Finite Group Databasebeta

← C151×#24382 #50329307

Subgroups — C151×#24382 #50329307

Order 38656.

1678 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic, complemented
2C2×#466×C151C211yesmaximal, characteristic, complemented
3C2×#465×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5C22×C22⋊C8×C151C211yesmaximal, characteristic, complemented
6#2847×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1893×C151C211yesmaximal, characteristic, complemented
12#1892×C151C211yesmaximal, characteristic, complemented
13#1875×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C24×C4×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic, complemented
19C22×D8×C151C2211yescharacteristic, complemented
20C23×C8×C151C2211yescharacteristic
21C23×C8×C151C2211yescharacteristic
22#525×C151—24no—
23#525×C151—24no—
24C2×#123×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×#120×C151—21no—
33C2×#120×C151—21no—
34C2×C4×D4×C151—21no—
35C2×C4×D4×C151—21no—
36C2×#117×C151C2211yescharacteristic
37#466×C151—24no—
38#465×C151—24no—
39#449×C151—24no—
40C2×#107×C151C2211yescharacteristic, complemented
41C2×#106×C151C2211yescharacteristic, complemented
42C2×#103×C151C2211yescharacteristic, complemented
43C2×#103×C151C2211yescharacteristic, complemented
44C2×#103×C151C2211yescharacteristic, complemented
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic, complemented
49C2×#102×C151C2211yescharacteristic, complemented
50C2×C22⋊C8×C151—24no—
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55#386×C151—21no—
56#386×C151—21no—
57#386×C151—21no—
58#380×C151C2211yescharacteristic
59#380×C151C2211yescharacteristic
60#380×C151C2211yescharacteristic
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×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151C2311yescharacteristic
80C22×D4×C151C2311yescharacteristic
81C23×C4×C151—22no—
82C23×C4×C151—21no—
83C23×C4×C151—22no—
84C23×C4×C151—22no—
85C23×C4×C151—22no—
86C23×C4×C151—41no—
87C23×C4×C151—41no—
88C23×C4×C151D411yescharacteristic
89C23×C4×C151D411yescharacteristic
90C23×C4×C151D411yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—41no—
97C2×D8×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—41no—
100C22×C8×C151—22no—
101C22×C8×C151—22no—
102C22×C8×C151—22no—
103C22×C8×C151—22no—
104C22×C8×C151—41no—
105C22×C8×C151—41no—
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108C22×C8×C151C2311yescharacteristic
109C22×C8×C151C2311yescharacteristic
110#123×C151—28no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151D414yescomplemented
115#121×C151—22no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—41no—
123#121×C151—41no—
124#121×C151D414yescomplemented
125#120×C151—28no—
126#120×C151—44no—
127C4×D4×C151—28no—
128C4×D4×C151—28no—
129#117×C151—22no—
130#117×C151—22no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C4⋊C4×C151C2311yescharacteristic
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×C22⋊C4×C151—21no—
149C2×C42×C151—21no—
150#107×C151—22no—
151#106×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151—41no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—22no—
159#102×C151—41no—
160C22⋊C8×C151—22no—
161C22⋊C8×C151—22no—
162C22⋊C8×C151—22no—
163C22⋊C8×C151D414yescomplemented
164#95×C151—21no—
165#95×C151—21no—
166#95×C151—21no—
167C24×C151—22no—
168C24×C151—22no—
169C24×C151—22no—
170C24×C151—22no—
171C24×C151—22no—
172C24×C151—21no—
173C24×C151—21no—
174C24×C151—41no—
175C24×C151—41no—
176C24×C151C2×D411yescharacteristic
177C24×C151C2×D411yescharacteristic
178C24×C151C2×D411yescharacteristic
179#41×C151—44no—
180#41×C151—44no—
181#41×C151—44no—
182#41×C151—44no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151C2×D412yes—
189C2×D4×C151—24no—
190C2×D4×C151—24no—
191C2×D4×C151—24no—
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—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—42no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
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—42no—
216C2×D4×C151—42no—
217C2×D4×C151—42no—
218C2×D4×C151C2×D412yes—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—24no—
228C22×C4×C151—22no—
229C22×C4×C151—22no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—22no—
234C22×C4×C151—22no—
235C22×C4×C151—22no—
236C22×C4×C151—22no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—41no—
247C22×C4×C151—41no—
248C22×C4×C151—41no—
249C22×C4×C151—44no—
250C22×C4×C151—44no—
251C22×C4×C151—44no—
252C22×C4×C151—44no—
253C22×C4×C151—42no—
254C22×C4×C151—42no—
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D412yes—
258C22×C4×C151C2×D412yes—
259C22×C4×C151C2×D411yescharacteristic
260C22×C4×C151C2×D412yes—
261C22×C4×C151#4112yes—
262C22×C4×C151C2411yescharacteristic
263SD16×C151—44no—
264D8×C151—44no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×C151—21no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—21no—
275C2×C8×C151—44no—
276C2×C8×C151—44no—
277C2×C8×C151C2×D412yes—
278C2×C8×C151C2×D412yes—
279C4⋊C4×C151—24no—
280C4⋊C4×C151—24no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151—21no—
289C4⋊C4×C151C2×D412yes—
290C4⋊C4×C151C2×D412yes—
291C22⋊C4×C151—24no—
292C22⋊C4×C151—24no—
293C22⋊C4×C151—24no—
294C22⋊C4×C151—24no—
295C22⋊C4×C151—24no—
296C22⋊C4×C151—42no—
297C22⋊C4×C151—42no—
298C22⋊C4×C151—42no—
299C22⋊C4×C151—42no—
300C22⋊C4×C151—42no—
301C22⋊C4×C151—42no—
302C42×C151—24no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—28no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—21no—
318C23×C151—21no—
319C23×C151—21no—
320C23×C151—22no—
321C23×C151—44no—
322C23×C151—44no—
323C23×C151—44no—
324C23×C151—44no—
325C23×C151—44no—
326C23×C151—44no—
327C23×C151—41no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151#12012yes—
341C23×C151#12112yes—
342C23×C151#13512yes—
343C23×C151#13512yes—
344C23×C151AGL(1,ℤ/8)12yes—
345C23×C151C22×D411yescharacteristic
346Q8×C151—22no—
347Q8×C151—22no—
348Q8×C151—41no—
349Q8×C151—41no—
350D4×C151—22no—
351D4×C151—22no—
352D4×C151—48no—
353D4×C151—48no—
354D4×C151—48no—
355D4×C151—41no—
356D4×C151—41no—
357D4×C151—41no—
358D4×C151—41no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—84no—
362D4×C151—84no—
363D4×C151—84no—
364C2×C4×C151—21no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—22no—
369C2×C4×C151—22no—
370C2×C4×C151—22no—
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—21no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—44no—
383C2×C4×C151—44no—
384C2×C4×C151—44no—
385C2×C4×C151—48no—
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—41no—
396C2×C4×C151—41no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—41no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151#12012yes—
406C2×C4×C151#12112yes—
407C2×C4×C151C22×D411yescharacteristic
408C2×C4×C151C22×D411yescharacteristic
409C2×C4×C151C22×D411yescharacteristic
410C2×C4×C151C2×#4111yescharacteristic
411C2×C4×C151H(5,𝔽2)11yescharacteristic
412C2×C4×C151H(5,𝔽2)11yescharacteristic
413C8×C151—22no—
414C8×C151—22no—
415C8×C151—41no—
416C8×C151—41no—
417C22×C151—22no—
418C22×C151—22no—
419C22×C151—22no—
420C22×C151—22no—
421C22×C151—22no—
422C22×C151—22no—
423C22×C151—22no—
424C22×C151—22no—
425C22×C151—22no—
426C22×C151—22no—
427C22×C151—22no—
428C22×C151—22no—
429C22×C151—416no—
430C22×C151—41no—
431C22×C151—41no—
432C22×C151—41no—
433C22×C151—41no—
434C22×C151—41no—
435C22×C151—41no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—42no—
439C22×C151—42no—
440C22×C151—42no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151—81no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151—81no—
450C22×C151—81no—
451C22×C151—81no—
452C22×C151#44914yescomplemented
453C22×C151C2×#12011yescharacteristic
454C22×C151C2×#12111yescharacteristic
455C22×C151#53411yescharacteristic
456C22×C151C2×#13511yescharacteristic
457C22×C151C2×#13511yescharacteristic
458C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
459C22×C151#57511yescharacteristic
460C4×C151—22no—
461C4×C151—22no—
462C4×C151—41no—
463C4×C151—42no—
464C4×C151—42no—
465C4×C151—42no—
466C4×C151—81no—
467C4×C151—81no—
468C4×C151—81no—
469C4×C151D4211yescharacteristic
470C4×C151D4211yescharacteristic
471C4×C151#54611yescharacteristic
472C4×C151#54611yescharacteristic
473C2×C151—24no—
474C2×C151—42no—
475C2×C151—42no—
476C2×C151—82no—
477C2×C151—161no—
478C2×C151#241011yescharacteristic
479C2×C151C2×#44911yescharacteristic
480C2×C151#300211yescharacteristic
481C2×C151#305011yescharacteristic
482C2×C151#305511yescharacteristic
483C2×C151#318811yescharacteristic
484C2×C151#319111yescharacteristic
485#24382C15111yesmaximal, characteristic, direct product factor, Sylow
486C151#2438211yescharacteristic, direct product factor, Sylow
487C2×#525C2×C15111yescharacteristic, complemented
488C2×#466C2×C15111yescharacteristic, complemented
489C2×#465C2×C15111yescharacteristic, complemented
490C2×#449C2×C15111yescharacteristic, complemented
491C22×C22⋊C8C2×C15111yescharacteristic, complemented
492#2847C2×C15111yescharacteristic, complemented
493#2036C2×C15111yescharacteristic, complemented
494#2034C2×C15111yescharacteristic, complemented
495#2000C2×C15111yescharacteristic, complemented
496#1999C2×C15111yescharacteristic, complemented
497#1893C2×C15111yescharacteristic, complemented
498#1892C2×C15111yescharacteristic, complemented
499#1875C2×C15111yescharacteristic, complemented
500#1854C2×C15111yescharacteristic, complemented
501#1788C2×C15111yescharacteristic, complemented
502C22×#41C22×C15111yescharacteristic
503C24×C4C22×C15111yescharacteristic
504C22×SD16C22×C15111yescharacteristic, complemented
505C22×D8C22×C15111yescharacteristic, complemented
506C23×C8C22×C15111yescharacteristic
507C23×C8C22×C15111yescharacteristic
508#525—24no—
509#525—24no—
510C2×#123—21no—
511C2×C22⋊Q8C22×C15111yescharacteristic
512C2×C22⋊Q8C22×C15111yescharacteristic
513C2×#121C22×C15111yescharacteristic
514C2×#121C22×C15111yescharacteristic
515C2×#121C22×C15111yescharacteristic
516C2×#121C22×C15111yescharacteristic
517C2×#121C22×C15111yescharacteristic
518C2×#120—21no—
519C2×#120—21no—
520C2×C4×D4—21no—
521C2×C4×D4—21no—
522C2×#117C22×C15111yescharacteristic
523#466—24no—
524#465—24no—
525#449—24no—
526C2×#107C22×C15111yescharacteristic, complemented
527C2×#106C22×C15111yescharacteristic, complemented
528C2×#103C22×C15111yescharacteristic, complemented
529C2×#103C22×C15111yescharacteristic, complemented
530C2×#103C22×C15111yescharacteristic, complemented
531C2×#102C22×C15111yescharacteristic, complemented
532C2×#102C22×C15111yescharacteristic, complemented
533C2×#102C22×C15111yescharacteristic, complemented
534C2×#102C22×C15111yescharacteristic, complemented
535C2×#102C22×C15111yescharacteristic, complemented
536C2×C22⋊C8—24no—
537C2×C22⋊C8C22×C15111yescharacteristic
538C2×C22⋊C8C22×C15111yescharacteristic
539C2×C22⋊C8C22×C15111yescharacteristic
540C2×C22⋊C8C22×C15111yescharacteristic
541#386—21no—
542#386—21no—
543#386—21no—
544#380C22×C15111yescharacteristic
545#380C22×C15111yescharacteristic
546#380C22×C15111yescharacteristic
547#340C22×C15111yescharacteristic, complemented
548#340C22×C15111yescharacteristic, complemented
549#340C22×C15111yescharacteristic, complemented
550#340C22×C15111yescharacteristic, complemented
551C25D4×C15111yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C15111yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C15111yescharacteristic
566C22×D4C23×C15111yescharacteristic
567C23×C4—22no—
568C23×C4—21no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C15111yescharacteristic
575C23×C4D4×C15111yescharacteristic
576C23×C4D4×C15111yescharacteristic
577C23×C4C23×C15111yescharacteristic
578C23×C4C23×C15111yescharacteristic
579C23×C4C23×C15111yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—22no—
589C22×C8—22no—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8C23×C15111yescharacteristic
593C22×C8C23×C15111yescharacteristic
594C22×C8C23×C15111yescharacteristic
595C22×C8C23×C15111yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C15114yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C15114yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C15111yescharacteristic
620C2×C4⋊C4C23×C15111yescharacteristic
621C2×C4⋊C4C23×C15111yescharacteristic
622C2×C4⋊C4C23×C15111yescharacteristic
623C2×C4⋊C4C23×C15111yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C15114yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—41no—
661C24—41no—
662C24C2×D4×C15111yescharacteristic
663C24C2×D4×C15111yescharacteristic
664C24C2×D4×C15111yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C15112yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C15112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C15111yescharacteristic
742C22×C4C2×D4×C15111yescharacteristic
743C22×C4C2×D4×C15112yes—
744C22×C4C2×D4×C15112yes—
745C22×C4C2×D4×C15111yescharacteristic
746C22×C4C2×D4×C15112yes—
747C22×C4#41×C15112yes—
748C22×C4C24×C15111yescharacteristic
749SD16—44no—
750D8—44no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—44no—
762C2×C8—44no—
763C2×C8C2×D4×C15112yes—
764C2×C8C2×D4×C15112yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C15112yes—
776C4⋊C4C2×D4×C15112yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—28no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23#120×C15112yes—
827C23#121×C15112yes—
828C23#135×C15112yes—
829C23#135×C15112yes—
830C23AGL(1,ℤ/8)×C15112yes—
831C23C22×D4×C15111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4#120×C15112yes—
892C2×C4#121×C15112yes—
893C2×C4C22×D4×C15111yescharacteristic
894C2×C4C22×D4×C15111yescharacteristic
895C2×C4C22×D4×C15111yescharacteristic
896C2×C4C2×#41×C15111yescharacteristic
897C2×C4H(5,𝔽2)×C15111yescharacteristic
898C2×C4H(5,𝔽2)×C15111yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—416no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22#449×C15114yescomplemented
939C22C2×#120×C15111yescharacteristic
940C22C2×#121×C15111yescharacteristic
941C22#534×C15111yescharacteristic
942C22C2×#135×C15111yescharacteristic
943C22C2×#135×C15111yescharacteristic
944C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
945C22#575×C15111yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C15111yescharacteristic
956C4D42×C15111yescharacteristic
957C4#546×C15111yescharacteristic
958C4#546×C15111yescharacteristic
959C2—24no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2#2410×C15111yescharacteristic
965C2C2×#449×C15111yescharacteristic
966C2#3002×C15111yescharacteristic
967C2#3050×C15111yescharacteristic
968C2#3055×C15111yescharacteristic
969C2#3188×C15111yescharacteristic
970C2#3191×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
1. C2×#525×C151C2semidirect
2. C2×#466×C151C2semidirect
3. C2×#465×C151C2semidirect
4. C2×#449×C151C2semidirect
5. C22×C22⋊C8×C151C2semidirect
6. #2847×C151C2semidirect
7. #2036×C151C2semidirect
8. #2034×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1893×C151C2semidirect
12. #1892×C151C2semidirect
13. #1875×C151C2semidirect
14. #1854×C151C2semidirect
15. #1788×C151C2semidirect
18. C22×SD16×C151C22semidirect
19. C22×D8×C151C22semidirect
40. C2×#107×C151C22semidirect
41. C2×#106×C151C22semidirect
42. C2×#103×C151C22semidirect
43. C2×#103×C151C22semidirect
44. C2×#103×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#102×C151C22semidirect
49. C2×#102×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
114. C22⋊Q8×C151D4semidirect
124. #121×C151D4semidirect
163. C22⋊C8×C151D4semidirect
452. C22×C151#449semidirect
485. #24382C151direct (N × H)
486. C151#24382direct (N × H)
487. C2×#525C2×C151semidirect
488. C2×#466C2×C151semidirect
489. C2×#465C2×C151semidirect
490. C2×#449C2×C151semidirect
491. C22×C22⋊C8C2×C151semidirect
492. #2847C2×C151semidirect
493. #2036C2×C151semidirect
494. #2034C2×C151semidirect
495. #2000C2×C151semidirect
496. #1999C2×C151semidirect
497. #1893C2×C151semidirect
498. #1892C2×C151semidirect
499. #1875C2×C151semidirect
500. #1854C2×C151semidirect
501. #1788C2×C151semidirect
504. C22×SD16C22×C151semidirect
505. C22×D8C22×C151semidirect
526. C2×#107C22×C151semidirect
527. C2×#106C22×C151semidirect
528. C2×#103C22×C151semidirect
529. C2×#103C22×C151semidirect
530. C2×#103C22×C151semidirect
531. C2×#102C22×C151semidirect
532. C2×#102C22×C151semidirect
533. C2×#102C22×C151semidirect
534. C2×#102C22×C151semidirect
535. C2×#102C22×C151semidirect
547. #340C22×C151semidirect
548. #340C22×C151semidirect
549. #340C22×C151semidirect
550. #340C22×C151semidirect
600. C22⋊Q8D4×C151semidirect
610. #121D4×C151semidirect
649. C22⋊C8D4×C151semidirect
938. C22#449×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×#466×C1512
C2×#465×C1512
C2×#449×C1512
C22×C22⋊C8×C1512
#2847×C1512
#2036×C1512
#2034×C1512
#2000×C1512
#1999×C1512
#1893×C1512
#1892×C1512
#1875×C1512
#1854×C1512
#1788×C1512
#24382151