Finite Group Databasebeta

← C151×#24275 #50329200

Subgroups — C151×#24275 #50329200

Order 38656.

1614 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic, complemented
2C2×#466×C151C211yesmaximal, characteristic, complemented
3C2×#465×C151C211yesmaximal, characteristic, complemented
4C2×#435×C151C211yesmaximal, characteristic, complemented
5#2408×C151C211yesmaximal, characteristic, complemented
6#2407×C151C211yesmaximal, characteristic, complemented
7#2055×C151C211yesmaximal, characteristic, complemented
8#2054×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1973×C151C211yesmaximal, characteristic, complemented
12#1972×C151C211yesmaximal, characteristic, complemented
13#1809×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C151—24no—
19C2×AGL(1,ℤ/8)×C151—24no—
20C2×AGL(1,ℤ/8)×C151—24no—
21C22×SD16×C151C2211yescharacteristic
22C22×SD16×C151C2211yescharacteristic
23C22×D8×C151C2211yescharacteristic
24C22×D8×C151C2211yescharacteristic
25C22×M16×C151C2211yescharacteristic
26C23×C8×C151C2211yescharacteristic, complemented
27C2×C22⋊Q8×C151C2211yescharacteristic, complemented
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic, complemented
31C2×#120×C151—21no—
32C2×C4×D4×C151C2211yescharacteristic
33#466×C151—24no—
34#465×C151—24no—
35#435×C151—24no—
36C2×#107×C151C2211yescharacteristic, complemented
37C2×#106×C151C2211yescharacteristic, complemented
38C2×C4⋊C8×C151C2211yescharacteristic, complemented
39C2×#103×C151C2211yescharacteristic, complemented
40C2×#103×C151C2211yescharacteristic, complemented
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic, complemented
49C2×#97×C151C2211yescharacteristic, complemented
50#394×C151—21no—
51#394×C151—21no—
52#392×C151—21no—
53#392×C151—21no—
54#391×C151C2211yescharacteristic, complemented
55#390×C151C2211yescharacteristic
56#390×C151C2211yescharacteristic
57#390×C151C2211yescharacteristic, complemented
58#386×C151—21no—
59#385×C151—21no—
60#380×C151C2211yescharacteristic
61#380×C151C2211yescharacteristic
62#379×C151—21no—
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—21no—
74C22×D4×C151—21no—
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×C151D411yescharacteristic
85C22×D4×C151C2311yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C23×C4×C151—21no—
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91AGL(1,ℤ/8)×C151—232no—
92C2×SD16×C151—22no—
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151D414yescomplemented
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—22no—
101C2×D8×C151—22no—
102C2×D8×C151—22no—
103C2×D8×C151D414yescomplemented
104C2×M16×C151—22no—
105C2×M16×C151—22no—
106C2×M16×C151D414yescomplemented
107C22×C8×C151—22no—
108C22×C8×C151—22no—
109C22×C8×C151—22no—
110C22×C8×C151C2311yescharacteristic
111C22×C8×C151C2311yescharacteristic
112C22×C8×C151C2311yescharacteristic
113C22×C8×C151C2311yescharacteristic
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—41no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—41no—
120#121×C151—41no—
121#121×C151—41no—
122#120×C151—44no—
123C4×D4×C151—22no—
124C4×D4×C151—22no—
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—21no—
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×C151—21no—
143C2×C22⋊C4×C151D411yescharacteristic
144C2×C22⋊C4×C151D411yescharacteristic
145C2×C42×C151C2311yescharacteristic
146#107×C151—22no—
147#106×C151—22no—
148C4⋊C8×C151—22no—
149#103×C151—22no—
150#103×C151—41no—
151#102×C151—22no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—41no—
155#102×C151—41no—
156#102×C151—41no—
157C22⋊C8×C151—22no—
158C22⋊C8×C151—22no—
159#97×C151—22no—
160#95×C151—21no—
161#95×C151—21no—
162#95×C151—21no—
163#95×C151—21no—
164C24×C151—21no—
165C24×C151—21no—
166C24×C151—21no—
167C24×C151—42no—
168C24×C151—42no—
169C24×C151—42no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—81no—
173C24×C151—81no—
174C24×C151C2×D411yescharacteristic
175C24×C151C2×D411yescharacteristic
176#41×C151—28no—
177#41×C151—44no—
178#41×C151—44no—
179#41×C151—44no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151C2×D412yes—
186C2×D4×C151—28no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
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—21no—
204C2×D4×C151—44no—
205C2×D4×C151—44no—
206C2×D4×C151—41no—
207C2×D4×C151—42no—
208C2×D4×C151—42no—
209C2×D4×C151—42no—
210C2×D4×C151—44no—
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×C151—42no—
219C2×D4×C151—42no—
220C2×D4×C151—81no—
221C2×D4×C151—81no—
222C2×D4×C151—81no—
223C2×D4×C151C2×D412yes—
224C2×D4×C151C2×D412yes—
225C2×D4×C151C2×D412yes—
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—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—42no—
242C22×C4×C151—42no—
243C22×C4×C151—42no—
244C22×C4×C151C2×D411yescharacteristic
245C22×C4×C151C2×D411yescharacteristic
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D412yes—
249C22×C4×C151#4112yes—
250C22×C4×C151C2411yescharacteristic
251SD16×C151—28no—
252SD16×C151—28no—
253D8×C151—28no—
254D8×C151—28no—
255M16×C151—28no—
256C2×C8×C151—21no—
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—44no—
265C2×C8×C151C2×D412yes—
266C2×C8×C151C2×D412yes—
267C2×C8×C151C2×D412yes—
268C2×C8×C151C2×D412yes—
269C4⋊C4×C151—22no—
270C4⋊C4×C151—21no—
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—42no—
279C22⋊C4×C151—22no—
280C22⋊C4×C151—22no—
281C22⋊C4×C151—42no—
282C22⋊C4×C151—42no—
283C22⋊C4×C151—42no—
284C22⋊C4×C151—42no—
285C22⋊C4×C151—42no—
286C22⋊C4×C151—42no—
287C22⋊C4×C151—42no—
288C22⋊C4×C151—42no—
289C22⋊C4×C151—81no—
290C22⋊C4×C151—81no—
291C22⋊C4×C151—81no—
292C22⋊C4×C151—81no—
293C42×C151—21no—
294C42×C151—21no—
295C23×C151—21no—
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—22no—
308C23×C151—22no—
309C23×C151—22no—
310C23×C151—48no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
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—84no—
330C23×C151—84no—
331C23×C151—84no—
332C23×C151—84no—
333C23×C151—84no—
334C23×C151—84no—
335C23×C151#12112yes—
336C23×C151AGL(1,ℤ/8)12yescomplemented
337C23×C151C22×D411yescharacteristic
338Q8×C151—22no—
339Q8×C151—22no—
340Q8×C151—41no—
341Q8×C151—41no—
342D4×C151—22no—
343D4×C151—22no—
344D4×C151—22no—
345D4×C151—22no—
346D4×C151—22no—
347D4×C151—22no—
348D4×C151—48no—
349D4×C151—44no—
350D4×C151—48no—
351D4×C151—41no—
352D4×C151—41no—
353D4×C151—41no—
354D4×C151—41no—
355D4×C151—41no—
356D4×C151—41no—
357D4×C151—84no—
358D4×C151—84no—
359D4×C151—84no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—22no—
363C2×C4×C151—22no—
364C2×C4×C151—22no—
365C2×C4×C151—22no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—22no—
370C2×C4×C151—21no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—21no—
376C2×C4×C151—48no—
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#12112yes—
396C2×C4×C151C22×D411yescharacteristic
397C2×C4×C151C22×D411yescharacteristic
398C2×C4×C151C22×D411yescharacteristic
399C2×C4×C151C2×#4111yescharacteristic
400C2×C4×C151H(5,𝔽2)11yescharacteristic
401C2×C4×C151H(5,𝔽2)11yescharacteristic
402C8×C151—22no—
403C8×C151—41no—
404C8×C151—41no—
405C8×C151#12014yescomplemented
406C22×C151—22no—
407C22×C151—22no—
408C22×C151—22no—
409C22×C151—22no—
410C22×C151—22no—
411C22×C151—22no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—42no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—42no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—42no—
429C22×C151—816no—
430C22×C151—81no—
431C22×C151—81no—
432C22×C151—81no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—81no—
437C22×C151—81no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151C2×#12111yescharacteristic
443C22×C151D4211yescharacteristic
444C22×C151D4211yescharacteristic
445C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
446C22×C151#57511yescharacteristic
447C22×C151#57611yescharacteristic
448C22×C151#57711yescharacteristic
449C4×C151—22no—
450C4×C151—41no—
451C4×C151—42no—
452C4×C151—41no—
453C4×C151—41no—
454C4×C151—81no—
455C4×C151—81no—
456C4×C151—81no—
457C4×C151—81no—
458C4×C151C2×#12011yescharacteristic
459C4×C151#53511yescharacteristic
460C4×C151#54611yescharacteristic
461C4×C151#54611yescharacteristic
462C2×C151—42no—
463C2×C151—42no—
464C2×C151—82no—
465C2×C151—82no—
466C2×C151—82no—
467C2×C151#240811yescharacteristic
468C2×C151#305511yescharacteristic
469C2×C151#306211yescharacteristic
470C2×C151#326411yescharacteristic
471C2×C151#326511yescharacteristic
472C2×C151#326711yescharacteristic
473C2×C151#326811yescharacteristic
474#24275C15111yesmaximal, characteristic, direct product factor, Sylow
475C151#2427511yescharacteristic, direct product factor, Sylow
476C22×AGL(1,ℤ/8)C2×C15111yescharacteristic, complemented
477C2×#466C2×C15111yescharacteristic, complemented
478C2×#465C2×C15111yescharacteristic, complemented
479C2×#435C2×C15111yescharacteristic, complemented
480#2408C2×C15111yescharacteristic, complemented
481#2407C2×C15111yescharacteristic, complemented
482#2055C2×C15111yescharacteristic, complemented
483#2054C2×C15111yescharacteristic, complemented
484#2000C2×C15111yescharacteristic, complemented
485#1999C2×C15111yescharacteristic, complemented
486#1973C2×C15111yescharacteristic, complemented
487#1972C2×C15111yescharacteristic, complemented
488#1809C2×C15111yescharacteristic, complemented
489#1788C2×C15111yescharacteristic, complemented
490#1786C2×C15111yescharacteristic, complemented
491C22×#41C22×C15111yescharacteristic
492C23×D4C22×C15111yescharacteristic
493C2×AGL(1,ℤ/8)—24no—
494C2×AGL(1,ℤ/8)—24no—
495C2×AGL(1,ℤ/8)—24no—
496C22×SD16C22×C15111yescharacteristic
497C22×SD16C22×C15111yescharacteristic
498C22×D8C22×C15111yescharacteristic
499C22×D8C22×C15111yescharacteristic
500C22×M16C22×C15111yescharacteristic
501C23×C8C22×C15111yescharacteristic, complemented
502C2×C22⋊Q8C22×C15111yescharacteristic, complemented
503C2×#121C22×C15111yescharacteristic
504C2×#121C22×C15111yescharacteristic
505C2×#121C22×C15111yescharacteristic, complemented
506C2×#120—21no—
507C2×C4×D4C22×C15111yescharacteristic
508#466—24no—
509#465—24no—
510#435—24no—
511C2×#107C22×C15111yescharacteristic, complemented
512C2×#106C22×C15111yescharacteristic, complemented
513C2×C4⋊C8C22×C15111yescharacteristic, complemented
514C2×#103C22×C15111yescharacteristic, complemented
515C2×#103C22×C15111yescharacteristic, complemented
516C2×#102C22×C15111yescharacteristic
517C2×#102C22×C15111yescharacteristic
518C2×#102C22×C15111yescharacteristic
519C2×#102C22×C15111yescharacteristic
520C2×#102C22×C15111yescharacteristic, complemented
521C2×#102C22×C15111yescharacteristic, complemented
522C2×C22⋊C8C22×C15111yescharacteristic
523C2×C22⋊C8C22×C15111yescharacteristic, complemented
524C2×#97C22×C15111yescharacteristic, complemented
525#394—21no—
526#394—21no—
527#392—21no—
528#392—21no—
529#391C22×C15111yescharacteristic, complemented
530#390C22×C15111yescharacteristic
531#390C22×C15111yescharacteristic
532#390C22×C15111yescharacteristic, complemented
533#386—21no—
534#385—21no—
535#380C22×C15111yescharacteristic
536#380C22×C15111yescharacteristic
537#379—21no—
538#340C22×C15111yescharacteristic, complemented
539#340C22×C15111yescharacteristic, complemented
540C25—21no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—41no—
546C2×#41—41no—
547C22×Q8C23×C15111yescharacteristic
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—22no—
555C22×D4—22no—
556C22×D4—21no—
557C22×D4—41no—
558C22×D4—41no—
559C22×D4D4×C15111yescharacteristic
560C22×D4C23×C15111yescharacteristic
561C22×D4C23×C15111yescharacteristic
562C22×D4C23×C15111yescharacteristic
563C23×C4—21no—
564C23×C4C23×C15111yescharacteristic
565C23×C4C23×C15111yescharacteristic
566AGL(1,ℤ/8)—232no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16D4×C15114yescomplemented
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8D4×C15114yescomplemented
579C2×M16—22no—
580C2×M16—22no—
581C2×M16D4×C15114yescomplemented
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—22no—
585C22×C8C23×C15111yescharacteristic
586C22×C8C23×C15111yescharacteristic
587C22×C8C23×C15111yescharacteristic
588C22×C8C23×C15111yescharacteristic
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#120—44no—
598C4×D4—22no—
599C4×D4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4D4×C15111yescharacteristic
602C2×C4⋊C4C23×C15111yescharacteristic
603C2×C4⋊C4C23×C15111yescharacteristic
604C2×C4⋊C4C23×C15111yescharacteristic
605C2×C4⋊C4C23×C15111yescharacteristic
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×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4D4×C15111yescharacteristic
619C2×C22⋊C4D4×C15111yescharacteristic
620C2×C42C23×C15111yescharacteristic
621#107—22no—
622#106—22no—
623C4⋊C8—22no—
624#103—22no—
625#103—41no—
626#102—22no—
627#102—22no—
628#102—22no—
629#102—41no—
630#102—41no—
631#102—41no—
632C22⋊C8—22no—
633C22⋊C8—22no—
634#97—22no—
635#95—21no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—42no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—81no—
648C24—81no—
649C24C2×D4×C15111yescharacteristic
650C24C2×D4×C15111yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C15112yes—
661C2×D4—28no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—41no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4C2×D4×C15112yes—
699C2×D4C2×D4×C15112yes—
700C2×D4C2×D4×C15112yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4C2×D4×C15111yescharacteristic
720C22×C4C2×D4×C15111yescharacteristic
721C22×C4C2×D4×C15111yescharacteristic
722C22×C4C2×D4×C15111yescharacteristic
723C22×C4C2×D4×C15112yes—
724C22×C4#41×C15112yes—
725C22×C4C24×C15111yescharacteristic
726SD16—28no—
727SD16—28no—
728D8—28no—
729D8—28no—
730M16—28no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—44no—
740C2×C8C2×D4×C15112yes—
741C2×C8C2×D4×C15112yes—
742C2×C8C2×D4×C15112yes—
743C2×C8C2×D4×C15112yes—
744C4⋊C4—22no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—42no—
754C22⋊C4—22no—
755C22⋊C4—22no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C22⋊C4—42no—
764C22⋊C4—81no—
765C22⋊C4—81no—
766C22⋊C4—81no—
767C22⋊C4—81no—
768C42—21no—
769C42—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—48no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—84no—
805C23—84no—
806C23—84no—
807C23—84no—
808C23—84no—
809C23—84no—
810C23#121×C15112yes—
811C23AGL(1,ℤ/8)×C15112yescomplemented
812C23C22×D4×C15111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—41no—
816Q8—41no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—22no—
821D4—22no—
822D4—22no—
823D4—48no—
824D4—44no—
825D4—48no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—48no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
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#121×C15112yes—
871C2×C4C22×D4×C15111yescharacteristic
872C2×C4C22×D4×C15111yescharacteristic
873C2×C4C22×D4×C15111yescharacteristic
874C2×C4C2×#41×C15111yescharacteristic
875C2×C4H(5,𝔽2)×C15111yescharacteristic
876C2×C4H(5,𝔽2)×C15111yescharacteristic
877C8—22no—
878C8—41no—
879C8—41no—
880C8#120×C15114yescomplemented
881C22—22no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—816no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#121×C15111yescharacteristic
918C22D42×C15111yescharacteristic
919C22D42×C15111yescharacteristic
920C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
921C22#575×C15111yescharacteristic
922C22#576×C15111yescharacteristic
923C22#577×C15111yescharacteristic
924C4—22no—
925C4—41no—
926C4—42no—
927C4—41no—
928C4—41no—
929C4—81no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4C2×#120×C15111yescharacteristic
934C4#535×C15111yescharacteristic
935C4#546×C15111yescharacteristic
936C4#546×C15111yescharacteristic
937C2—42no—
938C2—42no—
939C2—82no—
940C2—82no—
941C2—82no—
942C2#2408×C15111yescharacteristic
943C2#3055×C15111yescharacteristic
944C2#3062×C15111yescharacteristic
945C2#3264×C15111yescharacteristic
946C2#3265×C15111yescharacteristic
947C2#3267×C15111yescharacteristic
948C2#3268×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. C22×AGL(1,ℤ/8)×C151C2semidirect
2. C2×#466×C151C2semidirect
3. C2×#465×C151C2semidirect
4. C2×#435×C151C2semidirect
5. #2408×C151C2semidirect
6. #2407×C151C2semidirect
7. #2055×C151C2semidirect
8. #2054×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1973×C151C2semidirect
12. #1972×C151C2semidirect
13. #1809×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
26. C23×C8×C151C22semidirect
27. C2×C22⋊Q8×C151C22semidirect
30. C2×#121×C151C22semidirect
36. C2×#107×C151C22semidirect
37. C2×#106×C151C22semidirect
38. C2×C4⋊C8×C151C22semidirect
39. C2×#103×C151C22semidirect
40. C2×#103×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
48. C2×C22⋊C8×C151C22semidirect
49. C2×#97×C151C22semidirect
54. #391×C151C22semidirect
57. #390×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
97. C2×SD16×C151D4semidirect
103. C2×D8×C151D4semidirect
106. C2×M16×C151D4semidirect
336. C23×C151AGL(1,ℤ/8)semidirect
405. C8×C151#120semidirect
474. #24275C151direct (N × H)
475. C151#24275direct (N × H)
476. C22×AGL(1,ℤ/8)C2×C151semidirect
477. C2×#466C2×C151semidirect
478. C2×#465C2×C151semidirect
479. C2×#435C2×C151semidirect
480. #2408C2×C151semidirect
481. #2407C2×C151semidirect
482. #2055C2×C151semidirect
483. #2054C2×C151semidirect
484. #2000C2×C151semidirect
485. #1999C2×C151semidirect
486. #1973C2×C151semidirect
487. #1972C2×C151semidirect
488. #1809C2×C151semidirect
489. #1788C2×C151semidirect
490. #1786C2×C151semidirect
501. C23×C8C22×C151semidirect
502. C2×C22⋊Q8C22×C151semidirect
505. C2×#121C22×C151semidirect
511. C2×#107C22×C151semidirect
512. C2×#106C22×C151semidirect
513. C2×C4⋊C8C22×C151semidirect
514. C2×#103C22×C151semidirect
515. C2×#103C22×C151semidirect
520. C2×#102C22×C151semidirect
521. C2×#102C22×C151semidirect
523. C2×C22⋊C8C22×C151semidirect
524. C2×#97C22×C151semidirect
529. #391C22×C151semidirect
532. #390C22×C151semidirect
538. #340C22×C151semidirect
539. #340C22×C151semidirect
572. C2×SD16D4×C151semidirect
578. C2×D8D4×C151semidirect
581. C2×M16D4×C151semidirect
811. C23AGL(1,ℤ/8)×C151semidirect
880. C8#120×C151semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1512
C2×#466×C1512
C2×#465×C1512
C2×#435×C1512
#2408×C1512
#2407×C1512
#2055×C1512
#2054×C1512
#2000×C1512
#1999×C1512
#1973×C1512
#1972×C1512
#1809×C1512
#1788×C1512
#1786×C1512
#24275151