Finite Group Databasebeta

← C151×#24204 #50329129

Subgroups — C151×#24204 #50329129

Order 38656.

1208 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#442×C151C211yesmaximal, characteristic, complemented
4#2538×C151C211yesmaximal, characteristic, complemented
5#2042×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2012×C151C211yesmaximal, characteristic, complemented
8#2011×C151C211yesmaximal, characteristic
9#1985×C151C211yesmaximal, characteristic, complemented
10#1959×C151C211yesmaximal, characteristic, complemented
11#1880×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1865×C151C211yesmaximal, characteristic, complemented
14#1864×C151C211yesmaximal, characteristic, complemented
15#1802×C151C211yesmaximal, characteristic, complemented
16C22×SD16×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19#559×C151—24no—
20#559×C151—24no—
21C2×#127×C151C2211yescharacteristic
22C2×#124×C151—21no—
23C2×#124×C151C2211yescharacteristic
24C2×#124×C151C2211yescharacteristic
25C2×#123×C151—21no—
26C2×#123×C151—21no—
27C2×C22⋊Q8×C151—21no—
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×Q8×C151C2211yescharacteristic
30C2×C4×D4×C151—21no—
31C2×C4×D4×C151C2211yescharacteristic
32C2×C4×D4×C151C2211yescharacteristic
33C2×C4×D4×C151C2211yescharacteristic
34#463×C151—24no—
35#442×C151—24no—
36C2×#106×C151C2211yescharacteristic
37C2×C4⋊C8×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×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#97×C151C2211yescharacteristic
49#396×C151—21no—
50#396×C151—21no—
51#390×C151C2211yescharacteristic
52#390×C151C2211yescharacteristic
53#389×C151C2211yescharacteristic
54#389×C151C2211yescharacteristic
55#384×C151C2211yescharacteristic
56#380×C151—21no—
57#340×C151C2211yescharacteristic
58#340×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151D411yescharacteristic
64C22×Q8×C151C2311yescharacteristic
65C22×D4×C151—21no—
66C22×D4×C151—21no—
67C22×D4×C151C2311yescharacteristic
68C22×D4×C151C2311yescharacteristic
69C22×D4×C151C2311yescharacteristic
70C23×C4×C151—21no—
71C23×C4×C151—21no—
72C23×C4×C151—21no—
73C2×SD16×C151—22no—
74C2×SD16×C151—22no—
75C2×SD16×C151—41no—
76C2×D8×C151—22no—
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—41no—
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86#127×C151—22no—
87#127×C151—22no—
88#124×C151—28no—
89#124×C151—22no—
90#124×C151—22no—
91#124×C151—22no—
92#124×C151D414yes—
93#123×C151—28no—
94#123×C151—28no—
95C22⋊Q8×C151—44no—
96C4×Q8×C151—22no—
97C4×Q8×C151—22no—
98C4×Q8×C151—22no—
99C4×Q8×C151—22no—
100C4×D4×C151—28no—
101C4×D4×C151—22no—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151—22no—
106C4×D4×C151D414yes—
107C2×C4⋊C4×C151—21no—
108C2×C4⋊C4×C151—21no—
109C2×C4⋊C4×C151—21no—
110C2×C4⋊C4×C151—21no—
111C2×C4⋊C4×C151—21no—
112C2×C4⋊C4×C151D411yescharacteristic
113C2×C4⋊C4×C151D411yescharacteristic
114C2×C4⋊C4×C151D411yescharacteristic
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
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×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×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132C2×C42×C151C2311yescharacteristic
133C2×C42×C151C2311yescharacteristic
134#106×C151—22no—
135C4⋊C8×C151—22no—
136#103×C151—22no—
137#103×C151—22no—
138#103×C151—41no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—22no—
143#102×C151—41no—
144#102×C151—41no—
145#102×C151—41no—
146#97×C151—22no—
147#95×C151—21no—
148#95×C151—21no—
149C24×C151—21no—
150C24×C151—21no—
151C24×C151—21no—
152C2×Q8×C151—22no—
153C2×Q8×C151—22no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—21no—
157C2×Q8×C151—21no—
158C2×Q8×C151—21no—
159C2×Q8×C151—41no—
160C2×Q8×C151C2×D412yes—
161C2×D4×C151—24no—
162C2×D4×C151—24no—
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—21no—
171C2×D4×C151—21no—
172C2×D4×C151—21no—
173C2×D4×C151—21no—
174C2×D4×C151—21no—
175C2×D4×C151—21no—
176C2×D4×C151—21no—
177C2×D4×C151—21no—
178C2×D4×C151—42no—
179C2×D4×C151—42no—
180C2×D4×C151—81no—
181C2×D4×C151—81no—
182C2×D4×C151C2×D412yes—
183C2×D4×C151C2×D412yes—
184C2×D4×C151#4112yes—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—24no—
188C22×C4×C151—24no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—81no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151—81no—
199C22×C4×C151C2×D411yescharacteristic
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—44no—
207D8×C151—28no—
208D8×C151—44no—
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—21no—
219C2×C8×C151—21no—
220C2×C8×C151#4112yes—
221C4⋊C4×C151—24no—
222C4⋊C4×C151—22no—
223C4⋊C4×C151—22no—
224C4⋊C4×C151—22no—
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—21no—
232C4⋊C4×C151—42no—
233C4⋊C4×C151—42no—
234C4⋊C4×C151—42no—
235C4⋊C4×C151—81no—
236C4⋊C4×C151C2×D412yes—
237C22⋊C4×C151—24no—
238C22⋊C4×C151—24no—
239C22⋊C4×C151—24no—
240C22⋊C4×C151—24no—
241C22⋊C4×C151—24no—
242C22⋊C4×C151—24no—
243C22⋊C4×C151—42no—
244C22⋊C4×C151—42no—
245C22⋊C4×C151—42no—
246C22⋊C4×C151—81no—
247C22⋊C4×C151—81no—
248C42×C151—24no—
249C42×C151—21no—
250C42×C151—21no—
251C42×C151—21no—
252C42×C151—21no—
253C42×C151C2×D412yes—
254C42×C151C2×D412yes—
255C23×C151—22no—
256C23×C151—22no—
257C23×C151—22no—
258C23×C151—41no—
259C23×C151—41no—
260C23×C151—41no—
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—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151C22×D411yescharacteristic
277Q8×C151—22no—
278Q8×C151—22no—
279Q8×C151—44no—
280Q8×C151—41no—
281Q8×C151—41no—
282D4×C151—22no—
283D4×C151—22no—
284D4×C151—22no—
285D4×C151—22no—
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—48no—
289D4×C151—41no—
290D4×C151—41no—
291D4×C151—41no—
292D4×C151—41no—
293D4×C151—41no—
294D4×C151—41no—
295D4×C151—84no—
296C2×C4×C151—21no—
297C2×C4×C151—21no—
298C2×C4×C151—21no—
299C2×C4×C151—21no—
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—22no—
304C2×C4×C151—21no—
305C2×C4×C151—22no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—41no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
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—41no—
326C2×C4×C151—84no—
327C2×C4×C151—84no—
328C2×C4×C151—84no—
329C2×C4×C151#12012yes—
330C2×C4×C151#12012yes—
331C2×C4×C151AGL(1,ℤ/8)12yes—
332C2×C4×C151C22×D411yescharacteristic
333C2×C4×C151C22×D411yescharacteristic
334C2×C4×C151C2×#4111yescharacteristic
335C2×C4×C151C2×#4111yescharacteristic
336C2×C4×C151H(5,𝔽2)11yescharacteristic
337C2×C4×C1512−1+411yescharacteristic
338C8×C151—22no—
339C8×C151—41no—
340C8×C151—41no—
341C8×C151—41no—
342C22×C151—42no—
343C22×C151—42no—
344C22×C151—42no—
345C22×C151—42no—
346C22×C151—42no—
347C22×C151—42no—
348C22×C151—42no—
349C22×C151—42no—
350C22×C151—42no—
351C22×C151—81no—
352C22×C151—81no—
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×C151—81no—
362C22×C151—81no—
363C22×C151C2×#12011yescharacteristic
364C22×C151#54811yescharacteristic
365C22×C151#55011yescharacteristic
366C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C151#57511yescharacteristic
368C22×C151#57611yescharacteristic
369C22×C151#57711yescharacteristic
370C4×C151—22no—
371C4×C151—22no—
372C4×C151—22no—
373C4×C151—42no—
374C4×C151—41no—
375C4×C151—41no—
376C4×C151—41no—
377C4×C151—42no—
378C4×C151—81no—
379C4×C151—81no—
380C4×C151—81no—
381C4×C151#52511yescharacteristic
382C4×C151#53711yescharacteristic
383C4×C151#54611yescharacteristic
384C4×C151#54711yescharacteristic
385C2×C151—82no—
386C2×C151—82no—
387C2×C151—82no—
388C2×C151#240711yescharacteristic
389C2×C151#300611yescharacteristic
390C2×C151#301211yescharacteristic
391C2×C151#337011yescharacteristic
392C2×C151#337311yescharacteristic
393C2×C151#339911yescharacteristic
394C2×C151#340111yescharacteristic
395#24204C15111yesmaximal, characteristic, direct product factor, Sylow
396C151#2420411yescharacteristic, direct product factor, Sylow
397C2×#559C2×C15111yescharacteristic, complemented
398C2×#463C2×C15111yescharacteristic, complemented
399C2×#442C2×C15111yescharacteristic, complemented
400#2538C2×C15111yescharacteristic, complemented
401#2042C2×C15111yescharacteristic, complemented
402#2041C2×C15111yescharacteristic, complemented
403#2012C2×C15111yescharacteristic, complemented
404#2011C2×C15111yescharacteristic
405#1985C2×C15111yescharacteristic, complemented
406#1959C2×C15111yescharacteristic, complemented
407#1880C2×C15111yescharacteristic, complemented
408#1879C2×C15111yescharacteristic, complemented
409#1865C2×C15111yescharacteristic, complemented
410#1864C2×C15111yescharacteristic, complemented
411#1802C2×C15111yescharacteristic, complemented
412C22×SD16C22×C15111yescharacteristic
413C22×D8C22×C15111yescharacteristic
414C22×D8C22×C15111yescharacteristic
415#559—24no—
416#559—24no—
417C2×#127C22×C15111yescharacteristic
418C2×#124—21no—
419C2×#124C22×C15111yescharacteristic
420C2×#124C22×C15111yescharacteristic
421C2×#123—21no—
422C2×#123—21no—
423C2×C22⋊Q8—21no—
424C2×C4×Q8C22×C15111yescharacteristic
425C2×C4×Q8C22×C15111yescharacteristic
426C2×C4×D4—21no—
427C2×C4×D4C22×C15111yescharacteristic
428C2×C4×D4C22×C15111yescharacteristic
429C2×C4×D4C22×C15111yescharacteristic
430#463—24no—
431#442—24no—
432C2×#106C22×C15111yescharacteristic
433C2×C4⋊C8C22×C15111yescharacteristic
434C2×#103C22×C15111yescharacteristic
435C2×#103C22×C15111yescharacteristic
436C2×#103C22×C15111yescharacteristic
437C2×#102C22×C15111yescharacteristic
438C2×#102C22×C15111yescharacteristic
439C2×#102C22×C15111yescharacteristic
440C2×#102C22×C15111yescharacteristic
441C2×#102C22×C15111yescharacteristic
442C2×#102C22×C15111yescharacteristic
443C2×#102C22×C15111yescharacteristic
444C2×#97C22×C15111yescharacteristic
445#396—21no—
446#396—21no—
447#390C22×C15111yescharacteristic
448#390C22×C15111yescharacteristic
449#389C22×C15111yescharacteristic
450#389C22×C15111yescharacteristic
451#384C22×C15111yescharacteristic
452#380—21no—
453#340C22×C15111yescharacteristic
454#340C22×C15111yescharacteristic
455#336C22×C15111yescharacteristic
456#336C22×C15111yescharacteristic
457#336C22×C15111yescharacteristic
458#336C22×C15111yescharacteristic
459C22×Q8D4×C15111yescharacteristic
460C22×Q8C23×C15111yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C15111yescharacteristic
464C22×D4C23×C15111yescharacteristic
465C22×D4C23×C15111yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—21no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—41no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—41no—
478C22×C8C23×C15111yescharacteristic
479C22×C8C23×C15111yescharacteristic
480C22×C8C23×C15111yescharacteristic
481C22×C8C23×C15111yescharacteristic
482#127—22no—
483#127—22no—
484#124—28no—
485#124—22no—
486#124—22no—
487#124—22no—
488#124D4×C15114yes—
489#123—28no—
490#123—28no—
491C22⋊Q8—44no—
492C4×Q8—22no—
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4D4×C15114yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4D4×C15111yescharacteristic
509C2×C4⋊C4D4×C15111yescharacteristic
510C2×C4⋊C4D4×C15111yescharacteristic
511C2×C4⋊C4C23×C15111yescharacteristic
512C2×C4⋊C4C23×C15111yescharacteristic
513C2×C4⋊C4C23×C15111yescharacteristic
514C2×C4⋊C4C23×C15111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C42—21no—
527C2×C42C23×C15111yescharacteristic
528C2×C42C23×C15111yescharacteristic
529C2×C42C23×C15111yescharacteristic
530#106—22no—
531C4⋊C8—22no—
532#103—22no—
533#103—22no—
534#103—41no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541#102—41no—
542#97—22no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—41no—
556C2×Q8C2×D4×C15112yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4C2×D4×C15112yes—
579C2×D4C2×D4×C15112yes—
580C2×D4#41×C15112yes—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4C2×D4×C15111yescharacteristic
596C22×C4C2×D4×C15111yescharacteristic
597C22×C4C2×D4×C15111yescharacteristic
598C22×C4C2×D4×C15111yescharacteristic
599C22×C4C2×D4×C15111yescharacteristic
600C22×C4C2×D4×C15111yescharacteristic
601C22×C4C24×C15111yescharacteristic
602SD16—44no—
603D8—28no—
604D8—44no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8#41×C15112yes—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—81no—
632C4⋊C4C2×D4×C15112yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C42—24no—
645C42—21no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42C2×D4×C15112yes—
650C42C2×D4×C15112yes—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—41no—
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—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23C22×D4×C15111yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—44no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
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—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4#120×C15112yes—
726C2×C4#120×C15112yes—
727C2×C4AGL(1,ℤ/8)×C15112yes—
728C2×C4C22×D4×C15111yescharacteristic
729C2×C4C22×D4×C15111yescharacteristic
730C2×C4C2×#41×C15111yescharacteristic
731C2×C4C2×#41×C15111yescharacteristic
732C2×C4H(5,𝔽2)×C15111yescharacteristic
733C2×C42−1+4×C15111yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C22—42no—
739C22—42no—
740C22—42no—
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—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#120×C15111yescharacteristic
760C22#548×C15111yescharacteristic
761C22#550×C15111yescharacteristic
762C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
763C22#575×C15111yescharacteristic
764C22#576×C15111yescharacteristic
765C22#577×C15111yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4#525×C15111yescharacteristic
778C4#537×C15111yescharacteristic
779C4#546×C15111yescharacteristic
780C4#547×C15111yescharacteristic
781C2—82no—
782C2—82no—
783C2—82no—
784C2#2407×C15111yescharacteristic
785C2#3006×C15111yescharacteristic
786C2#3012×C15111yescharacteristic
787C2#3370×C15111yescharacteristic
788C2#3373×C15111yescharacteristic
789C2#3399×C15111yescharacteristic
790C2#3401×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2011×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#559×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#442×C151C2semidirect
4. #2538×C151C2semidirect
5. #2042×C151C2semidirect
6. #2041×C151C2semidirect
7. #2012×C151C2semidirect
9. #1985×C151C2semidirect
10. #1959×C151C2semidirect
11. #1880×C151C2semidirect
12. #1879×C151C2semidirect
13. #1865×C151C2semidirect
14. #1864×C151C2semidirect
15. #1802×C151C2semidirect
395. #24204C151direct (N × H)
396. C151#24204direct (N × H)
397. C2×#559C2×C151semidirect
398. C2×#463C2×C151semidirect
399. C2×#442C2×C151semidirect
400. #2538C2×C151semidirect
401. #2042C2×C151semidirect
402. #2041C2×C151semidirect
403. #2012C2×C151semidirect
405. #1985C2×C151semidirect
406. #1959C2×C151semidirect
407. #1880C2×C151semidirect
408. #1879C2×C151semidirect
409. #1865C2×C151semidirect
410. #1864C2×C151semidirect
411. #1802C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1512
C2×#463×C1512
C2×#442×C1512
#2538×C1512
#2042×C1512
#2041×C1512
#2012×C1512
#2011×C1512
#1985×C1512
#1959×C1512
#1880×C1512
#1879×C1512
#1865×C1512
#1864×C1512
#1802×C1512
#24204151