Finite Group Databasebeta

← C151×#24283 #50329208

Subgroups — C151×#24283 #50329208

Order 38656.

1304 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#137×C151C211yesmaximal, characteristic, complemented
2C2×#473×C151C211yesmaximal, characteristic, complemented
3C2×#471×C151C211yesmaximal, characteristic, complemented
4#3005×C151C211yesmaximal, characteristic
5#3004×C151C211yesmaximal, characteristic, complemented
6#2930×C151C211yesmaximal, characteristic, complemented
7#2047×C151C211yesmaximal, characteristic, complemented
8#2046×C151C211yesmaximal, characteristic, complemented
9#2020×C151C211yesmaximal, characteristic, complemented
10#2019×C151C211yesmaximal, characteristic, complemented
11#1979×C151C211yesmaximal, characteristic, complemented
12#1977×C151C211yesmaximal, characteristic, complemented
13#1811×C151C211yesmaximal, characteristic, complemented
14#1785×C151C211yesmaximal, characteristic, complemented
15#1784×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C2×#137×C151—24no—
19C2×#137×C151—24no—
20C2×#137×C151—22no—
21C2×#137×C151—22no—
22C2×#137×C151C2211yescharacteristic
23C2×#137×C151C2211yescharacteristic
24C2×#137×C151C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
26C22×Q16×C151C2211yescharacteristic
27C22×Q16×C151C2211yescharacteristic
28C22×SD16×C151C2211yescharacteristic
29C22×SD16×C151C2211yescharacteristic
30C2×#131×C151C2211yescharacteristic
31C22×M16×C151C2211yescharacteristic
32#525×C151C2211yescharacteristic
33#473×C151—24no—
34#471×C151—24no—
35#452×C151—22no—
36#451×C151—22no—
37#449×C151—22no—
38#448×C151—22no—
39#436×C151—22no—
40#435×C151—22no—
41C2×#108×C151C2211yescharacteristic
42C2×#108×C151C2211yescharacteristic
43#424×C151C2211yescharacteristic
44#419×C151C2211yescharacteristic
45#419×C151C2211yescharacteristic
46#419×C151C2211yescharacteristic
47#418×C151C2211yescharacteristic
48C2×#101×C151C2211yescharacteristic
49C2×#101×C151C2211yescharacteristic
50C2×#101×C151C2211yescharacteristic
51C2×#101×C151C2211yescharacteristic
52C2×#101×C151C2211yescharacteristic
53C2×#101×C151C2211yescharacteristic
54C2×#100×C151C2211yescharacteristic
55C2×#100×C151C2211yescharacteristic
56#408×C151C2211yescharacteristic
57#407×C151C2211yescharacteristic
58#407×C151C2211yescharacteristic
59#407×C151C2211yescharacteristic
60#405×C151C2211yescharacteristic
61#341×C151C2211yescharacteristic
62#341×C151C2211yescharacteristic
63C2×#41×C151—22no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—41no—
68C2×#41×C151—41no—
69C2×#41×C151C2311yescharacteristic
70C22×Q8×C151—22no—
71C22×Q8×C151—22no—
72C22×Q8×C151—22no—
73C22×Q8×C151—22no—
74C22×Q8×C151—21no—
75C22×Q8×C151—41no—
76C22×Q8×C151—41no—
77C22×Q8×C151C2311yescharacteristic
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×D4×C151—21no—
81C22×D4×C151C2311yescharacteristic
82C23×C4×C151—21no—
83C23×C4×C151—21no—
84C23×C4×C151C2311yescharacteristic
85#137×C151—216no—
86#137×C151—216no—
87#137×C151—22no—
88#137×C151—22no—
89#137×C151—22no—
90#137×C151—41no—
91#137×C151—41no—
92#137×C151—41no—
93AGL(1,ℤ/8)×C151—22no—
94AGL(1,ℤ/8)×C151—41no—
95C2×Q16×C151—22no—
96C2×Q16×C151—21no—
97C2×Q16×C151—21no—
98C2×Q16×C151—22no—
99C2×Q16×C151—22no—
100C2×Q16×C151—22no—
101C2×Q16×C151—21no—
102C2×Q16×C151—21no—
103C2×Q16×C151—21no—
104C2×Q16×C151D414yescomplemented
105C2×SD16×C151—22no—
106C2×SD16×C151—21no—
107C2×SD16×C151—21no—
108C2×SD16×C151—21no—
109C2×SD16×C151—22no—
110C2×SD16×C151—21no—
111C2×SD16×C151—21no—
112C2×SD16×C151—22no—
113C2×SD16×C151—22no—
114C2×SD16×C151—21no—
115C2×SD16×C151D414yescomplemented
116C2×D8×C151—21no—
117#131×C151—22no—
118#131×C151—22no—
119C2×M16×C151—22no—
120C2×M16×C151—22no—
121C2×M16×C151—21no—
122C2×M16×C151D412yes—
123C2×M16×C151D412yes—
124C2×M16×C151C2311yescharacteristic
125C2×M16×C151C2311yescharacteristic
126C2×M16×C151C2311yescharacteristic
127C2×M16×C151C2311yescharacteristic
128C2×M16×C151C2311yescharacteristic
129C2×M16×C151C2311yescharacteristic
130C22×C8×C151—21no—
131C22×C8×C151C2311yescharacteristic
132C22×C8×C151C2311yescharacteristic
133#123×C151—21no—
134C22⋊Q8×C151D412yes—
135#121×C151D412yes—
136#120×C151—21no—
137C4×D4×C151—22no—
138#117×C151C2311yescharacteristic
139#108×C151—22no—
140#108×C151—22no—
141C4⋊C8×C151—22no—
142#103×C151—22no—
143#103×C151—22no—
144#103×C151—22no—
145#102×C151—22no—
146#101×C151—22no—
147#101×C151—22no—
148#101×C151—22no—
149#101×C151—41no—
150#101×C151—41no—
151#101×C151—41no—
152#100×C151—22no—
153#100×C151—41no—
154C22⋊C8×C151—22no—
155C22⋊C8×C151—22no—
156C22⋊C8×C151—22no—
157C22⋊C8×C151—22no—
158#97×C151—21no—
159C4×C8×C151—21no—
160C24×C151—21no—
161C24×C151#4111yescharacteristic
162#41×C151—28no—
163#41×C151—21no—
164#41×C151—21no—
165#41×C151—21no—
166#41×C151—21no—
167#41×C151—44no—
168#41×C151—44no—
169#41×C151—44no—
170C2×Q8×C151—21no—
171C2×Q8×C151—21no—
172C2×Q8×C151—21no—
173C2×Q8×C151—28no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—42no—
187C2×Q8×C151—42no—
188C2×Q8×C151—44no—
189C2×Q8×C151—44no—
190C2×Q8×C151—44no—
191C2×Q8×C151—42no—
192C2×Q8×C151C2×D412yes—
193C2×Q8×C151C2×D412yes—
194C2×Q8×C151C2×D412yes—
195C2×Q8×C151C2×D411yescharacteristic
196C2×D4×C151—21no—
197C2×D4×C151—22no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151C2×D412yes—
207C2×D4×C151C2×D411yescharacteristic
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—42no—
217C22×C4×C151—42no—
218C22×C4×C151—42no—
219C22×C4×C151—42no—
220C22×C4×C151—42no—
221C22×C4×C151—42no—
222C22×C4×C151C2×D412yes—
223C22×C4×C151C2×D412yes—
224C22×C4×C151#4111yescharacteristic
225C22×C4×C151C2411yescharacteristic
226Q16×C151—28no—
227Q16×C151—24no—
228Q16×C151—24no—
229Q16×C151—42no—
230Q16×C151—42no—
231Q16×C151—42no—
232SD16×C151—28no—
233SD16×C151—24no—
234SD16×C151—24no—
235SD16×C151—42no—
236SD16×C151—42no—
237SD16×C151—42no—
238SD16×C151—42no—
239D8×C151—42no—
240M16×C151—24no—
241M16×C151—24no—
242M16×C151—21no—
243M16×C151—21no—
244M16×C151—21no—
245M16×C151—21no—
246M16×C151—21no—
247M16×C151—21no—
248M16×C151—21no—
249M16×C151—21no—
250M16×C151—21no—
251M16×C151—21no—
252M16×C151—21no—
253M16×C151—21no—
254M16×C151—42no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—42no—
264C2×C8×C151C2×D412yes—
265C2×C8×C151C2×D411yescharacteristic
266C2×C8×C151C2×D411yescharacteristic
267C2×C8×C151C2×D412yes—
268C2×C8×C151C2×D412yes—
269C4⋊C4×C151—22no—
270C4⋊C4×C151C2×D412yes—
271C22⋊C4×C151—22no—
272C22⋊C4×C151—21no—
273C22⋊C4×C151—22no—
274C42×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—22no—
279C23×C151—42no—
280C23×C151—41no—
281C23×C151—41no—
282C23×C151—82no—
283C23×C151#12112yes—
284C23×C151C2×#4111yescharacteristic
285Q8×C151—22no—
286Q8×C151—22no—
287Q8×C151—22no—
288Q8×C151—22no—
289Q8×C151—22no—
290Q8×C151—22no—
291Q8×C151—21no—
292Q8×C151—21no—
293Q8×C151—48no—
294Q8×C151—41no—
295Q8×C151—41no—
296Q8×C151—41no—
297Q8×C151—41no—
298Q8×C151—41no—
299Q8×C151—41no—
300D4×C151—22no—
301D4×C151—21no—
302D4×C151—21no—
303D4×C151—22no—
304D4×C151—48no—
305D4×C151—41no—
306D4×C151—41no—
307D4×C151—41no—
308D4×C151—41no—
309D4×C151—82no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—22no—
315C2×C4×C151—22no—
316C2×C4×C151—21no—
317C2×C4×C151—22no—
318C2×C4×C151—22no—
319C2×C4×C151—22no—
320C2×C4×C151—22no—
321C2×C4×C151—48no—
322C2×C4×C151—48no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151#12112yes—
332C2×C4×C151C22×D411yescharacteristic
333C2×C4×C151C22×D411yescharacteristic
334C2×C4×C151C22×D411yescharacteristic
335C2×C4×C151C22×D411yescharacteristic
336C2×C4×C151H(5,𝔽2)11yescharacteristic
337C2×C4×C151H(5,𝔽2)11yescharacteristic
338C8×C151—22no—
339C8×C151—41no—
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C8×C151—41no—
345C8×C151#12012yes—
346C8×C151#12012yes—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—22no—
350C22×C151—22no—
351C22×C151—42no—
352C22×C151—42no—
353C22×C151—42no—
354C22×C151—41no—
355C22×C151—42no—
356C22×C151—82no—
357C22×C151—82no—
358C22×C151—82no—
359C22×C151C2×#12111yescharacteristic
360C22×C151#54611yescharacteristic
361C22×C151#54611yescharacteristic
362C4×C151—22no—
363C4×C151—42no—
364C4×C151—42no—
365C4×C151—42no—
366C4×C151—41no—
367C4×C151—42no—
368C4×C151C2×#12011yescharacteristic
369C4×C151#53511yescharacteristic
370C4×C151D4211yescharacteristic
371C4×C151D4211yescharacteristic
372C2×C151—21no—
373C2×C151—21no—
374C2×C151—42no—
375C2×C151—81no—
376C2×C151—82no—
377C2×C151#240811yescharacteristic
378C2×C151#306912yes—
379#24283C15111yesmaximal, characteristic, direct product factor, Sylow
380C151#2428311yescharacteristic, direct product factor, Sylow
381C22×#137C2×C15111yescharacteristic, complemented
382C2×#473C2×C15111yescharacteristic, complemented
383C2×#471C2×C15111yescharacteristic, complemented
384#3005C2×C15111yescharacteristic
385#3004C2×C15111yescharacteristic, complemented
386#2930C2×C15111yescharacteristic, complemented
387#2047C2×C15111yescharacteristic, complemented
388#2046C2×C15111yescharacteristic, complemented
389#2020C2×C15111yescharacteristic, complemented
390#2019C2×C15111yescharacteristic, complemented
391#1979C2×C15111yescharacteristic, complemented
392#1977C2×C15111yescharacteristic, complemented
393#1811C2×C15111yescharacteristic, complemented
394#1785C2×C15111yescharacteristic, complemented
395#1784C2×C15111yescharacteristic, complemented
396C22×#41C22×C15111yescharacteristic
397C23×Q8C22×C15111yescharacteristic
398C2×#137—24no—
399C2×#137—24no—
400C2×#137—22no—
401C2×#137—22no—
402C2×#137C22×C15111yescharacteristic
403C2×#137C22×C15111yescharacteristic
404C2×#137C22×C15111yescharacteristic
405C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
406C22×Q16C22×C15111yescharacteristic
407C22×Q16C22×C15111yescharacteristic
408C22×SD16C22×C15111yescharacteristic
409C22×SD16C22×C15111yescharacteristic
410C2×#131C22×C15111yescharacteristic
411C22×M16C22×C15111yescharacteristic
412#525C22×C15111yescharacteristic
413#473—24no—
414#471—24no—
415#452—22no—
416#451—22no—
417#449—22no—
418#448—22no—
419#436—22no—
420#435—22no—
421C2×#108C22×C15111yescharacteristic
422C2×#108C22×C15111yescharacteristic
423#424C22×C15111yescharacteristic
424#419C22×C15111yescharacteristic
425#419C22×C15111yescharacteristic
426#419C22×C15111yescharacteristic
427#418C22×C15111yescharacteristic
428C2×#101C22×C15111yescharacteristic
429C2×#101C22×C15111yescharacteristic
430C2×#101C22×C15111yescharacteristic
431C2×#101C22×C15111yescharacteristic
432C2×#101C22×C15111yescharacteristic
433C2×#101C22×C15111yescharacteristic
434C2×#100C22×C15111yescharacteristic
435C2×#100C22×C15111yescharacteristic
436#408C22×C15111yescharacteristic
437#407C22×C15111yescharacteristic
438#407C22×C15111yescharacteristic
439#407C22×C15111yescharacteristic
440#405C22×C15111yescharacteristic
441#341C22×C15111yescharacteristic
442#341C22×C15111yescharacteristic
443C2×#41—22no—
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—41no—
448C2×#41—41no—
449C2×#41C23×C15111yescharacteristic
450C22×Q8—21no—
451C22×Q8—22no—
452C22×Q8—22no—
453C22×Q8—22no—
454C22×Q8—22no—
455C22×Q8—41no—
456C22×Q8—41no—
457C22×Q8C23×C15111yescharacteristic
458C22×Q8C23×C15111yescharacteristic
459C22×Q8C23×C15111yescharacteristic
460C22×D4—21no—
461C22×D4C23×C15111yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C23×C15111yescharacteristic
465#137—216no—
466#137—216no—
467#137—22no—
468#137—22no—
469#137—22no—
470#137—41no—
471#137—41no—
472#137—41no—
473AGL(1,ℤ/8)—22no—
474AGL(1,ℤ/8)—41no—
475C2×Q16—22no—
476C2×Q16—22no—
477C2×Q16—21no—
478C2×Q16—21no—
479C2×Q16—21no—
480C2×Q16—22no—
481C2×Q16—21no—
482C2×Q16—21no—
483C2×Q16—22no—
484C2×Q16D4×C15114yescomplemented
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—21no—
491C2×SD16—22no—
492C2×SD16—21no—
493C2×SD16—21no—
494C2×SD16—22no—
495C2×SD16D4×C15114yescomplemented
496C2×D8—21no—
497#131—22no—
498#131—22no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—21no—
502C2×M16D4×C15112yes—
503C2×M16D4×C15112yes—
504C2×M16C23×C15111yescharacteristic
505C2×M16C23×C15111yescharacteristic
506C2×M16C23×C15111yescharacteristic
507C2×M16C23×C15111yescharacteristic
508C2×M16C23×C15111yescharacteristic
509C2×M16C23×C15111yescharacteristic
510C22×C8—21no—
511C22×C8C23×C15111yescharacteristic
512C22×C8C23×C15111yescharacteristic
513#123—21no—
514C22⋊Q8D4×C15112yes—
515#121D4×C15112yes—
516#120—21no—
517C4×D4—22no—
518#117C23×C15111yescharacteristic
519#108—22no—
520#108—22no—
521C4⋊C8—22no—
522#103—22no—
523#103—22no—
524#103—22no—
525#102—22no—
526#101—22no—
527#101—22no—
528#101—22no—
529#101—41no—
530#101—41no—
531#101—41no—
532#100—22no—
533#100—41no—
534C22⋊C8—22no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538#97—21no—
539C4×C8—21no—
540C24—21no—
541C24#41×C15111yescharacteristic
542#41—28no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—28no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—42no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8—44no—
571C2×Q8—42no—
572C2×Q8C2×D4×C15112yes—
573C2×Q8C2×D4×C15112yes—
574C2×Q8C2×D4×C15112yes—
575C2×Q8C2×D4×C15111yescharacteristic
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4C2×D4×C15112yes—
587C2×D4C2×D4×C15111yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4C2×D4×C15112yes—
603C22×C4C2×D4×C15112yes—
604C22×C4#41×C15111yescharacteristic
605C22×C4C24×C15111yescharacteristic
606Q16—28no—
607Q16—24no—
608Q16—24no—
609Q16—42no—
610Q16—42no—
611Q16—42no—
612SD16—28no—
613SD16—24no—
614SD16—24no—
615SD16—42no—
616SD16—42no—
617SD16—42no—
618SD16—42no—
619D8—42no—
620M16—24no—
621M16—24no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—21no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—42no—
644C2×C8C2×D4×C15112yes—
645C2×C8C2×D4×C15111yescharacteristic
646C2×C8C2×D4×C15111yescharacteristic
647C2×C8C2×D4×C15112yes—
648C2×C8C2×D4×C15112yes—
649C4⋊C4—22no—
650C4⋊C4C2×D4×C15112yes—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C42—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—42no—
660C23—41no—
661C23—41no—
662C23—82no—
663C23#121×C15112yes—
664C23C2×#41×C15111yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—21no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—21no—
673Q8—48no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—41no—
680D4—22no—
681D4—21no—
682D4—22no—
683D4—21no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—82no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4#121×C15112yes—
712C2×C4C22×D4×C15111yescharacteristic
713C2×C4C22×D4×C15111yescharacteristic
714C2×C4C22×D4×C15111yescharacteristic
715C2×C4C22×D4×C15111yescharacteristic
716C2×C4H(5,𝔽2)×C15111yescharacteristic
717C2×C4H(5,𝔽2)×C15111yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C8#120×C15112yes—
726C8#120×C15112yes—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22C2×#121×C15111yescharacteristic
740C22#546×C15111yescharacteristic
741C22#546×C15111yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—41no—
747C4—42no—
748C4C2×#120×C15111yescharacteristic
749C4#535×C15111yescharacteristic
750C4D42×C15111yescharacteristic
751C4D42×C15111yescharacteristic
752C2—21no—
753C2—21no—
754C2—42no—
755C2—81no—
756C2—82no—
757C2#2408×C15111yescharacteristic
758C2#3069×C15112yes—
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3005×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#137×C151C2semidirect
2. C2×#473×C151C2semidirect
3. C2×#471×C151C2semidirect
5. #3004×C151C2semidirect
6. #2930×C151C2semidirect
7. #2047×C151C2semidirect
8. #2046×C151C2semidirect
9. #2020×C151C2semidirect
10. #2019×C151C2semidirect
11. #1979×C151C2semidirect
12. #1977×C151C2semidirect
13. #1811×C151C2semidirect
14. #1785×C151C2semidirect
15. #1784×C151C2semidirect
104. C2×Q16×C151D4semidirect
115. C2×SD16×C151D4semidirect
379. #24283C151direct (N × H)
380. C151#24283direct (N × H)
381. C22×#137C2×C151semidirect
382. C2×#473C2×C151semidirect
383. C2×#471C2×C151semidirect
385. #3004C2×C151semidirect
386. #2930C2×C151semidirect
387. #2047C2×C151semidirect
388. #2046C2×C151semidirect
389. #2020C2×C151semidirect
390. #2019C2×C151semidirect
391. #1979C2×C151semidirect
392. #1977C2×C151semidirect
393. #1811C2×C151semidirect
394. #1785C2×C151semidirect
395. #1784C2×C151semidirect
484. C2×Q16D4×C151semidirect
495. C2×SD16D4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#137×C1512
C2×#473×C1512
C2×#471×C1512
#3005×C1512
#3004×C1512
#2930×C1512
#2047×C1512
#2046×C1512
#2020×C1512
#2019×C1512
#1979×C1512
#1977×C1512
#1811×C1512
#1785×C1512
#1784×C1512
#24283151