Finite Group Databasebeta

← C151×#24245 #50329170

Subgroups — C151×#24245 #50329170

Order 38656.

1628 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×#546×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#449×C151C211yesmaximal, characteristic, complemented
4C2×#447×C151C211yesmaximal, characteristic, complemented
5C2×C4×D8×C151C211yesmaximal, characteristic, complemented
6#2535×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1958×C151C211yesmaximal, characteristic, complemented
12#1954×C151C211yesmaximal, characteristic, complemented
13#1804×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic, complemented
19C22×D8×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21#546×C151—24no—
22#546×C151—24no—
23C2×#124×C151C2211yescharacteristic
24C2×#123×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×#121×C151—21no—
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic, complemented
30C2×#120×C151—21no—
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C2×C4×D4×C151C2211yescharacteristic, complemented
34C22×C22⋊C4×C151—21no—
35#463×C151—24no—
36#449×C151—24no—
37#447×C151—24no—
38C4×D8×C151—24no—
39C2×#107×C151C2211yescharacteristic, complemented
40C2×C4⋊C8×C151C2211yescharacteristic, complemented
41C2×#103×C151C2211yescharacteristic, complemented
42C2×#103×C151C2211yescharacteristic, complemented
43C2×#103×C151C2211yescharacteristic, complemented
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic, complemented
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54C2×C22⋊C8×C151C2211yescharacteristic, complemented
55C2×C4×C8×C151C2211yescharacteristic, complemented
56#397×C151—21no—
57#392×C151—21no—
58#386×C151—21no—
59#386×C151—21no—
60#382×C151C2211yescharacteristic, complemented
61#380×C151C2211yescharacteristic
62#380×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64#340×C151C2211yescharacteristic, complemented
65C25×C151—21no—
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—22no—
74C22×D4×C151—22no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151—22no—
81C22×D4×C151—22no—
82C22×D4×C151—41no—
83C22×D4×C151—41no—
84C22×D4×C151D411yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C23×C4×C151—21no—
89C23×C4×C151—21no—
90C23×C4×C151—21no—
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—41no—
96C2×D8×C151—22no—
97C2×D8×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—41no—
101C2×D8×C151D414yescomplemented
102C22×C8×C151C2311yescharacteristic
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106#124×C151—22no—
107#124×C151D414yescomplemented
108#123×C151—28no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111#121×C151—28no—
112#121×C151—22no—
113#121×C151—22no—
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—41no—
117#121×C151—41no—
118#120×C151—28no—
119C4×D4×C151—22no—
120C4×D4×C151—22no—
121C4×D4×C151—22no—
122C4×D4×C151—22no—
123C4×D4×C151—22no—
124C4×D4×C151D414yescomplemented
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151D411yescharacteristic
127C2×C4⋊C4×C151C2311yescharacteristic
128C2×C4⋊C4×C151C2311yescharacteristic
129C2×C4⋊C4×C151C2311yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C22⋊C4×C151—28no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
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×C151D411yescharacteristic
143C2×C22⋊C4×C151D411yescharacteristic
144C2×C42×C151C2311yescharacteristic
145#107×C151—22no—
146C4⋊C8×C151—22no—
147#103×C151—22no—
148#103×C151—22no—
149#103×C151—41no—
150#102×C151—22no—
151#102×C151—22no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—41no—
157C22⋊C8×C151—22no—
158C22⋊C8×C151—22no—
159C22⋊C8×C151—41no—
160C22⋊C8×C151—41no—
161C4×C8×C151—22no—
162#95×C151—21no—
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151—24no—
168C24×C151—21no—
169C24×C151—21no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—42no—
173C24×C151—42no—
174C24×C151—81no—
175C24×C151—81no—
176C24×C151C2×D411yescharacteristic
177C24×C151C2×D411yescharacteristic
178#41×C151—44no—
179#41×C151—44no—
180#41×C151—44no—
181#41×C151—44no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151C2×D412yes—
188C2×D4×C151—24no—
189C2×D4×C151—24no—
190C2×D4×C151—22no—
191C2×D4×C151—24no—
192C2×D4×C151—22no—
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—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—41no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
209C2×D4×C151—44no—
210C2×D4×C151—44no—
211C2×D4×C151—44no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—44no—
215C2×D4×C151—42no—
216C2×D4×C151—42no—
217C2×D4×C151—42no—
218C2×D4×C151—42no—
219C2×D4×C151—81no—
220C2×D4×C151—81no—
221C2×D4×C151—81no—
222C2×D4×C151—81no—
223C2×D4×C151C2×D412yes—
224C2×D4×C151C2×D412yes—
225C2×D4×C151C2×D412yes—
226C2×D4×C151C2×D412yes—
227C2×D4×C151#4112yes—
228C22×C4×C151—24no—
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—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—24no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—42no—
248C22×C4×C151—42no—
249C22×C4×C151—42no—
250C22×C4×C151—81no—
251C22×C4×C151—81no—
252C22×C4×C151—81no—
253C22×C4×C151—81no—
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2411yescharacteristic
259SD16×C151—44no—
260D8×C151—28no—
261D8×C151—44no—
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—21no—
269C2×C8×C151—21no—
270C2×C8×C151—21no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151C2×D412yes—
274C4⋊C4×C151—24no—
275C4⋊C4×C151—22no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151C2×D412yes—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—24no—
286C22⋊C4×C151—22no—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—24no—
289C22⋊C4×C151—24no—
290C22⋊C4×C151—22no—
291C22⋊C4×C151—42no—
292C22⋊C4×C151—42no—
293C22⋊C4×C151—42no—
294C22⋊C4×C151—81no—
295C22⋊C4×C151—81no—
296C42×C151C2×D412yes—
297C42×C151C2×D412yes—
298C23×C151—21no—
299C23×C151—22no—
300C23×C151—22no—
301C23×C151—21no—
302C23×C151—22no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—22no—
308C23×C151—21no—
309C23×C151—22no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—48no—
317C23×C151—48no—
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—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—84no—
335C23×C151—84no—
336C23×C151—84no—
337C23×C151—84no—
338C23×C151—84no—
339C23×C151#13512yes—
340C23×C151C22×D411yescharacteristic
341Q8×C151—22no—
342Q8×C151—22no—
343Q8×C151—41no—
344Q8×C151—41no—
345D4×C151—22no—
346D4×C151—22no—
347D4×C151—22no—
348D4×C151—22no—
349D4×C151—22no—
350D4×C151—22no—
351D4×C151—22no—
352D4×C151—44no—
353D4×C151—48no—
354D4×C151—48no—
355D4×C151—41no—
356D4×C151—41no—
357D4×C151—41no—
358D4×C151—41no—
359D4×C151—84no—
360D4×C151—84no—
361D4×C151—84no—
362D4×C151#12114yes—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—21no—
366C2×C4×C151—21no—
367C2×C4×C151—22no—
368C2×C4×C151—22no—
369C2×C4×C151—21no—
370C2×C4×C151—21no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—48no—
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—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—84no—
398C2×C4×C151—84no—
399C2×C4×C151#12012yes—
400C2×C4×C151#12012yes—
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C22×D411yescharacteristic
403C2×C4×C151C22×D411yescharacteristic
404C2×C4×C151C2×#4111yescharacteristic
405C2×C4×C151H(5,𝔽2)11yescharacteristic
406C2×C4×C151H(5,𝔽2)11yescharacteristic
407C8×C151—22no—
408C8×C151—41no—
409C8×C151—41no—
410C8×C151—41no—
411C22×C151—24no—
412C22×C151—22no—
413C22×C151—22no—
414C22×C151—22no—
415C22×C151—41no—
416C22×C151—42no—
417C22×C151—42no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—42no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—41no—
424C22×C151—42no—
425C22×C151—41no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—41no—
429C22×C151—42no—
430C22×C151—41no—
431C22×C151—42no—
432C22×C151—41no—
433C22×C151—42no—
434C22×C151—42no—
435C22×C151—41no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—816no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151—81no—
447C22×C151C2×#12011yescharacteristic
448C22×C151D4211yescharacteristic
449C22×C151#54611yescharacteristic
450C22×C151C2×#13511yescharacteristic
451C22×C151#57511yescharacteristic
452C22×C151#57611yescharacteristic
453C22×C151#57611yescharacteristic
454C4×C151—22no—
455C4×C151—22no—
456C4×C151—41no—
457C4×C151—41no—
458C4×C151—42no—
459C4×C151—42no—
460C4×C151—81no—
461C4×C151—81no—
462C4×C151—81no—
463C4×C151C2×#12111yescharacteristic
464C4×C151#53511yescharacteristic
465C4×C151D4211yescharacteristic
466C4×C151#54611yescharacteristic
467C2×C151—42no—
468C2×C151—44no—
469C2×C151—81no—
470C2×C151—82no—
471C2×C151—82no—
472C2×C151#240811yescharacteristic
473C2×C151#300211yescharacteristic
474C2×C151#300811yescharacteristic
475C2×C151#327311yescharacteristic
476C2×C151#328011yescharacteristic
477C2×C151#329711yescharacteristic
478C2×C151#332211yescharacteristic
479#24245C15111yesmaximal, characteristic, direct product factor, Sylow
480C151#2424511yescharacteristic, direct product factor, Sylow
481C2×#546C2×C15111yescharacteristic, complemented
482C2×#463C2×C15111yescharacteristic, complemented
483C2×#449C2×C15111yescharacteristic, complemented
484C2×#447C2×C15111yescharacteristic, complemented
485C2×C4×D8C2×C15111yescharacteristic, complemented
486#2535C2×C15111yescharacteristic, complemented
487#2036C2×C15111yescharacteristic, complemented
488#2033C2×C15111yescharacteristic, complemented
489#2000C2×C15111yescharacteristic, complemented
490#1999C2×C15111yescharacteristic, complemented
491#1958C2×C15111yescharacteristic, complemented
492#1954C2×C15111yescharacteristic, complemented
493#1804C2×C15111yescharacteristic, complemented
494#1788C2×C15111yescharacteristic, complemented
495#1786C2×C15111yescharacteristic, complemented
496C22×#41C22×C15111yescharacteristic
497C23×D4C22×C15111yescharacteristic
498C22×SD16C22×C15111yescharacteristic, complemented
499C22×D8C22×C15111yescharacteristic
500C22×D8C22×C15111yescharacteristic
501#546—24no—
502#546—24no—
503C2×#124C22×C15111yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C15111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C15111yescharacteristic
508C2×#121C22×C15111yescharacteristic
509C2×#121C22×C15111yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C15111yescharacteristic
512C2×C4×D4C22×C15111yescharacteristic
513C2×C4×D4C22×C15111yescharacteristic, complemented
514C22×C22⋊C4—21no—
515#463—24no—
516#449—24no—
517#447—24no—
518C4×D8—24no—
519C2×#107C22×C15111yescharacteristic, complemented
520C2×C4⋊C8C22×C15111yescharacteristic, complemented
521C2×#103C22×C15111yescharacteristic, complemented
522C2×#103C22×C15111yescharacteristic, complemented
523C2×#103C22×C15111yescharacteristic, complemented
524C2×#102C22×C15111yescharacteristic
525C2×#102C22×C15111yescharacteristic
526C2×#102C22×C15111yescharacteristic
527C2×#102C22×C15111yescharacteristic
528C2×#102C22×C15111yescharacteristic
529C2×#102C22×C15111yescharacteristic
530C2×#102C22×C15111yescharacteristic, complemented
531C2×C22⋊C8C22×C15111yescharacteristic
532C2×C22⋊C8C22×C15111yescharacteristic
533C2×C22⋊C8C22×C15111yescharacteristic, complemented
534C2×C22⋊C8C22×C15111yescharacteristic, complemented
535C2×C4×C8C22×C15111yescharacteristic, complemented
536#397—21no—
537#392—21no—
538#386—21no—
539#386—21no—
540#382C22×C15111yescharacteristic, complemented
541#380C22×C15111yescharacteristic
542#380C22×C15111yescharacteristic, complemented
543#340C22×C15111yescharacteristic, complemented
544#340C22×C15111yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C15111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C15111yescharacteristic
565C22×D4C23×C15111yescharacteristic
566C22×D4C23×C15111yescharacteristic
567C22×D4C23×C15111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4—21no—
571C23×C4C23×C15111yescharacteristic
572C23×C4C23×C15111yescharacteristic
573C2×SD16—22no—
574C2×SD16—22no—
575C2×SD16—41no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8D4×C15114yescomplemented
582C22×C8C23×C15111yescharacteristic
583C22×C8C23×C15111yescharacteristic
584C22×C8C23×C15111yescharacteristic
585C22×C8C23×C15111yescharacteristic
586#124—22no—
587#124D4×C15114yescomplemented
588#123—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591#121—28no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#120—28no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4D4×C15114yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4D4×C15111yescharacteristic
607C2×C4⋊C4C23×C15111yescharacteristic
608C2×C4⋊C4C23×C15111yescharacteristic
609C2×C4⋊C4C23×C15111yescharacteristic
610C2×C4⋊C4C23×C15111yescharacteristic
611C2×C22⋊C4—28no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4D4×C15111yescharacteristic
623C2×C22⋊C4D4×C15111yescharacteristic
624C2×C42C23×C15111yescharacteristic
625#107—22no—
626C4⋊C8—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636#102—41no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8—41no—
640C22⋊C8—41no—
641C4×C8—22no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C15111yescharacteristic
657C24C2×D4×C15111yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C15112yes—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—22no—
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—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C15112yes—
704C2×D4C2×D4×C15112yes—
705C2×D4C2×D4×C15112yes—
706C2×D4C2×D4×C15112yes—
707C2×D4#41×C15112yes—
708C22×C4—24no—
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—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—81no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4—81no—
734C22×C4C2×D4×C15111yescharacteristic
735C22×C4C2×D4×C15111yescharacteristic
736C22×C4C2×D4×C15111yescharacteristic
737C22×C4C2×D4×C15111yescharacteristic
738C22×C4C24×C15111yescharacteristic
739SD16—44no—
740D8—28no—
741D8—44no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8C2×D4×C15112yes—
754C4⋊C4—24no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4C2×D4×C15112yes—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—22no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42C2×D4×C15112yes—
777C42C2×D4×C15112yes—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#135×C15112yes—
820C23C22×D4×C15111yescharacteristic
821Q8—22no—
822Q8—22no—
823Q8—41no—
824Q8—41no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—44no—
833D4—48no—
834D4—48no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—84no—
840D4—84no—
841D4—84no—
842D4#121×C15114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
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—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#120×C15112yes—
880C2×C4#120×C15112yes—
881C2×C4C22×D4×C15111yescharacteristic
882C2×C4C22×D4×C15111yescharacteristic
883C2×C4C22×D4×C15111yescharacteristic
884C2×C4C2×#41×C15111yescharacteristic
885C2×C4H(5,𝔽2)×C15111yescharacteristic
886C2×C4H(5,𝔽2)×C15111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—24no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—41no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—42no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—816no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C15111yescharacteristic
928C22D42×C15111yescharacteristic
929C22#546×C15111yescharacteristic
930C22C2×#135×C15111yescharacteristic
931C22#575×C15111yescharacteristic
932C22#576×C15111yescharacteristic
933C22#576×C15111yescharacteristic
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×#121×C15111yescharacteristic
944C4#535×C15111yescharacteristic
945C4D42×C15111yescharacteristic
946C4#546×C15111yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—82no—
952C2#2408×C15111yescharacteristic
953C2#3002×C15111yescharacteristic
954C2#3008×C15111yescharacteristic
955C2#3273×C15111yescharacteristic
956C2#3280×C15111yescharacteristic
957C2#3297×C15111yescharacteristic
958C2#3322×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
1. C2×#546×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#449×C151C2semidirect
4. C2×#447×C151C2semidirect
5. C2×C4×D8×C151C2semidirect
6. #2535×C151C2semidirect
7. #2036×C151C2semidirect
8. #2033×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1958×C151C2semidirect
12. #1954×C151C2semidirect
13. #1804×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
18. C22×SD16×C151C22semidirect
29. C2×#121×C151C22semidirect
33. C2×C4×D4×C151C22semidirect
39. C2×#107×C151C22semidirect
40. C2×C4⋊C8×C151C22semidirect
41. C2×#103×C151C22semidirect
42. C2×#103×C151C22semidirect
43. C2×#103×C151C22semidirect
50. C2×#102×C151C22semidirect
53. C2×C22⋊C8×C151C22semidirect
54. C2×C22⋊C8×C151C22semidirect
55. C2×C4×C8×C151C22semidirect
60. #382×C151C22semidirect
62. #380×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
101. C2×D8×C151D4semidirect
107. #124×C151D4semidirect
124. C4×D4×C151D4semidirect
479. #24245C151direct (N × H)
480. C151#24245direct (N × H)
481. C2×#546C2×C151semidirect
482. C2×#463C2×C151semidirect
483. C2×#449C2×C151semidirect
484. C2×#447C2×C151semidirect
485. C2×C4×D8C2×C151semidirect
486. #2535C2×C151semidirect
487. #2036C2×C151semidirect
488. #2033C2×C151semidirect
489. #2000C2×C151semidirect
490. #1999C2×C151semidirect
491. #1958C2×C151semidirect
492. #1954C2×C151semidirect
493. #1804C2×C151semidirect
494. #1788C2×C151semidirect
495. #1786C2×C151semidirect
498. C22×SD16C22×C151semidirect
509. C2×#121C22×C151semidirect
513. C2×C4×D4C22×C151semidirect
519. C2×#107C22×C151semidirect
520. C2×C4⋊C8C22×C151semidirect
521. C2×#103C22×C151semidirect
522. C2×#103C22×C151semidirect
523. C2×#103C22×C151semidirect
530. C2×#102C22×C151semidirect
533. C2×C22⋊C8C22×C151semidirect
534. C2×C22⋊C8C22×C151semidirect
535. C2×C4×C8C22×C151semidirect
540. #382C22×C151semidirect
542. #380C22×C151semidirect
543. #340C22×C151semidirect
544. #340C22×C151semidirect
581. C2×D8D4×C151semidirect
587. #124D4×C151semidirect
604. C4×D4D4×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×#463×C1512
C2×#449×C1512
C2×#447×C1512
C2×C4×D8×C1512
#2535×C1512
#2036×C1512
#2033×C1512
#2000×C1512
#1999×C1512
#1958×C1512
#1954×C1512
#1804×C1512
#1788×C1512
#1786×C1512
#24245151