Finite Group Databasebeta

← C151×#15412 #50320337

Subgroups — C151×#15412 #50320337

Order 38656.

2830 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C151C211yesmaximal, characteristic, complemented
2C2×#392×C151C211yesmaximal, characteristic, complemented
3C2×#392×C151C211yesmaximal, characteristic, complemented
4C2×#392×C151C212yesmaximal, complemented
5C2×#390×C151C211yesmaximal, characteristic, complemented
6C2×#386×C151C212yesmaximal, complemented
7#1445×C151C211yesmaximal, characteristic, complemented
8#1439×C151C212yesmaximal, complemented
9#1438×C151C212yesmaximal, complemented
10#1437×C151C211yesmaximal, characteristic, complemented
11#1437×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C23×D4×C151C2212yes—
14C23×D4×C151C2211yescharacteristic
15C23×D4×C151C2212yes—
16C24×C4×C151C2211yescharacteristic
17C2×#123×C151—24no—
18C2×#123×C151—24no—
19C2×#123×C151—24no—
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C22⋊C4×C151C2211yescharacteristic
23C22×C22⋊C4×C151C2212yes—
24C22×C22⋊C4×C151C2212yes—
25C22×C22⋊C4×C151C2212yes—
26C22×C22⋊C4×C151C2212yes—
27C22×C22⋊C4×C151C2212yes—
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2212yes—
31C22×C42×C151C2211yescharacteristic
32#392×C151—24no—
33#392×C151—24no—
34#392×C151—28no—
35#390×C151—24no—
36#386×C151—28no—
37C2×#95×C151C2211yescharacteristic
38C2×#95×C151C2211yescharacteristic
39C2×#95×C151C2212yes—
40C2×#95×C151C2212yes—
41C2×#95×C151C2212yes—
42C2×#95×C151C2212yes—
43C25×C151C2311yescharacteristic
44C25×C151C2312yes—
45C25×C151C2311yescharacteristic
46C22×D4×C151—22no—
47C22×D4×C151—22no—
48C22×D4×C151—24no—
49C22×D4×C151—22no—
50C22×D4×C151—22no—
51C22×D4×C151—24no—
52C22×D4×C151—24no—
53C22×D4×C151—22no—
54C22×D4×C151—22no—
55C22×D4×C151—24no—
56C22×D4×C151—24no—
57C22×D4×C151—24no—
58C22×D4×C151—24no—
59C22×D4×C151—24no—
60C22×D4×C151—24no—
61C22×D4×C151—24no—
62C22×D4×C151—42no—
63C22×D4×C151—42no—
64C22×D4×C151—42no—
65C22×D4×C151—42no—
66C22×D4×C151—42no—
67C22×D4×C151—42no—
68C22×D4×C151—42no—
69C22×D4×C151—42no—
70C23×C4×C151—22no—
71C23×C4×C151—22no—
72C23×C4×C151—22no—
73C23×C4×C151—24no—
74C23×C4×C151—42no—
75C23×C4×C151C2312yes—
76C23×C4×C151C2312yes—
77C23×C4×C151C2311yescharacteristic
78C23×C4×C151C2311yescharacteristic
79C23×C4×C151C2311yescharacteristic
80C23×C4×C151C2311yescharacteristic
81C23×C4×C151C2312yes—
82C23×C4×C151C2311yescharacteristic
83#123×C151—232no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—22no—
88C2×C4⋊C4×C151—22no—
89C2×C4⋊C4×C151D414yescomplemented
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—22no—
93C2×C22⋊C4×C151—22no—
94C2×C22⋊C4×C151—22no—
95C2×C22⋊C4×C151—22no—
96C2×C22⋊C4×C151—24no—
97C2×C22⋊C4×C151—24no—
98C2×C22⋊C4×C151—24no—
99C2×C22⋊C4×C151—24no—
100C2×C22⋊C4×C151—24no—
101C2×C22⋊C4×C151—24no—
102C2×C22⋊C4×C151—24no—
103C2×C22⋊C4×C151—24no—
104C2×C22⋊C4×C151—24no—
105C2×C22⋊C4×C151—24no—
106C2×C22⋊C4×C151—22no—
107C2×C22⋊C4×C151—42no—
108C2×C22⋊C4×C151—42no—
109C2×C22⋊C4×C151—42no—
110C2×C22⋊C4×C151—42no—
111C2×C22⋊C4×C151—42no—
112C2×C22⋊C4×C151—42no—
113C2×C22⋊C4×C151—42no—
114C2×C22⋊C4×C151D414yescomplemented
115C2×C22⋊C4×C151D414yescomplemented
116C2×C22⋊C4×C151D418yescomplemented
117C2×C42×C151—22no—
118C2×C42×C151—42no—
119#95×C151—24no—
120#95×C151—24no—
121#95×C151—24no—
122#95×C151—22no—
123#95×C151—22no—
124#95×C151—42no—
125C24×C151—21no—
126C24×C151—21no—
127C24×C151—22no—
128C24×C151—22no—
129C24×C151—22no—
130C24×C151—22no—
131C24×C151—22no—
132C24×C151—21no—
133C24×C151—21no—
134C24×C151—22no—
135C24×C151—22no—
136C24×C151—22no—
137C24×C151—22no—
138C24×C151—22no—
139C24×C151—22no—
140C24×C151—22no—
141C24×C151—22no—
142C24×C151—22no—
143C24×C151—22no—
144C24×C151—22no—
145C24×C151—22no—
146C24×C151—22no—
147C24×C151—22no—
148C24×C151—22no—
149C24×C151—22no—
150C24×C151—22no—
151C24×C151—22no—
152C24×C151—22no—
153C24×C151—22no—
154C24×C151C2×D412yes—
155C24×C151C2×D412yes—
156C24×C151C2×D414yes—
157C24×C151#4114yes—
158C24×C151C2411yescharacteristic
159C2×D4×C151—28no—
160C2×D4×C151—28no—
161C2×D4×C151—216no—
162C2×D4×C151—48no—
163C2×D4×C151—48no—
164C2×D4×C151—48no—
165C2×D4×C151—48no—
166C2×D4×C151—48no—
167C2×D4×C151—48no—
168C2×D4×C151—48no—
169C2×D4×C151—44no—
170C2×D4×C151—48no—
171C2×D4×C151—48no—
172C2×D4×C151—48no—
173C2×D4×C151—48no—
174C2×D4×C151—48no—
175C2×D4×C151—48no—
176C2×D4×C151—44no—
177C2×D4×C151—48no—
178C2×D4×C151—48no—
179C2×D4×C151—48no—
180C2×D4×C151—48no—
181C2×D4×C151—44no—
182C2×D4×C151—44no—
183C22×C4×C151—22no—
184C22×C4×C151—22no—
185C22×C4×C151—28no—
186C22×C4×C151—22no—
187C22×C4×C151—22no—
188C22×C4×C151—22no—
189C22×C4×C151—22no—
190C22×C4×C151—22no—
191C22×C4×C151—22no—
192C22×C4×C151—22no—
193C22×C4×C151—22no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—22no—
203C22×C4×C151—22no—
204C22×C4×C151—22no—
205C22×C4×C151—22no—
206C22×C4×C151—22no—
207C22×C4×C151—22no—
208C22×C4×C151—22no—
209C22×C4×C151—22no—
210C22×C4×C151—22no—
211C22×C4×C151—22no—
212C22×C4×C151—22no—
213C22×C4×C151—22no—
214C22×C4×C151—22no—
215C22×C4×C151—22no—
216C22×C4×C151—22no—
217C22×C4×C151—22no—
218C22×C4×C151—22no—
219C22×C4×C151—22no—
220C22×C4×C151—48no—
221C22×C4×C151—48no—
222C22×C4×C151—44no—
223C22×C4×C151—44no—
224C22×C4×C151C2×D414yes—
225C22×C4×C151C2×D414yes—
226C22×C4×C151C2×D412yes—
227C22×C4×C151C2×D412yes—
228C22×C4×C151C2×D412yes—
229C22×C4×C151C2×D412yes—
230C22×C4×C151C2×D412yes—
231C22×C4×C151C2×D412yes—
232C22×C4×C151C2×D412yes—
233C22×C4×C151#4114yes—
234C4⋊C4×C151—28no—
235C4⋊C4×C151—28no—
236C22⋊C4×C151—28no—
237C22⋊C4×C151—28no—
238C22⋊C4×C151—28no—
239C22⋊C4×C151—48no—
240C22⋊C4×C151—48no—
241C22⋊C4×C151—48no—
242C22⋊C4×C151—48no—
243C22⋊C4×C151—48no—
244C22⋊C4×C151—48no—
245C42×C151—44no—
246C23×C151—22no—
247C23×C151—24no—
248C23×C151—24no—
249C23×C151—22no—
250C23×C151—24no—
251C23×C151—24no—
252C23×C151—24no—
253C23×C151—24no—
254C23×C151—24no—
255C23×C151—24no—
256C23×C151—22no—
257C23×C151—24no—
258C23×C151—24no—
259C23×C151—22no—
260C23×C151—22no—
261C23×C151—24no—
262C23×C151—24no—
263C23×C151—24no—
264C23×C151—24no—
265C23×C151—24no—
266C23×C151—24no—
267C23×C151—24no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—42no—
273C23×C151—42no—
274C23×C151—42no—
275C23×C151—42no—
276C23×C151—42no—
277C23×C151—42no—
278C23×C151—42no—
279C23×C151—41no—
280C23×C151—42no—
281C23×C151—42no—
282C23×C151—41no—
283C23×C151—42no—
284C23×C151—42no—
285C23×C151—42no—
286C23×C151—42no—
287C23×C151—42no—
288C23×C151—41no—
289C23×C151—42no—
290C23×C151—42no—
291C23×C151—42no—
292C23×C151—41no—
293C23×C151—42no—
294C23×C151—42no—
295C23×C151—42no—
296C23×C151—42no—
297C23×C151—42no—
298C23×C151—42no—
299C23×C151—42no—
300C23×C151—42no—
301C23×C151—42no—
302C23×C151—42no—
303C23×C151—42no—
304C23×C151—42no—
305C23×C151—42no—
306C23×C151—42no—
307C23×C151—42no—
308C23×C151—42no—
309C23×C151—42no—
310C23×C151—42no—
311C23×C151—42no—
312C23×C151—42no—
313C23×C151—42no—
314C23×C151—42no—
315C23×C151—42no—
316C23×C151—42no—
317C23×C151—42no—
318C23×C151—42no—
319C23×C151—42no—
320C23×C151—42no—
321C23×C151—42no—
322C23×C151#12714yes—
323C23×C151C22×D411yescharacteristic
324C23×C151C22×D411yescharacteristic
325C23×C151C22×D411yescharacteristic
326C23×C151C22×D412yes—
327C23×C151C2×#4112yes—
328C23×C151C2×#4112yes—
329C23×C151H(5,𝔽2)12yes—
330C23×C151H(5,𝔽2)12yes—
331C23×C151H(5,𝔽2)12yes—
332D4×C151—416no—
333D4×C151—416no—
334D4×C151—432no—
335D4×C151—432no—
336C2×C4×C151—22no—
337C2×C4×C151—22no—
338C2×C4×C151—24no—
339C2×C4×C151—24no—
340C2×C4×C151—22no—
341C2×C4×C151—22no—
342C2×C4×C151—22no—
343C2×C4×C151—22no—
344C2×C4×C151—24no—
345C2×C4×C151—24no—
346C2×C4×C151—24no—
347C2×C4×C151—24no—
348C2×C4×C151—24no—
349C2×C4×C151—24no—
350C2×C4×C151—24no—
351C2×C4×C151—24no—
352C2×C4×C151—24no—
353C2×C4×C151—24no—
354C2×C4×C151—24no—
355C2×C4×C151—24no—
356C2×C4×C151—24no—
357C2×C4×C151—416no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—42no—
362C2×C4×C151—41no—
363C2×C4×C151—42no—
364C2×C4×C151—42no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—42no—
369C2×C4×C151—41no—
370C2×C4×C151—42no—
371C2×C4×C151—42no—
372C2×C4×C151—42no—
373C2×C4×C151—42no—
374C2×C4×C151—42no—
375C2×C4×C151—42no—
376C2×C4×C151—42no—
377C2×C4×C151—42no—
378C2×C4×C151—42no—
379C2×C4×C151—42no—
380C2×C4×C151—42no—
381C2×C4×C151—42no—
382C2×C4×C151#12014yes—
383C22×C151—24no—
384C22×C151—28no—
385C22×C151—42no—
386C22×C151—44no—
387C22×C151—44no—
388C22×C151—42no—
389C22×C151—44no—
390C22×C151—44no—
391C22×C151—44no—
392C22×C151—44no—
393C22×C151—42no—
394C22×C151—44no—
395C22×C151—44no—
396C22×C151—42no—
397C22×C151—42no—
398C22×C151—44no—
399C22×C151—44no—
400C22×C151—44no—
401C22×C151—44no—
402C22×C151—44no—
403C22×C151—44no—
404C22×C151—82no—
405C22×C151—82no—
406C22×C151—82no—
407C22×C151—82no—
408C22×C151—82no—
409C22×C151—82no—
410C22×C151—82no—
411C22×C151—82no—
412C22×C151—82no—
413C22×C151—82no—
414C22×C151—82no—
415C22×C151—82no—
416C22×C151C2×#12011yescharacteristic
417C22×C151#52511yescharacteristic
418C22×C151#52512yes—
419C22×C151C2×#12711yescharacteristic
420C22×C151#53211yescharacteristic
421C22×C151#53412yes—
422C22×C151#53511yescharacteristic
423C22×C151#53511yescharacteristic
424C22×C151#53511yescharacteristic
425C22×C151#53812yes—
426C22×C151#54012yes—
427C22×C151D4212yes—
428C22×C151D4212yes—
429C22×C151#54612yes—
430C22×C151#54612yes—
431C22×C151#54612yes—
432C22×C151#54612yes—
433C22×C151#54612yes—
434C22×C151#55012yes—
435C22×C151#55312yes—
436C22×C151#56012yes—
437C4×C151—24no—
438C4×C151—44no—
439C4×C151—44no—
440C4×C151—42no—
441C4×C151—42no—
442C4×C151—42no—
443C4×C151—42no—
444C4×C151—44no—
445C2×C151—44no—
446C2×C151—84no—
447C2×C151—82no—
448C2×C151#240411yescharacteristic
449C2×C151#243111yescharacteristic
450C2×C151#243311yescharacteristic
451C2×C151#245612yes—
452C2×C151#246412yes—
453C2×C151#253912yes—
454C2×C151#267312yes—
455C2×C151#267812yes—
456C2×C151#270312yes—
457#15412C15111yesmaximal, characteristic, direct product factor, Sylow
458C151#1541211yescharacteristic, direct product factor, Sylow
459C22×#123C2×C15111yescharacteristic, complemented
460C2×#392C2×C15112yescomplemented
461C2×#392C2×C15111yescharacteristic, complemented
462C2×#392C2×C15111yescharacteristic, complemented
463C2×#390C2×C15111yescharacteristic, complemented
464C2×#386C2×C15112yescomplemented
465#1445C2×C15111yescharacteristic, complemented
466#1439C2×C15112yescomplemented
467#1438C2×C15112yescomplemented
468#1437C2×C15111yescharacteristic, complemented
469#1437C2×C15111yescharacteristic, complemented
470C23×D4C22×C15111yescharacteristic
471C23×D4C22×C15112yes—
472C23×D4C22×C15111yescharacteristic
473C23×D4C22×C15112yes—
474C24×C4C22×C15111yescharacteristic
475C2×#123—24no—
476C2×#123—24no—
477C2×#123—24no—
478C22×C4⋊C4C22×C15111yescharacteristic
479C22×C4⋊C4C22×C15111yescharacteristic
480C22×C22⋊C4C22×C15111yescharacteristic
481C22×C22⋊C4C22×C15112yes—
482C22×C22⋊C4C22×C15112yes—
483C22×C22⋊C4C22×C15112yes—
484C22×C22⋊C4C22×C15112yes—
485C22×C22⋊C4C22×C15112yes—
486C22×C22⋊C4C22×C15111yescharacteristic
487C22×C22⋊C4C22×C15111yescharacteristic
488C22×C22⋊C4C22×C15112yes—
489C22×C42C22×C15111yescharacteristic
490#392—24no—
491#392—24no—
492#392—28no—
493#390—24no—
494#386—28no—
495C2×#95C22×C15111yescharacteristic
496C2×#95C22×C15111yescharacteristic
497C2×#95C22×C15112yes—
498C2×#95C22×C15112yes—
499C2×#95C22×C15112yes—
500C2×#95C22×C15112yes—
501C25C23×C15112yes—
502C25C23×C15111yescharacteristic
503C25C23×C15111yescharacteristic
504C22×D4—24no—
505C22×D4—24no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—24no—
513C22×D4—24no—
514C22×D4—24no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—24no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—42no—
521C22×D4—42no—
522C22×D4—42no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4—42no—
528C23×C4—22no—
529C23×C4—22no—
530C23×C4—22no—
531C23×C4—24no—
532C23×C4—42no—
533C23×C4C23×C15112yes—
534C23×C4C23×C15111yescharacteristic
535C23×C4C23×C15112yes—
536C23×C4C23×C15111yescharacteristic
537C23×C4C23×C15111yescharacteristic
538C23×C4C23×C15111yescharacteristic
539C23×C4C23×C15112yes—
540C23×C4C23×C15111yescharacteristic
541#123—232no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4D4×C15114yescomplemented
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4D4×C15114yescomplemented
573C2×C22⋊C4D4×C15114yescomplemented
574C2×C22⋊C4D4×C15118yescomplemented
575C2×C42—22no—
576C2×C42—42no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—22no—
581#95—22no—
582#95—42no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—21no—
591C24—21no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24C2×D4×C15112yes—
613C24C2×D4×C15112yes—
614C24C2×D4×C15114yes—
615C24#41×C15114yes—
616C24C24×C15111yescharacteristic
617C2×D4—28no—
618C2×D4—28no—
619C2×D4—216no—
620C2×D4—48no—
621C2×D4—48no—
622C2×D4—48no—
623C2×D4—48no—
624C2×D4—48no—
625C2×D4—48no—
626C2×D4—48no—
627C2×D4—44no—
628C2×D4—48no—
629C2×D4—48no—
630C2×D4—48no—
631C2×D4—48no—
632C2×D4—48no—
633C2×D4—48no—
634C2×D4—44no—
635C2×D4—48no—
636C2×D4—48no—
637C2×D4—48no—
638C2×D4—44no—
639C2×D4—48no—
640C2×D4—44no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—28no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—48no—
679C22×C4—48no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4C2×D4×C15114yes—
683C22×C4C2×D4×C15114yes—
684C22×C4C2×D4×C15112yes—
685C22×C4C2×D4×C15112yes—
686C22×C4C2×D4×C15112yes—
687C22×C4C2×D4×C15112yes—
688C22×C4C2×D4×C15112yes—
689C22×C4C2×D4×C15112yes—
690C22×C4C2×D4×C15112yes—
691C22×C4#41×C15114yes—
692C4⋊C4—28no—
693C4⋊C4—28no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—48no—
698C22⋊C4—48no—
699C22⋊C4—48no—
700C22⋊C4—48no—
701C22⋊C4—48no—
702C22⋊C4—48no—
703C42—44no—
704C23—22no—
705C23—24no—
706C23—24no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—41no—
749C23—41no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23#127×C15114yes—
781C23C22×D4×C15111yescharacteristic
782C23C22×D4×C15111yescharacteristic
783C23C22×D4×C15111yescharacteristic
784C23C22×D4×C15112yes—
785C23C2×#41×C15112yes—
786C23C2×#41×C15112yes—
787C23H(5,𝔽2)×C15112yes—
788C23H(5,𝔽2)×C15112yes—
789C23H(5,𝔽2)×C15112yes—
790D4—416no—
791D4—416no—
792D4—432no—
793D4—432no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—416no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4#120×C15114yes—
841C22—24no—
842C22—28no—
843C22—42no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—42no—
852C22—44no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22C2×#120×C15111yescharacteristic
875C22#525×C15111yescharacteristic
876C22#525×C15112yes—
877C22C2×#127×C15111yescharacteristic
878C22#532×C15111yescharacteristic
879C22#534×C15112yes—
880C22#535×C15111yescharacteristic
881C22#535×C15111yescharacteristic
882C22#535×C15111yescharacteristic
883C22#538×C15112yes—
884C22#540×C15112yes—
885C22D42×C15112yes—
886C22D42×C15112yes—
887C22#546×C15112yes—
888C22#546×C15112yes—
889C22#546×C15112yes—
890C22#546×C15112yes—
891C22#546×C15112yes—
892C22#550×C15112yes—
893C22#553×C15112yes—
894C22#560×C15112yes—
895C4—24no—
896C4—44no—
897C4—44no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—42no—
902C4—44no—
903C2—44no—
904C2—84no—
905C2—82no—
906C2#2404×C15111yescharacteristic
907C2#2431×C15111yescharacteristic
908C2#2433×C15111yescharacteristic
909C2#2456×C15112yes—
910C2#2464×C15112yes—
911C2#2539×C15112yes—
912C2#2673×C15112yes—
913C2#2678×C15112yes—
914C2#2703×C15112yes—
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C151C2semidirect
2. C2×#392×C151C2semidirect
3. C2×#392×C151C2semidirect
4. C2×#392×C151C2semidirect
5. C2×#390×C151C2semidirect
6. C2×#386×C151C2semidirect
7. #1445×C151C2semidirect
8. #1439×C151C2semidirect
9. #1438×C151C2semidirect
10. #1437×C151C2semidirect
11. #1437×C151C2semidirect
89. C2×C4⋊C4×C151D4semidirect
114. C2×C22⋊C4×C151D4semidirect
115. C2×C22⋊C4×C151D4semidirect
116. C2×C22⋊C4×C151D4semidirect
457. #15412C151direct (N × H)
458. C151#15412direct (N × H)
459. C22×#123C2×C151semidirect
460. C2×#392C2×C151semidirect
461. C2×#392C2×C151semidirect
462. C2×#392C2×C151semidirect
463. C2×#390C2×C151semidirect
464. C2×#386C2×C151semidirect
465. #1445C2×C151semidirect
466. #1439C2×C151semidirect
467. #1438C2×C151semidirect
468. #1437C2×C151semidirect
469. #1437C2×C151semidirect
547. C2×C4⋊C4D4×C151semidirect
572. C2×C22⋊C4D4×C151semidirect
573. C2×C22⋊C4D4×C151semidirect
574. C2×C22⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1512
C2×#392×C1512
C2×#390×C1512
C2×#386×C1512
#1445×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#15412151