Finite Group Databasebeta

← C151×#22865 #50327790

Subgroups — C151×#22865 #50327790

Order 38656.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#448×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic, complemented
3C2×#419×C151C211yesmaximal, characteristic, complemented
4#2363×C151C211yesmaximal, characteristic
5Q8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
6#1968×C151C211yesmaximal, characteristic, complemented
7#1935×C151C211yesmaximal, characteristic, complemented
8#1928×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic
10#1880×C151C211yesmaximal, characteristic, complemented
11#1877×C151C211yesmaximal, characteristic, complemented
12#1865×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14C4×#103×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C23×Q8×C151C2211yescharacteristic
17C22×SD16×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic
24C2×#117×C151C2211yescharacteristic
25#448×C151C418yescomplemented
26#440×C151—24no—
27C2×#107×C151C2211yescharacteristic
28C2×#106×C151C2211yescharacteristic
29#419×C151—24no—
30C2×#103×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2211yescharacteristic
34C2×#103×C151C2211yescharacteristic
35C2×#103×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×#97×C151C2211yescharacteristic
40C2×C4×C8×C151C2211yescharacteristic
41#391×C151—21no—
42#391×C151—21no—
43#391×C151C2211yescharacteristic
44#391×C151C2211yescharacteristic
45#390×C151—21no—
46#390×C151C2211yescharacteristic
47#389×C151C2211yescharacteristic
48#388×C151—21no—
49#386×C151—21no—
50#380×C151—21no—
51#380×C151C2211yescharacteristic
52C4×C4⋊C4×C151C2211yescharacteristic
53C4×C22⋊C4×C151—21no—
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×Q8×C151—22no—
63C22×Q8×C151—22no—
64C22×Q8×C151—21no—
65C22×Q8×C151—22no—
66C22×Q8×C151—41no—
67C22×Q8×C151—41no—
68C22×Q8×C151C2×C414yescomplemented
69C22×Q8×C151C2311yescharacteristic
70C22×Q8×C151C2311yescharacteristic
71C22×D4×C151—21no—
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151C2311yescharacteristic
76C2×SD16×C151—22no—
77C2×SD16×C151—22no—
78C2×SD16×C151—41no—
79C2×SD16×C151—41no—
80C2×SD16×C151C2×C414yes—
81C2×SD16×C151C2×C414yes—
82C2×M16×C151—22no—
83C2×M16×C151—22no—
84C2×M16×C151—41no—
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89#121×C151—22no—
90#121×C151C2×C414yes—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—41no—
94C4×Q8×C151—41no—
95C4×D4×C151—22no—
96C4×D4×C151—41no—
97#117×C151—22no—
98#117×C151—41no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151D411yescharacteristic
114C2×C22⋊C4×C151D411yescharacteristic
115C2×C42×C151—21no—
116C2×C42×C151—21no—
117C2×C42×C151—21no—
118C2×C42×C151—21no—
119C2×C42×C151C2311yescharacteristic
120C2×C42×C151C2311yescharacteristic
121#107×C151—22no—
122#106×C151—41no—
123#103×C151—22no—
124#103×C151—22no—
125#103×C151—22no—
126#103×C151C2×C414yescomplemented
127#103×C151C2×C414yescomplemented
128#103×C151D414yescomplemented
129#102×C151—22no—
130#102×C151—41no—
131C22⋊C8×C151C2×C414yescomplemented
132#97×C151—22no—
133C4×C8×C151—41no—
134#95×C151—21no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151—21no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151D411yescharacteristic
142#95×C151D411yescharacteristic
143C24×C151—21no—
144C24×C151C2×D411yescharacteristic
145C2×Q8×C151—24no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—28no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—42no—
156C2×Q8×C151—42no—
157C2×Q8×C151—44no—
158C2×Q8×C151—44no—
159C2×Q8×C151—44no—
160C2×Q8×C151C22×C412yes—
161C2×Q8×C151C22×C412yes—
162C2×Q8×C151C2×D412yes—
163C2×Q8×C151#4112yes—
164C2×D4×C151—24no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—81no—
171C2×D4×C151—81no—
172C2×D4×C151C22×C412yes—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—24no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—42no—
186C22×C4×C151—42no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151—81no—
190C22×C4×C151C22×C412yes—
191C22×C4×C151C2×D411yescharacteristic
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D411yescharacteristic
196C22×C4×C151#4112yes—
197C22×C4×C151C2411yescharacteristic
198SD16×C151—28no—
199SD16×C151—44no—
200M16×C151—44no—
201C2×C8×C151—21no—
202C2×C8×C151—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151C22×C412yes—
211C2×C8×C151C22×C412yes—
212C2×C8×C151C2×D412yes—
213C4⋊C4×C151—21no—
214C4⋊C4×C151—21no—
215C4⋊C4×C151—21no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—42no—
222C4⋊C4×C151—42no—
223C4⋊C4×C151—81no—
224C4⋊C4×C151C22×C412yes—
225C4⋊C4×C151C2×D412yes—
226C22⋊C4×C151—24no—
227C22⋊C4×C151—22no—
228C22⋊C4×C151—41no—
229C22⋊C4×C151—42no—
230C22⋊C4×C151—42no—
231C22⋊C4×C151—42no—
232C22⋊C4×C151—42no—
233C22⋊C4×C151—81no—
234C42×C151—21no—
235C42×C151—21no—
236C42×C151—21no—
237C42×C151—21no—
238C42×C151—42no—
239C42×C151—42no—
240C42×C151—42no—
241C42×C151—81no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—22no—
249C23×C151—41no—
250C23×C151—41no—
251C23×C151—41no—
252C23×C151—41no—
253C23×C151—41no—
254C23×C151—41no—
255C23×C151C4×D412yes—
256C23×C151C22×D411yescharacteristic
257Q8×C151—22no—
258Q8×C151—22no—
259Q8×C151—22no—
260Q8×C151—22no—
261Q8×C151—22no—
262Q8×C151—48no—
263Q8×C151—41no—
264Q8×C151—41no—
265Q8×C151C4×D414yes—
266D4×C151—22no—
267D4×C151—22no—
268D4×C151—41no—
269D4×C151—41no—
270D4×C151—84no—
271C2×C4×C151—22no—
272C2×C4×C151—22no—
273C2×C4×C151—21no—
274C2×C4×C151—22no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—22no—
279C2×C4×C151—22no—
280C2×C4×C151—22no—
281C2×C4×C151—22no—
282C2×C4×C151—22no—
283C2×C4×C151—22no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—22no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—48no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151—41no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—84no—
311C2×C4×C151C4×D412yes—
312C2×C4×C151#13712yes—
313C2×C4×C151C23×C411yescharacteristic
314C2×C4×C151C22×D411yescharacteristic
315C2×C4×C151C2×#4111yescharacteristic
316C2×C4×C151C2×#4111yescharacteristic
317C2×C4×C151H(5,𝔽2)11yescharacteristic
318C2×C4×C151H(5,𝔽2)11yescharacteristic
319C8×C151—22no—
320C8×C151—22no—
321C8×C151—22no—
322C8×C151—41no—
323C22×C151—22no—
324C22×C151—22no—
325C22×C151—22no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—42no—
331C22×C151—42no—
332C22×C151—42no—
333C22×C151—81no—
334C22×C151—81no—
335C22×C151—81no—
336C22×C151—81no—
337C22×C151C2×C4×D411yescharacteristic
338C22×C151D4211yescharacteristic
339C22×C151#54611yescharacteristic
340C22×C151C2×#13711yescharacteristic
341C22×C151#57511yescharacteristic
342C22×C151#57711yescharacteristic
343C22×C151#57711yescharacteristic
344C4×C151—22no—
345C4×C151—24no—
346C4×C151—22no—
347C4×C151—42no—
348C4×C151—42no—
349C4×C151—41no—
350C4×C151—42no—
351C4×C151—41no—
352C4×C151—41no—
353C4×C151—81no—
354C4×C151—81no—
355C4×C151—81no—
356C4×C151C2×C4×D411yescharacteristic
357C4×C151#51811yescharacteristic
358C4×C151#54611yescharacteristic
359C4×C151#55111yescharacteristic
360C2×C151—42no—
361C2×C151—82no—
362C2×C151#235811yescharacteristic
363C2×C151C4×#13711yescharacteristic
364C2×C151#294911yescharacteristic
365C2×C151#327511yescharacteristic
366C2×C151#327811yescharacteristic
367C2×C151#332011yescharacteristic
368C2×C151#332111yescharacteristic
369#22865C15111yesmaximal, characteristic, direct product factor, Sylow
370C151#2286511yescharacteristic, direct product factor, Sylow
371C2×#448C2×C15111yescharacteristic
372C2×#440C2×C15111yescharacteristic, complemented
373C2×#419C2×C15111yescharacteristic, complemented
374#2363C2×C15111yescharacteristic
375Q8×C22⋊C4C2×C15111yescharacteristic, complemented
376#1968C2×C15111yescharacteristic, complemented
377#1935C2×C15111yescharacteristic, complemented
378#1928C2×C15111yescharacteristic, complemented
379#1895C2×C15111yescharacteristic
380#1880C2×C15111yescharacteristic, complemented
381#1877C2×C15111yescharacteristic, complemented
382#1865C2×C15111yescharacteristic, complemented
383#1854C2×C15111yescharacteristic, complemented
384C4×#103C2×C15111yescharacteristic, complemented
385#1753C2×C15111yescharacteristic, complemented
386C23×Q8C22×C15111yescharacteristic
387C22×SD16C22×C15111yescharacteristic
388C22×SD16C22×C15111yescharacteristic
389C22×M16C22×C15111yescharacteristic
390C2×#121C22×C15111yescharacteristic
391C2×C4×Q8C22×C15111yescharacteristic
392C2×C4×Q8C22×C15111yescharacteristic
393C2×C4×D4C22×C15111yescharacteristic
394C2×#117C22×C15111yescharacteristic
395#448C4×C15118yescomplemented
396#440—24no—
397C2×#107C22×C15111yescharacteristic
398C2×#106C22×C15111yescharacteristic
399#419—24no—
400C2×#103C22×C15111yescharacteristic
401C2×#103C22×C15111yescharacteristic
402C2×#103C22×C15111yescharacteristic
403C2×#103C22×C15111yescharacteristic
404C2×#103C22×C15111yescharacteristic
405C2×#103C22×C15111yescharacteristic
406C2×#102C22×C15111yescharacteristic
407C2×#102C22×C15111yescharacteristic
408C2×C22⋊C8C22×C15111yescharacteristic
409C2×#97C22×C15111yescharacteristic
410C2×C4×C8C22×C15111yescharacteristic
411#391—21no—
412#391—21no—
413#391C22×C15111yescharacteristic
414#391C22×C15111yescharacteristic
415#390—21no—
416#390C22×C15111yescharacteristic
417#389C22×C15111yescharacteristic
418#388—21no—
419#386—21no—
420#380—21no—
421#380C22×C15111yescharacteristic
422C4×C4⋊C4C22×C15111yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4C22×C15111yescharacteristic
426#340C22×C15111yescharacteristic
427#340C22×C15111yescharacteristic
428#340C22×C15111yescharacteristic
429#340C22×C15111yescharacteristic
430#336C22×C15111yescharacteristic
431#336C22×C15111yescharacteristic
432C22×Q8—22no—
433C22×Q8—21no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C2×C4×C15114yescomplemented
439C22×Q8C23×C15111yescharacteristic
440C22×Q8C23×C15111yescharacteristic
441C22×D4—21no—
442C22×D4C23×C15111yescharacteristic
443C23×C4—21no—
444C23×C4—21no—
445C23×C4C23×C15111yescharacteristic
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×C4×C15114yes—
451C2×SD16C2×C4×C15114yes—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—41no—
455C22×C8C23×C15111yescharacteristic
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459#121—22no—
460#121C2×C4×C15114yes—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—41no—
464C4×Q8—41no—
465C4×D4—22no—
466C4×D4—41no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4C23×C15111yescharacteristic
473C2×C4⋊C4C23×C15111yescharacteristic
474C2×C4⋊C4C23×C15111yescharacteristic
475C2×C4⋊C4C23×C15111yescharacteristic
476C2×C4⋊C4C23×C15111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4D4×C15111yescharacteristic
484C2×C22⋊C4D4×C15111yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42C23×C15111yescharacteristic
490C2×C42C23×C15111yescharacteristic
491#107—22no—
492#106—41no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103C2×C4×C15114yescomplemented
497#103C2×C4×C15114yescomplemented
498#103D4×C15114yescomplemented
499#102—22no—
500#102—41no—
501C22⋊C8C2×C4×C15114yescomplemented
502#97—22no—
503C4×C8—41no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95D4×C15111yescharacteristic
512#95D4×C15111yescharacteristic
513C24—21no—
514C24C2×D4×C15111yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8C22×C4×C15112yes—
531C2×Q8C22×C4×C15112yes—
532C2×Q8C2×D4×C15112yes—
533C2×Q8#41×C15112yes—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C22×C4×C15112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—81no—
560C22×C4C22×C4×C15112yes—
561C22×C4C2×D4×C15111yescharacteristic
562C22×C4C2×D4×C15111yescharacteristic
563C22×C4C2×D4×C15111yescharacteristic
564C22×C4C2×D4×C15111yescharacteristic
565C22×C4C2×D4×C15111yescharacteristic
566C22×C4#41×C15112yes—
567C22×C4C24×C15111yescharacteristic
568SD16—28no—
569SD16—44no—
570M16—44no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8C22×C4×C15112yes—
581C2×C8C22×C4×C15112yes—
582C2×C8C2×D4×C15112yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—81no—
594C4⋊C4C22×C4×C15112yes—
595C4⋊C4C2×D4×C15112yes—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—81no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—42no—
610C42—42no—
611C42—81no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C4×D4×C15112yes—
626C23C22×D4×C15111yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8C4×D4×C15114yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4C4×D4×C15112yes—
682C2×C4#137×C15112yes—
683C2×C4C23×C4×C15111yescharacteristic
684C2×C4C22×D4×C15111yescharacteristic
685C2×C4C2×#41×C15111yescharacteristic
686C2×C4C2×#41×C15111yescharacteristic
687C2×C4H(5,𝔽2)×C15111yescharacteristic
688C2×C4H(5,𝔽2)×C15111yescharacteristic
689C8—22no—
690C8—22no—
691C8—22no—
692C8—41no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×C4×D4×C15111yescharacteristic
708C22D42×C15111yescharacteristic
709C22#546×C15111yescharacteristic
710C22C2×#137×C15111yescharacteristic
711C22#575×C15111yescharacteristic
712C22#577×C15111yescharacteristic
713C22#577×C15111yescharacteristic
714C4—22no—
715C4—24no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—41no—
720C4—42no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4C2×C4×D4×C15111yescharacteristic
727C4#518×C15111yescharacteristic
728C4#546×C15111yescharacteristic
729C4#551×C15111yescharacteristic
730C2—42no—
731C2—82no—
732C2#2358×C15111yescharacteristic
733C2C4×#137×C15111yescharacteristic
734C2#2949×C15111yescharacteristic
735C2#3275×C15111yescharacteristic
736C2#3278×C15111yescharacteristic
737C2#3320×C15111yescharacteristic
738C2#3321×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
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×#419×C151C2semidirect
5. Q8×C22⋊C4×C151C2semidirect
6. #1968×C151C2semidirect
7. #1935×C151C2semidirect
8. #1928×C151C2semidirect
10. #1880×C151C2semidirect
11. #1877×C151C2semidirect
12. #1865×C151C2semidirect
13. #1854×C151C2semidirect
14. C4×#103×C151C2semidirect
15. #1753×C151C2semidirect
25. #448×C151C4semidirect
68. C22×Q8×C151C2×C4semidirect
126. #103×C151C2×C4semidirect
127. #103×C151C2×C4semidirect
128. #103×C151D4semidirect
131. C22⋊C8×C151C2×C4semidirect
369. #22865C151direct (N × H)
370. C151#22865direct (N × H)
372. C2×#440C2×C151semidirect
373. C2×#419C2×C151semidirect
375. Q8×C22⋊C4C2×C151semidirect
376. #1968C2×C151semidirect
377. #1935C2×C151semidirect
378. #1928C2×C151semidirect
380. #1880C2×C151semidirect
381. #1877C2×C151semidirect
382. #1865C2×C151semidirect
383. #1854C2×C151semidirect
384. C4×#103C2×C151semidirect
385. #1753C2×C151semidirect
395. #448C4×C151semidirect
438. C22×Q8C2×C4×C151semidirect
496. #103C2×C4×C151semidirect
497. #103C2×C4×C151semidirect
498. #103D4×C151semidirect
501. C22⋊C8C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#448×C1512
C2×#440×C1512
C2×#419×C1512
#2363×C1512
Q8×C22⋊C4×C1512
#1968×C1512
#1935×C1512
#1928×C1512
#1895×C1512
#1880×C1512
#1877×C1512
#1865×C1512
#1854×C1512
C4×#103×C1512
#1753×C1512
#22865151