4×C15111yescharacteristic
440C2×C22⋊C4C23×C15111yescharacteristic
441C2×C42D4×C15111yescharacteristic
442#107—24no—
443#106—24no—
444#103—24no—
445#102—24no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8C23×C15112yes—
449C22⋊C8C23×C15112yes—
450#95—22no—
451#95—22no—
452#95C23×C15112yes—
453C24—21no—
454C24C2×D4×C15111yescharacteristic
455C24C2×D4×C15111yescharacteristic
456#41—82no—
457C2×Q8—21no—
458C2×Q8—42no—
459C2×Q8C2×D4×C15112yes—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4C2×D4×C15112yes—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—82no—
487C22×C4C2×D4×C15111yescharacteristic
488C22×C4C2×D4×C15111yescharacteristic
489C22×C4C2×D4×C15111yescharacteristic
490C22×C4C2×D4×C15111yescharacteristic
491C22×C4C2×D4×C15111yescharacteristic
492C22×C4C2×D4×C15111yescharacteristic
493C22×C4C2×D4×C15111yescharacteristic
494C22×C4C2×D4×C15111yescharacteristic
495C22×C4C24×C15111yescharacteristic
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—42no—
499C2×C8—42no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—42no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—82no—
516C4⋊C4C2×D4×C15112yes—
517C4⋊C4C2×D4×C15112yes—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—42no—
533C22⋊C4—82no—
534C42—22no—
535C42—22no—
536C42—21no—
537C42—21no—
538C23—21no—
539C23—22no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23#120×C15111yescharacteristic
550C23#120×C15111yescharacteristic
551C23#135×C15112yes—
552C23#137×C15112yes—
553C23C22×D4×C15111yescharacteristic
554Q8—42no—
555Q8—42no—
556D4—42no—
557D4—42no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—82no—
564D4—82no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4#120×C15111yescharacteristic
597C2×C4#120×C15111yescharacteristic
598C2×C4C22×D4×C15111yescharacteristic
599C2×C4C22×D4×C15111yescharacteristic
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—81no—
618C22—162no—
619C22#452×C15112yes—
620C22#452×C15112yes—
621C22C2×#120×C15111yescharacteristic
622C22C2×#135×C15111yescharacteristic
623C22C2×#137×C15111yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4#458×C15112yes—
636C2—21no—
637C2—21no—
638C2—22no—
639C2—22no—
640C2—81no—
641C2—82no—
642C2C2×#452×C15111yescharacteristic
643C2#3021×C15111yescharacteristic
644C2C2×#458×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3505×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#484×C151C2semidirect
3. C2×#481×C151C2semidirect
4. #2487×C151C2semidirect
5. #1618×C151C2semidirect
6. #1615×C151C2semidirect
7. #1520×C151C2semidirect
8. #1519×C151C2semidirect
9. #1459×C151C2semidirect
27. #484×C151C22semidirect
36. #400×C151C22semidirect
37. #399×C151C22semidirect
43. #328×C151C22semidirect
45. #324×C151C22semidirect
46. #323×C151C22semidirect
322. #18207C151direct (N × H)
323. C151#18207direct (N × H)
325. C2×#484C2×C151semidirect
326. C2×#481C2×C151semidirect
327. #2487C2×C151semidirect
328. #1618C2×C151semidirect
329. #1615C2×C151semidirect
330. #1520C2×C151semidirect
331. #1519C2×C151semidirect
332. #1459C2×C151semidirect
350. #484C22×C151semidirect
359. #400C22×C151semidirect
360. #399C22×C151semidirect
366. #328C22×C151semidirect
368. #324C22×C151semidirect
369. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3505×C1512
C2×#484×C1512
C2×#481×C1512
#2487×C1512
#1618×C1512
#1615×C1512
#1520×C1512
#1519×C1512
#1459×C1512
#18207151