Finite Group Databasebeta

← C151×#22423 #50327348

Subgroups — C151×#22423 #50327348

Order 38656.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C151C211yesmaximal, characteristic
2C2×#435×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4C22×#102×C151C211yesmaximal, characteristic, complemented
5#2352×C151C211yesmaximal, characteristic, complemented
6#1982×C151C211yesmaximal, characteristic, complemented
7#1961×C151C211yesmaximal, characteristic, complemented
8#1895×C151C211yesmaximal, characteristic, complemented
9#1893×C151C211yesmaximal, characteristic, complemented
10#1875×C151C211yesmaximal, characteristic, complemented
11#1874×C151C211yesmaximal, characteristic, complemented
12#1804×C151C211yesmaximal, characteristic, complemented
13#1786×C151C211yesmaximal, characteristic, complemented
14#1786×C151C211yesmaximal, characteristic, complemented
15#1762×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151—21no—
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic, complemented
20C23×C8×C151C2211yescharacteristic, complemented
21D42×C151—24no—
22D42×C151C418yescomplemented
23C2×#127×C151C2211yescharacteristic
24C2×#121×C151—21no—
25C2×#121×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27C2×#120×C151—21no—
28C2×#120×C151—21no—
29C2×C4×D4×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C2×#117×C151C2211yescharacteristic, complemented
32C22×C4⋊C4×C151C2211yescharacteristic, complemented
33#435×C151—24no—
34C2×C4⋊C8×C151C2211yescharacteristic, complemented
35#418×C151—24no—
36C2×#102×C151—24no—
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic, complemented
42C2×#102×C151C2211yescharacteristic, complemented
43C2×#102×C151C2211yescharacteristic, complemented
44C2×#102×C151C2211yescharacteristic, complemented
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic, complemented
49C2×C22⋊C8×C151C2211yescharacteristic, complemented
50C2×C22⋊C8×C151C2211yescharacteristic, complemented
51C2×#97×C151C2211yescharacteristic, complemented
52#388×C151—21no—
53#387×C151—21no—
54#386×C151—21no—
55#382×C151C2211yescharacteristic, complemented
56#380×C151C2211yescharacteristic, complemented
57#380×C151C2211yescharacteristic, complemented
58C4×C4⋊C4×C151C2211yescharacteristic, complemented
59C4×C22⋊C4×C151—21no—
60#340×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64C25×C151—21no—
65C25×C151—21no—
66C22×D4×C151—28no—
67C22×D4×C151—21no—
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—22no—
79C22×D4×C151—41no—
80C22×D4×C151—41no—
81C22×D4×C151—41no—
82C22×D4×C151—41no—
83C22×D4×C151—44no—
84C22×D4×C151—44no—
85C22×D4×C151C2×C414yes—
86C22×D4×C151C2×C414yescomplemented
87C22×D4×C151D411yescharacteristic
88C22×D4×C151C2311yescharacteristic
89C22×D4×C151C2311yescharacteristic
90C22×D4×C151C2311yescharacteristic
91C23×C4×C151—21no—
92C23×C4×C151—21no—
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C2×M16×C151—22no—
96C2×M16×C151—22no—
97C2×M16×C151—41no—
98C22×C8×C151—22no—
99C22×C8×C151—22no—
100C22×C8×C151—41no—
101C22×C8×C151C2311yescharacteristic
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105#127×C151—22no—
106#127×C151C2×C414yescomplemented
107#121×C151—22no—
108#121×C151—22no—
109#121×C151—28no—
110#121×C151C2×C414yes—
111#121×C151C2×C414yescomplemented
112#120×C151—28no—
113#120×C151—28no—
114C4×D4×C151—22no—
115C4×D4×C151C2×C414yes—
116C4×D4×C151C2×C414yescomplemented
117C4×D4×C151D414yes—
118#117×C151—22no—
119#117×C151—41no—
120C2×C4⋊C4×C151—22no—
121C2×C4⋊C4×C151—21no—
122C2×C4⋊C4×C151—41no—
123C2×C4⋊C4×C151D411yescharacteristic
124C2×C4⋊C4×C151C2311yescharacteristic
125C2×C4⋊C4×C151C2311yescharacteristic
126C2×C4⋊C4×C151C2311yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151D411yescharacteristic
136C2×C22⋊C4×C151D411yescharacteristic
137C2×C42×C151—21no—
138C2×C42×C151—21no—
139C2×C42×C151C2311yescharacteristic
140C4⋊C8×C151—22no—
141#102×C151—22no—
142#102×C151—22no—
143#102×C151—22no—
144#102×C151—22no—
145#102×C151—22no—
146#102×C151—22no—
147#102×C151—22no—
148#102×C151—41no—
149#102×C151—41no—
150#102×C151—41no—
151#102×C151—41no—
152#102×C151D414yescomplemented
153C22⋊C8×C151—22no—
154C22⋊C8×C151—22no—
155#97×C151—22no—
156#95×C151—21no—
157#95×C151—21no—
158#95×C151—21no—
159#95×C151—21no—
160#95×C151—21no—
161C24×C151—21no—
162C24×C151—21no—
163C24×C151—21no—
164C24×C151—24no—
165C24×C151—24no—
166C24×C151—42no—
167C24×C151—42no—
168C24×C151—42no—
169C24×C151—42no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—42no—
173C24×C151—42no—
174C24×C151—81no—
175C24×C151—81no—
176C24×C151—81no—
177C24×C151—81no—
178C24×C151C2×D411yescharacteristic
179C24×C151C2×D411yescharacteristic
180C2×D4×C151—22no—
181C2×D4×C151—22no—
182C2×D4×C151—28no—
183C2×D4×C151—28no—
184C2×D4×C151—24no—
185C2×D4×C151—24no—
186C2×D4×C151—24no—
187C2×D4×C151—24no—
188C2×D4×C151—24no—
189C2×D4×C151—24no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—44no—
204C2×D4×C151—44no—
205C2×D4×C151—44no—
206C2×D4×C151—44no—
207C2×D4×C151—44no—
208C2×D4×C151—44no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—432no—
216C2×D4×C151—42no—
217C2×D4×C151—42no—
218C2×D4×C151—42no—
219C2×D4×C151—42no—
220C2×D4×C151—81no—
221C2×D4×C151—81no—
222C2×D4×C151C22⋊C414yes—
223C2×D4×C151C22×C412yes—
224C2×D4×C151C22×C412yes—
225C2×D4×C151C22×C412yes—
226C2×D4×C151C2×D412yes—
227C2×D4×C151#4112yes—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—24no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—42no—
243C22×C4×C151—42no—
244C22×C4×C151—42no—
245C22×C4×C151—42no—
246C22×C4×C151—81no—
247C22×C4×C151C22×C412yes—
248C22×C4×C151C22×C412yes—
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D411yescharacteristic
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2×D411yescharacteristic
253C22×C4×C151C2×D412yes—
254C22×C4×C151C2×D412yes—
255C22×C4×C151C2411yescharacteristic
256M16×C151—44no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—44no—
269C2×C8×C151C2×D412yescomplemented
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—42no—
279C4⋊C4×C151C22⋊C414yes—
280C4⋊C4×C151C22×C412yes—
281C4⋊C4×C151C2×D412yescomplemented
282C22⋊C4×C151—24no—
283C22⋊C4×C151—24no—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—42no—
286C22⋊C4×C151—42no—
287C22⋊C4×C151—81no—
288C22⋊C4×C151C22⋊C414yes—
289C22⋊C4×C151C22⋊C414yes—
290C42×C151—42no—
291C42×C151—81no—
292C42×C151C22×C412yes—
293C42×C151C2×D412yes—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—22no—
299C23×C151—22no—
300C23×C151—21no—
301C23×C151—22no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—22no—
308C23×C151—22no—
309C23×C151—48no—
310C23×C151—48no—
311C23×C151—48no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—41no—
321C23×C151—41no—
322C23×C151—41no—
323C23×C151—41no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151—41no—
327C23×C151—41no—
328C23×C151—48no—
329C23×C151—84no—
330C23×C151—84no—
331C23×C151—84no—
332C23×C151—84no—
333C23×C151—84no—
334C23×C151—84no—
335C23×C151—84no—
336C23×C151—84no—
337C23×C151—84no—
338C23×C151—84no—
339C23×C151C2×C22⋊C412yes—
340C23×C151C2×C22⋊C412yes—
341C23×C151AGL(1,ℤ/8)12yes—
342C23×C151AGL(1,ℤ/8)12yes—
343C23×C151C22×D411yescharacteristic
344D4×C151—28no—
345D4×C151—22no—
346D4×C151—22no—
347D4×C151—22no—
348D4×C151—22no—
349D4×C151—22no—
350D4×C151—22no—
351D4×C151—22no—
352D4×C151—48no—
353D4×C151—48no—
354D4×C151—48no—
355D4×C151—48no—
356D4×C151—48no—
357D4×C151—41no—
358D4×C151—41no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—84no—
362D4×C151C4×D414yes—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—21no—
371C2×C4×C151—22no—
372C2×C4×C151—22no—
373C2×C4×C151—22no—
374C2×C4×C151—22no—
375C2×C4×C151—22no—
376C2×C4×C151—22no—
377C2×C4×C151—22no—
378C2×C4×C151—22no—
379C2×C4×C151—22no—
380C2×C4×C151—22no—
381C2×C4×C151—48no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
384C2×C4×C151—41no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—41no—
388C2×C4×C151—41no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—84no—
396C2×C4×C151C2×C22⋊C412yes—
397C2×C4×C151C2×C22⋊C412yes—
398C2×C4×C151C2×C22⋊C412yes—
399C2×C4×C151C2×C22⋊C412yes—
400C2×C4×C151C23×C411yescharacteristic
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C22×D411yescharacteristic
403C2×C4×C151C2×#4111yescharacteristic
404C2×C4×C151H(5,𝔽2)11yescharacteristic
405C2×C4×C151H(5,𝔽2)11yescharacteristic
406C8×C151—22no—
407C8×C151—41no—
408C8×C151—41no—
409C8×C151—41no—
410C22×C151—22no—
411C22×C151—22no—
412C22×C151—22no—
413C22×C151—22no—
414C22×C151—22no—
415C22×C151—22no—
416C22×C151—22no—
417C22×C151—24no—
418C22×C151—22no—
419C22×C151—22no—
420C22×C151—42no—
421C22×C151—42no—
422C22×C151—41no—
423C22×C151—42no—
424C22×C151—41no—
425C22×C151—42no—
426C22×C151—41no—
427C22×C151—42no—
428C22×C151—41no—
429C22×C151—42no—
430C22×C151—42no—
431C22×C151—42no—
432C22×C151—42no—
433C22×C151—42no—
434C22×C151—42no—
435C22×C151—42no—
436C22×C151—816no—
437C22×C151—816no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151#41814yescomplemented
447C22×C151C22×C22⋊C411yescharacteristic
448C22×C151D4211yescharacteristic
449C22×C151#54611yescharacteristic
450C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C151#57611yescharacteristic
453C22×C151#57711yescharacteristic
454C4×C151—22no—
455C4×C151—22no—
456C4×C151—22no—
457C4×C151—22no—
458C4×C151—42no—
459C4×C151—42no—
460C4×C151—81no—
461C4×C151—81no—
462C4×C151—81no—
463C4×C151C2×C4×D411yescharacteristic
464C4×C151#51811yescharacteristic
465C4×C151D4211yescharacteristic
466C4×C151#54611yescharacteristic
467C2×C151—24no—
468C2×C151—42no—
469C2×C151—44no—
470C2×C151—82no—
471C2×C151—82no—
472C2×C151D4×C22⋊C411yescharacteristic
473C2×C151C2×#41811yescharacteristic
474C2×C151#289711yescharacteristic
475C2×C151#326411yescharacteristic
476C2×C151#326511yescharacteristic
477C2×C151#331011yescharacteristic
478C2×C151#331811yescharacteristic
479#22423C15111yesmaximal, characteristic, direct product factor, Sylow
480C151#2242311yescharacteristic, direct product factor, Sylow
481C2×D42C2×C15111yescharacteristic
482C2×#435C2×C15111yescharacteristic, complemented
483C2×#418C2×C15111yescharacteristic, complemented
484C22×#102C2×C15111yescharacteristic, complemented
485#2352C2×C15111yescharacteristic, complemented
486#1982C2×C15111yescharacteristic, complemented
487#1961C2×C15111yescharacteristic, complemented
488#1895C2×C15111yescharacteristic, complemented
489#1893C2×C15111yescharacteristic, complemented
490#1875C2×C15111yescharacteristic, complemented
491#1874C2×C15111yescharacteristic, complemented
492#1804C2×C15111yescharacteristic, complemented
493#1786C2×C15111yescharacteristic, complemented
494#1786C2×C15111yescharacteristic, complemented
495#1762C2×C15111yescharacteristic, complemented
496C23×D4—21no—
497C23×D4C22×C15111yescharacteristic
498C23×D4C22×C15111yescharacteristic
499C22×M16C22×C15111yescharacteristic, complemented
500C23×C8C22×C15111yescharacteristic, complemented
501D42—24no—
502D42C4×C15118yescomplemented
503C2×#127C22×C15111yescharacteristic
504C2×#121—21no—
505C2×#121C22×C15111yescharacteristic
506C2×#121C22×C15111yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4C22×C15111yescharacteristic
510C2×C4×D4C22×C15111yescharacteristic
511C2×#117C22×C15111yescharacteristic, complemented
512C22×C4⋊C4C22×C15111yescharacteristic, complemented
513#435—24no—
514C2×C4⋊C8C22×C15111yescharacteristic, complemented
515#418—24no—
516C2×#102—24no—
517C2×#102C22×C15111yescharacteristic
518C2×#102C22×C15111yescharacteristic
519C2×#102C22×C15111yescharacteristic
520C2×#102C22×C15111yescharacteristic
521C2×#102C22×C15111yescharacteristic, complemented
522C2×#102C22×C15111yescharacteristic, complemented
523C2×#102C22×C15111yescharacteristic, complemented
524C2×#102C22×C15111yescharacteristic, complemented
525C2×#102C22×C15111yescharacteristic, complemented
526C2×#102C22×C15111yescharacteristic, complemented
527C2×#102C22×C15111yescharacteristic, complemented
528C2×#102C22×C15111yescharacteristic, complemented
529C2×C22⋊C8C22×C15111yescharacteristic, complemented
530C2×C22⋊C8C22×C15111yescharacteristic, complemented
531C2×#97C22×C15111yescharacteristic, complemented
532#388—21no—
533#387—21no—
534#386—21no—
535#382C22×C15111yescharacteristic, complemented
536#380C22×C15111yescharacteristic, complemented
537#380C22×C15111yescharacteristic, complemented
538C4×C4⋊C4C22×C15111yescharacteristic, complemented
539C4×C22⋊C4—21no—
540#340C22×C15111yescharacteristic, complemented
541#340C22×C15111yescharacteristic, complemented
542#340C22×C15111yescharacteristic, complemented
543#340C22×C15111yescharacteristic, complemented
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C15114yes—
566C22×D4C2×C4×C15114yescomplemented
567C22×D4D4×C15111yescharacteristic
568C22×D4C23×C15111yescharacteristic
569C22×D4C23×C15111yescharacteristic
570C22×D4C23×C15111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C15111yescharacteristic
574C23×C4C23×C15111yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C15111yescharacteristic
582C22×C8C23×C15111yescharacteristic
583C22×C8C23×C15111yescharacteristic
584C22×C8C23×C15111yescharacteristic
585#127—22no—
586#127C2×C4×C15114yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C15114yes—
591#121C2×C4×C15114yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C15114yes—
596C4×D4C2×C4×C15114yescomplemented
597C4×D4D4×C15114yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C15111yescharacteristic
604C2×C4⋊C4C23×C15111yescharacteristic
605C2×C4⋊C4C23×C15111yescharacteristic
606C2×C4⋊C4C23×C15111yescharacteristic
607C2×C4⋊C4C23×C15111yescharacteristic
608C2×C4⋊C4C23×C15111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C15111yescharacteristic
616C2×C22⋊C4D4×C15111yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C15111yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C15114yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C15111yescharacteristic
659C24C2×D4×C15111yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C15114yes—
703C2×D4C22×C4×C15112yes—
704C2×D4C22×C4×C15112yes—
705C2×D4C22×C4×C15112yes—
706C2×D4C2×D4×C15112yes—
707C2×D4#41×C15112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C15112yes—
728C22×C4C22×C4×C15112yes—
729C22×C4C2×D4×C15111yescharacteristic
730C22×C4C2×D4×C15111yescharacteristic
731C22×C4C2×D4×C15111yescharacteristic
732C22×C4C2×D4×C15111yescharacteristic
733C22×C4C2×D4×C15112yes—
734C22×C4C2×D4×C15112yes—
735C22×C4C24×C15111yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C15112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C15114yes—
760C4⋊C4C22×C4×C15112yes—
761C4⋊C4C2×D4×C15112yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C15114yes—
769C22⋊C4C22⋊C4×C15114yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C15112yes—
773C42C2×D4×C15112yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C15112yes—
820C23C2×C22⋊C4×C15112yes—
821C23AGL(1,ℤ/8)×C15112yes—
822C23AGL(1,ℤ/8)×C15112yes—
823C23C22×D4×C15111yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C15114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C15112yes—
877C2×C4C2×C22⋊C4×C15112yes—
878C2×C4C2×C22⋊C4×C15112yes—
879C2×C4C2×C22⋊C4×C15112yes—
880C2×C4C23×C4×C15111yescharacteristic
881C2×C4C22×D4×C15111yescharacteristic
882C2×C4C22×D4×C15111yescharacteristic
883C2×C4C2×#41×C15111yescharacteristic
884C2×C4H(5,𝔽2)×C15111yescharacteristic
885C2×C4H(5,𝔽2)×C15111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#418×C15114yescomplemented
927C22C22×C22⋊C4×C15111yescharacteristic
928C22D42×C15111yescharacteristic
929C22#546×C15111yescharacteristic
930C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
931C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
932C22#576×C15111yescharacteristic
933C22#577×C15111yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C15111yescharacteristic
944C4#518×C15111yescharacteristic
945C4D42×C15111yescharacteristic
946C4#546×C15111yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C15111yescharacteristic
953C2C2×#418×C15111yescharacteristic
954C2#2897×C15111yescharacteristic
955C2#3264×C15111yescharacteristic
956C2#3265×C15111yescharacteristic
957C2#3310×C15111yescharacteristic
958C2#3318×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×D42×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C151C2semidirect
3. C2×#418×C151C2semidirect
4. C22×#102×C151C2semidirect
5. #2352×C151C2semidirect
6. #1982×C151C2semidirect
7. #1961×C151C2semidirect
8. #1895×C151C2semidirect
9. #1893×C151C2semidirect
10. #1875×C151C2semidirect
11. #1874×C151C2semidirect
12. #1804×C151C2semidirect
13. #1786×C151C2semidirect
14. #1786×C151C2semidirect
15. #1762×C151C2semidirect
19. C22×M16×C151C22semidirect
20. C23×C8×C151C22semidirect
22. D42×C151C4semidirect
31. C2×#117×C151C22semidirect
32. C22×C4⋊C4×C151C22semidirect
34. C2×C4⋊C8×C151C22semidirect
41. C2×#102×C151C22semidirect
42. C2×#102×C151C22semidirect
43. C2×#102×C151C22semidirect
44. C2×#102×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#102×C151C22semidirect
49. C2×C22⋊C8×C151C22semidirect
50. C2×C22⋊C8×C151C22semidirect
51. C2×#97×C151C22semidirect
55. #382×C151C22semidirect
56. #380×C151C22semidirect
57. #380×C151C22semidirect
58. C4×C4⋊C4×C151C22semidirect
60. #340×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #340×C151C22semidirect
86. C22×D4×C151C2×C4semidirect
106. #127×C151C2×C4semidirect
111. #121×C151C2×C4semidirect
116. C4×D4×C151C2×C4semidirect
152. #102×C151D4semidirect
269. C2×C8×C151C2×D4semidirect
281. C4⋊C4×C151C2×D4semidirect
446. C22×C151#418semidirect
479. #22423C151direct (N × H)
480. C151#22423direct (N × H)
482. C2×#435C2×C151semidirect
483. C2×#418C2×C151semidirect
484. C22×#102C2×C151semidirect
485. #2352C2×C151semidirect
486. #1982C2×C151semidirect
487. #1961C2×C151semidirect
488. #1895C2×C151semidirect
489. #1893C2×C151semidirect
490. #1875C2×C151semidirect
491. #1874C2×C151semidirect
492. #1804C2×C151semidirect
493. #1786C2×C151semidirect
494. #1786C2×C151semidirect
495. #1762C2×C151semidirect
499. C22×M16C22×C151semidirect
500. C23×C8C22×C151semidirect
502. D42C4×C151semidirect
511. C2×#117C22×C151semidirect
512. C22×C4⋊C4C22×C151semidirect
514. C2×C4⋊C8C22×C151semidirect
521. C2×#102C22×C151semidirect
522. C2×#102C22×C151semidirect
523. C2×#102C22×C151semidirect
524. C2×#102C22×C151semidirect
525. C2×#102C22×C151semidirect
526. C2×#102C22×C151semidirect
527. C2×#102C22×C151semidirect
528. C2×#102C22×C151semidirect
529. C2×C22⋊C8C22×C151semidirect
530. C2×C22⋊C8C22×C151semidirect
531. C2×#97C22×C151semidirect
535. #382C22×C151semidirect
536. #380C22×C151semidirect
537. #380C22×C151semidirect
538. C4×C4⋊C4C22×C151semidirect
540. #340C22×C151semidirect
541. #340C22×C151semidirect
542. #340C22×C151semidirect
543. #340C22×C151semidirect
566. C22×D4C2×C4×C151semidirect
586. #127C2×C4×C151semidirect
591. #121C2×C4×C151semidirect
596. C4×D4C2×C4×C151semidirect
632. #102D4×C151semidirect
749. C2×C8C2×D4×C151semidirect
761. C4⋊C4C2×D4×C151semidirect
926. C22#418×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1512
C2×#435×C1512
C2×#418×C1512
C22×#102×C1512
#2352×C1512
#1982×C1512
#1961×C1512
#1895×C1512
#1893×C1512
#1875×C1512
#1874×C1512
#1804×C1512
#1786×C1512
#1762×C1512
#22423151