Finite Group Databasebeta

← C151×#22443 #50327368

Subgroups — C151×#22443 #50327368

Order 38656.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
4#2341×C151C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
6#1972×C151C211yesmaximal, characteristic, complemented
7#1970×C151C211yesmaximal, characteristic, complemented
8#1880×C151C211yesmaximal, characteristic, complemented
9#1880×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1809×C151C211yesmaximal, characteristic, complemented
13#1788×C151C211yesmaximal, characteristic, complemented
14#1786×C151C211yesmaximal, characteristic, complemented
15#1753×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)×C151C418yescomplemented
21C22×SD16×C151C2211yescharacteristic
22C22×SD16×C151C2211yescharacteristic
23C22×D8×C151C2211yescharacteristic
24C22×D8×C151C2211yescharacteristic
25C22×M16×C151C2211yescharacteristic
26C2×C4×Q8×C151C2211yescharacteristic, complemented
27C2×C4×Q8×C151C2211yescharacteristic, complemented
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C22×C22⋊C4×C151—21no—
31#440×C151—24no—
32C4×SD16×C151—24no—
33C2×#107×C151C2211yescharacteristic, complemented
34C2×#106×C151C2211yescharacteristic, complemented
35C2×#103×C151C2211yescharacteristic, complemented
36C2×#103×C151C2211yescharacteristic, complemented
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic, complemented
42C2×#102×C151C2211yescharacteristic, complemented
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×#97×C151C2211yescharacteristic, complemented
45C2×C4×C8×C151C2211yescharacteristic, complemented
46#390×C151—21no—
47#390×C151—21no—
48#390×C151C2211yescharacteristic
49#390×C151C2211yescharacteristic
50#390×C151C2211yescharacteristic, complemented
51#390×C151C2211yescharacteristic, complemented
52#386×C151—21no—
53#386×C151—21no—
54#380×C151—21no—
55#380×C151C2211yescharacteristic
56#380×C151C2211yescharacteristic
57#379×C151—21no—
58C4×C22⋊C4×C151—21no—
59C4×C22⋊C4×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#336×C151C2211yescharacteristic, complemented
63#336×C151C2211yescharacteristic, complemented
64C25×C151—21no—
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—41no—
69C2×#41×C151—41no—
70C2×#41×C151C2×C414yescomplemented
71C22×Q8×C151C2311yescharacteristic
72C22×D4×C151—21no—
73C22×D4×C151—22no—
74C22×D4×C151—21no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—41no—
78C22×D4×C151—41no—
79C22×D4×C151C2×C414yes—
80C22×D4×C151C2311yescharacteristic
81C22×D4×C151C2311yescharacteristic
82C22×D4×C151C2311yescharacteristic
83C23×C4×C151—21no—
84C23×C4×C151—21no—
85C23×C4×C151—21no—
86C23×C4×C151C2311yescharacteristic
87AGL(1,ℤ/8)×C151—232no—
88C2×SD16×C151—22no—
89C2×SD16×C151—22no—
90C2×SD16×C151C2×C414yes—
91C2×SD16×C151C2×C414yescomplemented
92C2×SD16×C151D414yes—
93C2×SD16×C151D414yes—
94C2×D8×C151—22no—
95C2×D8×C151—22no—
96C2×D8×C151—22no—
97C2×D8×C151—22no—
98C2×D8×C151C2×C414yes—
99C2×D8×C151C2×C414yescomplemented
100C2×M16×C151—22no—
101C2×M16×C151—22no—
102C2×M16×C151C2×C414yescomplemented
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107C4×Q8×C151—22no—
108C4×Q8×C151—22no—
109C4×Q8×C151—41no—
110C4×Q8×C151—41no—
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113C4×D4×C151—41no—
114C4×D4×C151—41no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151—21no—
131C2×C22⋊C4×C151—21no—
132C2×C22⋊C4×C151—21no—
133C2×C22⋊C4×C151—44no—
134C2×C22⋊C4×C151D411yescharacteristic
135C2×C22⋊C4×C151D411yescharacteristic
136C2×C42×C151—21no—
137C2×C42×C151—21no—
138C2×C42×C151C2311yescharacteristic
139C2×C42×C151C2311yescharacteristic
140#107×C151—22no—
141#106×C151—22no—
142#103×C151—22no—
143#103×C151—22no—
144#102×C151—22no—
145#102×C151—22no—
146#102×C151—41no—
147#102×C151—41no—
148#102×C151—41no—
149#102×C151—41no—
150C22⋊C8×C151—22no—
151#97×C151—22no—
152C4×C8×C151—22no—
153#95×C151—21no—
154#95×C151—21no—
155#95×C151D411yescharacteristic
156#95×C151D411yescharacteristic
157C24×C151—21no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—24no—
161C24×C151—42no—
162C24×C151—42no—
163C24×C151—42no—
164C24×C151—42no—
165C24×C151—81no—
166C24×C151—81no—
167C24×C151C2×D411yescharacteristic
168#41×C151—28no—
169#41×C151—44no—
170#41×C151—44no—
171#41×C151—44no—
172C2×Q8×C151—21no—
173C2×Q8×C151—21no—
174C2×Q8×C151—21no—
175C2×Q8×C151C22×C412yes—
176C2×Q8×C151C2×D412yes—
177C2×Q8×C151C2×D412yes—
178C2×D4×C151—28no—
179C2×D4×C151—24no—
180C2×D4×C151—24no—
181C2×D4×C151—21no—
182C2×D4×C151—21no—
183C2×D4×C151—21no—
184C2×D4×C151—21no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—44no—
195C2×D4×C151—44no—
196C2×D4×C151—44no—
197C2×D4×C151—42no—
198C2×D4×C151—42no—
199C2×D4×C151—42no—
200C2×D4×C151—42no—
201C2×D4×C151C22×C412yes—
202C2×D4×C151C22×C412yes—
203C2×D4×C151C22×C412yes—
204C2×D4×C151C2×D412yes—
205C2×D4×C151C2×D412yes—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—24no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—42no—
217C22×C4×C151—42no—
218C22×C4×C151—42no—
219C22×C4×C151—42no—
220C22×C4×C151—42no—
221C22×C4×C151—42no—
222C22×C4×C151—81no—
223C22×C4×C151—81no—
224C22×C4×C151C22×C412yes—
225C22×C4×C151C2×D411yescharacteristic
226C22×C4×C151C2×D411yescharacteristic
227C22×C4×C151C2×D411yescharacteristic
228C22×C4×C151C2×D411yescharacteristic
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151#4112yes—
231C22×C4×C151C2411yescharacteristic
232SD16×C151—28no—
233SD16×C151C22⋊C4116yescomplemented
234D8×C151—28no—
235D8×C151—28no—
236M16×C151—28no—
237C2×C8×C151—21no—
238C2×C8×C151—21no—
239C2×C8×C151—21no—
240C2×C8×C151—21no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C2×C8×C151C22×C412yes—
246C2×C8×C151C22×C412yes—
247C2×C8×C151C2×D412yes—
248C2×C8×C151C2×D412yes—
249C4⋊C4×C151—21no—
250C4⋊C4×C151—21no—
251C4⋊C4×C151—21no—
252C4⋊C4×C151—21no—
253C4⋊C4×C151—21no—
254C4⋊C4×C151—21no—
255C4⋊C4×C151—21no—
256C4⋊C4×C151—21no—
257C4⋊C4×C151—42no—
258C4⋊C4×C151—42no—
259C22⋊C4×C151—22no—
260C22⋊C4×C151—41no—
261C22⋊C4×C151—42no—
262C22⋊C4×C151—42no—
263C22⋊C4×C151—42no—
264C22⋊C4×C151—42no—
265C22⋊C4×C151—42no—
266C22⋊C4×C151—42no—
267C22⋊C4×C151—42no—
268C22⋊C4×C151—81no—
269C22⋊C4×C151—81no—
270C22⋊C4×C151—81no—
271C22⋊C4×C151—81no—
272C22⋊C4×C151—81no—
273C42×C151—21no—
274C42×C151—21no—
275C42×C151—21no—
276C42×C151—21no—
277C42×C151—42no—
278C42×C151—42no—
279C23×C151—22no—
280C23×C151—22no—
281C23×C151—22no—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—22no—
289C23×C151—22no—
290C23×C151—48no—
291C23×C151—48no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151—41no—
296C23×C151—41no—
297C23×C151—41no—
298C23×C151—41no—
299C23×C151—41no—
300C23×C151—41no—
301C23×C151—41no—
302C23×C151—41no—
303C23×C151—41no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
307C23×C151—41no—
308C23×C151—84no—
309C23×C151—84no—
310C23×C151—84no—
311C23×C151—84no—
312C23×C151—84no—
313C23×C151C4×D412yes—
314C23×C151C22×D411yescharacteristic
315Q8×C151—22no—
316Q8×C151—22no—
317Q8×C151—22no—
318Q8×C151C2×C22⋊C414yescomplemented
319D4×C151—22no—
320D4×C151—22no—
321D4×C151—22no—
322D4×C151—22no—
323D4×C151—22no—
324D4×C151—22no—
325D4×C151—22no—
326D4×C151—48no—
327D4×C151—48no—
328D4×C151—41no—
329D4×C151—41no—
330D4×C151—41no—
331D4×C151—41no—
332D4×C151C2×C22⋊C414yes—
333C2×C4×C151—22no—
334C2×C4×C151—22no—
335C2×C4×C151—22no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—22no—
341C2×C4×C151—22no—
342C2×C4×C151—22no—
343C2×C4×C151—22no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—21no—
347C2×C4×C151—21no—
348C2×C4×C151—21no—
349C2×C4×C151—21no—
350C2×C4×C151—21no—
351C2×C4×C151—21no—
352C2×C4×C151—21no—
353C2×C4×C151—48no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—84no—
367C2×C4×C151—84no—
368C2×C4×C151C4×D412yes—
369C2×C4×C151AGL(1,ℤ/8)12yescomplemented
370C2×C4×C151C23×C411yescharacteristic
371C2×C4×C151C22×D411yescharacteristic
372C2×C4×C151C22×D411yescharacteristic
373C2×C4×C151C2×#4111yescharacteristic
374C2×C4×C151H(5,𝔽2)11yescharacteristic
375C2×C4×C151H(5,𝔽2)11yescharacteristic
376C8×C151—22no—
377C8×C151—41no—
378C8×C151—41no—
379C8×C151C2×C22⋊C414yescomplemented
380C22×C151—22no—
381C22×C151—24no—
382C22×C151—22no—
383C22×C151—22no—
384C22×C151—42no—
385C22×C151—42no—
386C22×C151—42no—
387C22×C151—41no—
388C22×C151—41no—
389C22×C151—42no—
390C22×C151—42no—
391C22×C151—41no—
392C22×C151—41no—
393C22×C151—42no—
394C22×C151—42no—
395C22×C151—42no—
396C22×C151—42no—
397C22×C151—42no—
398C22×C151—42no—
399C22×C151—42no—
400C22×C151—816no—
401C22×C151—81no—
402C22×C151—81no—
403C22×C151—81no—
404C22×C151—81no—
405C22×C151—81no—
406C22×C151—81no—
407C22×C151—81no—
408C22×C151—81no—
409C22×C151C2×C4×D411yescharacteristic
410C22×C151D4211yescharacteristic
411C22×C151D4211yescharacteristic
412C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C151#57511yescharacteristic
414C22×C151#57611yescharacteristic
415C22×C151#57711yescharacteristic
416C4×C151—22no—
417C4×C151—24no—
418C4×C151—22no—
419C4×C151—41no—
420C4×C151—41no—
421C4×C151—41no—
422C4×C151—81no—
423C4×C151—81no—
424C4×C151—81no—
425C4×C151—81no—
426C4×C151C22×C22⋊C411yescharacteristic
427C4×C151#51811yescharacteristic
428C4×C151#54611yescharacteristic
429C4×C151#54611yescharacteristic
430C2×C151—42no—
431C2×C151—44no—
432C2×C151—82no—
433C2×C151—82no—
434C2×C151D4×C22⋊C411yescharacteristic
435C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
436C2×C151#294611yescharacteristic
437C2×C151#326511yescharacteristic
438C2×C151#326811yescharacteristic
439C2×C151#327411yescharacteristic
440C2×C151#327511yescharacteristic
441#22443C15111yesmaximal, characteristic, direct product factor, Sylow
442C151#2244311yescharacteristic, direct product factor, Sylow
443C22×AGL(1,ℤ/8)C2×C15111yescharacteristic
444C2×#440C2×C15111yescharacteristic, complemented
445C2×C4×SD16C2×C15111yescharacteristic, complemented
446#2341C2×C15111yescharacteristic, complemented
447D4×C22⋊C4C2×C15111yescharacteristic, complemented
448#1972C2×C15111yescharacteristic, complemented
449#1970C2×C15111yescharacteristic, complemented
450#1880C2×C15111yescharacteristic, complemented
451#1880C2×C15111yescharacteristic, complemented
452#1879C2×C15111yescharacteristic, complemented
453#1879C2×C15111yescharacteristic, complemented
454#1809C2×C15111yescharacteristic, complemented
455#1788C2×C15111yescharacteristic, complemented
456#1786C2×C15111yescharacteristic, complemented
457#1753C2×C15111yescharacteristic, complemented
458C22×#41C22×C15111yescharacteristic
459C23×D4C22×C15111yescharacteristic
460C2×AGL(1,ℤ/8)—24no—
461C2×AGL(1,ℤ/8)—24no—
462C2×AGL(1,ℤ/8)C4×C15118yescomplemented
463C22×SD16C22×C15111yescharacteristic
464C22×SD16C22×C15111yescharacteristic
465C22×D8C22×C15111yescharacteristic
466C22×D8C22×C15111yescharacteristic
467C22×M16C22×C15111yescharacteristic
468C2×C4×Q8C22×C15111yescharacteristic, complemented
469C2×C4×Q8C22×C15111yescharacteristic, complemented
470C2×C4×D4C22×C15111yescharacteristic
471C2×C4×D4C22×C15111yescharacteristic
472C22×C22⋊C4—21no—
473#440—24no—
474C4×SD16—24no—
475C2×#107C22×C15111yescharacteristic, complemented
476C2×#106C22×C15111yescharacteristic, complemented
477C2×#103C22×C15111yescharacteristic, complemented
478C2×#103C22×C15111yescharacteristic, complemented
479C2×#102C22×C15111yescharacteristic
480C2×#102C22×C15111yescharacteristic
481C2×#102C22×C15111yescharacteristic
482C2×#102C22×C15111yescharacteristic
483C2×#102C22×C15111yescharacteristic, complemented
484C2×#102C22×C15111yescharacteristic, complemented
485C2×C22⋊C8C22×C15111yescharacteristic
486C2×#97C22×C15111yescharacteristic, complemented
487C2×C4×C8C22×C15111yescharacteristic, complemented
488#390—21no—
489#390—21no—
490#390C22×C15111yescharacteristic
491#390C22×C15111yescharacteristic
492#390C22×C15111yescharacteristic, complemented
493#390C22×C15111yescharacteristic, complemented
494#386—21no—
495#386—21no—
496#380—21no—
497#380C22×C15111yescharacteristic
498#380C22×C15111yescharacteristic
499#379—21no—
500C4×C22⋊C4—21no—
501C4×C22⋊C4C22×C15111yescharacteristic
502#340C22×C15111yescharacteristic, complemented
503#340C22×C15111yescharacteristic, complemented
504#336C22×C15111yescharacteristic, complemented
505#336C22×C15111yescharacteristic, complemented
506C25—21no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C2×C4×C15114yescomplemented
513C22×Q8C23×C15111yescharacteristic
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×C4×C15114yes—
522C22×D4C23×C15111yescharacteristic
523C22×D4C23×C15111yescharacteristic
524C22×D4C23×C15111yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C23×C15111yescharacteristic
529AGL(1,ℤ/8)—232no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16C2×C4×C15114yes—
533C2×SD16C2×C4×C15114yescomplemented
534C2×SD16D4×C15114yes—
535C2×SD16D4×C15114yes—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8C2×C4×C15114yes—
541C2×D8C2×C4×C15114yescomplemented
542C2×M16—22no—
543C2×M16—22no—
544C2×M16C2×C4×C15114yescomplemented
545C22×C8C23×C15111yescharacteristic
546C22×C8C23×C15111yescharacteristic
547C22×C8C23×C15111yescharacteristic
548C22×C8C23×C15111yescharacteristic
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4C23×C15111yescharacteristic
560C2×C4⋊C4C23×C15111yescharacteristic
561C2×C4⋊C4C23×C15111yescharacteristic
562C2×C4⋊C4C23×C15111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—44no—
576C2×C22⋊C4D4×C15111yescharacteristic
577C2×C22⋊C4D4×C15111yescharacteristic
578C2×C42—21no—
579C2×C42—21no—
580C2×C42C23×C15111yescharacteristic
581C2×C42C23×C15111yescharacteristic
582#107—22no—
583#106—22no—
584#103—22no—
585#103—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593#97—22no—
594C4×C8—22no—
595#95—21no—
596#95—21no—
597#95D4×C15111yescharacteristic
598#95D4×C15111yescharacteristic
599C24—21no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—81no—
608C24—81no—
609C24C2×D4×C15111yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C22×C4×C15112yes—
618C2×Q8C2×D4×C15112yes—
619C2×Q8C2×D4×C15112yes—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×C4×C15112yes—
644C2×D4C22×C4×C15112yes—
645C2×D4C22×C4×C15112yes—
646C2×D4C2×D4×C15112yes—
647C2×D4C2×D4×C15112yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—81no—
666C22×C4C22×C4×C15112yes—
667C22×C4C2×D4×C15111yescharacteristic
668C22×C4C2×D4×C15111yescharacteristic
669C22×C4C2×D4×C15111yescharacteristic
670C22×C4C2×D4×C15111yescharacteristic
671C22×C4C2×D4×C15111yescharacteristic
672C22×C4#41×C15112yes—
673C22×C4C24×C15111yescharacteristic
674SD16—28no—
675SD16C22⋊C4×C151116yescomplemented
676D8—28no—
677D8—28no—
678M16—28no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8C22×C4×C15112yes—
688C2×C8C22×C4×C15112yes—
689C2×C8C2×D4×C15112yes—
690C2×C8C2×D4×C15112yes—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—42no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—48no—
733C23—48no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23C4×D4×C15112yes—
756C23C22×D4×C15111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C2×C22⋊C4×C15114yescomplemented
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊C4×C15114yes—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—84no—
809C2×C4—84no—
810C2×C4C4×D4×C15112yes—
811C2×C4AGL(1,ℤ/8)×C15112yescomplemented
812C2×C4C23×C4×C15111yescharacteristic
813C2×C4C22×D4×C15111yescharacteristic
814C2×C4C22×D4×C15111yescharacteristic
815C2×C4C2×#41×C15111yescharacteristic
816C2×C4H(5,𝔽2)×C15111yescharacteristic
817C2×C4H(5,𝔽2)×C15111yescharacteristic
818C8—22no—
819C8—41no—
820C8—41no—
821C8C2×C22⋊C4×C15114yescomplemented
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22C2×C4×D4×C15111yescharacteristic
852C22D42×C15111yescharacteristic
853C22D42×C15111yescharacteristic
854C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
855C22#575×C15111yescharacteristic
856C22#576×C15111yescharacteristic
857C22#577×C15111yescharacteristic
858C4—22no—
859C4—24no—
860C4—22no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4C22×C22⋊C4×C15111yescharacteristic
869C4#518×C15111yescharacteristic
870C4#546×C15111yescharacteristic
871C4#546×C15111yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—82no—
876C2D4×C22⋊C4×C15111yescharacteristic
877C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
878C2#2946×C15111yescharacteristic
879C2#3265×C15111yescharacteristic
880C2#3268×C15111yescharacteristic
881C2#3274×C15111yescharacteristic
882C2#3275×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×AGL(1,ℤ/8)×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C151C2semidirect
3. C2×C4×SD16×C151C2semidirect
4. #2341×C151C2semidirect
5. D4×C22⋊C4×C151C2semidirect
6. #1972×C151C2semidirect
7. #1970×C151C2semidirect
8. #1880×C151C2semidirect
9. #1880×C151C2semidirect
10. #1879×C151C2semidirect
11. #1879×C151C2semidirect
12. #1809×C151C2semidirect
13. #1788×C151C2semidirect
14. #1786×C151C2semidirect
15. #1753×C151C2semidirect
20. C2×AGL(1,ℤ/8)×C151C4semidirect
26. C2×C4×Q8×C151C22semidirect
27. C2×C4×Q8×C151C22semidirect
33. C2×#107×C151C22semidirect
34. C2×#106×C151C22semidirect
35. C2×#103×C151C22semidirect
36. C2×#103×C151C22semidirect
41. C2×#102×C151C22semidirect
42. C2×#102×C151C22semidirect
44. C2×#97×C151C22semidirect
45. C2×C4×C8×C151C22semidirect
50. #390×C151C22semidirect
51. #390×C151C22semidirect
60. #340×C151C22semidirect
61. #340×C151C22semidirect
62. #336×C151C22semidirect
63. #336×C151C22semidirect
70. C2×#41×C151C2×C4semidirect
91. C2×SD16×C151C2×C4semidirect
99. C2×D8×C151C2×C4semidirect
102. C2×M16×C151C2×C4semidirect
233. SD16×C151C22⋊C4semidirect
318. Q8×C151C2×C22⋊C4semidirect
369. C2×C4×C151AGL(1,ℤ/8)semidirect
379. C8×C151C2×C22⋊C4semidirect
441. #22443C151direct (N × H)
442. C151#22443direct (N × H)
444. C2×#440C2×C151semidirect
445. C2×C4×SD16C2×C151semidirect
446. #2341C2×C151semidirect
447. D4×C22⋊C4C2×C151semidirect
448. #1972C2×C151semidirect
449. #1970C2×C151semidirect
450. #1880C2×C151semidirect
451. #1880C2×C151semidirect
452. #1879C2×C151semidirect
453. #1879C2×C151semidirect
454. #1809C2×C151semidirect
455. #1788C2×C151semidirect
456. #1786C2×C151semidirect
457. #1753C2×C151semidirect
462. C2×AGL(1,ℤ/8)C4×C151semidirect
468. C2×C4×Q8C22×C151semidirect
469. C2×C4×Q8C22×C151semidirect
475. C2×#107C22×C151semidirect
476. C2×#106C22×C151semidirect
477. C2×#103C22×C151semidirect
478. C2×#103C22×C151semidirect
483. C2×#102C22×C151semidirect
484. C2×#102C22×C151semidirect
486. C2×#97C22×C151semidirect
487. C2×C4×C8C22×C151semidirect
492. #390C22×C151semidirect
493. #390C22×C151semidirect
502. #340C22×C151semidirect
503. #340C22×C151semidirect
504. #336C22×C151semidirect
505. #336C22×C151semidirect
512. C2×#41C2×C4×C151semidirect
533. C2×SD16C2×C4×C151semidirect
541. C2×D8C2×C4×C151semidirect
544. C2×M16C2×C4×C151semidirect
675. SD16C22⋊C4×C151semidirect
760. Q8C2×C22⋊C4×C151semidirect
811. C2×C4AGL(1,ℤ/8)×C151semidirect
821. C8C2×C22⋊C4×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×#440×C1512
C2×C4×SD16×C1512
#2341×C1512
D4×C22⋊C4×C1512
#1972×C1512
#1970×C1512
#1880×C1512
#1879×C1512
#1809×C1512
#1788×C1512
#1786×C1512
#1753×C1512
#22443151