Finite Group Databasebeta

← C151×#24432 #50329357

Subgroups — C151×#24432 #50329357

Order 38656.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C151C211yesmaximal, characteristic
2C2×#465×C151C211yesmaximal, characteristic, complemented
3C2×#450×C151C211yesmaximal, characteristic, complemented
4C2×#450×C151C211yesmaximal, characteristic, complemented
5C22×#102×C151C211yesmaximal, characteristic, complemented
6#2417×C151C211yesmaximal, characteristic, complemented
7#2041×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2014×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1874×C151C211yesmaximal, characteristic, complemented
13#1869×C151C211yesmaximal, characteristic, complemented
14#1864×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151—21no—
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic, complemented
21C22×SD16×C151C2211yescharacteristic, complemented
22C23×C8×C151C2211yescharacteristic, complemented
23D42×C151—24no—
24D42×C151—24no—
25C2×#127×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic, complemented
27C2×C22⋊Q8×C151C2211yescharacteristic, complemented
28C2×#121×C151—21no—
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#120×C151—21no—
32C2×#120×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic
34C2×C4×D4×C151C2211yescharacteristic
35C22×C4⋊C4×C151C2211yescharacteristic, complemented
36#465×C151—24no—
37#450×C151—24no—
38#450×C151—24no—
39C2×#106×C151C2211yescharacteristic, complemented
40C2×#103×C151C2211yescharacteristic, complemented
41C2×#102×C151—24no—
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic, complemented
49C2×#102×C151C2211yescharacteristic, complemented
50C2×#102×C151C2211yescharacteristic, complemented
51C2×C22⋊C8×C151C2211yescharacteristic, complemented
52C2×C22⋊C8×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54#398×C151—21no—
55#396×C151—21no—
56#391×C151C2211yescharacteristic, complemented
57#389×C151C2211yescharacteristic, complemented
58#386×C151—21no—
59#380×C151—21no—
60#380×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#336×C151C2211yescharacteristic, complemented
64#336×C151C2211yescharacteristic, complemented
65C25×C151—21no—
66C25×C151—21no—
67C22×Q8×C151C2311yescharacteristic
68C22×D4×C151—28no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—21no—
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151—22no—
75C22×D4×C151—21no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—22no—
79C22×D4×C151—22no—
80C22×D4×C151—22no—
81C22×D4×C151—22no—
82C22×D4×C151—41no—
83C22×D4×C151—41no—
84C22×D4×C151—41no—
85C22×D4×C151—41no—
86C22×D4×C151—44no—
87C22×D4×C151—44no—
88C22×D4×C151D414yes—
89C22×D4×C151D411yescharacteristic
90C22×D4×C151C2311yescharacteristic
91C22×D4×C151C2311yescharacteristic
92C22×D4×C151C2311yescharacteristic
93C23×C4×C151—21no—
94C23×C4×C151—21no—
95C23×C4×C151C2311yescharacteristic
96C23×C4×C151C2311yescharacteristic
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—22no—
100C2×SD16×C151—22no—
101C2×SD16×C151—22no—
102C2×SD16×C151—22no—
103C2×SD16×C151—41no—
104C2×SD16×C151—41no—
105C2×SD16×C151—41no—
106C22×C8×C151—22no—
107C22×C8×C151—22no—
108C22×C8×C151—41no—
109C22×C8×C151C2311yescharacteristic
110C22×C8×C151C2311yescharacteristic
111C22×C8×C151C2311yescharacteristic
112C22×C8×C151C2311yescharacteristic
113#127×C151—22no—
114#127×C151—22no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—22no—
117C22⋊Q8×C151—22no—
118C22⋊Q8×C151—41no—
119#121×C151—28no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151D414yes—
124#120×C151—28no—
125#120×C151—28no—
126C4×D4×C151—22no—
127C4×D4×C151—22no—
128C4×D4×C151—22no—
129C4×D4×C151—22no—
130C2×C4⋊C4×C151—22no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151—21no—
134C2×C4⋊C4×C151—21no—
135C2×C4⋊C4×C151—41no—
136C2×C4⋊C4×C151D411yescharacteristic
137C2×C4⋊C4×C151C2311yescharacteristic
138C2×C4⋊C4×C151C2311yescharacteristic
139C2×C4⋊C4×C151C2311yescharacteristic
140C2×C4⋊C4×C151C2311yescharacteristic
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×C151D411yescharacteristic
148C2×C22⋊C4×C151D411yescharacteristic
149C2×C42×C151C2311yescharacteristic
150#106×C151—22no—
151#103×C151—22no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—22no—
159#102×C151—41no—
160#102×C151D414yescomplemented
161C22⋊C8×C151—22no—
162C22⋊C8×C151—22no—
163C22⋊C8×C151—41no—
164#95×C151—21no—
165#95×C151—21no—
166#95×C151—21no—
167#95×C151—21no—
168C24×C151—21no—
169C24×C151—24no—
170C24×C151—21no—
171C24×C151—21no—
172C24×C151—24no—
173C24×C151—42no—
174C24×C151—42no—
175C24×C151—42no—
176C24×C151—42no—
177C24×C151—42no—
178C24×C151—42no—
179C24×C151—42no—
180C24×C151—42no—
181C24×C151—81no—
182C24×C151—81no—
183C24×C151—81no—
184C24×C151—81no—
185C24×C151C2×D411yescharacteristic
186C24×C151C2×D411yescharacteristic
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151—21no—
191C2×Q8×C151—21no—
192C2×Q8×C151—21no—
193C2×D4×C151—22no—
194C2×D4×C151—22no—
195C2×D4×C151—28no—
196C2×D4×C151—24no—
197C2×D4×C151—24no—
198C2×D4×C151—24no—
199C2×D4×C151—24no—
200C2×D4×C151—24no—
201C2×D4×C151—24no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—21no—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—21no—
212C2×D4×C151—21no—
213C2×D4×C151—21no—
214C2×D4×C151—21no—
215C2×D4×C151—44no—
216C2×D4×C151—44no—
217C2×D4×C151—44no—
218C2×D4×C151—42no—
219C2×D4×C151—42no—
220C2×D4×C151—42no—
221C2×D4×C151—42no—
222C2×D4×C151—42no—
223C2×D4×C151—44no—
224C2×D4×C151—44no—
225C2×D4×C151—432no—
226C2×D4×C151—44no—
227C2×D4×C151—42no—
228C2×D4×C151—42no—
229C2×D4×C151—42no—
230C2×D4×C151—42no—
231C2×D4×C151—44no—
232C2×D4×C151—42no—
233C2×D4×C151—81no—
234C2×D4×C151—81no—
235C2×D4×C151SD1614yescomplemented
236C2×D4×C151C2×D412yes—
237C2×D4×C151C2×D412yes—
238C2×D4×C151C2×D412yes—
239C2×D4×C151C2×D412yes—
240C2×D4×C151#4112yes—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—24no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—42no—
258C22×C4×C151—42no—
259C22×C4×C151—42no—
260C22×C4×C151—42no—
261C22×C4×C151—81no—
262C22×C4×C151C2×D411yescharacteristic
263C22×C4×C151C2×D411yescharacteristic
264C22×C4×C151C2×D411yescharacteristic
265C22×C4×C151C2×D412yes—
266C22×C4×C151C2×D412yes—
267C22×C4×C151C2×D411yescharacteristic
268C22×C4×C151C2411yescharacteristic
269SD16×C151—44no—
270SD16×C151—44no—
271SD16×C151—44no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—21no—
275C2×C8×C151—21no—
276C2×C8×C151—21no—
277C2×C8×C151—21no—
278C2×C8×C151—21no—
279C2×C8×C151—21no—
280C2×C8×C151—21no—
281C2×C8×C151—21no—
282C2×C8×C151—21no—
283C2×C8×C151—44no—
284C2×C8×C151C2×D412yescomplemented
285C4⋊C4×C151—22no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151—21no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151—21no—
292C4⋊C4×C151—42no—
293C4⋊C4×C151—42no—
294C4⋊C4×C151—42no—
295C4⋊C4×C151—81no—
296C4⋊C4×C151C2×D412yes—
297C4⋊C4×C151C2×D412yescomplemented
298C22⋊C4×C151—24no—
299C22⋊C4×C151—24no—
300C22⋊C4×C151—22no—
301C22⋊C4×C151—24no—
302C22⋊C4×C151—22no—
303C22⋊C4×C151—42no—
304C22⋊C4×C151—42no—
305C22⋊C4×C151—81no—
306C42×C151—21no—
307C42×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—22no—
313C23×C151—21no—
314C23×C151—22no—
315C23×C151—21no—
316C23×C151—22no—
317C23×C151—21no—
318C23×C151—21no—
319C23×C151—21no—
320C23×C151—21no—
321C23×C151—22no—
322C23×C151—22no—
323C23×C151—48no—
324C23×C151—48no—
325C23×C151—48no—
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—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—48no—
343C23×C151—84no—
344C23×C151—84no—
345C23×C151—84no—
346C23×C151—84no—
347C23×C151—84no—
348C23×C151—84no—
349C23×C151—84no—
350C23×C151—84no—
351C23×C151—84no—
352C23×C151—84no—
353C23×C151#12012yes—
354C23×C151C2×SD1612yes—
355C23×C151C2×SD1612yes—
356C23×C151AGL(1,ℤ/8)12yes—
357C23×C151C22×D411yescharacteristic
358Q8×C151—41no—
359Q8×C151—41no—
360Q8×C151—41no—
361Q8×C151—41no—
362D4×C151—28no—
363D4×C151—22no—
364D4×C151—22no—
365D4×C151—22no—
366D4×C151—22no—
367D4×C151—22no—
368D4×C151—22no—
369D4×C151—22no—
370D4×C151—48no—
371D4×C151—48no—
372D4×C151—48no—
373D4×C151—48no—
374D4×C151—48no—
375D4×C151—41no—
376D4×C151—41no—
377D4×C151—41no—
378D4×C151—41no—
379D4×C151—84no—
380D4×C151#12114yes—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—21no—
385C2×C4×C151—22no—
386C2×C4×C151—22no—
387C2×C4×C151—22no—
388C2×C4×C151—22no—
389C2×C4×C151—21no—
390C2×C4×C151—21no—
391C2×C4×C151—22no—
392C2×C4×C151—22no—
393C2×C4×C151—21no—
394C2×C4×C151—21no—
395C2×C4×C151—21no—
396C2×C4×C151—21no—
397C2×C4×C151—48no—
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—41no—
406C2×C4×C151—41no—
407C2×C4×C151—41no—
408C2×C4×C151—41no—
409C2×C4×C151—41no—
410C2×C4×C151—41no—
411C2×C4×C151—41no—
412C2×C4×C151—41no—
413C2×C4×C151—41no—
414C2×C4×C151—41no—
415C2×C4×C151—84no—
416C2×C4×C151#12012yes—
417C2×C4×C151C2×SD1612yes—
418C2×C4×C151C22×D411yescharacteristic
419C2×C4×C151C22×D411yescharacteristic
420C2×C4×C151C22×D411yescharacteristic
421C2×C4×C151C2×#4111yescharacteristic
422C2×C4×C151H(5,𝔽2)11yescharacteristic
423C2×C4×C151H(5,𝔽2)11yescharacteristic
424C8×C151—22no—
425C8×C151—41no—
426C8×C151—41no—
427C8×C151—41no—
428C22×C151—22no—
429C22×C151—22no—
430C22×C151—22no—
431C22×C151—22no—
432C22×C151—22no—
433C22×C151—22no—
434C22×C151—24no—
435C22×C151—22no—
436C22×C151—22no—
437C22×C151—22no—
438C22×C151—41no—
439C22×C151—42no—
440C22×C151—41no—
441C22×C151—42no—
442C22×C151—41no—
443C22×C151—42no—
444C22×C151—42no—
445C22×C151—42no—
446C22×C151—41no—
447C22×C151—42no—
448C22×C151—42no—
449C22×C151—42no—
450C22×C151—42no—
451C22×C151—42no—
452C22×C151—42no—
453C22×C151—42no—
454C22×C151—816no—
455C22×C151—816no—
456C22×C151—81no—
457C22×C151—81no—
458C22×C151—81no—
459C22×C151—81no—
460C22×C151—81no—
461C22×C151—81no—
462C22×C151—81no—
463C22×C151—81no—
464C22×C151#45014yescomplemented
465C22×C151C2×#12011yescharacteristic
466C22×C151D4211yescharacteristic
467C22×C151#54611yescharacteristic
468C22×C151C22×SD1611yescharacteristic
469C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C151#57611yescharacteristic
471C22×C151#57711yescharacteristic
472C4×C151—22no—
473C4×C151—22no—
474C4×C151—41no—
475C4×C151—42no—
476C4×C151—42no—
477C4×C151—41no—
478C4×C151—81no—
479C4×C151—81no—
480C4×C151—81no—
481C4×C151C2×#12111yescharacteristic
482C4×C151#53411yescharacteristic
483C4×C151D4211yescharacteristic
484C4×C151#54611yescharacteristic
485C2×C151—24no—
486C2×C151—42no—
487C2×C151—44no—
488C2×C151—82no—
489C2×C151—82no—
490C2×C151#241011yescharacteristic
491C2×C151C2×#45011yescharacteristic
492C2×C151#301211yescharacteristic
493C2×C151#326411yescharacteristic
494C2×C151D4×SD1611yescharacteristic
495C2×C151#329511yescharacteristic
496C2×C151#331011yescharacteristic
497#24432C15111yesmaximal, characteristic, direct product factor, Sylow
498C151#2443211yescharacteristic, direct product factor, Sylow
499C2×D42C2×C15111yescharacteristic
500C2×#465C2×C15111yescharacteristic, complemented
501C2×#450C2×C15111yescharacteristic, complemented
502C2×#450C2×C15111yescharacteristic, complemented
503C22×#102C2×C15111yescharacteristic, complemented
504#2417C2×C15111yescharacteristic, complemented
505#2041C2×C15111yescharacteristic, complemented
506#2034C2×C15111yescharacteristic, complemented
507#2014C2×C15111yescharacteristic, complemented
508#2000C2×C15111yescharacteristic, complemented
509#1877C2×C15111yescharacteristic, complemented
510#1874C2×C15111yescharacteristic, complemented
511#1869C2×C15111yescharacteristic, complemented
512#1864C2×C15111yescharacteristic, complemented
513#1786C2×C15111yescharacteristic, complemented
514C23×D4—21no—
515C23×D4C22×C15111yescharacteristic
516C23×D4C22×C15111yescharacteristic
517C22×SD16C22×C15111yescharacteristic
518C22×SD16C22×C15111yescharacteristic, complemented
519C22×SD16C22×C15111yescharacteristic, complemented
520C23×C8C22×C15111yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C15111yescharacteristic
524C2×C22⋊Q8C22×C15111yescharacteristic, complemented
525C2×C22⋊Q8C22×C15111yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C15111yescharacteristic
528C2×#121C22×C15111yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C15111yescharacteristic
532C2×C4×D4C22×C15111yescharacteristic
533C22×C4⋊C4C22×C15111yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C15111yescharacteristic, complemented
538C2×#103C22×C15111yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C15111yescharacteristic
541C2×#102C22×C15111yescharacteristic
542C2×#102C22×C15111yescharacteristic
543C2×#102C22×C15111yescharacteristic, complemented
544C2×#102C22×C15111yescharacteristic, complemented
545C2×#102C22×C15111yescharacteristic, complemented
546C2×#102C22×C15111yescharacteristic, complemented
547C2×#102C22×C15111yescharacteristic, complemented
548C2×#102C22×C15111yescharacteristic, complemented
549C2×C22⋊C8C22×C15111yescharacteristic, complemented
550C2×C22⋊C8C22×C15111yescharacteristic, complemented
551C2×C22⋊C8C22×C15111yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C15111yescharacteristic, complemented
555#389C22×C15111yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C15111yescharacteristic, complemented
559#340C22×C15111yescharacteristic, complemented
560#340C22×C15111yescharacteristic, complemented
561#336C22×C15111yescharacteristic, complemented
562#336C22×C15111yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C15111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C15111yescharacteristic
587C22×D4D4×C15114yes—
588C22×D4C23×C15111yescharacteristic
589C22×D4C23×C15111yescharacteristic
590C22×D4C23×C15111yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C15111yescharacteristic
594C23×C4C23×C15111yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C15111yescharacteristic
608C22×C8C23×C15111yescharacteristic
609C22×C8C23×C15111yescharacteristic
610C22×C8C23×C15111yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C15114yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C15111yescharacteristic
635C2×C4⋊C4C23×C15111yescharacteristic
636C2×C4⋊C4C23×C15111yescharacteristic
637C2×C4⋊C4C23×C15111yescharacteristic
638C2×C4⋊C4C23×C15111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C15111yescharacteristic
646C2×C22⋊C4D4×C15111yescharacteristic
647C2×C42C23×C15111yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C15114yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C15111yescharacteristic
684C24C2×D4×C15111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C15114yescomplemented
734C2×D4C2×D4×C15112yes—
735C2×D4C2×D4×C15112yes—
736C2×D4C2×D4×C15112yes—
737C2×D4C2×D4×C15112yes—
738C2×D4#41×C15112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C15111yescharacteristic
761C22×C4C2×D4×C15111yescharacteristic
762C22×C4C2×D4×C15111yescharacteristic
763C22×C4C2×D4×C15112yes—
764C22×C4C2×D4×C15112yes—
765C22×C4C2×D4×C15111yescharacteristic
766C22×C4C24×C15111yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C15112yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C15112yes—
795C4⋊C4C2×D4×C15112yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C15112yes—
852C23C2×SD16×C15112yes—
853C23C2×SD16×C15112yes—
854C23AGL(1,ℤ/8)×C15112yes—
855C23C22×D4×C15111yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C15114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C15112yes—
915C2×C4C2×SD16×C15112yes—
916C2×C4C22×D4×C15111yescharacteristic
917C2×C4C22×D4×C15111yescharacteristic
918C2×C4C22×D4×C15111yescharacteristic
919C2×C4C2×#41×C15111yescharacteristic
920C2×C4H(5,𝔽2)×C15111yescharacteristic
921C2×C4H(5,𝔽2)×C15111yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—24no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C15114yescomplemented
963C22C2×#120×C15111yescharacteristic
964C22D42×C15111yescharacteristic
965C22#546×C15111yescharacteristic
966C22C22×SD16×C15111yescharacteristic
967C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
968C22#576×C15111yescharacteristic
969C22#577×C15111yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C15111yescharacteristic
980C4#534×C15111yescharacteristic
981C4D42×C15111yescharacteristic
982C4#546×C15111yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2#2410×C15111yescharacteristic
989C2C2×#450×C15111yescharacteristic
990C2#3012×C15111yescharacteristic
991C2#3264×C15111yescharacteristic
992C2D4×SD16×C15111yescharacteristic
993C2#3295×C15111yescharacteristic
994C2#3310×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×D42×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×#465×C151C2semidirect
3. C2×#450×C151C2semidirect
4. C2×#450×C151C2semidirect
5. C22×#102×C151C2semidirect
6. #2417×C151C2semidirect
7. #2041×C151C2semidirect
8. #2034×C151C2semidirect
9. #2014×C151C2semidirect
10. #2000×C151C2semidirect
11. #1877×C151C2semidirect
12. #1874×C151C2semidirect
13. #1869×C151C2semidirect
14. #1864×C151C2semidirect
15. #1786×C151C2semidirect
20. C22×SD16×C151C22semidirect
21. C22×SD16×C151C22semidirect
22. C23×C8×C151C22semidirect
26. C2×C22⋊Q8×C151C22semidirect
27. C2×C22⋊Q8×C151C22semidirect
35. C22×C4⋊C4×C151C22semidirect
39. C2×#106×C151C22semidirect
40. C2×#103×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#102×C151C22semidirect
49. C2×#102×C151C22semidirect
50. C2×#102×C151C22semidirect
51. C2×C22⋊C8×C151C22semidirect
52. C2×C22⋊C8×C151C22semidirect
53. C2×C22⋊C8×C151C22semidirect
56. #391×C151C22semidirect
57. #389×C151C22semidirect
60. #380×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #336×C151C22semidirect
64. #336×C151C22semidirect
160. #102×C151D4semidirect
235. C2×D4×C151SD16semidirect
284. C2×C8×C151C2×D4semidirect
297. C4⋊C4×C151C2×D4semidirect
464. C22×C151#450semidirect
497. #24432C151direct (N × H)
498. C151#24432direct (N × H)
500. C2×#465C2×C151semidirect
501. C2×#450C2×C151semidirect
502. C2×#450C2×C151semidirect
503. C22×#102C2×C151semidirect
504. #2417C2×C151semidirect
505. #2041C2×C151semidirect
506. #2034C2×C151semidirect
507. #2014C2×C151semidirect
508. #2000C2×C151semidirect
509. #1877C2×C151semidirect
510. #1874C2×C151semidirect
511. #1869C2×C151semidirect
512. #1864C2×C151semidirect
513. #1786C2×C151semidirect
518. C22×SD16C22×C151semidirect
519. C22×SD16C22×C151semidirect
520. C23×C8C22×C151semidirect
524. C2×C22⋊Q8C22×C151semidirect
525. C2×C22⋊Q8C22×C151semidirect
533. C22×C4⋊C4C22×C151semidirect
537. C2×#106C22×C151semidirect
538. C2×#103C22×C151semidirect
543. C2×#102C22×C151semidirect
544. C2×#102C22×C151semidirect
545. C2×#102C22×C151semidirect
546. C2×#102C22×C151semidirect
547. C2×#102C22×C151semidirect
548. C2×#102C22×C151semidirect
549. C2×C22⋊C8C22×C151semidirect
550. C2×C22⋊C8C22×C151semidirect
551. C2×C22⋊C8C22×C151semidirect
554. #391C22×C151semidirect
555. #389C22×C151semidirect
558. #380C22×C151semidirect
559. #340C22×C151semidirect
560. #340C22×C151semidirect
561. #336C22×C151semidirect
562. #336C22×C151semidirect
658. #102D4×C151semidirect
733. C2×D4SD16×C151semidirect
782. C2×C8C2×D4×C151semidirect
795. C4⋊C4C2×D4×C151semidirect
962. C22#450×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1512
C2×#465×C1512
C2×#450×C1512
C22×#102×C1512
#2417×C1512
#2041×C1512
#2034×C1512
#2014×C1512
#2000×C1512
#1877×C1512
#1874×C1512
#1869×C1512
#1864×C1512
#1786×C1512
#24432151