Finite Group Databasebeta

← C151×#18423 #50323348

Subgroups — C151×#18423 #50323348

Order 38656.

934 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3538×C151C211yesmaximal, characteristic
2#3195×C151C211yesmaximal, characteristic, complemented
3#3190×C151C211yesmaximal, characteristic
4#2659×C151C211yesmaximal, characteristic, complemented
5#1611×C151C212yesmaximal, complemented
6#1609×C151C212yesmaximal, complemented
7#1605×C151C212yesmaximal, complemented
8#1603×C151C212yesmaximal, complemented
9#1504×C151C211yesmaximal, characteristic
10C2×#328×C151C211yesmaximal, characteristic, complemented
11#1472×C151C211yesmaximal, characteristic, complemented
12#563×C151—22no—
13#552×C151—21no—
14#552×C151—21no—
15#551×C151—22no—
16D4×Q8×C151—21no—
17D4×Q8×C151—21no—
18#544×C151—21no—
19#544×C151C2212yes—
20#541×C151—21no—
21#539×C151—21no—
22#539×C151C2212yes—
23#536×C151—21no—
24#525×C151C2211yescharacteristic
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28#485×C151—21no—
29#483×C151—21no—
30#483×C151C2212yes—
31#483×C151C2211yescharacteristic
32#480×C151C2211yescharacteristic
33#470×C151—22no—
34#467×C151—21no—
35#465×C151—21no—
36#452×C151—21no—
37#451×C151—21no—
38#451×C151C2212yes—
39#451×C151C2211yescharacteristic
40#448×C151C2211yescharacteristic
41#407×C151C2211yescharacteristic
42C2×C22⋊C8×C151C2211yescharacteristic
43#398×C151—21no—
44#398×C151C2212yes—
45#395×C151—21no—
46#395×C151C2212yes—
47#380×C151—22no—
48C2×#95×C151C2211yescharacteristic
49#328×C151C2212yes—
50#328×C151C2212yes—
51#328×C151C2212yes—
52#327×C151C2212yes—
53#324×C151C2212yes—
54#324×C151C2212yes—
55C2×#41×C151D411yescharacteristic
56C22×Q8×C151—21no—
57C22×Q8×C151D411yescharacteristic
58C22×Q8×C151D411yescharacteristic
59C22×Q8×C151C2311yescharacteristic
60C23×C4×C151—21no—
61C23×C4×C151C2311yescharacteristic
62C2×Q16×C151—22no—
63C2×Q16×C151—21no—
64C2×SD16×C151—21no—
65C2×M16×C151—21no—
66C22×C8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—22no—
70C4⋊Q8×C151—22no—
71#126×C151—22no—
72#126×C151—22no—
73#126×C151—22no—
74#126×C151—22no—
75#125×C151—21no—
76#125×C151—22no—
77#125×C151—22no—
78#125×C151—22no—
79#125×C151—22no—
80#124×C151—22no—
81#123×C151—22no—
82#123×C151—22no—
83#123×C151—22no—
84#123×C151—21no—
85#123×C151—22no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—22no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93C22⋊Q8×C151—21no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151—21no—
96C22⋊Q8×C151—22no—
97C22⋊Q8×C151—21no—
98C22⋊Q8×C151—21no—
99C22⋊Q8×C151—21no—
100C22⋊Q8×C151—21no—
101C22⋊Q8×C151—22no—
102C22⋊Q8×C151D411yescharacteristic
103C22⋊Q8×C151D412yes—
104C22⋊Q8×C151C2312yes—
105C22⋊Q8×C151C2311yescharacteristic
106#121×C151D411yescharacteristic
107#121×C151C2311yescharacteristic
108#120×C151—21no—
109C4×Q8×C151—21no—
110C4×Q8×C151—21no—
111C4×D4×C151—22no—
112C4×D4×C151—21no—
113C4×D4×C151—21no—
114C4×D4×C151—22no—
115#117×C151—21no—
116#117×C151—22no—
117#117×C151—22no—
118#117×C151D411yescharacteristic
119C2×C4⋊C4×C151—21no—
120C2×C4⋊C4×C151—21no—
121C2×C4⋊C4×C151—22no—
122C2×C4⋊C4×C151—22no—
123C2×C4⋊C4×C151D411yescharacteristic
124C2×C4⋊C4×C151D411yescharacteristic
125C2×C4⋊C4×C151C2311yescharacteristic
126C2×C4⋊C4×C151C2312yes—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151D412yes—
130#107×C151—21no—
131#106×C151—21no—
132#106×C151—22no—
133#103×C151—21no—
134#103×C151—21no—
135#103×C151—22no—
136#103×C151—22no—
137#103×C151—21no—
138#102×C151—21no—
139C22⋊C8×C151—21no—
140C22⋊C8×C151—21no—
141C22⋊C8×C151C2311yescharacteristic
142C22⋊C8×C151C2311yescharacteristic
143C22⋊C8×C151C2312yes—
144#95×C151—21no—
145#95×C151—22no—
146#95×C151—22no—
147#95×C151C2312yes—
148C24×C151C2×D411yescharacteristic
149#41×C151—81no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—81no—
157C2×Q8×C151—81no—
158C2×Q8×C151—82no—
159C2×Q8×C151—81no—
160C2×Q8×C151C2×D412yes—
161C2×Q8×C151C2×D411yescharacteristic
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151C2×D411yescharacteristic
166C22×C4×C151—21no—
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—24no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—81no—
175C22×C4×C151—81no—
176C22×C4×C151—81no—
177C22×C4×C151C2×D412yes—
178C22×C4×C151C2×D412yes—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151C2411yescharacteristic
185Q16×C151—81no—
186Q16×C151—82no—
187SD16×C151—81no—
188M16×C151—81no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—22no—
192C2×C8×C151—81no—
193C4⋊C4×C151—22no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—22no—
207C4⋊C4×C151—22no—
208C4⋊C4×C151—22no—
209C4⋊C4×C151—21no—
210C4⋊C4×C151—21no—
211C4⋊C4×C151—21no—
212C4⋊C4×C151—41no—
213C4⋊C4×C151—41no—
214C4⋊C4×C151—82no—
215C4⋊C4×C151—82no—
216C4⋊C4×C151C2×D412yes—
217C4⋊C4×C151C2×D411yescharacteristic
218C4⋊C4×C151C2×D411yescharacteristic
219C22⋊C4×C151—22no—
220C22⋊C4×C151—22no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—22no—
223C22⋊C4×C151—22no—
224C22⋊C4×C151—22no—
225C22⋊C4×C151—21no—
226C22⋊C4×C151—21no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—21no—
229C22⋊C4×C151—21no—
230C22⋊C4×C151—21no—
231C22⋊C4×C151—41no—
232C22⋊C4×C151—41no—
233C42×C151—22no—
234C42×C151—22no—
235C42×C151—22no—
236C42×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—22no—
240C23×C151—21no—
241C23×C151—41no—
242C23×C151#12011yescharacteristic
243C23×C151#12011yescharacteristic
244C23×C151C22×D411yescharacteristic
245Q8×C151—42no—
246Q8×C151—41no—
247Q8×C151—42no—
248Q8×C151—42no—
249Q8×C151—41no—
250Q8×C151—41no—
251Q8×C151—42no—
252Q8×C151—81no—
253Q8×C151—82no—
254D4×C151—41no—
255D4×C151—41no—
256D4×C151—41no—
257D4×C151—42no—
258D4×C151—81no—
259C2×C4×C151—24no—
260C2×C4×C151—22no—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
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—42no—
279C2×C4×C151—42no—
280C2×C4×C151—42no—
281C2×C4×C151—41no—
282C2×C4×C151—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—81no—
286C2×C4×C151—82no—
287C2×C4×C151—84no—
288C2×C4×C151#12011yescharacteristic
289C2×C4×C151#12011yescharacteristic
290C2×C4×C151C22×D411yescharacteristic
291C2×C4×C151C22×D411yescharacteristic
292C8×C151—41no—
293C8×C151—41no—
294C8×C151—42no—
295C22×C151—21no—
296C22×C151—21no—
297C22×C151—21no—
298C22×C151—21no—
299C22×C151—21no—
300C22×C151—21no—
301C22×C151—21no—
302C22×C151—42no—
303C22×C151—42no—
304C22×C151—41no—
305C22×C151—41no—
306C22×C151—41no—
307C22×C151#45612yes—
308C22×C151C2×#12011yescharacteristic
309C22×C151#57711yescharacteristic
310C22×C151#57811yescharacteristic
311C4×C151—21no—
312C4×C151—21no—
313C4×C151—21no—
314C4×C151—21no—
315C4×C151—44no—
316C4×C151—42no—
317C4×C151—41no—
318C4×C151—42no—
319C4×C151—41no—
320C4×C151—41no—
321C4×C151—42no—
322C4×C151—42no—
323C4×C151—81no—
324C4×C151—81no—
325C2×C151—21no—
326C2×C151—21no—
327C2×C151—22no—
328C2×C151—41no—
329C2×C151—81no—
330C2×C151#301311yescharacteristic
331C2×C151C2×#45611yescharacteristic
332C2×C151#302611yescharacteristic
333#18423C15111yesmaximal, characteristic, direct product factor, Sylow
334C151#1842311yescharacteristic, direct product factor, Sylow
335#3538C2×C15111yescharacteristic
336#3195C2×C15111yescharacteristic, complemented
337#3190C2×C15111yescharacteristic
338#2659C2×C15111yescharacteristic, complemented
339#1611C2×C15112yescomplemented
340#1609C2×C15112yescomplemented
341#1605C2×C15112yescomplemented
342#1603C2×C15112yescomplemented
343#1504C2×C15111yescharacteristic
344C2×#328C2×C15111yescharacteristic, complemented
345#1472C2×C15111yescharacteristic, complemented
346#563—22no—
347#552—21no—
348#552—21no—
349#551—22no—
350D4×Q8—21no—
351D4×Q8—21no—
352#544—21no—
353#544C22×C15112yes—
354#541—21no—
355#539—21no—
356#539C22×C15112yes—
357#536—21no—
358#525C22×C15111yescharacteristic
359C2×C22⋊Q8C22×C15111yescharacteristic
360C2×C22⋊Q8C22×C15111yescharacteristic
361C2×C22⋊Q8C22×C15111yescharacteristic
362#485—21no—
363#483—21no—
364#483C22×C15112yes—
365#483C22×C15111yescharacteristic
366#480C22×C15111yescharacteristic
367#470—22no—
368#467—21no—
369#465—21no—
370#452—21no—
371#451—21no—
372#451C22×C15112yes—
373#451C22×C15111yescharacteristic
374#448C22×C15111yescharacteristic
375#407C22×C15111yescharacteristic
376C2×C22⋊C8C22×C15111yescharacteristic
377#398—21no—
378#398C22×C15112yes—
379#395—21no—
380#395C22×C15112yes—
381#380—22no—
382C2×#95C22×C15111yescharacteristic
383#328C22×C15112yes—
384#328C22×C15112yes—
385#328C22×C15112yes—
386#327C22×C15112yes—
387#324C22×C15112yes—
388#324C22×C15112yes—
389C2×#41D4×C15111yescharacteristic
390C22×Q8—21no—
391C22×Q8D4×C15111yescharacteristic
392C22×Q8D4×C15111yescharacteristic
393C22×Q8C23×C15111yescharacteristic
394C23×C4—21no—
395C23×C4C23×C15111yescharacteristic
396C2×Q16—22no—
397C2×Q16—21no—
398C2×SD16—21no—
399C2×M16—21no—
400C22×C8—21no—
401C4⋊Q8—21no—
402C4⋊Q8—22no—
403C4⋊Q8—22no—
404C4⋊Q8—22no—
405#126—22no—
406#126—22no—
407#126—22no—
408#126—22no—
409#125—21no—
410#125—22no—
411#125—22no—
412#125—22no—
413#125—22no—
414#124—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418#123—21no—
419#123—22no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—22no—
423C22⋊Q8—22no—
424C22⋊Q8—22no—
425C22⋊Q8—21no—
426C22⋊Q8—21no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—22no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C22⋊Q8—21no—
435C22⋊Q8—21no—
436C22⋊Q8D4×C15112yes—
437C22⋊Q8D4×C15111yescharacteristic
438C22⋊Q8C23×C15112yes—
439C22⋊Q8C23×C15111yescharacteristic
440#121D4×C15111yescharacteristic
441#121C23×C15111yescharacteristic
442#120—21no—
443C4×Q8—21no—
444C4×Q8—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—22no—
449#117—21no—
450#117—22no—
451#117—22no—
452#117D4×C15111yescharacteristic
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4D4×C15111yescharacteristic
458C2×C4⋊C4D4×C15111yescharacteristic
459C2×C4⋊C4C23×C15111yescharacteristic
460C2×C4⋊C4C23×C15112yes—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C15112yes—
464#107—21no—
465#106—21no—
466#106—22no—
467#103—22no—
468#103—21no—
469#103—21no—
470#103—21no—
471#103—22no—
472#102—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8C23×C15112yes—
476C22⋊C8C23×C15111yescharacteristic
477C22⋊C8C23×C15111yescharacteristic
478#95—21no—
479#95—22no—
480#95—22no—
481#95C23×C15112yes—
482C24C2×D4×C15111yescharacteristic
483#41—81no—
484C2×Q8—22no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—81no—
491C2×Q8—81no—
492C2×Q8—82no—
493C2×Q8—81no—
494C2×Q8C2×D4×C15112yes—
495C2×Q8C2×D4×C15111yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4C2×D4×C15111yescharacteristic
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—81no—
511C22×C4C2×D4×C15112yes—
512C22×C4C2×D4×C15112yes—
513C22×C4C2×D4×C15111yescharacteristic
514C22×C4C2×D4×C15111yescharacteristic
515C22×C4C2×D4×C15111yescharacteristic
516C22×C4C2×D4×C15111yescharacteristic
517C22×C4C2×D4×C15111yescharacteristic
518C22×C4C24×C15111yescharacteristic
519Q16—81no—
520Q16—82no—
521SD16—81no—
522M16—81no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—22no—
526C2×C8—81no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—82no—
549C4⋊C4—82no—
550C4⋊C4C2×D4×C15112yes—
551C4⋊C4C2×D4×C15111yescharacteristic
552C4⋊C4C2×D4×C15111yescharacteristic
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—22no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—22no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C42—22no—
568C42—22no—
569C42—22no—
570C42—21no—
571C23—22no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—41no—
576C23#120×C15111yescharacteristic
577C23#120×C15111yescharacteristic
578C23C22×D4×C15111yescharacteristic
579Q8—42no—
580Q8—41no—
581Q8—42no—
582Q8—42no—
583Q8—41no—
584Q8—41no—
585Q8—42no—
586Q8—81no—
587Q8—82no—
588D4—41no—
589D4—42no—
590D4—41no—
591D4—41no—
592D4—81no—
593C2×C4—24no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—81no—
620C2×C4—84no—
621C2×C4—82no—
622C2×C4#120×C15111yescharacteristic
623C2×C4#120×C15111yescharacteristic
624C2×C4C22×D4×C15111yescharacteristic
625C2×C4C22×D4×C15111yescharacteristic
626C8—41no—
627C8—41no—
628C8—42no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—21no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22#456×C15112yes—
642C22C2×#120×C15111yescharacteristic
643C22#577×C15111yescharacteristic
644C22#578×C15111yescharacteristic
645C4—21no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—44no—
650C4—42no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—81no—
658C4—81no—
659C2—21no—
660C2—22no—
661C2—21no—
662C2—41no—
663C2—81no—
664C2#3013×C15111yescharacteristic
665C2C2×#456×C15111yescharacteristic
666C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#525×C151C22
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. #3195×C151C2semidirect
4. #2659×C151C2semidirect
5. #1611×C151C2semidirect
6. #1609×C151C2semidirect
7. #1605×C151C2semidirect
8. #1603×C151C2semidirect
10. C2×#328×C151C2semidirect
11. #1472×C151C2semidirect
333. #18423C151direct (N × H)
334. C151#18423direct (N × H)
336. #3195C2×C151semidirect
338. #2659C2×C151semidirect
339. #1611C2×C151semidirect
340. #1609C2×C151semidirect
341. #1605C2×C151semidirect
342. #1603C2×C151semidirect
344. C2×#328C2×C151semidirect
345. #1472C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3538×C1512
#3195×C1512
#3190×C1512
#2659×C1512
#1611×C1512
#1609×C1512
#1605×C1512
#1603×C1512
#1504×C1512
C2×#328×C1512
#1472×C1512
#18423151