Finite Group Databasebeta

← C151×#24389 #50329314

Subgroups — C151×#24389 #50329314

Order 38656.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic
2C2×#470×C151C211yesmaximal, characteristic, complemented
3C2×#468×C151C211yesmaximal, characteristic, complemented
4C2×#452×C151C211yesmaximal, characteristic, complemented
5C2×#407×C151C211yesmaximal, characteristic, complemented
6#2848×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2001×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1895×C151C211yesmaximal, characteristic, complemented
12#1894×C151C211yesmaximal, characteristic, complemented
13#1873×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C24×C4×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic, complemented
19C22×SD16×C151C2211yescharacteristic, complemented
20C22×M16×C151C2211yescharacteristic
21C22×M16×C151C2211yescharacteristic
22#525×C151—24no—
23#525×C151—24no—
24C2×#123×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×#120×C151—21no—
33C2×C4×D4×C151—21no—
34C2×C4×D4×C151—21no—
35C2×#117×C151C2211yescharacteristic
36#470×C151—24no—
37#468×C151—24no—
38#452×C151—24no—
39C2×#107×C151C2211yescharacteristic, complemented
40C2×#106×C151C2211yescharacteristic, complemented
41C2×#103×C151C2211yescharacteristic, complemented
42C2×#103×C151C2211yescharacteristic, complemented
43C2×#103×C151C2211yescharacteristic, complemented
44C2×#103×C151C2211yescharacteristic, complemented
45C2×#103×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic, complemented
49#407×C151—24no—
50C2×C22⋊C8×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#385×C151—21no—
55#385×C151—21no—
56#385×C151—21no—
57#380×C151C2211yescharacteristic
58#380×C151C2211yescharacteristic
59#380×C151C2211yescharacteristic
60#379×C151—21no—
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64#340×C151C2211yescharacteristic, complemented
65C25×C151D411yescharacteristic
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—41no—
71C2×#41×C151—41no—
72C22×Q8×C151C2311yescharacteristic
73C22×Q8×C151C2311yescharacteristic
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151C2311yescharacteristic
78C23×C4×C151—22no—
79C23×C4×C151—21no—
80C23×C4×C151—22no—
81C23×C4×C151—22no—
82C23×C4×C151—22no—
83C23×C4×C151—41no—
84C23×C4×C151—41no—
85C23×C4×C151D411yescharacteristic
86C23×C4×C151D411yescharacteristic
87C23×C4×C151D411yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151—41no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—41no—
97C2×M16×C151—22no—
98C2×M16×C151—22no—
99C2×M16×C151—22no—
100C2×M16×C151—22no—
101C2×M16×C151—41no—
102C2×M16×C151—41no—
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107#123×C151—28no—
108C22⋊Q8×C151—22no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—41no—
116C22⋊Q8×C151—41no—
117C22⋊Q8×C151D414yes—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151D414yes—
122#120×C151—28no—
123C4×D4×C151—28no—
124C4×D4×C151—28no—
125#117×C151—22no—
126#117×C151—22no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151C2311yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151—21no—
143C2×C22⋊C4×C151—21no—
144C2×C22⋊C4×C151—21no—
145C2×C22⋊C4×C151—21no—
146C2×C22⋊C4×C151—21no—
147C2×C22⋊C4×C151—21no—
148C2×C42×C151—21no—
149#107×C151—22no—
150#106×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151—22no—
155#103×C151—41no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—41no—
159C22⋊C8×C151—22no—
160C22⋊C8×C151—22no—
161C22⋊C8×C151—22no—
162C22⋊C8×C151D414yescomplemented
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—22no—
167C24×C151—22no—
168C24×C151—22no—
169C24×C151—21no—
170C24×C151—41no—
171C24×C151—41no—
172C24×C151—41no—
173C24×C151—41no—
174C24×C151C2×D411yescharacteristic
175C24×C151C2×D411yescharacteristic
176C24×C151C2×D411yescharacteristic
177#41×C151—44no—
178#41×C151—44no—
179#41×C151—44no—
180#41×C151—44no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151—21no—
191C2×Q8×C151—21no—
192C2×Q8×C151C2×D412yes—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—24no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—42no—
202C2×D4×C151—42no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151C2×D412yes—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—24no—
217C22×C4×C151—22no—
218C22×C4×C151—22no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—22no—
223C22×C4×C151—22no—
224C22×C4×C151—22no—
225C22×C4×C151—22no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
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—41no—
237C22×C4×C151—41no—
238C22×C4×C151—41no—
239C22×C4×C151—44no—
240C22×C4×C151—44no—
241C22×C4×C151—44no—
242C22×C4×C151—44no—
243C22×C4×C151—42no—
244C22×C4×C151—42no—
245C22×C4×C151C2×D411yescharacteristic
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2×D412yes—
248C22×C4×C151C2×D412yes—
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D412yes—
251C22×C4×C151#4112yes—
252C22×C4×C151C2411yescharacteristic
253Q16×C151—44no—
254SD16×C151—44no—
255M16×C151—44no—
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×C151C2×D412yes—
268C2×C8×C151C2×D412yes—
269C4⋊C4×C151—24no—
270C4⋊C4×C151—24no—
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—21no—
279C4⋊C4×C151—42no—
280C4⋊C4×C151—42no—
281C4⋊C4×C151—42no—
282C4⋊C4×C151C2×D412yes—
283C4⋊C4×C151C2×D412yes—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—24no—
286C22⋊C4×C151—24no—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—24no—
289C22⋊C4×C151—42no—
290C22⋊C4×C151—42no—
291C22⋊C4×C151—42no—
292C22⋊C4×C151—42no—
293C22⋊C4×C151—42no—
294C22⋊C4×C151—42no—
295C42×C151—24no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—22no—
315C23×C151—44no—
316C23×C151—44no—
317C23×C151—44no—
318C23×C151—44no—
319C23×C151—44no—
320C23×C151—44no—
321C23×C151—44no—
322C23×C151—41no—
323C23×C151—41no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151—41no—
327C23×C151—41no—
328C23×C151#12012yes—
329C23×C151#12112yes—
330C23×C151#13712yes—
331C23×C151C22×D411yescharacteristic
332Q8×C151—22no—
333Q8×C151—22no—
334Q8×C151—41no—
335Q8×C151—41no—
336Q8×C151—41no—
337Q8×C151—41no—
338Q8×C151—41no—
339Q8×C151—41no—
340D4×C151—22no—
341D4×C151—22no—
342D4×C151—48no—
343D4×C151—48no—
344D4×C151—48no—
345D4×C151—41no—
346D4×C151—41no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—22no—
355C2×C4×C151—22no—
356C2×C4×C151—22no—
357C2×C4×C151—22no—
358C2×C4×C151—22no—
359C2×C4×C151—22no—
360C2×C4×C151—22no—
361C2×C4×C151—22no—
362C2×C4×C151—21no—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—44no—
366C2×C4×C151—44no—
367C2×C4×C151—44no—
368C2×C4×C151—48no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—41no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
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#12012yes—
392C2×C4×C151#12112yes—
393C2×C4×C151C22×D411yescharacteristic
394C2×C4×C151C22×D411yescharacteristic
395C2×C4×C151C22×D411yescharacteristic
396C2×C4×C151C2×#4111yescharacteristic
397C2×C4×C151H(5,𝔽2)11yescharacteristic
398C2×C4×C151H(5,𝔽2)11yescharacteristic
399C8×C151—22no—
400C8×C151—22no—
401C8×C151—41no—
402C8×C151—41no—
403C22×C151—22no—
404C22×C151—22no—
405C22×C151—22no—
406C22×C151—22no—
407C22×C151—22no—
408C22×C151—22no—
409C22×C151—22no—
410C22×C151—22no—
411C22×C151—22no—
412C22×C151—416no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—41no—
421C22×C151—41no—
422C22×C151—41no—
423C22×C151—41no—
424C22×C151—41no—
425C22×C151—42no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—81no—
429C22×C151—81no—
430C22×C151—81no—
431C22×C151—81no—
432C22×C151C2×#12011yescharacteristic
433C22×C151C2×#12111yescharacteristic
434C22×C151#53411yescharacteristic
435C22×C151C2×#13711yescharacteristic
436C22×C151#57511yescharacteristic
437C22×C151#57511yescharacteristic
438C22×C151#57511yescharacteristic
439C4×C151—22no—
440C4×C151—22no—
441C4×C151—41no—
442C4×C151—42no—
443C4×C151—42no—
444C4×C151—42no—
445C4×C151—81no—
446C4×C151—81no—
447C4×C151—81no—
448C4×C151—81no—
449C4×C151D4211yescharacteristic
450C4×C151D4211yescharacteristic
451C4×C151#54611yescharacteristic
452C4×C151#54611yescharacteristic
453C2×C151—42no—
454C2×C151—42no—
455C2×C151—42no—
456C2×C151—82no—
457C2×C151#241011yescharacteristic
458C2×C151#300511yescharacteristic
459C2×C151#300711yescharacteristic
460C2×C151#305411yescharacteristic
461C2×C151#305611yescharacteristic
462C2×C151#319611yescharacteristic
463C2×C151#319711yescharacteristic
464#24389C15111yesmaximal, characteristic, direct product factor, Sylow
465C151#2438911yescharacteristic, direct product factor, Sylow
466C2×#525C2×C15111yescharacteristic
467C2×#470C2×C15111yescharacteristic, complemented
468C2×#468C2×C15111yescharacteristic, complemented
469C2×#452C2×C15111yescharacteristic, complemented
470C2×#407C2×C15111yescharacteristic, complemented
471#2848C2×C15111yescharacteristic, complemented
472#2036C2×C15111yescharacteristic, complemented
473#2034C2×C15111yescharacteristic, complemented
474#2001C2×C15111yescharacteristic, complemented
475#2000C2×C15111yescharacteristic, complemented
476#1895C2×C15111yescharacteristic, complemented
477#1894C2×C15111yescharacteristic, complemented
478#1873C2×C15111yescharacteristic, complemented
479#1854C2×C15111yescharacteristic, complemented
480#1788C2×C15111yescharacteristic, complemented
481C22×#41C22×C15111yescharacteristic
482C24×C4C22×C15111yescharacteristic
483C22×Q16C22×C15111yescharacteristic, complemented
484C22×SD16C22×C15111yescharacteristic, complemented
485C22×M16C22×C15111yescharacteristic
486C22×M16C22×C15111yescharacteristic
487#525—24no—
488#525—24no—
489C2×#123—21no—
490C2×C22⋊Q8C22×C15111yescharacteristic
491C2×C22⋊Q8C22×C15111yescharacteristic
492C2×C22⋊Q8C22×C15111yescharacteristic
493C2×C22⋊Q8C22×C15111yescharacteristic
494C2×C22⋊Q8C22×C15111yescharacteristic
495C2×#121C22×C15111yescharacteristic
496C2×#121C22×C15111yescharacteristic
497C2×#120—21no—
498C2×C4×D4—21no—
499C2×C4×D4—21no—
500C2×#117C22×C15111yescharacteristic
501#470—24no—
502#468—24no—
503#452—24no—
504C2×#107C22×C15111yescharacteristic, complemented
505C2×#106C22×C15111yescharacteristic, complemented
506C2×#103C22×C15111yescharacteristic, complemented
507C2×#103C22×C15111yescharacteristic, complemented
508C2×#103C22×C15111yescharacteristic, complemented
509C2×#103C22×C15111yescharacteristic, complemented
510C2×#103C22×C15111yescharacteristic, complemented
511C2×#102C22×C15111yescharacteristic, complemented
512C2×#102C22×C15111yescharacteristic, complemented
513C2×#102C22×C15111yescharacteristic, complemented
514#407—24no—
515C2×C22⋊C8C22×C15111yescharacteristic
516C2×C22⋊C8C22×C15111yescharacteristic
517C2×C22⋊C8C22×C15111yescharacteristic
518C2×C22⋊C8C22×C15111yescharacteristic
519#385—21no—
520#385—21no—
521#385—21no—
522#380C22×C15111yescharacteristic
523#380C22×C15111yescharacteristic
524#380C22×C15111yescharacteristic
525#379—21no—
526#340C22×C15111yescharacteristic, complemented
527#340C22×C15111yescharacteristic, complemented
528#340C22×C15111yescharacteristic, complemented
529#340C22×C15111yescharacteristic, complemented
530C25D4×C15111yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C15111yescharacteristic
538C22×Q8C23×C15111yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C15111yescharacteristic
543C23×C4—22no—
544C23×C4—21no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C15111yescharacteristic
551C23×C4D4×C15111yescharacteristic
552C23×C4D4×C15111yescharacteristic
553C23×C4C23×C15111yescharacteristic
554C23×C4C23×C15111yescharacteristic
555C23×C4C23×C15111yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C15111yescharacteristic
569C22×C8C23×C15111yescharacteristic
570C22×C8C23×C15111yescharacteristic
571C22×C8C23×C15111yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C15114yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C15114yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C15111yescharacteristic
598C2×C4⋊C4C23×C15111yescharacteristic
599C2×C4⋊C4C23×C15111yescharacteristic
600C2×C4⋊C4C23×C15111yescharacteristic
601C2×C4⋊C4C23×C15111yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C15114yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C15111yescharacteristic
640C24C2×D4×C15111yescharacteristic
641C24C2×D4×C15111yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C15112yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C15112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C15111yescharacteristic
711C22×C4C2×D4×C15111yescharacteristic
712C22×C4C2×D4×C15112yes—
713C22×C4C2×D4×C15112yes—
714C22×C4C2×D4×C15111yescharacteristic
715C22×C4C2×D4×C15112yes—
716C22×C4#41×C15112yes—
717C22×C4C24×C15111yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C15112yes—
733C2×C8C2×D4×C15112yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C15112yes—
748C4⋊C4C2×D4×C15112yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C15112yes—
794C23#121×C15112yes—
795C23#137×C15112yes—
796C23C22×D4×C15111yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—21no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C15112yes—
857C2×C4#121×C15112yes—
858C2×C4C22×D4×C15111yescharacteristic
859C2×C4C22×D4×C15111yescharacteristic
860C2×C4C22×D4×C15111yescharacteristic
861C2×C4C2×#41×C15111yescharacteristic
862C2×C4H(5,𝔽2)×C15111yescharacteristic
863C2×C4H(5,𝔽2)×C15111yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C15111yescharacteristic
898C22C2×#121×C15111yescharacteristic
899C22#534×C15111yescharacteristic
900C22C2×#137×C15111yescharacteristic
901C22#575×C15111yescharacteristic
902C22#575×C15111yescharacteristic
903C22#575×C15111yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C15111yescharacteristic
915C4D42×C15111yescharacteristic
916C4#546×C15111yescharacteristic
917C4#546×C15111yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2#2410×C15111yescharacteristic
923C2#3005×C15111yescharacteristic
924C2#3007×C15111yescharacteristic
925C2#3054×C15111yescharacteristic
926C2#3056×C15111yescharacteristic
927C2#3196×C15111yescharacteristic
928C2#3197×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#525×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#470×C151C2semidirect
3. C2×#468×C151C2semidirect
4. C2×#452×C151C2semidirect
5. C2×#407×C151C2semidirect
6. #2848×C151C2semidirect
7. #2036×C151C2semidirect
8. #2034×C151C2semidirect
9. #2001×C151C2semidirect
10. #2000×C151C2semidirect
11. #1895×C151C2semidirect
12. #1894×C151C2semidirect
13. #1873×C151C2semidirect
14. #1854×C151C2semidirect
15. #1788×C151C2semidirect
18. C22×Q16×C151C22semidirect
19. C22×SD16×C151C22semidirect
39. C2×#107×C151C22semidirect
40. C2×#106×C151C22semidirect
41. C2×#103×C151C22semidirect
42. C2×#103×C151C22semidirect
43. C2×#103×C151C22semidirect
44. C2×#103×C151C22semidirect
45. C2×#103×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#102×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
162. C22⋊C8×C151D4semidirect
464. #24389C151direct (N × H)
465. C151#24389direct (N × H)
467. C2×#470C2×C151semidirect
468. C2×#468C2×C151semidirect
469. C2×#452C2×C151semidirect
470. C2×#407C2×C151semidirect
471. #2848C2×C151semidirect
472. #2036C2×C151semidirect
473. #2034C2×C151semidirect
474. #2001C2×C151semidirect
475. #2000C2×C151semidirect
476. #1895C2×C151semidirect
477. #1894C2×C151semidirect
478. #1873C2×C151semidirect
479. #1854C2×C151semidirect
480. #1788C2×C151semidirect
483. C22×Q16C22×C151semidirect
484. C22×SD16C22×C151semidirect
504. C2×#107C22×C151semidirect
505. C2×#106C22×C151semidirect
506. C2×#103C22×C151semidirect
507. C2×#103C22×C151semidirect
508. C2×#103C22×C151semidirect
509. C2×#103C22×C151semidirect
510. C2×#103C22×C151semidirect
511. C2×#102C22×C151semidirect
512. C2×#102C22×C151semidirect
513. C2×#102C22×C151semidirect
526. #340C22×C151semidirect
527. #340C22×C151semidirect
528. #340C22×C151semidirect
529. #340C22×C151semidirect
627. C22⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1512
C2×#470×C1512
C2×#468×C1512
C2×#452×C1512
C2×#407×C1512
#2848×C1512
#2036×C1512
#2034×C1512
#2001×C1512
#2000×C1512
#1895×C1512
#1894×C1512
#1873×C1512
#1854×C1512
#1788×C1512
#24389151