Finite Group Databasebeta

← C151×#24100 #50329025

Subgroups — C151×#24100 #50329025

Order 38656.

1300 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic
2C2×#482×C151C211yesmaximal, characteristic, complemented
3C2×#428×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic, complemented
5#2058×C151C211yesmaximal, characteristic, complemented
6#2057×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1864×C151C211yesmaximal, characteristic, complemented
12#1862×C151C211yesmaximal, characteristic, complemented
13#1853×C151C211yesmaximal, characteristic, complemented
14#1852×C151C211yesmaximal, characteristic, complemented
15#1824×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151—21no—
17C22×M16×C151C2211yescharacteristic
18#547×C151—24no—
19#547×C151—24no—
20C2×C4⋊Q8×C151C2211yescharacteristic
21C2×#123×C151—21no—
22C2×#123×C151—21no—
23C2×C22⋊Q8×C151—21no—
24C2×#121×C151C2211yescharacteristic
25C2×#121×C151C2211yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C2×C4×D4×C151C2211yescharacteristic
28C2×#117×C151C2211yescharacteristic
29C22×C4⋊C4×C151C2211yescharacteristic
30C22×C4⋊C4×C151C2211yescharacteristic
31#482×C151—24no—
32#428×C151—24no—
33C2×#107×C151C2211yescharacteristic
34C2×#107×C151C2211yescharacteristic
35C2×#107×C151C2211yescharacteristic
36C2×#106×C151C2211yescharacteristic
37C2×#106×C151C2211yescharacteristic
38C2×#106×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic
40C2×#102×C151C2211yescharacteristic
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46#397×C151—21no—
47#394×C151—21no—
48#389×C151C2211yescharacteristic
49#389×C151C2211yescharacteristic
50#388×C151—21no—
51#387×C151—21no—
52#380×C151C2211yescharacteristic
53#380×C151C2211yescharacteristic
54#380×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#340×C151C2211yescharacteristic
60#340×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C2×#41×C151—28no—
64C2×#41×C151—44no—
65C2×#41×C151—44no—
66C22×Q8×C151—21no—
67C22×D4×C151—21no—
68C22×D4×C151—21no—
69C22×D4×C151D411yescharacteristic
70C22×D4×C151C2311yescharacteristic
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C23×C4×C151—21no—
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C2×M16×C151—22no—
77C2×M16×C151—22no—
78C2×M16×C151—22no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C4⋊Q8×C151—22no—
84C4⋊Q8×C151—22no—
85#123×C151—28no—
86#123×C151—28no—
87C22⋊Q8×C151—28no—
88#121×C151—22no—
89#121×C151—22no—
90#121×C151—22no—
91#121×C151D414yes—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96#117×C151—22no—
97#117×C151—22no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151—21no—
105C2×C4⋊C4×C151—21no—
106C2×C4⋊C4×C151D411yescharacteristic
107C2×C4⋊C4×C151D414yes—
108C2×C4⋊C4×C151C2311yescharacteristic
109C2×C4⋊C4×C151C2311yescharacteristic
110C2×C4⋊C4×C151C2311yescharacteristic
111C2×C4⋊C4×C151C2311yescharacteristic
112C2×C4⋊C4×C151C2311yescharacteristic
113C2×C4⋊C4×C151C2311yescharacteristic
114C2×C4⋊C4×C151C2311yescharacteristic
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×C151D411yescharacteristic
123C2×C22⋊C4×C151D411yescharacteristic
124C2×C42×C151—21no—
125C2×C42×C151C2311yescharacteristic
126#107×C151—22no—
127#107×C151—22no—
128#107×C151—22no—
129#106×C151—22no—
130#106×C151—22no—
131#106×C151—22no—
132#102×C151—22no—
133#102×C151—22no—
134#102×C151—22no—
135#102×C151—22no—
136C22⋊C8×C151—22no—
137C22⋊C8×C151—22no—
138C22⋊C8×C151—22no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142#95×C151—21no—
143#95×C151—21no—
144C24×C151—21no—
145C24×C151C2×D411yescharacteristic
146C24×C151C2×D411yescharacteristic
147#41×C151—432no—
148C2×Q8×C151—24no—
149C2×Q8×C151—42no—
150C2×Q8×C151—42no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—24no—
154C2×D4×C151—24no—
155C2×D4×C151—22no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—42no—
162C2×D4×C151—42no—
163C2×D4×C151—42no—
164C2×D4×C151—42no—
165C2×D4×C151C2×D412yes—
166C22×C4×C151—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—24no—
171C22×C4×C151—24no—
172C22×C4×C151—24no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
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—21no—
186C22×C4×C151—42no—
187C22×C4×C151—42no—
188C22×C4×C151—42no—
189C22×C4×C151—42no—
190C22×C4×C151—42no—
191C22×C4×C151—42no—
192C22×C4×C151C2×D411yescharacteristic
193C22×C4×C151C2×D411yescharacteristic
194C22×C4×C151C2×D411yescharacteristic
195C22×C4×C151C2×D412yes—
196C22×C4×C151C2×D412yes—
197C22×C4×C151C2×D411yescharacteristic
198C22×C4×C151C2411yescharacteristic
199M16×C151—28no—
200C2×C8×C151—21no—
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×C151#4112yescomplemented
211C2×C8×C151#4112yescomplemented
212C4⋊C4×C151—24no—
213C4⋊C4×C151—24no—
214C4⋊C4×C151—24no—
215C4⋊C4×C151—22no—
216C4⋊C4×C151—21no—
217C4⋊C4×C151—21no—
218C4⋊C4×C151—21no—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—42no—
228C4⋊C4×C151—81no—
229C4⋊C4×C151C2×D412yes—
230C4⋊C4×C151C2×D412yes—
231C4⋊C4×C151C2×D412yes—
232C22⋊C4×C151—24no—
233C22⋊C4×C151—24no—
234C22⋊C4×C151—22no—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—81no—
240C22⋊C4×C151—81no—
241C42×C151—21no—
242C42×C151—21no—
243C42×C151—42no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151—21no—
255C23×C151—21no—
256C23×C151—22no—
257C23×C151—41no—
258C23×C151—41no—
259C23×C151—41no—
260C23×C151—41no—
261C23×C151—41no—
262C23×C151—41no—
263C23×C151#12012yes—
264C23×C151AGL(1,ℤ/8)12yes—
265C23×C151C22×D411yescharacteristic
266Q8×C151—48no—
267D4×C151—28no—
268D4×C151—22no—
269D4×C151—22no—
270D4×C151—48no—
271D4×C151—48no—
272D4×C151—41no—
273D4×C151—41no—
274C2×C4×C151—21no—
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—48no—
292C2×C4×C151—48no—
293C2×C4×C151—48no—
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—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—41no—
311C2×C4×C151—41no—
312C2×C4×C151—41no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151#12012yes—
317C2×C4×C151AGL(1,ℤ/8)12yes—
318C2×C4×C151C22×D411yescharacteristic
319C2×C4×C151C22×D411yescharacteristic
320C2×C4×C151C2×#4111yescharacteristic
321C2×C4×C151C2×#4111yescharacteristic
322C2×C4×C1512−1+411yescharacteristic
323C2×C4×C1512−1+411yescharacteristic
324C8×C151—22no—
325C8×C151—22no—
326C8×C151—41no—
327C8×C151—41no—
328C22×C151—22no—
329C22×C151—22no—
330C22×C151—22no—
331C22×C151—22no—
332C22×C151—22no—
333C22×C151—22no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151—41no—
341C22×C151—41no—
342C22×C151—42no—
343C22×C151—42no—
344C22×C151—42no—
345C22×C151—81no—
346C22×C151—81no—
347C22×C151—81no—
348C22×C151—81no—
349C22×C151C2×#12011yescharacteristic
350C22×C151#54711yescharacteristic
351C22×C151#54711yescharacteristic
352C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C151#57711yescharacteristic
355C22×C151#57811yescharacteristic
356C4×C151—22no—
357C4×C151—22no—
358C4×C151—41no—
359C4×C151—42no—
360C4×C151—42no—
361C4×C151—42no—
362C4×C151—41no—
363C4×C151—81no—
364C4×C151—81no—
365C4×C151—81no—
366C4×C151—81no—
367C4×C151#52511yescharacteristic
368C4×C151#53611yescharacteristic
369C4×C151#54711yescharacteristic
370C4×C151#54711yescharacteristic
371C2×C151—42no—
372C2×C151—42no—
373C2×C151—82no—
374C2×C151#240611yescharacteristic
375C2×C151#300311yescharacteristic
376C2×C151#301311yescharacteristic
377C2×C151#334311yescharacteristic
378C2×C151#334511yescharacteristic
379C2×C151#335311yescharacteristic
380C2×C151#335411yescharacteristic
381#24100C15111yesmaximal, characteristic, direct product factor, Sylow
382C151#2410011yescharacteristic, direct product factor, Sylow
383C2×#547C2×C15111yescharacteristic
384C2×#482C2×C15111yescharacteristic, complemented
385C2×#428C2×C15111yescharacteristic, complemented
386#2485C2×C15111yescharacteristic, complemented
387#2058C2×C15111yescharacteristic, complemented
388#2057C2×C15111yescharacteristic, complemented
389#2034C2×C15111yescharacteristic, complemented
390#2033C2×C15111yescharacteristic, complemented
391#1895C2×C15111yescharacteristic, complemented
392#1870C2×C15111yescharacteristic, complemented
393#1864C2×C15111yescharacteristic, complemented
394#1862C2×C15111yescharacteristic, complemented
395#1853C2×C15111yescharacteristic, complemented
396#1852C2×C15111yescharacteristic, complemented
397#1824C2×C15111yescharacteristic, complemented
398C22×#41—21no—
399C22×M16C22×C15111yescharacteristic
400#547—24no—
401#547—24no—
402C2×C4⋊Q8C22×C15111yescharacteristic
403C2×#123—21no—
404C2×#123—21no—
405C2×C22⋊Q8—21no—
406C2×#121C22×C15111yescharacteristic
407C2×#121C22×C15111yescharacteristic
408C2×C4×D4C22×C15111yescharacteristic
409C2×C4×D4C22×C15111yescharacteristic
410C2×#117C22×C15111yescharacteristic
411C22×C4⋊C4C22×C15111yescharacteristic
412C22×C4⋊C4C22×C15111yescharacteristic
413#482—24no—
414#428—24no—
415C2×#107C22×C15111yescharacteristic
416C2×#107C22×C15111yescharacteristic
417C2×#107C22×C15111yescharacteristic
418C2×#106C22×C15111yescharacteristic
419C2×#106C22×C15111yescharacteristic
420C2×#106C22×C15111yescharacteristic
421C2×#102C22×C15111yescharacteristic
422C2×#102C22×C15111yescharacteristic
423C2×#102C22×C15111yescharacteristic
424C2×#102C22×C15111yescharacteristic
425C2×C22⋊C8C22×C15111yescharacteristic
426C2×C22⋊C8C22×C15111yescharacteristic
427C2×C22⋊C8C22×C15111yescharacteristic
428#397—21no—
429#394—21no—
430#389C22×C15111yescharacteristic
431#389C22×C15111yescharacteristic
432#388—21no—
433#387—21no—
434#380C22×C15111yescharacteristic
435#380C22×C15111yescharacteristic
436#380C22×C15111yescharacteristic
437#340C22×C15111yescharacteristic
438#340C22×C15111yescharacteristic
439#340C22×C15111yescharacteristic
440#340C22×C15111yescharacteristic
441#340C22×C15111yescharacteristic
442#340C22×C15111yescharacteristic
443#336C22×C15111yescharacteristic
444#336C22×C15111yescharacteristic
445C2×#41—28no—
446C2×#41—44no—
447C2×#41—44no—
448C22×Q8—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4D4×C15111yescharacteristic
452C22×D4C23×C15111yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4C23×C15111yescharacteristic
457C23×C4C23×C15111yescharacteristic
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C22×C8C23×C15111yescharacteristic
462C22×C8C23×C15111yescharacteristic
463C22×C8C23×C15111yescharacteristic
464C22×C8C23×C15111yescharacteristic
465C4⋊Q8—22no—
466C4⋊Q8—22no—
467#123—28no—
468#123—28no—
469C22⋊Q8—28no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121D4×C15114yes—
474C4×D4—22no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478#117—22no—
479#117—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4D4×C15111yescharacteristic
489C2×C4⋊C4D4×C15114yes—
490C2×C4⋊C4C23×C15111yescharacteristic
491C2×C4⋊C4C23×C15111yescharacteristic
492C2×C4⋊C4C23×C15111yescharacteristic
493C2×C4⋊C4C23×C15111yescharacteristic
494C2×C4⋊C4C23×C15111yescharacteristic
495C2×C4⋊C4C23×C15111yescharacteristic
496C2×C4⋊C4C23×C15111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C15111yescharacteristic
505C2×C22⋊C4D4×C15111yescharacteristic
506C2×C42—21no—
507C2×C42C23×C15111yescharacteristic
508#107—22no—
509#107—22no—
510#107—22no—
511#106—22no—
512#106—22no—
513#106—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—22no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526C24—21no—
527C24C2×D4×C15111yescharacteristic
528C24C2×D4×C15111yescharacteristic
529#41—432no—
530C2×Q8—24no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C2×D4×C15112yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4C2×D4×C15111yescharacteristic
575C22×C4C2×D4×C15111yescharacteristic
576C22×C4C2×D4×C15111yescharacteristic
577C22×C4C2×D4×C15112yes—
578C22×C4C2×D4×C15112yes—
579C22×C4C2×D4×C15111yescharacteristic
580C22×C4C24×C15111yescharacteristic
581M16—28no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8#41×C15112yescomplemented
593C2×C8#41×C15112yescomplemented
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—81no—
611C4⋊C4C2×D4×C15112yes—
612C4⋊C4C2×D4×C15112yes—
613C4⋊C4C2×D4×C15112yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—22no—
617C22⋊C4—24no—
618C22⋊C4—22no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—81no—
623C42—21no—
624C42—21no—
625C42—42no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23#120×C15112yes—
646C23AGL(1,ℤ/8)×C15112yes—
647C23C22×D4×C15111yescharacteristic
648Q8—48no—
649D4—28no—
650D4—22no—
651D4—22no—
652D4—48no—
653D4—48no—
654D4—41no—
655D4—41no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—48no—
674C2×C4—48no—
675C2×C4—48no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4#120×C15112yes—
699C2×C4AGL(1,ℤ/8)×C15112yes—
700C2×C4C22×D4×C15111yescharacteristic
701C2×C4C22×D4×C15111yescharacteristic
702C2×C4C2×#41×C15111yescharacteristic
703C2×C4C2×#41×C15111yescharacteristic
704C2×C42−1+4×C15111yescharacteristic
705C2×C42−1+4×C15111yescharacteristic
706C8—22no—
707C8—22no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#120×C15111yescharacteristic
732C22#547×C15111yescharacteristic
733C22#547×C15111yescharacteristic
734C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
735C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
736C22#577×C15111yescharacteristic
737C22#578×C15111yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4#525×C15111yescharacteristic
750C4#536×C15111yescharacteristic
751C4#547×C15111yescharacteristic
752C4#547×C15111yescharacteristic
753C2—42no—
754C2—42no—
755C2—82no—
756C2#2406×C15111yescharacteristic
757C2#3003×C15111yescharacteristic
758C2#3013×C15111yescharacteristic
759C2#3343×C15111yescharacteristic
760C2#3345×C15111yescharacteristic
761C2#3353×C15111yescharacteristic
762C2#3354×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#547×C151C2
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
2. C2×#482×C151C2semidirect
3. C2×#428×C151C2semidirect
4. #2485×C151C2semidirect
5. #2058×C151C2semidirect
6. #2057×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1895×C151C2semidirect
10. #1870×C151C2semidirect
11. #1864×C151C2semidirect
12. #1862×C151C2semidirect
13. #1853×C151C2semidirect
14. #1852×C151C2semidirect
15. #1824×C151C2semidirect
210. C2×C8×C151#41semidirect
211. C2×C8×C151#41semidirect
381. #24100C151direct (N × H)
382. C151#24100direct (N × H)
384. C2×#482C2×C151semidirect
385. C2×#428C2×C151semidirect
386. #2485C2×C151semidirect
387. #2058C2×C151semidirect
388. #2057C2×C151semidirect
389. #2034C2×C151semidirect
390. #2033C2×C151semidirect
391. #1895C2×C151semidirect
392. #1870C2×C151semidirect
393. #1864C2×C151semidirect
394. #1862C2×C151semidirect
395. #1853C2×C151semidirect
396. #1852C2×C151semidirect
397. #1824C2×C151semidirect
592. C2×C8#41×C151semidirect
593. C2×C8#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
C2×#482×C1512
C2×#428×C1512
#2485×C1512
#2058×C1512
#2057×C1512
#2034×C1512
#2033×C1512
#1895×C1512
#1870×C1512
#1864×C1512
#1862×C1512
#1853×C1512
#1852×C1512
#1824×C1512
#24100151