Finite Group Databasebeta

← C151×#23039 #50327964

Subgroups — C151×#23039 #50327964

Order 38656.

1082 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C151C211yesmaximal, characteristic
2C2×#442×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2363×C151C211yesmaximal, characteristic, complemented
5#2361×C151C211yesmaximal, characteristic, complemented
6#1970×C151C211yesmaximal, characteristic, complemented
7#1944×C151C211yesmaximal, characteristic, complemented
8#1926×C151C211yesmaximal, characteristic, complemented
9#1925×C151C211yesmaximal, characteristic, complemented
10#1875×C151C211yesmaximal, characteristic, complemented
11#1874×C151C211yesmaximal, characteristic, complemented
12#1864×C151C211yesmaximal, characteristic, complemented
13#1862×C151C211yesmaximal, characteristic, complemented
14C4×#106×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C22×D8×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C2×#121×C151C2211yescharacteristic
19C2×#121×C151C2211yescharacteristic
20C2×C4×D4×C151—21no—
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25#469×C151C418yescomplemented
26#442×C151—24no—
27#428×C151—24no—
28C2×#107×C151C2211yescharacteristic
29C2×#107×C151C2211yescharacteristic
30C2×#106×C151C2211yescharacteristic
31C2×#106×C151C2211yescharacteristic
32C2×#106×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic
41C2×C4×C8×C151C2211yescharacteristic
42#390×C151—21no—
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#389×C151C2211yescharacteristic
46#389×C151C2211yescharacteristic
47#388×C151—21no—
48#388×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#385×C151—21no—
52C4×C4⋊C4×C151C2211yescharacteristic
53C4×C4⋊C4×C151C2211yescharacteristic
54C4×C22⋊C4×C151—21no—
55C4×C22⋊C4×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151C2311yescharacteristic
65C22×D4×C151C2311yescharacteristic
66C23×C4×C151—21no—
67C23×C4×C151—21no—
68C23×C4×C151—21no—
69C23×C4×C151C2311yescharacteristic
70C2×D8×C151—22no—
71C2×D8×C151—22no—
72C2×D8×C151C2×C414yescomplemented
73C2×M16×C151—22no—
74C2×M16×C151—22no—
75C2×M16×C151C2×C414yescomplemented
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80#121×C151—22no—
81#121×C151—22no—
82#121×C151C2×C414yescomplemented
83#121×C151C2×C414yescomplemented
84C4×D4×C151—22no—
85C4×D4×C151—22no—
86C4×D4×C151—41no—
87C4×D4×C151—41no—
88C4×D4×C151—44no—
89#117×C151—22no—
90#117×C151—41no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—41no—
96C2×C4⋊C4×C151C2311yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151D411yescharacteristic
112C2×C22⋊C4×C151D411yescharacteristic
113C2×C42×C151—21no—
114C2×C42×C151—21no—
115C2×C42×C151—21no—
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118#107×C151—22no—
119#107×C151—22no—
120#106×C151—22no—
121#106×C151C2×C414yescomplemented
122#106×C151D414yescomplemented
123#102×C151—22no—
124#102×C151—22no—
125#102×C151—41no—
126#102×C151—41no—
127#102×C151C2×C414yescomplemented
128#102×C151C2×C414yescomplemented
129C22⋊C8×C151—22no—
130#97×C151—22no—
131C4×C8×C151—22no—
132#95×C151—21no—
133#95×C151—21no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151D411yescharacteristic
137#95×C151D411yescharacteristic
138C24×C151—21no—
139C24×C151—21no—
140C24×C151C2×D411yescharacteristic
141C2×D4×C151—24no—
142C2×D4×C151—24no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—21no—
149C2×D4×C151—21no—
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—42no—
154C2×D4×C151—42no—
155C2×D4×C151—81no—
156C2×D4×C151—81no—
157C2×D4×C151C22×C412yes—
158C2×D4×C151C22×C412yes—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—42no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
172C22×C4×C151—42no—
173C22×C4×C151—42no—
174C22×C4×C151—42no—
175C22×C4×C151—81no—
176C22×C4×C151—81no—
177C22×C4×C151—81no—
178C22×C4×C151C22×C412yes—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2×D411yescharacteristic
183C22×C4×C151C2×D411yescharacteristic
184C22×C4×C151#4112yes—
185C22×C4×C151C2411yescharacteristic
186D8×C151—28no—
187M16×C151—28no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151C22×C412yes—
197C2×C8×C151C22×C412yes—
198C2×C8×C151C2×D412yes—
199C2×C8×C151#4112yes—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—21no—
206C4⋊C4×C151—21no—
207C4⋊C4×C151—21no—
208C4⋊C4×C151—42no—
209C4⋊C4×C151—42no—
210C4⋊C4×C151—81no—
211C4⋊C4×C151C22×C412yes—
212C4⋊C4×C151C22×C412yes—
213C4⋊C4×C151C2×D412yes—
214C4⋊C4×C151C2×D412yes—
215C22⋊C4×C151—24no—
216C22⋊C4×C151—24no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—41no—
219C22⋊C4×C151—42no—
220C22⋊C4×C151—42no—
221C22⋊C4×C151—42no—
222C22⋊C4×C151—42no—
223C22⋊C4×C151—42no—
224C22⋊C4×C151—81no—
225C22⋊C4×C151—81no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—42no—
231C42×C151—42no—
232C42×C151—81no—
233C23×C151—21no—
234C23×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—22no—
240C23×C151—22no—
241C23×C151—41no—
242C23×C151—41no—
243C23×C151—41no—
244C23×C151—41no—
245C23×C151—41no—
246C23×C151—41no—
247C23×C151—41no—
248C23×C151—41no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151C4×D412yes—
254C23×C151C22×D411yescharacteristic
255D4×C151—22no—
256D4×C151—22no—
257D4×C151—22no—
258D4×C151—22no—
259D4×C151—48no—
260D4×C151—41no—
261D4×C151—41no—
262D4×C151—41no—
263D4×C151—41no—
264D4×C151—84no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—22no—
270C2×C4×C151—22no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—22no—
274C2×C4×C151—22no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—22no—
278C2×C4×C151—22no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—84no—
301C2×C4×C151—84no—
302C2×C4×C151—84no—
303C2×C4×C151C4×D412yes—
304C2×C4×C151AGL(1,ℤ/8)12yes—
305C2×C4×C151C23×C411yescharacteristic
306C2×C4×C151C22×D411yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151C2×#4111yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C2×C4×C1512−1+411yescharacteristic
311C8×C151—22no—
312C8×C151—41no—
313C8×C151—41no—
314C8×C151C4×D414yescomplemented
315C22×C151—22no—
316C22×C151—22no—
317C22×C151—22no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—42no—
323C22×C151—42no—
324C22×C151—42no—
325C22×C151—42no—
326C22×C151—42no—
327C22×C151—42no—
328C22×C151—81no—
329C22×C151—81no—
330C22×C151—81no—
331C22×C151—81no—
332C22×C151—81no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151C2×C4×D411yescharacteristic
337C22×C151D4211yescharacteristic
338C22×C151#54711yescharacteristic
339C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C151#57511yescharacteristic
341C22×C151#57611yescharacteristic
342C22×C151#57711yescharacteristic
343C4×C151—22no—
344C4×C151—22no—
345C4×C151—41no—
346C4×C151—42no—
347C4×C151—42no—
348C4×C151—41no—
349C4×C151—42no—
350C4×C151—41no—
351C4×C151—42no—
352C4×C151—81no—
353C4×C151—81no—
354C4×C151C2×C4×D411yescharacteristic
355C4×C151#52011yescharacteristic
356C4×C151#54811yescharacteristic
357C4×C151#55311yescharacteristic
358C2×C151—42no—
359C2×C151—82no—
360C2×C151—82no—
361C2×C151#236111yescharacteristic
362C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
363C2×C151#294611yescharacteristic
364C2×C151#327411yescharacteristic
365C2×C151#327511yescharacteristic
366C2×C151#334511yescharacteristic
367C2×C151#334711yescharacteristic
368#23039C15111yesmaximal, characteristic, direct product factor, Sylow
369C151#2303911yescharacteristic, direct product factor, Sylow
370C2×#469C2×C15111yescharacteristic
371C2×#442C2×C15111yescharacteristic, complemented
372C2×#428C2×C15111yescharacteristic, complemented
373#2363C2×C15111yescharacteristic, complemented
374#2361C2×C15111yescharacteristic, complemented
375#1970C2×C15111yescharacteristic, complemented
376#1944C2×C15111yescharacteristic, complemented
377#1926C2×C15111yescharacteristic, complemented
378#1925C2×C15111yescharacteristic, complemented
379#1875C2×C15111yescharacteristic, complemented
380#1874C2×C15111yescharacteristic, complemented
381#1864C2×C15111yescharacteristic, complemented
382#1862C2×C15111yescharacteristic, complemented
383C4×#106C2×C15111yescharacteristic, complemented
384#1753C2×C15111yescharacteristic, complemented
385C22×D8C22×C15111yescharacteristic
386C22×M16C22×C15111yescharacteristic
387C2×#121C22×C15111yescharacteristic
388C2×#121C22×C15111yescharacteristic
389C2×C4×D4—21no—
390C2×C4×D4C22×C15111yescharacteristic
391C2×C4×D4C22×C15111yescharacteristic
392C2×#117C22×C15111yescharacteristic
393C22×C4⋊C4C22×C15111yescharacteristic
394#469C4×C15118yescomplemented
395#442—24no—
396#428—24no—
397C2×#107C22×C15111yescharacteristic
398C2×#107C22×C15111yescharacteristic
399C2×#106C22×C15111yescharacteristic
400C2×#106C22×C15111yescharacteristic
401C2×#106C22×C15111yescharacteristic
402C2×#102C22×C15111yescharacteristic
403C2×#102C22×C15111yescharacteristic
404C2×#102C22×C15111yescharacteristic
405C2×#102C22×C15111yescharacteristic
406C2×#102C22×C15111yescharacteristic
407C2×#102C22×C15111yescharacteristic
408C2×C22⋊C8C22×C15111yescharacteristic
409C2×#97C22×C15111yescharacteristic
410C2×C4×C8C22×C15111yescharacteristic
411#390—21no—
412#390C22×C15111yescharacteristic
413#390C22×C15111yescharacteristic
414#389C22×C15111yescharacteristic
415#389C22×C15111yescharacteristic
416#388—21no—
417#388—21no—
418#386—21no—
419#386—21no—
420#385—21no—
421C4×C4⋊C4C22×C15111yescharacteristic
422C4×C4⋊C4C22×C15111yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4C22×C15111yescharacteristic
425#340C22×C15111yescharacteristic
426#340C22×C15111yescharacteristic
427#340C22×C15111yescharacteristic
428#340C22×C15111yescharacteristic
429#336C22×C15111yescharacteristic
430#336C22×C15111yescharacteristic
431C22×D4—21no—
432C22×D4—21no—
433C22×D4C23×C15111yescharacteristic
434C22×D4C23×C15111yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4C23×C15111yescharacteristic
439C2×D8—22no—
440C2×D8—22no—
441C2×D8C2×C4×C15114yescomplemented
442C2×M16—22no—
443C2×M16—22no—
444C2×M16C2×C4×C15114yescomplemented
445C22×C8C23×C15111yescharacteristic
446C22×C8C23×C15111yescharacteristic
447C22×C8C23×C15111yescharacteristic
448C22×C8C23×C15111yescharacteristic
449#121—22no—
450#121—22no—
451#121C2×C4×C15114yescomplemented
452#121C2×C4×C15114yescomplemented
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—44no—
458#117—22no—
459#117—41no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4C23×C15111yescharacteristic
466C2×C4⋊C4C23×C15111yescharacteristic
467C2×C4⋊C4C23×C15111yescharacteristic
468C2×C4⋊C4C23×C15111yescharacteristic
469C2×C4⋊C4C23×C15111yescharacteristic
470C2×C4⋊C4C23×C15111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4D4×C15111yescharacteristic
481C2×C22⋊C4D4×C15111yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42C23×C15111yescharacteristic
486C2×C42C23×C15111yescharacteristic
487#107—22no—
488#107—22no—
489#106—22no—
490#106C2×C4×C15114yescomplemented
491#106D4×C15114yescomplemented
492#102—22no—
493#102—22no—
494#102—41no—
495#102—41no—
496#102C2×C4×C15114yescomplemented
497#102C2×C4×C15114yescomplemented
498C22⋊C8—22no—
499#97—22no—
500C4×C8—22no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95D4×C15111yescharacteristic
506#95D4×C15111yescharacteristic
507C24—21no—
508C24—21no—
509C24C2×D4×C15111yescharacteristic
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C22×C4×C15112yes—
527C2×D4C22×C4×C15112yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4C22×C4×C15112yes—
548C22×C4C2×D4×C15111yescharacteristic
549C22×C4C2×D4×C15111yescharacteristic
550C22×C4C2×D4×C15111yescharacteristic
551C22×C4C2×D4×C15111yescharacteristic
552C22×C4C2×D4×C15111yescharacteristic
553C22×C4#41×C15112yes—
554C22×C4C24×C15111yescharacteristic
555D8—28no—
556M16—28no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8C22×C4×C15112yes—
566C2×C8C22×C4×C15112yes—
567C2×C8C2×D4×C15112yes—
568C2×C8#41×C15112yes—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—81no—
580C4⋊C4C22×C4×C15112yes—
581C4⋊C4C22×C4×C15112yes—
582C4⋊C4C2×D4×C15112yes—
583C4⋊C4C2×D4×C15112yes—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—22no—
587C22⋊C4—41no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C42—42no—
601C42—81no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—22no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23C4×D4×C15112yes—
623C23C22×D4×C15111yescharacteristic
624D4—22no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—48no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—84no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4—84no—
671C2×C4—84no—
672C2×C4C4×D4×C15112yes—
673C2×C4AGL(1,ℤ/8)×C15112yes—
674C2×C4C23×C4×C15111yescharacteristic
675C2×C4C22×D4×C15111yescharacteristic
676C2×C4C2×#41×C15111yescharacteristic
677C2×C4C2×#41×C15111yescharacteristic
678C2×C4H(5,𝔽2)×C15111yescharacteristic
679C2×C42−1+4×C15111yescharacteristic
680C8—22no—
681C8—41no—
682C8—41no—
683C8C4×D4×C15114yescomplemented
684C22—22no—
685C22—22no—
686C22—22no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C2×C4×D4×C15111yescharacteristic
706C22D42×C15111yescharacteristic
707C22#547×C15111yescharacteristic
708C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
709C22#575×C15111yescharacteristic
710C22#576×C15111yescharacteristic
711C22#577×C15111yescharacteristic
712C4—22no—
713C4—22no—
714C4—42no—
715C4—42no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4C2×C4×D4×C15111yescharacteristic
724C4#520×C15111yescharacteristic
725C4#548×C15111yescharacteristic
726C4#553×C15111yescharacteristic
727C2—42no—
728C2—82no—
729C2—82no—
730C2#2361×C15111yescharacteristic
731C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
732C2#2946×C15111yescharacteristic
733C2#3274×C15111yescharacteristic
734C2#3275×C15111yescharacteristic
735C2#3345×C15111yescharacteristic
736C2#3347×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#469×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×#442×C151C2semidirect
3. C2×#428×C151C2semidirect
4. #2363×C151C2semidirect
5. #2361×C151C2semidirect
6. #1970×C151C2semidirect
7. #1944×C151C2semidirect
8. #1926×C151C2semidirect
9. #1925×C151C2semidirect
10. #1875×C151C2semidirect
11. #1874×C151C2semidirect
12. #1864×C151C2semidirect
13. #1862×C151C2semidirect
14. C4×#106×C151C2semidirect
15. #1753×C151C2semidirect
25. #469×C151C4semidirect
72. C2×D8×C151C2×C4semidirect
75. C2×M16×C151C2×C4semidirect
82. #121×C151C2×C4semidirect
83. #121×C151C2×C4semidirect
121. #106×C151C2×C4semidirect
122. #106×C151D4semidirect
127. #102×C151C2×C4semidirect
128. #102×C151C2×C4semidirect
314. C8×C151C4×D4semidirect
368. #23039C151direct (N × H)
369. C151#23039direct (N × H)
371. C2×#442C2×C151semidirect
372. C2×#428C2×C151semidirect
373. #2363C2×C151semidirect
374. #2361C2×C151semidirect
375. #1970C2×C151semidirect
376. #1944C2×C151semidirect
377. #1926C2×C151semidirect
378. #1925C2×C151semidirect
379. #1875C2×C151semidirect
380. #1874C2×C151semidirect
381. #1864C2×C151semidirect
382. #1862C2×C151semidirect
383. C4×#106C2×C151semidirect
384. #1753C2×C151semidirect
394. #469C4×C151semidirect
441. C2×D8C2×C4×C151semidirect
444. C2×M16C2×C4×C151semidirect
451. #121C2×C4×C151semidirect
452. #121C2×C4×C151semidirect
490. #106C2×C4×C151semidirect
491. #106D4×C151semidirect
496. #102C2×C4×C151semidirect
497. #102C2×C4×C151semidirect
683. C8C4×D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1512
C2×#442×C1512
C2×#428×C1512
#2363×C1512
#2361×C1512
#1970×C1512
#1944×C1512
#1926×C1512
#1925×C1512
#1875×C1512
#1874×C1512
#1864×C1512
#1862×C1512
C4×#106×C1512
#1753×C1512
#23039151