Finite Group Databasebeta

← C151×#15310 #50320235

Subgroups — C151×#15310 #50320235

Order 38656.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#127×C151C211yesmaximal, characteristic, complemented
2C22×#121×C151C211yesmaximal, characteristic, complemented
3C2×#394×C151C211yesmaximal, characteristic, complemented
4C2×#392×C151C212yesmaximal, complemented
5C2×#392×C151C211yesmaximal, characteristic, complemented
6C2×#392×C151C212yesmaximal, complemented
7C2×#386×C151C212yesmaximal, complemented
8#1438×C151C211yesmaximal, characteristic, complemented
9#1438×C151C212yesmaximal, complemented
10#1437×C151C211yesmaximal, characteristic, complemented
11#1436×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14C23×D4×C151C2211yescharacteristic
15C23×D4×C151C2212yes—
16C23×D4×C151C2212yes—
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2212yes—
19C24×C4×C151C2211yescharacteristic
20C2×#127×C151—28no—
21C2×#127×C151—24no—
22C2×#121×C151—24no—
23C2×#121×C151—24no—
24C2×#121×C151—24no—
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C22⋊C4×C151C2212yes—
27C22×C22⋊C4×C151C2212yes—
28C22×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2212yes—
30C22×C22⋊C4×C151C2212yes—
31C22×C22⋊C4×C151C2212yes—
32C22×C22⋊C4×C151C2211yescharacteristic
33C22×C22⋊C4×C151C2212yes—
34C22×C42×C151C2211yescharacteristic
35#394×C151—24no—
36#392×C151—28no—
37#392×C151—24no—
38#392×C151—28no—
39#386×C151—28no—
40C2×#95×C151C2211yescharacteristic
41C2×#95×C151C2212yes—
42C2×#95×C151C2211yescharacteristic
43C2×#95×C151C2212yes—
44C2×#95×C151C2212yes—
45C25×C151C2312yes—
46C25×C151C2311yescharacteristic
47C25×C151C2311yescharacteristic
48C25×C151C2311yescharacteristic
49C22×D4×C151—24no—
50C22×D4×C151—22no—
51C22×D4×C151—22no—
52C22×D4×C151—22no—
53C22×D4×C151—22no—
54C22×D4×C151—22no—
55C22×D4×C151—24no—
56C22×D4×C151—24no—
57C22×D4×C151—22no—
58C22×D4×C151—24no—
59C22×D4×C151—24no—
60C22×D4×C151—22no—
61C22×D4×C151—24no—
62C22×D4×C151—24no—
63C22×D4×C151—22no—
64C22×D4×C151—22no—
65C22×D4×C151—22no—
66C22×D4×C151—22no—
67C22×D4×C151—24no—
68C22×D4×C151—24no—
69C22×D4×C151—24no—
70C22×D4×C151—24no—
71C22×D4×C151—24no—
72C22×D4×C151—24no—
73C22×D4×C151—24no—
74C22×D4×C151—24no—
75C22×D4×C151—24no—
76C22×D4×C151—42no—
77C22×D4×C151—42no—
78C22×D4×C151—42no—
79C22×D4×C151—42no—
80C22×D4×C151—42no—
81C22×D4×C151—42no—
82C22×D4×C151—42no—
83C22×D4×C151—42no—
84C22×D4×C151—42no—
85C22×D4×C151—42no—
86C22×D4×C151—42no—
87C22×D4×C151—42no—
88C22×D4×C151D418yescomplemented
89C22×D4×C151D414yescomplemented
90C23×C4×C151—22no—
91C23×C4×C151—22no—
92C23×C4×C151—24no—
93C23×C4×C151—22no—
94C23×C4×C151—42no—
95C23×C4×C151C2312yes—
96C23×C4×C151C2312yes—
97C23×C4×C151C2311yescharacteristic
98C23×C4×C151C2311yescharacteristic
99C23×C4×C151C2311yescharacteristic
100C23×C4×C151C2311yescharacteristic
101C23×C4×C151C2312yes—
102#127×C151—232no—
103#121×C151—232no—
104C2×C4⋊C4×C151—22no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151D414yescomplemented
107C2×C22⋊C4×C151—22no—
108C2×C22⋊C4×C151—22no—
109C2×C22⋊C4×C151—22no—
110C2×C22⋊C4×C151—22no—
111C2×C22⋊C4×C151—24no—
112C2×C22⋊C4×C151—24no—
113C2×C22⋊C4×C151—24no—
114C2×C22⋊C4×C151—24no—
115C2×C22⋊C4×C151—24no—
116C2×C22⋊C4×C151—24no—
117C2×C22⋊C4×C151—24no—
118C2×C22⋊C4×C151—24no—
119C2×C22⋊C4×C151—24no—
120C2×C22⋊C4×C151—24no—
121C2×C22⋊C4×C151—24no—
122C2×C22⋊C4×C151—22no—
123C2×C22⋊C4×C151—24no—
124C2×C22⋊C4×C151—24no—
125C2×C22⋊C4×C151—42no—
126C2×C22⋊C4×C151—42no—
127C2×C22⋊C4×C151—42no—
128C2×C22⋊C4×C151—42no—
129C2×C22⋊C4×C151—42no—
130C2×C22⋊C4×C151D414yescomplemented
131C2×C42×C151—22no—
132C2×C42×C151—24no—
133#95×C151—24no—
134#95×C151—22no—
135#95×C151—24no—
136#95×C151—22no—
137#95×C151D418yescomplemented
138C24×C151—22no—
139C24×C151—21no—
140C24×C151—21no—
141C24×C151—22no—
142C24×C151—22no—
143C24×C151—22no—
144C24×C151—22no—
145C24×C151—22no—
146C24×C151—22no—
147C24×C151—21no—
148C24×C151—21no—
149C24×C151—21no—
150C24×C151—21no—
151C24×C151—22no—
152C24×C151—22no—
153C24×C151—22no—
154C24×C151—22no—
155C24×C151—22no—
156C24×C151—22no—
157C24×C151—22no—
158C24×C151—22no—
159C24×C151—22no—
160C24×C151—22no—
161C24×C151—22no—
162C24×C151—22no—
163C24×C151—22no—
164C24×C151—22no—
165C24×C151—22no—
166C24×C151—22no—
167C24×C151—22no—
168C24×C151—22no—
169C24×C151—22no—
170C24×C151—22no—
171C24×C151—22no—
172C24×C151—22no—
173C24×C151—22no—
174C24×C151—22no—
175C24×C151C2×D412yes—
176C24×C151C2×D414yes—
177C24×C151C2×D412yes—
178C24×C151C2×D414yes—
179C24×C151C2×D412yes—
180C24×C151C2411yescharacteristic
181C2×D4×C151—28no—
182C2×D4×C151—28no—
183C2×D4×C151—28no—
184C2×D4×C151—216no—
185C2×D4×C151—216no—
186C2×D4×C151—28no—
187C2×D4×C151—28no—
188C2×D4×C151—216no—
189C2×D4×C151—48no—
190C2×D4×C151—44no—
191C2×D4×C151—48no—
192C2×D4×C151—48no—
193C2×D4×C151—48no—
194C2×D4×C151—48no—
195C2×D4×C151—48no—
196C2×D4×C151—48no—
197C2×D4×C151—48no—
198C2×D4×C151—48no—
199C2×D4×C151—48no—
200C2×D4×C151—48no—
201C2×D4×C151—48no—
202C2×D4×C151—48no—
203C2×D4×C151—48no—
204C2×D4×C151—48no—
205C2×D4×C151—48no—
206C2×D4×C151—48no—
207C2×D4×C151—48no—
208C2×D4×C151—44no—
209C2×D4×C151—48no—
210C2×D4×C151—44no—
211C2×D4×C151—48no—
212C2×D4×C151—48no—
213C2×D4×C151—48no—
214C2×D4×C151—44no—
215C2×D4×C151—48no—
216C2×D4×C151—48no—
217C2×D4×C151—48no—
218C2×D4×C151—44no—
219C2×D4×C151—44no—
220C2×D4×C151—48no—
221C2×D4×C151—44no—
222C22×C4×C151—22no—
223C22×C4×C151—22no—
224C22×C4×C151—22no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—22no—
228C22×C4×C151—22no—
229C22×C4×C151—22no—
230C22×C4×C151—22no—
231C22×C4×C151—28no—
232C22×C4×C151—22no—
233C22×C4×C151—22no—
234C22×C4×C151—22no—
235C22×C4×C151—22no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—22no—
241C22×C4×C151—22no—
242C22×C4×C151—22no—
243C22×C4×C151—22no—
244C22×C4×C151—22no—
245C22×C4×C151—22no—
246C22×C4×C151—22no—
247C22×C4×C151—22no—
248C22×C4×C151—22no—
249C22×C4×C151—22no—
250C22×C4×C151—22no—
251C22×C4×C151—22no—
252C22×C4×C151—22no—
253C22×C4×C151—48no—
254C22×C4×C151—48no—
255C22×C4×C151—44no—
256C22×C4×C151—44no—
257C22×C4×C151C2×D414yes—
258C22×C4×C151C2×D412yes—
259C22×C4×C151C2×D412yes—
260C22×C4×C151C2×D412yes—
261C22×C4×C151C2×D412yes—
262C22×C4×C151C2×D412yes—
263C22×C4×C151C2×D414yes—
264C22×C4×C151C2×D414yes—
265C22×C4×C151C2×D414yes—
266C22×C4×C151C2×D412yes—
267C22×C4×C151#4114yes—
268C4⋊C4×C151—28no—
269C22⋊C4×C151—28no—
270C22⋊C4×C151—28no—
271C22⋊C4×C151—48no—
272C22⋊C4×C151—48no—
273C22⋊C4×C151—48no—
274C22⋊C4×C151—48no—
275C22⋊C4×C151—48no—
276C22⋊C4×C151—48no—
277C42×C151—28no—
278C23×C151—22no—
279C23×C151—24no—
280C23×C151—24no—
281C23×C151—22no—
282C23×C151—24no—
283C23×C151—24no—
284C23×C151—24no—
285C23×C151—24no—
286C23×C151—24no—
287C23×C151—24no—
288C23×C151—22no—
289C23×C151—22no—
290C23×C151—22no—
291C23×C151—24no—
292C23×C151—24no—
293C23×C151—22no—
294C23×C151—22no—
295C23×C151—24no—
296C23×C151—22no—
297C23×C151—24no—
298C23×C151—24no—
299C23×C151—24no—
300C23×C151—24no—
301C23×C151—24no—
302C23×C151—24no—
303C23×C151—24no—
304C23×C151—24no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—42no—
309C23×C151—41no—
310C23×C151—42no—
311C23×C151—42no—
312C23×C151—42no—
313C23×C151—42no—
314C23×C151—42no—
315C23×C151—41no—
316C23×C151—42no—
317C23×C151—42no—
318C23×C151—42no—
319C23×C151—42no—
320C23×C151—42no—
321C23×C151—41no—
322C23×C151—41no—
323C23×C151—42no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151—42no—
327C23×C151—42no—
328C23×C151—42no—
329C23×C151—42no—
330C23×C151—42no—
331C23×C151—41no—
332C23×C151—42no—
333C23×C151—42no—
334C23×C151—42no—
335C23×C151—42no—
336C23×C151—42no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—42no—
340C23×C151—42no—
341C23×C151—42no—
342C23×C151—42no—
343C23×C151—42no—
344C23×C151—42no—
345C23×C151—42no—
346C23×C151—42no—
347C23×C151—42no—
348C23×C151—42no—
349C23×C151—42no—
350C23×C151—42no—
351C23×C151—42no—
352C23×C151—42no—
353C23×C151—42no—
354C23×C151—42no—
355C23×C151—42no—
356C23×C151—42no—
357C23×C151—42no—
358C23×C151—42no—
359C23×C151—42no—
360C23×C151—42no—
361C23×C151—42no—
362C23×C151—42no—
363C23×C151—42no—
364C23×C151—42no—
365C23×C151—42no—
366C23×C151—42no—
367C23×C151—42no—
368C23×C151—42no—
369C23×C151—42no—
370C23×C151—42no—
371C23×C151—42no—
372C23×C151—42no—
373C23×C151—42no—
374C23×C151—42no—
375C23×C151#12014yes—
376C23×C151C22×D411yescharacteristic
377C23×C151C22×D412yes—
378C23×C151C22×D411yescharacteristic
379C23×C151C22×D411yescharacteristic
380C23×C151C22×D412yes—
381C23×C151C2×#4112yes—
382C23×C151H(5,𝔽2)12yes—
383C23×C151H(5,𝔽2)12yes—
384C23×C151H(5,𝔽2)12yes—
385D4×C151—416no—
386D4×C151—432no—
387D4×C151—416no—
388D4×C151—432no—
389D4×C151—416no—
390D4×C151—416no—
391D4×C151—432no—
392C2×C4×C151—22no—
393C2×C4×C151—24no—
394C2×C4×C151—22no—
395C2×C4×C151—22no—
396C2×C4×C151—24no—
397C2×C4×C151—22no—
398C2×C4×C151—24no—
399C2×C4×C151—24no—
400C2×C4×C151—24no—
401C2×C4×C151—24no—
402C2×C4×C151—24no—
403C2×C4×C151—24no—
404C2×C4×C151—24no—
405C2×C4×C151—24no—
406C2×C4×C151—22no—
407C2×C4×C151—22no—
408C2×C4×C151—24no—
409C2×C4×C151—24no—
410C2×C4×C151—24no—
411C2×C4×C151—24no—
412C2×C4×C151—24no—
413C2×C4×C151—416no—
414C2×C4×C151—41no—
415C2×C4×C151—41no—
416C2×C4×C151—41no—
417C2×C4×C151—42no—
418C2×C4×C151—41no—
419C2×C4×C151—42no—
420C2×C4×C151—42no—
421C2×C4×C151—42no—
422C2×C4×C151—42no—
423C2×C4×C151—42no—
424C2×C4×C151—42no—
425C2×C4×C151—42no—
426C2×C4×C151—42no—
427C2×C4×C151—42no—
428C2×C4×C151—42no—
429C2×C4×C151—42no—
430C2×C4×C151—42no—
431C2×C4×C151#12014yes—
432C2×C4×C151#12118yescomplemented
433C2×C4×C151#12714yescomplemented
434C22×C151—24no—
435C22×C151—28no—
436C22×C151—44no—
437C22×C151—44no—
438C22×C151—44no—
439C22×C151—44no—
440C22×C151—42no—
441C22×C151—42no—
442C22×C151—44no—
443C22×C151—42no—
444C22×C151—44no—
445C22×C151—42no—
446C22×C151—44no—
447C22×C151—44no—
448C22×C151—44no—
449C22×C151—44no—
450C22×C151—44no—
451C22×C151—44no—
452C22×C151—44no—
453C22×C151—44no—
454C22×C151—44no—
455C22×C151—42no—
456C22×C151—42no—
457C22×C151—42no—
458C22×C151—42no—
459C22×C151—44no—
460C22×C151—82no—
461C22×C151—82no—
462C22×C151—82no—
463C22×C151—82no—
464C22×C151—82no—
465C22×C151—82no—
466C22×C151—82no—
467C22×C151—82no—
468C22×C151—82no—
469C22×C151—82no—
470C22×C151—82no—
471C22×C151—82no—
472C22×C151—82no—
473C22×C151—82no—
474C22×C151—82no—
475C22×C151—82no—
476C22×C151C2×#12011yescharacteristic
477C22×C151C2×#12011yescharacteristic
478C22×C151C2×#12112yes—
479C22×C151C2×#12711yescharacteristic
480C22×C151#53211yescharacteristic
481C22×C151#53411yescharacteristic
482C22×C151#53412yes—
483C22×C151#53511yescharacteristic
484C22×C151#53512yes—
485C22×C151#53511yescharacteristic
486C22×C151#54012yes—
487C22×C151D4212yes—
488C22×C151D4212yes—
489C22×C151D4212yes—
490C22×C151D4212yes—
491C22×C151D4212yes—
492C22×C151#54612yes—
493C22×C151#54612yes—
494C22×C151#55012yes—
495C22×C151#55012yes—
496C22×C151#56012yes—
497C4×C151—24no—
498C4×C151—28no—
499C4×C151—24no—
500C4×C151—42no—
501C4×C151—44no—
502C4×C151—42no—
503C4×C151—82no—
504C2×C151—44no—
505C2×C151—84no—
506C2×C151—82no—
507C2×C151—82no—
508C2×C151#240311yescharacteristic
509C2×C151#241012yes—
510C2×C151#242812yes—
511C2×C151#243111yescharacteristic
512C2×C151#243311yescharacteristic
513C2×C151#254112yes—
514C2×C151#266912yes—
515C2×C151#267312yes—
516C2×C151#267312yes—
517#15310C15111yesmaximal, characteristic, direct product factor, Sylow
518C151#1531011yescharacteristic, direct product factor, Sylow
519C22×#127C2×C15111yescharacteristic, complemented
520C22×#121C2×C15111yescharacteristic, complemented
521C2×#394C2×C15111yescharacteristic, complemented
522C2×#392C2×C15112yescomplemented
523C2×#392C2×C15112yescomplemented
524C2×#392C2×C15111yescharacteristic, complemented
525C2×#386C2×C15112yescomplemented
526#1438C2×C15112yescomplemented
527#1438C2×C15111yescharacteristic, complemented
528#1437C2×C15111yescharacteristic, complemented
529#1436C2×C15111yescharacteristic, complemented
530C23×D4C22×C15111yescharacteristic
531C23×D4C22×C15111yescharacteristic
532C23×D4C22×C15111yescharacteristic
533C23×D4C22×C15112yes—
534C23×D4C22×C15112yes—
535C23×D4C22×C15111yescharacteristic
536C23×D4C22×C15112yes—
537C24×C4C22×C15111yescharacteristic
538C2×#127—24no—
539C2×#127—28no—
540C2×#121—24no—
541C2×#121—24no—
542C2×#121—24no—
543C22×C4⋊C4C22×C15111yescharacteristic
544C22×C22⋊C4C22×C15112yes—
545C22×C22⋊C4C22×C15112yes—
546C22×C22⋊C4C22×C15111yescharacteristic
547C22×C22⋊C4C22×C15112yes—
548C22×C22⋊C4C22×C15112yes—
549C22×C22⋊C4C22×C15112yes—
550C22×C22⋊C4C22×C15111yescharacteristic
551C22×C22⋊C4C22×C15112yes—
552C22×C42C22×C15111yescharacteristic
553#394—24no—
554#392—28no—
555#392—24no—
556#392—28no—
557#386—28no—
558C2×#95C22×C15112yes—
559C2×#95C22×C15111yescharacteristic
560C2×#95C22×C15111yescharacteristic
561C2×#95C22×C15112yes—
562C2×#95C22×C15112yes—
563C25C23×C15112yes—
564C25C23×C15111yescharacteristic
565C25C23×C15111yescharacteristic
566C25C23×C15111yescharacteristic
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—24no—
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—24no—
580C22×D4—24no—
581C22×D4—24no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—22no—
591C22×D4—24no—
592C22×D4—24no—
593C22×D4—22no—
594C22×D4—42no—
595C22×D4—42no—
596C22×D4—42no—
597C22×D4—42no—
598C22×D4—42no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4—42no—
602C22×D4—42no—
603C22×D4—42no—
604C22×D4—42no—
605C22×D4—42no—
606C22×D4D4×C15114yescomplemented
607C22×D4D4×C15118yescomplemented
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—24no—
612C23×C4—42no—
613C23×C4C23×C15112yes—
614C23×C4C23×C15111yescharacteristic
615C23×C4C23×C15111yescharacteristic
616C23×C4C23×C15112yes—
617C23×C4C23×C15112yes—
618C23×C4C23×C15111yescharacteristic
619C23×C4C23×C15111yescharacteristic
620#127—232no—
621#121—232no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4D4×C15114yescomplemented
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4—42no—
645C2×C22⋊C4—42no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4D4×C15114yescomplemented
649C2×C42—22no—
650C2×C42—24no—
651#95—24no—
652#95—22no—
653#95—24no—
654#95—22no—
655#95D4×C15118yescomplemented
656C24—22no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24C2×D4×C15112yes—
694C24C2×D4×C15114yes—
695C24C2×D4×C15112yes—
696C24C2×D4×C15114yes—
697C24C2×D4×C15112yes—
698C24C24×C15111yescharacteristic
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—44no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4C2×D4×C15114yes—
776C22×C4C2×D4×C15112yes—
777C22×C4C2×D4×C15112yes—
778C22×C4C2×D4×C15112yes—
779C22×C4C2×D4×C15112yes—
780C22×C4C2×D4×C15112yes—
781C22×C4C2×D4×C15114yes—
782C22×C4C2×D4×C15114yes—
783C22×C4C2×D4×C15114yes—
784C22×C4C2×D4×C15112yes—
785C22×C4#41×C15114yes—
786C4⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C42—28no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—22no—
812C23—24no—
813C23—22no—
814C23—22no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—41no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—41no—
840C23—41no—
841C23—42no—
842C23—41no—
843C23—42no—
844C23—41no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23#120×C15114yes—
894C23C22×D4×C15111yescharacteristic
895C23C22×D4×C15112yes—
896C23C22×D4×C15111yescharacteristic
897C23C22×D4×C15111yescharacteristic
898C23C22×D4×C15112yes—
899C23C2×#41×C15112yes—
900C23H(5,𝔽2)×C15112yes—
901C23H(5,𝔽2)×C15112yes—
902C23H(5,𝔽2)×C15112yes—
903D4—416no—
904D4—432no—
905D4—416no—
906D4—432no—
907D4—416no—
908D4—416no—
909D4—432no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C15114yes—
950C2×C4#121×C15118yescomplemented
951C2×C4#127×C15114yescomplemented
952C22—24no—
953C22—28no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—42no—
959C22—42no—
960C22—44no—
961C22—42no—
962C22—44no—
963C22—42no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—44no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—82no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22C2×#120×C15111yescharacteristic
995C22C2×#120×C15111yescharacteristic
996C22C2×#121×C15112yes—
997C22C2×#127×C15111yescharacteristic
998C22#532×C15111yescharacteristic
999C22#534×C15111yescharacteristic
1000C22#534×C15112yes—
1001C22#535×C15111yescharacteristic
1002C22#535×C15112yes—
1003C22#535×C15111yescharacteristic
1004C22#540×C15112yes—
1005C22D42×C15112yes—
1006C22D42×C15112yes—
1007C22D42×C15112yes—
1008C22D42×C15112yes—
1009C22D42×C15112yes—
1010C22#546×C15112yes—
1011C22#546×C15112yes—
1012C22#550×C15112yes—
1013C22#550×C15112yes—
1014C22#560×C15112yes—
1015C4—24no—
1016C4—28no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—42no—
1021C4—82no—
1022C2—44no—
1023C2—84no—
1024C2—82no—
1025C2—82no—
1026C2#2403×C15111yescharacteristic
1027C2#2410×C15112yes—
1028C2#2428×C15112yes—
1029C2#2431×C15111yescharacteristic
1030C2#2433×C15111yescharacteristic
1031C2#2541×C15112yes—
1032C2#2669×C15112yes—
1033C2#2673×C15112yes—
1034C2#2673×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×#127×C151C2semidirect
2. C22×#121×C151C2semidirect
3. C2×#394×C151C2semidirect
4. C2×#392×C151C2semidirect
5. C2×#392×C151C2semidirect
6. C2×#392×C151C2semidirect
7. C2×#386×C151C2semidirect
8. #1438×C151C2semidirect
9. #1438×C151C2semidirect
10. #1437×C151C2semidirect
11. #1436×C151C2semidirect
88. C22×D4×C151D4semidirect
89. C22×D4×C151D4semidirect
106. C2×C4⋊C4×C151D4semidirect
130. C2×C22⋊C4×C151D4semidirect
137. #95×C151D4semidirect
432. C2×C4×C151#121semidirect
433. C2×C4×C151#127semidirect
517. #15310C151direct (N × H)
518. C151#15310direct (N × H)
519. C22×#127C2×C151semidirect
520. C22×#121C2×C151semidirect
521. C2×#394C2×C151semidirect
522. C2×#392C2×C151semidirect
523. C2×#392C2×C151semidirect
524. C2×#392C2×C151semidirect
525. C2×#386C2×C151semidirect
526. #1438C2×C151semidirect
527. #1438C2×C151semidirect
528. #1437C2×C151semidirect
529. #1436C2×C151semidirect
606. C22×D4D4×C151semidirect
607. C22×D4D4×C151semidirect
624. C2×C4⋊C4D4×C151semidirect
648. C2×C22⋊C4D4×C151semidirect
655. #95D4×C151semidirect
950. C2×C4#121×C151semidirect
951. C2×C4#127×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C1512
C22×#121×C1512
C2×#394×C1512
C2×#392×C1512
C2×#386×C1512
#1438×C1512
#1437×C1512
#1436×C1512
#15310151