Finite Group Databasebeta

← C151×#15070 #50319995

Subgroups — C151×#15070 #50319995

Order 38656.

2038 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C151C211yesmaximal, characteristic
2C2×#395×C151C211yesmaximal, characteristic, complemented
3C2×#394×C151C211yesmaximal, characteristic
4C2×#388×C151C212yesmaximal, complemented
5C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
6#1446×C151C211yesmaximal, characteristic, complemented
7#1439×C151C212yesmaximal, complemented
8#1439×C151C212yesmaximal, complemented
9#1438×C151C211yesmaximal, characteristic
10#1437×C151C212yesmaximal, complemented
11#1434×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C23×D4×C151C2211yescharacteristic
14C2×#124×C151—28no—
15C2×#124×C151—24no—
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C22⋊C4×C151C2212yes—
24C22×C22⋊C4×C151C2212yes—
25C22×C42×C151C2211yescharacteristic
26C22×C42×C151C2211yescharacteristic
27C22×C42×C151C2211yescharacteristic
28#395×C151—24no—
29#394×C151—24no—
30#388×C151—28no—
31C4×C4⋊C4×C151—24no—
32C2×#95×C151C2211yescharacteristic
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2212yes—
35C2×#95×C151C2212yes—
36C2×#95×C151C2212yes—
37C2×#95×C151C2211yescharacteristic
38C2×#95×C151C2211yescharacteristic
39C2×#95×C151C2212yes—
40C2×#95×C151C2212yes—
41C25×C151C2312yes—
42C22×Q8×C151—24no—
43C22×Q8×C151—22no—
44C22×Q8×C151—22no—
45C22×Q8×C151—22no—
46C22×Q8×C151—42no—
47C22×D4×C151—22no—
48C22×D4×C151—22no—
49C22×D4×C151—22no—
50C22×D4×C151—24no—
51C22×D4×C151—42no—
52C23×C4×C151C2312yes—
53C23×C4×C151C2311yescharacteristic
54C23×C4×C151C2312yes—
55C23×C4×C151C2311yescharacteristic
56C23×C4×C151C2311yescharacteristic
57C23×C4×C151C2312yes—
58C23×C4×C151C2311yescharacteristic
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C23×C4×C151C2311yescharacteristic
62#124×C151—232no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151—24no—
70C2×C4⋊C4×C151—42no—
71C2×C4⋊C4×C151D414yes—
72C2×C22⋊C4×C151—24no—
73C2×C22⋊C4×C151—24no—
74C2×C22⋊C4×C151—24no—
75C2×C22⋊C4×C151—24no—
76C2×C22⋊C4×C151—24no—
77C2×C22⋊C4×C151—24no—
78C2×C22⋊C4×C151—24no—
79C2×C22⋊C4×C151—24no—
80C2×C22⋊C4×C151—24no—
81C2×C22⋊C4×C151—24no—
82C2×C22⋊C4×C151—24no—
83C2×C22⋊C4×C151—24no—
84C2×C22⋊C4×C151—24no—
85C2×C22⋊C4×C151—24no—
86C2×C22⋊C4×C151—24no—
87C2×C22⋊C4×C151—42no—
88C2×C22⋊C4×C151—42no—
89C2×C22⋊C4×C151D418yes—
90C2×C42×C151—22no—
91C2×C42×C151—24no—
92C2×C42×C151—22no—
93C2×C42×C151—22no—
94C2×C42×C151—22no—
95C2×C42×C151—24no—
96C2×C42×C151D414yes—
97#95×C151—22no—
98#95×C151—22no—
99#95×C151—24no—
100#95×C151—24no—
101#95×C151—22no—
102#95×C151—22no—
103#95×C151—24no—
104#95×C151—24no—
105#95×C151—42no—
106C24×C151—22no—
107C24×C151—22no—
108C24×C151—22no—
109C24×C151—22no—
110C24×C151—22no—
111C24×C151—22no—
112C24×C151—22no—
113C24×C151—22no—
114C24×C151—22no—
115C24×C151—22no—
116C24×C151—22no—
117C24×C151—22no—
118C24×C151—22no—
119C24×C151—22no—
120C24×C151C2×D414yes—
121C24×C151C2411yescharacteristic
122C2×Q8×C151—28no—
123C2×Q8×C151—48no—
124C2×Q8×C151—48no—
125C2×Q8×C151—44no—
126C2×Q8×C151—44no—
127C2×D4×C151—28no—
128C2×D4×C151—48no—
129C2×D4×C151—48no—
130C2×D4×C151—44no—
131C2×D4×C151—44no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—21no—
142C22×C4×C151—22no—
143C22×C4×C151—22no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—21no—
154C22×C4×C151—22no—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—22no—
165C22×C4×C151—22no—
166C22×C4×C151—22no—
167C22×C4×C151—22no—
168C22×C4×C151—22no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—22no—
176C22×C4×C151C2×D412yes—
177C22×C4×C151C2×D414yes—
178C22×C4×C151C2×D412yes—
179C22×C4×C151C2×D414yes—
180C22×C4×C151C2×D412yes—
181C22×C4×C151C2×D412yes—
182C22×C4×C151C2×D412yes—
183C22×C4×C151C2×D412yes—
184C22×C4×C151#4114yes—
185C22×C4×C151#4112yes—
186C22×C4×C151#4112yes—
187C22×C4×C151#4112yes—
188C22×C4×C151#4112yes—
189C22×C4×C151#4112yes—
190C4⋊C4×C151—28no—
191C4⋊C4×C151—28no—
192C4⋊C4×C151—48no—
193C22⋊C4×C151—216no—
194C22⋊C4×C151—216no—
195C22⋊C4×C151—216no—
196C22⋊C4×C151—48no—
197C22⋊C4×C151—48no—
198C22⋊C4×C151—48no—
199C42×C151—28no—
200C42×C151—28no—
201C42×C151—44no—
202C23×C151—24no—
203C23×C151—24no—
204C23×C151—24no—
205C23×C151—24no—
206C23×C151—24no—
207C23×C151—24no—
208C23×C151—24no—
209C23×C151—42no—
210C23×C151—42no—
211C23×C151—42no—
212C23×C151—42no—
213C23×C151—42no—
214C23×C151—42no—
215C23×C151—42no—
216C23×C151—42no—
217C23×C151—42no—
218C23×C151—42no—
219C23×C151—42no—
220C23×C151—42no—
221C23×C151—42no—
222C23×C151—42no—
223C23×C151—42no—
224C23×C151—42no—
225C23×C151—42no—
226C23×C151—42no—
227C23×C151—42no—
228C23×C151—42no—
229C23×C151—42no—
230C23×C151—42no—
231C23×C151—42no—
232C23×C151—42no—
233C23×C151—42no—
234C23×C151—42no—
235C23×C151—42no—
236C23×C151—42no—
237C23×C151C22×D411yescharacteristic
238C23×C151C22×D412yes—
239C23×C151C22×D411yescharacteristic
240C23×C151C2×#4111yescharacteristic
241C23×C151C2×#4111yescharacteristic
242C23×C151C2×#4111yescharacteristic
243C23×C151C2×#4111yescharacteristic
244C23×C151C2×#4111yescharacteristic
245C23×C151C2×#4112yes—
246C23×C151H(5,𝔽2)12yes—
247C23×C1512−1+412yes—
248Q8×C151—416no—
249D4×C151—416no—
250C2×C4×C151—22no—
251C2×C4×C151—22no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—22no—
255C2×C4×C151—22no—
256C2×C4×C151—22no—
257C2×C4×C151—22no—
258C2×C4×C151—22no—
259C2×C4×C151—22no—
260C2×C4×C151—24no—
261C2×C4×C151—24no—
262C2×C4×C151—24no—
263C2×C4×C151—24no—
264C2×C4×C151—24no—
265C2×C4×C151—22no—
266C2×C4×C151—22no—
267C2×C4×C151—22no—
268C2×C4×C151—24no—
269C2×C4×C151—24no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—24no—
274C2×C4×C151—24no—
275C2×C4×C151—24no—
276C2×C4×C151—24no—
277C2×C4×C151—24no—
278C2×C4×C151—24no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—42no—
282C2×C4×C151—42no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—42no—
286C2×C4×C151—42no—
287C2×C4×C151—42no—
288C2×C4×C151—42no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—42no—
292C2×C4×C151—42no—
293C2×C4×C151—42no—
294C2×C4×C151—42no—
295C2×C4×C151—42no—
296C2×C4×C151—42no—
297C2×C4×C151—42no—
298C2×C4×C151—42no—
299C2×C4×C151—42no—
300C2×C4×C151—42no—
301C2×C4×C151—42no—
302C2×C4×C151—42no—
303C2×C4×C151—42no—
304C2×C4×C151—42no—
305C2×C4×C151#12014yes—
306C2×C4×C151#12114yes—
307C2×C4×C151#12414yescomplemented
308C22×C151—44no—
309C22×C151—44no—
310C22×C151—44no—
311C22×C151—44no—
312C22×C151—44no—
313C22×C151—44no—
314C22×C151—44no—
315C22×C151—82no—
316C22×C151—82no—
317C22×C151—82no—
318C22×C151—82no—
319C22×C151—82no—
320C22×C151—82no—
321C22×C151—82no—
322C22×C151—82no—
323C22×C151C2×#12011yescharacteristic
324C22×C151C2×#12111yescharacteristic
325C22×C151#52511yescharacteristic
326C22×C151#52511yescharacteristic
327C22×C151#52512yes—
328C22×C151C2×#12411yescharacteristic
329C22×C151#52911yescharacteristic
330C22×C151#52911yescharacteristic
331C22×C151#53211yescharacteristic
332C22×C151#53211yescharacteristic
333C22×C151#53212yes—
334C22×C151#53511yescharacteristic
335C22×C151#53611yescharacteristic
336C22×C151#54212yes—
337C22×C151#54212yes—
338C22×C151D4212yes—
339C22×C151#54612yes—
340C22×C151#54712yes—
341C22×C151#54712yes—
342C22×C151#54812yes—
343C22×C151#55112yes—
344C22×C151#55512yes—
345C22×C151#55612yes—
346C4×C151—24no—
347C4×C151—24no—
348C4×C151—24no—
349C4×C151—42no—
350C4×C151—42no—
351C4×C151—42no—
352C4×C151—42no—
353C4×C151—44no—
354C4×C151—44no—
355C4×C151—82no—
356C2×C151—84no—
357C2×C151#238811yescharacteristic
358C2×C151#240611yescharacteristic
359C2×C151#240811yescharacteristic
360C2×C151#246112yes—
361C2×C151#247412yes—
362C2×C151#249112yes—
363C2×C151#252112yes—
364C2×C151#254511yescharacteristic
365C2×C151#261011yescharacteristic
366C2×C151#263211yescharacteristic
367C2×C151#285011yescharacteristic
368#15070C15111yesmaximal, characteristic, direct product factor, Sylow
369C151#1507011yescharacteristic, direct product factor, Sylow
370C22×#124C2×C15111yescharacteristic
371C2×#395C2×C15111yescharacteristic, complemented
372C2×#394C2×C15111yescharacteristic
373C2×#388C2×C15112yescomplemented
374C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
375#1446C2×C15111yescharacteristic, complemented
376#1439C2×C15112yescomplemented
377#1439C2×C15112yescomplemented
378#1438C2×C15111yescharacteristic
379#1437C2×C15112yescomplemented
380#1434C2×C15111yescharacteristic, complemented
381C23×Q8C22×C15111yescharacteristic
382C23×D4C22×C15111yescharacteristic
383C2×#124—28no—
384C2×#124—24no—
385C22×C4⋊C4C22×C15111yescharacteristic
386C22×C4⋊C4C22×C15112yes—
387C22×C4⋊C4C22×C15111yescharacteristic
388C22×C22⋊C4C22×C15112yes—
389C22×C22⋊C4C22×C15112yes—
390C22×C22⋊C4C22×C15112yes—
391C22×C22⋊C4C22×C15112yes—
392C22×C22⋊C4C22×C15112yes—
393C22×C22⋊C4C22×C15112yes—
394C22×C42C22×C15111yescharacteristic
395C22×C42C22×C15111yescharacteristic
396C22×C42C22×C15111yescharacteristic
397#395—24no—
398#394—24no—
399#388—28no—
400C4×C4⋊C4—24no—
401C2×#95C22×C15111yescharacteristic
402C2×#95C22×C15111yescharacteristic
403C2×#95C22×C15112yes—
404C2×#95C22×C15112yes—
405C2×#95C22×C15112yes—
406C2×#95C22×C15111yescharacteristic
407C2×#95C22×C15111yescharacteristic
408C2×#95C22×C15112yes—
409C2×#95C22×C15112yes—
410C25C23×C15112yes—
411C22×Q8—22no—
412C22×Q8—24no—
413C22×Q8—22no—
414C22×Q8—22no—
415C22×Q8—42no—
416C22×D4—24no—
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—42no—
421C23×C4C23×C15112yes—
422C23×C4C23×C15112yes—
423C23×C4C23×C15111yescharacteristic
424C23×C4C23×C15111yescharacteristic
425C23×C4C23×C15111yescharacteristic
426C23×C4C23×C15112yes—
427C23×C4C23×C15111yescharacteristic
428C23×C4C23×C15111yescharacteristic
429C23×C4C23×C15111yescharacteristic
430C23×C4C23×C15111yescharacteristic
431#124—232no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4D4×C15114yes—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4D4×C15118yes—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—24no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—24no—
465C2×C42D4×C15114yes—
466#95—24no—
467#95—22no—
468#95—22no—
469#95—24no—
470#95—24no—
471#95—22no—
472#95—22no—
473#95—24no—
474#95—42no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24C2×D4×C15114yes—
490C24C24×C15111yescharacteristic
491C2×Q8—28no—
492C2×Q8—48no—
493C2×Q8—48no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×D4—28no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—44no—
500C2×D4—44no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4C2×D4×C15112yes—
546C22×C4C2×D4×C15114yes—
547C22×C4C2×D4×C15112yes—
548C22×C4C2×D4×C15114yes—
549C22×C4C2×D4×C15112yes—
550C22×C4C2×D4×C15112yes—
551C22×C4C2×D4×C15112yes—
552C22×C4C2×D4×C15112yes—
553C22×C4#41×C15114yes—
554C22×C4#41×C15112yes—
555C22×C4#41×C15112yes—
556C22×C4#41×C15112yes—
557C22×C4#41×C15112yes—
558C22×C4#41×C15112yes—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—48no—
562C22⋊C4—216no—
563C22⋊C4—216no—
564C22⋊C4—216no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C42—28no—
569C42—28no—
570C42—44no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23C22×D4×C15111yescharacteristic
607C23C22×D4×C15112yes—
608C23C22×D4×C15111yescharacteristic
609C23C2×#41×C15111yescharacteristic
610C23C2×#41×C15111yescharacteristic
611C23C2×#41×C15111yescharacteristic
612C23C2×#41×C15111yescharacteristic
613C23C2×#41×C15111yescharacteristic
614C23C2×#41×C15112yes—
615C23H(5,𝔽2)×C15112yes—
616C232−1+4×C15112yes—
617Q8—416no—
618D4—416no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4#120×C15114yes—
675C2×C4#121×C15114yes—
676C2×C4#124×C15114yescomplemented
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—44no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22—82no—
692C22C2×#120×C15111yescharacteristic
693C22C2×#121×C15111yescharacteristic
694C22#525×C15111yescharacteristic
695C22#525×C15111yescharacteristic
696C22#525×C15112yes—
697C22C2×#124×C15111yescharacteristic
698C22#529×C15111yescharacteristic
699C22#529×C15111yescharacteristic
700C22#532×C15111yescharacteristic
701C22#532×C15111yescharacteristic
702C22#532×C15112yes—
703C22#535×C15111yescharacteristic
704C22#536×C15111yescharacteristic
705C22#542×C15112yes—
706C22#542×C15112yes—
707C22D42×C15112yes—
708C22#546×C15112yes—
709C22#547×C15112yes—
710C22#547×C15112yes—
711C22#548×C15112yes—
712C22#551×C15112yes—
713C22#555×C15112yes—
714C22#556×C15112yes—
715C4—24no—
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—44no—
722C4—42no—
723C4—44no—
724C4—82no—
725C2—84no—
726C2#2388×C15111yescharacteristic
727C2#2406×C15111yescharacteristic
728C2#2408×C15111yescharacteristic
729C2#2461×C15112yes—
730C2#2474×C15112yes—
731C2#2491×C15112yes—
732C2#2521×C15112yes—
733C2#2545×C15111yescharacteristic
734C2#2610×C15111yescharacteristic
735C2#2632×C15111yescharacteristic
736C2#2850×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#395×C151C2semidirect
4. C2×#388×C151C2semidirect
5. C2×C4×C4⋊C4×C151C2semidirect
6. #1446×C151C2semidirect
7. #1439×C151C2semidirect
8. #1439×C151C2semidirect
10. #1437×C151C2semidirect
11. #1434×C151C2semidirect
307. C2×C4×C151#124semidirect
368. #15070C151direct (N × H)
369. C151#15070direct (N × H)
371. C2×#395C2×C151semidirect
373. C2×#388C2×C151semidirect
374. C2×C4×C4⋊C4C2×C151semidirect
375. #1446C2×C151semidirect
376. #1439C2×C151semidirect
377. #1439C2×C151semidirect
379. #1437C2×C151semidirect
380. #1434C2×C151semidirect
676. C2×C4#124×C151semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1512
C2×#395×C1512
C2×#394×C1512
C2×#388×C1512
C2×C4×C4⋊C4×C1512
#1446×C1512
#1439×C1512
#1438×C1512
#1437×C1512
#1434×C1512
#15070151