Finite Group Databasebeta

← C151×#24909 #50329834

Subgroups — C151×#24909 #50329834

Order 38656.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C2×#442×C151C211yesmaximal, characteristic, complemented
3#2420×C151C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5#2092×C151C211yesmaximal, characteristic, complemented
6#2077×C151C211yesmaximal, characteristic, complemented
7#2054×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1936×C151C211yesmaximal, characteristic, complemented
10#1924×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1862×C151C211yesmaximal, characteristic, complemented
14#1804×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic, complemented
23C22×C22⋊C4×C151—21no—
24#447×C151—24no—
25#442×C151—24no—
26C2×#107×C151C2211yescharacteristic, complemented
27C2×#106×C151C2211yescharacteristic, complemented
28C2×C4⋊C8×C151C2211yescharacteristic, complemented
29C2×#102×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic, complemented
36C2×#102×C151C2211yescharacteristic, complemented
37C2×C22⋊C8×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic, complemented
40#397×C151—21no—
41#394×C151—21no—
42#390×C151C2211yescharacteristic
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic, complemented
45#389×C151C2211yescharacteristic, complemented
46#386×C151—21no—
47#386×C151—21no—
48#386×C151—21no—
49#382×C151C2211yescharacteristic, complemented
50#381×C151—21no—
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53#379×C151—21no—
54C4×C22⋊C4×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic, complemented
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151—21no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151C2311yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—41no—
82C2×D8×C151D414yes—
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87#121×C151—22no—
88#121×C151—41no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—41no—
93C4×D4×C151—41no—
94C4×D4×C151—41no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—44no—
114C2×C22⋊C4×C151D411yescharacteristic
115C2×C22⋊C4×C151D411yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#107×C151—41no—
119#106×C151—22no—
120C4⋊C8×C151—41no—
121#102×C151—22no—
122#102×C151—22no—
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—41no—
128#102×C151—41no—
129C22⋊C8×C151—22no—
130C22⋊C8×C151—41no—
131#97×C151—22no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151D411yescharacteristic
138#95×C151D411yescharacteristic
139C24×C151—21no—
140C24×C151—24no—
141C24×C151—21no—
142C24×C151—21no—
143C24×C151—42no—
144C24×C151—42no—
145C24×C151—42no—
146C24×C151—42no—
147C24×C151—81no—
148C24×C151—81no—
149C24×C151C2×D411yescharacteristic
150C2×D4×C151—24no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—42no—
165C2×D4×C151—42no—
166C2×D4×C151—44no—
167C2×D4×C151—44no—
168C2×D4×C151—44no—
169C2×D4×C151—44no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—81no—
173C2×D4×C151C2×D412yes—
174C2×D4×C151C2×D412yes—
175C2×D4×C151#4112yes—
176C2×D4×C151#4112yes—
177C2×D4×C151#4112yes—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—42no—
190C22×C4×C151—42no—
191C22×C4×C151—42no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—81no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151C2×D411yescharacteristic
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2411yescharacteristic
204D8×C151—28no—
205D8×C151—44no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151C2×D412yes—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—81no—
229C22⋊C4×C151—22no—
230C22⋊C4×C151—41no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—42no—
233C22⋊C4×C151—42no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—81no—
239C22⋊C4×C151—81no—
240C22⋊C4×C151—81no—
241C22⋊C4×C151—81no—
242C22⋊C4×C151—81no—
243C42×C151—21no—
244C42×C151—21no—
245C42×C151—21no—
246C42×C151—21no—
247C23×C151—21no—
248C23×C151—22no—
249C23×C151—22no—
250C23×C151—21no—
251C23×C151—22no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—22no—
257C23×C151—22no—
258C23×C151—48no—
259C23×C151—48no—
260C23×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—84no—
277C23×C151—84no—
278C23×C151—84no—
279C23×C151—84no—
280C23×C151—84no—
281C23×C151AGL(1,ℤ/8)12yes—
282C23×C151C22×D411yescharacteristic
283D4×C151—22no—
284D4×C151—22no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—22no—
290D4×C151—48no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—84no—
296D4×C151#12314yes—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—84no—
332C2×C4×C151—84no—
333C2×C4×C151—84no—
334C2×C4×C151C22×D411yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151C2×#4111yescharacteristic
337C2×C4×C151C2×#4111yescharacteristic
338C2×C4×C151H(5,𝔽2)11yescharacteristic
339C2×C4×C151H(5,𝔽2)11yescharacteristic
340C8×C151—22no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C22×C151—22no—
345C22×C151—24no—
346C22×C151—22no—
347C22×C151—22no—
348C22×C151—42no—
349C22×C151—41no—
350C22×C151—42no—
351C22×C151—41no—
352C22×C151—42no—
353C22×C151—41no—
354C22×C151—42no—
355C22×C151—42no—
356C22×C151—41no—
357C22×C151—42no—
358C22×C151—42no—
359C22×C151—42no—
360C22×C151—42no—
361C22×C151—42no—
362C22×C151—42no—
363C22×C151—42no—
364C22×C151—816no—
365C22×C151—81no—
366C22×C151—81no—
367C22×C151—81no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151#52511yescharacteristic
374C22×C151D4211yescharacteristic
375C22×C151#54611yescharacteristic
376C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C151#57511yescharacteristic
378C22×C151#57611yescharacteristic
379C22×C151#57611yescharacteristic
380C4×C151—41no—
381C4×C151—41no—
382C4×C151—41no—
383C4×C151—41no—
384C4×C151—41no—
385C4×C151—81no—
386C4×C151—81no—
387C4×C151—81no—
388C4×C151—81no—
389C4×C151—81no—
390C4×C151C2×#12311yescharacteristic
391C4×C151#53811yescharacteristic
392C4×C151#54611yescharacteristic
393C4×C151#55111yescharacteristic
394C2×C151—42no—
395C2×C151—44no—
396C2×C151—82no—
397C2×C151—82no—
398C2×C151#241811yescharacteristic
399C2×C151#311411yescharacteristic
400C2×C151#312211yescharacteristic
401C2×C151#326411yescharacteristic
402C2×C151#327311yescharacteristic
403C2×C151#331811yescharacteristic
404C2×C151#331911yescharacteristic
405#24909C15111yesmaximal, characteristic, direct product factor, Sylow
406C151#2490911yescharacteristic, direct product factor, Sylow
407C2×#447C2×C15111yescharacteristic
408C2×#442C2×C15111yescharacteristic, complemented
409#2420C2×C15111yescharacteristic, complemented
410D4×C22⋊C4C2×C15111yescharacteristic, complemented
411#2092C2×C15111yescharacteristic, complemented
412#2077C2×C15111yescharacteristic, complemented
413#2054C2×C15111yescharacteristic, complemented
414#2033C2×C15111yescharacteristic, complemented
415#1936C2×C15111yescharacteristic, complemented
416#1924C2×C15111yescharacteristic, complemented
417#1879C2×C15111yescharacteristic, complemented
418#1879C2×C15111yescharacteristic, complemented
419#1862C2×C15111yescharacteristic, complemented
420#1804C2×C15111yescharacteristic, complemented
421#1786C2×C15111yescharacteristic, complemented
422C23×D4C22×C15111yescharacteristic
423C22×D8C22×C15111yescharacteristic
424C22×D8C22×C15111yescharacteristic
425C2×#121C22×C15111yescharacteristic
426C2×C4×D4C22×C15111yescharacteristic
427C2×C4×D4C22×C15111yescharacteristic
428C2×C4×D4C22×C15111yescharacteristic, complemented
429C22×C22⋊C4—21no—
430#447—24no—
431#442—24no—
432C2×#107C22×C15111yescharacteristic, complemented
433C2×#106C22×C15111yescharacteristic, complemented
434C2×C4⋊C8C22×C15111yescharacteristic, complemented
435C2×#102C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×#102C22×C15111yescharacteristic
438C2×#102C22×C15111yescharacteristic
439C2×#102C22×C15111yescharacteristic
440C2×#102C22×C15111yescharacteristic
441C2×#102C22×C15111yescharacteristic, complemented
442C2×#102C22×C15111yescharacteristic, complemented
443C2×C22⋊C8C22×C15111yescharacteristic
444C2×C22⋊C8C22×C15111yescharacteristic
445C2×#97C22×C15111yescharacteristic, complemented
446#397—21no—
447#394—21no—
448#390C22×C15111yescharacteristic
449#390C22×C15111yescharacteristic
450#390C22×C15111yescharacteristic, complemented
451#389C22×C15111yescharacteristic, complemented
452#386—21no—
453#386—21no—
454#386—21no—
455#382C22×C15111yescharacteristic, complemented
456#381—21no—
457#380C22×C15111yescharacteristic
458#380C22×C15111yescharacteristic
459#379—21no—
460C4×C22⋊C4C22×C15111yescharacteristic
461#340C22×C15111yescharacteristic, complemented
462#340C22×C15111yescharacteristic, complemented
463#340C22×C15111yescharacteristic, complemented
464#340C22×C15111yescharacteristic, complemented
465#336C22×C15111yescharacteristic, complemented
466#336C22×C15111yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C15111yescharacteristic
477C22×D4C23×C15111yescharacteristic
478C22×D4C23×C15111yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C15111yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C15114yes—
489C22×C8C23×C15111yescharacteristic
490C22×C8C23×C15111yescharacteristic
491C22×C8C23×C15111yescharacteristic
492C22×C8C23×C15111yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C15111yescharacteristic
503C2×C4⋊C4C23×C15111yescharacteristic
504C2×C4⋊C4C23×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—44no—
520C2×C22⋊C4D4×C15111yescharacteristic
521C2×C22⋊C4D4×C15111yescharacteristic
522C2×C42C23×C15111yescharacteristic
523C2×C42C23×C15111yescharacteristic
524#107—41no—
525#106—22no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537#97—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C15111yescharacteristic
544#95D4×C15111yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C15111yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C15112yes—
580C2×D4C2×D4×C15112yes—
581C2×D4#41×C15112yes—
582C2×D4#41×C15112yes—
583C2×D4#41×C15112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C15111yescharacteristic
605C22×C4C2×D4×C15111yescharacteristic
606C22×C4C2×D4×C15111yescharacteristic
607C22×C4C2×D4×C15111yescharacteristic
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C24×C15111yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×D4×C15112yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—81no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23AGL(1,ℤ/8)×C15112yes—
688C23C22×D4×C15111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C15114yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4C22×D4×C15111yescharacteristic
741C2×C4C2×#41×C15111yescharacteristic
742C2×C4C2×#41×C15111yescharacteristic
743C2×C4C2×#41×C15111yescharacteristic
744C2×C4H(5,𝔽2)×C15111yescharacteristic
745C2×C4H(5,𝔽2)×C15111yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—24no—
752C22—22no—
753C22—22no—
754C22—42no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#525×C15111yescharacteristic
780C22D42×C15111yescharacteristic
781C22#546×C15111yescharacteristic
782C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
783C22#575×C15111yescharacteristic
784C22#576×C15111yescharacteristic
785C22#576×C15111yescharacteristic
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C15111yescharacteristic
797C4#538×C15111yescharacteristic
798C4#546×C15111yescharacteristic
799C4#551×C15111yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2#2418×C15111yescharacteristic
805C2#3114×C15111yescharacteristic
806C2#3122×C15111yescharacteristic
807C2#3264×C15111yescharacteristic
808C2#3273×C15111yescharacteristic
809C2#3318×C15111yescharacteristic
810C2#3319×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#442×C151C2semidirect
3. #2420×C151C2semidirect
4. D4×C22⋊C4×C151C2semidirect
5. #2092×C151C2semidirect
6. #2077×C151C2semidirect
7. #2054×C151C2semidirect
8. #2033×C151C2semidirect
9. #1936×C151C2semidirect
10. #1924×C151C2semidirect
11. #1879×C151C2semidirect
12. #1879×C151C2semidirect
13. #1862×C151C2semidirect
14. #1804×C151C2semidirect
15. #1786×C151C2semidirect
22. C2×C4×D4×C151C22semidirect
26. C2×#107×C151C22semidirect
27. C2×#106×C151C22semidirect
28. C2×C4⋊C8×C151C22semidirect
35. C2×#102×C151C22semidirect
36. C2×#102×C151C22semidirect
39. C2×#97×C151C22semidirect
44. #390×C151C22semidirect
45. #389×C151C22semidirect
49. #382×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
405. #24909C151direct (N × H)
406. C151#24909direct (N × H)
408. C2×#442C2×C151semidirect
409. #2420C2×C151semidirect
410. D4×C22⋊C4C2×C151semidirect
411. #2092C2×C151semidirect
412. #2077C2×C151semidirect
413. #2054C2×C151semidirect
414. #2033C2×C151semidirect
415. #1936C2×C151semidirect
416. #1924C2×C151semidirect
417. #1879C2×C151semidirect
418. #1879C2×C151semidirect
419. #1862C2×C151semidirect
420. #1804C2×C151semidirect
421. #1786C2×C151semidirect
428. C2×C4×D4C22×C151semidirect
432. C2×#107C22×C151semidirect
433. C2×#106C22×C151semidirect
434. C2×C4⋊C8C22×C151semidirect
441. C2×#102C22×C151semidirect
442. C2×#102C22×C151semidirect
445. C2×#97C22×C151semidirect
450. #390C22×C151semidirect
451. #389C22×C151semidirect
455. #382C22×C151semidirect
461. #340C22×C151semidirect
462. #340C22×C151semidirect
463. #340C22×C151semidirect
464. #340C22×C151semidirect
465. #336C22×C151semidirect
466. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C2×#442×C1512
#2420×C1512
D4×C22⋊C4×C1512
#2092×C1512
#2077×C1512
#2054×C1512
#2033×C1512
#1936×C1512
#1924×C1512
#1879×C1512
#1862×C1512
#1804×C1512
#1786×C1512
#24909151