Finite Group Databasebeta

← C151×#23903 #50328828

Subgroups — C151×#23903 #50328828

Order 38656.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C151C211yesmaximal, characteristic, complemented
2C2×#534×C151C211yesmaximal, characteristic, complemented
3C2×#458×C151C211yesmaximal, characteristic, complemented
4C2×B(4,𝔽2)×C151C211yesmaximal, characteristic, complemented
5#2613×C151C212yesmaximal, complemented
6#2022×C151C212yesmaximal, complemented
7#2021×C151C212yesmaximal, complemented
8#1898×C151C212yesmaximal, complemented
9#1890×C151C211yesmaximal, characteristic, complemented
10#1889×C151C211yesmaximal, characteristic, complemented
11#1781×C151C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14C23×D4×C151C2211yescharacteristic, complemented
15#546×C151—24no—
16D42×C151—24no—
17#535×C151—21no—
18#534×C151—21no—
19#534×C151—24no—
20#534×C151—24no—
21#534×C151C2212yes—
22#525×C151—21no—
23C2×#123×C151—21no—
24C2×#123×C151C2211yescharacteristic
25C2×#123×C151C2211yescharacteristic, complemented
26C2×#123×C151C2212yescomplemented
27C2×#121×C151—21no—
28C2×#121×C151—21no—
29C2×#120×C151—21no—
30C2×#120×C151—21no—
31C2×#120×C151C2211yescharacteristic
32C2×#120×C151C2212yes—
33C2×#120×C151C2211yescharacteristic, complemented
34C2×#120×C151C2212yescomplemented
35#518×C151C2211yescharacteristic
36C22×C22⋊C4×C151C2211yescharacteristic, complemented
37#458×C151—24no—
38B(4,𝔽2)×C151—24no—
39C2×#99×C151C2211yescharacteristic
40C2×#99×C151C2211yescharacteristic
41C2×#99×C151C2212yescomplemented
42C2×#99×C151C2212yescomplemented
43C2×#99×C151C2212yescomplemented
44#394×C151—24no—
45#392×C151—24no—
46#381×C151C2212yescomplemented
47#379×C151C2212yescomplemented
48#379×C151C2212yescomplemented
49#342×C151C2212yescomplemented
50#342×C151C2212yescomplemented
51C25×C151D411yescharacteristic, complemented
52C25×C151C2311yescharacteristic
53C25×C151C2311yescharacteristic
54H(5,𝔽2)×C151—22no—
55H(5,𝔽2)×C151—22no—
56H(5,𝔽2)×C151—42no—
57C2×#41×C151—21no—
58C2×#41×C151—22no—
59C22×D4×C151—22no—
60C22×D4×C151—22no—
61C22×D4×C151—22no—
62C22×D4×C151—22no—
63C22×D4×C151—21no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—24no—
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—24no—
71C22×D4×C151—22no—
72C22×D4×C151—22no—
73C22×D4×C151—42no—
74C22×D4×C151—42no—
75C22×D4×C151D411yescharacteristic, complemented
76C22×D4×C151D411yescharacteristic, complemented
77C22×D4×C151D414yescomplemented
78C22×D4×C151C2312yes—
79C22×D4×C151C2311yescharacteristic
80C22×D4×C151C2311yescharacteristic
81C23×C4×C151—21no—
82C23×C4×C151D411yescharacteristic, complemented
83C23×C4×C151C2311yescharacteristic
84#127×C151—22no—
85#124×C151—22no—
86#123×C151—28no—
87#123×C151—22no—
88#123×C151—22no—
89#123×C151—22no—
90#123×C151—22no—
91#123×C151—22no—
92#123×C151—22no—
93#123×C151—24no—
94#123×C151—42no—
95#123×C151D414yescomplemented
96C22⋊Q8×C151—22no—
97#121×C151—28no—
98#121×C151—28no—
99#121×C151—22no—
100#121×C151—24no—
101#121×C151—24no—
102#121×C151—24no—
103#120×C151—28no—
104#120×C151—24no—
105#120×C151—22no—
106#120×C151—22no—
107#120×C151—22no—
108#120×C151—22no—
109#120×C151—22no—
110#120×C151—22no—
111#120×C151—24no—
112#120×C151—22no—
113#120×C151—22no—
114#120×C151—24no—
115#120×C151—42no—
116#120×C151D414yescomplemented
117C4×D4×C151—24no—
118C4×D4×C151—24no—
119#117×C151—21no—
120C2×C4⋊C4×C151—21no—
121C2×C4⋊C4×C151—21no—
122C2×C4⋊C4×C151—22no—
123C2×C22⋊C4×C151—22no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—24no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151—24no—
136C2×C22⋊C4×C151D414yescomplemented
137C2×C22⋊C4×C151C2312yes—
138C2×C22⋊C4×C151C2312yes—
139C2×C22⋊C4×C151C2312yes—
140C2×C22⋊C4×C151C2311yescharacteristic
141C2×C22⋊C4×C151C2311yescharacteristic
142#99×C151—22no—
143#99×C151—22no—
144#99×C151—24no—
145#99×C151—24no—
146#99×C151—42no—
147#95×C151—24no—
148C24×C151—21no—
149C24×C151—21no—
150C24×C151—22no—
151C24×C151—21no—
152C24×C151—22no—
153C24×C151—21no—
154C24×C151—22no—
155C24×C151—22no—
156C24×C151—21no—
157C24×C151—22no—
158C24×C151—41no—
159C24×C151—82no—
160C24×C151—82no—
161C24×C151—82no—
162C24×C151C2×D411yescharacteristic
163C24×C151C2×D412yes—
164C24×C151C2×D411yescharacteristic
165C24×C151C2×D414yes—
166C24×C151C2×D411yescharacteristic
167C24×C151C2×D411yescharacteristic
168C24×C151C2×D412yescomplemented
169C24×C151C2411yescharacteristic
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—42no—
173#41×C151—42no—
174C2×Q8×C151—21no—
175C2×D4×C151—22no—
176C2×D4×C151—22no—
177C2×D4×C151—22no—
178C2×D4×C151—24no—
179C2×D4×C151—24no—
180C2×D4×C151—21no—
181C2×D4×C151—24no—
182C2×D4×C151—22no—
183C2×D4×C151—22no—
184C2×D4×C151—22no—
185C2×D4×C151—22no—
186C2×D4×C151—22no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—24no—
196C2×D4×C151—24no—
197C2×D4×C151—24no—
198C2×D4×C151—24no—
199C2×D4×C151—22no—
200C2×D4×C151—41no—
201C2×D4×C151—41no—
202C2×D4×C151—48no—
203C2×D4×C151—48no—
204C2×D4×C151—48no—
205C2×D4×C151—44no—
206C2×D4×C151—44no—
207C2×D4×C151—48no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—44no—
215C2×D4×C151—84no—
216C2×D4×C151—82no—
217C2×D4×C151—82no—
218C2×D4×C151—84no—
219C2×D4×C151—84no—
220C2×D4×C151C2×D412yes—
221C2×D4×C151C2×D412yes—
222C22×C4×C151—21no—
223C22×C4×C151—22no—
224C22×C4×C151—22no—
225C22×C4×C151—22no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—22no—
231C22×C4×C151—22no—
232C22×C4×C151—24no—
233C22×C4×C151—22no—
234C22×C4×C151—22no—
235C22×C4×C151—22no—
236C22×C4×C151—41no—
237C22×C4×C151—82no—
238C22×C4×C151C2×D412yes—
239C22×C4×C151C2×D411yescharacteristic
240C22×C4×C151C2×D411yescharacteristic
241C22×C4×C151C2×D414yes—
242C22×C4×C151C2×D412yescomplemented
243C4⋊C4×C151—24no—
244C4⋊C4×C151—22no—
245C4⋊C4×C151—24no—
246C4⋊C4×C151—24no—
247C4⋊C4×C151—44no—
248C22⋊C4×C151—24no—
249C22⋊C4×C151—22no—
250C22⋊C4×C151—24no—
251C22⋊C4×C151—24no—
252C22⋊C4×C151—24no—
253C22⋊C4×C151—24no—
254C22⋊C4×C151—24no—
255C22⋊C4×C151—24no—
256C22⋊C4×C151—24no—
257C22⋊C4×C151—21no—
258C22⋊C4×C151—21no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—22no—
261C22⋊C4×C151—24no—
262C22⋊C4×C151—22no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—22no—
265C22⋊C4×C151—22no—
266C22⋊C4×C151—44no—
267C22⋊C4×C151—44no—
268C22⋊C4×C151—84no—
269C22⋊C4×C151—84no—
270C22⋊C4×C151C2×D412yescomplemented
271C22⋊C4×C151C2×D412yescomplemented
272C42×C151—22no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—24no—
280C23×C151—24no—
281C23×C151—21no—
282C23×C151—22no—
283C23×C151—21no—
284C23×C151—22no—
285C23×C151—24no—
286C23×C151—21no—
287C23×C151—22no—
288C23×C151—22no—
289C23×C151—42no—
290C23×C151—42no—
291C23×C151—42no—
292C23×C151—44no—
293C23×C151—44no—
294C23×C151—44no—
295C23×C151—42no—
296C23×C151—42no—
297C23×C151—44no—
298C23×C151—44no—
299C23×C151—42no—
300C23×C151—42no—
301C23×C151—44no—
302C23×C151—42no—
303C23×C151—44no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—42no—
307C23×C151—82no—
308C23×C151—82no—
309C23×C151—82no—
310C23×C151—82no—
311C23×C151—82no—
312C23×C151—84no—
313C23×C151—84no—
314C23×C151—84no—
315C23×C151—82no—
316C23×C151—84no—
317C23×C151#12012yes—
318C23×C151#12012yes—
319C23×C151#12012yes—
320C23×C151C22×D411yescharacteristic
321C23×C151C22×D412yes—
322C23×C151C22×D411yescharacteristic
323C23×C151C22×D411yescharacteristic
324C23×C151H(5,𝔽2)12yes—
325Q8×C151—42no—
326D4×C151—24no—
327D4×C151—24no—
328D4×C151—44no—
329D4×C151—42no—
330D4×C151—44no—
331D4×C151—44no—
332D4×C151—48no—
333D4×C151—48no—
334D4×C151—48no—
335D4×C151—42no—
336D4×C151—42no—
337D4×C151—42no—
338D4×C151—42no—
339D4×C151—42no—
340D4×C151—42no—
341D4×C151—84no—
342D4×C151—84no—
343D4×C151—84no—
344D4×C151—84no—
345D4×C151—88no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—22no—
349C2×C4×C151—22no—
350C2×C4×C151—21no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—24no—
354C2×C4×C151—21no—
355C2×C4×C151—21no—
356C2×C4×C151—22no—
357C2×C4×C151—22no—
358C2×C4×C151—24no—
359C2×C4×C151—44no—
360C2×C4×C151—44no—
361C2×C4×C151—42no—
362C2×C4×C151—42no—
363C2×C4×C151—42no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—42no—
367C2×C4×C151—44no—
368C2×C4×C151—44no—
369C2×C4×C151—44no—
370C2×C4×C151—42no—
371C2×C4×C151—42no—
372C2×C4×C151—84no—
373C2×C4×C151—82no—
374C2×C4×C151#12012yes—
375C22×C151—24no—
376C22×C151—22no—
377C22×C151—22no—
378C22×C151—22no—
379C22×C151—22no—
380C22×C151—22no—
381C22×C151—24no—
382C22×C151—22no—
383C22×C151—41no—
384C22×C151—41no—
385C22×C151—42no—
386C22×C151—42no—
387C22×C151—42no—
388C22×C151—42no—
389C22×C151—42no—
390C22×C151—42no—
391C22×C151—42no—
392C22×C151—42no—
393C22×C151—42no—
394C22×C151—44no—
395C22×C151—44no—
396C22×C151—42no—
397C22×C151—42no—
398C22×C151—42no—
399C22×C151—41no—
400C22×C151—44no—
401C22×C151—42no—
402C22×C151—84no—
403C22×C151—84no—
404C22×C151—81no—
405C22×C151—82no—
406C22×C151—82no—
407C22×C151—81no—
408C22×C151—84no—
409C22×C151—82no—
410C22×C151—88no—
411C22×C151—82no—
412C22×C151—162no—
413C22×C151C2×#12011yescharacteristic
414C22×C151C2×#12011yescharacteristic
415C22×C151#53411yescharacteristic
416C22×C151D4212yes—
417C22×C151D4212yes—
418C4×C151—22no—
419C4×C151—42no—
420C4×C151—42no—
421C4×C151—41no—
422C4×C151—42no—
423C4×C151—42no—
424C4×C151—44no—
425C4×C151—82no—
426C4×C151—82no—
427C2×C151—21no—
428C2×C151—22no—
429C2×C151—22no—
430C2×C151—21no—
431C2×C151—42no—
432C2×C151—42no—
433C2×C151—42no—
434C2×C151—82no—
435C2×C151—81no—
436C2×C151—82no—
437C2×C151#240311yescharacteristic
438C2×C151#302612yes—
439#23903C15111yesmaximal, characteristic, direct product factor, Sylow
440C151#2390311yescharacteristic, direct product factor, Sylow
441#3484C2×C15111yescharacteristic, complemented
442C2×#534C2×C15111yescharacteristic, complemented
443C2×#458C2×C15111yescharacteristic, complemented
444C2×B(4,𝔽2)C2×C15111yescharacteristic, complemented
445#2613C2×C15112yescomplemented
446#2022C2×C15112yescomplemented
447#2021C2×C15112yescomplemented
448#1898C2×C15112yescomplemented
449#1890C2×C15111yescharacteristic, complemented
450#1889C2×C15111yescharacteristic, complemented
451#1781C2×C15111yescharacteristic, complemented
452C2×H(5,𝔽2)C22×C15111yescharacteristic
453C23×D4C22×C15111yescharacteristic
454C23×D4C22×C15111yescharacteristic, complemented
455#546—24no—
456D42—24no—
457#535—21no—
458#534—21no—
459#534—24no—
460#534—24no—
461#534C22×C15112yes—
462#525—21no—
463C2×#123—21no—
464C2×#123C22×C15111yescharacteristic
465C2×#123C22×C15111yescharacteristic, complemented
466C2×#123C22×C15112yescomplemented
467C2×#121—21no—
468C2×#121—21no—
469C2×#120—21no—
470C2×#120—21no—
471C2×#120C22×C15111yescharacteristic
472C2×#120C22×C15112yes—
473C2×#120C22×C15111yescharacteristic, complemented
474C2×#120C22×C15112yescomplemented
475#518C22×C15111yescharacteristic
476C22×C22⋊C4C22×C15111yescharacteristic, complemented
477#458—24no—
478B(4,𝔽2)—24no—
479C2×#99C22×C15111yescharacteristic
480C2×#99C22×C15111yescharacteristic
481C2×#99C22×C15112yescomplemented
482C2×#99C22×C15112yescomplemented
483C2×#99C22×C15112yescomplemented
484#394—24no—
485#392—24no—
486#381C22×C15112yescomplemented
487#379C22×C15112yescomplemented
488#379C22×C15112yescomplemented
489#342C22×C15112yescomplemented
490#342C22×C15112yescomplemented
491C25D4×C15111yescharacteristic, complemented
492C25C23×C15111yescharacteristic
493C25C23×C15111yescharacteristic
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—42no—
497C2×#41—21no—
498C2×#41—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—24no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—24no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4D4×C15111yescharacteristic, complemented
516C22×D4D4×C15111yescharacteristic, complemented
517C22×D4D4×C15114yescomplemented
518C22×D4C23×C15112yes—
519C22×D4C23×C15111yescharacteristic
520C22×D4C23×C15111yescharacteristic
521C23×C4—21no—
522C23×C4D4×C15111yescharacteristic, complemented
523C23×C4C23×C15111yescharacteristic
524#127—22no—
525#124—22no—
526#123—28no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532#123—22no—
533#123—24no—
534#123—42no—
535#123D4×C15114yescomplemented
536C22⋊Q8—22no—
537#121—28no—
538#121—28no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#120—28no—
544#120—24no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—22no—
549#120—24no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—24no—
555#120—42no—
556#120D4×C15114yescomplemented
557C4×D4—24no—
558C4×D4—24no—
559#117—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4D4×C15114yescomplemented
577C2×C22⋊C4C23×C15112yes—
578C2×C22⋊C4C23×C15112yes—
579C2×C22⋊C4C23×C15112yes—
580C2×C22⋊C4C23×C15111yescharacteristic
581C2×C22⋊C4C23×C15111yescharacteristic
582#99—22no—
583#99—22no—
584#99—24no—
585#99—24no—
586#99—42no—
587#95—24no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—22no—
598C24—41no—
599C24—82no—
600C24—82no—
601C24—82no—
602C24C2×D4×C15111yescharacteristic
603C24C2×D4×C15112yes—
604C24C2×D4×C15111yescharacteristic
605C24C2×D4×C15114yes—
606C24C2×D4×C15111yescharacteristic
607C24C2×D4×C15111yescharacteristic
608C24C2×D4×C15112yescomplemented
609C24C24×C15111yescharacteristic
610#41—44no—
611#41—44no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—84no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—84no—
659C2×D4—84no—
660C2×D4C2×D4×C15112yes—
661C2×D4C2×D4×C15112yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—41no—
677C22×C4—82no—
678C22×C4C2×D4×C15112yes—
679C22×C4C2×D4×C15111yescharacteristic
680C22×C4C2×D4×C15111yescharacteristic
681C22×C4C2×D4×C15114yes—
682C22×C4C2×D4×C15112yescomplemented
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—44no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—84no—
709C22⋊C4—84no—
710C22⋊C4C2×D4×C15112yescomplemented
711C22⋊C4C2×D4×C15112yescomplemented
712C42—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—24no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—82no—
748C23—82no—
749C23—82no—
750C23—82no—
751C23—82no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—82no—
756C23—84no—
757C23#120×C15112yes—
758C23#120×C15112yes—
759C23#120×C15112yes—
760C23C22×D4×C15111yescharacteristic
761C23C22×D4×C15112yes—
762C23C22×D4×C15111yescharacteristic
763C23C22×D4×C15111yescharacteristic
764C23H(5,𝔽2)×C15112yes—
765Q8—42no—
766D4—24no—
767D4—24no—
768D4—44no—
769D4—42no—
770D4—44no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—88no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4#120×C15112yes—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—24no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—44no—
841C22—42no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—88no—
851C22—82no—
852C22—162no—
853C22C2×#120×C15111yescharacteristic
854C22C2×#120×C15111yescharacteristic
855C22#534×C15111yescharacteristic
856C22D42×C15112yes—
857C22D42×C15112yes—
858C4—22no—
859C4—42no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—82no—
866C4—82no—
867C2—21no—
868C2—22no—
869C2—22no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—42no—
874C2—82no—
875C2—81no—
876C2—82no—
877C2#2403×C15111yescharacteristic
878C2#3026×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C25×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3484×C151C2semidirect
2. C2×#534×C151C2semidirect
3. C2×#458×C151C2semidirect
4. C2×B(4,𝔽2)×C151C2semidirect
5. #2613×C151C2semidirect
6. #2022×C151C2semidirect
7. #2021×C151C2semidirect
8. #1898×C151C2semidirect
9. #1890×C151C2semidirect
10. #1889×C151C2semidirect
11. #1781×C151C2semidirect
14. C23×D4×C151C22semidirect
25. C2×#123×C151C22semidirect
26. C2×#123×C151C22semidirect
33. C2×#120×C151C22semidirect
34. C2×#120×C151C22semidirect
36. C22×C22⋊C4×C151C22semidirect
41. C2×#99×C151C22semidirect
42. C2×#99×C151C22semidirect
43. C2×#99×C151C22semidirect
46. #381×C151C22semidirect
47. #379×C151C22semidirect
48. #379×C151C22semidirect
49. #342×C151C22semidirect
50. #342×C151C22semidirect
51. C25×C151D4semidirect
75. C22×D4×C151D4semidirect
76. C22×D4×C151D4semidirect
77. C22×D4×C151D4semidirect
82. C23×C4×C151D4semidirect
95. #123×C151D4semidirect
116. #120×C151D4semidirect
136. C2×C22⋊C4×C151D4semidirect
168. C24×C151C2×D4semidirect
242. C22×C4×C151C2×D4semidirect
270. C22⋊C4×C151C2×D4semidirect
271. C22⋊C4×C151C2×D4semidirect
439. #23903C151direct (N × H)
440. C151#23903direct (N × H)
441. #3484C2×C151semidirect
442. C2×#534C2×C151semidirect
443. C2×#458C2×C151semidirect
444. C2×B(4,𝔽2)C2×C151semidirect
445. #2613C2×C151semidirect
446. #2022C2×C151semidirect
447. #2021C2×C151semidirect
448. #1898C2×C151semidirect
449. #1890C2×C151semidirect
450. #1889C2×C151semidirect
451. #1781C2×C151semidirect
454. C23×D4C22×C151semidirect
465. C2×#123C22×C151semidirect
466. C2×#123C22×C151semidirect
473. C2×#120C22×C151semidirect
474. C2×#120C22×C151semidirect
476. C22×C22⋊C4C22×C151semidirect
481. C2×#99C22×C151semidirect
482. C2×#99C22×C151semidirect
483. C2×#99C22×C151semidirect
486. #381C22×C151semidirect
487. #379C22×C151semidirect
488. #379C22×C151semidirect
489. #342C22×C151semidirect
490. #342C22×C151semidirect
491. C25D4×C151semidirect
515. C22×D4D4×C151semidirect
516. C22×D4D4×C151semidirect
517. C22×D4D4×C151semidirect
522. C23×C4D4×C151semidirect
535. #123D4×C151semidirect
556. #120D4×C151semidirect
576. C2×C22⋊C4D4×C151semidirect
608. C24C2×D4×C151semidirect
682. C22×C4C2×D4×C151semidirect
710. C22⋊C4C2×D4×C151semidirect
711. C22⋊C4C2×D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3484×C1512
C2×#534×C1512
C2×#458×C1512
C2×B(4,𝔽2)×C1512
#2613×C1512
#2022×C1512
#2021×C1512
#1898×C1512
#1890×C1512
#1889×C1512
#1781×C1512
#23903151