Finite Group Databasebeta

← C151×#24405 #50329330

Subgroups — C151×#24405 #50329330

Order 38656.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C151C211yesmaximal, characteristic
2C2×#458×C151C211yesmaximal, characteristic, complemented
3C22×#99×C151C211yesmaximal, characteristic, complemented
4#2412×C151C212yesmaximal, complemented
5#2405×C151C211yesmaximal, characteristic, complemented
6#2044×C151C212yesmaximal, complemented
7#2022×C151C212yesmaximal, complemented
8#1898×C151C212yesmaximal, complemented
9#1890×C151C211yesmaximal, characteristic, complemented
10#1867×C151C211yesmaximal, characteristic, complemented
11#1790×C151C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14#546×C151—22no—
15#546×C151—22no—
16D42×C151—22no—
17D42×C151—22no—
18#535×C151—21no—
19#534×C151—21no—
20#534×C151C2212yes—
21#525×C151—21no—
22C2×#123×C151C2211yescharacteristic
23C2×#123×C151C2212yescomplemented
24C2×#123×C151C2211yescharacteristic, complemented
25C2×#120×C151—21no—
26C2×#120×C151C2212yes—
27#518×C151C2211yescharacteristic
28C22×C22⋊C4×C151C2211yescharacteristic, complemented
29C22×C22⋊C4×C151C2212yescomplemented
30#458×C151—24no—
31C2×#99×C151—24no—
32C2×#99×C151C2211yescharacteristic
33C2×#99×C151C2211yescharacteristic
34C2×#99×C151C2212yescomplemented
35C2×#99×C151C2212yescomplemented
36C2×#99×C151C2212yescomplemented
37#397×C151—22no—
38#394×C151—21no—
39#394×C151—21no—
40#394×C151—22no—
41#386×C151—22no—
42#386×C151C2211yescharacteristic
43#386×C151C2211yescharacteristic, complemented
44#386×C151C2212yescomplemented
45#385×C151—21no—
46#385×C151C2212yescomplemented
47#381×C151C2212yescomplemented
48#380×C151—22no—
49#379×C151—21no—
50#379×C151C2211yescharacteristic, complemented
51#342×C151C2212yescomplemented
52#342×C151C2212yescomplemented
53C25×C151D411yescharacteristic
54C25×C151C2311yescharacteristic
55H(5,𝔽2)×C151—22no—
56H(5,𝔽2)×C151—22no—
57H(5,𝔽2)×C151—42no—
58C2×#41×C151—21no—
59C2×#41×C151—22no—
60C22×D4×C151—21no—
61C22×D4×C151—21no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—21no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—42no—
69C22×D4×C151D411yescharacteristic
70C22×D4×C151D411yescharacteristic
71C22×D4×C151D412yes—
72C22×D4×C151D412yes—
73C22×D4×C151C2312yes—
74C22×D4×C151C2311yescharacteristic
75C22×D4×C151C2311yescharacteristic
76C23×C4×C151—22no—
77C23×C4×C151D411yescharacteristic
78C23×C4×C151C2311yescharacteristic
79C23×C4×C151C2311yescharacteristic
80#127×C151—22no—
81#124×C151—22no—
82#123×C151—22no—
83#123×C151—22no—
84#123×C151—22no—
85#123×C151—22no—
86#123×C151—22no—
87#123×C151—24no—
88#123×C151—42no—
89#123×C151—42no—
90C22⋊Q8×C151—21no—
91C22⋊Q8×C151—21no—
92#121×C151—21no—
93#121×C151—21no—
94#121×C151—22no—
95#121×C151—22no—
96#121×C151—22no—
97#121×C151—22no—
98#121×C151—22no—
99#121×C151—22no—
100#120×C151—22no—
101#120×C151—22no—
102#120×C151—22no—
103#120×C151—22no—
104#120×C151—22no—
105#120×C151—22no—
106#120×C151—22no—
107#120×C151—22no—
108#120×C151—22no—
109C4×D4×C151—22no—
110C4×D4×C151—22no—
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113#117×C151—21no—
114C2×C4⋊C4×C151—22no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151—22no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—24no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—22no—
130C2×C22⋊C4×C151—22no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151—42no—
136C2×C22⋊C4×C151D412yes—
137C2×C22⋊C4×C151D412yes—
138C2×C22⋊C4×C151C2311yescharacteristic
139C2×C22⋊C4×C151C2311yescharacteristic
140C2×C22⋊C4×C151C2312yes—
141C2×C22⋊C4×C151C2312yes—
142C2×C22⋊C4×C151C2312yes—
143#99×C151—22no—
144#99×C151—24no—
145#99×C151—24no—
146#99×C151—42no—
147#99×C151D414yescomplemented
148#95×C151—22no—
149#95×C151—22no—
150#95×C151—22no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—22no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151—22no—
157C24×C151—21no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—22no—
161C24×C151—41no—
162C24×C151—42no—
163C24×C151—42no—
164C24×C151—81no—
165C24×C151—81no—
166C24×C151C2×D411yescharacteristic
167C24×C151C2×D412yes—
168C24×C151C2×D411yescharacteristic
169C24×C151C2×D412yes—
170C24×C151C2×D412yes—
171C24×C151C2×D411yescharacteristic
172C24×C151C2×D411yescharacteristic
173C24×C151C2411yescharacteristic
174#41×C151—44no—
175#41×C151—44no—
176#41×C151—42no—
177#41×C151—42no—
178C2×Q8×C151—21no—
179C2×D4×C151—22no—
180C2×D4×C151—22no—
181C2×D4×C151—22no—
182C2×D4×C151—21no—
183C2×D4×C151—22no—
184C2×D4×C151—22no—
185C2×D4×C151—22no—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—21no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—21no—
194C2×D4×C151—22no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—22no—
198C2×D4×C151—22no—
199C2×D4×C151—22no—
200C2×D4×C151—22no—
201C2×D4×C151—22no—
202C2×D4×C151—22no—
203C2×D4×C151—41no—
204C2×D4×C151—41no—
205C2×D4×C151—44no—
206C2×D4×C151—44no—
207C2×D4×C151—44no—
208C2×D4×C151—44no—
209C2×D4×C151—44no—
210C2×D4×C151—44no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—44no—
214C2×D4×C151—82no—
215C2×D4×C151—82no—
216C2×D4×C151—82no—
217C2×D4×C151C2×D412yes—
218C2×D4×C151#4112yes—
219C22×C4×C151—21no—
220C22×C4×C151—22no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—22no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—22no—
227C22×C4×C151—22no—
228C22×C4×C151—21no—
229C22×C4×C151—22no—
230C22×C4×C151—22no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—22no—
237C22×C4×C151—41no—
238C22×C4×C151—44no—
239C22×C4×C151—44no—
240C22×C4×C151—81no—
241C22×C4×C151—82no—
242C22×C4×C151C2×D412yes—
243C22×C4×C151C2×D411yescharacteristic
244C22×C4×C151C2×D411yescharacteristic
245C22×C4×C151C2×D412yes—
246C22×C4×C151C2×D412yes—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—22no—
250C4⋊C4×C151—22no—
251C4⋊C4×C151—44no—
252C4⋊C4×C151—42no—
253C4⋊C4×C151—42no—
254C4⋊C4×C151—82no—
255C22⋊C4×C151—22no—
256C22⋊C4×C151—22no—
257C22⋊C4×C151—22no—
258C22⋊C4×C151—22no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—22no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—22no—
265C22⋊C4×C151—22no—
266C22⋊C4×C151—22no—
267C22⋊C4×C151—22no—
268C22⋊C4×C151—21no—
269C22⋊C4×C151—21no—
270C22⋊C4×C151—22no—
271C22⋊C4×C151—22no—
272C22⋊C4×C151—44no—
273C22⋊C4×C151—44no—
274C22⋊C4×C151—42no—
275C22⋊C4×C151—42no—
276C22⋊C4×C151—41no—
277C22⋊C4×C151—42no—
278C22⋊C4×C151—41no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—81no—
281C22⋊C4×C151—81no—
282C22⋊C4×C151—81no—
283C22⋊C4×C151—82no—
284C22⋊C4×C151C2×D414yescomplemented
285C42×C151—22no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—22no—
290C23×C151—22no—
291C23×C151—22no—
292C23×C151—24no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—22no—
297C23×C151—22no—
298C23×C151—21no—
299C23×C151—22no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—22no—
303C23×C151—22no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—42no—
307C23×C151—41no—
308C23×C151—42no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—42no—
312C23×C151—42no—
313C23×C151—42no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—42no—
319C23×C151—42no—
320C23×C151—42no—
321C23×C151—42no—
322C23×C151—42no—
323C23×C151—81no—
324C23×C151—81no—
325C23×C151—82no—
326C23×C151—82no—
327C23×C151—84no—
328C23×C151—81no—
329C23×C151—81no—
330C23×C151—84no—
331C23×C151—84no—
332C23×C151#12011yescharacteristic
333C23×C151#12012yes—
334C23×C151#12011yescharacteristic
335C23×C151#12112yes—
336C23×C151C22×D411yescharacteristic
337C23×C151C22×D412yes—
338C23×C151C22×D411yescharacteristic
339C23×C151C2×#4111yescharacteristic
340C23×C151H(5,𝔽2)12yes—
341Q8×C151—42no—
342D4×C151—24no—
343D4×C151—24no—
344D4×C151—44no—
345D4×C151—42no—
346D4×C151—44no—
347D4×C151—44no—
348D4×C151—44no—
349D4×C151—42no—
350D4×C151—42no—
351D4×C151—42no—
352D4×C151—42no—
353D4×C151—42no—
354D4×C151—42no—
355D4×C151—44no—
356D4×C151—82no—
357D4×C151—82no—
358D4×C151—82no—
359D4×C151—82no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—22no—
363C2×C4×C151—22no—
364C2×C4×C151—22no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—22no—
369C2×C4×C151—24no—
370C2×C4×C151—22no—
371C2×C4×C151—42no—
372C2×C4×C151—42no—
373C2×C4×C151—44no—
374C2×C4×C151—42no—
375C2×C4×C151—42no—
376C2×C4×C151—42no—
377C2×C4×C151—42no—
378C2×C4×C151—42no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—42no—
384C2×C4×C151—42no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—42no—
388C2×C4×C151—42no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—42no—
396C2×C4×C151—42no—
397C2×C4×C151—42no—
398C2×C4×C151—81no—
399C2×C4×C151—81no—
400C2×C4×C151—88no—
401C2×C4×C151#12112yes—
402C22×C151—21no—
403C22×C151—22no—
404C22×C151—21no—
405C22×C151—22no—
406C22×C151—21no—
407C22×C151—21no—
408C22×C151—21no—
409C22×C151—22no—
410C22×C151—22no—
411C22×C151—22no—
412C22×C151—21no—
413C22×C151—21no—
414C22×C151—22no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—42no—
418C22×C151—44no—
419C22×C151—44no—
420C22×C151—42no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—41no—
425C22×C151—41no—
426C22×C151—42no—
427C22×C151—41no—
428C22×C151—42no—
429C22×C151—41no—
430C22×C151—42no—
431C22×C151—41no—
432C22×C151—82no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—82no—
437C22×C151—84no—
438C22×C151—82no—
439C22×C151—82no—
440C22×C151—81no—
441C22×C151—84no—
442C22×C151—162no—
443C22×C151#45812yescomplemented
444C22×C151C2×#12011yescharacteristic
445C22×C151C2×#12111yescharacteristic
446C22×C151#53411yescharacteristic
447C22×C151D4212yes—
448C22×C151#54612yes—
449C4×C151—22no—
450C4×C151—44no—
451C4×C151—41no—
452C4×C151—42no—
453C4×C151—42no—
454C4×C151—42no—
455C4×C151—81no—
456C4×C151—81no—
457C4×C151—82no—
458C4×C151—81no—
459C4×C151—81no—
460C2×C151—22no—
461C2×C151—21no—
462C2×C151—21no—
463C2×C151—22no—
464C2×C151—22no—
465C2×C151—42no—
466C2×C151—41no—
467C2×C151—42no—
468C2×C151—81no—
469C2×C151—82no—
470C2×C151#241011yescharacteristic
471C2×C151C2×#45811yescharacteristic
472C2×C151#302611yescharacteristic
473#24405C15111yesmaximal, characteristic, direct product factor, Sylow
474C151#2440511yescharacteristic, direct product factor, Sylow
475#3484C2×C15111yescharacteristic
476C2×#458C2×C15111yescharacteristic, complemented
477C22×#99C2×C15111yescharacteristic, complemented
478#2412C2×C15112yescomplemented
479#2405C2×C15111yescharacteristic, complemented
480#2044C2×C15112yescomplemented
481#2022C2×C15112yescomplemented
482#1898C2×C15112yescomplemented
483#1890C2×C15111yescharacteristic, complemented
484#1867C2×C15111yescharacteristic, complemented
485#1790C2×C15111yescharacteristic, complemented
486C2×H(5,𝔽2)C22×C15111yescharacteristic
487C23×D4C22×C15111yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C15112yes—
495#525—21no—
496C2×#123C22×C15111yescharacteristic
497C2×#123C22×C15112yescomplemented
498C2×#123C22×C15111yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C15112yes—
501#518C22×C15111yescharacteristic
502C22×C22⋊C4C22×C15111yescharacteristic, complemented
503C22×C22⋊C4C22×C15112yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C15111yescharacteristic
507C2×#99C22×C15111yescharacteristic
508C2×#99C22×C15112yescomplemented
509C2×#99C22×C15112yescomplemented
510C2×#99C22×C15112yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C15111yescharacteristic
517#386C22×C15111yescharacteristic, complemented
518#386C22×C15112yescomplemented
519#385—21no—
520#385C22×C15112yescomplemented
521#381C22×C15112yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C15111yescharacteristic, complemented
525#342C22×C15112yescomplemented
526#342C22×C15112yescomplemented
527C25D4×C15111yescharacteristic
528C25C23×C15111yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C15111yescharacteristic
544C22×D4D4×C15111yescharacteristic
545C22×D4D4×C15112yes—
546C22×D4D4×C15112yes—
547C22×D4C23×C15112yes—
548C22×D4C23×C15111yescharacteristic
549C22×D4C23×C15111yescharacteristic
550C23×C4—22no—
551C23×C4D4×C15111yescharacteristic
552C23×C4C23×C15111yescharacteristic
553C23×C4C23×C15111yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C15112yes—
611C2×C22⋊C4D4×C15112yes—
612C2×C22⋊C4C23×C15112yes—
613C2×C22⋊C4C23×C15111yescharacteristic
614C2×C22⋊C4C23×C15111yescharacteristic
615C2×C22⋊C4C23×C15112yes—
616C2×C22⋊C4C23×C15112yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C15114yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C15111yescharacteristic
641C24C2×D4×C15112yes—
642C24C2×D4×C15111yescharacteristic
643C24C2×D4×C15112yes—
644C24C2×D4×C15112yes—
645C24C2×D4×C15111yescharacteristic
646C24C2×D4×C15111yescharacteristic
647C24C24×C15111yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C15112yes—
692C2×D4#41×C15112yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C15112yes—
717C22×C4C2×D4×C15111yescharacteristic
718C22×C4C2×D4×C15111yescharacteristic
719C22×C4C2×D4×C15112yes—
720C22×C4C2×D4×C15112yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C15114yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—41no—
779C23—42no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C15111yescharacteristic
807C23#120×C15112yes—
808C23#120×C15111yescharacteristic
809C23#121×C15112yes—
810C23C22×D4×C15111yescharacteristic
811C23C22×D4×C15112yes—
812C23C22×D4×C15111yescharacteristic
813C23C2×#41×C15111yescharacteristic
814C23H(5,𝔽2)×C15112yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C15112yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C15112yescomplemented
918C22C2×#120×C15111yescharacteristic
919C22C2×#121×C15111yescharacteristic
920C22#534×C15111yescharacteristic
921C22D42×C15112yes—
922C22#546×C15112yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2#2410×C15111yescharacteristic
945C2C2×#458×C15111yescharacteristic
946C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radical#3484×C151C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C151C2semidirect
3. C22×#99×C151C2semidirect
4. #2412×C151C2semidirect
5. #2405×C151C2semidirect
6. #2044×C151C2semidirect
7. #2022×C151C2semidirect
8. #1898×C151C2semidirect
9. #1890×C151C2semidirect
10. #1867×C151C2semidirect
11. #1790×C151C2semidirect
23. C2×#123×C151C22semidirect
24. C2×#123×C151C22semidirect
28. C22×C22⋊C4×C151C22semidirect
29. C22×C22⋊C4×C151C22semidirect
34. C2×#99×C151C22semidirect
35. C2×#99×C151C22semidirect
36. C2×#99×C151C22semidirect
43. #386×C151C22semidirect
44. #386×C151C22semidirect
46. #385×C151C22semidirect
47. #381×C151C22semidirect
50. #379×C151C22semidirect
51. #342×C151C22semidirect
52. #342×C151C22semidirect
147. #99×C151D4semidirect
284. C22⋊C4×C151C2×D4semidirect
443. C22×C151#458semidirect
473. #24405C151direct (N × H)
474. C151#24405direct (N × H)
476. C2×#458C2×C151semidirect
477. C22×#99C2×C151semidirect
478. #2412C2×C151semidirect
479. #2405C2×C151semidirect
480. #2044C2×C151semidirect
481. #2022C2×C151semidirect
482. #1898C2×C151semidirect
483. #1890C2×C151semidirect
484. #1867C2×C151semidirect
485. #1790C2×C151semidirect
497. C2×#123C22×C151semidirect
498. C2×#123C22×C151semidirect
502. C22×C22⋊C4C22×C151semidirect
503. C22×C22⋊C4C22×C151semidirect
508. C2×#99C22×C151semidirect
509. C2×#99C22×C151semidirect
510. C2×#99C22×C151semidirect
517. #386C22×C151semidirect
518. #386C22×C151semidirect
520. #385C22×C151semidirect
521. #381C22×C151semidirect
524. #379C22×C151semidirect
525. #342C22×C151semidirect
526. #342C22×C151semidirect
621. #99D4×C151semidirect
758. C22⋊C4C2×D4×C151semidirect
917. C22#458×C151semidirect

Maximal subgroups

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

subgroupindex
#3484×C1512
C2×#458×C1512
C22×#99×C1512
#2412×C1512
#2405×C1512
#2044×C1512
#2022×C1512
#1898×C1512
#1890×C1512
#1867×C1512
#1790×C1512
#24405151