Finite Group Databasebeta

← C151×#23011 #50327936

Subgroups — C151×#23011 #50327936

Order 38656.

1058 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic
4#2367×C151C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C151C211yesmaximal, characteristic, complemented
6#1959×C151C211yesmaximal, characteristic, complemented
7#1947×C151C211yesmaximal, characteristic, complemented
8#1936×C151C211yesmaximal, characteristic, complemented
9#1933×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic
11#1877×C151C211yesmaximal, characteristic, complemented
12#1863×C151C211yesmaximal, characteristic, complemented
13#1862×C151C211yesmaximal, characteristic, complemented
14#1771×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C2×#124×C151C2211yescharacteristic
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C22×C4⋊C4×C151—21no—
25#463×C151C418yescomplemented
26#440×C151—24no—
27C4×D8×C151—24no—
28C2×#107×C151C2211yescharacteristic
29C2×#107×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic
42#391×C151C2211yescharacteristic
43#390×C151C2211yescharacteristic
44#389×C151C2211yescharacteristic
45#389×C151C2211yescharacteristic
46#388×C151—21no—
47#388×C151—21no—
48#385×C151—21no—
49#385×C151—21no—
50#385×C151—21no—
51#384×C151C2211yescharacteristic
52#380×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C4⋊C4×C151C2211yescharacteristic
55C4×C22⋊C4×C151—21no—
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62C22×Q8×C151C2311yescharacteristic
63C22×D4×C151C2311yescharacteristic
64C22×D4×C151C2311yescharacteristic
65C23×C4×C151—21no—
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C2×SD16×C151—22no—
70C2×SD16×C151—22no—
71C2×SD16×C151C2×C414yescomplemented
72C2×D8×C151—22no—
73C2×D8×C151—22no—
74C2×D8×C151C2×C414yes—
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79#124×C151—22no—
80#124×C151C2×C414yescomplemented
81C4×Q8×C151—22no—
82C4×Q8×C151—41no—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87C4×D4×C151—41no—
88C4×D4×C151—41no—
89C4×D4×C151—41no—
90C4×D4×C151C2×C414yescomplemented
91C2×C4⋊C4×C151—21no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151—44no—
97C2×C4⋊C4×C151D411yescharacteristic
98C2×C4⋊C4×C151D411yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
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×C42×C151—21no—
113C2×C42×C151—21no—
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117#107×C151—22no—
118#107×C151—22no—
119C4⋊C8×C151C2×C414yescomplemented
120#103×C151—22no—
121#103×C151—41no—
122#103×C151C2×C414yescomplemented
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151C2×C414yescomplemented
127#102×C151D414yes—
128#97×C151—22no—
129#97×C151—22no—
130C4×C8×C151—22no—
131#95×C151—21no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—21no—
144C2×Q8×C151—21no—
145C2×Q8×C151C22×C412yes—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151C22×C412yes—
155C2×D4×C151C22×C412yes—
156C2×D4×C151C2×D412yes—
157C2×D4×C151#4112yes—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—24no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—42no—
166C22×C4×C151—42no—
167C22×C4×C151—42no—
168C22×C4×C151—42no—
169C22×C4×C151—42no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
172C22×C4×C151—42no—
173C22×C4×C151—81no—
174C22×C4×C151—81no—
175C22×C4×C151—81no—
176C22×C4×C151C2×D411yescharacteristic
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2×D411yescharacteristic
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2411yescharacteristic
183SD16×C151—28no—
184D8×C151—28no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151C22×C412yes—
195C2×C8×C151C22×C412yes—
196C2×C8×C151C2×D412yes—
197C4⋊C4×C151—22no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—41no—
207C4⋊C4×C151—42no—
208C4⋊C4×C151—42no—
209C4⋊C4×C151—42no—
210C4⋊C4×C151—42no—
211C4⋊C4×C151—81no—
212C4⋊C4×C151C22×C412yes—
213C4⋊C4×C151C2×D412yes—
214C22⋊C4×C151—24no—
215C22⋊C4×C151—24no—
216C22⋊C4×C151—24no—
217C22⋊C4×C151—42no—
218C22⋊C4×C151—42no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—81no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—42no—
227C42×C151—81no—
228C42×C151C22×C412yes—
229C42×C151#4112yes—
230C23×C151—22no—
231C23×C151—22no—
232C23×C151—22no—
233C23×C151—22no—
234C23×C151—41no—
235C23×C151—41no—
236C23×C151—41no—
237C23×C151—41no—
238C23×C151—41no—
239C23×C151—41no—
240C23×C151—41no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151C22×D411yescharacteristic
245Q8×C151—22no—
246Q8×C151—22no—
247Q8×C151—41no—
248Q8×C151—41no—
249D4×C151—22no—
250D4×C151—22no—
251D4×C151—22no—
252D4×C151—22no—
253D4×C151—22no—
254D4×C151—41no—
255D4×C151—41no—
256D4×C151C4×D414yes—
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—22no—
264C2×C4×C151—22no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—22no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—48no—
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—41no—
283C2×C4×C151—41no—
284C2×C4×C151—41no—
285C2×C4×C151—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—84no—
292C2×C4×C151—84no—
293C2×C4×C151—84no—
294C2×C4×C151C4×D412yes—
295C2×C4×C151C4×D412yes—
296C2×C4×C151AGL(1,ℤ/8)12yes—
297C2×C4×C151C23×C411yescharacteristic
298C2×C4×C151C22×D411yescharacteristic
299C2×C4×C151C2×#4111yescharacteristic
300C2×C4×C151C2×#4111yescharacteristic
301C2×C4×C151H(5,𝔽2)11yescharacteristic
302C2×C4×C1512−1+411yescharacteristic
303C8×C151—22no—
304C8×C151—22no—
305C8×C151—22no—
306C8×C151—41no—
307C22×C151—24no—
308C22×C151—42no—
309C22×C151—42no—
310C22×C151—42no—
311C22×C151—42no—
312C22×C151—42no—
313C22×C151—42no—
314C22×C151—42no—
315C22×C151—42no—
316C22×C151—42no—
317C22×C151—81no—
318C22×C151—81no—
319C22×C151—81no—
320C22×C151—81no—
321C22×C151C2×C4×D411yescharacteristic
322C22×C151D4211yescharacteristic
323C22×C151#54811yescharacteristic
324C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C151#57511yescharacteristic
326C22×C151#57611yescharacteristic
327C22×C151#57811yescharacteristic
328C4×C151—22no—
329C4×C151—22no—
330C4×C151—22no—
331C4×C151—42no—
332C4×C151—42no—
333C4×C151—41no—
334C4×C151—42no—
335C4×C151—41no—
336C4×C151—41no—
337C4×C151—81no—
338C4×C151—81no—
339C4×C151—81no—
340C4×C151C2×C4×D411yescharacteristic
341C4×C151#52011yescharacteristic
342C4×C151#54711yescharacteristic
343C4×C151#55311yescharacteristic
344C2×C151—44no—
345C2×C151—82no—
346C2×C151#236111yescharacteristic
347C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
348C2×C151#295111yescharacteristic
349C2×C151#326411yescharacteristic
350C2×C151#326911yescharacteristic
351C2×C151#336711yescharacteristic
352C2×C151#337011yescharacteristic
353#23011C15111yesmaximal, characteristic, direct product factor, Sylow
354C151#2301111yescharacteristic, direct product factor, Sylow
355C2×#463C2×C15111yescharacteristic
356C2×#440C2×C15111yescharacteristic, complemented
357C2×C4×D8C2×C15111yescharacteristic
358#2367C2×C15111yescharacteristic, complemented
359D4×C4⋊C4C2×C15111yescharacteristic, complemented
360#1959C2×C15111yescharacteristic, complemented
361#1947C2×C15111yescharacteristic, complemented
362#1936C2×C15111yescharacteristic, complemented
363#1933C2×C15111yescharacteristic, complemented
364#1879C2×C15111yescharacteristic
365#1877C2×C15111yescharacteristic, complemented
366#1863C2×C15111yescharacteristic, complemented
367#1862C2×C15111yescharacteristic, complemented
368#1771C2×C15111yescharacteristic, complemented
369#1762C2×C15111yescharacteristic, complemented
370C22×SD16C22×C15111yescharacteristic
371C22×D8C22×C15111yescharacteristic
372C2×#124C22×C15111yescharacteristic
373C2×C4×Q8C22×C15111yescharacteristic
374C2×C4×D4C22×C15111yescharacteristic
375C2×C4×D4C22×C15111yescharacteristic
376C2×C4×D4C22×C15111yescharacteristic
377C2×C4×D4C22×C15111yescharacteristic
378C22×C4⋊C4—21no—
379#463C4×C15118yescomplemented
380#440—24no—
381C4×D8—24no—
382C2×#107C22×C15111yescharacteristic
383C2×#107C22×C15111yescharacteristic
384C2×C4⋊C8C22×C15111yescharacteristic
385C2×#103C22×C15111yescharacteristic
386C2×#103C22×C15111yescharacteristic
387C2×#103C22×C15111yescharacteristic
388C2×#102C22×C15111yescharacteristic
389C2×#102C22×C15111yescharacteristic
390C2×#102C22×C15111yescharacteristic
391C2×#102C22×C15111yescharacteristic
392C2×#102C22×C15111yescharacteristic
393C2×#97C22×C15111yescharacteristic
394C2×#97C22×C15111yescharacteristic
395C2×C4×C8C22×C15111yescharacteristic
396#391C22×C15111yescharacteristic
397#390C22×C15111yescharacteristic
398#389C22×C15111yescharacteristic
399#389C22×C15111yescharacteristic
400#388—21no—
401#388—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384C22×C15111yescharacteristic
406#380—21no—
407C4×C4⋊C4C22×C15111yescharacteristic
408C4×C4⋊C4C22×C15111yescharacteristic
409C4×C22⋊C4—21no—
410#340C22×C15111yescharacteristic
411#340C22×C15111yescharacteristic
412#340C22×C15111yescharacteristic
413#340C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416C22×Q8C23×C15111yescharacteristic
417C22×D4C23×C15111yescharacteristic
418C22×D4C23×C15111yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—21no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×C4×C15114yescomplemented
426C2×D8—22no—
427C2×D8—22no—
428C2×D8C2×C4×C15114yes—
429C22×C8C23×C15111yescharacteristic
430C22×C8C23×C15111yescharacteristic
431C22×C8C23×C15111yescharacteristic
432C22×C8C23×C15111yescharacteristic
433#124—22no—
434#124C2×C4×C15114yescomplemented
435C4×Q8—22no—
436C4×Q8—41no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—41no—
442C4×D4—41no—
443C4×D4—41no—
444C4×D4C2×C4×C15114yescomplemented
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—44no—
451C2×C4⋊C4D4×C15111yescharacteristic
452C2×C4⋊C4D4×C15111yescharacteristic
453C2×C4⋊C4C23×C15111yescharacteristic
454C2×C4⋊C4C23×C15111yescharacteristic
455C2×C4⋊C4C23×C15111yescharacteristic
456C2×C4⋊C4C23×C15111yescharacteristic
457C2×C4⋊C4C23×C15111yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C15111yescharacteristic
469C2×C42C23×C15111yescharacteristic
470C2×C42C23×C15111yescharacteristic
471#107—22no—
472#107—22no—
473C4⋊C8C2×C4×C15114yescomplemented
474#103—22no—
475#103—41no—
476#103C2×C4×C15114yescomplemented
477#102—22no—
478#102—22no—
479#102—41no—
480#102C2×C4×C15114yescomplemented
481#102D4×C15114yes—
482#97—22no—
483#97—22no—
484C4×C8—22no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95D4×C15111yescharacteristic
491#95D4×C15111yescharacteristic
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×C4×C15112yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C15112yes—
509C2×D4C22×C4×C15112yes—
510C2×D4C2×D4×C15112yes—
511C2×D4#41×C15112yes—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4C2×D4×C15111yescharacteristic
531C22×C4C2×D4×C15111yescharacteristic
532C22×C4C2×D4×C15111yescharacteristic
533C22×C4C2×D4×C15111yescharacteristic
534C22×C4C2×D4×C15111yescharacteristic
535C22×C4C2×D4×C15111yescharacteristic
536C22×C4C24×C15111yescharacteristic
537SD16—28no—
538D8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C22×C4×C15112yes—
549C2×C8C22×C4×C15112yes—
550C2×C8C2×D4×C15112yes—
551C4⋊C4—22no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—41no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4C22×C4×C15112yes—
567C4⋊C4C2×D4×C15112yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—81no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—42no—
581C42—81no—
582C42C22×C4×C15112yes—
583C42#41×C15112yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22×D4×C15111yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4C4×D4×C15114yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—48no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C4×D4×C15112yes—
649C2×C4C4×D4×C15112yes—
650C2×C4AGL(1,ℤ/8)×C15112yes—
651C2×C4C23×C4×C15111yescharacteristic
652C2×C4C22×D4×C15111yescharacteristic
653C2×C4C2×#41×C15111yescharacteristic
654C2×C4C2×#41×C15111yescharacteristic
655C2×C4H(5,𝔽2)×C15111yescharacteristic
656C2×C42−1+4×C15111yescharacteristic
657C8—22no—
658C8—22no—
659C8—22no—
660C8—41no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C4×D4×C15111yescharacteristic
676C22D42×C15111yescharacteristic
677C22#548×C15111yescharacteristic
678C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
679C22#575×C15111yescharacteristic
680C22#576×C15111yescharacteristic
681C22#578×C15111yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4C2×C4×D4×C15111yescharacteristic
695C4#520×C15111yescharacteristic
696C4#547×C15111yescharacteristic
697C4#553×C15111yescharacteristic
698C2—44no—
699C2—82no—
700C2#2361×C15111yescharacteristic
701C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
702C2#2951×C15111yescharacteristic
703C2#3264×C15111yescharacteristic
704C2#3269×C15111yescharacteristic
705C2#3367×C15111yescharacteristic
706C2#3370×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C151C2semidirect
4. #2367×C151C2semidirect
5. D4×C4⋊C4×C151C2semidirect
6. #1959×C151C2semidirect
7. #1947×C151C2semidirect
8. #1936×C151C2semidirect
9. #1933×C151C2semidirect
11. #1877×C151C2semidirect
12. #1863×C151C2semidirect
13. #1862×C151C2semidirect
14. #1771×C151C2semidirect
15. #1762×C151C2semidirect
25. #463×C151C4semidirect
71. C2×SD16×C151C2×C4semidirect
80. #124×C151C2×C4semidirect
90. C4×D4×C151C2×C4semidirect
119. C4⋊C8×C151C2×C4semidirect
122. #103×C151C2×C4semidirect
126. #102×C151C2×C4semidirect
353. #23011C151direct (N × H)
354. C151#23011direct (N × H)
356. C2×#440C2×C151semidirect
358. #2367C2×C151semidirect
359. D4×C4⋊C4C2×C151semidirect
360. #1959C2×C151semidirect
361. #1947C2×C151semidirect
362. #1936C2×C151semidirect
363. #1933C2×C151semidirect
365. #1877C2×C151semidirect
366. #1863C2×C151semidirect
367. #1862C2×C151semidirect
368. #1771C2×C151semidirect
369. #1762C2×C151semidirect
379. #463C4×C151semidirect
425. C2×SD16C2×C4×C151semidirect
434. #124C2×C4×C151semidirect
444. C4×D4C2×C4×C151semidirect
473. C4⋊C8C2×C4×C151semidirect
476. #103C2×C4×C151semidirect
480. #102C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1512
C2×#440×C1512
C2×C4×D8×C1512
#2367×C1512
D4×C4⋊C4×C1512
#1959×C1512
#1947×C1512
#1936×C1512
#1933×C1512
#1879×C1512
#1877×C1512
#1863×C1512
#1862×C1512
#1771×C1512
#1762×C1512
#23011151