Finite Group Databasebeta

← C151×#24050 #50328975

Subgroups — C151×#24050 #50328975

Order 38656.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C151C211yesmaximal, characteristic
2C2×#485×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic, complemented
5#2042×C151C211yesmaximal, characteristic, complemented
6#2042×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1894×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1864×C151C211yesmaximal, characteristic, complemented
12#1862×C151C211yesmaximal, characteristic, complemented
13#1788×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×M16×C151C2211yescharacteristic
19#546×C151—24no—
20#546×C151—24no—
21C2×#124×C151C2211yescharacteristic
22C2×#123×C151—21no—
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×#121×C151—21no—
25C2×#121×C151C2211yescharacteristic
26C2×#120×C151—21no—
27C2×C4×D4×C151C2211yescharacteristic
28C2×C4×D4×C151C2211yescharacteristic
29C2×#117×C151C2211yescharacteristic
30C22×C22⋊C4×C151—21no—
31#485×C151—24no—
32C2×#107×C151C2211yescharacteristic, complemented
33C2×#106×C151C2211yescharacteristic, complemented
34#418×C151—24no—
35C2×#103×C151C2211yescharacteristic, complemented
36C2×#103×C151C2211yescharacteristic, complemented
37C2×#103×C151C2211yescharacteristic, complemented
38C2×#103×C151C2211yescharacteristic, complemented
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic, complemented
49C2×C22⋊C8×C151C2211yescharacteristic, complemented
50#397×C151—21no—
51#394×C151—21no—
52#389×C151C2211yescharacteristic, complemented
53#389×C151C2211yescharacteristic, complemented
54#388×C151—21no—
55#387×C151—21no—
56#380×C151C2211yescharacteristic
57#380×C151C2211yescharacteristic, complemented
58#380×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61#336×C151C2211yescharacteristic, complemented
62#336×C151C2211yescharacteristic, complemented
63C25×C151—21no—
64C2×#41×C151—22no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C22×Q8×C151C2311yescharacteristic
71C22×D4×C151—21no—
72C22×D4×C151—22no—
73C22×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—41no—
78C22×D4×C151—41no—
79C22×D4×C151D414yes—
80C22×D4×C151D411yescharacteristic
81C22×D4×C151C2311yescharacteristic
82C22×D4×C151C2311yescharacteristic
83C23×C4×C151—21no—
84C23×C4×C151—21no—
85C23×C4×C151C2311yescharacteristic
86C23×C4×C151C2311yescharacteristic
87C2×M16×C151—22no—
88C2×M16×C151—41no—
89C2×M16×C151—41no—
90C22×C8×C151C2311yescharacteristic
91C22×C8×C151C2311yescharacteristic
92C22×C8×C151C2311yescharacteristic
93C22×C8×C151C2311yescharacteristic
94#124×C151—22no—
95#124×C151—22no—
96#123×C151—28no—
97C22⋊Q8×C151—22no—
98C22⋊Q8×C151D414yes—
99#121×C151—28no—
100#121×C151—22no—
101#121×C151—22no—
102#120×C151—28no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107#117×C151—22no—
108#117×C151—22no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C22⋊C4×C151—28no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151D411yescharacteristic
129C2×C22⋊C4×C151D411yescharacteristic
130C2×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132#107×C151—22no—
133#106×C151—22no—
134#103×C151—22no—
135#103×C151—22no—
136#103×C151—41no—
137#103×C151—41no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—22no—
143#102×C151—22no—
144#102×C151—41no—
145#102×C151—41no—
146C22⋊C8×C151—22no—
147C22⋊C8×C151—41no—
148C22⋊C8×C151—41no—
149#95×C151—21no—
150#95×C151—21no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154C24×C151—21no—
155C24×C151—21no—
156C24×C151—24no—
157C24×C151—42no—
158C24×C151—42no—
159C24×C151—42no—
160C24×C151—42no—
161C24×C151—81no—
162C24×C151—81no—
163C24×C151C2×D411yescharacteristic
164C24×C151C2×D411yescharacteristic
165#41×C151—44no—
166#41×C151—44no—
167#41×C151—44no—
168#41×C151—44no—
169C2×Q8×C151—21no—
170C2×Q8×C151—21no—
171C2×Q8×C151—21no—
172C2×Q8×C151—21no—
173C2×Q8×C151—21no—
174C2×Q8×C151C2×D412yes—
175C2×D4×C151—28no—
176C2×D4×C151—24no—
177C2×D4×C151—22no—
178C2×D4×C151—24no—
179C2×D4×C151—24no—
180C2×D4×C151—21no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—44no—
189C2×D4×C151—44no—
190C2×D4×C151—44no—
191C2×D4×C151—41no—
192C2×D4×C151—41no—
193C2×D4×C151—42no—
194C2×D4×C151—42no—
195C2×D4×C151—42no—
196C2×D4×C151—42no—
197C2×D4×C151—81no—
198C2×D4×C151—81no—
199C2×D4×C151C2×D412yes—
200C2×D4×C151C2×D412yes—
201C2×D4×C151#4112yes—
202C2×D4×C151#4112yes—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—24no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—24no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—42no—
222C22×C4×C151—42no—
223C22×C4×C151—81no—
224C22×C4×C151—81no—
225C22×C4×C151C2×D411yescharacteristic
226C22×C4×C151C2×D411yescharacteristic
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D412yes—
230C22×C4×C151C2×D412yes—
231C22×C4×C151C2411yescharacteristic
232M16×C151—44no—
233C2×C8×C151—21no—
234C2×C8×C151—21no—
235C2×C8×C151—21no—
236C2×C8×C151—21no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C4⋊C4×C151—24no—
246C4⋊C4×C151—22no—
247C4⋊C4×C151—21no—
248C4⋊C4×C151—21no—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151—21no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—42no—
257C4⋊C4×C151—81no—
258C4⋊C4×C151C2×D412yes—
259C22⋊C4×C151—24no—
260C22⋊C4×C151—24no—
261C22⋊C4×C151—24no—
262C22⋊C4×C151—24no—
263C22⋊C4×C151—22no—
264C22⋊C4×C151—24no—
265C22⋊C4×C151—22no—
266C22⋊C4×C151—42no—
267C22⋊C4×C151—42no—
268C22⋊C4×C151—81no—
269C22⋊C4×C151—81no—
270C42×C151—21no—
271C42×C151—21no—
272C42×C151—42no—
273C23×C151—22no—
274C23×C151—22no—
275C23×C151—22no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151—21no—
279C23×C151—21no—
280C23×C151—21no—
281C23×C151—21no—
282C23×C151—22no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—21no—
289C23×C151—21no—
290C23×C151—48no—
291C23×C151—48no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—84no—
303C23×C151—84no—
304C23×C151—84no—
305C23×C151—84no—
306C23×C151—84no—
307C23×C151#12012yes—
308C23×C151C22×D411yescharacteristic
309Q8×C151—22no—
310Q8×C151—22no—
311Q8×C151—41no—
312Q8×C151—41no—
313D4×C151—22no—
314D4×C151—22no—
315D4×C151—22no—
316D4×C151—22no—
317D4×C151—22no—
318D4×C151—48no—
319D4×C151—48no—
320D4×C151—44no—
321D4×C151—41no—
322D4×C151—41no—
323D4×C151—84no—
324D4×C151#12314yes—
325C2×C4×C151—21no—
326C2×C4×C151—21no—
327C2×C4×C151—22no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—22no—
335C2×C4×C151—21no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—21no—
341C2×C4×C151—21no—
342C2×C4×C151—48no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—84no—
364C2×C4×C151#12012yes—
365C2×C4×C151C22×D411yescharacteristic
366C2×C4×C151C22×D411yescharacteristic
367C2×C4×C151C2×#4111yescharacteristic
368C2×C4×C151C2×#4111yescharacteristic
369C2×C4×C151H(5,𝔽2)11yescharacteristic
370C2×C4×C151H(5,𝔽2)11yescharacteristic
371C8×C151—41no—
372C8×C151—41no—
373C8×C151—41no—
374C8×C151—41no—
375C22×C151—22no—
376C22×C151—24no—
377C22×C151—22no—
378C22×C151—22no—
379C22×C151—42no—
380C22×C151—42no—
381C22×C151—41no—
382C22×C151—42no—
383C22×C151—41no—
384C22×C151—42no—
385C22×C151—41no—
386C22×C151—42no—
387C22×C151—41no—
388C22×C151—42no—
389C22×C151—41no—
390C22×C151—42no—
391C22×C151—41no—
392C22×C151—42no—
393C22×C151—41no—
394C22×C151—42no—
395C22×C151—41no—
396C22×C151—41no—
397C22×C151—41no—
398C22×C151—41no—
399C22×C151—816no—
400C22×C151—81no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151—81no—
404C22×C151C2×#12011yescharacteristic
405C22×C151#54611yescharacteristic
406C22×C151#54611yescharacteristic
407C22×C151#57511yescharacteristic
408C22×C151#57511yescharacteristic
409C22×C151#57611yescharacteristic
410C22×C151#57711yescharacteristic
411C4×C151—22no—
412C4×C151—41no—
413C4×C151—42no—
414C4×C151—41no—
415C4×C151—41no—
416C4×C151—42no—
417C4×C151—81no—
418C4×C151—81no—
419C4×C151—81no—
420C4×C151—81no—
421C4×C151C2×#12311yescharacteristic
422C4×C151#53411yescharacteristic
423C4×C151#54611yescharacteristic
424C4×C151#54611yescharacteristic
425C2×C151—42no—
426C2×C151—44no—
427C2×C151—81no—
428C2×C151—82no—
429C2×C151#240511yescharacteristic
430C2×C151#300511yescharacteristic
431C2×C151#301211yescharacteristic
432C2×C151#331111yescharacteristic
433C2×C151#331911yescharacteristic
434C2×C151#332211yescharacteristic
435C2×C151#332311yescharacteristic
436#24050C15111yesmaximal, characteristic, direct product factor, Sylow
437C151#2405011yescharacteristic, direct product factor, Sylow
438C2×#546C2×C15111yescharacteristic
439C2×#485C2×C15111yescharacteristic, complemented
440C2×#418C2×C15111yescharacteristic, complemented
441#2485C2×C15111yescharacteristic, complemented
442#2042C2×C15111yescharacteristic, complemented
443#2042C2×C15111yescharacteristic, complemented
444#2034C2×C15111yescharacteristic, complemented
445#2033C2×C15111yescharacteristic, complemented
446#1894C2×C15111yescharacteristic, complemented
447#1870C2×C15111yescharacteristic, complemented
448#1864C2×C15111yescharacteristic, complemented
449#1862C2×C15111yescharacteristic, complemented
450#1788C2×C15111yescharacteristic, complemented
451#1788C2×C15111yescharacteristic, complemented
452#1786C2×C15111yescharacteristic, complemented
453C22×#41C22×C15111yescharacteristic
454C23×D4C22×C15111yescharacteristic
455C22×M16C22×C15111yescharacteristic
456#546—24no—
457#546—24no—
458C2×#124C22×C15111yescharacteristic
459C2×#123—21no—
460C2×C22⋊Q8C22×C15111yescharacteristic
461C2×#121—21no—
462C2×#121C22×C15111yescharacteristic
463C2×#120—21no—
464C2×C4×D4C22×C15111yescharacteristic
465C2×C4×D4C22×C15111yescharacteristic
466C2×#117C22×C15111yescharacteristic
467C22×C22⋊C4—21no—
468#485—24no—
469C2×#107C22×C15111yescharacteristic, complemented
470C2×#106C22×C15111yescharacteristic, complemented
471#418—24no—
472C2×#103C22×C15111yescharacteristic, complemented
473C2×#103C22×C15111yescharacteristic, complemented
474C2×#103C22×C15111yescharacteristic, complemented
475C2×#103C22×C15111yescharacteristic, complemented
476C2×#102C22×C15111yescharacteristic
477C2×#102C22×C15111yescharacteristic
478C2×#102C22×C15111yescharacteristic
479C2×#102C22×C15111yescharacteristic
480C2×#102C22×C15111yescharacteristic
481C2×#102C22×C15111yescharacteristic
482C2×#102C22×C15111yescharacteristic
483C2×#102C22×C15111yescharacteristic
484C2×C22⋊C8C22×C15111yescharacteristic
485C2×C22⋊C8C22×C15111yescharacteristic, complemented
486C2×C22⋊C8C22×C15111yescharacteristic, complemented
487#397—21no—
488#394—21no—
489#389C22×C15111yescharacteristic, complemented
490#389C22×C15111yescharacteristic, complemented
491#388—21no—
492#387—21no—
493#380C22×C15111yescharacteristic
494#380C22×C15111yescharacteristic, complemented
495#380C22×C15111yescharacteristic, complemented
496#340C22×C15111yescharacteristic, complemented
497#340C22×C15111yescharacteristic, complemented
498#336C22×C15111yescharacteristic, complemented
499#336C22×C15111yescharacteristic, complemented
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8C23×C15111yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C15114yes—
517C22×D4D4×C15111yescharacteristic
518C22×D4C23×C15111yescharacteristic
519C22×D4C23×C15111yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C15111yescharacteristic
523C23×C4C23×C15111yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C23×C15111yescharacteristic
528C22×C8C23×C15111yescharacteristic
529C22×C8C23×C15111yescharacteristic
530C22×C8C23×C15111yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C15114yes—
536#121—28no—
537#121—22no—
538#121—22no—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C15111yescharacteristic
550C2×C4⋊C4C23×C15111yescharacteristic
551C2×C4⋊C4C23×C15111yescharacteristic
552C2×C4⋊C4C23×C15111yescharacteristic
553C2×C4⋊C4C23×C15111yescharacteristic
554C2×C4⋊C4C23×C15111yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C15111yescharacteristic
566C2×C22⋊C4D4×C15111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C15111yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—21no—
593C24—24no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C15111yescharacteristic
601C24C2×D4×C15111yescharacteristic
602#41—44no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C15112yes—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C15112yes—
637C2×D4C2×D4×C15112yes—
638C2×D4#41×C15112yes—
639C2×D4#41×C15112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C15111yescharacteristic
663C22×C4C2×D4×C15111yescharacteristic
664C22×C4C2×D4×C15111yescharacteristic
665C22×C4C2×D4×C15111yescharacteristic
666C22×C4C2×D4×C15112yes—
667C22×C4C2×D4×C15112yes—
668C22×C4C24×C15111yescharacteristic
669M16—44no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C15112yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—22no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23#120×C15112yes—
745C23C22×D4×C15111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—44no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C15114yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C15112yes—
802C2×C4C22×D4×C15111yescharacteristic
803C2×C4C22×D4×C15111yescharacteristic
804C2×C4C2×#41×C15111yescharacteristic
805C2×C4C2×#41×C15111yescharacteristic
806C2×C4H(5,𝔽2)×C15111yescharacteristic
807C2×C4H(5,𝔽2)×C15111yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C15111yescharacteristic
842C22#546×C15111yescharacteristic
843C22#546×C15111yescharacteristic
844C22#575×C15111yescharacteristic
845C22#575×C15111yescharacteristic
846C22#576×C15111yescharacteristic
847C22#577×C15111yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C15111yescharacteristic
859C4#534×C15111yescharacteristic
860C4#546×C15111yescharacteristic
861C4#546×C15111yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2#2405×C15111yescharacteristic
867C2#3005×C15111yescharacteristic
868C2#3012×C15111yescharacteristic
869C2#3311×C15111yescharacteristic
870C2#3319×C15111yescharacteristic
871C2#3322×C15111yescharacteristic
872C2#3323×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#546×C151C2
LCSG ▷ C22×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×#485×C151C2semidirect
3. C2×#418×C151C2semidirect
4. #2485×C151C2semidirect
5. #2042×C151C2semidirect
6. #2042×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1894×C151C2semidirect
10. #1870×C151C2semidirect
11. #1864×C151C2semidirect
12. #1862×C151C2semidirect
13. #1788×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
32. C2×#107×C151C22semidirect
33. C2×#106×C151C22semidirect
35. C2×#103×C151C22semidirect
36. C2×#103×C151C22semidirect
37. C2×#103×C151C22semidirect
38. C2×#103×C151C22semidirect
48. C2×C22⋊C8×C151C22semidirect
49. C2×C22⋊C8×C151C22semidirect
52. #389×C151C22semidirect
53. #389×C151C22semidirect
57. #380×C151C22semidirect
58. #380×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
61. #336×C151C22semidirect
62. #336×C151C22semidirect
436. #24050C151direct (N × H)
437. C151#24050direct (N × H)
439. C2×#485C2×C151semidirect
440. C2×#418C2×C151semidirect
441. #2485C2×C151semidirect
442. #2042C2×C151semidirect
443. #2042C2×C151semidirect
444. #2034C2×C151semidirect
445. #2033C2×C151semidirect
446. #1894C2×C151semidirect
447. #1870C2×C151semidirect
448. #1864C2×C151semidirect
449. #1862C2×C151semidirect
450. #1788C2×C151semidirect
451. #1788C2×C151semidirect
452. #1786C2×C151semidirect
469. C2×#107C22×C151semidirect
470. C2×#106C22×C151semidirect
472. C2×#103C22×C151semidirect
473. C2×#103C22×C151semidirect
474. C2×#103C22×C151semidirect
475. C2×#103C22×C151semidirect
485. C2×C22⋊C8C22×C151semidirect
486. C2×C22⋊C8C22×C151semidirect
489. #389C22×C151semidirect
490. #389C22×C151semidirect
494. #380C22×C151semidirect
495. #380C22×C151semidirect
496. #340C22×C151semidirect
497. #340C22×C151semidirect
498. #336C22×C151semidirect
499. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1512
C2×#485×C1512
C2×#418×C1512
#2485×C1512
#2042×C1512
#2034×C1512
#2033×C1512
#1894×C1512
#1870×C1512
#1864×C1512
#1862×C1512
#1788×C1512
#1786×C1512
#24050151