Finite Group Databasebeta

← C151×#22201 #50327126

Subgroups — C151×#22201 #50327126

Order 38656.

878 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C151C211yesmaximal, characteristic
2#2324×C151C211yesmaximal, characteristic
3#2323×C151C211yesmaximal, characteristic, complemented
4#1928×C151C211yesmaximal, characteristic, complemented
5#1925×C151C211yesmaximal, characteristic, complemented
6#1921×C151C211yesmaximal, characteristic, complemented
7#1918×C151C211yesmaximal, characteristic, complemented
8#1893×C151C211yesmaximal, characteristic
9#1892×C151C211yesmaximal, characteristic, complemented
10#1880×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1865×C151C211yesmaximal, characteristic, complemented
13#1864×C151C211yesmaximal, characteristic, complemented
14#1809×C151C211yesmaximal, characteristic, complemented
15#1729×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#468×C151C418yescomplemented
25C2×#107×C151C2211yescharacteristic
26C2×#107×C151C2211yescharacteristic
27C2×#106×C151C2211yescharacteristic
28C2×#103×C151C2211yescharacteristic
29C2×#103×C151C2211yescharacteristic
30C2×#103×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34#391×C151C2211yescharacteristic
35#390×C151—21no—
36#390×C151C2211yescharacteristic
37#389×C151—21no—
38#389×C151C2211yescharacteristic
39#389×C151C2211yescharacteristic
40#388×C151—21no—
41#388×C151—21no—
42#388×C151—21no—
43#387×C151—21no—
44#386×C151—21no—
45#385×C151—21no—
46#380×C151C2211yescharacteristic
47#380×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49C4×C4⋊C4×C151C2211yescharacteristic
50#340×C151C2211yescharacteristic
51#340×C151C2211yescharacteristic
52#340×C151C2211yescharacteristic
53#340×C151C2211yescharacteristic
54#340×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60C22×Q8×C151C2311yescharacteristic
61C22×D4×C151—21no—
62C22×D4×C151C2311yescharacteristic
63C23×C4×C151—21no—
64C23×C4×C151C2311yescharacteristic
65C2×SD16×C151—41no—
66C2×SD16×C151—41no—
67C2×SD16×C151C2×C414yes—
68C2×M16×C151—41no—
69C2×M16×C151—41no—
70C2×M16×C151C2×C414yescomplemented
71C22×C8×C151—22no—
72C22×C8×C151—41no—
73C22×C8×C151—41no—
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151C2×C414yescomplemented
80#121×C151—22no—
81#121×C151C2×C414yes—
82C4×Q8×C151—41no—
83C4×Q8×C151—41no—
84C4×D4×C151—41no—
85C4×D4×C151—41no—
86#117×C151—41no—
87#117×C151—41no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151D411yescharacteristic
93C2×C4⋊C4×C151D411yescharacteristic
94C2×C4⋊C4×C151C2311yescharacteristic
95C2×C4⋊C4×C151C2311yescharacteristic
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C22⋊C4×C151—21no—
101C2×C22⋊C4×C151—21no—
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151D411yescharacteristic
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C42×C151—21no—
110C2×C42×C151—21no—
111C2×C42×C151—21no—
112C2×C42×C151C2311yescharacteristic
113C2×C42×C151C2311yescharacteristic
114#107×C151—41no—
115#107×C151C2×C414yescomplemented
116#106×C151—41no—
117#103×C151—41no—
118#103×C151—41no—
119#103×C151C2×C414yescomplemented
120#102×C151—41no—
121#102×C151—41no—
122#102×C151C2×C414yes—
123#95×C151—21no—
124#95×C151—21no—
125#95×C151—21no—
126#95×C151—21no—
127#95×C151—21no—
128#95×C151—21no—
129#95×C151—21no—
130#95×C151—21no—
131C24×C151—21no—
132C24×C151C2×D411yescharacteristic
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151—21no—
136C2×Q8×C151—21no—
137C2×Q8×C151—21no—
138C2×Q8×C151C22×C412yes—
139C2×D4×C151—24no—
140C2×D4×C151—21no—
141C2×D4×C151—21no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—81no—
146C2×D4×C151—81no—
147C2×D4×C151C22×C412yes—
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—42no—
160C22×C4×C151—81no—
161C22×C4×C151—81no—
162C22×C4×C151C22×C412yes—
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151#4112yes—
169C22×C4×C151C2411yescharacteristic
170SD16×C151—44no—
171M16×C151—44no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—44no—
183C2×C8×C151C22×C412yes—
184C2×C8×C151C22×C412yes—
185C4⋊C4×C151—24no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—41no—
197C4⋊C4×C151—41no—
198C4⋊C4×C151—42no—
199C4⋊C4×C151—81no—
200C4⋊C4×C151—81no—
201C4⋊C4×C151C22×C412yes—
202C4⋊C4×C151C22×C412yes—
203C22⋊C4×C151—24no—
204C22⋊C4×C151—24no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—42no—
208C22⋊C4×C151—81no—
209C22⋊C4×C151—81no—
210C22⋊C4×C151—81no—
211C22⋊C4×C151—81no—
212C42×C151—21no—
213C42×C151—21no—
214C42×C151—21no—
215C42×C151—21no—
216C42×C151—42no—
217C42×C151—81no—
218C42×C151—81no—
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—21no—
222C23×C151—21no—
223C23×C151—21no—
224C23×C151—21no—
225C23×C151—22no—
226C23×C151—41no—
227C23×C151—41no—
228C23×C151—41no—
229C23×C151—41no—
230C23×C151—41no—
231C23×C151—41no—
232C23×C151C4×D412yes—
233C23×C151C22×D411yescharacteristic
234Q8×C151—22no—
235Q8×C151—22no—
236Q8×C151—41no—
237Q8×C151—41no—
238D4×C151—22no—
239D4×C151—22no—
240D4×C151—41no—
241D4×C151—41no—
242D4×C151—84no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—22no—
246C2×C4×C151—22no—
247C2×C4×C151—22no—
248C2×C4×C151—22no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—22no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—41no—
275C2×C4×C151—41no—
276C2×C4×C151—41no—
277C2×C4×C151—41no—
278C2×C4×C151—41no—
279C2×C4×C151—41no—
280C2×C4×C151—41no—
281C2×C4×C151—41no—
282C2×C4×C151—84no—
283C2×C4×C151C4×D412yes—
284C2×C4×C151C23×C411yescharacteristic
285C2×C4×C151C2×#4111yescharacteristic
286C2×C4×C151H(5,𝔽2)11yescharacteristic
287C2×C4×C151H(5,𝔽2)11yescharacteristic
288C2×C4×C151H(5,𝔽2)11yescharacteristic
289C2×C4×C1512−1+411yescharacteristic
290C8×C151—22no—
291C8×C151—22no—
292C8×C151—41no—
293C8×C151—41no—
294C22×C151—22no—
295C22×C151—22no—
296C22×C151—22no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—41no—
301C22×C151—42no—
302C22×C151—42no—
303C22×C151—42no—
304C22×C151—81no—
305C22×C151—81no—
306C22×C151—81no—
307C22×C151—81no—
308C22×C151C2×C4×D411yescharacteristic
309C22×C151#53411yescharacteristic
310C22×C151#53711yescharacteristic
311C22×C151#57611yescharacteristic
312C22×C151#57711yescharacteristic
313C22×C151#57711yescharacteristic
314C22×C151#57811yescharacteristic
315C4×C151—22no—
316C4×C151—42no—
317C4×C151—41no—
318C4×C151—41no—
319C4×C151—42no—
320C4×C151—42no—
321C4×C151—41no—
322C4×C151—41no—
323C4×C151—81no—
324C4×C151—81no—
325C4×C151—81no—
326C4×C151—81no—
327C4×C151#51811yescharacteristic
328C4×C151#52011yescharacteristic
329C4×C151#53811yescharacteristic
330C4×C151#53911yescharacteristic
331C2×C151—42no—
332C2×C151—82no—
333C2×C151#232511yescharacteristic
334C2×C151#294611yescharacteristic
335C2×C151#294711yescharacteristic
336C2×C151#320011yescharacteristic
337C2×C151#320311yescharacteristic
338C2×C151#325711yescharacteristic
339C2×C151#325811yescharacteristic
340#22201C15111yesmaximal, characteristic, direct product factor, Sylow
341C151#2220111yescharacteristic, direct product factor, Sylow
342C2×#468C2×C15111yescharacteristic
343#2324C2×C15111yescharacteristic
344#2323C2×C15111yescharacteristic, complemented
345#1928C2×C15111yescharacteristic, complemented
346#1925C2×C15111yescharacteristic, complemented
347#1921C2×C15111yescharacteristic, complemented
348#1918C2×C15111yescharacteristic, complemented
349#1893C2×C15111yescharacteristic
350#1892C2×C15111yescharacteristic, complemented
351#1880C2×C15111yescharacteristic, complemented
352#1877C2×C15111yescharacteristic, complemented
353#1865C2×C15111yescharacteristic, complemented
354#1864C2×C15111yescharacteristic, complemented
355#1809C2×C15111yescharacteristic, complemented
356#1729C2×C15111yescharacteristic, complemented
357C22×SD16C22×C15111yescharacteristic
358C22×M16C22×C15111yescharacteristic
359C23×C8C22×C15111yescharacteristic
360C2×C22⋊Q8C22×C15111yescharacteristic
361C2×#121C22×C15111yescharacteristic
362C2×C4×Q8C22×C15111yescharacteristic
363C2×C4×D4C22×C15111yescharacteristic
364C2×#117C22×C15111yescharacteristic
365#468C4×C15118yescomplemented
366C2×#107C22×C15111yescharacteristic
367C2×#107C22×C15111yescharacteristic
368C2×#106C22×C15111yescharacteristic
369C2×#103C22×C15111yescharacteristic
370C2×#103C22×C15111yescharacteristic
371C2×#103C22×C15111yescharacteristic
372C2×#102C22×C15111yescharacteristic
373C2×#102C22×C15111yescharacteristic
374C2×#102C22×C15111yescharacteristic
375#391C22×C15111yescharacteristic
376#390—21no—
377#390C22×C15111yescharacteristic
378#389—21no—
379#389C22×C15111yescharacteristic
380#389C22×C15111yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#386—21no—
386#385—21no—
387#380C22×C15111yescharacteristic
388#380C22×C15111yescharacteristic
389C4×C4⋊C4C22×C15111yescharacteristic
390C4×C4⋊C4C22×C15111yescharacteristic
391#340C22×C15111yescharacteristic
392#340C22×C15111yescharacteristic
393#340C22×C15111yescharacteristic
394#340C22×C15111yescharacteristic
395#340C22×C15111yescharacteristic
396#340C22×C15111yescharacteristic
397#336C22×C15111yescharacteristic
398#336C22×C15111yescharacteristic
399#336C22×C15111yescharacteristic
400#336C22×C15111yescharacteristic
401C22×Q8C23×C15111yescharacteristic
402C22×D4—21no—
403C22×D4C23×C15111yescharacteristic
404C23×C4—21no—
405C23×C4C23×C15111yescharacteristic
406C2×SD16—41no—
407C2×SD16—41no—
408C2×SD16C2×C4×C15114yes—
409C2×M16—41no—
410C2×M16—41no—
411C2×M16C2×C4×C15114yescomplemented
412C22×C8—22no—
413C22×C8—41no—
414C22×C8—41no—
415C22×C8C23×C15111yescharacteristic
416C22×C8C23×C15111yescharacteristic
417C22×C8C23×C15111yescharacteristic
418C22×C8C23×C15111yescharacteristic
419C22⋊Q8—22no—
420C22⋊Q8C2×C4×C15114yescomplemented
421#121—22no—
422#121C2×C4×C15114yes—
423C4×Q8—41no—
424C4×Q8—41no—
425C4×D4—41no—
426C4×D4—41no—
427#117—41no—
428#117—41no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C15111yescharacteristic
434C2×C4⋊C4D4×C15111yescharacteristic
435C2×C4⋊C4C23×C15111yescharacteristic
436C2×C4⋊C4C23×C15111yescharacteristic
437C2×C4⋊C4C23×C15111yescharacteristic
438C2×C4⋊C4C23×C15111yescharacteristic
439C2×C4⋊C4C23×C15111yescharacteristic
440C2×C4⋊C4C23×C15111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4D4×C15111yescharacteristic
449C2×C22⋊C4D4×C15111yescharacteristic
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42C23×C15111yescharacteristic
454C2×C42C23×C15111yescharacteristic
455#107—41no—
456#107C2×C4×C15114yescomplemented
457#106—41no—
458#103—41no—
459#103—41no—
460#103C2×C4×C15114yescomplemented
461#102—41no—
462#102—41no—
463#102C2×C4×C15114yes—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C24—21no—
473C24C2×D4×C15111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C22×C4×C15112yes—
480C2×D4—24no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4C22×C4×C15112yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4C22×C4×C15112yes—
504C22×C4C2×D4×C15111yescharacteristic
505C22×C4C2×D4×C15111yescharacteristic
506C22×C4C2×D4×C15111yescharacteristic
507C22×C4C2×D4×C15111yescharacteristic
508C22×C4C2×D4×C15111yescharacteristic
509C22×C4#41×C15112yes—
510C22×C4C24×C15111yescharacteristic
511SD16—44no—
512M16—44no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—44no—
524C2×C8C22×C4×C15112yes—
525C2×C8C22×C4×C15112yes—
526C4⋊C4—24no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4C22×C4×C15112yes—
543C4⋊C4C22×C4×C15112yes—
544C22⋊C4—24no—
545C22⋊C4—24no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—81no—
559C42—81no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C4×D4×C15112yes—
574C23C22×D4×C15111yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—84no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—84no—
624C2×C4C4×D4×C15112yes—
625C2×C4C23×C4×C15111yescharacteristic
626C2×C4C2×#41×C15111yescharacteristic
627C2×C4H(5,𝔽2)×C15111yescharacteristic
628C2×C4H(5,𝔽2)×C15111yescharacteristic
629C2×C4H(5,𝔽2)×C15111yescharacteristic
630C2×C42−1+4×C15111yescharacteristic
631C8—22no—
632C8—22no—
633C8—41no—
634C8—41no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×C4×D4×C15111yescharacteristic
650C22#534×C15111yescharacteristic
651C22#537×C15111yescharacteristic
652C22#576×C15111yescharacteristic
653C22#577×C15111yescharacteristic
654C22#577×C15111yescharacteristic
655C22#578×C15111yescharacteristic
656C4—22no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—42no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4#518×C15111yescharacteristic
669C4#520×C15111yescharacteristic
670C4#538×C15111yescharacteristic
671C4#539×C15111yescharacteristic
672C2—42no—
673C2—82no—
674C2#2325×C15111yescharacteristic
675C2#2946×C15111yescharacteristic
676C2#2947×C15111yescharacteristic
677C2#3200×C15111yescharacteristic
678C2#3203×C15111yescharacteristic
679C2#3257×C15111yescharacteristic
680C2#3258×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2323×C151C2semidirect
4. #1928×C151C2semidirect
5. #1925×C151C2semidirect
6. #1921×C151C2semidirect
7. #1918×C151C2semidirect
9. #1892×C151C2semidirect
10. #1880×C151C2semidirect
11. #1877×C151C2semidirect
12. #1865×C151C2semidirect
13. #1864×C151C2semidirect
14. #1809×C151C2semidirect
15. #1729×C151C2semidirect
24. #468×C151C4semidirect
70. C2×M16×C151C2×C4semidirect
79. C22⋊Q8×C151C2×C4semidirect
115. #107×C151C2×C4semidirect
119. #103×C151C2×C4semidirect
340. #22201C151direct (N × H)
341. C151#22201direct (N × H)
344. #2323C2×C151semidirect
345. #1928C2×C151semidirect
346. #1925C2×C151semidirect
347. #1921C2×C151semidirect
348. #1918C2×C151semidirect
350. #1892C2×C151semidirect
351. #1880C2×C151semidirect
352. #1877C2×C151semidirect
353. #1865C2×C151semidirect
354. #1864C2×C151semidirect
355. #1809C2×C151semidirect
356. #1729C2×C151semidirect
365. #468C4×C151semidirect
411. C2×M16C2×C4×C151semidirect
420. C22⋊Q8C2×C4×C151semidirect
456. #107C2×C4×C151semidirect
460. #103C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1512
#2324×C1512
#2323×C1512
#1928×C1512
#1925×C1512
#1921×C1512
#1918×C1512
#1893×C1512
#1892×C1512
#1880×C1512
#1877×C1512
#1865×C1512
#1864×C1512
#1809×C1512
#1729×C1512
#22201151