Finite Group Databasebeta

← C151×#23569 #50328494

Subgroups — C151×#23569 #50328494

Order 38656.

1272 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic, complemented
4C4×#121×C151C211yesmaximal, characteristic, complemented
5#2059×C151C211yesmaximal, characteristic, complemented
6#2042×C151C211yesmaximal, characteristic, complemented
7#2036×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2025×C151C211yesmaximal, characteristic, complemented
10#2012×C151C211yesmaximal, characteristic, complemented
11#2000×C151C211yesmaximal, characteristic, complemented
12#1999×C151C211yesmaximal, characteristic
13C4×#103×C151C211yesmaximal, characteristic, complemented
14C4×#102×C151C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18#529×C151—24no—
19#529×C151—24no—
20C2×#126×C151—21no—
21C2×#125×C151C2211yescharacteristic
22C2×#124×C151C2211yescharacteristic
23C2×#123×C151—21no—
24C2×C22⋊Q8×C151C2211yescharacteristic
25C2×#121×C151C2211yescharacteristic
26C2×#121×C151C2211yescharacteristic
27C2×C4×Q8×C151C2211yescharacteristic
28C2×C4×D4×C151—21no—
29C2×C4×D4×C151—21no—
30C2×C4×D4×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151—21no—
33C22×C42×C151C2211yescharacteristic
34C4×SD16×C151—24no—
35C4×D8×C151—24no—
36C2×#107×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×#103×C151C2211yescharacteristic
39C2×#103×C151C2211yescharacteristic
40C2×#103×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C4×C8×C151C2211yescharacteristic
49C2×C4×C8×C151C2211yescharacteristic
50#390×C151C2211yescharacteristic
51#389×C151C2211yescharacteristic
52#388×C151—21no—
53#386×C151—21no—
54#380×C151C2211yescharacteristic
55C4×C4⋊C4×C151C2211yescharacteristic
56C4×C22⋊C4×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151C2311yescharacteristic
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151C2311yescharacteristic
67C22×D4×C151C2311yescharacteristic
68C23×C4×C151—21no—
69C23×C4×C151—21no—
70C23×C4×C151D411yescharacteristic
71C23×C4×C151D411yescharacteristic
72C23×C4×C151C2311yescharacteristic
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—22no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83#126×C151—28no—
84#125×C151—22no—
85#125×C151—22no—
86#124×C151—22no—
87#124×C151—22no—
88#123×C151—28no—
89C22⋊Q8×C151—22no—
90C22⋊Q8×C151—22no—
91#121×C151—22no—
92#121×C151—22no—
93#121×C151—22no—
94#121×C151—22no—
95C4×Q8×C151—22no—
96C4×Q8×C151D414yescomplemented
97C4×D4×C151—28no—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—44no—
102C4×D4×C151D414yescomplemented
103#117×C151—28no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151—21no—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—21no—
120C2×C22⋊C4×C151—21no—
121C2×C22⋊C4×C151—21no—
122C2×C22⋊C4×C151—21no—
123C2×C22⋊C4×C151—21no—
124C2×C42×C151—21no—
125C2×C42×C151—22no—
126C2×C42×C151—22no—
127C2×C42×C151—21no—
128C2×C42×C151D411yescharacteristic
129C2×C42×C151D411yescharacteristic
130C2×C42×C151C2311yescharacteristic
131C2×C42×C151C2311yescharacteristic
132#107×C151—22no—
133#106×C151—22no—
134#103×C151—22no—
135#103×C151—22no—
136#103×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142C22⋊C8×C151—22no—
143C22⋊C8×C151—22no—
144C4×C8×C151—22no—
145C4×C8×C151—22no—
146#95×C151—21no—
147#95×C151—21no—
148#95×C151—21no—
149C24×C151—21no—
150C24×C151—21no—
151C24×C151C2×D411yescharacteristic
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151C2×D412yes—
158C2×D4×C151—24no—
159C2×D4×C151—24no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—42no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—42no—
174C2×D4×C151C2×D412yes—
175C2×D4×C151#4112yes—
176C22×C4×C151—22no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—22no—
182C22×C4×C151—22no—
183C22×C4×C151—24no—
184C22×C4×C151—22no—
185C22×C4×C151—22no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—41no—
195C22×C4×C151—42no—
196C22×C4×C151—42no—
197C22×C4×C151—42no—
198C22×C4×C151—42no—
199C22×C4×C151—42no—
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2411yescharacteristic
206SD16×C151—28no—
207D8×C151—28no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151#4112yes—
219C2×C8×C151#4112yes—
220C4⋊C4×C151—24no—
221C4⋊C4×C151—24no—
222C4⋊C4×C151—24no—
223C4⋊C4×C151—24no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—42no—
232C4⋊C4×C151C2×D412yes—
233C4⋊C4×C151C2×D412yes—
234C4⋊C4×C151#4112yes—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—24no—
237C22⋊C4×C151—24no—
238C22⋊C4×C151—24no—
239C22⋊C4×C151—24no—
240C22⋊C4×C151—24no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—42no—
243C22⋊C4×C151—42no—
244C22⋊C4×C151—42no—
245C42×C151—22no—
246C42×C151—22no—
247C42×C151—24no—
248C42×C151—21no—
249C42×C151—21no—
250C42×C151—42no—
251C42×C151C2×D412yes—
252C42×C151C2×D412yes—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—22no—
260C23×C151—22no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151#13512yes—
274C23×C151C22×D411yescharacteristic
275Q8×C151—22no—
276Q8×C151—22no—
277Q8×C151—41no—
278Q8×C151—41no—
279D4×C151—22no—
280D4×C151—22no—
281D4×C151—22no—
282D4×C151—22no—
283D4×C151—48no—
284D4×C151—48no—
285D4×C151—41no—
286D4×C151—41no—
287D4×C151—41no—
288D4×C151—41no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—22no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—22no—
296C2×C4×C151—22no—
297C2×C4×C151—21no—
298C2×C4×C151—22no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—44no—
305C2×C4×C151—41no—
306C2×C4×C151—41no—
307C2×C4×C151—41no—
308C2×C4×C151—41no—
309C2×C4×C151—41no—
310C2×C4×C151—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—44no—
318C2×C4×C151—48no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—84no—
326C2×C4×C151#12012yes—
327C2×C4×C151#12012yes—
328C2×C4×C151#13512yes—
329C2×C4×C151AGL(1,ℤ/8)12yes—
330C2×C4×C151C22×D411yescharacteristic
331C2×C4×C151C22×D411yescharacteristic
332C2×C4×C151C2×#4111yescharacteristic
333C2×C4×C151C2×#4111yescharacteristic
334C2×C4×C151C2×#4111yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C8×C151—22no—
337C8×C151—22no—
338C8×C151—41no—
339C8×C151—41no—
340C22×C151—22no—
341C22×C151—22no—
342C22×C151—22no—
343C22×C151—41no—
344C22×C151—41no—
345C22×C151—41no—
346C22×C151—41no—
347C22×C151—42no—
348C22×C151—42no—
349C22×C151—42no—
350C22×C151—42no—
351C22×C151—42no—
352C22×C151—42no—
353C22×C151—81no—
354C22×C151—81no—
355C22×C151—81no—
356C22×C151—81no—
357C22×C151—81no—
358C22×C151—81no—
359C22×C151—81no—
360C22×C151—81no—
361C22×C151C2×#12011yescharacteristic
362C22×C151#52511yescharacteristic
363C22×C151#53211yescharacteristic
364C22×C151C2×#13511yescharacteristic
365C22×C151C2×#13511yescharacteristic
366C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C151#57511yescharacteristic
368C4×C151—22no—
369C4×C151—42no—
370C4×C151—41no—
371C4×C151—42no—
372C4×C151—41no—
373C4×C151—42no—
374C4×C151—41no—
375C4×C151—42no—
376C4×C151—81no—
377C4×C151—81no—
378C4×C151#44914yes—
379C4×C151#52511yescharacteristic
380C4×C151#52511yescharacteristic
381C4×C151#53211yescharacteristic
382C4×C151#53211yescharacteristic
383C2×C151—42no—
384C2×C151—82no—
385C2×C151—82no—
386C2×C151#238811yescharacteristic
387C2×C151C2×#44911yescharacteristic
388C2×C151#300211yescharacteristic
389C2×C151#310211yescharacteristic
390C2×C151#310511yescharacteristic
391C2×C151#316811yescharacteristic
392C2×C151#317111yescharacteristic
393#23569C15111yesmaximal, characteristic, direct product factor, Sylow
394C151#2356911yescharacteristic, direct product factor, Sylow
395C2×#529C2×C15111yescharacteristic, complemented
396C2×C4×SD16C2×C15111yescharacteristic, complemented
397C2×C4×D8C2×C15111yescharacteristic, complemented
398C4×#121C2×C15111yescharacteristic, complemented
399#2059C2×C15111yescharacteristic, complemented
400#2042C2×C15111yescharacteristic, complemented
401#2036C2×C15111yescharacteristic, complemented
402#2034C2×C15111yescharacteristic, complemented
403#2025C2×C15111yescharacteristic, complemented
404#2012C2×C15111yescharacteristic, complemented
405#2000C2×C15111yescharacteristic, complemented
406#1999C2×C15111yescharacteristic
407C4×#103C2×C15111yescharacteristic, complemented
408C4×#102C2×C15111yescharacteristic, complemented
409C4×C22⋊C8C2×C15111yescharacteristic, complemented
410C22×SD16C22×C15111yescharacteristic
411C22×D8C22×C15111yescharacteristic
412#529—24no—
413#529—24no—
414C2×#126—21no—
415C2×#125C22×C15111yescharacteristic
416C2×#124C22×C15111yescharacteristic
417C2×#123—21no—
418C2×C22⋊Q8C22×C15111yescharacteristic
419C2×#121C22×C15111yescharacteristic
420C2×#121C22×C15111yescharacteristic
421C2×C4×Q8C22×C15111yescharacteristic
422C2×C4×D4—21no—
423C2×C4×D4—21no—
424C2×C4×D4C22×C15111yescharacteristic
425C2×C4×D4C22×C15111yescharacteristic
426C2×#117—21no—
427C22×C42C22×C15111yescharacteristic
428C4×SD16—24no—
429C4×D8—24no—
430C2×#107C22×C15111yescharacteristic
431C2×#106C22×C15111yescharacteristic
432C2×#103C22×C15111yescharacteristic
433C2×#103C22×C15111yescharacteristic
434C2×#103C22×C15111yescharacteristic
435C2×#102C22×C15111yescharacteristic
436C2×#102C22×C15111yescharacteristic
437C2×#102C22×C15111yescharacteristic
438C2×#102C22×C15111yescharacteristic
439C2×#102C22×C15111yescharacteristic
440C2×C22⋊C8C22×C15111yescharacteristic
441C2×C22⋊C8C22×C15111yescharacteristic
442C2×C4×C8C22×C15111yescharacteristic
443C2×C4×C8C22×C15111yescharacteristic
444#390C22×C15111yescharacteristic
445#389C22×C15111yescharacteristic
446#388—21no—
447#386—21no—
448#380C22×C15111yescharacteristic
449C4×C4⋊C4C22×C15111yescharacteristic
450C4×C22⋊C4—21no—
451#340C22×C15111yescharacteristic
452#340C22×C15111yescharacteristic
453#340C22×C15111yescharacteristic
454#340C22×C15111yescharacteristic
455#336C22×C15111yescharacteristic
456#336C22×C15111yescharacteristic
457C22×Q8C23×C15111yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C15111yescharacteristic
461C22×D4C23×C15111yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4D4×C15111yescharacteristic
465C23×C4D4×C15111yescharacteristic
466C23×C4C23×C15111yescharacteristic
467C2×SD16—22no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C22×C8C23×C15111yescharacteristic
474C22×C8C23×C15111yescharacteristic
475C22×C8C23×C15111yescharacteristic
476C22×C8C23×C15111yescharacteristic
477#126—28no—
478#125—22no—
479#125—22no—
480#124—22no—
481#124—22no—
482#123—28no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—22no—
489C4×Q8—22no—
490C4×Q8D4×C15114yescomplemented
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—44no—
496C4×D4D4×C15114yescomplemented
497#117—28no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4C23×C15111yescharacteristic
504C2×C4⋊C4C23×C15111yescharacteristic
505C2×C4⋊C4C23×C15111yescharacteristic
506C2×C4⋊C4C23×C15111yescharacteristic
507C2×C4⋊C4C23×C15111yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—21no—
522C2×C42D4×C15111yescharacteristic
523C2×C42D4×C15111yescharacteristic
524C2×C42C23×C15111yescharacteristic
525C2×C42C23×C15111yescharacteristic
526#107—22no—
527#106—22no—
528#103—22no—
529#103—22no—
530#103—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—22no—
535#102—22no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C4×C8—22no—
539C4×C8—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543C24—21no—
544C24—21no—
545C24C2×D4×C15111yescharacteristic
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8C2×D4×C15112yes—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C2×D4×C15112yes—
569C2×D4#41×C15112yes—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4C2×D4×C15111yescharacteristic
595C22×C4C2×D4×C15111yescharacteristic
596C22×C4C2×D4×C15111yescharacteristic
597C22×C4C2×D4×C15111yescharacteristic
598C22×C4C2×D4×C15111yescharacteristic
599C22×C4C24×C15111yescharacteristic
600SD16—28no—
601D8—28no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8#41×C15112yes—
613C2×C8#41×C15112yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C15112yes—
627C4⋊C4C2×D4×C15112yes—
628C4⋊C4#41×C15112yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C42—22no—
640C42—22no—
641C42—24no—
642C42—21no—
643C42—21no—
644C42—42no—
645C42C2×D4×C15112yes—
646C42C2×D4×C15112yes—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23#135×C15112yes—
668C23C22×D4×C15111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—41no—
672Q8—41no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—48no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—84no—
720C2×C4#120×C15112yes—
721C2×C4#120×C15112yes—
722C2×C4#135×C15112yes—
723C2×C4AGL(1,ℤ/8)×C15112yes—
724C2×C4C22×D4×C15111yescharacteristic
725C2×C4C22×D4×C15111yescharacteristic
726C2×C4C2×#41×C15111yescharacteristic
727C2×C4C2×#41×C15111yescharacteristic
728C2×C4C2×#41×C15111yescharacteristic
729C2×C4C2×#41×C15111yescharacteristic
730C8—22no—
731C8—22no—
732C8—41no—
733C8—41no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#120×C15111yescharacteristic
756C22#525×C15111yescharacteristic
757C22#532×C15111yescharacteristic
758C22C2×#135×C15111yescharacteristic
759C22C2×#135×C15111yescharacteristic
760C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
761C22#575×C15111yescharacteristic
762C4—22no—
763C4—42no—
764C4—41no—
765C4—42no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—42no—
770C4—81no—
771C4—81no—
772C4#449×C15114yes—
773C4#525×C15111yescharacteristic
774C4#525×C15111yescharacteristic
775C4#532×C15111yescharacteristic
776C4#532×C15111yescharacteristic
777C2—42no—
778C2—82no—
779C2—82no—
780C2#2388×C15111yescharacteristic
781C2C2×#449×C15111yescharacteristic
782C2#3002×C15111yescharacteristic
783C2#3102×C15111yescharacteristic
784C2#3105×C15111yescharacteristic
785C2#3168×C15111yescharacteristic
786C2#3171×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutator, Frattini, cosocleC22×C4C24×C151
socleC23×C151C22×D4
prime radical#1999×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#529×C151C2semidirect
2. C2×C4×SD16×C151C2semidirect
3. C2×C4×D8×C151C2semidirect
4. C4×#121×C151C2semidirect
5. #2059×C151C2semidirect
6. #2042×C151C2semidirect
7. #2036×C151C2semidirect
8. #2034×C151C2semidirect
9. #2025×C151C2semidirect
10. #2012×C151C2semidirect
11. #2000×C151C2semidirect
13. C4×#103×C151C2semidirect
14. C4×#102×C151C2semidirect
15. C4×C22⋊C8×C151C2semidirect
96. C4×Q8×C151D4semidirect
102. C4×D4×C151D4semidirect
393. #23569C151direct (N × H)
394. C151#23569direct (N × H)
395. C2×#529C2×C151semidirect
396. C2×C4×SD16C2×C151semidirect
397. C2×C4×D8C2×C151semidirect
398. C4×#121C2×C151semidirect
399. #2059C2×C151semidirect
400. #2042C2×C151semidirect
401. #2036C2×C151semidirect
402. #2034C2×C151semidirect
403. #2025C2×C151semidirect
404. #2012C2×C151semidirect
405. #2000C2×C151semidirect
407. C4×#103C2×C151semidirect
408. C4×#102C2×C151semidirect
409. C4×C22⋊C8C2×C151semidirect
490. C4×Q8D4×C151semidirect
496. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1512
C2×C4×SD16×C1512
C2×C4×D8×C1512
C4×#121×C1512
#2059×C1512
#2042×C1512
#2036×C1512
#2034×C1512
#2025×C1512
#2012×C1512
#2000×C1512
#1999×C1512
C4×#103×C1512
C4×#102×C1512
C4×C22⋊C8×C1512
#23569151