Finite Group Databasebeta

← C151×#24284 #50329209

Subgroups — C151×#24284 #50329209

Order 38656.

1432 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
2C2×#472×C151C211yesmaximal, characteristic, complemented
3C2×#471×C151C211yesmaximal, characteristic, complemented
4#3005×C151C211yesmaximal, characteristic, complemented
5#3003×C151C211yesmaximal, characteristic, complemented
6#2930×C151C211yesmaximal, characteristic, complemented
7#2046×C151C211yesmaximal, characteristic, complemented
8#2045×C151C211yesmaximal, characteristic, complemented
9#2019×C151C211yesmaximal, characteristic, complemented
10#2018×C151C211yesmaximal, characteristic, complemented
11#1978×C151C211yesmaximal, characteristic, complemented
12#1977×C151C211yesmaximal, characteristic, complemented
13#1811×C151C211yesmaximal, characteristic, complemented
14#1785×C151C211yesmaximal, characteristic, complemented
15#1783×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C2×#137×C151C2211yescharacteristic, complemented
19C2×AGL(1,ℤ/8)×C151—24no—
20C2×AGL(1,ℤ/8)×C151—24no—
21C2×AGL(1,ℤ/8)×C151—22no—
22C2×AGL(1,ℤ/8)×C151—22no—
23C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
26C22×SD16×C151C2211yescharacteristic
27C22×SD16×C151C2211yescharacteristic
28C22×D8×C151C2211yescharacteristic
29C22×D8×C151C2211yescharacteristic
30C2×#131×C151C2211yescharacteristic, complemented
31C22×M16×C151C2211yescharacteristic
32#525×C151C2211yescharacteristic
33#472×C151—24no—
34#471×C151—24no—
35#452×C151—22no—
36#450×C151—22no—
37#449×C151—22no—
38#447×C151—22no—
39#436×C151—22no—
40#435×C151—22no—
41C2×#108×C151C2211yescharacteristic, complemented
42C2×#108×C151C2211yescharacteristic, complemented
43#424×C151C2211yescharacteristic, complemented
44#419×C151C2211yescharacteristic, complemented
45#418×C151C2211yescharacteristic
46#418×C151C2211yescharacteristic
47#418×C151C2211yescharacteristic, complemented
48C2×#101×C151C2211yescharacteristic, complemented
49C2×#101×C151C2211yescharacteristic, complemented
50C2×#100×C151C2211yescharacteristic
51C2×#100×C151C2211yescharacteristic
52C2×#100×C151C2211yescharacteristic
53C2×#100×C151C2211yescharacteristic
54C2×#100×C151C2211yescharacteristic, complemented
55C2×#100×C151C2211yescharacteristic, complemented
56#408×C151C2211yescharacteristic, complemented
57#407×C151C2211yescharacteristic
58#407×C151C2211yescharacteristic
59#407×C151C2211yescharacteristic
60#405×C151C2211yescharacteristic, complemented
61#341×C151C2211yescharacteristic, complemented
62#341×C151C2211yescharacteristic, complemented
63C25×C151—21no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C2×#41×C151C2311yescharacteristic
71C22×Q8×C151C2311yescharacteristic
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151—22no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—41no—
79C22×D4×C151—41no—
80C22×D4×C151C2311yescharacteristic
81C22×D4×C151C2311yescharacteristic
82C22×D4×C151C2311yescharacteristic
83C23×C4×C151—21no—
84C23×C4×C151C2311yescharacteristic
85#137×C151—22no—
86#137×C151—41no—
87AGL(1,ℤ/8)×C151—216no—
88AGL(1,ℤ/8)×C151—216no—
89AGL(1,ℤ/8)×C151—22no—
90AGL(1,ℤ/8)×C151—22no—
91AGL(1,ℤ/8)×C151—22no—
92AGL(1,ℤ/8)×C151—41no—
93AGL(1,ℤ/8)×C151—41no—
94AGL(1,ℤ/8)×C151—41no—
95C2×Q16×C151—21no—
96C2×SD16×C151—22no—
97C2×SD16×C151—21no—
98C2×SD16×C151—22no—
99C2×SD16×C151—21no—
100C2×SD16×C151—21no—
101C2×SD16×C151—22no—
102C2×SD16×C151—22no—
103C2×SD16×C151—21no—
104C2×SD16×C151—21no—
105C2×SD16×C151—21no—
106C2×SD16×C151D414yescomplemented
107C2×D8×C151—22no—
108C2×D8×C151—22no—
109C2×D8×C151—21no—
110C2×D8×C151—21no—
111C2×D8×C151—21no—
112C2×D8×C151—22no—
113C2×D8×C151—21no—
114C2×D8×C151—21no—
115C2×D8×C151—22no—
116C2×D8×C151D414yescomplemented
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#102×C151—22no—
144#102×C151—22no—
145#102×C151—22no—
146#101×C151—22no—
147#101×C151—41no—
148#100×C151—22no—
149#100×C151—22no—
150#100×C151—22no—
151#100×C151—41no—
152#100×C151—41no—
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—21no—
162C24×C151—21no—
163C24×C151—42no—
164C24×C151—42no—
165C24×C151—42no—
166C24×C151—84no—
167C24×C151#4111yescharacteristic
168#41×C151—28no—
169#41×C151—21no—
170#41×C151—21no—
171#41×C151—21no—
172#41×C151—21no—
173#41×C151—44no—
174#41×C151—44no—
175#41×C151—44no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151C2×D412yes—
182C2×Q8×C151C2×D411yescharacteristic
183C2×D4×C151—28no—
184C2×D4×C151—21no—
185C2×D4×C151—22no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—44no—
202C2×D4×C151—44no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—44no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151C2×D412yes—
211C2×D4×C151C2×D412yes—
212C2×D4×C151C2×D412yes—
213C2×D4×C151C2×D411yescharacteristic
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—42no—
221C22×C4×C151—42no—
222C22×C4×C151—42no—
223C22×C4×C151C2×D412yes—
224C22×C4×C151C2×D412yes—
225C22×C4×C151#4111yescharacteristic
226C22×C4×C151C2411yescharacteristic
227Q16×C151—42no—
228SD16×C151—28no—
229SD16×C151—24no—
230SD16×C151—24no—
231SD16×C151—42no—
232SD16×C151—42no—
233SD16×C151—42no—
234SD16×C151—42no—
235D8×C151—28no—
236D8×C151—24no—
237D8×C151—24no—
238D8×C151—42no—
239D8×C151—42no—
240D8×C151—42no—
241M16×C151—24no—
242M16×C151—24no—
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—21no—
255M16×C151—42no—
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—21no—
264C2×C8×C151—42no—
265C2×C8×C151C2×D412yes—
266C2×C8×C151C2×D411yescharacteristic
267C2×C8×C151C2×D411yescharacteristic
268C2×C8×C151C2×D412yes—
269C2×C8×C151C2×D412yes—
270C4⋊C4×C151—22no—
271C4⋊C4×C151C2×D412yes—
272C22⋊C4×C151—22no—
273C22⋊C4×C151—21no—
274C22⋊C4×C151—22no—
275C42×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—22no—
280C23×C151—22no—
281C23×C151—22no—
282C23×C151—42no—
283C23×C151—48no—
284C23×C151—41no—
285C23×C151—41no—
286C23×C151—41no—
287C23×C151—41no—
288C23×C151—41no—
289C23×C151—41no—
290C23×C151—82no—
291C23×C151—82no—
292C23×C151—82no—
293C23×C151—84no—
294C23×C151—84no—
295C23×C151—88no—
296C23×C151—88no—
297C23×C151#12112yes—
298C23×C151C2×#4111yescharacteristic
299Q8×C151—22no—
300Q8×C151—22no—
301Q8×C151—21no—
302Q8×C151—21no—
303Q8×C151—41no—
304Q8×C151—41no—
305D4×C151—22no—
306D4×C151—22no—
307D4×C151—22no—
308D4×C151—21no—
309D4×C151—21no—
310D4×C151—22no—
311D4×C151—22no—
312D4×C151—22no—
313D4×C151—48no—
314D4×C151—48no—
315D4×C151—41no—
316D4×C151—41no—
317D4×C151—41no—
318D4×C151—41no—
319D4×C151—41no—
320D4×C151—41no—
321D4×C151—41no—
322D4×C151—41no—
323D4×C151—82no—
324C2×C4×C151—21no—
325C2×C4×C151—21no—
326C2×C4×C151—22no—
327C2×C4×C151—22no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—21no—
331C2×C4×C151—22no—
332C2×C4×C151—22no—
333C2×C4×C151—48no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—41no—
338C2×C4×C151#12112yes—
339C2×C4×C151C22×D411yescharacteristic
340C2×C4×C151C22×D411yescharacteristic
341C2×C4×C151C22×D411yescharacteristic
342C2×C4×C151C22×D411yescharacteristic
343C2×C4×C151H(5,𝔽2)11yescharacteristic
344C2×C4×C151H(5,𝔽2)11yescharacteristic
345C8×C151—22no—
346C8×C151—41no—
347C8×C151—41no—
348C8×C151—41no—
349C8×C151—41no—
350C8×C151—41no—
351C8×C151—41no—
352C8×C151#12012yes—
353C8×C151#12012yes—
354C22×C151—22no—
355C22×C151—22no—
356C22×C151—22no—
357C22×C151—22no—
358C22×C151—42no—
359C22×C151—42no—
360C22×C151—42no—
361C22×C151—41no—
362C22×C151—42no—
363C22×C151—42no—
364C22×C151—42no—
365C22×C151—82no—
366C22×C151—82no—
367C22×C151—82no—
368C22×C151—82no—
369C22×C151—82no—
370C22×C151—82no—
371C22×C151—816no—
372C22×C151—82no—
373C22×C151—82no—
374C22×C151—82no—
375C22×C151C2×#12111yescharacteristic
376C22×C151#54611yescharacteristic
377C22×C151#54611yescharacteristic
378C4×C151—22no—
379C4×C151—42no—
380C4×C151—41no—
381C4×C151—42no—
382C4×C151C2×#12011yescharacteristic
383C4×C151#53511yescharacteristic
384C4×C151D4211yescharacteristic
385C4×C151D4211yescharacteristic
386C2×C151—21no—
387C2×C151—21no—
388C2×C151—42no—
389C2×C151—81no—
390C2×C151—82no—
391C2×C151—82no—
392C2×C151—82no—
393C2×C151#240811yescharacteristic
394C2×C151#306812yes—
395#24284C15111yesmaximal, characteristic, direct product factor, Sylow
396C151#2428411yescharacteristic, direct product factor, Sylow
397C22×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
398C2×#472C2×C15111yescharacteristic, complemented
399C2×#471C2×C15111yescharacteristic, complemented
400#3005C2×C15111yescharacteristic, complemented
401#3003C2×C15111yescharacteristic, complemented
402#2930C2×C15111yescharacteristic, complemented
403#2046C2×C15111yescharacteristic, complemented
404#2045C2×C15111yescharacteristic, complemented
405#2019C2×C15111yescharacteristic, complemented
406#2018C2×C15111yescharacteristic, complemented
407#1978C2×C15111yescharacteristic, complemented
408#1977C2×C15111yescharacteristic, complemented
409#1811C2×C15111yescharacteristic, complemented
410#1785C2×C15111yescharacteristic, complemented
411#1783C2×C15111yescharacteristic, complemented
412C22×#41C22×C15111yescharacteristic
413C23×D4C22×C15111yescharacteristic
414C2×#137C22×C15111yescharacteristic, complemented
415C2×AGL(1,ℤ/8)—24no—
416C2×AGL(1,ℤ/8)—24no—
417C2×AGL(1,ℤ/8)—22no—
418C2×AGL(1,ℤ/8)—22no—
419C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
420C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
421C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
422C22×SD16C22×C15111yescharacteristic
423C22×SD16C22×C15111yescharacteristic
424C22×D8C22×C15111yescharacteristic
425C22×D8C22×C15111yescharacteristic
426C2×#131C22×C15111yescharacteristic, complemented
427C22×M16C22×C15111yescharacteristic
428#525C22×C15111yescharacteristic
429#472—24no—
430#471—24no—
431#452—22no—
432#450—22no—
433#449—22no—
434#447—22no—
435#436—22no—
436#435—22no—
437C2×#108C22×C15111yescharacteristic, complemented
438C2×#108C22×C15111yescharacteristic, complemented
439#424C22×C15111yescharacteristic, complemented
440#419C22×C15111yescharacteristic, complemented
441#418C22×C15111yescharacteristic
442#418C22×C15111yescharacteristic
443#418C22×C15111yescharacteristic, complemented
444C2×#101C22×C15111yescharacteristic, complemented
445C2×#101C22×C15111yescharacteristic, complemented
446C2×#100C22×C15111yescharacteristic
447C2×#100C22×C15111yescharacteristic
448C2×#100C22×C15111yescharacteristic
449C2×#100C22×C15111yescharacteristic
450C2×#100C22×C15111yescharacteristic, complemented
451C2×#100C22×C15111yescharacteristic, complemented
452#408C22×C15111yescharacteristic, complemented
453#407C22×C15111yescharacteristic
454#407C22×C15111yescharacteristic
455#407C22×C15111yescharacteristic
456#405C22×C15111yescharacteristic, complemented
457#341C22×C15111yescharacteristic, complemented
458#341C22×C15111yescharacteristic, complemented
459C25—21no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41C23×C15111yescharacteristic
467C22×Q8C23×C15111yescharacteristic
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C15111yescharacteristic
477C22×D4C23×C15111yescharacteristic
478C22×D4C23×C15111yescharacteristic
479C23×C4—21no—
480C23×C4C23×C15111yescharacteristic
481#137—22no—
482#137—41no—
483AGL(1,ℤ/8)—216no—
484AGL(1,ℤ/8)—216no—
485AGL(1,ℤ/8)—22no—
486AGL(1,ℤ/8)—22no—
487AGL(1,ℤ/8)—22no—
488AGL(1,ℤ/8)—41no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491C2×Q16—21no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—21no—
495C2×SD16—21no—
496C2×SD16—21no—
497C2×SD16—21no—
498C2×SD16—22no—
499C2×SD16—21no—
500C2×SD16—21no—
501C2×SD16—22no—
502C2×SD16D4×C15114yescomplemented
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—21no—
506C2×D8—21no—
507C2×D8—21no—
508C2×D8—22no—
509C2×D8—21no—
510C2×D8—21no—
511C2×D8—22no—
512C2×D8D4×C15114yescomplemented
513#131—22no—
514#131—22no—
515C2×M16—22no—
516C2×M16—22no—
517C2×M16—21no—
518C2×M16D4×C15112yes—
519C2×M16D4×C15112yes—
520C2×M16C23×C15111yescharacteristic
521C2×M16C23×C15111yescharacteristic
522C2×M16C23×C15111yescharacteristic
523C2×M16C23×C15111yescharacteristic
524C2×M16C23×C15111yescharacteristic
525C2×M16C23×C15111yescharacteristic
526C22×C8—21no—
527C22×C8C23×C15111yescharacteristic
528C22×C8C23×C15111yescharacteristic
529#123—21no—
530C22⋊Q8D4×C15112yes—
531#121D4×C15112yes—
532#120—21no—
533C4×D4—22no—
534#117C23×C15111yescharacteristic
535#108—22no—
536#108—22no—
537C4⋊C8—22no—
538#103—22no—
539#102—22no—
540#102—22no—
541#102—22no—
542#101—22no—
543#101—41no—
544#100—22no—
545#100—22no—
546#100—22no—
547#100—41no—
548#100—41no—
549#100—41no—
550C22⋊C8—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554#97—21no—
555C4×C8—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—42no—
560C24—42no—
561C24—42no—
562C24—84no—
563C24#41×C15111yescharacteristic
564#41—28no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—44no—
570#41—44no—
571#41—44no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C15112yes—
578C2×Q8C2×D4×C15111yescharacteristic
579C2×D4—28no—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—44no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4C2×D4×C15112yes—
607C2×D4C2×D4×C15112yes—
608C2×D4C2×D4×C15112yes—
609C2×D4C2×D4×C15111yescharacteristic
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C2×D4×C15112yes—
620C22×C4C2×D4×C15112yes—
621C22×C4#41×C15111yescharacteristic
622C22×C4C24×C15111yescharacteristic
623Q16—42no—
624SD16—28no—
625SD16—24no—
626SD16—24no—
627SD16—42no—
628SD16—42no—
629SD16—42no—
630SD16—42no—
631D8—28no—
632D8—24no—
633D8—24no—
634D8—42no—
635D8—42no—
636D8—42no—
637M16—24no—
638M16—24no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—21no—
646M16—21no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—42no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—42no—
661C2×C8C2×D4×C15112yes—
662C2×C8C2×D4×C15111yescharacteristic
663C2×C8C2×D4×C15111yescharacteristic
664C2×C8C2×D4×C15112yes—
665C2×C8C2×D4×C15112yes—
666C4⋊C4—22no—
667C4⋊C4C2×D4×C15112yes—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C42—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—42no—
679C23—48no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—82no—
687C23—82no—
688C23—82no—
689C23—84no—
690C23—84no—
691C23—88no—
692C23—88no—
693C23#121×C15112yes—
694C23C2×#41×C15111yescharacteristic
695Q8—22no—
696Q8—21no—
697Q8—21no—
698Q8—22no—
699Q8—41no—
700Q8—41no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—21no—
705D4—21no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—48no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4#121×C15112yes—
735C2×C4C22×D4×C15111yescharacteristic
736C2×C4C22×D4×C15111yescharacteristic
737C2×C4C22×D4×C15111yescharacteristic
738C2×C4C22×D4×C15111yescharacteristic
739C2×C4H(5,𝔽2)×C15111yescharacteristic
740C2×C4H(5,𝔽2)×C15111yescharacteristic
741C8—22no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—41no—
747C8—41no—
748C8#120×C15112yes—
749C8#120×C15112yes—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—816no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22C2×#121×C15111yescharacteristic
772C22#546×C15111yescharacteristic
773C22#546×C15111yescharacteristic
774C4—22no—
775C4—42no—
776C4—41no—
777C4—42no—
778C4C2×#120×C15111yescharacteristic
779C4#535×C15111yescharacteristic
780C4D42×C15111yescharacteristic
781C4D42×C15111yescharacteristic
782C2—21no—
783C2—21no—
784C2—42no—
785C2—81no—
786C2—82no—
787C2—82no—
788C2—82no—
789C2#2408×C15111yescharacteristic
790C2#3068×C15112yes—
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC22×C4C24×C151
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×AGL(1,ℤ/8)×C151C2semidirect
2. C2×#472×C151C2semidirect
3. C2×#471×C151C2semidirect
4. #3005×C151C2semidirect
5. #3003×C151C2semidirect
6. #2930×C151C2semidirect
7. #2046×C151C2semidirect
8. #2045×C151C2semidirect
9. #2019×C151C2semidirect
10. #2018×C151C2semidirect
11. #1978×C151C2semidirect
12. #1977×C151C2semidirect
13. #1811×C151C2semidirect
14. #1785×C151C2semidirect
15. #1783×C151C2semidirect
18. C2×#137×C151C22semidirect
25. C2×AGL(1,ℤ/8)×C151C22semidirect
30. C2×#131×C151C22semidirect
41. C2×#108×C151C22semidirect
42. C2×#108×C151C22semidirect
43. #424×C151C22semidirect
44. #419×C151C22semidirect
47. #418×C151C22semidirect
48. C2×#101×C151C22semidirect
49. C2×#101×C151C22semidirect
54. C2×#100×C151C22semidirect
55. C2×#100×C151C22semidirect
56. #408×C151C22semidirect
60. #405×C151C22semidirect
61. #341×C151C22semidirect
62. #341×C151C22semidirect
106. C2×SD16×C151D4semidirect
116. C2×D8×C151D4semidirect
395. #24284C151direct (N × H)
396. C151#24284direct (N × H)
397. C22×AGL(1,ℤ/8)C2×C151semidirect
398. C2×#472C2×C151semidirect
399. C2×#471C2×C151semidirect
400. #3005C2×C151semidirect
401. #3003C2×C151semidirect
402. #2930C2×C151semidirect
403. #2046C2×C151semidirect
404. #2045C2×C151semidirect
405. #2019C2×C151semidirect
406. #2018C2×C151semidirect
407. #1978C2×C151semidirect
408. #1977C2×C151semidirect
409. #1811C2×C151semidirect
410. #1785C2×C151semidirect
411. #1783C2×C151semidirect
414. C2×#137C22×C151semidirect
421. C2×AGL(1,ℤ/8)C22×C151semidirect
426. C2×#131C22×C151semidirect
437. C2×#108C22×C151semidirect
438. C2×#108C22×C151semidirect
439. #424C22×C151semidirect
440. #419C22×C151semidirect
443. #418C22×C151semidirect
444. C2×#101C22×C151semidirect
445. C2×#101C22×C151semidirect
450. C2×#100C22×C151semidirect
451. C2×#100C22×C151semidirect
452. #408C22×C151semidirect
456. #405C22×C151semidirect
457. #341C22×C151semidirect
458. #341C22×C151semidirect
502. C2×SD16D4×C151semidirect
512. C2×D8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1512
C2×#472×C1512
C2×#471×C1512
#3005×C1512
#3003×C1512
#2930×C1512
#2046×C1512
#2045×C1512
#2019×C1512
#2018×C1512
#1978×C1512
#1977×C1512
#1811×C1512
#1785×C1512
#1783×C1512
#24284151