Finite Group Databasebeta

← C151×#14141 #50319066

Subgroups — C151×#14141 #50319066

Order 38656.

1938 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#390×C151C211yesmaximal, characteristic
2C2×#390×C151C211yesmaximal, characteristic
3C2×#390×C151C211yesmaximal, characteristic
4C2×#389×C151C211yesmaximal, characteristic, complemented
5C2×#388×C151C212yesmaximal, complemented
6C2×C4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
7#1440×C151C212yesmaximal, complemented
8#1439×C151C212yesmaximal, complemented
9#1437×C151C212yesmaximal, complemented
10C4⋊#95×C151C211yesmaximal, characteristic, complemented
11C4×#95×C151C211yesmaximal, characteristic, complemented
12C23×D4×C151C2211yescharacteristic
13C22×C4⋊C4×C151C2212yes—
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17C22×C22⋊C4×C151C2212yes—
18C22×C22⋊C4×C151C2212yes—
19C22×C22⋊C4×C151C2212yes—
20C22×C22⋊C4×C151C2212yes—
21C22×C22⋊C4×C151C2212yes—
22C22×C22⋊C4×C151C2212yes—
23C22×C42×C151C2211yescharacteristic
24C22×C42×C151C2211yescharacteristic
25C22×C42×C151C2212yes—
26C22×C42×C151C2211yescharacteristic
27#390×C151—24no—
28#390×C151—24no—
29#390×C151C418yescomplemented
30#389×C151—24no—
31#388×C151—28no—
32C4×C4⋊C4×C151—24no—
33C2×#95×C151C2211yescharacteristic
34C2×#95×C151C2211yescharacteristic
35C2×#95×C151C2211yescharacteristic
36C2×#95×C151C2212yes—
37C2×#95×C151C2212yes—
38C2×#95×C151C2212yes—
39C2×#95×C151C2212yes—
40C2×#95×C151C2211yescharacteristic
41C25×C151C2312yes—
42C22×D4×C151—22no—
43C22×D4×C151—22no—
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151—22no—
47C22×D4×C151—22no—
48C22×D4×C151C2×C414yes—
49C23×C4×C151C2311yescharacteristic
50C23×C4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C23×C4×C151C2312yes—
53C23×C4×C151C2312yes—
54C23×C4×C151C2311yescharacteristic
55C23×C4×C151C2311yescharacteristic
56C23×C4×C151C2311yescharacteristic
57C23×C4×C151C2311yescharacteristic
58C23×C4×C151C2311yescharacteristic
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—24no—
66C2×C4⋊C4×C151—24no—
67C2×C4⋊C4×C151—42no—
68C2×C4⋊C4×C151C2×C414yes—
69C2×C4⋊C4×C151D414yes—
70C2×C4⋊C4×C151D414yes—
71C2×C22⋊C4×C151—24no—
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—42no—
82C2×C22⋊C4×C151—42no—
83C2×C22⋊C4×C151—42no—
84C2×C22⋊C4×C151—42no—
85C2×C22⋊C4×C151—42no—
86C2×C22⋊C4×C151—42no—
87C2×C22⋊C4×C151C2×C418yes—
88C2×C22⋊C4×C151C2×C418yes—
89C2×C42×C151—22no—
90C2×C42×C151—22no—
91C2×C42×C151—24no—
92C2×C42×C151—24no—
93C2×C42×C151—22no—
94C2×C42×C151—22no—
95C2×C42×C151—22no—
96C2×C42×C151—22no—
97C2×C42×C151—22no—
98C2×C42×C151—22no—
99C2×C42×C151—42no—
100C2×C42×C151C2×C414yes—
101#95×C151—24no—
102#95×C151—24no—
103#95×C151—24no—
104#95×C151—22no—
105#95×C151—22no—
106#95×C151—22no—
107#95×C151—42no—
108#95×C151D414yescomplemented
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×C151—22no—
121C24×C151—22no—
122C24×C151—22no—
123C24×C151C22×C414yes—
124C24×C151C2411yescharacteristic
125C2×D4×C151—28no—
126C2×D4×C151—28no—
127C2×D4×C151—28no—
128C2×D4×C151—44no—
129C2×D4×C151—44no—
130C2×D4×C151—44no—
131C2×D4×C151—44no—
132C22×C4×C151—21no—
133C22×C4×C151—21no—
134C22×C4×C151—21no—
135C22×C4×C151—21no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—22no—
139C22×C4×C151—22no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—22no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
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—21no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—22no—
180C22×C4×C151—22no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151C22×C412yes—
185C22×C4×C151C22×C414yes—
186C22×C4×C151C22×C412yes—
187C22×C4×C151C22×C412yes—
188C22×C4×C151C2×D412yes—
189C22×C4×C151C2×D414yes—
190C22×C4×C151C2×D414yes—
191C22×C4×C151C2×D412yes—
192C22×C4×C151C2×D412yes—
193C22×C4×C151C2×D412yes—
194C22×C4×C151C2×D412yes—
195C22×C4×C151#4112yes—
196C22×C4×C151#4112yes—
197C22×C4×C151#4112yes—
198C22×C4×C151#4112yes—
199C22×C4×C151#4112yes—
200C22×C4×C151#4112yes—
201C22×C4×C151#4112yes—
202C4⋊C4×C151—28no—
203C4⋊C4×C151—28no—
204C4⋊C4×C151—28no—
205C4⋊C4×C151—48no—
206C22⋊C4×C151—216no—
207C22⋊C4×C151—48no—
208C22⋊C4×C151—48no—
209C22⋊C4×C151—48no—
210C22⋊C4×C151—48no—
211C22⋊C4×C151—48no—
212C42×C151—28no—
213C42×C151—48no—
214C42×C151—44no—
215C42×C151—44no—
216C23×C151—24no—
217C23×C151—24no—
218C23×C151—24no—
219C23×C151—24no—
220C23×C151—24no—
221C23×C151—24no—
222C23×C151—24no—
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×C151—42no—
238C23×C151—42no—
239C23×C151—42no—
240C23×C151—42no—
241C23×C151—42no—
242C23×C151—42no—
243C23×C151—42no—
244C23×C151—42no—
245C23×C151—42no—
246C23×C151—42no—
247C23×C151—42no—
248C23×C151—42no—
249C23×C151—42no—
250C23×C151—42no—
251C23×C151C23×C411yescharacteristic
252C23×C151C22×D411yescharacteristic
253C23×C151C22×D411yescharacteristic
254C23×C151C22×D411yescharacteristic
255C23×C151C2×#4111yescharacteristic
256C23×C151C2×#4111yescharacteristic
257C23×C151C2×#4111yescharacteristic
258C23×C151C2×#4111yescharacteristic
259C23×C151C2×#4111yescharacteristic
260C23×C151C2×#4111yescharacteristic
261C23×C151C2×#4111yescharacteristic
262C23×C151H(5,𝔽2)11yescharacteristic
263C23×C151H(5,𝔽2)11yescharacteristic
264C23×C151H(5,𝔽2)11yescharacteristic
265C23×C1512−1+411yescharacteristic
266D4×C151—416no—
267C2×C4×C151—22no—
268C2×C4×C151—22no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—22no—
274C2×C4×C151—24no—
275C2×C4×C151—24no—
276C2×C4×C151—22no—
277C2×C4×C151—22no—
278C2×C4×C151—24no—
279C2×C4×C151—24no—
280C2×C4×C151—24no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—22no—
285C2×C4×C151—24no—
286C2×C4×C151—22no—
287C2×C4×C151—22no—
288C2×C4×C151—24no—
289C2×C4×C151—22no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—24no—
293C2×C4×C151—24no—
294C2×C4×C151—22no—
295C2×C4×C151—22no—
296C2×C4×C151—22no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—42no—
302C2×C4×C151—42no—
303C2×C4×C151—41no—
304C2×C4×C151—42no—
305C2×C4×C151—42no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—42no—
310C2×C4×C151—42no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—42no—
317C2×C4×C151—42no—
318C2×C4×C151—41no—
319C2×C4×C151—42no—
320C2×C4×C151—41no—
321C2×C4×C151—42no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—42no—
328C2×C4×C151—42no—
329C2×C4×C151#11714yes—
330C2×C4×C151C4×D414yes—
331C2×C4×C151C4×D414yes—
332C2×C4×C151C4×D414yes—
333C2×C4×C151#12114yes—
334C2×C4×C151#12314yes—
335C2×C4×C151#12414yes—
336C2×C4×C151#12614yes—
337C22×C151—44no—
338C22×C151—44no—
339C22×C151—44no—
340C22×C151—44no—
341C22×C151—44no—
342C22×C151—44no—
343C22×C151—44no—
344C22×C151—82no—
345C22×C151—82no—
346C22×C151—82no—
347C22×C151—82no—
348C22×C151—82no—
349C22×C151—82no—
350C22×C151—82no—
351C22×C151—82no—
352C22×C151C2×#11711yescharacteristic
353C22×C151C2×C4×D411yescharacteristic
354C22×C151C2×C4×D411yescharacteristic
355C22×C151C2×C4×D411yescharacteristic
356C22×C151C4×#4111yescharacteristic
357C22×C151#51811yescharacteristic
358C22×C151#52011yescharacteristic
359C22×C151C2×#12111yescharacteristic
360C22×C151C2×#12311yescharacteristic
361C22×C151C2×#12411yescharacteristic
362C22×C151C2×#12611yescharacteristic
363C22×C151#52911yescharacteristic
364C22×C151#52911yescharacteristic
365C22×C151#53211yescharacteristic
366C22×C151#53211yescharacteristic
367C22×C151#54011yescharacteristic
368C22×C151#54011yescharacteristic
369C22×C151#54211yescharacteristic
370C22×C151#54211yescharacteristic
371C22×C151D4211yescharacteristic
372C22×C151D4211yescharacteristic
373C22×C151#54611yescharacteristic
374C22×C151#54611yescharacteristic
375C22×C151#54711yescharacteristic
376C22×C151#54811yescharacteristic
377C22×C151#54811yescharacteristic
378C22×C151#55011yescharacteristic
379C22×C151#55011yescharacteristic
380C22×C151#55011yescharacteristic
381C22×C151#55311yescharacteristic
382C22×C151#55311yescharacteristic
383C22×C151#55511yescharacteristic
384C22×C151#55611yescharacteristic
385C22×C151#55911yescharacteristic
386C22×C151#55911yescharacteristic
387C4×C151—24no—
388C4×C151—42no—
389C4×C151—44no—
390C4×C151—42no—
391C4×C151—44no—
392C4×C151—42no—
393C4×C151—44no—
394C4×C151—42no—
395C4×C151—42no—
396C4×C151#38818yescomplemented
397C2×C151—84no—
398C2×C151C2×#38811yescharacteristic
399C2×C151#229311yescharacteristic
400C2×C151#231911yescharacteristic
401C2×C151#236111yescharacteristic
402C2×C151#236311yescharacteristic
403C2×C151#236611yescharacteristic
404C2×C151#236711yescharacteristic
405C2×C151#242611yescharacteristic
406C2×C151#242811yescharacteristic
407C2×C151#244511yescharacteristic
408C2×C151#244811yescharacteristic
409C2×C151#249011yescharacteristic
410C2×C151#249111yescharacteristic
411C2×C151#251211yescharacteristic
412C2×C151#251311yescharacteristic
413#14141C15111yesmaximal, characteristic, direct product factor, Sylow
414C151#1414111yescharacteristic, direct product factor, Sylow
415C2×#390C2×C15111yescharacteristic
416C2×#390C2×C15111yescharacteristic
417C2×#390C2×C15111yescharacteristic
418C2×#389C2×C15111yescharacteristic, complemented
419C2×#388C2×C15112yescomplemented
420C2×C4×C4⋊C4C2×C15111yescharacteristic, complemented
421#1440C2×C15112yescomplemented
422#1439C2×C15112yescomplemented
423#1437C2×C15112yescomplemented
424C4⋊#95C2×C15111yescharacteristic, complemented
425C4×#95C2×C15111yescharacteristic, complemented
426C23×D4C22×C15111yescharacteristic
427C22×C4⋊C4C22×C15112yes—
428C22×C4⋊C4C22×C15111yescharacteristic
429C22×C4⋊C4C22×C15111yescharacteristic
430C22×C4⋊C4C22×C15111yescharacteristic
431C22×C22⋊C4C22×C15112yes—
432C22×C22⋊C4C22×C15112yes—
433C22×C22⋊C4C22×C15112yes—
434C22×C22⋊C4C22×C15112yes—
435C22×C22⋊C4C22×C15112yes—
436C22×C22⋊C4C22×C15112yes—
437C22×C42C22×C15111yescharacteristic
438C22×C42C22×C15111yescharacteristic
439C22×C42C22×C15112yes—
440C22×C42C22×C15111yescharacteristic
441#390—24no—
442#390—24no—
443#390C4×C15118yescomplemented
444#389—24no—
445#388—28no—
446C4×C4⋊C4—24no—
447C2×#95C22×C15111yescharacteristic
448C2×#95C22×C15111yescharacteristic
449C2×#95C22×C15111yescharacteristic
450C2×#95C22×C15112yes—
451C2×#95C22×C15112yes—
452C2×#95C22×C15112yes—
453C2×#95C22×C15112yes—
454C2×#95C22×C15111yescharacteristic
455C25C23×C15112yes—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4C2×C4×C15114yes—
463C23×C4C23×C15111yescharacteristic
464C23×C4C23×C15111yescharacteristic
465C23×C4C23×C15112yes—
466C23×C4C23×C15111yescharacteristic
467C23×C4C23×C15112yes—
468C23×C4C23×C15111yescharacteristic
469C23×C4C23×C15112yes—
470C23×C4C23×C15111yescharacteristic
471C23×C4C23×C15111yescharacteristic
472C23×C4C23×C15111yescharacteristic
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4C2×C4×C15114yes—
483C2×C4⋊C4D4×C15114yes—
484C2×C4⋊C4D4×C15114yes—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4C2×C4×C15118yes—
502C2×C22⋊C4C2×C4×C15118yes—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—24no—
509C2×C42—24no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—42no—
514C2×C42C2×C4×C15114yes—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—24no—
519#95—24no—
520#95—24no—
521#95—42no—
522#95D4×C15114yescomplemented
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24C22×C4×C15114yes—
538C24C24×C15111yescharacteristic
539C2×D4—28no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4C22×C4×C15112yes—
599C22×C4C22×C4×C15114yes—
600C22×C4C22×C4×C15112yes—
601C22×C4C22×C4×C15112yes—
602C22×C4C2×D4×C15112yes—
603C22×C4C2×D4×C15114yes—
604C22×C4C2×D4×C15114yes—
605C22×C4C2×D4×C15112yes—
606C22×C4C2×D4×C15112yes—
607C22×C4C2×D4×C15112yes—
608C22×C4C2×D4×C15112yes—
609C22×C4#41×C15112yes—
610C22×C4#41×C15112yes—
611C22×C4#41×C15112yes—
612C22×C4#41×C15112yes—
613C22×C4#41×C15112yes—
614C22×C4#41×C15112yes—
615C22×C4#41×C15112yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—48no—
620C22⋊C4—216no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C42—28no—
627C42—48no—
628C42—44no—
629C42—44no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23C23×C4×C15111yescharacteristic
666C23C22×D4×C15111yescharacteristic
667C23C22×D4×C15111yescharacteristic
668C23C22×D4×C15111yescharacteristic
669C23C2×#41×C15111yescharacteristic
670C23C2×#41×C15111yescharacteristic
671C23C2×#41×C15111yescharacteristic
672C23C2×#41×C15111yescharacteristic
673C23C2×#41×C15111yescharacteristic
674C23C2×#41×C15111yescharacteristic
675C23C2×#41×C15111yescharacteristic
676C23H(5,𝔽2)×C15111yescharacteristic
677C23H(5,𝔽2)×C15111yescharacteristic
678C23H(5,𝔽2)×C15111yescharacteristic
679C232−1+4×C15111yescharacteristic
680D4—416no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4#117×C15114yes—
744C2×C4C4×D4×C15114yes—
745C2×C4C4×D4×C15114yes—
746C2×C4C4×D4×C15114yes—
747C2×C4#121×C15114yes—
748C2×C4#123×C15114yes—
749C2×C4#124×C15114yes—
750C2×C4#126×C15114yes—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22C2×#117×C15111yescharacteristic
767C22C2×C4×D4×C15111yescharacteristic
768C22C2×C4×D4×C15111yescharacteristic
769C22C2×C4×D4×C15111yescharacteristic
770C22C4×#41×C15111yescharacteristic
771C22#518×C15111yescharacteristic
772C22#520×C15111yescharacteristic
773C22C2×#121×C15111yescharacteristic
774C22C2×#123×C15111yescharacteristic
775C22C2×#124×C15111yescharacteristic
776C22C2×#126×C15111yescharacteristic
777C22#529×C15111yescharacteristic
778C22#529×C15111yescharacteristic
779C22#532×C15111yescharacteristic
780C22#532×C15111yescharacteristic
781C22#540×C15111yescharacteristic
782C22#540×C15111yescharacteristic
783C22#542×C15111yescharacteristic
784C22#542×C15111yescharacteristic
785C22D42×C15111yescharacteristic
786C22D42×C15111yescharacteristic
787C22#546×C15111yescharacteristic
788C22#546×C15111yescharacteristic
789C22#547×C15111yescharacteristic
790C22#548×C15111yescharacteristic
791C22#548×C15111yescharacteristic
792C22#550×C15111yescharacteristic
793C22#550×C15111yescharacteristic
794C22#550×C15111yescharacteristic
795C22#553×C15111yescharacteristic
796C22#553×C15111yescharacteristic
797C22#555×C15111yescharacteristic
798C22#556×C15111yescharacteristic
799C22#559×C15111yescharacteristic
800C22#559×C15111yescharacteristic
801C4—24no—
802C4—42no—
803C4—44no—
804C4—42no—
805C4—44no—
806C4—42no—
807C4—44no—
808C4—42no—
809C4—42no—
810C4#388×C15118yescomplemented
811C2—84no—
812C2C2×#388×C15111yescharacteristic
813C2#2293×C15111yescharacteristic
814C2#2319×C15111yescharacteristic
815C2#2361×C15111yescharacteristic
816C2#2363×C15111yescharacteristic
817C2#2366×C15111yescharacteristic
818C2#2367×C15111yescharacteristic
819C2#2426×C15111yescharacteristic
820C2#2428×C15111yescharacteristic
821C2#2445×C15111yescharacteristic
822C2#2448×C15111yescharacteristic
823C2#2490×C15111yescharacteristic
824C2#2491×C15111yescharacteristic
825C2#2512×C15111yescharacteristic
826C2#2513×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#389×C151C2semidirect
5. C2×#388×C151C2semidirect
6. C2×C4×C4⋊C4×C151C2semidirect
7. #1440×C151C2semidirect
8. #1439×C151C2semidirect
9. #1437×C151C2semidirect
10. C4⋊#95×C151C2semidirect
11. C4×#95×C151C2semidirect
29. #390×C151C4semidirect
108. #95×C151D4semidirect
396. C4×C151#388semidirect
413. #14141C151direct (N × H)
414. C151#14141direct (N × H)
418. C2×#389C2×C151semidirect
419. C2×#388C2×C151semidirect
420. C2×C4×C4⋊C4C2×C151semidirect
421. #1440C2×C151semidirect
422. #1439C2×C151semidirect
423. #1437C2×C151semidirect
424. C4⋊#95C2×C151semidirect
425. C4×#95C2×C151semidirect
443. #390C4×C151semidirect
522. #95D4×C151semidirect
810. C4#388×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#390×C1512
C2×#389×C1512
C2×#388×C1512
C2×C4×C4⋊C4×C1512
#1440×C1512
#1439×C1512
#1437×C1512
C4⋊#95×C1512
C4×#95×C1512
#14141151